How can I convert CIELCH to CIE 1931 x,y coordinates?
The first step is to convert CIELAB L*C*h (there is no such thing as CIELCH) back to CIELAB L*a*b*. That is a simple coordinate transformation from the cylindrical coordinates (L*C*h) to the rectangular coordinates (L*a*b*). You will then need the CIE XYZ tristimulus values of the illuminant (which were used to compute CIELAB coordinates). With those, it is fairly straightforward to invert the CIELAB equations to compute the CIE XYZ values of your sample. From there you need to convert XYZ to xy in the normal way. All the necessary equations can be found in any good text on colorimetry such as Berns’ “Principles of Color Technology, 3rd Ed.
