Hello ! I would like to characterize experimentally Stokes vector of light passing through a half-waveplate with a polarimeter in order to fit the parameters of the angle and the retardance. Up to now I fit S1, S2 and S3 singularly in Mathematica. The best way would be to fit simultaneously S1, S2 and S3. How can I do it ?
If you have some underlying parametric expectation of what the component is, then you can use all of the data together to find a best fit of the parameters.
Say, for example, you are testing a pseudo zero order wave plate. This is composed of two wave plates stacked together. One is supposed to be, say, 3.0 waves and the other is supposed to be, say, 3.5 waves, and they are supposed to be oriented orthogonal to each other. You expect with manufacturing tolerances they might be slightly off in retardation and orientation. Then a parametric model of the component would be a pure retardation of 3.0 +\- dr1 waves at an angle of 0 +\- dq1 degrees followed by a pure retardation of 3.5 +\- dr2 waves at 90 +\- dq2 degrees. The goal would be to find dr1, dr2, dq1, and dq2 that best fit the data. To do this, for a particular choice of the parameters you calculate the expected experimental data and then calculate the least squares difference from the actual data and then minimize. If there are reasons to think one measurement is more accurate than the others, you can weight the least squares minimization.
That was an example, but you can easily imagine doing similar with different kinds of components.
In the absence of some kind of expectation of what the component being tested is, I don’t see how your question makes sense. For an arbitrary unknown component, the measurements are separate and independent. They can independently take on any value and there is nothing to link them together. In that case the independent results are the best you can do.
Mike Albert thanks ! Yes, in my case the light passes through a GlanThomson and then a HWP or QWP. So I would like to characterize the total optical set-up of these two elements and then through a polarimeter perform a fitting of S1, S2 and S3 simultaneously.I do not think it makes sense if I fit separatly S1, S2 and S3.
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