Sources of error

Although the Mie algorithm provides the rigorous solution to scattering from a sphere of arbitrary size, it is essential to understand whether the results produced by the MiePlot program are accurate.  The graphs may be accurate in numerical terms, but what about the coloured depictions of optical phenomena such as rainbows?

There are numerous sources of potential error.  Some are obviously beyond the control of the MiePlot program: the performance of display devices depends on user settings (brightness, contrast and gamma) and on fundamental characteristics (colour temperature, monitor phosphors, white balance, etc.).  Even more restricting is the limited dynamic range of computer displays: we would not want our display to emulate the brightness of thesun!

Use the grey-scale in Fig. 1 to set up the brightness and contrast of your computer display.  You should see uniform steps in brightness between adjacent blocks - whilst ensuring that you can also see the small squares in the centre of the left and right blocks.

However, the following uncertainties affect the basic accuracy of the MiePlot program:

• the relationship between wavelength and colour;
• the refractive index of water as a function of wavelength;
• the spectrum of "white" sunlight.

Fig. 2    Conversion of wavelength into RGB values and resulting spectrum

To convert a particular wavelength of light into a colour that can be displayed on a computer monitor, an algorithm is necessary to generate RGB values (the amplitude of Red, Green and Blue signals) used by the computer display. The MiePlot program is based on an algorithm from Dan Bruton's Color Science Page.  The conversion process from wavelength to RGB values is shown graphically in Fig. 2, together with the resulting display of spectrum from 380 to 700 nm. The Bruton algorithm is obviously a simplification of a complex process.  More complex algorithms have been investigated, such as those developed by CIE (Commission Internationale Eclairage - International Lighting Commission) but none of them produce an aesthetically pleasing spectrum! As the coloured depictions of optical phenomena depend crucially on the relationship between wavelength and colour, more work is required in this area.