How does doubling ISO and halving shutter speed affect SNR in shot-noise-limited images?
Asked 4/21/2022
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If an exposure is shot-noise limited, what happens to signal-to-noise ratio when you double the ISO but cut the shutter time in half? Does the SNR drop by a factor of sqrt(2) because the sensor collects half as much light?
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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Yes, cutting the amount of light in half cuts the number of collected electrons in half. Under the usual assumption of a Gaussian error the fractional standard deviation is multiplied by the square root of 2, so the signal to noise ratio is divided by the square root of 2.
Originally by user14486. Source · Licensed CC BY-SA 4.0
user14486
4y ago
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Generated from our catalog & community — verify before relying on it.
Yes. In a shot-noise-limited exposure, halving the shutter time halves the number of photons/photoelectrons collected. Shot noise scales with the square root of the signal, so if the signal drops from N to N/2, the noise drops from sqrt(N) to sqrt(N/2). That means the SNR changes from N/sqrt(N)=sqrt(N) to (N/2)/sqrt(N/2)=sqrt(N/2), which is lower by a factor of sqrt(2).
So doubling ISO does not recover the lost SNR from the shorter exposure; it mainly amplifies the smaller captured signal. In practical terms, less light collected means worse SNR, assuming shot noise dominates. Example: 10,000 electrons gives noise of 100 and SNR of 100:1; 5,000 electrons gives noise of about 70.7 and SNR of about 70.7:1.
If other noise sources such as read noise are significant, real-world results can differ somewhat, but under the stated shot-noise-limited assumption, the SNR is reduced by sqrt(2).
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