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"Meteorological optics" or "Atmospheric optics", please click here.

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Simulation of Rainbows, Coronas, and Glories by use of Mie Theory Free download (2.40 MB)
Philip Laven
Applied Optics, Volume 42, Issue 3, pp. 436-444 (January 2003)
Abstract: 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.

The above paper was published in Applied Optics and is made available as an electronic reprint with the permission of OSA. The paper can be found here on the OSA website. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.

Simulation of rainbows, coronas and glories using Mie theory and the Debye series Free download (940 kB)
Philip Laven
Journal of Quantitative Spectroscopy & Radiative Transfer 89 (2004) 257–269
Abstract: The scattering of light from homogeneous spheres might be considered to be a trivial problem because rigorous solutions, such as Mie theory, were developed almost 100 years ago. Nevertheless, full-colour simulations of atmospheric optical effects, such as rainbows, coronas and glories, reveal several intriguing issues. Calculations using the Debye series can help us to understand the scattering mechanisms causing specific effects: for example, the atmospheric glory seems to be caused by light rays that have suffered one internal reflection within water drops.

Rings around the sun and moon: coronae and diffraction Free download (0.99 MB)
Les Cowley, Philip Laven and Michael Vollmer
Physics Education, Volume 40, Issue 1, pp. 51-59 (January 2005)
Abstract: Atmospheric optical effects can teach much about physics and especially optics. Coronae—coloured rings around the sun or moon—are large-scale consequences of diffraction, which is often thought of as only a small effect confined to the laboratory. We describe coronae, how they are formed and experiments that can be conducted on ones in the sky. Recognizing that this is not always convenient, we show how students can also learn about coronae and thus diffraction from experiments with accurate full-colour computer simulations and laboratory demonstrations.

Atmospheric glories: simulations and observations Free download (1.93 MB)
Philip Laven
Applied Optics, Volume 44, Issue 27, pp. 5667-5674 (September 2005)
Abstract: 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.

The above paper was published in Applied Optics and is made available as an electronic reprint with the permission of OSA. The paper can be found here on the OSA website. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.

How are glories formed? Free download (2.48 MB)
Philip Laven
Applied Optics, Volume 44, Issue 27, pp. 5675-5683 (September 2005)
Abstract: 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 θ = 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 θ = 180°), scattering in a specific direction θ = 180° - δ can be considered as the vector sum of two surface waves: one deflecting the incident light by 180° - δ and the other by 180° + δ. 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.

The above paper was published in Applied Optics and is made available as an electronic reprint with the permission of OSA. The paper can be found here on the OSA website. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.

Rainbows from inhomogeneous transparent spheres: a ray-theoretic approach Free download (580 kB)
John A. Adam and Philip Laven
Applied Optics, Vol. 46, Issue 6, pp. 922-929 (February 2007)
Abstract: A ray-theoretic account of the passage of light through a radially inhomogeneous transparent sphere has been used to establish the existence of multiple primary rainbows for some refractive index profiles. The existence of such additional bows is a consequence of a sufficiently attractive potential in the interior of the drop, i.e., the refractive index gradient should be sufficiently negative there. The profiles for which this gradient is monotonically increasing do not result in this phenomenon, but nonmonotone profiles can do so, depending on the form of n. Sufficiently oscillatory profiles can lead to apparently singular behavior in the deviation angle (within the geometrical optics approximation) as well as multiple rainbows. These results also apply to systems with circular cylindrical cross sections, and may be of value in the field of rainbow refractometry.

The above paper was published in Applied Optics and is made available as an electronic reprint with the permission of OSA. The paper can be found here on the OSA website. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.

Noncircular glories and their relationship to cloud droplet size Free download (8.18 MB)
Philip Laven
Applied Optics, Vol. 47, Issue 34, pp. H25-H30 (December 2008)
Abstract: 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.

The above paper was published in Applied Optics and is made available as an electronic reprint with the permission of OSA. The paper can be found here on the OSA website. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.

Effects of refractive index on glories Free download (8.77 MB)
Philip Laven
Applied Optics, Vol. 47, Issue 34, pp. H133-H142 (December 2008)
Abstract: 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.

The above paper was published in Applied Optics and is made available as an electronic reprint with the permission of OSA. The paper can be found here on the OSA website. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.

Separating diffraction from scattering: the million-dollar challenge Free download (634 kB)
Philip Laven
J. Nanophotonics, Vol. 4, 041593 (2010); http://nanophotonics.spiedigitallibrary.org/mobile/article.aspx?articleid=1028682 (March 2010)
Abstract: Craig Bohren has offered a million-dollar prize to anyone who can devise a detector that accepts scattered light but rejects diffracted light. This challenge was examined from a theoretical perspective by considering the scattering of red light by a spherical droplet of water with diameter 20 μm. Illumination of the droplet by short pulses (e.g. a duration of 5 fs) could allow a detector to distinguish between light scattered by various mechanisms, such as diffraction, transmission, reflections and surface waves. Although such techniques would not satisfy the precise terms of the challenge, the time domain approach can deliver remarkable insights into the details of the scattering processes.

The above paper was published in the Journal of Nanophotonics and is made available as an electronic reprint with the permission of SPIE. Copyright 2010 Society of Photo-Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited. The paper can be found here on the Journal of Nanophotonics website.

Mie scattering in the time domain. Part 1. The role of surface waves Free download (944 kB)
James A. Lock and Philip Laven
Journal of Optical Society of America A, Vol. 28, Issue 6, pp. 1086-1095 (June 2011)
Abstract: We computed the Debye series p = 1 and p = 2 terms of the Mie scattered intensity as a function of scattering angle and delay time for a linearly polarized plane wave pulse incident on a spherical dielectric particle and physically interpreted the resulting numerical data. Radiation shed by electromagnetic surface waves plays a prominent role in the scattered intensity. We determined the surface wave phase and damping rate and studied the structure of the p = 1, 2 surface wave glory in the time domain.

The above paper was published in JOSA A and is made available as an electronic reprint with the permission of OSA. The paper can be found here on the OSA website. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.

Mie scattering in the time domain. Part II. The role of diffraction Free download (815 kB)
James A. Lock and Philip Laven
Journal of Optical Society of America A, Vol. 28, Issue 6, pp. 1096-1106 (June 2011)
Abstract: The p = 0 term of the Mie–Debye scattering amplitude contains the effects of external reflection and diffraction. We computed the reflected intensity in the time domain as a function of the scattering angle and delay time for a short electromagnetic pulse incident on a spherical particle and compared it to the predicted behavior in the forward-focusing region, the specular reflection region, and the glory region. We examined the physical consequences of three different approaches to the exact diffraction amplitude, and determined the signature of diffraction in the time domain. The external reflection surface wave amplitude gradually replaces the diffraction amplitude in the angular transition region between forward-focusing and the region of specular reflection. The details of this replacement were studied in the time domain.

The above paper was published in JOSA A and is made available as an electronic reprint with the permission of OSA. The paper can be found here on the OSA website. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.

Light and Color in the Open Air: introduction to the feature issue Free download (45 kB)
Joseph A. Shaw, Raymond L. Lee, Jr., and Philip Laven
Applied Optics, Vol. 58, Issue 28, pp. LC1-LC2 (October 2011)
Abstract: This is a feature issue devoted to optical phenomena that can be observed in nature, primarily with the naked eye. Many of the papers published in this feature issue are based on presentations given at the “Light & Color in Nature” conference held in June 2010 at St. Mary’s College of Maryland.

The above paper was published in Applied Optics and is made available as an electronic reprint with the permission of OSA. The paper can be found here on the OSA website. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.

Time domain analysis of scattering by a water droplet Free download (1.17 MB)
Philip Laven
Applied Optics, Vol. 50, Issue 28, pp. F29-F38 (October 2011)
Abstract: Rainbows, coronas and glories are caused by the scattering of sunlight from water droplets in the atmosphere. Although these optical phenomena are seen fairly frequently, even scientifically minded people sometimes struggle to provide explanations for their formation. This paper offers explanations of these phenomena based on numerical computations the scattering of a 5 fs pulse of red light by a spherical droplet of water. The results reveal the intricate details of the various scattering mechanisms, some of which are essentially undetectable except in the time domain.

The above paper was published in Applied Optics and is made available as an electronic reprint with the permission of OSA. The paper can be found here on the OSA website. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.

Visibility of natural tertiary rainbows Free download (548 kB)
Raymond L. Lee, Jr. and Philip Laven
Applied Optics, Vol. 50, Issue 28, pp. F152-F161 (October 2011)
Abstract: Naturally occurring tertiary rainbows are extraordinarily rare and only a handful of reliable sightings and photographs have been published. Indeed, tertiaries are sometimes assumed to be inherently invisible because of sun glare and strong forward scattering by raindrops. To analyze the natural tertiary’s visibility, we use Lorenz–Mie theory, the Debye series, and a modified geometrical optics model (including both interference and nonspherical drops) to calculate the tertiary’s (1) chromaticity gamuts, (2) luminance contrasts, and (3) color contrasts as seen against dark cloud backgrounds. Results from each model show that natural tertiaries are just visible for some unusual combinations of lighting conditions and raindrop size distributions.

The above paper was published in Applied Optics and is made available as an electronic reprint with the permission of OSA. The paper can be found here on the OSA website. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.

Physically-based simulation of rainbows Free download
Iman Sadeghi, Adolfo Munoz, Philip Laven, Wojciech Jarosz, Francisco Seron, Diego Gutierrez and Henrik Wann Jensen
ACM Transactions on Graphics (TOG), Vol. 31, Issue 1, Article No. 3 (January 2012)
Abstract: In this article, we derive a physically-based model for simulating rainbows. Previous techniques for simulating rainbows have used either geometric optics (ray tracing) or Lorenz-Mie theory. Lorenz-Mie theory is by far the most accurate technique as it takes into account optical effects such as dispersion, polarization, interference, and diffraction. These effects are critical for simulating rainbows accurately. However, as Lorenz-Mie theory is restricted to scattering by spherical particles, it cannot be applied to real raindrops which are nonspherical, especially for larger raindrops. We present the first comprehensive technique for simulating the interaction of a wavefront of light with a physically-based water drop shape. Our technique is based on ray tracing extended to account for dispersion, polarization, interference, and diffraction. Our model matches Lorenz-Mie theory for spherical particles, but it also enables the accurate simulation of nonspherical particles. It can simulate many different rainbow phenomena including double rainbows and supernumerary bows. We show how the nonspherical raindrops influence the shape of the rainbows, and we provide a simulation of the rare twinned rainbow, which is believed to be caused by nonspherical water drops.

Understanding Light Scattering by a Coated Sphere. Part 1: Theoretical Considerations Free download (792 kB)
James A. Lock and Philip Laven
Journal of Optical Society of America A, Vol. 29, Issue 8, pp. 1489-1497 (2012)
Abstract: Although scattering of light by a coated sphere is much more complicated than scattering by a homogeneous sphere, each of the partial wave amplitudes for scattering of a plane wave by a coated sphere can be expanded in a Debye series. The Debye series can then be rearranged in terms of the various reflections that each partial wave undergoes inside the coated sphere. For a given number of internal reflections, it is found that many different Debye terms produce the same scattered intensity as a function of scattering angle. This is called path degeneracy. In addition, some of the ray trajectories are repeats of those occurring for a smaller number of internal reflections in the sense that they produce identical time delays as a function of scattering angle. These repeated paths, however, have a different intensity as a function of scattering angle than their predecessors. The degenerate paths and repeated paths considerably simplify the interpretation of scattering within the coated sphere, thus making it possible to catalog the contributions of the various paths.

The above paper was published in JOSA A and is made available as an electronic reprint with the permission of OSA. The paper can be found here on the OSA website. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.

Understanding Light Scattering by a Coated Sphere. Part 2: Time Domain Analysis Free download (1667 kB)
Philip Laven and James A. Lock
Journal of Optical Society of America A, Vol. 29, Issue 8, pp. 1498-1507 (2012)
Abstract: Numerical computations were made of scattering of an incident electromagnetic pulse by a coated sphere that is large compared to the dominant wavelength of the incident light. The scattered intensity was plotted as a function of the scattering angle and delay time of the scattered pulse. For fixed core and coating radii, the Debye series terms that most strongly contribute to the scattered intensity in different regions of scattering angle-delay time space were identified and analyzed. For a fixed overall radius and an increasing core radius, the first-order rainbow was observed to evolve into three separate components. The original component faded away, while the two new components eventually merged together. The behavior of surface waves generated by grazing incidence at the core/coating and coating/exterior interfaces was also examined and discussed.

The above paper was published in JOSA A and is made available as an electronic reprint with the permission of OSA. The paper can be found here on the OSA website. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.

Color-coordinate system from a 13th-century account of rainbows Free download (2.83 MB)
Hannah E. Smithson, Philip S. Anderson, Greti Dinkova-Bruun, Robert A. E. Fosbury, Giles E. M. Gasper, Philip Laven, Tom C. B. McLeish, Cecilia Panti, and Brian K. Tanner
Journal of Optical Society of America A, Vol. 31, Issue 4, pp. A341-349 (2014)
Abstract: We present a new analysis of Robert Grosseteste’s account of color in his treatise De iride (On the Rainbow), dating from the early 13th century. The work explores color within the 3D framework set out in Grosseteste’s De colore [see J. Opt. Soc. Am. A 29, A346 (2012)], but now links the axes of variation to observable properties of rainbows. We combine a modern understanding of the physics of rainbows and of human color perception to resolve the linguistic ambiguities of the medieval text and to interpret Grosseteste’s key terms.

The above paper was published in JOSA A and is made available as an electronic reprint with the permission of OSA. The paper can be found here on the OSA website. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.
Re-visiting the atmospheric corona Free download (972 kB)
Philip Laven
Applied Optics, Vol. 54, Issue 4, pp. B46-B53 (February 2015)
Abstract: The atmospheric corona is a well-known diffraction phenomenon, typically seen as colored rings surrounding the Sun or Moon. In many respects, Fraunhofer diffraction provides a good explanation of the corona. As the angular sizes of the corona’s rings are inversely proportional to the radius, r, of the spherical particles causing the corona, it should be easy to estimate the particle size from observations and photographs. Noting that some of the techniques commonly used for particle sizing based on diffraction theory can give misleading results for coronas caused by the scattering of sunlight, this paper uses Mie theory simulations to demonstrate that the inner 3 red rings of the corona have angular radii of θ ≈ 16/r, 31/r, and 47/r, when θ is measured in degrees and r is measured in μm.

The above paper was published in Applied Optics and is made available as an electronic reprint with the permission of OSA. The paper can be found here on the OSA website. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.

Page updated on 21 November 2014

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