Truncated singular value decomposition method for calibrating a Stokes Polarimeter

We present a method for calibrating Polarimeters that uses a set of well-characterized reference polarizations and makes no assumptions about the optics contained in the Polarimeter other than their linearity. The method requires that a matrix be constructed that contains the data acquired for each of the reference polarization states and that this matrix be pseudo-inverted. Since this matrix is usually singular, we improve the method by performing the pseudo-inversion by singular value decomposition, keeping only the four largest singular values. We demonstrate the calibration technique using an imaging Polarimeter based upon liquid crystal variable retarders and with light emitting diode (LED) illumination centered at 472 nm, 525 nm, and 630 nm. We generate the reference polarizations by an unpolarized source, a single polarizer, and a Fresnel rhomb. This method is particularly useful when calibrations are performed on field-grade instruments at a centrally maintained facility and when a traceability chain needs to be maintained.