The part where he takes the human sensitivity into account has grabbed my attention. It looks a little suspicious to me the way he simply just multiplies the normalized relative sensitivity measure with the spectral fluxes.
The way it is calculated now, the only way for a spectral flux (SLF) to be optimal considering its spectral luminous flux (LF) is to be entirely concentrated at ~550nm, laser-like. However, such a light would leave many of the cones in our eyes unsatisfied, hinting that this shouldn't really be the optimal.
I am by no means an expert, but I would expect a LF to be optimal when it matches the relative human sensitivity in shape, instead of the one focused as an impulse at the peak of the relative human sensitivity.
> It looks a little suspicious to me the way he simply just multiplies the normalized relative sensitivity measure with the spectral fluxes.
What is suspicious about it? This is how all response functions work mathematically, both for humans and animals, as well as for mechanical sensors.
The response function is the measured ratio of the input value to the output response (for a given wavelength in this case, but it could be for any measurement at all.) Because it's a ratio, simulating the response is a multiplication, no other operation will be correct.
> I would expect a LF to be optimal when it matches the relative human sensitivity in shape
Arriving at that idea does make some intuitive sense, but it would not be optimal. For the best possible response, you'd put all your energy into the maximum of the response function and nowhere else.
Imagine you could bet on a coin toss where the coin is known to land on heads 2/3rds of the time and tails 1/3 of the time. You can guess the tosses in advance, and for every correct guess you win $1. Should you bet on heads 2/3rds of the time and tails 1/3rd of the time, because that matches the roll probability? Or should you bet on heads all the time? It's simple to show that always betting on heads will net more money, statistically speaking.
An analogy of filling a curved-bottom tub would be a better fit than of someone making bets optimally when the chances are non-uniform. Our cones can be stimulated only up to some certain amount. At the point of saturation, any further stimuli would have no effect, other than perhaps frying the receptors.
I would also suspect that the receptors are becoming less and less sensitive to the stimuli they accept as they get closer to saturation, making the relation non-linear, and shaped more like a saturation curve.
If that really is the case, then a LF really would be better off if it was more bell-shaped and wide as the relative human sensitivity, than being an impulsive one at the peak. It would be like that because as the LF starts doubling down on the highest bid (~550nm), the marginal response other wavelengths would start becoming more viable, eventually taking 550nm off the first place.
There also is the possibility that the author has done his research well before spending so much effort on preparing the article. Even then, this could be the reality that we are yet to discover.
You're right that once you saturate your green cones, the marginal response of other wavelengths will overtake 550nm. But until you hit saturation, the most efficient use of energy is to put everything on 550nm, not spread it out. You're saying that changing the response curve (e.g. by saturating the green cones) changes the optimal wavelength, but that doesn't change the fact that there's always a single optimal wavelength that is the argmax of the current marginal response curve.
In any case, we're talking about displaying color on computer monitors here. If your computer monitor is getting anywhere near saturating your cones, you have a big problem.
> An analogy of filling a curved-bottom tub would be a better fit
No, it would not. That rationalizes your concept of trying to match the input distribution with the response function, but it is specious and incorrect to apply it to a response function. Filling a tub with liquid allows liquid in one place to move to another place. Light doesn't work that way, light at 550nm doesn't spill over to 600nm. The incoming light at 550nm is completely accounted for in the output response, and doesn't affect the response at 500nm or 600nm, and isn't affected by input at 500nm or 600nm.
The response function is literally an efficiency curve. If you want maximum efficiency or maximum output, you give it inputs that land at the apex of the efficiency curve.
> I would also suspect that the receptors are becoming less and less sensitive to the stimuli they accept as they get closer to saturation
That is correct, but outside the bounds of what this article is discussing. For all practical normal daylight situations, which the range of all monitors lands inside, response is roughly logarithmic (or linear on a log scale). Clamping or saturation in the response happens in extreme darkness and extreme brightness. Response to the night sky in between stars, or to staring directly at the sun have a non-log. Response to computer monitors and almost everything you see during the day is linear on a log scale.
> If that really is the case, then a LF really would be better off if it was more bell-shaped
It's extremely unlikely that there's any real-world scenario under which this is true. But if you want to do this thought experiment, then you need to account for the receptors saturating. If you push the receptors to saturation, then their entire response goes flat, changing the overall shape of the response function. By matching the shape of the response function and then saturating, you force your target to move, and then get the wrong answer anyway.
If you push one receptor to saturation, the next best answer would be to put the remaining portion of your power distribution at the apex of response sensitivity for the other two receptors, so you'd have three specific wavelengths, but not a bell shape.
Look specifically at figure 242. Monitor level brightness response is very near the center-line (vertically) in the chart. All normal daylight conditions are represented between the "cone threshold" (0.001mL) and "discomfort" (100,000mL) marks vertically. You will note that no response clamping occurs between these values.
> the only way for a spectral flux (SLF) to be optimal considering its spectral luminous flux (LF) is to be entirely concentrated at ~550nm, laser-like.
Yes, that's correct. For maximum brightness given a limited amount of energy, you want all the light to be emitted at a wavelength matching the maximum of the eye's luminosity function. Of course, if the light is very bright, it will saturate your green cones, at which point you would want to stop adding 550nm light and switch to a wavelength that matches one of your other cones.
The way it is calculated now, the only way for a spectral flux (SLF) to be optimal considering its spectral luminous flux (LF) is to be entirely concentrated at ~550nm, laser-like. However, such a light would leave many of the cones in our eyes unsatisfied, hinting that this shouldn't really be the optimal.
I am by no means an expert, but I would expect a LF to be optimal when it matches the relative human sensitivity in shape, instead of the one focused as an impulse at the peak of the relative human sensitivity.