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Most microscope software provides options for line average or line integrate as a function that helps the signal to noise ratio when taking an image. The math behind line average seems straight forward, but not so much for line integrate.

Line average takes X number of scans per pixel and averages the scans into a final pixel intensity. The same principal of multiple scans for a single pixel is taken for line integrate, but the math involved in the integration of the intensity is not clear to me. I assume it involves summing pixel intensity and operating on that somehow, but it simultaneously is able to reduce noise in the system so I am not sure what else it is doing.

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Most microscope software provides options for line average or line integrate as a function that helps the signal to noise ratio when taking an image.

Averaging sums the lines and then divides by the average number. Integration sums the lines without dividing. They're functionally the same thing just with different scales.

I assume it involves summing pixel intensity and operating on that somehow, but it simultaneously is able to reduce noise in the system so I am not sure what else it is doing.

In terms of shot noise, both have an equal reduction. If you are averaging over extremely dim signals at low gain (particularly those averaging less than 1 DN per pixel), integration can save you signal from being rounded down to zero.

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