Calculating tristimulus (XYZ) values from spectral reflectance or transmission data

Tristimulus.xls is a spreadsheet for calculating tristimulus (XYZ) values from spectral reflectance or spectral transmission data. The layout of the spreadsheet is based on Hunt, R. 'Measuring Colour' Fountain Press (1999).

It uses the CIE 1931 Standard Colorimetric Observer 2 degree colour matching functions, the values of which are alongside the corresponding wavelengths in column A (Note 1) and D50 illuminant. The ISO 13655 sheet premultiplies the illuminant data with the matching function data; the ISO cmfs are arrived at by a slightly different interpolation.

To use the spreadsheet, open it in a spreadsheet application such as MS Excel. You then replace the spectral reflectance data in column G with the values for the colour for which you want to find the tristimulus values or chromaticity coordinates. The XYZ tristimulus appear in cells F44-46. The corresponding chromaticity coordinates are also calculated and appear in I44-46.

The easiest way of using the spreadsheet is to capture the reflectance values from your spectrophotometer or spectroradiometer directly into cells G5-G40 if your instrument can be configured to do so. Alternatively paste the column of data into the cells.

You may find that your instrument gives reflectance data for a different wavelength range (e.g. 400-700nm). If this is the case, make sure that your data is entered into the cells corresponding to the correct wavelengths and the remaining cells are empty. Because the values of the matching functions are very low at the ends of the visible spectrum, this will not normally have a significant effect on the final XYZ values.

For a general explanation of the calculation of tristimulus values, see chapter 2 in Understanding Digital Color. For further detail on CIE colorimetry and the layout of the calculation, see Hunt (1999).

Adapting this spreadsheet

You can adjust the spreadsheet in the following ways:

The spreadsheet is copyright Phil Green and may not be transmitted or reproduced in any form without express permission.

Notes
1. The function values are linearly interpolated from the values for 5nm intervals defined by the CIE.
References
Hunt, R. W. G. (1999) Measuring Colour. (2nd edn) Tolworth, UK: Fountain Press