Adjust colour by mired

Well, my point was that if you use polarizers/cross-polarization, micro-shifts in color balance is the least of your problems. The changes in contrast curve and saturation are a much more urgent problem.

I suppose this boils down to two different philosophies in reproduction of art. Out front, my own experience is that micro-correcting to a perfect colorimetric match simply does not look right in the end. It does not look like a faithful reproduction, and the reason is probably differences in how the eye/brain processes visual information. Matching a single color is easy, but as complexity grows, it starts to fall apart.

There is also the output medium to consider. For print, the paper and process superimposes a limited dynamic range that needs to be compensated.

What I aim for is equivalent color. In short, if it looks right, it is right. I trust my eyes. It helps that I have five years art academy education, so I know and recognize how pigments and materials behave.

So, in summary, I've probably excluded myself from this discussion. I do not accept the basic premises 😉

Thank you for the extra insights.

I am trying to create archive images of C19th prints at high resolution.

I am likely to be using Lee 239 polariser which has a published lumpy transmission curve

Obviously this will cause colour shifts across the whole spectrum and lightness.  The mired shift is single number which provides a compromise adjustment, and its calculation itself has number of compromises and assumptions.

So far better than using mired shift, the image should be calibrated across the (chosen) 3D colour space, presumably AdobeRGB since that it what this software defaults to.

I have two colour targets: an ISO 12641-2 (measured) and an ISA Golden Thread (off the shelf). 

But I have not found a way to get images of these targets with their associated data into Photoshop then create a calibration matrix (for each photographic setup).  This would be used to adjust the object's image pixel AdobeRGB values.  The  increase in available computing power would mean that these calculations should be fairly quick.

I have not found that neutral density patches provide decent calibration even between neutral density patches, still less colours, possibly because the camera sensors' responses are both not linear and not matching, just like eyes.

Just so we're all on the same page: mired is a unit for indicating color temperature shift, as the inverse/reciprocal of the Kelvin scale. It's a different way to express Kelvin values, in a way that makes it linear and evenly scaled so that it's easier to compensate a temperature shift.

So far so good. However, there is a fundamental problem here.

Color compensation needs to observe two dimensions, two axes, not just the blue-amber axis (K), but also the green-magenta axis. A color cast in a filter can be along either or both of these axes. Focusing only on one misses the other. Whether Kelvin or mired, it is only applicable to a series of dedicated temperature-compensating gels. It is not applicable to, say, a polarizer which is supposed to be neutral along both axes.

As you say yourself, the color of the light in the original scene cannot be known. As such, the only way to neutralize color is to make sure R=G=B in any patch that is supposed to be neutral. The concept of temperature is meaningless in a rendered finished image; it only applies to the original scene. So there is no temperature correction in Photoshop. It wouldn't make any sense.

(There is one in Lightroom/ACR, as a scale for compensating the original scene lighting, expressed rather arbitrarily in Kelvin numbers. But that's just an approximation and shouldn't be misinterpreted as "absolute" numbers.)

I've been working as a photographer at an art museum for over 20 years. Polarizers do a lot of things that need to be compensated, if the result is supposed to match the visual perception. Notably, they steepen the tone curve and increase saturation. Any color cast is corrected as part of the same process. You need a set of neutral patches with standardized Lab numbers to compensate for this, such as a common color checker chart: