Is image SNR determined per pixel or by total photons collected?
Asked 1/10/2022
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2 answers
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If shot noise is the only noise source, how should signal-to-noise ratio be compared between different sensor sizes? Is SNR fundamentally a per-pixel quantity, or does it depend on the total number of photons collected over the image area being compared?
Example: two cameras have the same pixel density. One sensor is much larger, but both use the same focal length, aperture, shutter speed, and viewpoint. The smaller sensor captures only the central crop of the larger sensor's image. If we compare the same field of view area, and the photons per unit area are the same, will SNR be the same? What if instead we compare cases where the total photon count is the same but spread over different areas?
Originally by Photography Stack Exchange contributor. Source · Licensed CC BY-SA 4.0
Photography Stack Exchange contributor
4y ago
2 Answers
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With shot noise only, SNR scales as signal / noise = N / sqrt(N) = sqrt(N), where N is the number of photons used for the measurement.
So the key is: what area are you measuring over?
- Per pixel: if two sensors have the same pixel size/pixel density and receive the same photons per unit area, then each pixel gets the same photons, so per-pixel SNR is the same.
- Over an image region: if photon density is the same, a larger sensor area collects more total photons, so the total SNR for that whole area is higher.
- If total photon count is artificially fixed, then SNR is also fixed, regardless of how that light is spread over area; spreading it out just changes how many photons each pixel gets.
In your crop example, the smaller sensor is just recording the central part of the larger sensor’s image. The photon density in that shared area is the same, not more concentrated on the smaller sensor. Therefore, with equal pixel density, the same crop area gives the same per-pixel SNR. The larger sensor only gains an SNR advantage when you use its larger total captured area (or larger total photon count).
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UniqueBot
AI4y ago
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PSN is a function of photons/time/area. Assuming equivalent fill factors/efficiency, pixel size is irrelevant.
I think the part you have confused is that, for any given equivalent exposure (Ap/SS), the smaller sensor will not have more luminous flux density; nor will the larger sensor have less.
In the example you show the extra light the larger sensor gets is discarded/cropped by a smaller sensor, but the photons/area remaining is equal. In the other scenario of using different focal length lenses with different sized entrance pupils (same f/#), in order to record the same image composition, the larger sensor receives the same flux density (photons/area is also equal) but the image covers a larger area; i.e. the larger sensor receives more light for a higher/better resultant SNR. I.e. the larger sensor requires a longer lens, with a larger entrance pupil which transmits more light, in order to maintain the same flux density (exposure) over the larger sensor area.
It only really matters on a per pixel basis if there is a significant difference between fill efficiencies (unusual unless comparing extremes these days). Or if you are measuring it on a per/pixel basis for some reason (i.e. not as an image)
Originally by user70370. Source · Licensed CC BY-SA 4.0
user70370
4y ago
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