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Suppose I want to measure the polarization state (i.e. Stokes parameters) of an incoming laser beam. I want to split the incoming beam into two branches. In the first, I have a polarizer aligned along x-axis, while in the second along the y-axis. There is a detector after each polarizer.

In theory this set up would be able to detect the polarization state of any elliptically polarized light. However, it seems to me that a linearly polarized light can have its polarization angle such that it is indistinguishable from the elliptically polarized light.

Without changing the set up (e.g. to have a rotating polarizer), is there anyway to differentiate the linear from the elliptical light?

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