Originally Posted by EvLee
I think you are drawing the conclusion that 4.5907 cd/m2 of green has more energy than 0.0601 cd/m2 of blue by direct comparison of the numbers. This is not correct. Remember that cd/m2 is a measure of luminance, not radiant energy. In essence, that measurement already has the spectral sensitivity weighting built into it. You have to back out the luminous efficiency function, y(lambda), to find out how much energy is really in that particular blue. If you do that, you'll find that the blue light is not two orders of magnitude less energetic than the green.
yep, thanks for pointing this out. I ended up learning what the spectral luminous efficiency function - V(lambda) - actually was through the photometry chapter from McCluney. There was no hint of an explanation of it in Schanda's chapter, although it was referenced. Also pretty cool that Y(lambda) turns out to equal the same function.
It is interesting. Intuitively you might suppose that, with this efficiency function taken into account, you would need equal nits of red green and blue to produce a perceptual sensation of whiteness.
But perhaps it has more to do with the balance of actual photons. If you combine the luminance ratios they used to get white (1:4.5907:0.0601) with V(lambda)
, you can find out the radiance ratios they used to get white.
Original RGB primary wavelengths:R:
V(700) = 0.004102G:
V(546.1) = 0.978980B:
V(435.8) = 0.00334487 (this value and above through linear interpolation)
Luminance ratios to get white:R:
To get the radiance ratios, we divide the luminance ratio (R) by V(R), and luminance ratio(G) by V(G), and so on for B. (we need not divide by the factor of 683 to get radiance, since we're not interested in watts/m^2 but rather relative radiance).
1/0.004102 = 243.78G:
4.5907/.97898 = 4.689B:
0.0601/0.00334487 = 17.968
Let's normalize them so that the radiance ratio has R = 1:R:
So, when you ignore the fact that our eyes are more sensitive to green light, and are just interested in the relative amounts of raw power from each of the three wavelengths that are required to produce a sense of whiteness, you get 1:0.0192:0.0737 (R:G:B), or, very roughly, about 50:1:4
This means you need roughly 50 times as many photons of red light than you do green light to produce a sense of whiteness, and four times as much blue as you do green. So this resolves the apparent paradox I thought existed when I didn't take into account V(lambda) - thanks EvLee!
So what I think this tells us is that it's not about the balance of photons that produces white (the radiance ratio is not 1:1:1) , and it's not about the balance of stimulation that produces white (the luminance ratio is not 1:1:1). I think this suggests that whiteness, perceptually speaking, is not only about energy balance, whether that be radiant energy, or cortical stimulation "energy".