Help for TRISTIM

"tristim" is a Vicar applications program that will calculate the tristimulus
values and chromaticity coordinates for a given spectrum, which may be of
intensity, reflectivity, or transmittivity. Tristimulus values and chromaticity
coordinates are quantities which must be known to do color reconstruction.  
For a complete discussion of colorimetry, see Reference 1.
 
EXECUTION:

tristim PARAMS

where PARAMS are parameters listed in Tutor mode.  (There are no input or
output datasets.)
OPERATION:
 
"tristim" computes tristimulus values for a spectrum by the formulas:
 
  X = k * SUM( F(i) * x'(i) )
  Y = k * SUM( F(i) * y'(i) )
  Z = k * SUM( F(i) * z'(i) )
 
where:   X, Y, and Z are the tristimulus values,
 
         F is the input spectral distribution of intensity, reflectivity,
         or transmittivity.
 
         x', y', and z' are the C.I.E. standard colorimetric observer
         values, also known as the color matching functions, optionally
         weighted by a specified illuminant,
 
         and i is the wavelength.
 
The sums are taken from i = 380 nm to 770 nm.

The constant k is defined by the relation:

                    100
         k = -------------------
             SUM( S(i) * y'(i) )

         where S(i) is the spectral radiance of the illuminant.
 
For standard illuminants D55, D65, D75, A, B, and C, the color matching
functions have been weighted by the relative spectral power distributions
of these illuminants in such a way that k=1.  The XENON illuminant
weighting functions have also been computed so that k=1.  However, XENON
is not a standard of the C.I.E. and refers only to the JPL 12-inch light
cannon on 13 April 1976 (see Reference 2).
 
If the user is using some other illuminant, k will have to be computed
separately.  This can easily be done with another execution of TRISTIM,
inputting the spectral radiance of the illuminant for the 40 radiance
values, and then taking the ratio of 100 and the Y tristimulus value.
 
"tristim" also outputs the chromaticity coordinates of the spectrum in
question.  These are related by the equations:
 
          X                  Y                  Z
    x = ----- ,        y = ----- ,        z = ----- .
        X+Y+Z              X+Y+Z              X+Y+Z
The user-supplied input spectrum (RADIANCE) may be specified as a multiple 
of up to ten separate spectral distributions, of exactly 40 points each 
(R1,...,R400). This can represent a series of filters through which light 
passes.
 
The RADIANCE values R1,...,R40 can also be modified (for whatever reason) 
by the equation:
 
   NEW_RADIANCE(i) = Ri * MULT + ADD

where MULT and ADD are the values specified for the parameters of those
names.
In addition, the user may specify Continuum and Background spectra, CONTIN
and BACK, which will be applied to the input spectrum according to the
following formula:

                        (Ri - BACK(i))
   NEW_RADIANCE(i) = -------------------
                     (CONTIN(i) - BACK(i))

This can be useful to process spectrophotometric tracings of inputs in
certain colors and of a white reference input.
REFERENCES

1. Judd, D.B., and G, Wyszecki, "Color in Business, Science, and Industry",
   Third Edition, 1975, John Wiley and Sons.
 
2. JPL IOM 26 April 1976, To: L. Snyder, From: M. Benesh, New Photometric
   Characteristics of 12" (30-cm) Light Cannon No. 1.
 
 
TIMING
 
TRISTIM takes about 4 CPU seconds to run.
COGNIZANT PROGRAMMER
 
Written by:  Joel Mosher,  1 Oct. 1977
 
Converted to VAX by:  L. W. Kamp,  10 Jan. 1984
 
Current Cognizant Programmer:  L. W. Kamp

Made portable for UNIX   Alan Scop (CRI) 2 May 1994