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.
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
The whole calculation is repeated for
a large number of angles over the range required for the fogbow
or other phenomenon calculation.
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.
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.
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
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
IRIS has two colour models, "CIE"
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
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
scattering, cloud backgrounds
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.
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).
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.
theory, Airy theory, and the natural rainbow," Applied
Optics 37, 1506-1519 (1998)
Bruton of Stephen F. Austin State University, "Color Science",