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I have obtained a value for the background illumination with an associated error which was kept constant during a double slit experiment. Also, I have acquired a value for the average noise/fluctuations of the measured voltage values.

Now I want to plot the intensity distribution. Can I just subtract the background illumination (treating it as an offset)? Furthermore, do I have to calculate the resulting error using the error propagation formula for adding two measurements for every point on the intensity distribution graph?

In addition, do I have to simply add the noise to each of the errors?

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  • $\begingroup$ Probably best to distinguish between error, bias, and uncertainty. If you aren't already familiar with it (from your talk of propagation of error I think you might be but even still), look into uncertainty analysis, like the GUM document. Should help make things like this more straightforward. $\endgroup$
    – Sam Gallagher
    Dec 21, 2018 at 14:48
  • $\begingroup$ In general, something like noise is simply going to translate to uncertainty, whether you subtract it or not. The only way to properly get rid of uncertainty is to take many measurements and to use the mean. Simply subtracting the noise isn't going to help the signal, you need to attack the source of uncertainty in the measurement. $\endgroup$
    – Sam Gallagher
    Dec 21, 2018 at 14:53

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If the background illumination is really just sensor noise than this should be random in nature and it will be included in your signal, you would need to average many images or signals to get the best result. If you have a fixed noise (or background) offset (which you can see by averaging many noise signals) than you can subtract it but ensure exposure times are equal to that of the signal. In general there is noise in light itself, called photon shot noise (different from electronic shot noise), i.e. if a bulb or laser is lit and has a flux of 1M photons per second it really is releasing 1M +- square root of 1M or 1000 photons per second, one std deviation. So that's typically 999,000 or 1001,000 photons actually measured. Light itself is statistical in its emission.

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