Question about Color blend mode

[J Isner]

According to Adobe

"Color mode creates a result color with the luminance of the base color and the hue and saturation of the blend color. This preserves the gray levels in the image and is useful for coloring monochrome images and for tinting color images."

This is exactly what I needed!  I have a grayscale (R=G=B) step table in Adobe RGB mode having 20 equal steps from K = 0 to K = 100. I want to colorize the step table but I do not want the grayscale (K) values to change. But if I add a Color Fill layer in Color Mode, the K values are NOT preserved.  Instead of 

0%   5%   10%   15%   20% ... 95%   100%

The corresponding eyedropper readings are

0%   4%   8%   12%   14% ... 93%   100%

Furthermore,  the Hue and Saturation of the result color is NOT the same as those of the blend color.  For a blend color of (120,100,100), the Hue and Saturation of the result color is

(120,0)   (120,12)   (120,24) ...

I suspect that Adobe's definition refers to the HSL model, rather than HSB, but I have no way of verifying that since the eyedropper doesn't offer HSL.

Since my results contradict everything in Adobe's definition, I must be doing something really wrong. 

Photoshop file attached.

[D Fosse]

RGB and grayscale numbers are relative to color space. K values are not fixed, but depend on the tone response curve of the grayscale profile used. In this case they will depend on whatever you have set as working gray.

It will be visually unchanged - which is exactly why the numbers change. With the same numbers, the visual appearance would change.

If you need stable numbers you should be working in Lab, which (unlike RGB) completely separates the luminance component from the color component.

[J Isner]

The document profile is Adobe RGB. The RGB working space is Adobe RGB and the Gray working space is Gray Gamma 2.2. 

When I'm working on this document, the eyedropper grayscale (K) readings have a fixed relationship to the Brightness values of HSB, specifically: B = 1 - K. For example,

I know that if the gray working space and the RGB space have different gammas, this relationship does not hold, although the appearance does not change.

My goal is to colorize a grayscale step table in such a way that the gray levels (Adobe's terminology) in the original table do not change.  The Hue and Sat may change, but the brightness is constrained to go in equal steps from 100% to 0% in steps of 5% (exactly opposite to the original grayscale values, which went from 0% to 100% in steps of 5%). That's all there is to it. This has nothing to do with human perception of tone. It's strictly a requirement that gray levels be preserved when the step table is colorized.

This is what I THOUGHT Color blend mode was supposed to do. If you read Adobe's definition, how could you come to any other conclusion?

[J Isner · Accepted solution]

I'm going to try to answer my own question. I just read Gimp's description of Color mode:

"This mode combines the foreground hue and saturation with the background lightness. Lightness ... is always a bit less bright than value. The expression for this blending mode is

R=[h(F),s(F),l(B)]

where h(F) and s(F) are the hue and saturation of the foreground, and l(B) is the lightness of the background.

------

Value is what Adobe calls Brightness in HSB, which some people write as HSV.  HSL is a different system from HSB/HSV, and the L of HSL is "always a bit less bright than value." In other words, gray levels are NOT preserved when when you colorize using Color mode. They are made "a little less bright." So instead of  the expected brightness values of

B = 0   5   10   15  20 ...

I get

B = 0   4   8   12   14

which seems quite a bit less bright to me! Anyway, mystery solved.  I can say that Color Mode does NOT preserve gray levels. It makes them "a little less bright."

I think I need a correction to scale the values back up from L to B.

[D Fosse]

I'd still say do it in Lab. You can always convert back to Adobe RGB when finished.

HSB/HSL are not defined color spaces and numbers are relative to everything else. They are just generic models to use within a given color space. Both depend on a formula for brightness that is undefined in terms of color spaces - just a ratio of R:G:B.

Lab has the special property that the luminance and color components are completely separate. IOW, when you change one the other is unaffected. That can never be true with RGB, where color is in fact defined by brightness in each color channel.

[J Isner]

What value would you specify as the solid color, such that when applied over the step table in Color mode, each cell of the result has the a and b components of the solid color and the Lightness of the underlying cell? I played around with this in Lab and couldn't get anywhere close to what I need.  For example, if done correctly, the white cell should be white, the black cell should be black, and the intermediate cells should be intermediate shades of green.

[Kukurykus]

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