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What is the theoretical upper limit on ISO for a digital image sensor?

(I imagine any limit must be a function of sensor pixel size, since once all electronic noise has been eliminated then shot noise dominates and that can only be reduced by increasing sensel area?)

(ETA: I suspect physics is the source of a limit because you can't amplify something that isn't there, and light is quantized into photons. So if we ignore all noise that can theoretically be minimized, and then consider a limiting scenario where the sensels are trying to noiselessly count as low as single photons, perhaps we arrive at an upper bound?)

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    The answer is, obviously, there is no limit, because you can always increase the amplification. Asking what is the highest theoretical ISO having some specific signal-to-noise ratio and resolution would be more interesting!
    – szulat
    Jul 23, 2019 at 19:40
  • @szulat: That might be part of an answer. I'm thinking of the question from the side of maximum light sensitivity per sensel. I therefore think there must be a physical limit, because you can't amplify something that isn't there, and the minimum quantum of light is a photon....
    – feetwet
    Jul 23, 2019 at 21:03
  • How much do you want to spend supercooling the sensor?
    – Michael C
    Jul 23, 2019 at 21:38
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    I'm voting to close this question as off-topic because it presents no actual problem about the actual practice of photography.
    – Michael C
    Jul 23, 2019 at 21:55
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    @feetwet You could probably start with What is “ISO” on a digital camera? and Is it true that the best images from all digital cameras can be obtained at ISO 200? and What are physical causes of clipping?
    – Michael C
    Jul 24, 2019 at 10:13

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On paper, the limit gets set when we can accurately and reliably measure individual photons hitting the sensor.

However, due to the awkward nature of the number series for 'Whole stops' used in the ISO scale where the number keeps doubling, the 'full answer' is an awkward math problem that rounds out to something that would look like x*10^y or use a rather large amount of space on a page.

  • I need more coffee before attempting the actual estimate, but hopefully someone else more familiar with photon count estimates might come along and work it out for us...

[However, we have technically already well surpassed the upper limit of the formal ISO scale as far as I'm aware, given that the official standard only went out so far, and what is currently used in Cameras is 'a bit fuzzy' and driven by general convention rather than strict standards at this time.]

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There are a few ways to look at this problem.

ISO as applied gain

At face value... ISO is really an application of gain which occurs after the shutter closes. (For this reason, ISO is technically not part of exposure even though most of us think of it that way and it's easier to talk about it as if it were part of exposure.) Just recognize that it is always applied after the shutter closes and it is simply an amplification or gain applied (sometimes via analog amplification or sometimes digitally by mathematically multiplying the digital information and sometimes a little of both.) But as it is always "applied gain", you can, in theory, go as far as you want.

But there are some practical reasons why you don't want to go crazy with application of gain. One big reason is because each time you increase ISO on a digital camera (and this is specific to digital cameras) you also decrease the overall dynamic range.

Why?

Digital sensors and bit-depth

I'm specifically referring to doing this in-camera because a digital camera has a given bit-depth of the pixels. In other words there is a largest numeric value that a pixels color channel can hold and if we multiply the information by values that exceed this max value ... we can't store the result.

Suppose your camera sensor has 8-bits of color depth per channel (most cameras are much more, but I'll use this example). 8-bits means that each color channel can represent 256 possible values ... where 0 is darkest and 255 is the brightest value.

Assume the camera boosts ISO only via digital gain. This means that each time you want to increase ISO by 1 full stop (1 full stop "doubles" the brightness of something) you multiply the value the camera actually recorded by 2x.

Suppose we take a photo and something in the image has a brightness value of 10 ... and something else has a brightness of 100 ... and something else has a brightness of 200 (that's the value of that specific color channel of the pixel and we have to use the term pixel colloquially to simplify how the sensor works... the truth is slightly more complicated.)

If we double the brightness by going from ISO 100 to ISO 200, then the pixel that was previously a value of 10 doubles and now has a value of 20. The pixel that was 100 now doubles and has a value of 200.

BUT... the pixel that was 200... doubles and now has a value of 400. 400 is brighter than the camera can record in 8-bit depth (maximum value is 255) ... so this pixels "clips" and is simply now just "255" instead of 400. In fact every pixel with a native value greater than 127 will now clip.

Increase the ISO again (so now we use ISO 400) and all the values are multiplied by 4x. Even more information clips.

We can raise the value of the darkest pixels safely without clipping ... but the brightest values clip. This results in a loss of dynamic range.

Camera vendors can play a few tricks ... for example do we really have to apply a linear amplification of the information. Suppose we increase the darkest pixels by 4x ... but we only increase the brightest pixels by a small fraction of that? This is a bit of a cheat to avoid clipping, but we're now losing overall contrast. No matter how we slice it or what tricks we apply, we're probably losing dynamic range.

When you think about the dynamic range problem ... the maximum that we can boost ISO is based on the number of bits. If we raise ISO by more than 8 stops on an 8-bit sensor (or more than 14 stops on a 14-bit sensor) then we effectively get the dynamic range down to nothing.

Suppose we transfer the image to a computer and apply the gain on the computer ... and the computer is using 64-bit tiff images. We can now go much farther without clipping ... but conceptually this 64-bit depth becomes the new limit.

Noise and the signal to noise ratio

One last reason why going crazy with ISO gain isn't necessarily desirable (even though you can do it) is because when you apply gain to an image, you apply gain to "everything". The values in an image file partly represent true "signal" (useful information) and also "noise" (non-useful information).

All sensors have "noise" even at base ISO. But at base ISO the noise is often so subtle that our eyes don't notice it. As you boost ISO, you increase all values (the good signal and the bad noise) and based on clipping limits, you start to degrade the signal-to-noise ratio (SNR). This is where images just look bad.

There are numerous techniques to attempt to deal with the noise problems, but it is a reality of digital photography.

In other words just because you can crank the ISO doesn't mean you'll like the results.

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    The answer seems sidetracked by a terrible misunderstanding of dynamic range - Over exposure doesn't decrease dynamic range, it merely makes terrible use of it. Whether you clip your highlights by cranking the ISO too high, using too long of a shutter speed, or too large of an aperture, it has not decreased dynamic range; it has only over exposed the highlights.
    – TheLuckless
    Jul 23, 2019 at 22:10
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    @TheLuckless, it isn't over-exposure per se that reduces DR (you can over-expose an image shot at base ISO). It's boosting the gain (aka increasing ISO) that results in a decrease of DR. This occurs because the ceiling is capped by the bit-depth of the camera. Applying gain can't make the brightest pixels any brighter. But it can make the darkest pixels brighter. This effectively narrows the total DR.
    – Tim Campbell
    Jul 24, 2019 at 14:36
  • Are this answer asuming adding gain digitally? If the gain is applied analogly using analog electronics before analog digital conversion in the sensor does this hold up? Also if done digitally there is nothing that prevents a camera manufacturer from just storing the raw unboosted digital signals and a flag of how much to boost so where does the loss of information come in? Once digital we could have infinite bith depth if anyone cared to program it and accept possibly a bit larger file sizes.
    – lijat
    Jul 25, 2019 at 6:40

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