Why doesn't noise depend on exposure time?

Question

In the post Why do cameras use a single exposure rather than integrating across many very quick reads? an important question was if the noise depends on the exposure time or not. By noise I mean the absolute noise (N), not the relative noise (S/N). I was convinced about this correlation because I was thinking that the noise is accumulated during the exposure time, so if it is longer the noise would be higher.

To test this hypothesis I tried to shoot black images with the lens cap on the lenses, in such a way to have S=0. I am using Canon 600D, ISO100 and f/3.5

I wrote a python script to compute the mean value averaging over all the pixel with a simple mean or with a quadratic mean (sqrt(sum_i (R_i^2)) where R_i is the ith-pixel considering only the red channel.

I used jpeg, because I'm not able to read raw from python. Using jpeg the resolution of the noise is quite small (1/256), but I have obtained interesting results.

Here the plot: on the y-axis the noise, on the x-axis the exposure time.

it seems that the noise is quite constant up to exposure of 1s, then it start to increase

I have also tried to shot with ISO3200, here the results:

as expected the noise is much bigger (~10 times) but the behaviour with exposure time is similar (probably it raise a bit faster).

Why this behaviour?

Why is the green channel more noisy?

Answer 1

First off, you cannot really evaluate any form of noise via JPEG. Compression, even minimal compression, has a measurable/visible impact on the appearance of noise. You can only really evaluate noise with a RAW image.

---

Just to make sure, you understand that the primary source of image noise is photon shot noise? The noise you are evaluating is camera read noise, noise produced by the electricity passing through the electronic circuits and potentially caused by slight imperfections in the material used in the image sensor. Read noise is generally a fixed aspect of the sensor for a given ISO level, until additional factors such as heat begin to change it. Additionally, to bring signal into the discussion for a moment...read noise is a minuscule fraction of maximum signal, so even at it's peak of 0.009 @ ISO 3200 in your graph, when you slap a strong enough image signal on top of that, the impact of read noise is actually so negligible as to be effectively meaningless. Photon shot noise, or noise in the image signal itself that arises from a weaker signal (compared to the physical full well capacity of a single photo-diode) and a widely distributed inconsistent pattern of photon strikes, is by far the primary contributor to high ISO noise. You would have to dig really deep into the darkest shadows of an ISO 3200 photo to find any indication of read noise.

When you expose up to 1 second, I would assume that the amount of read noise is flat because you aren't accumulating enough heat in the circuit to have an impact. According to your tests, by the time you reach a 1s exposure, heat is probably starting to build up, and does have an impact. As you continue to expose for a longer and longer period of time, the impact of thermal noise on the overall read noise increases.

I am not a CMOS Image Sensor engineer, so I can't get any deeper than that. I would offer, based on the numerous patents I've read that have been published by both Sony and Canon, that there are other reasons why noise increases with exposure time. There are quite a number of noise mitigation patents floating out in the patent-nether that aim to identify, track, and eliminate a variety of possible sources of noise. Most deal with dark current noise, amplifier noise, or A/D converter noise, but there are other sources. Some patents go so far as to cut off the primary power supply to noise mitigation and readout capacitance circuitry during readout to eliminate the potential that dark current from the power supply itself increases noise during readout (I believe that was a Canon patent, and I'm not exactly sure how it works from a voltage or current standpoint.)

Suffice it to say, thermal noise definitely becomes a primary noise producer as exposure passes a certain threshold. I wouldn't have guessed that threshold to be exactly 1s, but your tests would certainly seem to indicate as much.