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I have a photo of a laser beam (taken by sending the laser into a CCD). I then took the image and ran it through an image reader that gave an intensity surface plot. I then took a single cut from that plot and got a standard scatter plot from it. As an example, the image and final scatter plot are below.

Is there is statistically appropriate way to find the uncertainties in the points?

Picture of beam by CCD.

Scatter plot of single cut of beam photo.

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  • $\begingroup$ Looking at the image, it seems to me that most of the uncertainties are actually highly correlated optical diffraction effects (probably from dust?). A simple statistical measure would not apply in that case. You could vastly improve the quality of this by using a diffuse filter that would remove most of the diffraction. I have seen fast rotating semi-transparent screens being used for that purpose. By integrating over sufficiently long time, the diffraction pattern would disappear below the actual noise level. $\endgroup$ – CuriousOne Apr 17 '16 at 7:08
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You do not have enough information. If you could relate the intensity in the picture with the number of photons detected by the CCD, you could use square root of that number. So say 49 in your graph correspond to 49 photons. Then the error bar on that point is 7. But if the same intensity correspond to 4900, the square root is 70, and your error bar is 0.7

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It depends on what error you want to quantify.

You can take several images of the same beam at different times (frames of a movie), then for every pixel you find the time-average and standard deviation. This will give the time average and uncertainty, related to the stability of the laser intensity.

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