Optical - How do I calculate CIEx and CIEy from an SPD?

Calculating CIEx and CIEy is a fundamental starting point for more advanced colorimetric calculations.  It is actually a simple process if you have access to an SPD and the tabulated tristimulus functions.

The CIE 1931 color space uses the coordinates CIEx and CIEy.  The “horseshoe” is constructed using monochromatic SPDs for each wavelength in the visible spectrum. The interior of the horseshoe contains all of the colors that can be perceived by a Standard Observer’s eye response which were determined experimentally in the in the late 1920s.

The calculation is as follows.

After calculating X, Y, and Z, the coordinates CIEx and CIEy are simply

The attached Excel file contains the Standard Observer Functions interpolated to 1 nm increments, an example of the calculation, and a few reference SPDs.

Different SPDs having the same chromaticity coordinates are said to be metameric. Even though for each spectral power distribution there is one corresponding point in the chromaticity diagram, the reverse is not true—for most points in the chromaticity diagram, there are many possible SPDs that have exactly that same chromaticity.

Luminus provides SPD files on request. Email a request to [e-mail].

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