I was curious about which values are valid in the CIELAB color space. The lightness coordinate, L, is defined to range from 0 to 100, but the chromaticity coordinates, a and b, have no defined bounds. So I wrote a program to find which CIELAB coordinates can be created physically.
Each wavelength of light produces a well defined color that be found in a table. But as most colors are a combination of different wavelengths, you need to solve a number of equations to find which wavelengths that are needed to create that color. This can be modeled as a Linear Programming Problem. A color is physically possible if the Linear Programming Problem has at least one solution.
I ran the program to create images of the a and b plane for a given L-value. The Physically reproducible colors are drawn in a light gray color, and if the color is whithin the sRGB gamut, it is drawn as is.
|L* = , a* ∈ [-128, 128], b* ∈ [-128, 128]|
©2017 Mats Mattsson