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   How IRIS works 


    History

IRIS uses Mie scattering theory to produce accurate simulations. Formulated by Gustav Mie in 1908 for scattering by a sphere, it derives without compromise from Maxwell's equations of electromagnetism. However, Mie calculations are so lengthy and complicated that they were not really practicable until large mainframe computers were developed. Even then, their tabular output did not allow the computed glories or coronae to be easily visualised. Now, everyone's PCs can do the arithmetic quickly and display the results in full colour.

   

Mie calculation

For a given scattering angle it calculates the Mie scattered intensity(1) which depends on the droplet diameter, wavelength of light and the complex refractive indices(2) of the droplet and surrounding medium.  

The Mie functions for each scattered polarised light component are averaged to ultimately present a simulation as would be seen by eye or camera without a polarising filter. The average function is then weighted by the intensity of light actually present at the selected wavelength. When sunlight is simulated, the weighting function is the spectral solar radiance used by Raymond Lee(3) and kindly supplied by him in detailed tabular form for use in IRIS. The scattering results in Lee's paper were also used during the validation of the IRIS code.

   

Scattering angles

The whole calculation is repeated for a large number of angles over the range required for the fogbow or other phenomenon calculation.
   
   

   

Droplet size distribution

For non monodisperse droplets, IRIS uses a droplet population function lognormally distributed in radius. All of the above calculations have to be repeated up to 31 times over for the different droplet radii.

   

Wavelengths

At this stage IRIS has a series of scattered intensities for monochromatic light of the selected wavelength. The whole calculation is then repeated up to several hundred times for different wavelengths from 380 to 700 nm. A further small integration is needed if a solar or lunar disc source is to be simulated rather than a point.

   

Colours on screen

The accuracy of Mie theory is in contrast to the ability to represent colours of natural phenomena. Neither monitors, TV screens, photographs nor the printed page can accurately display all possible colours. In particular, no pure spectral colour is properly displayed. This is because of limitations of phosphors, pigments and inks and the limited number of them employed -- a mere three in PC monitors for example. The set of limited colours that ARE accurately displayed is the colour gamut of the display device. The problem is how best to approximate the non displayable colours, the out of gamut colours, using ones within the device gamut.

Further challenges are how to deal with issues of white balance, individual perceptions and the circumstances in which real droplet scattering phenomena are viewed. In contrast to rigorous Mie theory, colour representation involves empiricism and approximations and its perception is to a greater or lesser extent subjective.

IRIS has two colour models, "CIE" and "Bruton"

In the "CIE" model IRIS takes empirical CIE (Commission Internationale Eclairage - International Lighting Commission) 1931 tristimulus values for pure spectral components to weight the scattered intensities for a given wavelength. Final out of gamut colour components are approximated to in-gamut values by projective techniques. A Rec709 D65 monitor colour gamut is used with a 6500K white point.

The "Bruton" model is more straightforward. Dan Bruton(4) developed an empirical algorithm to generate in gamut RGB components that represent pure spectral colours. The algorithm produces very realistic spectra. In Bruton colour mode IRIS adds R, G and B components for each wavelength into bins to arrive at final RGB components for each scattering angle.

    Quality and execution time

The final simulation is the outcome of complicated Mie scattering calculations done for a whole range of different angle, droplet size and wavelength combinations. The fidelity of the result depends much on the way the various integrations over these parameters are conducted. IRIS has four different quality settings that balance accuracy against execution time. The highest setting produces simulations that are visually indistinguishable from those using even more precise integrations. Depending on the simulation type, this high quality setting might use several hundred different wavelengths and over 30 different drop sizes. The surprisingly large numbers of wavelengths or colours are sometimes needed because of the Nature of Mie scattering results: the intensities can ripple and fluctuate considerably with only very minor wavelength changes. This is not an artefact, it can be thought of as resulting from interference between different ray paths through (or reflected from) the droplet. The consequence is that broadband simulations require sampling at a large number of individual wavelengths.

 

Multiple scattering, cloud backgrounds

IRIS computes ideal glories, fogbows and coronae in the sense that the simulations correspond to what would be seen if each light ray reaching the eye had only been scattered once. In Nature, there is inevitably some multiple scattering and the phenomena are viewed against or through cloud or bright backgrounds. IRIS has a purely empirical facility to combine the simulation intensities with those of cloud background light. There are also standard image processor functions to adjust contrast, brightness or gamma. These are particularly useful for corona simulations where the tremendous brightness range between the aureole and outer rings is well beyond the puny 256 intensity levels of present day PC monitors.

   
(1)  The Mie algorithm is based on BHMIE by Craig Bohren and Donald R. Huffman in "Absorption and Scattering of Light by Small Particles", Wiley-Interscience (ISBN 0-471-29340-7).
   
(2)  Water refractive indices are from IAPWS (International Association for the Properties of Water and Steam) which are in turn based on P. Schiebener, J. Straub, J. M. H. L. Sengers, J. S. Gallagher, "Refractive index of water and steam as function of wavelength, temperature and density," J. Phys. Ch. R.,19, 677-717, (1990). The imaginary component is from Pope and Fry (1977). IRIS has several droplet substances and the user can add more.
   
(3)  "Mie theory, Airy theory, and the natural rainbow," Applied Optics 37, 1506-1519 (1998)
http://www.usna.edu/Users/oceano/raylee/papers/RLee_papers.html
   
(4)  Dan Bruton of Stephen F. Austin State University, "Color Science", http://www.physics.sfasu.edu/astro/color.html