General solution to the calculation of peak luminance of primaries in multi-primary display systems

For a display system, a wide-color gamut can significantly improve the viewing experience. It is known that an ultra-wide color gamut can be achieved using more primaries. However, for multi-primary displays (MPDs), choosing the parameters of the primaries (e.g., wavelength and luminance) is not trivial because the necessary theoretical foundation is still lacking. In this study, starting from three-primary display, we proposed a method for calculating all possible peak luminances of MPDs. This is done by mathematically representing the added new primaries with the original three primaries. Of all the possible results, by optimizing the peak luminance of each primary color, the theoretical gamut volume satisfying specific requirements could be obtained. The method provided can be extended to N primaries (N > 6). Using this method, we have successfully built a six-primary display system and used it to verify the validity of the method. Combined with the calculation of color gamut volume, the theoretical framework provided can be used to guide the selection of wavelength, spectrum width, and luminances of primaries in MPDs.