Derivation and calibration of spectral response for a channeled spectropolarimeter

The channeled spectropolarimeter (CSP) measures the spectrally-resolved Stokes vector from a snapshot by employing spectral modulation. The spectral modulation transfer function (SMTF) of the spectrometer preferentially suppresses the high-frequency channel amplitude in CSP, resulting in reduced measurement accuracy. This paper rigorously derives the SMTF theory and proposes an efficient calibration method for SMTF via channel shifting in a CSP. The SMTF value, obtained by channel shifting, is used to correct the high-frequency channel amplitude. Moreover, alignment and phase errors, as well as nonlinear dispersion, are compensated in situ. Other than rotating the retarder twice, no additional instruments or algorithms are required in the proposed method. In simulations and experiments, the proposed method shows high accuracy, with a maximum root-mean-square error (RMSE) of the reconstructed Stokes spectrum below 0.01, demonstrating its potential for enhancing the simplicity and practicability of Stokes CSP.