In CCD detection is integration better than accumulations

[gujax]

In CCD detection, is integration better than accumulation

Hi,
I have carefully experimented and found this to be a true observation with CCD detection in general.
Signal to noise improves if one integrates a signal (e.g. over x seconds) versus accumulating over many short integration times (i.e. integrate over x/n seconds, n number of times and add the result).
I will appreciate if some one can help me derive why this is so (if it really is). Or else please point out if it is some artifact (e.g., readout noise increases in the later case or digitization noise?)
Thanks

 

[Claude Bile]

Going purely off quantisation noise, I would expect the latter case to yield a better S/N because there are more greyscale intensity levels available for the end result of the measurement.

To rephrase; in the first instance, if you integrate a signal over x seconds, there is only 255 greyscale intensity levels available (assuming an 8-bit depth). If you accumulate n signals then the number of greyscale intensity levels is n*255.

Claude.

 

[JeffKoch]

All other things being equal, integrating for a long time will be better because you get one addition of read noise, whereas integrating n images adds read noise n times. Quantization in terms of bits in an image isn't a random process, it's a rounding process, so I don't see how this could have an impact though I'd have to think more carefully about it. A 16-bit image will have more dynamic range than an 8-bit image, but that doesn't fundamentally change the signal-to-noise.

In practice there are other factors. In astronomy, for example, you can get a much better image by adding many short exposures with integration times shorter than the timescale of changing turbulence - leaving the camera on for a long time produces an average blurred image, but adding a number of selected short exposures can produces a sharp image. Tracking errors in a telescope mount is another complication - to get a good single long exposure, the tracking must be accurate over the entire duration of the exposure, but adding many short exposures allows you to reference them individually and the tracking need only be accurate over the duration of each short exposure.

 

[gujax]

Thank you Claude and Jeff.
You may be correct about the graylevels Claude but I want to compare "same amount of signal" either by integrating or by accumulating. In your case comparing 255 to n*255 is unfair - I think. I was meaning to compare X and n*Y such that X= n*Y and then compare their signal to noise.
I think Jeff is perhaps correct and it looks to me like a readout noise issue. Though, quantization issue seem to only affect resolution i.e., imagine I am trying to locate a spectral peak and imagine the well-depth being 300,000 electrons and the CCD having only 12 bit conversion. Then in integration, let us say I readout 250000 e, with a Poissonian noise of 500, I would have 10 levels of bits to operate on.
But if I end up accumulating 25000 counts 10 times, the noise on every readout just from shot-noise (ignoring readout for the time being) will be 160 counts and I will have only 3 bit depth for resolving this noise. However, what I am unclear about is after accumulations, would the increased graylevels show up in noise as Claude suggests.
Or will I be able to discern the spectral peak..
Also, my measurements are not on transients i.e., no blurring effects are encountered.
But under those circumstances, Jeff has a point.
Thank you,
gujax

 

[JeffKoch]

Try it with a simple computer program. Add electrons to a bunch of mathematical pixels according to some random Poisson distribution representing signal, the add read noise to each pixel, then add A/D conversion noise to some defined number of bits representing full scale. Try it with short exposures (low number of signal electrons) summed up, long exposures, 8 bit bins, 16 bit bins, etc., and see what you get. A simple basic or fortran program combined with plotting/analysis software like Kaleidagraph would suffice - you could probably even do the whole thing in Excel.