Is Poisson Noise ("Shot Noise") a significant source of noise for typical photography?

Question

In this answer, @jrista states that even a camera with a perfect, noiseless sensor would still have noise due to "Poisson noise" aka "Photon Shot Noise" - noise caused by the random variations of photons, which cause more photons to enter one sensel than another.

I'm just curious - is this a significant concern for real-world photographers? I would assume that this noise would be so infinitesimally small that we can consider it to be basically 0. Are there any studies that measure how much noise is from shot noise, vs other causes (like electrical or thermal noise from the electronics) ?

Answer 1

In most parts of most photographs, photon shot noise is the largest contributor to noise.

Mostly, we're comparing it to read noise. (Dark current is negligible in short exposures, and quantization noise is also pretty small when you're talking about 12- and 14-bit ADCs.) Read noise depends on the sensor. This 2007 paper presents read noise measurements for a few DSLRs. We see, for example, that a Canon 40D at ISO 200 has about 10 electrons (e-) of read noise.

Photon shot noise is a Poisson process, so the noise is the square root of the count of signal photoelectrons. So if we record 100 signal photoelectrons in a pixel from our subject, we expect the shot noise per pixel to be sqrt(100)=10 e-, equal to the 40D's read noise.

Is 100 photoelectrons a lot? No, the same paper estimates the full-well capacity of a 40D pixel to be 56,000 e-, so a pixel with only 100 e- is a very dark part of the scene, about 9 stops darker than full-well. In a pixel with more than 100 e-, the shot noise continues to increase, up to sqrt(56000)=236 at full-well, so the shot noise dominates the read noise by a larger and larger margin. (The bright tones appear less noisy than the dark tones, because the signal-to-noise ratio continues to increase, as the noise is only the square root of the signal. But what noise there is, is due increasingly to shot noise, not read noise.)

In the very dark shadows, the read noise may be significant. And in a long, dark exposure (such as astrophotography under dark skies), dark current and read noise may both be important. But for general photography of well-exposed subjects with short exposure times, shot noise is the dominant source of noise.

Answer 2

Photon shot noise, or noise that results from the Poisson distribution of photons as they reach the sensor, may be an issue that real-world photographers might need to at least be aware of. As ISO is increased, the maximum potential for the signal also drops. For every stop of increase in ISO, your maximum signal drops by a factor of two. In most exposures, photon shot noise is by far the most significant contributor to noise. Electronic sources of noise only affect the deep shadows, and usually only exhibit when you start pushing exposure around in post (i.e. lifting shadows by a significant degree.)

Assuming a full-frame sensor with a Full Well Capacity (FWC) of 60,000 electrons, at ISO 100 you have a Maximum Saturation Point (MaxSat) of 60,000 electrons (e-). At ISO 200 you would a MaxSat of 30,000e-, ISO 400/15,000e-, ISO 800/7500e-, ISO 1600/3750e-, ISO 3200/1875e-. Increasing ISO intrinsically reduces the maximum potential signal to noise ratio.

This factor is probably most important when deciding what camera to buy. A full-frame sensor will have larger pixels than an APS-C sensor of the same megapixel count. Our 60k FWC on our hypothetical FF sensor might be a 20k-25k FWC on an APS-C sensor. If you need superior low-light performance, going with a full-frame sensor and fewer megapixels will increase pixel size, thus having a DIRECT impact on the amount of visible noise at higher ISO settings.

Photon shot noise, as a ratio of the total signal, drops as signal strength increases. As an absolute factor (standard deviation around mean signal level), photon shot noise is probably roughly constant. Assuming a standard deviation of 5 units, if the signal strength is also 5, you would have an image that appears to be mostly noise, possibly with partial but largely indistinct "shapes". If the signal strength is 10 units, then the SNR is 50%. You will still have a very noisy image, but it will be an image with more distinct shape and structure. In actual terms, photon shot noise, which follows a Poisson distribution function, is equal to the square root of the signal level. At ISO 100, FF sensor with a 60,000e- FWC will have photon shot noise equivalent to 244e-. An APS-C sensor with a 20,000e- FWC will have photon shot noise equivalent to 141e-. At ISO 200, the photon shot noise would be 173e- and 122e- respectively, ISO 400 would be 122e- and 70e-, etc. As a matter of ratios, at ISO 100 FF photon noise is 0.004% of the signal, ISO 200 its 0.006%, ISO 400 its 0.008%, etc. Conversely, for APS-C these values are ISO 100/0.007%, ISO 200/0.012%, ISO 400/0.014%, etc.

Smaller sensors will have slightly lower SNR than FF sensors to start with, as row/column activate and read wiring tend to consumer more relative photodiode space. Combined with the smaller FWC, you are immediately at a disadvantage when it comes to increasing ISO. The FF sensor has a noise advantage of approximately 60% (By: 244/60000 / 141/20000 = 0.577). At the same ISO setting, assuming noise is generally visible at that setting, the FF sensor will always appear to be less noisy than an APS-C sensor. In the case of our two hypothetical sensors, ISO 100 on the APS-C is only marginally better than ISO 400 on the FF, almost a two full stops difference in relative noise performance! The same would go for two FF sensors, one with large pixels and one with smaller pixels by a factor of 1.6. This assumes observation a 100% crop (i.e. pixel peeping.) It is always the case that you can downscale the size of a higher resolution image to match that of a lower resolution image, and reduce noise by simple averaging (although you will usually have to downscale the image from the higher resolution sensor by a greater degree to completely normalize noise.)

As for how much noise is from shot noise, and how much from other sources. The "other sources" really depends on the sensor. Read noise is usually measured in terms of DU (digital units, or post-ADC) or e- (electrons, analog signal charge). The Canon 7D has read noise of 8.6e- at ISO 100, but 4.7e- at ISO 200, 3.3e- at ISO 400, etc. The Canon 1D X has read noise of 38.2e- (!) at ISO 100. The greater read noise is ultimately proportional to the area of the photodiode...larger pixels carry more current, so dark current will be higher, and downstream amplification will be increasing a larger quantity of electronic noise relative to the signal. The 1D X has a FWC 90,300 though, which means that 38e- worth of read noise is a minuscule fraction of the maximum potential ISO100 signal (0.00042% to be exact).

In all cases of noise, it really depends on your goals. If you tend to shoot low light, or need very high shutter speeds, finding a camera with larger pixels will probably produce the best noise characteristics. If you shoot high detail subjects, higher pixel density is probably more important than low noise. There is no real cut and dry answer here.

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^{† Quantity of light, assuming a fixed illuminant, the amount of light that reaches the sensor for a given aperture and shutter speed, or any equivalent ratios thereof: f/16 1/100s, f/8 1/200s, f/4 1/800s, all the same EV.}

Answer 3

You are definitely getting into the range of fringe photography when trying to identify shot noise vs signal. Luckily, the astrophotographers have been here before.

There's a decent series of articles intended for laypeople that goes into understanding noise vs signal that was published by Craig Stark.

In part one here, he describes the basic premise of shot noise and why skyglow is so bad for astronomy -- it increases shot noise without adding more information. Essentially, you can have a higher plateau of light level but it's flat and thus robbing contrast.

In part two here, he goes into further detail about the differences of shot vs read vs thermal noise for example photographs.

In part three here, he describes a method to measure the performance of specific cameras and thus gain a model for noise profiles. This may best answer your question of "what's the differences between the types of noise."

Back to your basic question: is it relevant for most photography? Not really, until you start shooting in the extremes of other types of noise (thermal and read) when the SNR becomes skewed.