Introduction
Tristimulus colorimeters are used extensively in manufacturing and testing of CRTs, as in-process and performance verification tools. Tristimulus colorimeters are often preferred to spectroradiometers because of their lower cost and ease of use, though they are usually less accurate. Tristimulus colorimeters employ broad-band filter-detector combinations, the spectral responsivities of which are approximated to the CIE color matching functions, (see footnote 1)
  
In such broad-band measurements, due to the imperfect realization of the filter-detector responsivities, measurement errors are inevitable when the spectral power distribution of a test source is dissimilar to that of the calibration source. Tristimulus colorimeters and luminance meters are often calibrated with CIE Illuminant A (2856 K Planckian source), and thus, inaccuracies can occur in color CRT measurements.
Matrix techniques have been known for over 20 years
to improve the accuracy of tristimulus colorimeters for
CRT measurements, utilizing the fact that colored light
produced by a CRT is a linear superposition of the spectral
power distributions of three primaries.² For
example, ASTM Standard E 1455-92³ concerns the transfer
of calibration from a reference instrument (which reads
the tristimulus values X, Y, Z for a test patch on a display)
to a target colorimeter (which initially reads Xm, Ym,
Zm for
the same test patch). Its goal is to derive a correction
matrix that transforms Xm, Ym, Zm values
into better agreement with the reference values.
Two cases are given in this standard. Case 1 assumes that the reference instrument, target instrument, and display screen act ideally. In this case, only three test colors (such as red, green, and blue on the CRT) would be needed to derive a correction matrix for the target instrument, which is referred to as the R matrix. Not only does the R matrix allow the target instrument to express tristimulus values exactly (with respect to the reference), but all values derived from the tristimulus values, such as the chromaticity coordinates x, y, would agree exactly between the two instruments as well (at least when measuring a display of that type). Case 2 allows for measurement noise and other imperfections, and therefore, instead of using just three colors, the correction matrix (referred to as the R¢ matrix) is derived from at least eight different colors using least-squares data fitting.
This ASTM standard restricts the use of the method to color displays consisting of three primaries, and warns that the correction matrix thus obtained is valid only for the particular display type for which it is determined. If different types of displays using different phosphors are to be measured, correction matrices for each type of display must be prepared.
While the R¢ matrix in the ASTM standard minimizes the differences between the corresponding tristimulus values, it does not necessarily minimize the differences between values derived from tristimulus values, such as chromaticity x, y. Another way to derive the R¢ matrix is to minimize the measurement differences in chromaticity coordinates rather than tristimulus values. This method requires an iterative solution to the problem of finding the optimum R¢ matrix, since there is no longer a closed form solution. An additional feature of this method is that other types of colored light sources (which are not linear superpositions of fixed primaries) can be included in the determination of the R¢ matrix.
To evaluate the new technique, experiments have been performed with a four-channel tristimulus colorimeter and a reference spectroradiometer measuring colors on a CRT and 9 colored glasses backlit by an incandescent lamp. Correction matrices are computed that minimize differences in x, y, and Y, rather than the tristimulus values, for sets of sample colors. The evaluation is not restricted to CRT colors in these calculations, to see how the inclusion of data from the colored glasses changes the results. |
