Matrix-based color measurement corrections of tristimulus colorimeters.

For colorimetric imaging 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 large. It is described how the systematic errors can be significantly reduced by using matrix-based color corrections and how the matrix elements can be optimized to obtain the smallest spectral mismatch errors for different light-source distributions. An approach for decreasing the systematic errors is to increase the number of the colorimeter channels (or filters) used for a measurement. Using five channels in a colorimeter is an optimum choice. Determination of the optimum matrices for the five channels is discussed. The correction matrices are designed such that the spectral mismatch errors of the realized functions are minimized relative to the CIE standard color matching functions for several selected test-source distributions. The optimum matrix depends on the (test) light source to be measured. Adaptive matrix values are determined by using the channel outputs and the spectral power distribution of color LEDs approximated with a simple approximation function. The systematic errors are evaluated for a number of colored and white LEDs. The noise propagation with the applied matrix corrections is investigated.