How do I determine whether I have pattern-free noise? For microscopy, we're frequently testing cameras. Since my applications involve very low signal-to-noise ratio, it becomes important that the noise is free of correlations and patterns, because local correlation is all that really distinguishes signal from background.

To test the noise, I usually acquire a series of ~100 dark frames, i.e. frames where no external light hits the camera, determine the fixed camera pattern by time-averaging, and subtract that from the series. 

I've observed patterns in the noise by simply taking the standard deviation for each pixel through time and looking at the resulting image (where e.g. different rows/columns of the camera had different noise standard deviations), and by doing row and column-wise cross-correlation (where I noticed for some interleaved camera that the noise was correlated between every other row). 

The first of these tests is qualitative only, and the second only gives me (relatively) global correlations. Are there better (and faster?) ways to determine whether there is any correlation or dynamic pattern in the noise of the camera?
If I were you, I would simply take a large number of no-signal, where you aren't measuring any real signal. Run it through whatever identification algorithms you have, and see if you see anything. If you do, then you need to worry about correlations.

I think what you might be missing is that correlation does not always mean a false detection, especially if you have a robust algorithm to this kind of noise.