Thanks Bill. Can you show me how to convert the R,G,B value of 117,117,117 to a density of 0.75?
Hi, first realize that the conversion to density is only legit because we think there is a flat spectral reflectance curve, otherwise...?
To get there from RGB numbers, there must be a known color space assigned, otherwise the RGB numbers don't have a firm meaning.
The easiest way is to use an online calculator, such as found on the excellent (and never wrong) website brucelindbloom.com. Start with the "calc" button, then the "CIE Color Calculator." Near the bottom, select the appropriate "RGB Model" (for the example I used sRGB, but you need to use the specific one that your data is in). Also, check the box, "scale RGB" to allow direct entry of your numbers.
Next, in the RGB row, enter your numbers, 117, 117, and 117. Then click on the RGB button at the beginning of the row - this will populate everything in the grid.
Now, there's no direct link to density, but the top row - "XYZ," uses linear data, normalized to a 100% reflective scene element. It's based on either 1 or 100, depending on whether you checked the "scale..." box. Now, when the CIE (International Commission on Illumination) set the imaginary "primaries" they made the "Y" correlate to the human sense of luminance, which is why I used it. I rounded it to 0.18, but it should display to something like 0.177888. Anyway, you should see it as rough equivalent to 0.18 reflectance.
Finally, to get from 0.18 reflectance to density (associated the neutral image with flat spectral response) convert according to the definition. It's something like density = the inverse log of transmission (or reflection). Without verifying (like I normally would do, but not today) I think you would raise 10 to the power of the density, and then invert that number to get reflectance. To crosscheck, a density value of 0.301 should reflect 50% (rounded) of the light, and density of 0.602 reflects ~25% of the light. (To get from reflectance to density, reverse the flow of the math.)
I'm speaking strictly off the top of my head, so if anything disagrees with the formal literature, I'm sure I would be the one in error, but please raise the question.
For the most part it's not a good idea to try to correlate a densitometer reading to these colorimetric data, except in limited cases.