Linear operator theory of channeled spectropolarimetry

Channeled spectropolarimetry is a snapshot method of measuring the spectral and polarization content of light. Wave-number domain amplitude modulation is employed to encode all four Stokes component spectra into a single optical power spectrum. We model the channeled spectropolarimeter as a linear operator, which facilitates treatment of nonideal effects and provides a convenient framework for simulations, calibration, and reconstruction. The operator's singular value decomposition is treated with analytic and computational approaches. This analysis highlights the importance of the choice of object space in constraining and imparting prior knowledge to linear reconstructions of data from underdetermined systems.