In a laser interferometry experiment, we project a pattern of interference fring

Question

In a laser interferometry experiment, we project a pattern of interference fringes onto a CCD sensor. For best results, we want good contrast between the bright and dark fringes, and we carefully compensate for various sources of noise - for example, by taking camera images with no fringes present, and with the laser turned off, and subtracting these images in the proper sequence. We'd expect therefore that the remaining signal should be highly linear, with the CCD signal at each pixel in direct proportion to the number of photons reaching it during the shutter time.

What we actually find is that, as we vary the laser intensity and shutter time such that the average intensity across the image remains constant, with no pixels saturated, there is a definite "sweet spot" where the fringes are much more well-defined than at other settings. Either increasing or decreasing the laser intensity away from this point (with corresponding decreases or increases in shutter time) causes the fringe definition to deteriorate.

I can't think of any reason why this should be. I know that in cases where the process generating the pattern has a time-constant (for example, using laser speckle interferometry to measure Brownian motion), there is an optimum exposure setting, but that shouldn't be the case in our system which is entirely static. So, what am I missing? I assume it's some property of the CCD sensor that I've overlooked.

Explanation / Answer

The CCD is not perfectly linear, and the electronics in the analog pathway are not perfectly linear either. You should map the response of the system over your experimental range before you diagnose further, i.e. sweep a known calibrated source and measure and plot the pixel response. Especially since you are forming data by subtracting, small non-linearities will be much more visible.

Usually you either find a region which is linear enough for the purpose, and you make sure you're always in that region, or you fit a curve to the response and use that to linearize any data before analysis.

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