So I've been doing some more reading, and I'm revisiting the assumption that the spectral signature of the display will have an interaction with the accuracy of any given colorimeter.

Schanda cites the three empirical laws of color matching (in the context of additive mixtures). In particular, notice the second:

**"For an additive mixture of color stimuli, only their tristimulus values are relevant, not their spectral compositions."** (p 27).

In 1915, Herbert Ives wrote a paper titled: "The Transformation of Color-Mixture Equations from one system to another", showing how if you know the tristimulus values, as measured by tristimulus device A, of the primaries of tristimulus device B, then you can mathematically derive the linear transformations necessary to compute (rather than empirically measure) the color matching functions of device B, across the entire visible spectrum.

This property, in effect, is what allowed the derivation of the XYZ color matching functions, based off of the empirically based R G B functions.

So, as long as the transformations between two color spaces remains consistent (i.e. no drift), then it follows that for any given (visible) spectral source, one can derive the color matching functions for any given tristimulus device, so long as we know the mapping functions between that device and a reference device.

According to the x-rite

white paper:

Quote:
The only difficulty with the production of an XYZ colorimeter is the filters. The XYZ response curves are complex. In order to create these complex filters, many separate filters must be stacked together to achieve the final curves. The filters achieved are never perfect matches to the XYZ curves. However they don’t need to be. By calibrating a colorimeter at the factory against reference sources, a mathematical correction called a “calibration matrix” is stored in the colorimeter. This corrects the minor errors that are introduced by inaccuracies of the filters. This does not create a device that can measure “any” color with perfect accuracy. **Instead a colorimeter of this type will produce very accurate results from most sources. Certain sources that have very narrow bandwidths like lasers will not be as accurate.**

Notice the bolded part. My take on this is that lasers, being so narrow, provide a low signal to noise ratio.

However,

*assuming* that the tristimulus device in question was

*perfectly* characterized (i.e. we knew exactly how it mapped onto a set of reference color matching functions), and had an arbitrarily high signal to noise ratio, it wouldn't matter what the color matching functions were on that device! In other words, the validity of such a device would not depend on how close the filters matched the XYZ reference functions, but rather on how well characterized the particular filters were.

At least this is my tentative understanding.

So why the need for different calibration matrices depending on the display source?