Distinguishing between different types of elliptical polarization How to distinguish between a mixture of plane polarized and unpolarized light, and a mixture of
elliptically polarized and unpolarized light?
When we pass plane polarized wave though quarter wave plate it becomes elliptically polarized light and unpolarized light remains the same . So when this light is passed through a rotating polaroid we get intensity having 2 maxima and 2 undiminished minima. Now for 2nd part elliptically polarized wave when passed through the same plate we get plane polarized and unpolarized remains same and when this type is passed we get intensity having 2 maxima and 2 undiminished minima. So how do we differentiate the two types?
 A: Just rotate the quarter-waveplate to achieve maximum contrast. This way you ensure that whichever light falls onto your detection will extinguish to the unpolarized minimum. What you effectively do is make sure that after the quarter waveplate you always get linearly polarized light: in the case of linearly polarized light, this means aligning the quarter waveplate to match the light's polarization either on it's slow or fast axis, while for the elliptically polarized light you align the fast/slow axis to those of the ellipse. In both these cases light will come out linearly polarized after the quarter waveplate and rotation of a polarizer will show you the greatest contrast between maxima and minima.
EDIT:
To find if you have elliptical+unpolarized or linear+unpolarized, first find quarter-waveplate angle (via rotation) which results in the highest possible contrast between maxima and minima after rotation of the polarizer. Then remove quarter-waveplate and compare the new contrast between maxima and minima. If the quarter waveplate setup had a higher contrast, then the incoming light is elliptical+unpolarized, if the contrast is about the same, then it is linear+unpolarized.
