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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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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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ANSWER 1 You're asking about error propagation. In your case: $\sigma_{M+N} = \sqrt{\sigma_M^2 + \sigma_N^2}$ $3\dfrac{\sigma_A}{A} = \sqrt{2(\dfrac{\sigma_B}{b})^2 + (\dfrac{\sigma_{M+N}}{M+N})^2} $ The wrinkle in my calculation is that I assume that the errors in B, M and N are independent. Since M and N are functions of B that isn't strictly true. (I ...


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This is because $dn_i$ can be arbitrary. You get an infinite number of equations by choosing different $dn_i$. For these equations to be statisfied simultaneously, you need the coefficient to be zero. \begin{equation} \ln n_i + \alpha + \beta \epsilon_i = 0 \end{equation} Note because you have included Lagrange multipliers, $dn_i$ can be treated as ...



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