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I am using two polarizers (one for an halogen light source and one for a camera) to measure light reflected in parallel and perpendicular polarization setups. Should the light source used along with the polarizer be a collimated light beam or can it be a diffuse illumination ? (and, if it should, why?)

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Yes, you should collimate your beam. The reason for this is that polarizers work well at the angles of incidence they were designed for, and increasingly worse at other angles. The reason for this is that they rely on optical reflectivity (and interference for thin film polarizers) of the two orthogonal polarizations, which obviously depends on the angle of incidence. Often, there is an acceptance angle indicated on the polarizer's datasheet. For example, for Glan-Taylor polarizers this angle is usually about 1-2 degrees.

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