Random sub-Nyquist polarimetric modulator

We show that it is possible to measure polarization with a polarimeter that gets rid of the seeing while still measuring at a frequency well below that of the seeing. We study a standard polarimeter made of two retarders and a beamsplitter. The retarders are modulated at $\sim 500$ Hz, a frequency comparable to that of the variations of the refraction index in the Earth atmosphere, what is usually termed as seeing in astronomical observations. However, we assume that the camera is slow, so that our measurements are time integrations of these modulated signals. In order to recover the time variation of the seeing and obtain the Stokes parameters, we use the theory of compressed sensing to solve the demodulation by impose a sparsity constraint on the Fourier coefficients of the seeing. We demonstrate the feasibility of this sub-Nyquist polarimeter using numerical simulations, both in the case without noise and with noise. We show that a sensible modulation scheme is obtained by randomly changing the fast axis of the modulators or their retardances in specific ways. We finally demonstrate that the value of the Stokes parameters can be recovered with great precision at almost maximum efficiency, although it slightly degrades when the signal-to-noise ratio of the observations increase, a consequence of the multiplexing under the presence of photon noise.