The Shack–Hartmann wavefront sensor (SHWFS) is commonly used for its high speed and precision in adaptive optics. However, its performance is limited in low light conditions, particularly when observing faint objects in astronomical applications. Instead of a pixelated detector, we present a new approach for wavefront sensing using a single-pixel detector, which is able to code the spatial position of a light spot array into the polarization dimension and decode the polarization state in the polar coordinate. We propose validation experiments with simple and complex wavefront distortions to demonstrate our approach as a promising alternative to traditional SHWFS systems, with potential applications in a wide range of fields.

We report a spatially modulated polarimetry scheme by using a zero-order vortex half-wave retarder (ZVHR) and a spatial Fourier analysis method. A ZVHR is employed to analyze the input polarized light and convert it into a vectorial optical field, and an analyzer is set after the ZVHR to form an hourglass intensity pattern due to the spatial polarization modulation. Then, the input light’s Stokes parameters can be calculated by spatial Fourier analysis of the hourglass pattern with a single shot. The working principle of the polarimeter has been analyzed by the Stokes–Mueller formalism, and some quantitative measuring experiments of different polarization states have been demonstrated. The experimental results indicate that the proposed polarimeter is accurate, robust, and simple to use.