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Matrix-based color measurement corrections of tristimulus colorimeters



George P. Eppeldauer, Z. T. Kosztyan, J. D. Schanda


For image taking colorimetry the tristimulus technique is still the best practical method to keep the measurement time within reasonable limits. However, the achievable color measurement uncertainties for special sources can be significant because of the spectral mismatch errors of the realized colorimeter channels relative to the CIE standard color matching functions (CMF). The spectral mismatch errors of traditionally made tristimulus colorimeters cannot be decreased to the required small values because the number of both the available color filter types and the layers in a filter package is limited. The spectral mismatch errors can be high when measuring narrowband solid-state light sources, such as LEDs. In this paper, we investigated how these systematic errors can be significantly reduced using matrix-based color corrections for different light-source distributions. It is described how the matrix elements can be optimized to obtain the smallest spectral mismatch errors for different test light-source distributions. A possibility to decrease the systematic errors is to increase the number of the colorimeter channels used for a measurement, i.e. to use one or more additional channels in addition to the, X1=Xlong, X2=Xshort, Y, and Z channels. More filters can be utilized in the additional channels. It is discussed what the optimum/reasonable number of the colorimeter channels should be. A five channel tristimulus colorimeter has been designed and the optimum matrices for this arrangement were determined. The correction matrices were designed such that the spectral mismatch errors of the realized functions were minimized relative to the CIE standard CMF functions for several selected test-source distributions. The systematic errors were evaluated for a number of colored and white LED measurements. The noise propagation with the applied matrix corrections was investigated. The described matrix correction can be used in traditional and imaging colorimeters.
Applied Optics


colorimetry, detector-based colorimeter calibration, matrix corrections, tristimulus


Eppeldauer, G. , Kosztyan, Z. and Schanda, J. (2012), Matrix-based color measurement corrections of tristimulus colorimeters, Applied Optics, [online], (Accessed April 18, 2024)
Created April 20, 2012, Updated November 10, 2018