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
sx and sy 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. |
