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by Promit
3165 days ago
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This was certainly not meant to be a crucial piece of information, but sure, let's get into it. Much of the post comes from a general assumption that the goal of computer graphics is primarily to replicate how a camera sees the world around it. Thus I think it's easiest to start from the idea of real world light entering a digital image sensor. Light in this setting is not continuous! Each subpixel in an image sensor acts as a photon counter. One photon hits the sensor, the count ticks up by one. There's no question of being able to perceive the values between 1 and 2 because they don't even exist. Either the sensor counted one photon or two. If you were going to literally create a digital camera that can process the entire world, you need 20 bits to count up to a million photons without losing any along the way. So if you were to build the hypothetical rendering pipeline that works on "real world" data about the scene, that 20 bit value would be the input. As a practical matter, nearly all modern games store lighting levels internally in floating point, in arbitrary units chosen by the developers. Lighting pipelines are not integer based, but they're linear and not perceptual. The conversion to perceptual 8 bit (gamma curve) happens as part of the tone map stage. Doing things in floating point physical units is a better idea than the photon counter anyway, but the line you're confused about was really written with idealized cameras in mind. (Technically an image sensor is an analog device and the voltage increases with each photon detection by an increment that is subject to noise of all sorts and pre-amplification before hitting ADC. Don't jump me on the photon counter thing.) |
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But it's rather important, and not even for those reasons. This is not meant to jump on you! (and I really loved your article, like you said it's not a crucial point at all)
The 1:1000000 or 1:2^20 contrast ratio only corresponds to exactly 20 bits if the 1 on the low end of this ratio corresponds to exactly one discrete unit of light (photon). If it's off by a factor of 0.5, 1.618 or whatever, that's what the whole argument is about.
First, the sensor counts not photons but a value relating to photons per second (because exposure time). If the 1 on the low end of the range corresponds to some exact minimum number of photons, it's going to be "one discrete unit of light per <exposure time>". Making the whole thing analog from the start.
Second, those sensors most probably aren't able to count individual photons any way[0]. The human eye, after about 30 minutes to get optimally adjusted to darkness, can sort of perceive individual photons, or small bunches of maybe 2 or 3, kind of. Those barely-perceptible specks of light in the utter darkness aren't the sort of resolution issues we're worrying about in the dark end of these types of scenes. And, as soon as you make a light source that can be described as "emitting single photons" in a certain context, you get uncertainty effects and all that quantum jazz (show me a photon/path tracer renderer that gets the slit experiment correct[1] and you can have your integer photon counters :) ).
So the sensor output values can (and should), for all intents and purposes, be assumed to be an analogue value.
The amount of bits you represent it with just puts an upper bound on your signal-to-noise ratio (as per Shannon entropy). But since we're dealing with 2D images, the distribution of this noise over the spatial resolution (either as a result of sensor noise at the input or explicit noise shaping dithering at the end of the pipeline) also comes into play when considering the quality of the output.
If the signal-to-noise ratio of a sensor output happens to allow for 20 bits of precision, for a sensor that happens to have a 1:2^20 brightness range, that's coincidental. Sure it correlates because higher-end sensors tend to perform better in both range and SNR. But I don't believe that the 1 on the very low end of a discrete range represents precisely one photon per <power-of-two times minimum exposure time>.
[0] correct me if I'm wrong about this btw. There might be specialized scientific equipment that can, but I doubt even high-end cameras bother to go to the accuracy of single photons. But, I mostly know about digital signal processing, not about state of the art of camera hardware. Yet even if they are able to detect individual photons, that's going to be a probabilistic and per-unit-of-time measurement, so the rest of my argument holds.
[1] these probably exist, but aren't used for games or photorealistic rendering purposes