# Signal averaging CCD

I'm thinking about signal to noise ratio of CCDs and I hope this is the right location to post my question. The Hamamatsu Learning Center seems to be a good starting point to learn about CCDs. I learned the SNR is proportional to the square root of the integration time. With signal averaging it's similar, the SNR is proportional to the square root of the number of measurements. Now if I have 5s time to expose the CCD to a light source, should I integrate for 5s and then read the CCD for a better SNR or should I read the CCD after let's say 0.1s of accumulation and therefore increase the number of repetitions to 50? Is there a difference? (Assuming reading is instantaneous)

• What ADC resolution? Are you going to use a faster integration time for 50 samples? What is the charge injection error from resetting the integrator? How accurate is your sample (reading) timer? How linear is your integrator? How might your integrator drift over time and might it be worse if the integration time is smaller? Other than that, the readings of SNR should be identical. Feb 13, 2021 at 14:05
• @Andyaka my question is in theory. I work with spectrophotometers and can adjust the reading interval and the integration time and this got me thinking, because I could either have 5 repetitions with 1s exposure or 50 repetitions with 0.1s exposure and was wondering what should result in a better SNR. I don't know about the technical details of the spectrophotometer. So the answer would be: "it depends"? Feb 13, 2021 at 14:15
• Then, the answer to your formal question is; it depends. Feb 13, 2021 at 14:17
• The theory only applies to Gaussian Noise. When other types of noise such as impulse , drift and repetitive, then denoising requires more samples and a different algorithm that might ignore an impulse measurement for example Feb 13, 2021 at 14:51

CCDs have several types of noise, but only two are relevant here:

1. Read noise. This is the integration time independent component of the read out process. Every time you read out the circuit you get this noise.

2. Dark current. These are randomly generated thermal electrons that contribute additional (non-photon) shot noise. As such they are proportional to integration time.

From these it should be obvious that multiple read outs are going to have more read noise and thus will not be better. Less obviously they may not be worse if your dark shot noise component swamps the read noise, but this is uncommon unless your integration time is very long.

For example, a contemporary midrange sensor (which will probably be CMOS since almost no one makes CCDs anymore), read noise might be 4 electrons and dark current 10 electrons per second. The dark shot noise for 2 seconds would be sqrt(20) electrons. Thus if you read out a few shorter exposures you would quickly swamp the dark noise with read noise.

Note that averaging multiple read outs does increase dynamic range, so if you have a very bright signal this may still be a good idea.

The theory only applies to Gaussian Noise. When other types of noise such as impulse , drift and repetitive, then denoising requires more samples and a different algorithm that might ignore an impulse measurement for example.

In the case of a photospectrometer , if the calibration response was in error, it may indicate the diffraction grating is dirty for example using high resolution measurements and measuring std deviation of response in error.