I would like to use the grey patches row of my X-Rite ColorChecker Classic to set correct exposure in post processing, but I can't seem to find the data for the chart on X-Rite website or elsewhere.
Are these values public ?
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The reference data contains the CIELAB data for the following colour rendition charts:
The formulation has changed in November 2014, so you must check which version of the chart you are using. Keep in mind that the pigments are stable only a few years, especially after long sunlight exposition, and that X-Rite recommends changing them every two years.
Note : according to the link in Kel Solaar's answer, these values are obsolete since they correspond to charts made before November 2014 and pigments are not supposed to be stable that long.