Correction measurement for tristimulus instruments (spot and video photometers)

Tristimulus instruments are often used for the chromaticity measurement of displays, projections and other colored scenes. An ideal tristimulus instrument can be described by the following formula in matrix notation:

(X_m, Y_m and Z_m – tristimulis values, F₁, F₂ and F₃ – signals from filtered detectors and C_ij – calibration coefficients)

Due to imperfect spectral matching of the three channels to the color matching functions (CMF) measurement errors occure, which rise with incrising spectral difference between calibration source and test source. It is possible to profile tristimulus instruments (both spot and video photometers) using spectroradiometers to give more precise results measuring RGB light sources. This is done with matrix methods and based on the fact, that the color of such sources is produced by a superposition of the three primaries (RGB). An easy procedure is described in [1]. A better approach is shown in [2]. The correction matrix is determined by the three primaries and their mixture (white). Furthermore this procedure is independent from possible variations of the luminance. The measuring results of the target and reference instrument for the primaries can be shown as follows:

Measuring instrument:

Reference instrument:

The k factors are relative factors for the measured luminance of each display color.
Due to the additivity of the tristimulus values and the measured white coordinates one can write

The same relation is valid for the white measurement with the reference instrument. All k values can be obtained from

and the similar equation for the reference instrument. Now the correction matrix R is calculated by

and each measuring result M of the target instrument can be corrected using

Afterwards the chromaticity coordinate is computed from M′.

[1] Standard Practice for Obtaining Colorimetric Data from a Visual Display Unit Using Tristimulus Colorimeters. ASTM E 1455-03
[2] Four-Color Matrix Method for Correction of Tristimulus Colorimeters. Ohno, Y., Hardis, J.: The fifth Color Imaging Conference. Color Science, Systems and Applications. p. 301