Help for SPECTOXYY

PURPOSE
Spectoxyy converts up to 10 registered multispectral images taken through
narrow band filters and either in units of spectral radiance or in
units of spectral reflectance and converts these into three images
representing x and y chromaticity coordinates and Y tristimulus.

EXECUTION EXAMPLES:
spectoxyy inp=(in1,in2,in3,in4) out=(x,y,Y)    convert=(.0001,.0001,.0001,.0001) lamda=(460,540,590,630)    illumin=SUN mode=REFLECT
or
spectoxyy inp=(in1,in2,in3,in4) out=(x,y,Y,hist)    convert=(1.,1.,1.,1.) lamda=(460,540,590,630)    illumin=D65 mode=RADIANCE

Note: "hist" is a 2 dimensional histogram of the chromaticity space.
The x and y axes pass through (0,0) and the diagonal passes through 
(0,1) and (1,0). The enclosed triangle contains the valid chromaticity
space. Each pixel or bin contains the log of the accumulated counts
falling on that location. Horizontal is x and vertical is y.

WRITTEN BY: 		J Lorre 5/23/96

THEORY:

Colorimetric units of xyY are obtainable from an input spectrum by
integrating the spectrum with color matching functions. 

If S is the radiance spectrum of the target,
   R is the reflectance spectrum of the target,
   I is the illuminating spectrum,
   Cx is the x color matching function, 
   Cy is the y color matching function, 
   Cz is the z color matching function, 

then one can compute tristimulus values Tx,Ty,Tz from:
   Tx=k*sum(S*Cx) radiance
   Ty=k*sum(S*Cy)
   Tz=k*sum(S*Cz)
or
   Tx=k*sum(R*I*Cx) reflectance
   Ty=k*sum(R*I*Cy)
   Tz=k*sum(R*I*Cz)

where k=100/sum(I*Cy)

Then x=Tx/(Tx+Ty+Tz)
     y=Ty/(Tx+Ty+Tz)
     Y=Ty

I is corrected for the distance of the target (RANGE keyword) from the sun
by dividing it by 1/(RANGE*RANGE), RANGE is in AU.
Notice that in reflectance mode the sun distance is ignored.

ILLUMINANTS:

You have a choice of two illuminants. These are:
1. D65 which represents a 
daylight spectrum on Earth with direct filtered sunlight and blue sky
scattering, and 
2. Unfiltered sunlight above the Earth's atmosphere.

With these you can reconstruct the color of a scene as it appears on Mars or
as it would appear on Earth (even if it isn't).

IMPLEMENTATION:

The program steps are as follows:

1. Reorder the input files into ascending wavelength order.
2. For each pixel:
3.	Compute the second derivative spline coefficients for interpolation.
4.	Loop on wavelength from 380 to 780 nm by 10 nm intervals.
5.		Interpolate spectrum amplitude.
6.		Integrate spectrum with color matching functions.
7.	Get x,y,Y
8.	Update 2-d chromaticity space histogram (option).
9. Write log of histogram.

Warning 1: There is no colorimetric absolute for Y tristimulus value.
Data typically ranges from 0 to 100, 100 being for a perfect Lambertian
surface. Calibrated devices expect
to see Y on the order of 10 to 90 or so. If your outputs for Y are wildly
far from this (like 20000 or .0003) then the display device cannot 
represent them. You can adjust your output using the CONVERT parameters, the
RANGE parameter, or just multiply the Y image by a constant. 

Warning 2: This program takes the highly unusual step of adjusting the D65
spectrum to match the solar spectrum above the atmosphere at the 780 nm
point. This is to help to get reasonable Y tristimulus values in the radiance
mode should you wish to use D65.