## Abstract

A new calibration technique for improving the accuracy of chromaticity and luminance values obtained from a tristimulus colorimeter has been developed. Matrix manipulations similar to ASTM standard practice E 1455 are applied with a goal of minimizing the errors in x, y, and Y measurement, rather than those of the tristimulus values X, Y, Z. Correction matrices are determined from CRT colors, as well as CRT colors together with other light-source colors. 15 colors of a CRT and nine colored filter glasses are measured with a four-channel tristimulus colorimeter using such matrices. The matrix computed from CRT colors reduced CRT measurement errors to < 0.0011 in x, y, and 0.9 % in Y, and the matrix computed from both CRT and glass colors reduced errors to < 0.0025 in x, y and 0.7 % in Y for both CRT colors and filter colors. Both cases show improvement over current practice.

A Summary of Results is presented in Colorimeter Luminance Table. (PDF Format)

## 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, x(λ)y(λ)z(λ) (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 nine 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.

## Theory

A reference instrument and a target instrument are used to measure a set of sample colors (different colors on a display and/or a collection of colored objects). Internally, each instrument measures tristimulus values (X, Y, Z), from which chromaticity coordinates (x, y) are computed in the usual manner. The instruments then report x, y, and Y to the user.

The goal is to determine the nine elements of a correction matrix R¢ that the target instrument would use to transform an initial (X, Y, Z) into a corrected (X, Y, Z), which would then be used to compute (x, y, Y). The nine elements of R¢ must jointly minimize a variable q that is derived from all the measured samples and which is based on a difference metric relating an (x, y, Y) measurement by the reference instrument to the corresponding (x, y, Y) measurement by the target instrument (which includes the effect of R¢). For convenience, we used

s_{x} and s_{y} are the root mean square (RMS) differences between the reference and target x and y values, and sy is the RMS relative difference of the luminance (Y) values, which is the difference divided by the reference value. Relative differences are used in the latter to keep these terms to the same magnitude as the x and y differences. In this work, the weighting factor a = 0.1 . A computer program varied the matrix elements of R¢ until q was minimized.

By definition, the R¢ determined in this fashion gives the best calibration of the target instrument for the sample colors, no matter what their origin, with respect to the metric embodied in q. What needs to be determined is whether this R¢ remains the best, according to the same or some other metric, when a larger or different group of color samples is measured.

## Experiment

The reference instrument used in this work was a spectroradiometer comprised of a scanning type, double-grating monochromator in subtractive mode, that was equipped with imaging optics (with a viewfinder) which provided an acceptance angle of approximately 3°. Its three slits were adjusted to provide a triangular bandshape with 5 nm half-width. The scanning interval was matched to the bandwidth, which is an important requirement for accurate colorimetry.4 The relative spectral responsivity of the spectroradiometer was calibrated immediately before and after the measurements against two standard lamps traceable to the NIST spectral irradiance scale. The spectroradiometer measurements on the standard lamps reproduced to ± 0.0002 in x and y. The luminance of each sample color was also measured with a reference luminance meter of known spectral responsivity. The reference luminance values (Y) were obtained from the luminance meter values, which were corrected for the spectral mismatch of the instrument using the relative spectral power distribution of each sample color obtained by the spectroradiometer. The Y values obtained in this manner were more stable and reproducible than the Y values obtained from the spectroradiometer itself which employed a photomultiplier.

The target instrument was a four-channel tristimulus colorimeter. It incorporated four colored glass filters that essentially matched its detectors’ relative spectral responsivities to the CIE color-matching functions. (Two of the filter-detector combinations were used to construct the x(λ) function.) The input optics included a holographic optical element that distributed the incident light to the four filtered detectors. The colorimeter head was equipped with a suction cup, which both held the instrument to the CRT screen and shielded ambient light. The linearity of the current-to-voltage converters in the colorimeter were verified to be within 0.5 % across their full operating range.

A broadcast-quality color CRT was used in combination with a video signal generator. The CRT was selected for spatial uniformity and stability. After changing to a new color, the monitor was allowed to stabilize for » 2 min. The colorimeter was located so that it measured the same position on the CRT as the spectroradiometer.

Eight colored glasses were selected that fell within the CRT’s color gamut. They were backlit by a 200 W, frosted quartz-halogen lamp operating at 2856 K approximately 50 cm away. A plastic diffuser (165 mm square and 5 mm thick) was placed in front of the glass being measured. (A ninth case consisted of the diffuser alone, without a colored glass.) A kinematic base was used to reproducibly position the tristimulus colorimeter head very close to the diffuser for the measurement of the various glasses. A significant amount of interreflection between the diffuser and the colorimeter head was noted. This caused the luminance of the diffuser, as measured by the colorimeter, to be 10.6% higher, on average, than the corresponding measurements made by the spectroradiometer. For the purpose of combining colorimetric measurements of the colored glasses (and diffuser) with those of the CRT, we have reduced the glass measurements by this factor to account for this effect.

To eliminate the effects of ambient light, all measurements were taken in a darkened environment. Measurements took place with each instrument sequentially. The spectroradiometer scan required »10 min; the tristimulus colorimeter gave results in < 1 min. The luminance for each color was recorded before and after the two measurements. When the two luminance values varied by more than 0.2 %, the measurements were repeated.

## Results

The Colorimeter Luminance Table shows a summary of the results. The first column lists the 15 CRT colors and 9 filter colors measured. The second column contains the colorimetric information measured by the reference spectroradiometer and luminance meter. The third column compares the readings of the tristimulus colorimeter to the reference spectroradiometer before applying any matrix corrections. The colorimeter readings are based on a calibration using the first CRT color (white). The chromaticity differences for some colors exceed 0.010, and the luminance differences range over several percent.

Three different R¢ matrices were computed. The first was computed following the procedure given in ASTM Standard E 1455-92. The first eight CRT color measurements were used as the input data. The second R¢ matrix was computed using the same eight CRT colors as the sample colors, but following the procedure introduced in this work, above. The third R¢ matrix was computed similarly using the first four CRT colors and the first four glass-filter colors (including that of the diffuser alone).

The next three columns in Table 1 show how the differences between the reference and target instruments narrow for the three R¢ matrices. In each column, one of the matrices is applied to measurements of all the CRT colors and the glass-filter colors. For the CRT measurements, the results are summarized in two ways: the differences including those samples that went into the computation of R¢, and those excluding those samples. For the filter-glass measurements, the summary includes all 9 samples. In each case, the RMS and maximum differences are shown.

The results show that all three R¢ matrices provide significant improvement in the operation of the tristimulus colorimeter. The measurements of the filtered-glasses also improved with the two R¢ matrices that were based solely on the CRT measurements. In these two cases, for the CRT measurements, the RMS differences in x, y were all £ 0.001. The new minimization technique (column 5) is seen to yield better results than the ASTM formula (column 4). Additional analysis shows that much of this improvement with the minimization in (x, y, Y) space arises due to common mode noise in the (X, Y, Z) values of a single measurement (e.g., from display flicker). The data in the last column show a good compromise between improvements in the CRT measurements and improvements in the measurements of the colored glasses.

## Conclusion

These initial data show that a matrix transformation based on an (x, y, Y) difference metric may improve the calibration accuracy of a tristimulus colorimeter for these measurables (chromaticity and luminance), as compared to the current standard for display measurements. The data also show that the technique works well with other light sources.

While this work to date has produced a limited amount of data, the technique that motivated it is clearly shown to hold promise in some situations. More experiments are necessary using different colorimeters, displays, and other colored samples. It would be interesting to experiment with other difference metrics, such as those based on a uniform color space or standard color difference equations.

The authors thank Ed Kelley of NIST for providing the color monitor for the experiment and for discussions. This work was conducted under a Cooperative Research and Development Agreement between NIST and UDT.

## The Authors

C. Leone, S. Sojourner, E. Vargas, UDT,Orlando, FL

C. Cromer, Y. Ohno, J. Hardis, NIST, Gaithersburg, MD

## Additional Colorimeter Resources from Gamma Scientific

- SLS 9400 Colorimeter Product Page
- SLS-9400 Colorimeter Data Sheet
- 11 Reasons to Upgrade Your Colorimeter
- What is Colorimetry?
- What You Need to Know About Display Calibration
- Key Concepts in Monitor Calibration

## References

1. CIE/ISO 10527 Standard Colorimetric Observers (1991).

2. Wagner, H.G., Farbmessungen an Fernseh-Farbbilddröhren nach dem Driebereichsverfahren,” Farbe 22, 31-43 (1973).

3. ASTM E 1455-92 “Standard Practice for Obtaining Colorimetric Data from a Visual Display Unit Using Tristimulus Colorimeters,” ASTM Standards on Color Appearance Measurement, 4th Ed.

4. IES LM-58-1994, IESNA Guide to Spectroradiometric Measurements.

Reprinted with permission, SID 96 Digest.