Removal of spectro-polarimetric fringes by two-dimensional principal component analysis

We investigate the application of two-dimensional Principal Component Analysis (2D PCA) to the problem of removal of polarization fringes from spectro-polarimetric data sets. We show how the transformation of the PCA basis through a series of carefully chosen rotations allows us to confine polarization fringes (and other stationary instrumental effects) to a reduced set of basis "vectors," which at the same time are largely devoid of the spectral signal from the observed target. It is possible to devise algorithms for the determination of the optimal series of rotations of the PCA basis, thus opening the possibility of automating the procedure of defringing of spectro-polarimetric data sets. We compare the performance of the proposed method with the more traditional Fourier filtering of Stokes spectra.