We always measure the color difference by using d/8 spectrophotometer with included specular reflectance. But why do we always measure the white with excluded one?

I don't know. Normally an instrument will have calibration values for the standard for both specular included and excluded. A more normal procedure is to set up the instrument in the desired configuration and then calibrate with the tile.

It might be possible that your instrument can be calibrated in one geometry and used for measurements in the other, but I would encourage you to use the same setup for both the calibration and measurements if that is possible. More.

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