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September 17th, 2010, 02:00 PM
 Doug Kerr Senior Member Join Date: May 2006 Location: Alamogordo, New Mexico, USA Posts: 8,519
"Amounts" of the RGB primaries

For today's technical lecture, I have chosen a topic I hope has no possible practical application to photographic practice and technique.

**************

In color spaces of the RGB family, we describe a color in terms of the amounts of three "primaries" - light of three different specified chromaticities - that are to be combined to produce the color of interest.

But we might wonder what is meant by amount? Is it in volts or gallons? It's a thing that is never revealed, even in complicated discussions of color spaces. The authors assume that we just know - and they probably have no idea. The guys that really know are dead.

We might guess that the amount would be defined in one of these ways:

• As the "luminance" of the primary ingredient

• As the "power" of the primary ingredient
I have put "luminance" in quotations since, depending on what physical aspect of the primary "light ingredient" we visualize, the actual quantity might be luminance, or illuminance, or luminous intensity, or luminous flux, or luminous flux density. But because we aren't actually measuring a physical "light ingredient', but rather working with an abstract concept, it doesn't matter. And in such cases, we use luminance as a proxy for whatever photometric quantity might be involved.

The same is true of "power". In a physical case, we might be actually interested in power, power per unit area, power per unit solid angle, or power per unit solid angle per unit area (these all have radiometric names). But I'll use power to mean any or all of those radiometric quantities.
It turns out, however, that it is neither of those. The "unit" of amount of a primary is a unit that is defined, arbitrarily, for each primary in the specific color space, defined in terms of its luminance. (That is of course a relative luminance; in none of these cases are we working with absolute luminance.) And of course, that also implies a power for the unit, since, for any given spectral distribution of light, there is a direct relationship between power and luminance.

Well, how is that different than giving the amount in terms of luminance, or power? Because the unit represents a different luminance, and a different power, for each primary, for each color space.

So if our "recipe" for a color, in the sRGB color space, is r=0.5, g=0.5, and b=0.5 (the lower case letters here imply "linear" measures of the amount, rather than the nonlinear measures we have in the color space coordinates, R, G, and B), it implies primary ingredients with relative luminance of 0.106, 0.358, and 0.036, respectively.

However, it turns out that stating r, g, and b in terms of those three different "units" is not very different from stating them in terms of power - just not quite the same, nor defined as such.

Why did the wonks that defined these color spaces not choose to define the amounts of the primaries in terms of their "power" (they almost did)? Because for each color space, the wonks chose a specific chromaticity to be the white point, and decreed that any color for which r=g=b shall have that chromaticity. Well, that won't happen (except maybe by accident) if the values of r, g, and b are stated in terms of power.

So they chose "units" for r, g, and b such that if r=g=b, the chromaticity produced is that already chosen for the reference white for the color space.

How are the values of those "units" stated in the color space specification? In terms of the luminance corresponding to one unit (different for each primary)!
Mea culpa: in a series or articles on color spaces in this forum in 2006, I said that the values of r, g, and b are in terms of power. I was in error.
Best regards,

Doug

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