Scientific publications on "Light & Color in Nature"

Many scientific papers have been published on subjects related to "Meteorological Optics" or "Atmospheric Optics". A significant proportion of these papers have been triggered by a series of international meetings on "Light & Color in Nature" which attracts scientists from around the world who love to observe and explain optical phenomena in their natural environment. This series of meetings began (and continues) because these people enjoy getting together to learn from and share with each other. Here is a brief outline of the meeting history:

1) Meteorological Optics, August 28-29, 1978, Keystone, Colorado (coordinated by David Lynch)

2) Atmospheric Optics, January 3-5, 1983, Incline Village, Nevada (coordinated by William Mach & Alistair Fraser)

3) Meteorological Optics, April 2-3, 1986, Honolulu, Hawaii (coordinated by David Lynch)

4) Light & Color in the Open Air, July 11-13, 1990, Washington, D.C.(coordinated by Robert Greenler)

5) Light & Color in the Open Air, June 16-18, 1993, State College, Pennsylvania (coordinated by Craig Bohren)

6) Light & Color in the Open Air, February 10-12, 1997, Santa Fe, New Mexico (coordinated by Ken Sassen)

7) Meteorological Optics, June 6-8, 2001, Boulder, Colorado (coordinated by Stanley Gedzelman)

8) Atmospheric/Meteorological Optics, June 13-17, 2004, Bad Honnef, Germany (coordinated by Michael Vollmer)

9) Light & Color in Nature, June 25-29, 2007, Bozeman, Montana (coordinated by Joseph Shaw)

10) Light & Color in Nature, June 16-20, 2010, St. Mary's City, Maryland (coordinated by Chuck Adler)

Following each of these meetings, the Optical Society of America (OSA) has generously published a Feature Issue of one of its peer-reviewed journals. These Feature Issues draw heavily (but not exclusively) on contributions made at these meetings.

Journal of Optical Society of America: August 1979

Journal of Optical Society of America: December 1983

Journal of Optical Society of America A: March 1987

Applied Optics: August 1991

Applied Optics: July 1994

Applied Optics: March 1998

Applied Optics: January 2003

Applied Optics: September 2005

Applied Optics: December 2008

The following very long list shows relevant papers published by the OSA. This list is in reverse chronological order, but you can easily search for key words (e.g "halo" or "rainbow") or for the name of a particular author using the "Find" feature of your web browser.

If you have a subscription to the relevant OSA Journal, you can download a PDF version of each paper by clicking on the link marked OSA Optics InfoBase and then clicking on "View Full Text: PDF". If you do not have such a subscription, you can purchase a PDF version (currently at a price of $15 per paper) by following the same link.

However, the following authors have made their papers freely available via their non-commercial web sites - as indicated by the Free download links.
John Adam
Michael Berry
Javier Hernández-Andrés
Gábor Horváth
Günther Können
Philip Laven
Raymond L. Lee Jr
David K. Lynch
Michael Mishchenko
Joe Shaw
Walter Tape
Michael Vollmer
Siebren van der Werf

Please note that OSA's Copyright Policy states that "Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law".

2008
Feature issue: Applied Optics, December 2008

Light and Color in the Open Air: introduction to the feature issue Free download
Joseph A. Shaw, Raymond L. Lee, Jr., and Charles L. Adler
Applied Optics, Vol. 47, Issue 34, pp. LC1-LC2 (December 2008) OSA Optics InfoBase
This feature issue is a celebration of the joy and scientific richness of observing optical phenomena in nature. The majority of papers are adapted from presentations given at the Ninth International Meeting on Light and Color in Nature, held in Bozeman, Montana, from 25 to 29 June 2007.

Spatiotemporal change of sky polarization during the total solar eclipse on 29 March 2006 in Turkey: polarization patterns of the eclipsed sky observed by full-sky imaging polarimetry Free download
Brigitta Sipocz, Ramón Hegedüs, György Kriska and Gábor Horváth
Applied Optics, Vol. 47, No. 34, p H1-H10 (December 2008) OSA Optics InfoBase
Using 180° field-of-view (full-sky) imaging polarimetry, we measured the spatiotemporal change of the polarization of skylight during the total solar eclipse on 29 March 2006 in Turkey. We present our observations here on the temporal variation of the celestial patterns of the degree p and angle α of linear polarization of the eclipsed sky measured in the red (650 nm), green (550 nm), and blue (450 nm) parts of the spectrum. We also report on the temporal and spectral change of the positions of neutral (unpolarized, p = 0) points, and points with local minima or maxima of p of the eclipsed sky. Our results are compared with the observations performed by the same polarimetric technique during the total solar eclipse on 11 August 1999 in Hungary. Practically the same characteristics of celestial polarization were encountered during both eclipses. This shows that the observed polarization phenomena of the eclipsed sky may be general.

Geometric optics and rainbows: generalization of a result by Huygens Free download
John A. Adam
Applied Optics, Vol. 47, Issue 34, pp. H11-H13 (December 2008) OSA Optics InfoBase
In 1652 Huygens derived a formula specifying the rainbow angle for the primary bow (k = 1) in terms of the refractive index only. A generalization of this result for any k ≥ 1 is outlined, along with an alternative representation. The details of the derivation can be found in (Adam, Mathematics Magazine, 2008, under review), but the results as stated may be of interest to the atmospheric optics community.

Visibility of stars, halos, and rainbows during solar eclipses Free download
Gunther P. Können and Claudia Hinz
Applied Optics, Vol. 47, Issue 34, pp. H14-H24 (December 2008) OSA Optics InfoBase
The visibility of stars, planets, diffraction coronas, halos, and rainbows during the partial and total phases of a solar eclipse is studied. The limiting magnitude during various stages of the partial phase is presented. The sky radiance during totality with respect to noneclipse conditions is revisited and found to be typically 1/4000. The corresponding limiting magnitude is +3.5. At totality, the signal-to-background ratio of diffraction coronas, halos, and rainbows has dropped by a factor of 250. It is found that diffraction coronas around the totally eclipsed Sun may nevertheless occur. Analyses of lunar halo observations during twilight indicate that bright halo displays may also persist during totality. Rainbows during totality seem impossible.

Noncircular glories and their relationship to cloud droplet size Free download
Philip Laven
Applied Optics, Vol. 47, Issue 34, pp. H25-H30 (December 2008) OSA Optics InfoBase
The atmospheric glory caused by backscattering of sunlight from clouds usually has circular colored rings. However, glories with noncircular rings are frequently observed, especially along the edges of clouds. Noting that the angular radius of the rings of glories is a sensitive indicator of the size of the water droplets in clouds, several images of glories have been examined in an attempt to explain the formation of noncircular glories.

Using a trichromatic CCD camera for spectral skylight estimation Free download
Miguel A. López-Álvarez, Javier Hernández-Andrés, Javier Romero, F. J. Olmo, A. Cazorla, and L. Alados-Arboledas
Applied Optics, Vol. 47, Issue 34, pp. H31-H38 (December 2008) OSA Optics InfoBase
In a previous work [J. Opt. Soc. Am. A 24, 942-956 (2007)] we showed how to design an optimum multispectral system aimed at spectral recovery of skylight. Since high-resolution multispectral images of skylight could be interesting for many scientific disciplines, here we also propose a nonoptimum but much cheaper and faster approach to achieve this goal by using a trichromatic RGB charge-coupled device (CCD) digital camera. The camera is attached to a fish-eye lens, hence permitting us to obtain a spectrum of every point of the skydome corresponding to each pixel of the image. In this work we show how to apply multispectral techniques to the sensors' responses of a common trichromatic camera in order to obtain skylight spectra from them. This spectral information is accurate enough to estimate experimental values of some climate parameters or to be used in algorithms for automatic cloud detection, among many other possible scientific applications.

Visually discerning the curvature of the Earth Free download
David K. Lynch
Applied Optics, Vol. 47, Issue 34, pp. H39-H43 (December 2008) OSA Optics InfoBase
Reports and photographs claiming that visual observers can detect the curvature of the Earth from high mountains or high-flying commercial aircraft are investigated. Visual daytime observations show that the minimum altitude at which curvature of the horizon can be detected is at or slightly below 35,000 ft, providing that the field of view is wide (60°) and nearly cloud free. The high-elevation horizon is almost as sharp as the sea-level horizon, but its contrast is less than 10% that of the sea-level horizon. Photographs purporting to show the curvature of the Earth are always suspect because virtually all camera lenses project an image that suffers from barrel distortion. To accurately assess curvature from a photograph, the horizon must be placed precisely in the center of the image, i.e., on the optical axis.

Maximum deviation of light in a transparent wedge Free download
Walter Tape
Applied Optics, Vol. 47, Issue 34, pp. H44-H51 (December 2008) OSA Optics InfoBase
The maximum is found for the deviation of light passing through a transparent wedge of refractive index n and wedge angle α. The methods are conceptual and geometric, and they require very little calculation. There turn out to be two qualitatively different ray path candidates for maximum deviation, and the geometric approach leads naturally to a criterion involving n and α that decides between the two candidates. Finding the maximum deviation is equivalent to finding the outer radius of a circular halo.

Simulating irradiance during lunar eclipses: the spherically symmetric case Free download
Michael Vollmer and Stanley David Gedzelman
Applied Optics, Vol. 47, Issue 34, pp. H52-H61 (December 2008) OSA Optics InfoBase
Irradiance during total lunar eclipses is simulated using a pinhole model. The Moon is illuminated by direct sunlight that is refracted into the Earth's shadow as it passes through the atmosphere at the terminator but is depleted by scattering by molecules, extinction by aerosol particles, absorption by ozone, and obstruction by clouds and elevated land. On a spherical, sea-level Earth, and a cloudless, molecular atmosphere with no ozone, the eclipsed Moon appears red and calculated irradiance at the center of the umbra is reduced by a factor of about 2400 from direct moonlight. Selective absorption mainly of light around 600 nm by stratospheric ozone turns the periphery of the umbra pale blue. Typical distributions of aerosol particles, ozone, mountains, and clouds around the terminator reduce irradiance by an additional factor of the order of 100.
Lunar eclipse photometry: absolute luminance measurements and modeling Free download
Nina Hernitschek, Elmar Schmidt, and Michael Vollmer
Applied Optics, Vol. 47, Issue 34, pp. H62-H71 (December 2008) OSA Optics InfoBase
The Moon's time-dependent luminance was determined during the 9 February 1990 and 3 March 2007 total lunar eclipses by using calibrated, industry standard photometers. After the results were corrected to unit air mass and to standard distances for both Moon and Sun, an absolute calibration was accomplished by using the Sun's known luminance and a pre-eclipse lunar albedo of approximately 13.5%. The measured minimum level of brightness in the total phase of both eclipses was relatively high, namely −3.32 mvis and −1.7 mvis, which hints at the absence of pronounced stratospheric aerosol. The light curves were modeled in such a way as to let the Moon move through an artificial Earth shadow composed of a multitude of disk and ring zones, containing a relative luminance data set from an atmospheric radiative transfer calculation.

The legendary Rome halo displays Free download
Walter Tape, Eva Seidenfaden, and Gunther P. Können
Applied Optics, Vol. 47, Issue 34, pp. H72-H84 (December 2008) OSA Optics InfoBase
The two Rome halo displays of 1629 and 1630 are prominent in the early halo literature, and the 1629 display is still cited today for having contained a 28° circular halo. We have examined seventeenth century correspondence and publications in order to learn as much as possible about the existing documentation of the two displays. We find the documentation to be too weak to support a definitive interpretation of either display, and we see little evidence for a 28° halo or for other rare halos. The two displays remain important for their role in initiating modern halo science.

When Huygens and Mariotte agree Free download
Walter Tape
Applied Optics, Vol. 47, Issue 34, pp. H85-H90 (December 2008) OSA Optics InfoBase
Edme Mariotte in the seventeenth century attributed halos to tiny ice prisms in the atmosphere. Christiaan Huygens attributed them to tiny spheres or cylinders. The two seemingly incompatible theories largely agree in their predictions for the common halos. This article explains why.

Variability in low altitude astronomical refraction as a function of altitude
Russell D. Sampson, Edward P. Lozowski, and Arsha Fathi-Nejad
Applied Optics, Vol. 47, Issue 34, pp. H91-H94 (December 2008) OSA Optics InfoBase
Low altitude astronomical refraction (LAAR) of the setting Sun was measured over a sea horizon from a coastal location in Barbados, West Indies. The altitude of the upper limb of the Sun and the apparent horizon were determined using a digital video camera (Canon XL2) and a digital SLR camera (Canon EOS 5D). A total of 14 sunsets were measured between 2005 and 2007. From these measurements LAAR variability was estimated at 14 standard altitudes of the refracted Sun between 0°.01 and 4°.5. The relative variability decreases with increasing altitude from ± 0.0195 of mean refraction at an altitude of 0°.01 to ± 0.0142 at 4°.5. If extrapolated to an altitude of 15°, a linear fit to the data produces a relative variability of ± 0.0038 and an absolute variability of ± 0".45. Statistical analysis of the relative variability in LAAR appears to support the decreasing trend. However, error propagation analysis further suggests that the observed values of refraction may exceed the accuracy of the measurement system at altitudes higher than 2°.

Isaac Newton and the astronomical refraction
Waldemar H. Lehn
Applied Optics, Vol. 47, Issue 34, pp. H95-H105 (December 2008) OSA Optics InfoBase
In a short interval toward the end of 1694, Isaac Newton developed two mathematical models for the theory of the astronomical refraction and calculated two refraction tables, but did not publish his theory. Much effort has been expended, starting with Biot in 1836, in the attempt to identify the methods and equations that Newton used. In contrast to previous work, a closed form solution is identified for the refraction integral that reproduces the table for his first model (in which density decays linearly with elevation). The parameters of his second model, which includes the exponential variation of pressure in an isothermal atmosphere, have also been identified by reproducing his results. The implication is clear that in each case Newton had derived exactly the correct equations for the astronomical refraction; furthermore, he was the first to do so.

Measuring overcast colors with all-sky imaging Free download
Raymond L. Lee, Jr.
Applied Optics, Vol. 47, Issue 34, pp. H106-H115 (December 2008) OSA Optics InfoBase
Digital images of overcast skies as seen from the earth's surface open new windows onto the angular details of overcast colors and visible-wavelength spectra. After calibration with a spectroradiometer, a commercial CCD camera equipped with a fisheye lens can produce colorimetrically accurate all-sky maps of overcast spectra. Histograms and azimuthally averaged curves of the resulting chromaticities show consistent, but unexpected, patterns in time-averaged overcast colors. Although widely used models such as LOWTRAN7 and MODTRAN4 cannot explain these characteristic patterns, a simple semiempirical model based on the radiative transfer equation does, and it provides insights into the visible consequences of absorption and scattering both within and beneath overcasts.

Observed brightness distributions in overcast skies Free download
Raymond L. Lee, Jr., and David E. Devan
Applied Optics, Vol. 47, Issue 34, pp. H116-H127 (December 2008) OSA Optics InfoBase
Beneath most overcasts, clouds' motions and rapidly changing optical depths complicate mapping their angular distributions of luminance Lv and visible-wavelength radiance L. Fisheye images of overcast skies taken with a radiometer-calibrated digital camera provide a useful new approach to solving this problem. Maps calculated from time-averaged images of individual overcasts not only show their brightness distributions in unprecedented detail, but they also help solve a long-standing puzzle about where brightness maxima of overcasts are actually located. When combined with simulated radiance distributions from MODTRAN4, our measured radiances also let us estimate the gradients of cloud thickness observed in some overcasts.

Quantifying the “milky sky” experiment Free download
Stanley David Gedzelman, Miguel Ángel López-Álvarez, Javier Hernandez-Andrés, and Robert Greenler
Applied Optics, Vol. 47, Issue 34, pp. H128-H132 (December 2008) OSA Optics InfoBase
Spectra of direct and scattered light that passed through a tank of water mixed with up to 25 ml of homogenized skim milk were measured with a spectroradiometer in a classic experiment used to illustrate why the sky is blue and why the Sun turns red near the horizon. The direct light penetrating the tank was reddened by preferential scattering of short waves by the milk particles (protein casein micelles and fat globules). Scattered light was blue near the light source when the optical thickness was small and red far from the source when the optical thickness was large. The measured radiance spectra and Mie theory were used to estimate that the optically effective mean diameters of protein casein micelles and fat globules were 170 and 610 nm.

Effects of refractive index on glories Free download
Philip Laven
Applied Optics, Vol. 47, Issue 34, pp. H133-H142 (December 2008) OSA Optics InfoBase
Atmospheric glories are caused by backscattering of sunlight from spherical droplets of water (e.g., from fog or clouds). But what would glories look like if they were caused by scattering from more exotic substances, such as clouds of ethane as found on Titan? Examining backscattering as a function of the refractive index n of spherical droplets leads to the surprising conclusion that a glory's appearance is almost independent of n (at least for 1.03 < n < 1.7) - unlike the colors of rainbows, which are critically dependent on the variation of n across the visible spectrum.

Color of smoke from brush fires Free download
David K. Lynch and Lawrence S. Bernstein
Applied Optics, Vol. 47, Issue 34, pp. H143-H148 (December 2008) OSA Optics InfoBase
Smoke clouds from brush fires usually appear reddish or brownish when viewed from below in transmission, while a thin smoke cloud or part of a thick cloud near its periphery is noticeably bluish. Yet, when viewed from above in backscatter, the smoke appears bluish-white. We present observations of smoke clouds and explain their varied colors using a simple one-dimensional two-stream multiple scattering/absorbing radiative transfer approach for a model cloud whose particles are much smaller than the wavelength of visible light, the Rayleigh limit. The colors are purely the result of Rayleigh scattering and are not significantly influenced by the intrinsic color (wavelength-dependent albedo) of the particles.

Simulating irradiance and color during lunar eclipses using satellite data Free download
Stanley David Gedzelman and Michael Vollmer
Applied Optics, Vol. 47, Issue 34, pp. H149-H156 (December 2008) OSA Optics InfoBase
Irradiance and color during the total lunar eclipses of 2007 and 2008 are simulated using a ray tracing model that includes refraction, scattering by molecules, and observed or climatological distributions of aerosols, ozone, clouds, and topography around the terminator. Central portions of the umbra appear deep red for almost all eclipses due to preferential removal of short wavelengths in the spectrum of sunlight by scattering in the lower troposphere. The fringe of the umbra appears turquoise or blue due to selective removal of wavelengths around 600 nm by the Chappuis absorption bands of ozone in the stratosphere. Asymmetric distributions of clouds and aerosols, particularly for the 2008 eclipse, produce minimum calculated irradiance up to 17 arc min from the umbra center, while high ozone content over the arctic makes the northern edge of the umbra deepest blue.

Simulating halos and coronas in their atmospheric environment
Stanley David Gedzelman
Applied Optics, Vol. 47, Issue 34, pp. H157-H166 (December 2008) OSA Optics InfoBase
Models are developed that simulate the light and color of the sky and of circular halos and coronas as a function of atmospheric pressure, cloud height, width, and optical depth, solar zenith angle, aerosol concentration and size, and ozone content. Halos, coronas, and skylight are treated as singly scattered sunbeams that are depleted in their passage through the atmosphere and cloud. Multiple scattering is included only for background cloud light. Halos produced by hexagonal crystal prisms and coronas produced by monodisperse droplets are visible for cloud optical depths in the range 0.0003 ≤ τcld ≤ 7 and are brightest and most colorful when τcld is somewhat less than the cosine of the observer's zenith angle. When the Sun is low in the sky, halos and coronas can be bright only at smaller cloud optical depths and tend to be faint at their bottoms when produced in high cloud layers but can be bright at the horizon when produced by narrow cloud cells near ground level.

Antisolar halospot Free download
Gunther P. Können, Mónika Bodó, and Ágnes Kiricsi
Applied Optics, Vol. 47, Issue 34, pp. H167-H170 (December 2008) OSA Optics InfoBase
An isolated colorless spot of 1° diameter located at the antisolar point was observed from a plane on the clouds beneath it. The spot can be explained by light scattering on randomly oriented ice crystals via light paths similar to those responsible for the subparhelic circle. Its peculiar polarization properties potentially permit its detection in cases where the spot is embedded in a glory.

The rainbow as interactive art: modeling the Elaisson Beauty installation at SFMOMA
Kenneth Sassen and Jiang Zhu
Applied Optics, Vol. 47, Issue 34, pp. H171-H175 (December 2008) OSA Optics InfoBase
The rainbow has had an important role in religion, art, and science. Recently, artists have attempted to create indoor rainbow displays as interactive exhibitions of art, but based, nonetheless, on the principles of the scattering behavior of raindrops and the experience of experiment. Motivated by recently viewing the Beauty, 1993, installation at the San Francisco Museum of Modern Art (SFMOMA), we describe here a modeling program to explain the diversity of rainbow phenomena one can see visually in the gallery. The most significant impression gleaned in the museum is the acute spatial dependence of rainbow form on the viewing position in the presence of a local divergent light source (i.e., a floodlamp), in stark contrast to the unchangeable natural rainbow produced by an unimaginably distant Sun. This represents a case of the local (divergent) versus solar (parallel) light ray source distinction in atmospheric optical displays, which is one of a handful of anthropogenic versus natural situations responsible for optics displays that have been so far described. Through geometrical optics and Airy's theory simulations we show a rich relationship between the locally produced rainbow phenomena and the chamber equipment geometry and viewing position.

Simulating rainbows in their atmospheric environment
Stanley David Gedzelman
Applied Optics, Vol. 47, Issue 34, pp. H176-H181 (December 2008) OSA Optics InfoBase
Light and color of geometric optics rainbows are simulated in their atmospheric environment. Sunlight passes through a molecular atmosphere with ozone and an aerosol layer near the ground to strike a cuboidal rain shaft below an overhanging cuboidal cloud. The rainbows are treated as singly scattered sunbeams that are depleted as they pass through the atmosphere and rain shaft. They appear in a setting illuminated by scattered light from behind the observer, from the background beyond the rain shaft, and from the rain shaft. In dark backgrounds the primary and secondary bows first become visible when the optical thickness of rain shafts τR ≅ 0.0003 and τR ≅ 0.003, respectively. The bows are brightest and most colorful for 0.1≤ τR ≤ 3, a range that is typical for most showers. The peaks of the scattering phase function for raindrops that correspond to the geometric optics rainbow are so pronounced that rainbows remain bright and colorful for optically thick rain shafts seen against dark backgrounds, but the bows appear washed out or vanish as the background brightens or where the rain shaft is shaded by an overhanging cloud. Rainbows also redden as the Sun approaches the horizon.

Retrieval of the optical depth using an all-sky CCD camera Free download
Francisco J. Olmo, Alberto Cazorla, Lucas Alados-Arboledas, Miguel A. López-Álvarez, Javier Hernández-Andrés, and Javier Romero
Applied Optics, Vol. 47, Issue 34, pp. H182-H189 (December 2008) OSA Optics InfoBase
A new method is presented for retrieval of the aerosol and cloud optical depth using a CCD camera equipped with a fish-eye lens (all-sky imager system). In a first step, the proposed method retrieves the spectral radiance from sky images acquired by the all-sky imager system using a linear pseudoinverse algorithm. Then, the aerosol or cloud optical depth at 500 nm is obtained as that which minimizes the residuals between the zenith spectral radiance retrieved from the sky images and that estimated by the radiative transfer code. The method is tested under extreme situations including the presence of nonspherical aerosol particles. The comparison of optical depths derived from the all-sky imager with those retrieved with a sunphotometer operated side by side shows differences similar to the nominal error claimed in the aerosol optical depth retrievals from sunphotometer networks.

Digital all-sky polarization imaging of partly cloudy skies Free download
Nathan J. Pust and Joseph A. Shaw
Applied Optics, Vol. 47, Issue 34, pp. H190-H198 (December 2008) OSA Optics InfoBase
Clouds reduce the degree of linear polarization (DOLP) of skylight relative to that of a clear sky. Even thin subvisual clouds in the “twilight zone” between clouds and aerosols produce a drop in skylight DOLP long before clouds become visible in the sky. In contrast, the angle of polarization (AOP) of light scattered by a cloud in a partly cloudy sky remains the same as in the clear sky for most cases. In unique instances, though, select clouds display AOP signatures that are oriented 90° from the clear-sky AOP. For these clouds, scattered light oriented parallel to the scattering plane dominates the perpendicularly polarized Rayleigh-scattered light between the instrument and the cloud. For liquid clouds, this effect may assist cloud particle size identification because it occurs only over a relatively limited range of particle radii that will scatter parallel polarized light. Images are shown from a digital all-sky-polarization imager to illustrate these effects. Images are also shown that provide validation of previously published theories for weak (∼2%) polarization parallel to the scattering plane for a 22° halo.

Rare display of eight concentric halos in Tampere, Finland, on 5 June 2008
Jari Luomanen
Applied Optics, Vol. 47, Issue 34, pp. H199-H202 (December 2008) OSA Optics InfoBase
On 5 June 2008 there was a rare display of eight concentric halos in Tampere, Finland. I present a preliminary analysis of this display. A brief comparison with earlier major odd-radius displays is made. Short faint arcs intersecting the Sun and their resemblance to the theoretical odd-radius helic arcs are discussed. A stacked image consisting of 72 individual frames of the display is presented. A single frame is provided for comparison, and the visual observation is described in some detail. Postprocessing techniques for halo photographs are discussed. A stacked simulation and the relevant crystal populations are presented.

Rainbows in the grass. I. External-reflection rainbows from pendant droplets
James A. Lock, Charles L. Adler, and Richard W. Fleet
Applied Optics, Vol. 47, Issue 34, pp. H203-H213 (December 2008) OSA Optics InfoBase
In the mid-morning on a sunny day one can sometimes see glare spots associated with uncolored “rainbow” (i.e., fold) caustics due to the sunlight reflected from the surface of dew or guttation drops. We show that these dewdrop reflection rainbows are due to places on the droplet (i.e., from an “inflection circle”) where its Gaussian curvature becomes zero. We work out the theory of such caustics with horizontally incident light and present a comparison of the theory to measurements made in the laboratory.

Rainbows in the grass. II. Arbitrary diagonal incidence
Charles L. Adler, James A. Lock, and Richard W. Fleet
Applied Optics, Vol. 47, Issue 34, pp. H214-H219 (December 2008) OSA Optics InfoBase
We consider external reflection rainbow caustics due to the reflection of light from a pendant droplet where the light rays are at an arbitrary angle with respect to the horizontal. We compare this theory to observation of glare spots from pendant drops on grass; we also consider the potential application of this theory to the determination of liquid surface tension.

Fountain rainbows Free download
Stanley David Gedzelman and Javier Hernández-Andrés
Applied Optics, Vol. 47, Issue 34, pp. H220-H224 (December 2008) OSA Optics InfoBase
We present the first measurements of radiance spectra of rainbows. The bows on two sunny days (3 and 6 June 2008) were produced by the fountain in the Parque de las Ciencias, Granada, Spain, that consists of a rectangular perimeter of 40 spray nozzles. Optical thickness of the spray from each nozzle was approximately 0.5. Spectral purity of the primary bow was highest for orange and blue, reaching values of 23% and 7%, respectively, while skylight 90° from the Sun had a color purity of 34% (on 6 June). The secondary bow had much lower color purity with red absent because the regions around the bows and in Alexander's dark band were pale blue. The narrow sickle shape of the chromaticity curves for the primary bows and the absence of supernumerary bows indicated that the drop radius was between 0.2 and 0.4 mm.


Solar glint from oriented crystals in cirrus clouds
Claire Lavigne, Antoine Roblin, and Patrick Chervet
Applied Optics, Vol. 47, Issue 33, pp. 6266-6276 (November 2008) OSA Optics InfoBase
Solar scattering on oriented cirrus crystals near the specular reflection direction is modeled using a mix method combining geometric optics and diffraction effects at three wavelengths in the visible and infrared domains. Different potential sources of phase function broadening around the specular direction, such as multiple scattering, solar disk, or tilt effects, are studied by means of a Monte Carlo method. The radiance detected by an airborne sensor located a few kilometers above the cirrus cloud and pointing in the specular scattering direction is calculated at four solar zenith angles showing a dramatic increase of the signal in relation to the usual assumption of random crystal orientation.

Comment on "Improved ray tracing air mass numbers model" Free download
Siebren Y. van der Werf
Applied Optics, Vol. 47, Issue 2, pp. 153-156 (January 2008) OSA Optics InfoBase
Air mass numbers have traditionally been obtained by techniques that use height as the integration variable. This introduces an inherent singularity at the horizon, and ad hoc solutions have been invented to cope with it. A survey of the possible options including integration by height, zenith angle, and horizontal distance or path length is presented. Ray tracing by path length is shown to avoid singularities both at the horizon and in the zenith. A fourth-order Runge-Kutta numerical integration scheme is presented, which treats refraction and air mass as path integrals. The latter may optionally be split out into separate contributions of the atmosphere's constituents.

2007
Selecting algorithms, sensors and linear bases for optimum spectral recovery of skylight Free download
Miguel A. López-Álvarez, Javier Hernández-Andrés, Eva M. Valero, and J. Romero
Journal of the Optical Society of America A, Vol. 24, No. 4, pp. 942-956, April 2007 OSA Optics InfoBase
In a previous work [Appl. Opt. 44, 5688 (2005)] we found the optimum sensors for a planned multispectral system for measuring skylight in the presence of noise by adapting a linear spectral recovery algorithm proposed by Maloney and Wandell [J. Opt. Soc. Am. A 3, 29 (1986)]. Here we continue along these lines by simulating the responses of three to five Gaussian sensors and recovering spectral information from noise-affected sensor data by trying out four different estimation algorithms, three different sizes for the training set of spectra, and various linear bases. We attempt to find the optimum combination of sensors, recovery method, linear basis, and matrix size to recover the best skylight spectral power distributions from colorimetric and spectral (in the visible range) points of view. We show how all these parameters play an important role in the practical design of a real multispectral system and how to obtain several relevant conclusions.

Anomalous celestial polarization caused by forest fire smoke: why do some insects become visually disoriented under smoky skies? Free download
Ramón Hegedüs, Susanne Åkesson, and Gábor Horváth
Applied Optics, Vol. 46, No. 14, p. 2717, May 2007 OSA Optics InfoBase
The effects of forest fire smoke on sky polarization and animal orientation are practically unknown. Using full-sky imaging polarimetry, we therefore measured the celestial polarization pattern under a smoky sky in Fairbanks, Alaska, during the forest fire season in August 2005. It is quantitatively documented here that the celestial polarization, a sky attribute that is necessary for orientation of many polarization sensitive animal species, above Fairbanks on 17 August 2005 was in several aspects anomalous due to the forest fire smoke: (i) The pattern of the degree of linear polarization p of the reddish smoky sky differed considerably from that of the corresponding clear blue sky. (ii) Due to the smoke, p of skylight was drastically reduced (pmax ≤14%, paverage ≤8%). (iii) Depending on wavelength and time, the Arago, Babinet, and Brewster neutral points of sky polarization had anomalous positions. We suggest that the disorientation of certain insects observed by Canadian researchers under smoky skies during the forest fire season in August 2003 in British Columbia was the consequence of the anomalous sky polarization caused by the forest fire smoke.

Recovering fluorescent spectra with an RGB digital camera and color filters using different matrix factorizations Free download
Juan L. Nieves, Eva M. Valero, Javier Hernández-Andrés and Javier Romero
Applied Optics, vol. 46, No. 19, p 4144-4154 (June 2007) OSA Optics InfoBase
The aim of a multispectral system is to recover a spectral function at each image pixel, but when a scene is digitally imaged under a light of unknown spectral power distribution (SPD), the image pixels give incomplete information about the spectral reflectances of objects in the scene. We have analyzed here how accurately the spectra of artificial fluorescent light sources can be recovered with a digital CCD camera. The RGB sensor outputs are modified by the use of successive cut-off color filters. Three algorithms for simplifying the spectra datasets are used: non-negative matrix factorization (NMF), independent component analysis (ICA), a direct pseudo-inverse method, and principal component analysis (PCA). The algorithms are tested using both simulated data and data from a real RGB digital camera. The methods are compared in terms of the minimum rank of factorization and the number of sensors required to derive acceptable spectral and colorimetric SPD estimations; PCA results are also given for the sake of comparison. The results show that all the algorithms surpass PCA when a reduced number of sensors is used. Experimental results suggest a significant loss of quality when more than one color filter is used, which agrees with previous results for reflectances. Nevertheless, an RGB digital camera with or without prefilter is found to provide good spectral and colorimetric recovery of indoor fluorescent lighting and can be used for color correction without need of a telespectroradiometer.
2006
 Influence of crystal tilt on solar irradiance of cirrus clouds
Susann Klotzsche and Andreas Macke
Applied Optics, Vol. 45, No. 5, p. 1034, February 2006 OSA Optics InfoBase
The single and multiple scattering and absorption properties of hexagonal ice columns with different degrees of particle orientation are modeled in the solar spectral range by means of a ray-tracing singlescattering code and a Monte Carlo radiative-transfer code. The scattering properties are most sensitive to particle orientation for the solar zenith angles of 50° (asymmetry parameter) and 90° (single-scattering albedo). Provided that the ice columns are horizontally oriented, the usual assumption of random orientation leads to an overestimation (underestimation) of the reflected (transmitted) solar broadband radiation at high Sun elevation and to an underestimation (overestimation) at medium solar zenith angles. The orientation effect is more (less) pronounced in scattering and transmission (absorption) for smaller ice crystals.

Attenuation and impulse response for multiple scattering of light in atmospheric clouds and aerosols
Adrian C. Selden
Applied Optics, Vol. 45, No. 13, p. 3144, May 2006 OSA Optics InfoBase
Model phase functions for atmospheric clouds and aerosols typically comprise a narrow forward lobe (corona), a broad diffuse background, and a narrow backscattering peak (glory), which can reach relatively high values, especially for polyhedral scattering particles, such as hexagonal ice columns and plates. The influence of these three major components on the asymptotic and transient attenuation of the scattered light is compared for several analytic phase functions to assess the dependence of radiative transfer in clouds and aerosols on the choice of phase function. The impulse response (temporal evolution of the angular intensity distribution) is sensitive to the higher moments of the phase function and could prove to be a useful technique for inferring the optical scattering parameters of clouds and aerosols.

Celestial polarization patterns during twilight
Thomas W. Cronin, Eric J. Warrant, and Birgit Greiner
Applied Optics, Vol. 45, No. 22, p. 5582, August 2006 OSA Optics InfoBase
Scattering of sunlight produces patterns of partially linearly polarized light in the sky throughout the day, and similar patterns appear at night when the Moon is bright. We studied celestial polarization patterns during the period of twilight, when the Sun is below the horizon, determining the degree and orientation of the polarized-light field and its changes before sunrise and after sunset. During twilight, celestial polarized light occurs in a wide band stretching perpendicular to the location of the hidden Sun and reaching typical degrees of polarization near 80% at wavelengths > 600 nm. In the tropics, this pattern appears ∼ 1 h before local sunrise or disappears ∼ 1 h after local sunset (within 10 min after the onset of astronomical twilight at dawn, or before its end at dusk) and extends with little change through the entire twilight period.

Polarization properties of Scarabaeidae
Dennis H. Goldstein
Applied Optics, Vol. 45, No. 30, p. 7944, October 2006 OSA Optics InfoBase
Beetles of the scarab family are known to reflect circularly polarized light from incident unpolarized light. They are unusual in that there are many animals that use polarized light in some form and several that actually create it, but there are few examples of the creation of circularly polarized light by animals. Scarabs have been measured with a spectropolarimetric reflectometer and are found to reflect light that is generally left-hand circularly polarized. Previous work is summarized, and what is believed to be new measurements of several scarab specimens are presented.

Effect of aerosol microphysical properties on polarization of skylight: sensitivity study and measurements
Eyk Boesche, Piet Stammes, Thomas Ruhtz, Réne Preusker, and Juergen Fischer
Applied Optics, Vol. 45, No. 34, p. 8790, December 2006 OSA Optics InfoBase
We analyze the sensitivity of the degree of linear polarization in the Sun’s principal plane as a function of aerosol microphysical parameters: the real and imaginary parts of the refractive index, the median radius and geometric standard deviation of the bimodal size distribution (both fine and coarse modes), and the relative number weight of the fine mode at a wavelength of 675 nm. We use Mie theory for single-scattering simulations and the doubling–adding method with the inclusion of polarization for multiple scattering. It is shown that the behavior of the degree of linear polarization is highly sensitive to both the small mode of the bimodal size distribution and the real part of the refractive index of aerosols, as well as to the aerosol optical thickness; whereas not all parameters influence the polarization equally. A classification of the importance of the input parameters is given. This sensitivity study is applied to an analysis of ground-based polarization measurements. For the passive remote sensing of microphysical and optical properties of aerosols, a ground-based spectral polarization measuring system was built, which aims to measure the Stokes parameters I, Q, and U in the visible (from 410 to 789 nm) and near-infrared (from 674 to 995 nm) spectral range with a spectral resolution of 7 nm in the visible and 2.4 nm in the near infrared. We compare polarization measurements taken with radiative transfer simulations under both clear- and hazy-sky conditions in an urban area (Cabauw, The Netherlands, 51.58° N, 4.56° E). Conclusions about the microphysical properties of aerosol are drawn from the comparison.
2005
Feature issue: Applied Optics, September 2005
Light and color in the open air: introduction to the feature issue
Charles L. Adler and Raymond L. Lee, Jr.
Applied Optics, Volume 44, Issue 27, 5623 September 2005 OSA Optics InfoBase

Atmospheric refraction: a history Free download
Waldemar H. Lehn and Siebren van der Werf
Applied Optics, Volume 44, Issue 27, 5624 September 2005 OSA Optics InfoBase
We trace the history of atmospheric refraction from the ancient Greeks up to the time of Kepler. The concept that the atmosphere could refract light entered Western science in the second century B.C. Ptolemy, 300 years later, produced the first clearly defined atmospheric model, containing air of uniform density up to a sharp upper transition to the ether, at which the refraction occurred. Alhazen and Witelo transmitted his knowledge to medieval Europe. The first accurate measurements were made by Tycho Brahe in the 16th century. Finally, Kepler, who was aware of unusually strong refractions, used the Ptolemaic model to explain the first documented and recognized mirage (the Novaya Zemlya effect).

Speculations on the possible causes of the Whymper apparition Free download
Cedric John Hardwick and Jason C. Knievel
Applied Optics, Volume 44, Issue 27, 5637 September 2005 OSA Optics InfoBase
During the first ascent of the Matterhorn, a remarkable optical effect comprising three crosses surrounded by a great arch was observed by Edward Whymper, the British mountaineer. The authors review previous published explanations of the apparition. There are no photographs, only a woodcut and sketch, so the size of the apparition is not known, and it is not possible to make a definitive conclusion about what caused it. A fogbow and ice crystal arcs could have produced a circle and crosses in a direction consistent with the apparition. Some simulations are presented; one has a form approximating Whymper’s sketch. However, while this simulation used a crystal type that can occur, it required an unusual alignment that would be very rare.

The Toboggan Sun Free download
Wayne P. S. Davidson and Siebren Y. van der Werf
Applied Optics, Volume 44, Issue 27, 5644 September 2005 OSA Optics InfoBase
Special variants of the Novaya Zemlya effect may arise from localized temperature inversions that follow the height profile of hills or mountains. Rather than following its natural path, the rising or setting Sun may, under such circumstances, appear to slide along a distant mountain slope. We found early observations of this effect in the literature by Willem Barents (1597) and by Captain Scott and H. G. Ponting (1911). We show recent photographic material of the effect and present ray-tracing calculations to explain its essentials.

Variability of observed low-altitude astronomical refraction (LAAR) from different geographic locations: progress toward a global map of LAAR variability
Russell D. Sampson, Edward P. Lozowski, and Hans G. Machel
Applied Optics, Volume 44, Issue 27, 5652 September 2005 OSA Optics InfoBase22:36 03/11/2007
The variability of the astronomical refraction of the setting Sun as measured from Holetown, Barbados, West Indies, is compared to sunset refraction measured from Edmonton, Alberta, during the same time of year. At about 13 °N latitude, Holetown experiences a marine tropical climate, while Edmonton (53 °N) has a subarctic continental climate. The 17 sunsets recorded from Holetown between 27 December 2003, and 21 February 2004, and between 25 and 30 December 2004, show a mean astronomical refraction of 0°.475 and standard deviation of 0°.012. The 26 sunsets recorded from Edmonton between 31 December 1992, and 17 February 1993, show a mean astronomical refraction of 0°.699 and standard deviation of 0°.118. The Barbados mean is significantly less than the Edmonton mean, while the variability of the Barbados data is an order of magnitude less than the Edmonton data. The variability of refraction appears to be strongly correlated with the variability in the surface vertical temperature gradient recorded on the same day as the sunset observations. This suggests that mapping of the geographic distribution of low-altitude astronomical refraction variability could be based on climatology of the surface vertical temperature gradient.

Effects of absorbing particles on coronas and glories Free download
Michael Vollmer
Applied Optics, Volume 44, Issue 27, 5658 September 2005 OSA Optics InfoBase
Light scattering from small particles changes if the particles are absorbing. Whereas the effect is small for coronas and Bishop’s ring, glories show pronounced attenuation with increasing absorption. Results indicate suitable wavelength regions for studies of glory scattering from cloud tops. The behavior of core–shell particles could have applications for studying the atmosphere of Venus; in addition it provides more insight into the simple ray-path model of the glory.

Atmospheric glories: simulations and observations Free download
Philip Laven
Applied Optics, Volume 44, Issue 27, 5667 September 2005 OSA Optics InfoBase
Mie theory can be used to provide full-color simulations of atmospheric glories. Comparison of such simulations with images of real glories suggests that most glories are caused by spherical water droplets with radii between 4 and 25 µm. This paper also examines the appearance of glories taking into account the size of the droplets and the width of the droplet size distributions. Simulations of glories viewed through a linear polarizer compare well with the few available pictures, but they show some features that need corroboration by more observations.

How are glories formed? Free download
Philip Laven
Applied Optics, Volume 44, Issue 27, 5675 September 2005 OSA Optics InfoBase
Mie theory can be used to generate full-color simulations of atmospheric glories, but it offers no explanation for the formation of glories. Simulations using the Debye series indicate that glories are caused by rays that have suffered one internal reflection within spherical droplets of water. In 1947, van de Hulst suggested that backscattering (i.e., scattering angle theta = 180°) could be caused by surface waves, which would generate a toroidal wavefront due to spherical symmetry. Furthermore, he postulated that the glory is the interference pattern corresponding to this toroidal wavefront. Although van de Hulst’s explanation for the glory has been widely accepted, the author offers a slightly different explanation. Noting that surface waves shed radiation continuously around the droplet (not just at theta = 180°), scattering in a specific direction theta = 180° + d can be considered as the vector sum of two surface waves: one deflecting the incident light by 180° + d and the other by 180° - d. The author suggests that the glory is the result of two-ray interference between these two surface waves. Simple calculations indicate that this model produces more accurate results than van de Hulst’s model.

Halos in cirrus clouds: why are classic displays so rare?
Kenneth Sassen
Applied Optics, Volume 44, Issue 27, 5684 September 2005 OSA Optics InfoBase
Upper tropospheric cirrus clouds consist of hexagonal ice crystals, which geometrical ray-tracing-theory predicts should regularly produce a variety of optical phenomena such as vivid 22° and 46° halos. Yet, cirrus inconsistently generate such optical displays, while a class of more exotic displays are reported, albeit rarely. I review current knowledge of the cirrus cloud microphysical factors that control ice crystal shape, and hence haloarc formation, but also appeal to halo enthusiasts to help investigate the causes of unusually complex, brilliant, or rare optical displays. Currently, a wealth of meteorological information can be tapped from the Internet to help advance our knowledge of the basic meteorological factors leading to these rare events

Designing a practical system for spectral imaging of skylight Free download
Miguel A. López-Álvarez, Javier Hernández-Andrés, Javier Romero, and Raymond L. Lee, Jr.
Applied Optics, Volume 44, Issue 27, 5688 September 2005 OSA Optics InfoBase
In earlier work [J. Opt. Soc. Am. A 21, 13–23 (2004)], we showed that a combination of linear models and optimum Gaussian sensors obtained by an exhaustive search can recover daylight spectra reliably from broadband sensor data. Thus our algorithm and sensors could be used to design an accurate, relatively inexpensive system for spectral imaging of daylight. Here we improve our simulation of the multispectral system by (1) considering the different kinds of noise inherent in electronic devices such as changecoupled devices (CCDs) or complementary metal-oxide semiconductors (CMOS) and (2) extending our research to a different kind of natural illumination, skylight. Because exhaustive searches are expensive computationally, here we switch to a simulated annealing algorithm to define the optimum sensors for recovering skylight spectra. The annealing algorithm requires us to minimize a single cost function, and so we develop one that calculates both the spectral and colorimetric similarity of any pair of skylight spectra. We show that the simulated annealing algorithm yields results similar to the exhaustive search but with much less computational effort. Our technique lets us study the properties of optimum sensors in the presence of noise, one side effect of which is that adding more sensors may not improve the spectral recovery.

Multispectral synthesis of daylight using a commercial digital CCD camera Free download
Juan L. Nieves, Eva M. Valero, Sérgio M. C. Nascimento, Javier Hernández-Andrés, and Javier Romero
Applied Optics, Volume 44, Issue 27, 5696 September 2005 OSA Optics InfoBase
Performance of multispectral devices in recovering spectral data has been intensively investigated in some applications, as in spectral characterization of art paintings, but has received little attention in the context of spectral characterization of natural illumination. This study investigated the quality of the spectral estimation of daylight-type illuminants using a commercial digital CCD camera and a set of broadband colored filters. Several recovery algorithms that did not need information about spectral sensitivities of the camera sensors nor eigenvectors to describe the spectra were tested. Tests were carried out both with virtual data, using simulated camera responses, and real data obtained from real measurements. It was found that it is possible to recover daylight spectra with high spectral and colorimetricaccuracy with a reduced number of three to nine spectral bands.

Short-term variability of overcast brightness Free download
Raymond L. Lee, Jr. and Javier Hernández-Andrés
Applied Optics, Volume 44, Issue 27, 5704 September 2005 OSA Optics InfoBase
Overcasts seen from below seldom are uniform, unchanging cloud shields, yet little is known about their short-term photometric variability (periods < 2 h). Visible-wavelength spectra of daytime and twilight overcast skies measured at 30-s intervals reveal unexpected temporal variability in horizontal illuminance Ev and zenith luminance Lv. Fourier analysis of these time series shows peak fluctuations at periods of 2–40 min. Factors such as cloud type and optical depth, presence of fog or snow, and instrument field of view can affect overcast brightness variability. Surprisingly, under some circumstances overcasttwilight Ev exceeds clear-sky Ev at the same Sun elevation.

Colors of the daytime overcast sky Free download
Raymond L. Lee, Jr. and Javier Hernández-Andrés
Applied Optics, Volume 44, Issue 27, 5712 September 2005 OSA Optics InfoBase
Time-series measurements of daylight (skylight plus direct sunlight) spectra beneath overcast skies reveal an unexpectedly wide gamut of pastel colors. Analyses of these spectra indicate that at visible wavelengths, overcasts are far from spectrally neutral transmitters of the daylight incident on their tops. Colorimetric analyses show that overcasts make daylight bluer and that the amount of bluing increases with cloud optical depth. Simulations using the radiative-transfer model MODTRAN4 help explain the observed bluing: multiple scattering within optically thick clouds greatly enhances spectrally selective absorption by water droplets. However, other factors affecting overcast colors seen from below range from minimal (cloud-top heights) to moot (surface colors).

Simulating colors of clear and partly cloudy skies
Stanley David Gedzelman
Applied Optics, Volume 44, Issue 27, 5723 September 2005 OSA Optics InfoBase
A model (SKYCOLOR) is developed that simulates the light and color of the sky and open cloud decks in the vertical plane including the Sun and the observer and animates the changes as the Sun goes down. Model skylight consists of sunbeams that are scattered toward the observer, but depleted by scattering and absorption in the Chappuis bands of ozone. SKYCOLOR includes the Earth’s curvature, atmospheric refraction, cloud shadows, and solar eclipses. Scattering is given a wavelength (lambda) dependence of lambda-4 for air molecules (Rayleigh scattering), lambda-1 for tropospheric aerosols, and lambda+1 for volcanic aerosol particles. Multiple scattering is calculated directly in clouds but is parameterized in clear air by decreasing the scattering rates of sunlight and of skylight in the Earth’s shadow by 30%.

On the colors of distant objects Free download
David K. Lynch and S. Mazuk Applied Optics, Volume 44, Issue 27, 5737 September 2005 OSA Optics InfoBase
Distant objects like clouds, mountains, and the Sun can appear to have colors that are significantly different from their intrinsic colors: the low Sun is often red, white clouds and snow-capped peaks appear yellow or pink, and dark green or gray mountains can appear blue or purple. The color alteration increases with distance, or alternatively, optical depth. We investigate the perceived colors of distant objects by computing the CIE chromaticity coordinates from their spectra. For sources viewed through significant amounts of atmosphere (e.g., the low Sun), MODTRAN4 radiative-transfer calculations are used to retrieve the spectra. In addition to clouds and mountains, the colors of stars, the Sun, and the sky are presented as a function of solar elevation under a variety of atmospheric conditions.

Experimental simulations of pollen coronas Free download
Werner B. Schneider and Michael Vollmer
Applied Optics, Volume 44, Issue 27, 5746 September 2005 OSA Optics InfoBase
A procedure to experimentally simulate pollen coronas is discussed. Observed coronas are due to pine and birch pollen having different geometries. Using computer simulations, two-dimensional projections of a large number of pollenlike objects with adjustable shapes, with or without preferential orientation and statistical or regular spatial distribution, are generated. The photograph of the printout allows samples with typical sizes between 20 and 200 µm. Their diffraction patterns can closely resemble the ones observed in nature and predicted by theory.

Ice analog halos
Zbigniew Ulanowski
Applied Optics, Volume 44, Issue 27, 5754 September 2005 OSA Optics InfoBase
Crystals of sodium fluorosilicate are used to produce easy to set up visual displays of atmospheric halos, including the 22° halo, the Parry arc, and upper tangent arcs. Scattering phase functions for single ice-analog rosettes, including a rough one, and a column aggregate, measured in randomized orientation, are also given. The phase functions show prominent halo features, with the exception of the rough crystal.

Turbulent ship wakes: further evidence that the Earth is round Free download
David K. Lynch
Applied Optics, Volume 44, Issue 27, 5759 September 2005 OSA Optics InfoBase
When viewed from the stern, a ship’s turbulent wake appears as a narrow strip of bubble-whitened water converging toward the horizon. The wake does not reach a sharp point on the horizon but has a finite angular width, indicating that the Earth is not flat, but rather round. A simple analysis of the geometry of the observations shows that the radius of the Earth can be estimated using only simple instruments and observations.
2004
Spectral-daylight recovery by use of only a few sensors Free download
Javier Hernández-Andrés, Juan L. Nieves, Eva M. Valero, and Javier Romero
J. Opt. Soc. Am. A, Vol. 21, No. 1, p. 13 January 2004 OSA Optics InfoBase
Linear models have already been proved accurate enough to recover spectral functions. We have resorted to such linear models to recover spectral daylight with the response of no more than a few real sensors. We performed an exhaustive search to obtain the best set of Gaussian sensors with a combination of optimum spectral position and bandwidth. We also examined to what extent the accuracy of daylight estimation depends on the number of sensors and their spectral properties. A set of 2600 daylight spectra [J. Opt. Soc. Am. A 18, 1325 (2001)] were used to determine the basis functions in the linear model and also to evaluate the accuracy of the search. The estimated spectra are compared with the original ones for different spectral daylight and skylight sets of data within the visible spectrum. Spectral similarity, colorimetric differences, and integrated spectral irradiance errors were all taken into account. We compare our best results with those obtained by using a commercial CCD, revealing the CCD’s potential as a daylight-estimation device.

Spectral-reflectance linear models for color pattern recognition Free download
Juan L. Nieves, Javier Hernández-Andrés, Eva M. Valero and Javier Romero
Applied Optics, vol. 43, N. 9, pp. 1880-1891, March 2004 OSA Optics InfoBase
We suggest a new method for color pattern recognition using a linear description of spectral reflectance functions and the spectral power distribution of illuminants containing very few parameters. We report on methods in which these spectral functions are derived from linear models based on principal component analysis (PCA). The correlation is made in the subspace spanned by the coefficients that describe each reflectance according to a suitable basis. The method is first illustrated in a control experiment where the scenes are captured under known illuminant conditions. The discrimination capacity of the algorithm improves upon conventional RGB multi-channel decomposition when scenes are captured under different illuminant conditions, and is comparable to color recognition based on CIELab system. Then we tested the coefficient method in situations where the target is captured under a reference illuminant and the scene containing the target under an unknown spectrally different one. We show that the method avoid false alarms under changes in the illuminant. The correlation results are satisfactory even for the reduced dimensional basis used here to represent the surface reflectance function of the image pixels.

How well does the Rayleigh model describe the E-vector distribution of skylight in clear and cloudy conditions? A full-sky polarimetric study Free download
Bence Suhai and Gábor Horváth
J. Opt. Soc. Am. A, Vol. 21, No. 9, p. 1669 September 2004 OSA Optics InfoBase
We present the first high-resolution maps of Rayleigh behavior in clear and cloudy sky conditions measured by full-sky imaging polarimetry at the wavelengths of 650 nm (red), 550 nm (green), and 450 nm (blue) versus the solar elevation angle θs . Our maps display those celestial areas at which the deviation Δα < │αmeas - αRayleigh│ is below the threshold αthres < 5°, where αmeas is the angle of polarization of skylight measured by full-sky imaging polarimetry, and αRayleigh is the celestial angle of polarization calculated on the basis of the single-scattering Rayleigh model. From these maps we derived the proportion r of the full sky for which the single-scattering Rayleigh model describes well (with an accuracy of Δα < 5°) the E-vector alignment of skylight. Depending on θs , r is high for clear skies, especially for low solar elevations (40% < r < 70% for θs ≤ 13°). Depending on the cloud cover and the solar illumination, r decreases more or less under cloudy conditions, but sometimes its value remains remarkably high, especially at low solar elevations (rmax = 69% for θs = 0°). The proportion r of the sky that follows the Rayleigh model is usually higher for shorter wavelengths under clear as well as cloudy sky conditions. This partly explains why the shorter wavelengths are generally preferred by animals navigating by means of the celestial polarization. We found that the celestial E-vector pattern generally follows the Rayleigh pattern well, which is a fundamental hypothesis in the studies of animal orientation and human navigation (e.g. in aircraft flying near the geomagnetic poles and using a polarization sky compass) with the use of the celestial α pattern.
2003
Feature issue: Applied Optics, January 2003

Light and color in the open air: introduction to the feature issue
Charles L. Adler, James A. Lock
Applied Optics, Volume 42, Issue 3, 307-308 January 2003 OSA Optics InfoBase
This special feature of Applied Optics reports the results of new experimental and theoretical research concerning a number of naked-eye optical phenomena, including ice-crystal halo displays, mirages, rainbows, glories, optical caustics, clear-sky phenomena, cloud coronas, cloud iridescence, and the extinction of skylight.

Halo Polarization Profiles and Sampled Ice Crystals: Observations and Interpretation Free download
Gunther P. Können, Herman R. A. Wessels, Jaap Tinbergen
Applied Optics, Volume 42, Issue 3, 309-317 January 2003 OSA Optics InfoBase
Simultaneous two-wavelength polarization and radiance distributions have been obtained for 22 ° parhelia in four Antarctic ice-crystal swarms that extended to ground level. Samples of crystals that produced these parhelia were collected and replicated. The wavelength dependence of the width of the halo polarization peak agrees with Fraunhofer diffraction theory, indicating that the broadening of the halos is caused primarily by diffraction. However, the observed broadening is much more than predicted from the size distribution of the replicated crystals. From one halo display to the other, the ratio of observed /predicted broadening is erratic, suggesting size-dependent collection efficiency in the sampling. This would imply that, for South Pole conditions, halo polarimetry (or even photometry) is a more reliable method for crystal size determination than actual sampling. It also implies that shapes of the sampled crystals need not necessarily be representative for the shapes of the halo-making crystals in the swarm. Our previous hypothesis [Appl. Opt. 33, 4569 (1994) , that a spread of interfacial angles is the dominating cause of halo broadening, has proved untenable.]

Symmetry in Halo Displays and Symmetry in Halo-Making Crystals Free download
Gunther P. Können
Applied Optics, Volume 42, Issue 3, 318-331 January 2003 OSA Optics InfoBase
The relation between the symmetry in halo displays and crystal symmetry is investigated for halo displays that are generated by ensembles of crystals. It is found that, regardless of the symmetry of the constituent crystals, such displays are always left-right (L -R) symmetric if the crystals are formed from the surrounding vapor. L -R symmetry of a halo display implies here that the cross sections for formation of a halo arc on the left-hand side of the solar vertical and its right-hand side mirror image are equal. This property leaves room for two types of halo display only: a full symmetric one (mmm -symmetric), and a partial symmetric one (mm2 -symmetric) in which halo constituents lack their counterparts on the other side of the parhelic circle. A partial symmetric display can occur only for point halos. Its occurrence implies that a number of symmetry elements are not present in the shape of the halo-making crystals. These elements are a center of inversion, any rotatory-inversion axis that is parallel to the crystal spin axis P , a mirror plane perpendicular to the P axis, and a twofold rotation axis perpendicular to the P axis. A simple conceptual method is presented to reconstruct possible shapes of the halo-generating crystals from the halos in the display. The method is illustrated in two examples. Halos that may occur on the Saturnian satellite Titan are discussed. The possibilities for the Huygens probe to detect these halos during its descent through the Titan clouds in 2005 are detailed.

Midlatitude Cirrus Cloud Climatology from the Facility for Atmospheric Remote Sensing. IV. Optical Displays
Kenneth Sassen, Jiang Zhu, Sally Benson
Applied Optics, Volume 42, Issue 3, 332-341 January 2003 OSA Optics InfoBase
In this fourth of a series of papers that describe long-term cloud research at the Facility for Atmospheric Remote Sensing at Salt Lake City, Utah, a ~10-year record of polarization lidar and photographic observations is analyzed to characterize the occurrence of optical displays in our local varieties of midlatitude cirrus clouds. The frequencies of occurrence of various types of halo, arc, and corona displays are evaluated according to their appearance and longevity over nominal 1-h observation periods and to the meteorological source of the cirrus. We find that complex halo-arc displays are rare at our locale and that even the so-called common 22° halo occurs infrequently as a complete long-lived ring. For example, only ~6% of the 1561-h daytime cirrus periods have bright and prolonged 22° halos, although a total of 37.3% have some indications of this halo, even if they are brief and fragmentary. Other fairly frequent features are the 22° upper tangent arc (8.6%), 22° parhelia (8.5%), and solar corona (7.2%). Of the optical displays observed, 83.6% are refraction based, only 1.9% are due to reflection phenomena, and a surprising 15.4% are caused by diffraction. Complex halo-arc displays are disproportionally associated with cirrus formed in tropical or subtropical airflow and also contain more horizontally oriented planar ice crystals. Lidar linear depolarization ratios from a subset of vivid displays show significant differences between halo- and the corona-producing cirrus, reflecting the effects of particle shape. Halos are associated with relatively warm cirrus that contain randomly and horizontally oriented planar ice crystals, whereas the colder corona cirrus produce much stronger depolarization from crystals too small to be uniformly oriented. Comparisons are made with available information from other locales, and we attempt to explain the geographical differences in terms of basic cirrus cloud processes

Comparison of Modeled and Observed Astronomical Refraction of the Setting Sun
Russell D. Sampson, Edward P. Lozowski, Arthur E. Peterson
Applied Optics, Volume 42, Issue 3, 342-353 January 2003 OSA Optics InfoBase
In this study a ray-tracing model that uses atmospheric data from VIZ and Vaisala RS80 rawinsondes is compared with the observed astronomical refraction presented by the setting Sun as seen from Stony Plain, Alberta, Canada. Photogrammetric measurements taken from photographs of the setting Sun show good agreement with the model for the 14 and 22 December 1998 sunsets. The poorer model results for the 8 December sunset appear to be caused by an obsolete and possibly defective VIZ rawinsonde. The results suggest that the ray-tracing model can produce improved refraction values when compared with the Pulkovo tables [Pulkovo Observatory, Refraction Tables of the Pulkovo Observatory , 5th ed. (Nauka, Leningrad, 1985) . However, they also indicate that the inverse solution (i.e., extracting the temperature profile from refraction measurements) may produce no improvement on U.S. Standard Atmosphere adjusted to the surface conditions.]

Ray Tracing and Refraction in the Modified US1976 Atmosphere Free download
Siebren Y. van der Werf
Applied Optics, Volume 42, Issue 3, 354-366 January 2003 OSA Optics InfoBase
A new and flexible ray-tracing procedure for calculating astronomical refraction is outlined and applied to the US1976 standard atmosphere. This atmosphere is generalized to allow for a free choice of the temperature and pressure at sea level, and in this form it has been named the modified US1976 (MUSA76) atmosphere. Analytical expressions and numerical procedures are presented for calculating dry-air refractions and for the water-vapor correction. Results for all apparent altitudes are presented and compared with The Star Almanac for Land Surveyors (1951), The Nautical Almanac (1958), and the Pulkovo tables (Refraction Tables of the Pulkovo Observatory , 1985). Dependences on sea-level pressure, temperature, and temperature gradient and on humidity are discussed.

Novaya Zemlya Effect and Sunsets Free download
Siebren Y. van der Werf, Günther P. Können, Waldemar H. Lehn
Applied Optics, Volume 42, Issue 3, 367-378 January 2003 OSA Optics InfoBase
Systematics of the Novaya Zemlya (NZ) effect are discussed in the context of sunsets. We distinguish full mirages, exhibiting oscillatory light paths and their onsets, the subcritical mirages. Ray-tracing examples and sequences of solar images are shown. We discuss two historical observations by Fridtjof Nansen and by Vivian Fuchs, and we report a recent South Pole observation of the NZ effect for the Moon.

Gerrit de Veer's True and Perfect Description of the Novaya Zemlya Effect, 24 -27 January 1597 Free download
Siebren Y. van der Werf, Günther P. Können, Waldemar H. Lehn, Frits Steenhuisen, Wayne P. S. Davidson
Applied Optics, Volume 42, Issue 3, 379-389 January 2003 OSA Optics InfoBase
The first recordings of the Novaya Zemlya (NZ) effect were made during Willem Barents ’ third Arctic expedition. Ray-tracing analyses of the three key observations, on 24 -27 January 1597, show that all the reported details can be explained by adopting one common and realistic type of temperature inversion. In particular, the Moon-Jupiter conjunction could have been visible over the central mountain ridge of the island. We show that the NZ effect distorts the relative positions of Jupiter and the Moon in such a way that the looked-for fingerprint of the conjunction occurred almost 2 h after the true conjunction. The quoted direction for the apparent Moon-Jupiter conjunction is then found to be accurate to within 1°. This delay of the apparent conjunction largely explains the error of 29° in their longitude determination. The truthfulness of these observations, debated for four centuries, now appears to be beyond doubt.

Bright Superior Mirages
Waldemar H. Lehn
Applied Optics, Volume 42, Issue 3, 390-393 January 2003 OSA Optics InfoBase
Superior mirages of unusual brightness are occasionally observed. Two such cases, photographed over the frozen surface of Lake Winnipeg, Canada, are documented. Visually, these mirages appear as featureless bright barriers far out on the lake. They are just images of the lake ice, yet the luminance in one case was 2.5 times (in the other, 1.7 times) the luminance of the ice surface in front of the mirage. The mirage itself can be modeled by means of a conduction inversion, but a proper explanation of the brightness is not yet available.

Halo and Mirage Demonstrations in Atmospheric Optics Free download
Michael Vollmer, Robert Greenler
Applied Optics, Volume 42, Issue 3, 394-398 January 2003 OSA Optics InfoBase
Some laboratory demonstrations on atmospheric optics are presented. The focus is on dispersion effects in mirages, lateral mirages, and inferior mirages produced with small hot plates. We also show a demonstration of the upper-tangent-arc halo, produced with a hexagonal prism, rotating about two axes.

Imaging Polarimetry of the Rainbow Free download
András Barta, Gábor Horváth, Balázs Bernáth, Viktor Benno Meyer-Rochow
Applied Optics, Volume 42, Issue 3, 399-405 January 2003 OSA Optics InfoBase
Using imaging polarimetry, we measured the polarization patterns of a rainbow on the shore of the Finnish town of Oulu in July 2001. We present here high-resolution color-coded maps of the spatial distributions of the degree and angle of linear polarization of the rainbow in the red (650 +/- 30 nm), green (550 +/- 30 nm), and blue (450 +/- 30 nm) ranges of the spectrum. The measured polarization characteristics of the investigated rainbow support earlier theoretical and computational results and are in accordance with previous qualitative observations. To our knowledge, this is the first imaging polarimetric study of rainbow polarization.

Experimental Observation of Total-Internal-Reflection Rainbows
Charles L. Adler, James A. Lock, Jonathon Mulholland, Brian Keating, Diana Ekelman
Applied Optics, Volume 42, Issue 3, 406-411 January 2003 OSA Optics InfoBase
A new class of rainbows is created when a droplet is illuminated from the inside by a point light source. The position of the rainbow depends on both the index of refraction of the droplet and the position of the light source, and the rainbow vanishes when the point source is too close to the center of the droplet. Here we experimentally measure the position of the transmission and one-internal-reflection total-internal-reflection rainbows, and the standard (primary) rainbow, as a function of light-source position.

Observation of the enhanced backscattering of light by the end of a tilted dielectric cylinder owing to the caustic merging transition
Philip L. Marston, Yibing Zhang, David B. Thiessen
Applied Optics, Volume 42, Issue 3, 412-417 January 2003 OSA Optics InfoBase
The scattering of light by obliquely illuminated circular dielectric cylinders was previously demonstrated to be enhanced by a merger of Airy caustics at a critical tilt angle. [Appl. Opt. 37 , 1534 (1998)]. A related enhancement is demonstrated here for backward and near-backward scattering for cylinders cut with a flat end perpendicular to the cylinder's axis. It is expected that merged caustics will enhance the backscattering by clouds of randomly oriented circular cylinders that have appropriately flat ends.

Analysis of the Shadow-Sausage Effect Caustic
James A. Lock, Charles L. Adler, Diana Ekelman, Jonathan Mulholland, Brian Keating
Applied Optics, Volume 42, Issue 3, 418-428 January 2003 OSA Optics InfoBase
We analyze the optical caustic produced by light refracted at the curved meniscus surrounding a cylindrical rod standing partially out of a liquid-filled container. When the rod is tilted from the vertical or when light is diagonally incident, the caustic is a four-cusped astroid with two of its cusps obscured by the rod's shadow. If a portion of the flat end of the rod is raised above the water level, the caustic evolves into a pattern of five interlocking cusps. The five cusps result from symmetry breaking of a three-cusped surface perturbation caustic.

Simulating glories and cloudbows in color
Stanley D. Gedzelman
Applied Optics, Volume 42, Issue 3, 429-435 January 2003 OSA Optics InfoBase
Glories and cloudbows are simulated in color by use of the Mie scattering theory of light upwelling from small-droplet clouds of finite optical thickness embedded in a Rayleigh scattering atmosphere. Glories are generally more distinct for clouds of droplets of as much as ~10 µm in radius. As droplet radius increases, the glory shrinks and becomes less prominent, whereas the cloudbow becomes more distinct and eventually colorful. Cloudbows typically consist of a broad, almost white band with a slightly orange outer edge and a dark inner band. Multiple light and dark bands that are related to supernumerary rainbows first appear inside the cloudbow as droplet radius increases above ~10 µm and gradually become more prominent when all droplets are the same size. Bright glories with multiple rings and high color purity are simulated when all droplets are the same size and every light beam is scattered just once. Color purity decreases and outer rings fade as the range of droplet sizes widens and when skylight, reflected light from the ground or background, and multiply scattered light from the cloud are included. Consequently, the brightest and most colorful glories and bows are seen when the observer is near a cloud or a rain swath with optical thickness of ~0.25 that consists of uniform-sized drops and when a dark or shaded background lies a short distance behind the cloud.

Simulation of Rainbows, Coronas, and Glories by use of Mie Theory Free download
Philip Laven OSA Optics InfoBase
Applied Optics, Volume 42, Issue 3, 436-444 January 2003
Mie theory offers an exact solution to the problem of scattering of sunlight by spherical drops of water. Until recently, most applications of Mie theory to scattering of light were restricted to a single wavelength. Mie theory can now be used on modern personal computers to produce full-color simulations of atmospheric optical effects, such as rainbows, coronas, and glories. Comparison of such simulations with observations of natural glories and cloudbows is encouraging.

Measuring and Modeling Twilight's Purple Light Free download
Raymond L. Lee, Javier Hernández-Andrés
Applied Optics, Volume 42, Issue 3, 445-457 January 2003 OSA Optics InfoBase
During many clear twilights, much of the solar sky is dominated by pastel purples. This purple light’s red component has long been ascribed to transmission through and scattering by stratospheric dust and other aerosols. Clearly the vivid purples of post-volcanic twilights are related to increased stratospheric aerosol loading. Yet our time-series measurements of purple-light spectra, combined with radiative transfer modeling and satellite soundings, indicate that background stratospheric aerosols by themselves do not redden sunlight enough to cause the purple light's reds. Furthermore, scattering and extinction in both the troposphere and the stratosphere are needed to explain most purple lights.

Color and Luminance Asymmetries in the Clear Sky Free download
Javier Hernández-Andrés, Raymond L. Lee, Javier Romero
Applied Optics, Volume 42, Issue 3, 458-464 January 2003 OSA Optics InfoBase
A long-standing assumption about the clear sky is that its colors and luminances are distributed symmetrically about the principal plane. As useful as this approximation is, our digital-image analyses show that clear-sky color and luminance routinely depart perceptibly from exact symmetry. These analyses reconfirm our earlier measurements with narrow field-of-view spectroradiometers [J. Opt. Soc. Am. A 18, 1325 (2001) , and they do so with much higher temporal and angular resolution across the entire sky dome.

Neutral Points of Skylight Polarization Observed During the Total Eclipse on 11 August 1999 Free download
Gábor Horváth, István Pomozi, József Gál
Applied Optics, Volume 42, Issue 3, 465-475 January 2003 OSA Optics InfoBase
We report here on the observation of unpolarized (neutral) points in the sky during the total solar eclipse on 11 August 1999. Near the zenith a neutral point was observed at 450 nm at two different points of time during totality. Around this celestial point the distribution of the angle of polarization was heterogeneous: The electric field vectors on the one side were approximately perpendicular to those on the other side. At another moment of totality, near the zenith a local minimum of the degree of linear polarization occurred at 550 nm. Near the antisolar meridian, at a low elevation another two neutral points occurred at 450 nm at a certain moment during totality. Approximately at the position of these neutral points, at another moment of totality a local minimum of the degree of polarization occurred at 550 nm, whereas at 450 nm a neutral point was observed, around which the angle-of-polarization pattern was homogeneous: The electric field vectors were approximately horizontal on both sides of the neutral point.

Coronas and iridescence in mountain wave clouds Free download
Joseph A. Shaw, Paul J. Neiman
Applied Optics, Volume 42, Issue 3, 476-485 January 2003 OSA Optics InfoBase
We use Fraunhofer diffraction theory and meterological data to determine the nature of cloud-particle distributions and the mean particle sizes required for interpreting photographs of coronas and iridescence in mountain wave clouds. Traditional descriptions of coronas and iridescence usually explain these optical phenomena as diffraction by droplets of liquid water. Our analysis shows that the photographed displays have mean particle sizes from 7.6 to 24.3 µm, with over half the cases requiring diffraction by small ( ~20 µm) quasispherical ice particles rather than liquid water droplets. Previous documentation of coronas produced by ice particles are limited to observations in cirrus clouds that appear to be composed of small ice crystals, whereas our observations suggest that coronas and iridescence quite often can be created by tiny quasispherical ice particles that might be unique to mountain wave clouds. Furthermore, we see that the dominant colors in mountain wave-cloud coronas are red and blue, rather than the traditionally described red and green.

Cirrus cloud iridescence: a rare case study
Kenneth Sassen
Applied Optics, Volume 42, Issue 3, 486-491 January 2003 OSA Optics InfoBase
On the evening of 25 November 1998, a cirrus cloud revealing the pastel colors of the iridescence phenomenon was photographed and studied by a polarization lidar system at the University of Utah Facility for Atmospheric Remote Sensing (FARS). The diffraction of sunlight falling on relatively minute cloud particles, which display spatial gradients in size, is the cause of iridescence. According to the 14-year study of midlatitude cirrus clouds at FARS, cirrus rarely produce even poor iridescent patches, making this particularly long-lived and vivid occurrence unique. In this unusually high (13.2 -14.4 km) and cold ( -69.7 ° to -75.5 °) tropopause-topped cirrus cloud, iridescence was noted from ~6.0 ° to ~13.5 ° from the Sun. On the basis of simple diffraction theory, this indicates the presence of particles of 2.5 - 5.5 µm effective diameter. The linear depolarization ratios of d = 0.5 measured by the lidar verify that the cloud particles were nonspherical ice crystals. The demonstration that ice clouds can generate iridescence has led to the conclusion that iridescence is rarely seen in midlatitude cirrus clouds because populations of such small particles do not exist for long in the presence of the relatively high water-vapor supersaturations needed for ice-particle nucleation.

Solar Aureoles Caused by Dust, Smoke, and Haze
Forrest M. Mims
Applied Optics, Volume 42, Issue 3, 492-496 January 2003 OSA Optics InfoBase
The forward scattering of sunlight by atmospheric aerosols causes a bright glow to appear around the Sun. This phenomenon, the simplest manifestation of the solar corona, is called the solar aureole. Simple methods can be used to photograph the solar aureole with conventional and digital cameras. Aureole images permit both a visually qualitative and an analytically quantitative comparison of aureoles caused by dust, smoke, haze, pollen, and other aerosols. Many hundreds of aureole photographs have been made at Geronimo Creek Observatory in Texas, including a regular time series since September 1998. These images, and measurements extracted from them, provide an important supplement to studies of atmospheric aerosols.

Simulating Coronas in Color
Stanley D. Gedzelman, James A. Lock
Applied Optics, Volume 42, Issue 3, 497-504 January 2003 OSA Optics InfoBase
Coronas are simulated in color by use of the Mie scattering theory of light by small droplets through clouds of finite optical thickness embedded in a Rayleigh scattering atmosphere. The primary factors that affect color, visibility, and number of rings of coronas are droplet size, width of the size distribution, and cloud optical thickness. The color sequence of coronas and iridescence varies when the droplet radius is smaller than ~6- µm. As radius increases to approximately 3.5 µm, new color bands appear at the center of the corona and fade as they move outward. As the radius continues to increase to ~6 µm, successively more inner rings become fixed in the manner described by classical diffraction theory, while outer rings continue their outward migration. Wave clouds or rippled cloud segments produce the brightest and most vivid multiple ringed coronas and iridescence because their integrated drop size distributions along sunbeams are much narrower than in convective or stratiform clouds. The visibility of coronas and the appearance of the background sky vary with cloud optical depth t. First the corona becomes visible as a white aureole in a blue sky when t ~ 0.001. Color purity then rapidly increases to an almost flat maximum in the range 0.05 < t < 0.5 and then decreases, so coronas are almost completely washed out by a bright gray background when t >= 4.

Evaluation of a one-dimensional cloud model for yellow and green thunderstorms
Frank W. Gallagher, William H. Beasley
Applied Optics, Volume 42, Issue 3, 505-510 January 2003 OSA Optics InfoBase
Many observers have reported observations of green light emanating from severe thunderstorms in the midwestern United States. Spectral measurements have demonstrated that the dominant wavelength of the light is in the green portion of the visible spectrum and that this is not just a subjective impression. According to the theory proposed by Bohren and Fraser [Bull. Am. Meteorol. Soc. 74 , 2185 (1993)], two effects combine to produce green light from thunderstorms. First, incident solar radiation is reddened by selective scattering by air molecules and particles in the atmosphere before it enters the cloud. Second, the radiation that passes through an optically thick cloud is attenuated in the longer wavelengths because of selective absorption by liquid water. Model calculations indicate that realizable combinations of mean drop diameters, mean liquid-water contents, and cloud thicknesses can satisfy the conditions required for shifting the dominant wavelength of the incident solar radiation to green.

Polarization-Based Vision Through Haze
Yoav Y. Schechner, Srinivasa G. Narasimhan, Shree K. Nayar
Applied Optics, Volume 42, Issue 3, 511-525 January 2003 OSA Optics InfoBase
We present an approach for easily removing the effects of haze from passively acquired images. Our approach is based on the fact that usually the natural illuminating light scattered by atmospheric particles (airlight) is partially polarized. Optical filtering alone cannot remove the haze effects, except in restricted situations. Our method, however, stems from physics-based analysis that works under a wide range of atmospheric and viewing conditions, even if the polarization is low. The approach does not rely on specific scattering models such as Rayleigh scattering and does not rely on the knowledge of illumination directions. It can be used with as few as two images taken through a polarizer at different orientations. As a byproduct, the method yields a range map of the scene, which enables scene rendering as if imaged from different viewpoints. It also yields information about the atmospheric particles. We present experimental results of complete dehazing of outdoor scenes, in far-from-ideal conditions for polarization filtering. We obtain a great improvement of scene contrast and correction of color.

Role of the tunneling ray in near-critical-angle scattering by a dielectric sphere
James A. Lock
J. Opt. Soc. Am. A, Vol. 20, No. 3, p. 499 March 2003 OSA Optics InfoBase
The scattering far zone for light transmitted through a sphere following p - 1 internal reflections by a family of near-grazing incident rays is subdivided into a lit region and a shadow region. The sharpness of the ray theory transition between the lit and the shadow regions is smoothed in wave theory by radiation shed by electromagnetic surface waves. It is shown that when higher-order terms in the physical optics approximation to the phase of the partial-wave scattering amplitudes are included, the transition between the lit and the shadow regions becomes a two-ray-to-zero-ray transition, called a superweak caustic in analogy to the more familiar scattering caustics and weak scattering caustics. One of the merged rays is a tunneling ray.

Analytical models of optical refraction in the troposphere
Brett D. Nener, Neville Fowkes, and Laurent Borredon
J. Opt. Soc. Am. A, Vol. 20, No. 5, p. 867 May 2003 OSA Optics InfoBase
An extremely accurate but simple asymptotic description (with known error) is obtained for the path of a ray propagating over a curved Earth with radial variations in refractive index. The result is sufficiently simple that analytic solutions for the path can be obtained for linear and quadratic index profiles. As well as rendering the inverse problem trivial for these profiles, this formulation shows that images are uniformly magnified in the vertical direction when viewed through a quadratic refractive-index profile. Non-uniform vertical distortions occur for higher-order refractive-index profiles.

Scattering matrices for large ice crystal particles
Anatoli G. Borovoi and Igor A. Grishin
J. Opt. Soc. Am. A, Vol. 20, No. 11, p. 2071 November 2003 OSA Optics InfoBase
The problem of light scattering by ice crystal particles whose sizes are essentially larger than the incident wavelength is divided into two parts. First, the scattered field is represented as a set of plane-parallel outgoing beams in the near zone of the particle. Then, in the far zone the scattered field is represented as a result of both diffraction and interference of these beams within the framework of physical optics. A proper ray-tracing algorithm for calculation of the amplitude (Jones) scattering matrix is developed and applied. For large particles, a number of reduced Mueller matrices are introduced and discussed, since the pure Mueller matrix obtained from the Jones matrix becomes a rather cumbersome and quickly oscillating value. Backscattering by hexagonal ice crystals, including polarization properties, is considered in detail.
2001

Colorimetric and spectroradiometric characteristics of narrow-field-of-view clear skylight in Granada, Spain Free download
Javier Hernandez-Andrés, Javier Romero and Raymond L. Lee, Jr.
J. Opt. Soc. Am. A, Vol. 18, No. 2, p. 412 February 2001 OSA Optics InfoBase
As part of our ongoing research into the clear daytime sky’s visible structure, we analyze over 1500 skylight spectra measured during a seven-month period in Granada, Spain. We use spectral radiances measured within 3° fields of view (FOV’s) to define colorimetric characteristics along four sky meridians: the solar meridian and three meridians at azimuths of 45°, 90°, and 315° relative to it. The resulting clear-sky chromaticities in 44 different view directions (1) are close to but do not coincide with the CIE daylight locus, (2) form V-shaped meridional chromaticity curves along it (as expected from theory), and (3) have correlated color temperatures (CCT’s) ranging from 3800 K to ` K. We also routinely observe that sky color and luminance are asymmetric about the solar meridian, usually perceptibly so. A principal-components analysis shows that three vectors are required for accurate clear-sky colorimetry, whereas six are needed for spectral analyses.

Color and spectral analysis of daylight in southern Europe Free download
Javier Hernandez-Andrés, Javier Romero, Juan L. Nieves and Raymond L. Lee, Jr.
J. Opt. Soc. Am. A, Vol. 18, No. 6, p. 1325 June 2001 OSA Optics InfoBase
We have analyzed the colorimetric and spectral characteristics of 2600 daylight spectra (global spectral irradiances on a horizontal surface) measured for all sky states during a 2-year period at Granada, Spain. We describe in detail the chromaticity coordinates, correlated color temperatures (CCT), luminous efficacies, and relative UV and IR contents of Granada daylight. The chromaticity coordinates of Granada daylight lie far above the CIE locus at high CCTs (.9000 K), and a CCT of 5700 K best typifies this daylight. Our principal components analysis shows that Granada daylight spectra can be adequately represented by using sixdimensional linear models in the visible, whereas seven-dimensional models are required if we include the UV or near-IR. Yet on average only three-dimensional models are needed to reconstruct spectra that are colorimetrically indistinguishable from the original spectra.

Heiligenschein and Related Phenomena in Divergent Light
Jan O. Mattsson, Lars Bärring
Applied Optics, Volume 40, Issue 27, 4799-4806 September 2001 OSA Optics InfoBase
When seen in divergent light, atmospheric optical phenomena could appear to be modified. We describe some geometric and retroreflectional effects of light divergence on heiligenschein and related phenomena that, to our knowledge, have not been previously reported. These geometric effects are compared with and set in relation to the geometric effects on other atmospheric optical phenomena.

Blue Spot on the Parhelic Circle
Mika Sillanp, Jarmo Moilanen, Marko Riikonen, Marko Pekkola
Applied Optics, Volume 40, Issue 30, 5275-5279 October 2001 OSA Optics InfoBase
We develop a theory for a new effect on the parhelic circle. We show that there is a colored segment on the parhelic circle at a certain large azimuth that depends on solar elevation. The color segment appears at solar elevations below 32° and is explained as a transition between total and partial internal reflection in the main ray paths of the parhelic circle in oriented ice crystals. Based on our simple refraction theory and computer simulations, we find that the color of the segment is mainly green and blue. The theory is tested with available photographs of the effect.
2000

Experimenting with Minnaert's Cigar
Jan O. Mattsson, Lars Bärring, Esben Almqvist
Applied Optics, Volume 39, Issue 21, 3604-3611 July 2000 OSA Optics InfoBase
We have studied the seldom-seen halo phenomenon that can arise in divergent light, Minnaert's Cigar, which we produced in laboratory experiments and computer simulation. In the laboratory experiments halos or transections were produced in clouds of alum crystals precipitated in a solution of ethyl alcohol or in alum crystals deposited upon glass plates. The three-dimensional cigar form was less pronounced in our small-scale experiments than when the form was observed over several meters. In our experiments and simulations transections through Minnaert's Cigar include different halo forms that may arise on window panes or windshields covered with halo-active ice crystals or as horizontal halos on glittering frost-covered ground.

Halo Observations Provide Evidence of Airborne Cubic Ice in the Earth's Atmosphere
Marko Riikonen, Mika Sillanp, Leena Virta, Daniel Sullivan, Jarmo Moilanen, Ismo Luukkonen
Applied Optics, Volume 39, Issue 33, 6080-6085 November 2000 OSA Optics InfoBase
An ice crystal halo display that contains several previously unknown halo phenomena was observed in Northern Chile. Analysis of computer simulations of the halos demonstrates that most of the new halo arcs in the display can be explained by the presence of airborne and preferentially oriented crystals of cubic ice. These observations therefore provide evidence of the existence of the cubic phase of ice in the Earth's atmosphere.

Parry Arc: A Polarization Lidar, Ray-Tracing, and Aircraft Case Study
Kenneth Sassen, Yoshihide Takano
Applied Optics, Volume 39, Issue 36, 6738-6745 December 2000 OSA Optics InfoBase
Using simple ray-tracing simulations, the cause of the rare Parry arc has been linked historically to horizontally oriented columns that display the peculiar ability to fall with a pair of prism faces closely parallel to the ground. Although we understand the aerodynamic forces that orient the long-column axis in the horizontal plane, which gives rise to the relatively common tangent arcs of the 22° halo, the mechanism leading to the Parry crystal orientation has never been resolved adequately. On 16 November 1998, at the University of Utah Facility for Atmospheric Remote Sensing, we studied a cirrus cloud producing a classic upper Parry arc using polarization lidar and an aircraft with a new high-resolution ice crystal imaging probe. Scanning lidar data, which reveal extremely high linear depolarization ratios d a few degrees off the zenith direction, are simulated with ray-tracing theory to determine the ice crystal properties that reproduce this previously unknown behavior. It is found that a limited range of thick-plate crystal axis (length-to-diameter) ratios from 0.75 to 0.93 generates a maximum d =2.0 - 5.0 for vertically polarized 0.532 µm light when the lidar is tilted 1°-2° off the zenith. Halo simulations based on these crystal properties also generate a Parry arc. However, although such particles are abundant in the in situ data in the height interval indicated by the lidar, one still has to invoke an aerodynamic stabilization force to produce properly oriented particles. Although we speculate on a possible mechanism, further research is needed into this new explanation for the Parry arc.

Sunset science. III. Visual adaptation and green flashes
Andrew T. Young
J. Opt. Soc. Am. A, Vol. 17, No. 12, p. 2129 December 2000 OSA Optics InfoBase
Photographs of green flashes do not preclude a role for physiological effects in these phenomena. While green flashes are certainly not after-images, there is compelling evidence that adaptation in the visual system strongly affects the perceived color of most sunset green flashes. Furthermore, the retinal image of the setting Sun is usually bright enough to bleach most of the red-sensitive photopigment in a few seconds, making the yellow stage of a sunset flash appear green. Even in air so hazy that no green light reaches the eye, a yellow flash may occur and appear green. Many, but not all, visual observations of sunset green flashes are of this yellow flash. The yellow portion of sunset green flashes helps explain their reported durations, which exceed those expected for the appearance of green light alone.
N.B. see related articles:
Sunset science. I. The mock mirage (Applied Optics, Vol. 36, No. 12, p. 2689, April 1997) OSA Optics InfoBase
Sunset science. II. A useful diagram (Applied Optics, Vol. 37, No. 18, p. 3785, June 1998) OSA Optics InfoBase
Sunset science. IV. Low-altitude Refraction (The Astronomical Journal, Vol. 127, pp. 3622–3637, June 2004) Free download

1999
A General Setting for Halo Theory Free download
Walter Tape, Günther P. Können
Applied Optics, Volume 38, Issue 9, 1552-1625 March 1999 OSA Optics InfoBase
We describe a general framework for systematically treating halos that are due to refraction in preferentially oriented ice wedges, and we construct an atlas of such halos. Initially we are constrained neither by the interfacial angles nor the orientations of real ice crystals. Instead we consider all possible refraction halos. We therefore make no assumption regarding the wedge angle, and only a weak assumption regarding the allowable wedge orientations. The atlas is thus a very general collection of refraction halos that includes known halos as a small fraction. Each halo in the atlas is characterized by three parameters: the wedge angle, the zenith angle of the spin vector, and the spin vector expressed in the wedge frame. Together with the sun elevation, the three parameter values for a halo not only permit calculation of the halo shape, they also give much information about the halo without extensive calculation, so that often a crude estimate of the halo s appearance is possible merely from inspection of its parameters. As a result, the theory reveals order in what seems initially to be a staggering variety of halo shapes, and in particular it explains why halos look the way they do. Having constructed and studied the atlas, we then see where real or conceivable refraction halos, arising in specific crystal shapes and crystal orientations, fit into the atlas. Although our main goal is to understand halos arising in pyramidal crystals, the results also clarify and unify the classical halos arising in hexagonal prismatic crystals.

Ray theory analysis of the shadow blister effect
James A. Lock
Applied Optics, Vol. 38, No. 9, pp. 1573-1578, 20 March 1999 OSA Optics InfoBase
When an extended light source such as the Sun illuminates two objects so that their shadows lie close to each other, the shadow of one of the objects occasionally appears to bulge out toward the shadow of the other. This effect is caused by the overlap of the penumbras of the shadows and is analyzed here with ray theory. A laboratory demonstration of this phenomenon is performed and compared with theoretical predictions.

How big should hexagonal ice crystals be to produce halos? Free download
M. I. Mishchenko, A.Macke
Applied Optics Vol. 38, No. 9, 20 March 1999, pp. 1626 -1629 OSA Optics InfoBase
It has been hypothesized that the frequent lack of halos in observations of cirrus and contrails and laboratory measurements is caused by small ice crystal sizes that put the particles outside the geometrical optics domain of size parameters. We test this hypothesis by exploiting a strong similarity of ray tracing phase functions for finite hexagonal and circular ice cylinders and using T -matrix computations of electromagnetic scattering by circular cylinders with size parameters up to 180 in the visible. We conclude that well-defined halos should be observable for ice crystal size parameters of the order of 100 and larger and discuss remote-sensing implications of this result.

Unusual Pyramidal Ice in the Atmosphere as the Origin of Elliptical Halos
Mika Sillanp, Jarmo Moilanen, Marko Pekkola, Martti Penttinen, Jari Piikki
Applied Optics, Volume 38, Issue 24, 5089-5095 August 1999 OSA Optics InfoBase
The formation mechanism of elliptical halos and Bottlinger s rings has long remained uncertain. The current model for elliptical halos requires multiple scattering from two different populations of ice crystals in a complex mode of motion. New evidence indicates that elliptical halos, and possibly Bottlinger s rings, are due to refraction through ice crystals shaped like obtuse pyramids. This unusual ice crystal may not have been documented previously.

Calculating Correlated Color Temperatures Across the Entire Gamut of Daylight and Skylight Chromaticities Free download
Javier Hernandez-Andres, Raymond L. Lee, Javier Romero
Applied Optics, Volume 38, Issue 27, 5703-5709 September 1999 OSA Optics InfoBase
Natural outdoor illumination daily undergoes large changes in its correlated color temperature (CCT), yet existing equations for calculating CCT from chromaticity coordinates span only part of this range. To improve both the gamut and accuracy of these CCT calculations, we use chromaticities calculated from our measurements of nearly 7000 daylight and skylight spectra to test an equation that accurately maps CIE 1931 chromaticities x and y into CCT. We extend the work of McCamy Color Res. Appl. 12, 285 287 (1992) by using a chromaticity epicenter for CCT and the inverse slope of the line that connects it to x and y . With two epicenters for different CCT ranges, our simple equation is accurate across wide chromaticity and CCT ranges (3000 - 106 K) spanned by daylight and skylight.

1998
Feature issue: Applied Optics, March 1998

Light and color in the open air: introduction to the feature issue
Kenneth Sassen and W. Patrick Arnott
Applied Optics, Vol. 37, No. 9, pp. 1425 - 1426, 20 March 1998 OSA Optics InfoBase
The topical meeting on light and color in the open air was held 9–12 February 1997 in Santa Fe, New Mexico. The series of papers that follows represents the fruition of this meeting, revealing the range of current scientific explorations into the play of light and color in nature.

Can cirrus clouds produce glories?
Kenneth Sassen, W. Patrick Arnott, Jennifer M. Barnett, and Steve Aulenbach
Applied Optics, Vol. 37, No. 9, pp. 1427 - 1433, 20 March 1998 OSA Optics InfoBase
A vague glory display was photographed over central Utah from an airplane beginning its descent through a cirrus cloud layer with an estimated cloud top temperature of -45 and -55 °C. Photographic analysis reveals a single reddish-brown ring of 2.5–3.0° radius around the antisolar point, although a second ring appeared visually to have been present over the brief observation period. Mie and approximate nonspherical theory scattering simulations predict a population of particles with modal diameters between 9 and 15 µm. Although it is concluded that multiple-ringed glories can be accounted for only through the backscattering of light from particles that are strictly spherical in shape, the poor glory colorization in this case could imply the presence of slightly aspherical ice particles. The location of this display over mountainous terrain suggests that it was generated by an orographic wave cloud, which we speculate produced numerous frozen cloud droplets that only gradually took on crystalline characteristics during growth.

Halo arcs from airborne, pyramidal ice crystals falling with their c axes in vertical orientation
Marko Pekkola, Marko Riikonen, Jarmo Moilanen, and Jukka Ruoskanen
Applied Optics, Vol. 37, No. 9, pp. 1435 - 1440, 20 March 1998 OSA Optics InfoBase
Many halo arcs are caused by pyramidal crystals that have [1 0 - 1 1] crystal faces. We treat halo arcs arising from pyramidal crystals that fall in the air with their c axes vertically oriented. To our knowledge only 6 of the 12 possible halo phenomena that belong to this category have been dealt with in the literature. Surprisingly the yet undiscussed halos are predicted to be of comparable intensity with those already treated. They are produced by reflections from pyramidal crystal basal faces. A theoretical summary and computer simulations are presented of the mentioned 12 halo phenomena and of the individual arcs into which they break in the sky. We give an overview to the current level of documentation of these phenomena by listing the first published photographs of each phenomenon known to the authors.

Comparison of Sun pillars with light pillars from nearby light sources
A. James Mallmann, Jeffrey L. Hock, and Robert G. Greenler
Applied Optics, Vol. 37, No. 9, pp. 1441 - 1449, 20 March 1998 OSA Optics InfoBase
Using a Monte Carlo method, we simulate the appearance of light pillars produced by nearby light sources and compare their appearance with simulations of Sun pillars. Photographs of light pillars are also compared with the simulations. We expand the idea of light and Sun pillars by examining the reflected-light patterns from several different known distributions of airborne ice crystals. Polarization properties of light pillars from nearly horizontally oriented plate crystals are also simulated.

Identification of odd-radius halo arcs and of 44°/46° parhelia by their inner-edge polarization Free download
Günther P. Können
Applied Optics, Vol. 37, No. 9, pp. 1450 - 1456, 20 March 1998 OSA Optics InfoBase
Birefringence of ice causes the inner edges of refraction halos to be polarized. The direction of this polarization relates directly to the projection of the crystal main axis onto the sky. This implies that the inner-edge polarization can serve as an observational diagnostic for determining the actual nature of a halo arc if two competing explanations exist. The direction and the visibility of the inner-edge polarization of arcs and circular halos arising from usual ice crystals and from ice crystals with pyramidal ends are calculated. It is found that the observation of inner-edge polarization can be decisive for the identification of a spot that might be either a 44° parhelion or a 46° parhelion, of an arc that might be either a 22° sunvex Parry arc or a 20° Parroid arc arising from plate-oriented pyramidal crystals, and of an arc that might be either a 22° suncave Parry arc or a 23° Parroid arc from plate-oriented pyramidal crystals. (With a Parroid arc, a halo is that which arises from an ice wedge made up of two faces of a crystal that rotates about a vertically oriented spin axis, and the edge of the wedge is perpendicular to this spin axis.) Polarization properties of other rare arcs are discussed. Practical hints are given for observing visually the inner-edge polarization of halos.

Polarization structures in parhelic circles and in 120° parhelia Free download
Günther P. Können and Jaap Tinbergen
Applied Optics, Vol. 37, No. 9, pp. 1457 - 1464, 20 March 1998 OSA Optics InfoBase
Parhelic circles due to plate-oriented crystals ~hence, with main axes vertical! and 120° parhelia change in position when viewed through a rotating polarizer. The parhelic circle moves vertically; its largest shift is found at an azimuthal distance between 90° and 120° from the Sun. The 120° parhelia move both vertically and horizontally. The magnitudes of the shifts are between 0.1° and 0.3°, depending on solar elevation. The mechanism is polarization-sensitive internal reflection by prism faces of the ice crystals. We outline the theory and present three visual and one instrumental observation of the displacements of these halos in polarized light.

Digital imaging of clear-sky polarization Free download
Raymond L. Lee, Jr.
Applied Optics, Vol. 37, No. 9, pp. 1465 - 1476, 20 March 1998 OSA Optics InfoBase
If digital images of clear daytime or twilight skies are acquired through a linear polarizing filter, they can be combined to produce high-resolution maps of skylight polarization. Here polarization P and normalized Stokes parameter Q are measured near sunset at one inland and two coastal sites. Maps that include the principal plane consistently show that the familiar Arago and Babinet neutral points are part of broader areas in which skylight polarization is often indistinguishably different from zero. A simple multiple-scattering model helps explain some of these polarization patterns.

Corona-producing ice clouds: a case study of a cold mid-latitude cirrus layer
Kenneth Sassen, Gerald G. Mace, John Hallett, and Michael R. Poellot
Applied Optics, Vol. 37, No. 9, pp. 1477 - 1485, 20 March 1998 OSA Optics InfoBase
A high (14.0-km), cold (-71.0 °C) cirrus cloud was studied by ground-based polarization lidar and millimeter radar and aircraft probes on the night of 19 April 1994 from the Cloud and Radiation Testbed site in northern Oklahoma. A rare cirrus cloud lunar corona was generated by this 1–2-km-deep cloud, thus providing an opportunity to measure the composition in situ, which had previously been assumed only on the basis of lidar depolarization data and simple diffraction theory for spheres. In this case, corona ring analysis indicated an effective particle diameter of ~22 µm. A variety of in situ data corroborates the approximate ice-particle size derived from the passive retrieval method, especially near the cloud top, where impacted cloud samples show simple solid crystals. The homogeneous freezing of sulfuric acid droplets of stratospheric origin is assumed to be the dominant ice-particle nucleation mode acting in corona-producing cirrus clouds. It is speculated that this process results in a previously unrecognized mode of acid-contaminated ice-particle growth and that such small-particle cold cirrus clouds are potentially a radiatively distinct type of cloud.

Solar corona caused by juniper pollen in Texas
Forrest M. Mims III
Applied Optics, Vol. 37, No. 9, pp. 1486 - 1488, 20 March 1998 OSA Optics InfoBase
Coronas are colorful, concentric rings centered on a bright light such as the Sun, the Moon, or even a streetlamp. Coronas are most commonly caused by water droplets or ice particles of relatively uniform size. Observers in Finland have reported spectacular clear-sky coronas caused by pollen grains. A clear-sky corona in central Texas occurred during the peak of the juniper pollinating season. The aerosol optical thickness at each of three wavelengths was highest when the corona was most prominent. Photographic measurements of the corona infer a particle diameter of ~32.4 µm. Because juniper pollen grains have a diameter of from 22 to 30 µm, they are the aerosol most likely to have caused the corona.

Long-range superior mirages
Waldemar H. Lehn and Thomas L. Legal
Applied Optics, Vol. 37, No. 9, pp. 1489 - 1494, 20 March 1998 OSA Optics InfoBase
Superior mirages of simple appearance are occasionally observed over distances exceeding 70 km. These mirages cannot be explained in terms of standard textbook models; rather, they are shown to arise from fairly complex atmospheres. Two observations of different types, observed at Resolute Bay, Canada, are presented. The first is the basic three-image mirage in which one inverted and one erect image float above the object. The second is a single-image mirage in which the object is elevated but undistorted. For each, the most suitable atmospheric model contains several distinct atmospheres, and the first one requires sloped atmospheric layers as well.

Simulation of inferior mirages observed at the Halligen Sea
Eberhard Tränkle
Applied Optics, Vol. 37, No. 9, pp. 1495 - 1505, 20 March 1998 OSA Optics InfoBase
Two unusual forms of inferior mirage are observed and photographed at the Halligen Sea. With heuristic analytic functions for the temperature profiles, numerical integration of the refraction differential equation on a flat earth is performed. The simulation shows that a double inferior mirage can appear if a light wind carries hot air from above dry sandbanks in the mud flats. Horizontal stripes can appear in the mirage image if a water channel crosses the line of sight between the observer and the object.

Mie theory, Airy theory, and the natural rainbow Free download
Raymond L. Lee, Jr.
Applied Optics, Vol. 37, No. 9, pp. 1506-1519, 20 March 1998 OSA Optics InfoBase
Compared with Mie scattering theory, Airy rainbow theory clearly miscalculates some monochromatic details of scattering by small water drops. Yet when monodisperse Airy theory is measured by perceptual (rather than purely physical) standards such as chromaticity and luminance contrast, it differs very little from Mie theory. Considering only the angular positions of luminance extrema, Airy theory’s errors are largest for small droplets such as those that dominate cloudbows and fogbows. However, integrating over a realistic drop-size distribution for these bows eliminates most perceptible color and luminance differences between the two theories.

Generalized tertiary rainbow of slightly oblate drops: observations with laser illumination
Dean S. Langley and Philip L. Marston
Applied Optics, Vol. 37, No. 9, pp. 1520-1526, 20 March 1998 OSA Optics InfoBase
The tertiary rainbow of acoustically levitated water drops was observed in the laboratory. Nontrivial caustics were observed for relatively small values of eccentricity. The angular locations of caustics were modeled with matrix methods of generalized ray tracing. Photographs of the scattering were in general agreement with models. Possible effects on the appearance of natural tertiary bow features are discussed.

Amplification of High-Order Rainbows of a Cylinder with an Elliptical Cross Section
James A. Lock, Charles L. Adler, Bradley R. Stone, Patrick D. Zajak
Applied Optics, Volume 37, Issue 9, 1527-1533 March 1998 OSA Optics InfoBase
The intensity of high-order rainbows for normally incident light and certain rotation angles of a cylinder with an elliptical cross section is greatly amplified with respect to the intensity for a circular cross-sectional cylinder. The amplification is due to a number of the internal reflections occurring past the critical angle for total internal reflection, and the effect is especially strong for odd-order rainbows, beginning with the third order. Experimentally, the fourth- and the fifth-order rainbows of a nearly elliptical cross-sectional glass rod were observed and analyzed.

Scattering observations for tilted transparent fibers: evolution of Airy caustics with cylinder tilt and the caustic merging transition
Catherine M. Mount, David B. Thiessen, and Philip L. Marston
Applied Optics, Vol. 37, No. 9, pp. 1534-1539, 20 March 1998 OSA Optics InfoBase
When a dielectric circular cylinder is obliquely illuminated, the scattering angle associated with the Airy caustics of the cylinder’s primary rainbow depends on the tilt of the cylinder. We display records of the scattering pattern for a transparent poly (methyl methacrylate) fiber ranging from small values of tilt through values of tilt that are sufficiently large for the Airy caustics from both sides of the fiber to merge in a meridional plane containing the incident wave vector and the fiber’s axis. The records are compared directly with the evolution of the caustic projected onto the observation plane, and certain qualitative features of the global evolution of the caustics are confirmed. Although the observations used laser illumination, they are relevant to anticipating the scattering by sunlit transparent tilted cylinders.

Rainbow scattering by a cylinder with a nearly elliptical cross section
Charles L. Adler, James A. Lock, and Bradley R. Stone
Applied Optics, Vol. 37, No. 9, pp. 1540-1550, 20 March 1998 OSA Optics InfoBase
We both theoretically and experimentally examine the behavior of the first- and the second-order rainbows produced by a normally illuminated glass rod, which has a nearly elliptical cross section, as it is rotated about its major axis. We decompose the measured rainbow angle, taken as a function of the rod’s rotation angle, into a Fourier series and find that the rod’s refractive index, average ellipticity, and deviation from ellipticity are encoded primarily in the m = 0, 2, 3 Fourier coefficients, respectively. We determine these parameters for our glass rod and, where possible, compare them with independent measurements. We find that the average ellipticity of the rod agrees well with direct measurements, but that the rod’s diameter inferred from the spacing of the supernumeraries of the first-order rainbow is significantly larger than that obtained by direct measurement. We also determine the conditions under which the deviation of falling water droplets from an oblate spheroidal shape permits the first few supernumeraries of the second-order rainbow to be observed in a rain shower.

Descartes glare points in scattering by icicles: color photographs and a tilted dielectric cylinder model of caustic and glare-point evolution
Philip L. Marston
Applied Optics, Vol. 37, No. 9, pp. 1551-1556, 20 March 1998 OSA Optics InfoBase
Glare points associated with the Airy caustics of once and twice internally reflected rays are visible in the scattering by sunlit icicles. Supporting color photographs include an image of the far-field scattering. Relevant rays are analogous to the Descartes rays of primary and secondary rainbows of drops; however, the caustic conditions for the icicle are predicted to be affected by tilt of the illumination relative to the axis of the icicle. A model for the caustic evolution, given for a circular dielectric cylinder, manifests a transition in which the Airy caustic (and associated glare points) merge in the meridional plane at a critical tilt. At this critical tilt the merged glare point is predicted to be very bright. The calculations use the Bravais effective refractive index and generalized ray tracing.

Laboratory experiments in atmospheric optics Free download
Michael Vollmer and Robert Tammer
Applied Optics, Vol. 37, No. 9, pp. 1557-1568,20 March 1998 OSA Optics InfoBase
Old and new laboratory experiments on atmospheric optics with a focus on mirages, rainbows, and halos are presented. Some qualitative demonstrations serve primarily didactical purposes, e.g., by proving the existence of curved light rays in media with a gradient of the index of refraction, by directly visualizing the minimum-deviation curve for rainbow paths in water droplets, or by helping to elucidate the ray classes in hexagons that contribute to a specific halo. In addition, quantitative experiments allow a direct comparison of angular positions and intensities with analytical computations or simulations of light scattering from small water droplets or ice hexagons. In particular, the latter can help us to understand complex halo phenomena.

Observations of glistening in the environment and its relationship to stereovision
Harry E. Bates and Grant Warner
Applied Optics, Vol. 37, No. 9, pp. 1569-1572, 20 March 1998 OSA Optics InfoBase
The relationship between glistening and stereovision is explored. Glistening is defined as the existence of points of light in the field of view of the observer that are observed substantially in only one eye. We define each glistening point to be essentially a point of stereonoise. A theory of the probability of glistening is developed and shows that a threshold point for 100% glistening should exist. The results of field experiments are presented.

Effects of a butterfly scale microstructure on the iridescent color observed at different angles
Haruna Tada, Seth E. Mann, Ioannis N. Miaoulis, and Peter Y. Wong
Applied Optics, Vol. 37, No. 9, pp. 1579-1584, 20 March 1998 OSA Optics InfoBase
Multilayer thin-film structures in butterfly wing scales produce a colorful iridescence from reflected sunlight. Because of optical phenomena, changes in the angle of incidence of light and the viewing angle of an observer result in shifts in the color of butterfly wings. Colors ranging from green to purple, which are due to nonplanar specular reflection, can be observed on Papilio blumei iridescent scales. This refers to a phenomenon in which the curved surface patterns in the thin-film structure cause the specular component of the reflected light to be directed at various angles while affecting the spectral reflectivity at the same time by changing the optical path length through the structure. We determined the spectral reflectivities of P. blumei iridescent scales numerically by using models of a butterfly scale microstructure and experimentally by using a microscale-reflectance spectrometer. The numerical models accurately predict the shifts in spectral reflectivity observed experimentally.

Thirty years of observing and documenting sky optical phenomena
Peter-Paul Hattinga Verschure
Applied Optics, Vol. 37, No. 9, pp. 1585-1588, 20 March 1998 OSA Optics InfoBase
A homogeneous series of systematic observations of sky optical phenomena in the Netherlands has been gathered by the Dutch Observing Network since 1965. This continues the Dutch observation series that started at the end of the nineteenth century. A time series of ice-crystal halo frequencies from 1920 to 1996 and frequency diagrams of some specific halos the period from 1970 to 1996 are shown and discussed. Systematic observation recording by means of diaries and exchanging routines among observers are described. Methods are given for establishing and maintaining a network of volunteers that can provide, in a homogeneous time series, sky optical phenomena recordings.

Sunset science. II. A useful diagram
Andrew T. Young and George W. Kattawar
Applied Optics, Vol. 37, No. 18, pp. 3785-3792, June 1998 OSA Optics InfoBase
We present diagrams that show how layers in atmospheric thermal structure are related to the altitudes at which they are seen tangentially. These dip diagrams show that the inferior mirage greatly magnifies the apparent angular size of the lowest few centimeters of atmosphere. Conversely, inversion layers below eye level are compressed—even to zero apparent thickness, in ducts. The diagrams show that, even when distant objects are miraged, the ray crossings occur beyond the lowest point on each ray where the line of sight is tangent to a horizontal surface in the atmosphere. Therefore the apparent altitudes of these tangent points are a monotonic function of their actual heights in the atmosphere. This monotonicity explains an apparent paradox in low-Sun images.
1997
 Sunset science: 1. The mock mirage
Andrew T. Young, George W. Kattawar, and Pekka Parviainen
Applied Optics, Volume 36, Issue 12, p. 2689 April 1997 OSA Optics InfoBase
A previously unrecognized phenomenon, which we call the mock mirage, produces inverted images of the Sun and Moon near the horizon when the observer looks downward through a thermal inversion. No ducting is involved; the rays can be concave toward the Earth throughout their length, with a radius of curvature larger than the radius of the Earth. Quite mild inversions produce surprisingly large effects, which increase with the height of the observer. Although the phenomenon has frequently been photographed, published pictures have been misinterpreted. Finally, we distinguish between features that are due to waves on inversion layers and the larger features that are due to the inversions themselves.

Origin of Kern’s arc
Yoshihide Takano and Kuo-Nan Liou
Applied Optics, Volume 36, Issue 15, p. 3560 May 1997 OSA Optics InfoBase
With the aid of computer-simulated halo patterns, we show that Kern’s arc, as seen on the latitude of the circumzenithal arc and on the other side of the zenith, is produced by double-plate ice crystals with a vertical principal axis. Light rays that contribute to Kern’s arc are demonstrated by geometric ray tracing. We also discuss the condition under which an arc that is opposite a circumhorizontal arc can appear.
1996
Ray scattering by an arbitrarily oriented spheroid: 1. Diffraction and specular reflection
James A. Lock
Applied Optics, Vol. 35 Issue 3 Page 500 (January 1996) OSA Optics InfoBase
Diffraction and reflection of an arbitrarily polarized plane wave by an arbitrarily oriented spheroid in the short-wavelength limit are considered in the context of ray theory. A closed-form solution for both diffraction and reflection is obtained, and the polarization character of the diffracted plus reflected electric field is obtained. It is found that the magnitude of the reflected electric field is multivalued for forward scattering. This is interpreted in terms of the variation of the spheroid’s Gaussian curvature at the points where grazing ray incidence occurs.

Ray scattering by an arbitrarily oriented spheroid. 2. Transmission and cross-polarization effects
James A. Lock
Applied Optics, Vol. 35 Issue 3 Page 515 (January 1996) OSA Optics InfoBase
Transmission of an arbitrarily polarized plane wave by an arbitrarily oriented spheroid in the short-wavelength limit is considered in the context of ray theory. The transmitted electric field is added to the diffracted plus reflected ray-theory electric field that was previously derived to obtain an approximation to the far-zone scattered intensity in the forward hemisphere. Two different types of cross-polarization effects are found. These are (a) a rotation of the polarization state of the transmitted rays from when they are referenced with respect to their entrance into the spheroid to when they are referenced with respect to their exit from it and (b) a rotation of the polarization state of the transmitted rays when they are referenced with respect to the polarization state of the diffracted plus reflected rays.

Elliptical halos, Bottlinger's rings, and the ice-plate snow-star transition
Eberhard Tränkle, Marko Riikonen
Applied Optics, Volume 35, Issue 24, p. 4871-4878, August 1996 OSA Optics InfoBase
Elliptical halos and Bottlinger's rings are simulated by the use of a Monte Carlo algorithm that includes multiple scattering. High multiple reflections are required to obtain a sufficient brightness of the elliptical halos. By introducing three populations of nearly horizontal, gyrating, and swinging crystals, we obtain good agreement for four photographs of displays with ringlike and disklike structures. Through model experiments on the aerodynamical behavior of crystals, we find a new interpretation of the three populations. In this view elliptical halos and Bottlinger's rings occur in the transition region of ice plates with broad branches and stellar crystals at temperatures near 15 C and large supersaturations. This interpretation is supported by a review of 23 reports of elliptical halo phenomena by members of the Finnish Halo Observers Network.
1994
Feature issue: Applied Optics, July 1994

Light and color in the open air -- introduction by the feature editors
James A. Lock, Craig F. Bohren
Applied Optics, Vol. 33 Issue 21 Page 4535 (July 1994) OSA Optics InfoBase
The natural environment is still rich in new observable phenomena despite centuries of scientific observation. Reflecting this fact, the papers in this feature issue of Applied Optics report the observation and analysis of both new and well-known naked-eye optical phenomena.

Observations of vertically elliptical halos
Marko Riikonen, Jukka Ruoskanen
Applied Optics, Vol. 33 Issue 21 Page 4537 (July 1994) OSA Optics InfoBase
The Finnish Amateur Astronomers' Network, working under the Ursa Astronomical Association, has photographed several vertically elliptical halo displays. Four of these observations with photographs are presented.

The sylvanshine: retroreflection from dew-covered trees
Alistair B. Fraser
Applied Optics, Vol. 33 Issue 21 Page 4539 (July 1994) OSA Optics InfoBase
Some dew-covered plants are strongly retroreflective. The bright glow seen when the antisolar point falls on grass is known as the heiligenschein. Its widely accepted explanation requires that the grass be covered with hair. The discovery of the sylvanshine, a closely related phenomenon best seen at night, revealed that strong retroreflection can occur on hairless dew-covered plants. A simple model shows that below a contact angle of 90°, the enhancement in the backscatter direction is virtually identical to that given by a diffusely reflecting surface, but as the contact angle climbs to 140°, enhancement increases by 2 orders of magnitude. Plants that exhibit such large contact angles are not the norm, but can be found chiefly among coniferous trees, a few of which display the sylvanshine with great brilliance.

Vertical elliptical coronas caused by pollen
Pekka Parviainen, Craig F. Bohren, Veikko Makela
Applied Optics, Vol. 33 Issue 21 Page 4548 (July 1994) OSA Optics InfoBase
Near-forward scattering by cloud droplets is known to give rise to colored rings, centered on the Sun or the Moon, which are called the corona. Because of the spherical shape of the droplets, the corona can be circular. A Finnish amateur astronomers' network has found a corona, in a seemingly cloudless sky, with a regular vertically elliptical shape. The aspect ratio of these ellipses changes with the altitude of the Sun or the Moon. Some brightening in the coronas has also been reported. Because of observations of high pollen concentrations at the time of occurrence of these coronas, we propose that some coronas can be explained as a result of scatteringbybirch pollen grains, which are more or less spheroidal. To explain other observed coronas, pollen grains with more complicated shapes, such as pine and spruce pollen grains, must be invoked. Our analysis is limited to spheroidal grains, for which the Fraunhofer theory gives analytical expressions of simple form. The more complicated shapes require numerical simulations or laboratory experiments, which we have not done.

Simulation and analysis of pollen coronas
Eberhard Trankle, Bernd Mielke
Applied Optics, Vol. 33 Issue 21 Page 4552 (July 1994) OSA Optics InfoBase
By numerical simulation of light scattering by birch and pine pollen grains, we create color plates of coronas with vertical elliptical shapes and strong brightenings, respectively. The shape of the pollen is modeled by the union of n ellipsoids. The Fraunhofer integral is solved by the use of the fast Hartley transform. The sensitivity of the patterns to pollen orientation, Sun elevation, and pollen shape and size is discussed. Good agreement is obtained with amazing photographs made by a Finnish network of amateur astonomers, in the case of strong vertical orientation of the pollen axis.

Supernumerary ice-crystal halos? Free download
Michael V. Berry
Applied Optics, Vol. 33 Issue 21 Page 4563 (July 1994) OSA Optics InfoBase
Geometric-optics singularities in the intensity profiles of refraction halos formed by randomly oriented ice crystals are softened by diffraction and decorated with fine supernumerary fringes. If the crystals have a fixed symmetry axis (as in parhelia), the geometric singularity is a square-root divergence, as in the rainbow. However, the universal curve that describes diffraction is different from the rainbow's Airy function, with weak maxima (supernumerary fringes) on the geometrically dark region inside the halo (and even fainter fringes outside); these are much smaller than their counterparts on the light side of rainbows. If the crystals have no preferred orientation (as in the 22° halo), the geometric singularity is a step. In this case the universal diffraction function has no maxima, and its supernumeraries are shoulders rather than maxima. The low contrast of the fringes is probably the main reason why supernumerary halos are rarely if ever seen.

Halo polarization profiles and the interfacial angles of ice crystals Free download
G. P. Konnen, Sara H. Muller, J. Tinbergen
Applied Optics, Vol. 33 Issue 21 Page 4569 (July 1994) OSA Optics InfoBase
Polarization and radiance of various types of refraction halo in ice-crystal swarms that extend to ground level were measured as a function of scattering angle. Simultaneously, samples of the crystals that produce these halos were collected and replicated. The halo polarization peaks are wider than the Fraunhofer theory of diffraction predicts for the observed size distribution of the replicated crystals. The explanation we put forward is that the angles between crystal prism faces are not always exact integer multiples of 60°, and the basal faces are not always exactly parallel, as is usually assumed. The collected crystals confirm this. The widths of the halo polarization peaks can be explained if the distributions of the interfacial angles around their means reach their half-maximum values at a deviation of 0.49° ± 0.05°. This corresponds to a deviation of 0.35° ± 0.03° of the face normals from their crystallographic positions. The presence of variation in interfacial angles in low-level halos seems to arise from the fact that the crystals are growing. Some hitherto unexplained features in halo displays can be understood by considering variations in the interfacial angles.

Subsuns, Bottlinger's rings, and elliptical halos Free download
David K. Lynch, Stanley D. Gedzelman, Alistair B. Fraser
Applied Optics, Vol. 33 Issue 21 Page 4580 (July 1994) OSA Optics InfoBase
Subsuns, Bottlinger's rings, and elliptical halos are simulated by the use of a Monte Carlo model; reflection of sunlight from almost horizontal ice crystals is assumed. Subsuns are circular or elliptical spots seen at the specular reflection point when one flies over cirrus or cirrostratus clouds. Bottlinger's rings are rare, almost elliptical rings centered about the subsun. Elliptical halos are small rings of light centered around the Sun or the Moon that rarely occur with other halo phenomena. Subsuns and Bottlinger's rings can be explained by reflection from a single crystal, whereas elliptical halos require reflection from two separate crystals. All three phenomena are colorless and vertically elongated with an eccentricity that increases with increasing solar zenith angle. For several cases of Bottlinger's rings the simulations are compared with density scans of photographs. Clouds that consist of large swinging or gyrating plates and dendritic crystals, which form near -15 °C, seem the most likely candidates to produce the rings and elliptical halos. Meteorological evidence is presented that supports these conditions for elliptical halos. Simulations suggest that the most distinct elliptical halos may be produced by hybrid clouds that contain both horizontal and gyrating crystals.

Effects of ice-crystal structure on halo formation: cirrus cloud experimental and ray-tracing modeling studies
Kenneth Sassen, Nancy C. Knight, Yoshihide Takano, Andrew J. Heymsfield
Applied Optics, Vol. 33 Issue 21 Page 4590 (July 1994) OSA Optics InfoBase
During the 1986 Project FIRE (First International Satellite Cloud Climatology Project Regional Experiment) field campaign, four 220 halo-producing cirrus clouds were studied jointly from a groundbased polarization lidar and an instrumented aircraft. The lidar data show the vertical cloud structure and the relative position of the aircraft, which collected a total of 84 slides by impaction, preserving the ice crystals for later microscopic examination. Although many particles were too fragile to survive impaction intact, a large fraction of the identifiable crystals were columns and radial bullet rosettes, with both displaying internal cavitations, and radial plate-column combinations. Particles that were solid or displayed only a slight amount of internal structure were relatively rare, which shows that the usual model postulated by halo theorists, i.e., the randomly oriented, solid hexagonal crystal, is inappropriate for typical cirrus clouds. With the aid of new ray-tracing simulations for hexagonal hollow-ended column and bullet-rosette models, we evaluate the effects of more realistic ice-crystal structures on halo formation and lidar depolarization and consider why the common halo is not more common in cirrus clouds.

Volcanic Bishop's ring: evidence for a sulfuric acid tetrahydrate particle aureole
Kenneth Sassen, Thomas Peter, Beiping P. Luo, Paul J. Crutzen
Applied Optics, Vol. 33 Issue 21 Page 4602 (July 1994) OSA Optics InfoBase
Following the massive 1883 Krakatoa volcanic eruption, a new atmospheric optical phenomeon was identified by Rev. S. E. Bishop. This inconspicuous one-ringed corona, or aureole, was immediately linked to the global spread of volcanic debris injected into the stratosphere, but little refinement in the mechanisms responsible for Bishop's ring has since been made. On the basis of our combined studies of sulfuric acid droplet-freezing theory and polarization (0.694 μm) lidar measurements of Bishop's ring aerosols from the June 1991 Mt. Pinatubo eruption that show average linear depolarization ratios of 0.05, it appears that this solar diffraction phenomenon is caused by accumulations of nonspherical sulfuric acid tetrahydrate (SAT) particles. The diffraction-theory aureole-derived SAT particle radius of about 0.8 μm is consistent with the freezing of the large mode of volcanic acid droplets created by coagulation, which, according to theory, is necessary for concentrating a sufficient insoluble mass to promote heterogeneous drop freezing at temperatures below approximately -65 °C.

Simulating rainbows and halos in color
Stanley David Gedzelman
Applied Optics, Vol. 33 Issue 21 Page 4607 (July 1994) OSA Optics InfoBase
Geometric optics rainbows and ice-crystal halos that include some effects of a Rayleigh-scattering atmosphere and a cloud of finite optical thickness are simulated in color by the use of a Monte Carlo approach.

Influence of a solar eclipse on twilight
Edward H. Geyer, M. Hoffmann, H. Volland
Applied Optics, Vol. 33 Issue 21 Page 4614 (July 1994) OSA Optics InfoBase
The morning twilight of the pre-sunrise sky was measured at the Hoher-List Observatory during the total eclipse of 22 July 1990. The location of observation was far away from the central eclipse zone. The luminance showed a deep minimum in twilight during the main phase of the solar eclipse compared with normal conditions. A first order scattering model explains the observations reasonably well and shows that the sky radiation during the first phase of twilight at a location far away from the central umbra depends primarily on the height profile of the air pressure between 100 and 200 km.

Horizon brightness revisited: measurements and a model of clear-sky radiances Free download
Raymond L. Lee, Jr.
Applied Optics, Vol. 33 Issue 21 Page 4620 (July 1994) OSA Optics InfoBase
Clear daytime skies persistently display a subtle local maximum of radiance near the astronomical horizon. Spectroradiometry and digital image analysis confirm this maximum's reality, and they show that its angular width and elevation vary with solar elevation, azimuth relative to the Sun, and aerosol optical depth. Many existing models of atmospheric scattering do not generate this near-horizon radiance maximum, but a simple second-order scattering model does, and it reproduces many of the maximum's details.

Twilight and daytime colors of the clear sky Free download
Raymond L. Lee, Jr.
Applied Optics, Vol. 33 Issue 21 Page 4629 (July 1994) OSA Optics InfoBase
Digital image analysis of the cloudless sky's daytime and twilight chromaticities challenges some existing ideas about sky colors. First, although the observed colors of the clear daytime sky do lie near the blackbody locus, their meridional chromaticity curves may resemble it very little. Second, analyses of twilight colors show that their meridional chromaticity curves vary greatly, with some surprising consequences for their calorimetric gamuts.

Mirages with atmospheric gravity waves
Waldemar H. Lehn, Wayne K. Silvester, David M. Fraser
Applied Optics, Vol. 33 Issue 21 Page 4639 (July 1994) OSA Optics InfoBase
The temperature inversions that produce superior mirages are capable of supporting gravity (buoyancy) waves of very low frequency and long wavelength. This paper describes the optics of single mode gravity waves that propagate in a four-layer atmosphere. Images calculated by ray tracing show that (1) relatively short waves add a fine structure to the basic static mirage, and (2) long waves produce cyclic images, similar to those observed in the field, that display significant variation from a base image.

Moving through a mirage
Peter D. Sozou, George Loizou
Applied Optics, Vol. 33 Issue 21 Page 4644 (July 1994) OSA Optics InfoBase
We consider image motion in the visual field of an observer moving through a rigid environment under mirage conditions, in which light rays follow curved trajectories as a result of a non-uniform atmospheric refractive index. We show that, under these conditions, the translation motion field does not conform to the simple pattern observed in the absence of refraction; instead it depends on the transfer characteristic of the mirage. An interesting finding is that if the mirage has a transfer characteristic that folds, as occurs for example in the desert mirage, the motion field will, in general, be infinite at the fold point.

Glory of clouds in the near infrared
James D. Spinhirne, Teruyuki Nakajima
Applied Optics, Vol. 33 Issue 21 Page 4652 (July 1994) OSA Optics InfoBase
Spectrally resolved visible and infrared images of marine stratus clouds were acquired from the NASA ER-2 high-altitude aircraft during the 1987 First International Cloud Climatology Program Regional Experiment. The images were obtained by cross-track scanning radiometers. Data images at near-infrared wavelengths show frequent and readily apparent brightness features that are due to glory single scattering. The observations and subsequent analysis by radiative transfer calculations show that the glory is a significant feature of near-infrared solar reflectance from water clouds. Glory observations and calculations based on in-cloud microphysics measurements agree well. The most dramatic difference from the visible glory is that the scattering angles are significantly larger in the near infrared. The glory is also apparently more distinct in the near infrared than in the visible, as scattering size parameters are in a range that effectively produces a glory feature, and also there is less obscuration by multiple scattering reflectance because of absorption of radiation by droplets in the near infrared. For both the visible and the near infrared, the principal factors that wash out the glory are dispersion and, to a lesser degree, the effective radius of the cloud droplet-size distribution. The obscuration by multiple scattering in optically thick clouds is secondary. Rather than being a novelty, glory observations would be an accurate and unambiguous technique to sense the droplet size of water clouds remotely.

Correlated light scattering by a dense distribution of condensation droplets on a window pane
James A. Lock, Chin-Lien Chiu
Applied Optics, Vol. 33 Issue 21 Page 4663 (July 1994) OSA Optics InfoBase
An analytical model of the scattering structure factor for an assembly of non-interacting hard disks has recently appeared in the literature [Phys. Rev. A 42, 5978-5989 (1990)]. We employ this model to calculate correlated light scattering by monodispersions and binary mixtures of condensation droplets on a window pane. We find that an area fraction of f ≥ 0.6 is required for producing the near-forward direction scattering suppression and that a moderately wide polydispersion of droplet sizes is capable of producing the experimentally observed bright ring of colored light.

Rainbow-enhanced forward glory from fused-silica spheres
John J. D'Amico, Marcus D. Knudson, Dean S. Langley
Applied Optics, Vol. 33 Issue 21 Page 4672 (July 1994) OSA Optics InfoBase
A tertiary rainbow enhances the forward glory scattering from a fused-silica sphere because of its refractive index m 1.465. The scattered light contains a strong cross-polarized component and varies rapidly in brightness with changes in m. In experiments m is varied by the use of a range of argon and dye laser wavelengths. The forward cross-polarized scattering is found to be in agreement with Mie theory calculations. A reflective coating on small areas around the equator and polar caps of the sphere increases the forward scattering by a factor of 180.

Rainbow scattering by a coated sphere
James A. Lock, J. Michael Jamison, Chih-Yang Lin
Applied Optics, Vol. 33 Issue 21 Page 4677 (July 1994) OSA Optics InfoBase
We examine the behavior of the first-order rainbow for a coated sphere by using both ray theory and Aden-Kerker wave theory as the radius of the core α12 and the thickness of the coating δ are varied. As the ratio δ/α12 increases from 10-4 to 0.33, we find three classes of rainbow phenomena that cannot occur for a homogeneous-sphere rainbow. For δ/α12 < 10-3, the rainbow intensity is an oscillatory function of the coating thickness; for δ/α12 ≈ 10-2, the first-order rainbow breaks into a pair of twin rainbows; and for δ/α12 ≈ 0.33, various rainbow-extinction transitions occur. Each of these effects is analyzed, and their physical interpretations are given. A Debye series decomposition of coated-sphere partial-wave scattering amplitudes is also performed and aids in the analysis.

E6 diffraction catastrophe of the primary rainbow of oblate water drops: observations with white-light and laser illumination
Gregory Kaduchak, Philip L. Marston, Harry J. Simpson
Applied Optics, Vol. 33 Issue 21 Page 4691 (July 1994) OSA Optics InfoBase
Oblate drops of water illuminated perpendicular to their symmetry axis exhibit catastrophe patterns near the primary-rainbow scattering angle. Previous patterns include the hyperbolic umbilic focal section and separate lips events [see, e.g., H. J. Simpson and P. L. Marston, Appl. Opt. 30, 3468 (1991)]. The present observations concern a much higher-order singularity analyzed by J. F. Nye [Proc. R. Soc. London Ser. A 438, 397 (1992)], the E6 or symbolic umbilic, in the scattering by levitated drops with monochromatic and collimated white-light illumination. Photographs show the colors produced when the drop is illuminated by white light. The E6 occurs when the Gaussian curvature of the scattered wave front vanishes in both principal directions, resulting in a high degree of directional focusing. This type of focusing, although only slightly explored, is applicable to the more general problem of scattering from penetrable spheroids.

Hyperbolic umbilic and E6 diffraction catastrophes associated with the secondary rainbow of oblate water drops: observations with laser illumination
Gregory Kaduchak, Philip L. Marston
Applied Optics, Vol. 33 Issue 21 Page 4697 (July 1994) OSA Optics InfoBase
Previous observations of oblate drops of water illuminated perpendicular to their axis of symmetry exhibit catastrophe patterns near the primary-rainbow scattering angle [see, e.g., Appl. Opt. 30, 3468 (1991). The present research concerns observation of diffraction catastrophes near the secondary-rainbow scattering angle under similar experimental conditions. Illumination with laser light exhibits similar caustic structures in the secondary rainbow including the hyperbolic umbilic focal section and the E6 or symbolic umbilic focal section. The range of drop aspect ratios explored includes aspect ratios as small as those found for freely falling drops in air as well as highly flattened drops. The new features of the secondary rainbow occur for highly flattened drops.

Generalized rainbows and unfolded glories of oblate drops: organization for multiple internal reflections and extension of cusps into Alexander's dark band
Philip L. Marston, Gregory Kaduchak
Applied Optics, Vol. 33 Issue 21 Page 4702 (July 1994) OSA Optics InfoBase
Oblate drops of water can produce caustics where, unlike a simple Airy caustic, more than two rays merge. We extend previous treatments of generalized primary rainbows based on catastrophe optics [Opt. Lett. 10, 588 (1985); Proc. R. Soc. (London) A 438, 397 (1992)] to rays having (p - 1) = 2 to 5 internal reflections. The analysis is for a horizontally illuminated ellipsoid with a vertical symmetry axis. Aspect ratios causing a vanishing of the vertical curvature at the equator for the outgoing wave front are found from generalized ray tracing. In response to infinitesimal deformation, the axial caustic of real glory rays unfolds producing cusps. Laboratory observations with laser illumination demonstrate that cusps resulting from rays with five internal reflections extend into Alexander's dark band when the drop's aspect ratio is near 1.08. The evolution of this p = 6 scattering pattern as cusps meet the quinary rainbow is suggestive of an E6 catastrophe. For ellipsoids of varying aspect ratio and refractive index N, there is an organizing singularity associated with an exceptionally flat outgoing wave front from spheres with N = p.

Black-and-white fringes and the colors of caustics Free download
Michael V. Berry, A. N. Wilson
Applied Optics, Vol. 33 Issue 21 Page 4714 (July 1994) OSA Optics InfoBase
Fine-scale interference fringes that decorate caustics produced with white light appear black and white with high contrast. This is surprising, as the elementary expectation, supported by theory and computer simulation, is that the fringes should be highly colored. The fringe separation is several arc minutes and therefore close to the resolution limit of the eye. Under magnification (even of a photograph), the colors are revealed. Therefore black-and-white fringes are an illusion, giving a dramatic naked-eye illustration of the fact that the angular resolution of the visual system is better for luminance than for color.

Blue shadows: physical, physiological, and psychological causes
Michael E. Churma
Applied Optics, Vol. 33 Issue 21 Page 4719 (July 1994) OSA Optics InfoBase
The apparent blueness of outdoor shadows has two main causes: the illumination of the shadows by blue skylight and the enhancement of the perception of blue by simultaneous color contrast. Other physiological mechanisms, such as brightness contrast and afterimages, can also affect the perception of a shadow's blueness. Preferential scattering by the cornea does not seem to make a major contribution. Despite these effects, color constancy causes most people to observe an empirically blue shadow as colorless.

Mach bands and airplane shadows cast on dry terrain
J. T. Enright
Applied Optics, Vol. 33 Issue 21 Page 4723 (July 1994) OSA Optics InfoBase
Luminous rings are often seen surrounding the shadow of a high-flying airplane. Some of these phenomena are due to water droplets (glories, the Heiligenschein), but a different sort of explanation is required when a luminous ring (sometimes simply a bright spot) is seen while the plane is flying over dry terrain. Demonstrations involving distances and shadows manyfold smaller than those of an airliner's shadow show that Mach bands can produce illusory luminance phenomena that greatly resemble those associated with a plane's shadow over dry terrain. Luminance rings have recently also been observed over dry, sparsely vegetated terrain, around the shadow of an adjacent airplane (i.e., far from the observer's antisolar point), thereby excluding all previous alternative interpretations; Mach bands are thus a likely explanation for at least some instances of dry-terrain luminous rings around airplane shadows.

Colors of the spectrum: Do you wonder where the yellow went?
John N. Kidder
Applied Optics, Vol. 33 Issue 21 Page 4727 (July 1994) OSA Optics InfoBase
The spectrum of white light dispersed by a prism or grating often appears as just three main colored bands, red, green, and blue, with yellow barely discernible. When this spectrum is compared with the appearance of narrow wavelength bands seen in isolation, the lack of color is surprising. An explanation is offered based on two factors: (1) The yellow-appearing wavelengths of the spectrum comprise only 5% of the whole and have a luminance comparable with that of the adjacent red and green portions and (2) the response of double-opponent cells, observed in the primate visual cortex, could enhance the red and green and obscure the yellow in the spectral image.

Appearance of the Sun and the Moon seen through clouds
Jeffery R. Linskens, Craig F. Bohren
Applied Optics, Vol. 33 Issue 21 Page 4733 (July 1994) OSA Optics InfoBase
If the Sun can be seen at all through thin clouds it usually has a sharp edge, although occasionally it appears fuzzy, especially through altostratus, but rarely, if ever, through fog. Experiments with suspensions of polystyrene spheres of different sizes and optical thicknesses suggest that the range of cloud optical thicknesses over which a fuzzy Sun is seen increases with particle size. Nonsphericity, turbulence, and cloud horizontal inhomogeneity are not necessary for fuzziness. A possible explanation for what is observed is that, for a given optical thickness, the modulation contrast function of a cloud decreases more rapidly with increasing frequency the greater the particle size. Consequently the transition from optical thicknesses for which contrast is above the contrast threshold at all spatial frequencies to optical thicknesses for which contrast is below the threshold at high frequencies is sufficiently gradual to permit fuzziness of the Sun to be observed through clouds of constantly changing optical thickness.

Color recognition and discrimination under full-moon light
George Smith, Algis J. Vingrys, Jennifer D. Maddocks, Christopher P. Hely
Applied Optics, Vol. 33 Issue 21 Page 4741 (July 1994) OSA Optics InfoBase
The ability to recognize and discriminate colors under full-moon light was measured. Color naming was performed at three sizes (0.5°, 20° and 40°) by the use of one white and six colored chips that spanned the spectrum at two levels of saturation. The results show that correct color recognition is possible under full-moon light. However, the recognition rate depends on a complex interaction between hue, level of saturation, and size of test field. For small fields and desaturated colors, the recognition rate is low. However, for saturated colors, most hues can be recognized at better than chance levels, with red being recognized very accurately.

Intraocular light scattering in vision, artistic painting and photography
Claes Beckman, Olle Nilsson, Lars-Erik Paulsson
Applied Optics, Vol. 33 Issue 21 Page 4749 (July 1994) OSA Optics InfoBase
Light scattering in the eye is reviewed, and its influence on vision is discussed in some detail. Isotropic scattering and formation of halos around point sources are described with reference to theory and experiments. Artists usually take intraocularly scattered light into account when painting natural scenes. A method to achieve similar effects in photography by the use of diffraction filters in front of the camera lens is demonstrated. A number of photos that illustrate the effects of such filters are shown.

Disputing Viking navigation by polarized skylight
Curt Roslund
Applied Optics, Vol. 33 Issue 21 Page 4754 (July 1994) OSA Optics InfoBase
The widely held notion that the Vikings utilized polarization of skylight on overcast days for navigational purposes is demonstrated to have no scientific basis. The use of polarized skylight for navigation under partly cloud-free skies should be treated with caution and skepticism.

Possible halo depictions in the prehistoric rock art of Utah
Kenneth Sassen
Applied Optics, Vol. 33 Issue 21 Page 4756 (July 1994) OSA Optics InfoBase
In western American rock art the concentric circle symbol, which is widely regarded as a sun symbol, is ubiquitous. We provide evidence from Archaic and Fremont Indian rock art sites in northwestern Utah that at least one depiction was motivated by an observation of a complex halo display. Cirrus cloud optical displays are linked in both folklore and meteorology to precipitation-producing weather situations, which, in combination with an abundance of weather-related rock art symbolism, indicate that such images reflected the ceremonial concerns of the indigenous cultures for ensuring adequate precipitation. As has been shown to be the case with rock art rainbows, conventionalization of the halo image may have resulted in simple patterns that lacked recognizable details of atmospheric optical phenomena. However, in one case in which an Archaic-style petroglyph (probably 1500 yr or more old) satisfactorily reproduced a complicated halo display that contained parhelia and tangent arcs, sufficient geometric information is rendered to indicate a solar elevation angle of 40° at the time of observation.

Variability in atmospheric light-scattering properties with altitude
Frank W. Gibson
Applied Optics, Vol. 33 Issue 21 Page 4919 (July 1994) OSA Optics InfoBase
The altitudinal variability in angular scattering properties of the troposphere and stratosphere was measured with a balloonborne polar nephelometer. An analysis of interdependent experimental parameters provides information on the scattering phase function and inferred size distribution of aerosol particles as a function of altitude. These aerosol characteristics are extractable from the scattering dissymmetry index and its relationship to spectral dispersion in turbidity and the aerosol phase function. The problem of the correlation between backscatter and extinction is addressed from the perspectives of in situ observations.

Color Plates (strangely in black & white)
Applied Optics, Vol. 33 Issue 21 Page 4953 (July 1994) OSA Optics InfoBase

1993
 Scattering of light by polyhedral ice crystals
Andreas Macke
Applied Optics, Vol. 32 Issue 15 Page 2780 (May 1993) OSA Optics InfoBase
The single-scattering phase functions of polyhedral-shaped ice particles are calculated by means of geometric optics and the diffraction theory. Particle orientation is assumed to be random in space. Particle shapes are taken both from ice-crystal classifications and from in situ measurements. The effects of particle concavity on the scattering signature are discussed in detail. A common feature is the pronounced forward-scattering peak, as well as different halo peaks that are due to a minimum deviation at corresponding ice prisms. An unusual halo phenomena, which results from a minimum deviation in a double-prism configuration, is found and verified. The comparison of different particle types shows that backscattering is a sensitive indicator for the identification of types of ice-crystal. Aggregate particles, like bullet rosettes, basically show the scattering characteristics of their individual components.
1992
 Simulation of mirages
W. H. Lehn and W. Friesen
Applied Optics, Vol. 31 Issue 9 Page 1267 (March 1992) OSA Optics InfoBase
A mirage is seen when atmospheric refraction distorts or displaces an image. We describe a mirage simulator that uses digital imaging equipment to generate mirage images from normal photographs. The I simulation program relocates horizontal image lines into positions that they appear to occupy, according to rays traced from observer to object. Image-brightness adjustments are not required; we show that, while the atmosphere can change the size or shape of an object, it does not change its apparent brightness. The realistic quality of the computed images makes this simulator a useful tool in mirage analysis.

Assessing the contributions of surface waves and complex rays to far-field Mie scattering by use of the Debye series
Edward A. Hovenac and James A. Lock
J. Opt. Soc. Am. A, Vol. 9, No. 5, p. 781 May 1992 OSA Optics InfoBase
The contributions of complex rays and the secondary radiation shed by surface waves to scattering by a dielectric sphere are calculated in the context of the Debye-series expansion of the Mie scattering amplitudes. Also, the contributions of geometrical rays are reviewed and compared with those of the Debye series. Interference effects among surface waves, complex rays, and geometrical rays are calculated, and the possibility of observing these interference effects is discussed. Experimental data supporting the observation of a surface-wave geometrical-ray-interference pattern are presented.
1991
 Rainbows: Mie computations and the Airy approximation
Ru T. Wang and H. C. van de Hulst
Applied Optics Vol. 30, 1, p. 106 1 January 1991 OSA Optics InfoBase
Efficient and accurate computation of the scattered intensity pattern by the Mie formulas is now feasible for size parameters up to x = 50,000 at least, which in visual light means spherical drops with diameters up to 6 mm. We present a method for evaluating the Mie coefficients from the ratios between Riccati-Bessel and Neumann functions of successive order. We probe the applicability of the Airy approximation, which we generalize to rainbows of arbitrary p (number of internal reflections = p - 1), by comparing the Mie and Airy intensity patterns. Millimeter size water drops show a match in all details, including the position and intensity of the supernumerary maxima and the polarization. A fairly good match is still seen for drops of 0.1 mm. A small spread in sizes helps to smooth out irrelevant detail. The dark band between the rainbows is used to test more subtle features. We conclude that this band contains not only externally reflected light (p = 0) but also a sizable contribution from the p = 6 and p = 7 rainbows, which shift rapidly with wavelength. The higher the refractive index, the closer both theories agree on the first primary rainbow (p = 2) peak for drop diameters as small as 0.02 mm. This may be useful in supporting experimental work.

Feature issue: Applied Optics, August 1991

Light and color in the open air: introduction by the feature editor
Applied Optics, Vol. 30 Issue 24 Page 3381 (August 1991) OSA Optics InfoBase
James A. Lock

Polarimetry of a 22° halo Free download
G. P. Können, J. Tinbergen
Applied Optics, Vol. 30 Issue 24 Page 3382 (August 1991) OSA Optics InfoBase
The linear polarization and intensity of a 22° halo has been measured simultaneously at seven wavelengths as a function of scattering angle. The polarization pattern is found to be dominated by a narrow peak centered at the halo angle. The amount of polarization in this peak is much higher than expected from Fresnel refraction alone. The observations are explained with a birefringence-diffraction halo polarization model. The effective diameter of the hexagonal face of the halo-generating crystals is found to be 41 and 54 μm for two separate scans. An independent single-wavelength parhelion observation indicates a stronger birefringence peak concentrated in an even smaller angular scattering range and a crystal diameter of 220 μm. Crystal sizes derived from the halo intensity distributions are found to be consistent with those obtained from polarization. The data demonstrate the power of halo polarimetry as a tool for detection and identification of birefringent crystals in terrestrial or extraterrestrial atmospheres.

What are “all the colors of the rainbow”? Free download
Raymond L. Lee, Jr.
Applied Optics, Vol. 30 Issue 24 Page 3401 (August 1991) OSA Optics InfoBase
Both folklore and theory imply that naturally occurring rainbows display a wide range of nearly pure colors. However, digital image analysis of color slides shows that the natural rainbow's colors are not especially pure and that the bow's background causes much of this desaturation.

Mie theory model of the corona
James A. Lock, Leiming Yang
Applied Optics, Vol. 30 Issue 24 Page 3408 (August 1991) OSA Optics InfoBase
We performed a calculation of the corona colors that employed Mie theory to obtain the scattered light intensity. The scattered intensity was integrated over the visible spectrum for a number of different cloud droplet size distributions. The results were converted to chromaticity coordinates, convolved with the angular size of the sun, and plotted on the 1931 CIE chromaticity diagram. The results were compared to observations of multiple-ring coronas. It was found that, when using Mie theory to estimate cloud droplet sizes, water droplets with diameters in the 7 μm < D < 15 μm range produced the 13 multiple-ring coronas that were observed.

Rainbows and fogbows Free download
David K. Lynch, Ptolemy Schwartz
Applied Optics, Vol. 30 Issue 24 Page 3415 (August 1991) OSA Optics InfoBase
The optics of rainbows and fogbows is investigated theoretically for monodisperse drops using Mie theory. Included in the calculations are a realistic solar illumination spectrum and the finite size of the sun. Drop sizes range from 3 to 300 μm (3800 > X > 38). Results are presented on the location, width, contrast, polarization, and color of both primary and secondary rainbows. Particular attention is given to rainbows formed in small drops (fogbows).

Corona-producing cirrus cloud properties derived from polarization lidar and photographic analyses
Kenneth Sassen
Applied Optics, Vol. 30 Issue 24 Page 3421 (August 1991) OSA Optics InfoBase
Polarization lidar data are used to demonstrate that clouds composed of hexagonal ice crystals can generate multiple-ringed colored coronas. Although relatively uncommon in our mid-latitude cirrus sample (derived from Project FIRE extended time observations), the coronas are associated with unusual cloud conditions that appear to be effective in generating the displays. Invariably, the cirrus cloud tops are located at or slightly above elevated tropopauses (12.7-km MSL average height) at temperatures between -60° and -701C. The cloud top region also generates relatively strong laser backscattering and unusually high 0.5-0.7 linear depolarization ratios. Color photograph analysis of corona ring angles indicates crystals with mean diameters of from 12 to 30 μm. The cirrus cloud types were mainly subvisual to thin (i.e., bluish-colored) cirrostratus, but also included fibrous cirrus. Estimated cloud optical thicknesses at the 0.694 μm laser wavelength ranged from 0.001 to 0.2, where the upper limit reflects the effects of multiple scattering and/or unfavorable changes in particle characteristics in deep cirrus clouds.

Unfolded optical glory of spheriods: backscattering of laser light from freely rising spheriodal air bubbles in water
W. Patrick Arnott, Philip L. Marston
Applied Optics, Vol. 30 Issue 24 Page 3429 (August 1991) OSA Optics InfoBase
Enhancement in backscattering known as glory scattering results from geometric and material properties of spherically symmetric scatterers. The wave-front shape near the spherical scatterer is locally a circular torus. Radiation from a toroidal wave front is axially focused on the backward-directed axis. It is shown that the axial point caustic unfolds to an astroid caustic as the scatterer's shape changes from spherical to slightly spheroidal. The wave front pertinent for slightly spheroidal scatterers was modeled as a toroidal wave front with a superimposed harmonic angular perturbation. Experimental observations are displayed for crosspolarized backscattering by freely vertical rising, slightly oblate spheroidal air bubbles in water illuminated by a horizontally propagating laser beam. These patterns were recorded with a camera for two different incident-beam polarization directions relative to the axis of rotational symmetry of the bubble. Angular scattering patterns were also computed using a perturbation analysis based on use of the harmonically perturbed toroidal wave front and physical optics. Bubble oblateness was estimated from features of the angular scattering pattern and from hydrodynamic relations.

Opening rate of the transverse cusp diffraction catastrophe in light scattered by oblate spheroidal drops
Cleon E. Dean, Philip L. Marston
Applied Optics, Vol. 30 Issue 24 Page 3443 (August 1991) OSA Optics InfoBase
Light scattered by an oblate drop of water has been observed to produce cusp caustics in the general vicinity of the rainbow region [P. L. Marston and E. H. Trinh, Nature London 312, 529-531 (1984)]. The principal curvatures of the generic local wave front that produces the far-field transverse cusp are examined. This wave front is shown to generate a transverse cusp curve (U - Uc)3 = - d∞ V2, where U and V are horizontal and vertical scattering angles and Uc is the cusp point direction. The far-field opening rate d∞ is calculated for the transverse cusp. It is shown that d∞ has a simple dependence on the parameters of the generic wave front. We define the aspect ratio of the drop q = D/H, where H is the height and D is the equatorial width for the scattering drop. The method of generalized ray tracing is used to relate q to principal curvatures and shape parameters of the outgoing wave front and hence to d∞. Measurements of d∞ for scattering laser light from acoustically levitated drops appear to support the calculation. As q goes to q4 ≈ 1.31, the critical value for generation of a hyperbolic-umbilic focal section, the predicted d∞ goes to infinity. The nature of the divergence was numerically investigated as was the rate at which d∞ vanishes as q approaches critical values for lips and transition events.

Forward glory scattering from bubbles
Dean S. Langley, Philip L. Marston
Applied Optics, Vol. 30 Issue 24 Page 3452 (August 1991) OSA Optics InfoBase
The scattering enhancement known as the glory was observed in forward scattering from bubbles in liquids. A physical-optics model of the forward glory is detailed, based on transmitted waves reflected within the bubble. Some aspects of the model are compared with the Mie theory and with features in the cross-polarized light from single bubbles. Clouds of small bubbles rising in water show an angular structure in the forward glory light that is useful for estimating the bubble size.

Rainbow-enhanced forward and backward glory scattering
Dean S. Langley, Michael J. Morrell
Applied Optics, Vol. 30 Issue 24 Page 3459 (August 1991) OSA Optics InfoBase
When the refractive index m of a sphere is such that rainbows occur in the forward or backward direction, the glory scattering becomes exceptionally strong. A number of these refractive-index values have been determined from the geometry of ray paths. A physical-optics model of the scattering leads to an a2x4/3 dependence in the scattered irradiance, where a is the radius of the sphere, and x = ka is the size parameter. Normal glory scattering gives an irradiance proportional to x. Mie theory computations illustrate the presence of rainbow glories at predicted m values and the x4/3 irradiance factor. As in normal glory scattering, the rainbow-enhanced glory light contains a strong cross-polarized component. Experiments using single glass spheres immersed in liquids show the predicted cross-polarized scattering with a sensitive dependence on m.

Scattering of white light from levitated oblate water drops near rainbows and other diffraction catastrophes
Harry J. Simpson, Philip L. Marston
Applied Optics, Vol. 30 Issue 24 Page 3468 (August 1991) OSA Optics InfoBase
Oblate drops of water illuminated perpendicular to their symmetry axis generate a hyperbolic-umbilic diffraction catastrophe near the primary rainbow [P. L. Marston and E. H. Trinh, Nature London 312, 529- 531 (1984)]. Observations were made of this diffraction catastrophe generated by white-light illumination of acoustically levitated drops of water in air. The observations suggest what generalized rainbows would look like if they were produced in nature when sunlight illuminates large raindrops. Unlike the usual rainbow arc, the transverse cusp of the unfolded catastrophe is not distinctly colored. The hyperbolic-umbilic focal section is distinctly colored as is another diffraction catastrophe generated in the rainbow region when the drop is highly oblate.

On the gamut of colors seen through birefringent airplane windows
Craig F. Bohren
Applied Optics, Vol. 30 Issue 24 Page 3474 (August 1991) OSA Optics InfoBase
Colors in birefringent airplane windows seen through polarizing filters are not especially pure nor are all colors equally probable. This is a consequence of the shape of transmission vs wavelength for a retarder-polarizer combination illuminated by partially polarized skylight. Although transmission can have a single peak in the blue or green, a peak in the red is accompanied by one in the blue. This and the general blueness of skylight are why the purest colors seen in airplane windows are greens, yellowish-greens, and purples (mixtures of red and blue). Purer colors and a wider gamut are obtained for birefringent sheets interposed between dichroic polarizing filters and illuminated by tungsten light.

Colors observed when sunlight is scattered by bubble clouds in seawater
Philip L. Marston
Applied Optics, Vol. 30 Issue 24 Page 3479 (August 1991) OSA Optics InfoBase
Colored bands photographed in sunlit subsurface bubble clouds are described. The colors are found to be associated with the transition from partial-to-total reflection by the bubbles. The most pronounced band is a red-yellow band located near the transition region. Theoretical evidence is also summarized that the colored bands observed are only weakly affected by thin coatings and the oblate shape of freely rising bubbles.

Investigation into the scattering of light by human hair
Helen K. Bustard, Robin W. Smith
Applied Optics, Vol. 30 Issue 24 Page 3485 (August 1991) OSA Optics InfoBase
We describe a general investigation into the scattering of light by human hair. The main features of the intensity distribution produced by light scattered by an individual hair are identified. Qualitative explanations for the features are advanced in terms of the arrangement of the outer structure of the hair and its level of pigmentation. Contrast gloss values are calculated in an attempt to quantify the appearance of hair. These values are found to depend not only on the properties of hair, such as color and condition, but also on the direction and polarization state of the incident light. In assessing the effects of cosmetic treatments on hair, gloss values are shown to be useful where readings from treated hairs are compared with those from a control sample investigated in the same conditions.

Light and color on the wing: structural colors in butterflies and moths
Helen Ghiradella
Applied Optics, Vol. 30 Issue 24 Page 3492 (August 1991) OSA Optics InfoBase
All butterfly and moth scales share the same basic architecture, but various elements of this architecture are particularly complex in those scales that exhibit structural colors. These elements include the scales' ridges and their associated lamellae and microribs, and the trabeculae, the pillars normally that act as spacers within scales. The additional ornamentation produces thin film, Tyndall blue or diffraction colors and represents a particularly striking example of precision in biological pattern formation.

Can normal outdoor activities be carried out during civil twilight?
Herschel W. Leibowitz, D. A. Owens
Applied Optics, Vol. 30 Issue 24 Page 3501 (August 1991) OSA Optics InfoBase
Ambient illumination during civil twilight, which occurs approximately a half hour before sunrise and after sunset, has traditionally been characterized as posing no restriction on normal visual activities. However, consideration of the selective degradation of visual-recognition functions and the concurrent sparing of visual-guidance functions at the prevailing (relevant) luminance levels suggests that this characterization of civil twilight is no longer appropriate, particularly in light of the visual demands of industrialized society. Rather, special notice should be taken of the implications of selective degradation of visual recognition during civil twilight for traffic safety and other visually demanding hazardous tasks.

Toying with the moon illusion
G. R. Lockhead, Myron L. Wolbarsht
Applied Optics, Vol. 30 Issue 24 Page 3504 (August 1991) OSA Optics InfoBase
We propose that the correct interpretation of the moon illusion is that the zenith moon appears small, not that the horizon moon appears large. This illusion is caused by the visual gap between the observer and the overhead moon. Because of the gap, the observer has no or little optical information about the distance of the moon. This results in empty field myopia where the moon is neurally, although not necessarily cognitively, processed as being at about arm's length. When the moon is seen on the horizon, there usually is optical information about distance. That results in reduced accommodation, and so the moon is processed as at a greater distance. Consistent with the size-distance-invariance hypothesis, the moon is then judged as large. This is a specific example of the more general fact that all distant objects appear small in the absence of a stimulus for accommodation to be distant. This outcome produces the toy illusion.

Step brightness changes of distant mountain ridges and their perception Free download
David K. Lynch
Applied Optics, Vol. 30 Issue 24 Page 3508 (August 1991) OSA Optics InfoBase
When successive ridges of distant mountains are seen, observers often report that, near the ridge where the brightness changes abruptly, the upper part of the nearer ridge appears darker than at its lower portions. Similarly, they report that the base of the more distant mountain seems brighter adjacent to the nearer ridge than on its upper portions. The explanation of this phenomenon, known as the step contrast effect, is a special case of Mach bands. It is usually attributed to a visual illusion involving lateral inhibition in the eye, which is most apparent in the vicinity of step brightness changes. Using analytic techniques and numerical integrations to simulate the airlight-induced brightness distributions of such scenes, we show that in many cases the perceived brightness distribution is qualitatively similar to the true brightness distribution and thus is not a visual illusion.

Atmospheric optics in art
Stanley David Gedzelman
Applied Optics, Vol. 30 Issue 24 Page 3514 (August 1991) OSA Optics InfoBase
A brief historical overview of the atmospheric optical phenomena that appear in works of fine art is presented. It is shown that artists have recorded many features of the color and brightness of the sky and clouds, aerial perspective and visibility effects, and phenomena, including crepuscular rays, rainbows, halos, and coronas. Artistic biases resulting from prevailing styles and societal influences are noted. Attention is drawn to a number of phenomena recorded by artists that have not yet been explained or modeled.

Rainbows in the Indian rock art of desert western America
Kenneth Sassen
Applied Optics, Vol. 30 Issue 24 Page 3523 (August 1991) OSA Optics InfoBase
For thousands of years the image of the rainbow was pecked and painted by native Americans onto the rocks of the Great Basin and the Southwest. This long-lived tradition, which transcended major developments in lifestyles and cultures, underscores the important symbolic significance of the rainbow to the inhabitants of this arid region. The rainbow rock art depictions were usually associated with humanlike ceremonial figures, snakes, clouds, rain, and lightning bolts, suggesting that the rainbow symbol was employed as part of an elaborate sacred tradition. Although such ceremonial usage of the rainbow image tends to lead to abstraction and symbolic representation, there are examples, including a properly colorized rainbow painting from central Utah (approximately a thousand years old), that indicate observationally based rainbow reproductions of relatively great antiquity.

Ulloa's observations of the glory, fogbow, and an unidentified phenomenon Free download
David K. Lynch, Susan N. Futterman
Applied Optics, Vol. 30 Issue 24 Page 3538 (August 1991) OSA Optics InfoBase
Ulloa's complete print of the glories and fogbows on Mt. Pambamarca in Peru (now Ecuador) is presented. It shows two other phenomena, an erupting volcano and an as yet unidentified optical effect. The glories and fogbow are analyzed to obtain the drop size of the fog, and the unidentified features are discussed.

Finnish Halo Observing Network: search for rare halo phenomena
Marko Pekkola
Applied Optics, Vol. 30 Issue 24 Page 3542 (August 1991) OSA Optics InfoBase
The Finnish Halo Observing Network obtains information about rare halos through literature study and amateur network observations. Recent photographs and historical drawings of some yet unexplained halo effects are presented.

Glare points
H. C. van de Hulst, Ru T. Wang
Applied Optics, Vol. 30 Issue 33 Page 4755 (November 1991) OSA Optics InfoBase
Glare points are the intensity maxima seen when a water drop illuminated by a wide beam is viewed from a certain direction and imaged. We show that good resolution in both the scattering angle and the glare point position can be achieved only if the size parameter x = 2πa/λ is >> 1 and that the positions of the glare points can be computed by a Fourier transform from the familiar Lorenz-Mie scattering function. Sample computations made with x = 10,000 and x = 20,000 are presented. Glare points corresponding to rays that have suffered as many as 15 internal reflections can be identified, in agreement with experimental findings.
1990
Halo phenomena modified by multiple scattering
Yoshihide Takano and Kuo-Nan Liou
J. Opt. Soc. Am. A, Vol. 7, No. 5, p. 885 May 1990 OSA Optics InfoBase
Halo phenomena produced by horizontally oriented plate and column ice crystals are computed. Owing to the effect of multiple scattering, a number of optical features, in addition to the well-known halos and arcs caused by single scattering, can be produced in the sky. These include the 44° parhelion, the 66° parhelion, the anthelion, the uniform and white parhelic circle, and the uniform and white circumzenithal circle in the case of horizontally oriented plates. The anthelion is a result of double scattering that involves horizontally oriented columns that produce the Parry arc. The optical phenomena identified in the present study are compared with those of previous research and discussed. .

Green icebergs and remote sensing Free download
Raymond L. Lee, Jr.
J. Opt. Soc. Am. A, Vol. 7, No. 10, p. 1862 October 1990 OSA Optics InfoBase
The curious phenomenon of green icebergs has fascinated polar travelers for centuries. Although translucent green icebergs might be caused by colorants, a recently obtained sample of a green iceberg contained little inherently green material. This fact, combined with the blue-green absorption minimum of pure, homogeneous ice, suggests that a sufficient (rather than necessary) condition for green icebergs may be reddened sunlight illuminating intrinsically blue-green ice. Lacking in situ spectral reflectances of green icebergs, we develop two remote-sensing techniques to analyze their optical properties. Estimates of a green iceberg's reflectance spectra are derived from spectrodensitometry and from video digitizing of original color slides. Proxies for polar daylight spectra yield the iceberg's chromaticities, which agree closely with those predicted by two multiple-scattering theories.
1989
Non-Debye enhancements in the Mie scattering of light from a single water droplet
James A. Lock and Judith R. Woodruf
Applied Optics Vol. 28, 3, p. 523 (February 1989) OSA Optics InfoBase
The glare spots usually seen on a single water droplet which has been illuminated by a plane wave are produced by geometrical rays which correspond to the different terms of the Debye series expansion of the Mie scattered field. Recently other glare spot enhancements have been predicted which correspond to scattering resonances coupling to the orbiting rays associated with high-order geometrical rainbows. We observed the non-Debye enhancement of the eleventh-order rainbow glare spot at an observation angle of 90° on a 3.5-mm water droplet illuminated by polarized He-Ne laser light.

Scattering of light by crystals: a modified Kirchhoff approximation
Karri Muinonen
Applied Optics Vol. 28, 15, p. 3044 (August 1989) OSA Optics InfoBase
A modified Kirchhoff approximation (MKA) is developed for the scattering of light by randomly oriented crystals. The reflected and transmitted near fields are calculated from ray tracing; the corresponding far fields are then obtained via the vector Kirchhoff integral. On the shadow side of the particle, an additional near field exactly cancels the incident field and causes the forward diffraction. MKA contains a particle size dependence, which is not included in ray optics treatments, and satisfactory results can be obtained for size parameters larger than ten. The scattering phase functions and degrees of linear polarization are calculated for some hexagonal and cubic water ice crystals using MKA. The Kirchhoff approximation for particles other than crystals is discussed, and attention is paid to the backscattering enhancement due to the cyclic passage of internally or multiply externally reflected electromagnetic waves.

Observability of atmospheric glories and supernumerary rainbows
James A. Lock
J. Opt. Soc. Am. A, Vol. 6, No. 12, p. 1924 December 1989 OSA Optics InfoBase
The finite spatial coherence width of sunlight at the Earth imposes restrictions on the production of scattering phenomena based on the interference of light waves. With the spatial coherence properties of sunlight taken into account, the visibility of the supernumerary rainbow sequence adjacent to the primary rainbow and the radii of the water droplets that produce the optimum glory intensity were calculated. A substantial reduction was found in the contrast of all the supernumeraries beyond the first few, and the peak observability of the glory occurred for water droplets with radii between 10 and 20 µm.
1988
Optical glory of small freely rising gas bubbles in water: observed and computed cross-polarized backscattering patterns
W. Patrick Arnott and Philip L. Marston
J. Opt. Soc. Am. A, Vol. 5, No. 4, p. 496 April 1988 OSA Optics InfoBase
Light scattered from spherical bubbles in water manifests an enhancement in the backward direction analogous to the well-known optical glory of a drop. Unlike the glory for water drops, in which the rays travel partially on the drop's surface, the glory for bubbles is due to rays that are refracted and multiply reflected within the scatterer and is an example of a transmitted wave glory. Photographs of glory scattering for freely rising air bubbles in water are displayed for bubbles having diameters of less than 300 µm. A physical-optics model for backscattering is developed for spherical bubbles. Computed glory patterns from both Mie-series calculations and the physical optics model agree with the observed patterns. The patterns of freely rising air bubbles having a diameter of <300 µm are essentially those predicted for a spherical scatterer. The interference of different classes of glory rays is more clearly seen for bubbles in water than for the previously studied case of bubbles in oil.

Optical simulation of Huygens's principle
G. Bickel and G. Hausler
J. Opt. Soc. Am. A, Vol. 5, No. 6, p. 843 June 1988 OSA Optics InfoBase
The two-dimensional stationary-wave equation (Helmholtz equation) can be solved by a simple linear-optical filtering experiment for arbitrary source distributions. The experiment can be considered as direct visualization of Huygens's principle, i.e., each point of an initial wave front can be regarded as the source of an elementary wave. Many phenomena can be visualized: diffraction, interference (including Talbot effect, Bragg effect) with monochromatic and polychromatic light, birefringence, etc. Optical filtering can be applied to other linear differential equations with constant coefficients too, such as the Poisson equation and the diffusion equation.

Rainbows in strong vertical atmospheric electric fields
Stanley David Gedzelman
J. Opt. Soc. Am. A, Vol. 5, No. 10, p. 1717 October 1988 OSA Optics InfoBase
The effects of strong vertical atmospheric electric fields and electrically charged raindrops on the primary rainbow are considered. A vertical electric field alters the bow by stretching the raindrops vertically. The effects may be visible only for the extremely large electric fields (E > 105 V/m) sometimes encountered in thunderstorms. The electric field raises and brightens the top of the primary bow but reduces the relative intensity and spacing between the supernumeraries. Electrical charges do not have any visible effect on the rainbow because they significantly increase the ellipticity of only the largest and most highly charged drops, which do not contribute to the bow's top.
1987
Feature issue: Journal of Optical Society of America A, March 1987

Disruption of images: the caustic-touching theorem Free download
M. V. Berry
J. Opt. Soc. Am. A, Vol. 4, No. 3, p. 561 March 1987 OSA Optics InfoBase
Because of the distortions of geometrical optics, image curves and the outlines of the objects that generate them need not have the same topology. New image loops appear when the object curve touches the caustic of the family of (imaginary) rays emitted by the observing eye. Such disruption may be elliptic (loop born from an isolated point) or hyperbolic (loop pinched off from an already existing one). The number of images need not be odd (unlike the number of rays reaching the eye from each object point). Two examples are employed to illustrate caustic touching. The first is the Sun's disk seen in rippled water (as the height of the eye increases, the boundary of all the images becomes a fractal curve with dimension 2). The second is sunset seen through the Earth's atmosphere from near space (when there is an inversion layer) or from the Moon during a lunar eclipse (when there need not be one).

Polarization and Brewster angle properties of light pillars
Kenneth Sassen
J. Opt. Soc. Am. A, Vol. 4, No. 3. p. 570 March 1987 OSA Optics InfoBase
Numerical simulation of the nocturnal light pillar, an atmospheric optical phenomenon inadvertently caused by humans, reveals that the pillars are virtually completely polarized at the Brewster angle for ice as a result of the geometry of rays reflected off near-horizontally aligned ice crystals from a nearby light source. It s also shown for plate crystals that the first-order internal reflection contributes importantly to the display and that the depth of the crystal-containing layer and the effects of atmospheric attenuation serve to limit the height above the horizon to which the pillars are visible. The model findings have been verified with experiments involving the generation of artificial pillars from linearly polarized light sources. Both observations and model predictions support the view that the plate ice crystals causing the display have tilt angles that are distributed normally from the horizontal plane.

Faceted snow crystals
John Hallett
J. Opt. Soc. Am. A, Vol. 4, No. 3, p. 581 March 1987 OSA Optics InfoBase
Colored halos are produced by refraction of light by solid hexagonal snow crystals with well-defined facets whose size is sufficiently large (>20 ,um) to avoid significant diffraction effects. Large crystals fall with their major axes horizontal and oscillate by eddy shedding to give dogs and arcs. The formation of such crystals is strongly dependent on changing growth conditions, particularly ice supersaturation, air pressure, temperature, and the thermal radiation environment. Optimum meteorological conditions for formation of such crystals are suggested.

Laboratory simulation of inferior and superior mirages
Robert G. Greenler
J. Opt. Soc. Am. A, Vol. 4, No. 3, p. 589 March 1987 OSA Optics InfoBase
A small scene, viewed over a heated plate, exhibits many of the typical inferior-mirage effects. As the viewing point is lowered, a mirage lake appears, and a vanishing line rises on the scene, showing objects apparently reflected in a rising surface of water. Several kinds of superior mirages are simulated by viewing objects through a water tank containing fresh water layered over salt water. The system simulates towering, stooping, various forms of the Fata Morgana, and the three-part mirage.

Multiple-scattering effects in halo phenomena
E. Trankle & Robert G. Greenler
J. Opt. Soc. Am. A, Vol. 4, No. 3, p. 591 March 1987 OSA Optics InfoBase
Using a hit-and-miss Monte Carlo method, we followed many paths of Sun rays through a layer of hexagonal ice crystals. The angle of scattering by a single crystal is determined by tracing the path of the Sun rays through the crystal with its particular orientation. In this way we produced point plots of the intensity of the scattered sunlight for a specified population of crystals. By comparing the intensity patterns from single and multiple scattering, we looked for additional effects caused by multiple scattering. Several new secondary structures appear; however, their intensities are significant only when they result from spotlike primary structures. It appears that secondary structures from two combinations should be observable: from thick-plate crystals, the sun dogs of the sun dogs; and for long-column crystals in the Parry-arc orientation, the subsun of the lower tangent arc for Sun elevations around 15°. We show that multiple scattering is essential to explain the Saskatoon display.

Skylight polarization during a total solar eclipse: a quantitative model Free download
G. P. Konnen
J. Opt. Soc. Am. A, Vol. 4, No. 3, p. 601 March 1987 OSA Optics InfoBase
The polarization distribution in the sky during a total solar eclipse is calculated with a simple secondary light scattering model. This model uses the light-intensity measurements near the horizon during the eclipse and the pretotality and posttotality skylight polarization observations as input. It is found thaf the model can explain various observations during totality, including the quantitative measurements of Shaw [Appl. Opt. 14, 388 (1975)] of the polarization distribution of the sky in the solar vertical during the 1973 total eclipse.

Optics of sunbeams Free download
David K. Lynch
J. Opt. Soc. Am. A, Vol. 4, No. 3, p. 609 March 1987 OSA Optics InfoBase
Crepuscular and solar rays are visible by means of the contrast between sunlit and (usually) cloud-shaded portions of the atmosphere. Their visibility depends on (1) the volume angular-scattering coefficient β(φ), (2) the brightness of the sunlit sky, and (3) the integrated optical path through the shadowed regions of the atmosphere. We show that the geometry of path length through the umbra (3) is sufficiently important that it can account for most of the observed properties of rays, except when the volume angular-scattering coefficient β(φ) is sharply peaked in the forward direction.

Appearance of supernumeraries of the secondary rainbow in rain showers Free download
G. P. Konnen
J. Opt. Soc. Am. A/Vol. 4, No. 5, p. 810 May 1987 OSA Optics InfoBase
The secondary rainbow scattering angle for spheroidal drops of water is virtually independent of aspect ratio for most visible wavelengths. For most solar heights the residual aspect-ratio dependence shifts the bow toward a smaller deviation angle if the drop size increases. These two facts explain why the supernumeraries of the secondary rainbow are never seen in rain showers. At high solar elevations the flattening of drops results in a shift of the secondary rainbow toward a larger deviation angle. -It is shown that this shift is still large enough to cause the formation of the first supernumerary in red light. This red supernumerary of the secondary rainbow may be observable by eye in natural showers if a red filter is used to remove the obscuring contribution of shorter wavelengths to the light of the rainbow. For indices of refraction far from that of water, a strong aspect-ratio dependence of the secondary rainbow angle is shown to be present. Some possible implications of this for the formation of a hyperbolic umbilic diffraction catastrophe in the secondary rainbow pattern are indicated.

Theory of the observations made of high-order rainbows from a single water droplet
James A. Lock
Applied Optics Vol. 26, 24, p. 5291 (December 1987) OSA Optics InfoBase
Over a dozen rainbows have been observed in a single water droplet. They appear as glare spots on the water droplet which take on coloration at the appropriate rainbow angles. The appearance of rainbows as colored glare spots in this situation is understood in terms of the caustics created in the vicinity of the droplet by the refracting light rays. The angular positions of the glare spots are understood in terms of the Fourier transform of the geometric scattering amplitude. The rainbow glare spots are also found to appear numerically in the Fourier transform of the Mie scattered fields. An additional glare spot produced by rays at grazing incidence and not attributable to geometric optics also appears numerically in the Fourier transformed Mie fields.
1986
What size of ice crystals causes the halos?: comment
Andrew J. Weinheimer
J. Opt. Soc. Am. A, Vol.3, No. 3, p. 376 March 1986 OSA Optics InfoBase
The paper by Fraser [A. B. Fraser, J. Opt. Soc. Am. 69, 1112 (1979)] provides a critical assessment of the commonly made assumption that halos around the Sun are produced by randomly oriented ice crystals. He concludes that crystals that are small enough to be randomly oriented are, in addition, too small to contribute significantly to the production of a halo; thus the commonly made assumption is false. However, some doubt is cast on this conclusion by the fact that it is based on what may be regarded either as a misapplication of Maxwell-Boltzmann statistics or as, perhaps, a mathematical error. The purpose of this Communication is simply to point this out. Left unanswered are the important questions of how big an error this is and even of whether its correction would weaken or strengthen Fraser's main conclusion.
1985
Intensity profile of the 22° halo Free download
David K. Lynch and Ptolemy Schwartz
J. Opt. Soc. Am. A, Vol. 2, No. 4, p. 584 April 1985 OSA Optics InfoBase
We report the first relative intensity measurements made to our knowledge of the 22° halo, obtained from photographic photometry of a halo of exceptional brightness and uniformity. The maximum brightness occurs at 22.8°, and a relative minimum occurs at 19.7°. The full width at one half the maximum intensity is 3.4°. A low-intensity tail reaches from 29° to 39°.
1984
Monte Carlo simulation and analysis of halo phenomena
F. Pattloch and E. Trankle
J. Opt. Soc. Am. A, Vol. 1, No. 5, p. 520 May 1984 OSA Optics InfoBase
We trace the paths of sun rays through hexagonal ice crystals by a hit-and-miss Monte Carlo algorithm, interpreting the Fresnel equations as reflection and transmission probabilities. In this way, we calculate the intensity of the scattered sunlight for a specified distribution of crystals. In particular, we obtain the relative intensities of all arcs and spots produced by the crystals. The distribution function for the tilting and rotation angles of oriented crystals corresponds to a superposition of damped oscillations. We use the method to analyze the relative intensities of the 22° and 46° halos and to simulate a complex ice-crystal display produced by oriented column-like, oriented plate-like, and unoriented cube-like crystals.

Refraction halos in the solar system. I. Halos from cubic crystals that may occur in atmospheres in the solar system
Edward Whalley and Graham E. McLaurin
J. Opt. Soc. Am. A, Vol. 1, No. 12, p. 1166 December 1984 OSA Optics InfoBase
It is suggested that halos and other refraction effects caused by crystals of various solids that may occur in their atmospheres might occur on the planets of the solar system and their satellites. The detection of the halos would provide valuable information about the nature and the crystalline form of the solids. The halos caused by the octahedral and cubic crystals of carbon monoxide, carbon dioxide, ice Ic, ammonia, methane, and the structure-I clathrate hydrates of nitrogen, carbon monoxide, carbon dioxide, sulfur dioxide, and methane have been predicted over the range of temperatures that may occur in the atmospheres of the planets.
1983
Effects on skylight at South Pole Station, Antarctica, by ice crystal precipitation in the atmosphere
Bruce W. Fitch and Kinsell L. Coulson
Applied Optics Vol. 22, 1, p. 71 (January 1983) OSA Optics InfoBase
Measurements of the radiance and polarization of the skylight at South Pole Station, Antarctica, were made for clear cloud-free skies and cloudless skies with ice crystal precipitation. The measurements were made at six narrowband wavelengths from 321 to 872 nm in the principal plane. The data show that scattering by ice crystals increases the radiance in the backscatter plane, decreases it in the solar plane, and shifts the radiance minfimum to a point closer to the sun. The crystals decrease the maximum value of linear polarization and shift the position of the maximum away from the sun. The influence of ice crystal scattering is greatest at the longer wavelengths.

Effects of the El Chichon volcanic cloud in the stratosphere on the polarization of light from the sky
Kinsell L. Coulson
Applied Optics Vol. 22, 7, p. 1036 (April 1983) OSA Optics InfoBase
A dense volcanic cloud from the El Chichon volcanic eruption has been observed in the stratosphere over Hawaii since it was first discovered at the Mauna Loa Observatory 9 Apr. 1982. Lidar observations have shown the cloud to have been dense and highly layered in its early stages, but as the cloud matured it became more homogeneous and the top portion underwent considerable enhancement. Measurements of the degree of polarization of skylight at the zenith and across the sky in the sun's vertical show that the polarization field is strongly modified by the effects of the cloud and that the modifications are of a different nature from those produced by high turbidity in the lower layers of the atmosphere. The degree of polarization at the zenith during twilight shows a secondary maximum at a solar depression D = 4.8-5°, a secondary minimum at D = 4, a primary maximum at D = 1-2°, and a rapid decrease to values generally <10% in the immediate sunrise period. The positions of the neutral points are strongly affected by the cloud, the Arago point being shifted from its normal position by as much as 15-20° and the Babinet point being shifted even farther. Multiple Babinet points were observed on some occasions. The measurements indicate the polarization field to be modified more by the El Chichon cloud than it was by the clouds from previous eruptions which have occurred during this century.

Video polarimetry: a new imaging technique in atmospheric science
T. Prosch, D. Hennings, and E. Raschke
Applied Optics Vol. 22, 9, p. 1360 (May 1983) OSA Optics InfoBase
An imaging polarimeter has been built to study the polarization of solar radiation (X = 550 nm) scattered and reflected from the natural environment. The instrument generates false color images as multiparameter display of the degree of polarization, azimuth of polarization, and the radiance. These video signals can be digitized into a computer-compatible format. As an example of application, the polarization properties of light reflected from a lake and its environment are discussed here.

Light scattering by horizontally oriented spheroidal particles
Shoji Asano
Applied Optics Vol. 22, 9, p. 1390 (May 1983) OSA Optics InfoBase
Light scattering properties of spheroidal particles oriented randomly with their long axes in the horizontal are studied. A computational scheme has been developed to calculate the scattering matrices as well as the extinction and scattering cross sections and asymmetry factors in a manner consistent with our previous treatment of 3-D orientations. The single scattering properties strongly depend on the elevation angle of incident light. The dependence of the extinction and scattering cross sections is particularly prominent, while the dependence of the single scattering albedo and asymmetry factor is rather small but still significant. For a given elevation angle, the scattered intensity is a function of not only the scattering angle but also the azimuth angle of emergence. Implications of the anisotropic scattering by horizontally oriented nonspherical particles with respect to the elevation angle are also discussed.

Effects of the El Chichon volcanic cloud in the stratosphere on the intensity of light from the sky
Kinsell L. Coulson
Applied Optics Vol. 22, 15, p. 2265 (August 1983) OSA Optics InfoBase
This is the second of two papers dealing with the effects of volcanic debris from the eruption of El Chichon on light from the sunlit sky. The polarization of skylight was considered in the first of the two, whereas this one is devoted to skylight intensity. It is shown here that the magnitude of the skylight intensity is modified very significantly from its clear sky value by the volcanic cloud, as is its change with solar depression angle during twilight and its distribution over the sky during the day. Emphasis is on measurements at a wavelength of 0.07 Atm. Generally the volcanic cloud produces a diminution of zenith intensity during twilight with a considerable enhancement of intensity over the sky throughout the main part of the day. The solar aureole is not as sharp as it is in normally clear conditions, but the volcanic cloud causes a very diffuse type of aureole which covers a large portion of the sky. The preferential scattering of the longer wavelengths of sunlight, which is made evident by brilliant red and yellow colors in the sunrise period, causes a pronounced change of longwave/shortwave color ratios during twilight from their values in clear atmospheric conditions. The combination of intensity data shown here with polarization data in the previous paper should give a relatively complete picture of the effects of volcanic debris on solar radiation in the atmosphere and be useful in the verification of radiative transfer models of atmospheric turbidity.
Feature issue: Journal of Optical Society of America, December 1983

Inversion of superior mirage data to compute temperature profiles
Waldemar H. Lehn
J. Opt. Soc. Am., Vol. 73, No. 12, p. 1622 December 1983 OSA Optics InfoBase
Information derived from the superior mirage is used to compute the average vertical temperature profile in the atmosphere between the observer and a known object. The image is described by a plot of ray-elevation angle at the eye against elevation at which that ray intersects the object. The computational algorithm, based on the tracing of rays that have at most one vertex, iteratively adjusts the temperature profile until the observed image characteristics are reproduced. An example based on an observation made on the Beaufort Sea illustrates the process.

Why can the supernumerary bows be seen in a rain shower?
Alistair B. Fraser
J. Opt. Soc. Am., Vol. 73, No. 12, p. 1626 December 1983 OSA Optics InfoBase
Although the spectra of drop radii in rain showers are broad, the supernumerary bows are caused by only those drops with radii of about 0.25 mm. The angle of minimum deviation, the rainbow angle, is a function of drop size, being large for big drops, owing to drop distortion, and large for small drops, owing to interference. Between these extremes, there is a minimum rainbow angle. The drops that cause it give rise to the supernumerary bows

Polarization and intensity distributions of refraction halos Free download
G. P. Konnen
J. Opt. Soc. Am., Vol. 73, No. 12, p. 1629 December 1983 OSA Optics InfoBase
By using Taylor expansions, simple expressions are obtained for the deflection of light by ice crystals. With these simplified formulas, the intensity distributions of halos as a function of scattering angle are calculated analytically near the halo angle. It is found that the intensity distributions of halos depend on the number of degrees of freedom of the generating set of crystals. The differences in the purity of the colors of various types of halo are explained subsequently on the basis of their intensity distributions. An analytical description of the shape of the halo or of the halocaustic near the halo angle is obtained also. On the basis of the obtained intensity distributions, the polarization of refraction halos as a function of scattering angle is calculated, in which both contributions (birefringence of ice and polarization by refraction) are taken into account. It is found that the polarization of parhelia and tangent arcs shows a strong maximum near the inner edge of the halo over an angular range of 0.1°, followed by a similar maximum of reversed polarization at 0.5° from the first one. The 22° halo shows a less strong maximum near its edge over an angular range of 0.5°. Halos at 46° from the sun also show a strong polarization near their inner edges, but the direction of the polarization is perpendicular to the polarization of the 22° halo edges. The possibility for detecting ice crystals on Venus by polarimetry near the halo angle is discussed briefly.

Some ice crystals that made halos
Walter Tape
J. Opt. Soc. Am., Vol. 73, No. 12, p. 1641 December 1983 OSA Optics InfoBase
During low-level halo displays, ice crystals in the atmosphere at ground level were collected and studied. I discuss the crystals in connection with the halos present at the time of collection.

Colors of snow, frozen waterfalls, and icebergs
Craig F. Bohren
J. Opt. Soc. Am., Vol. 73, No. 12, p. 1646 December 1983 OSA Optics InfoBase
Snow presents more than just a uniformly white face. Beneath its surface a vivid blueness, the purity of which exceeds that of the bluest sky, may be seen. This subnivean blue light results from preferential absorption of red light by ice; multiple scattering by ice grains, which is not spectrally selective, merely serves to increase the path length that photons travel before reaching a given depth. Although snow is usually white on reflection, bubbly ice, which can be found in frozen waterfalls and icebergs, may not be. To a first approximation, bubbly ice is equivalent to snow with an effective grain size that increases with decreasing bubble volume fraction. Ice grains in snow are too small to give it a spectrally selective albedo, but the much larger effective grain sizes of bubbly ice can give it bluish-green hues of low purity on reflection.

Landscape as viewed in the 320-nm ultraviolet
W. Livingston
J. Opt. Soc. Am., Vol. 73, No. 12, p. 1653 December 1983 OSA Optics InfoBase
Wood's 1910 study of the UV landscape by photography [R. W. Wood, Photog. J. 50, 329 (1910)] is resumed. Through a narrow-band filter at 320 nm we find uniform skies even under broken clouds, a Rayleigh veiling that attenuates distant detail, an absence of shadows, and a low reflectivity for most natural substances (except snow). Rainbows broaden by a factor of more than 2 when the UV is included. The fact that glass is opaque at 320 nm causes cities to be dark at night in this wavelength, with astronomical consequences. The aphakic human eye (i.e., the eye after removal of its crystalline lens for a cataract condition) proves to have a practical sensitivity at 320 nm so that the aphakic observer can verify the unique character of the UV scene.

Critical-angle scattering of white light from a cylindrical bubble in glass: photographs of colors and computations
P. L. Marston, J. L. Johnson, S. P. Love and B. L. Brim
J. Opt. Soc. Am., Vol. 73, No. 12, p. 1658 December 1983 OSA Optics InfoBase
A novel effect in the scattering of white light from bubbles consists of colored bands that appear near the critical scattering angle. The bands were photographed in the far-zone scattering from a cylindrical bubble in glass. Their existence is associated with the coarse structure present in the exact scattered intensity. A digital Butterworth filter was developed to remove (from computed intensities) fine structures that are lost when the optical bandwidth is large. The colors are found to be due to the combined effects of interference and diffraction (near the critical scattering angle) and dispersion of the refractive index. Coarse structures were previously modeled in the monochromatic scattering from spherical air bubbles in water. Colors are also to be expected in the appearance of clouds of bubbles in water. Such colors were reported [C. Pulfrich, Ann. Phys. Chem. (Leipzig) 33, 209 (1888)]. Some implications for the optical measurement of bubble size and surface quality are noted.

1982
Glory in backscattering: Mie and model predictions for bubbles and conditions on refractive index in drops
Philip L. Marston and Dean S. Langley
J. Opt. Soc. Am., Vol. 72, No. 4, p. 456 April 1982 OSA Optics InfoBase
Mie calculations illustrate the dependences of scattered intensity on polarization, angle, and size for bubbles with radii ~0.3 mm in a siloxane liquid. Computations give evidence of the axial focusing observed in recent experiments and predicted by a model. Conditions for glory rays in drops and bubbles are derived, and errors in the literature are noted.

Rainbow brightness
Stanley David Gedzelman
Applied Optics Vol. 21, 16, p. 3032 (August 1982) OSA Optics InfoBase
A theory for the brightness of rainbows is presented. The light reaching the observer consists of a beam of singly scattered sunlight, originating from the directly illuminated portion of a rainswath, which, in turn, has suffered depletion by scattering or absorption in its path through the atmosphere. The model incorporates the relevant features of cloud geometry and solar position in relation to the observer appropriate to rainbows. The model helps explain why the bottom (or near-horizon portion) of the rainbow tends to be both brighter and redder than the top (or horizontal portion furthest above the ground) when the sun is near the horizon. The greater brightness of the bottom of the bow derives principally from the greater length of the directly illuminated part of the rainswath near the horizon, while the increased redness of the bow’s bottom is due to the severe depletion of the short-wavelength contribution to the rainbow beam in its passage through the atmosphere.

Polarized light scattering by hexagonal ice crystals: theory
Qiming Cai and Kuo-Nan Liou
Applied Optics Vol. 21, 19, p. 3569 (October 1982) OSA Optics InfoBase
A scattering model involving complete polarization information for arbitrarily oriented hexagonal columns and plates is developed on the basis of the ray tracing principle which includes contributions from geometric reflection and refraction and Fraunhofer diffraction. We present a traceable and analytic procedure for computation of the scattered electric field and the associated path length for rays undergoing external reflection, two refractions, and internal reflections. We also derive an analytic