My densitometer shows the values for red, green and blue but not the integrated value for black resp. gray. How can I calculate it from the three other values?
On most of the reflection densitometers I worked with there was a yellow filter for reading just the gray scale or black portion of colored copy I suspect the filter was to compensate for the color of the light bulb in the pickup head. If you are using a transmission densitometer I would imagine there is a similar setting on the head for the same purpose, there was on the ones I used. As we had to read the separation negatives to calculate screening exposure.
I have a X-Rite 361T which has ortho and UV settings so I haven't done that much research but I remember reading Bob Herbst's paper "A Densitometer for Reading Pyro Negatives" and he claimed that the difference between his X-Rite 820TR's Green channel and the 361T's ortho channel was within 0.02. You might search for his paper online. His interest at the time was in scanning Pyro negatives at UV but his comparison between the RGB and Ortho densitometers was enlightening to me.
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