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    This study introduces a novel sub-Nyquist polarimeter capable of measuring polarization by mitigating atmospheric seeing effects. It utilizes compressed sensing to accurately recover Stokes parameters from modulated signals, even with slow camera integration.

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    Area of Science:

    • Astronomy
    • Optical Physics
    • Signal Processing

    Background:

    • Atmospheric seeing, caused by refractive index variations, distorts astronomical observations.
    • Traditional polarimeters struggle to overcome seeing effects due to modulation frequencies near atmospheric fluctuation rates.
    • Slow camera integration in polarimeters necessitates advanced signal recovery techniques.

    Purpose of the Study:

    • To develop and demonstrate a polarimeter that effectively eliminates atmospheric seeing distortions.
    • To recover Stokes parameters with high precision using sub-Nyquist sampling techniques.
    • To investigate the feasibility of a polarimeter operating below the atmospheric seeing frequency.

    Main Methods:

    • A standard polarimeter design with two retarders and a beam splitter was employed.
    • Retarders were modulated at approximately 500 Hz, a frequency comparable to atmospheric seeing.
    • Compressed sensing theory was applied to demodulate signals and recover seeing variations by imposing sparsity constraints on Fourier coefficients.
    • Numerical simulations were conducted with and without noise to validate the method.

    Main Results:

    • The feasibility of the sub-Nyquist polarimeter was demonstrated through numerical simulations.
    • A modulation scheme involving random changes in modulator properties was found to be effective.
    • Stokes parameters were recovered with high precision and near-maximum efficiency.
    • A slight degradation in precision was observed with increasing signal-to-noise ratio due to photon noise and multiplexing.

    Conclusions:

    • The proposed sub-Nyquist polarimeter effectively mitigates atmospheric seeing effects for polarization measurements.
    • Compressed sensing provides a robust framework for signal recovery in the presence of atmospheric distortions.
    • The technique offers a promising approach for high-precision polarimetry in astronomical observations.