Rapid High‐Dimensional State Tomography Enabled by Spatial Autocorrelation

Abstract High‐dimensional states encoded in the spatial degrees of freedom of structured light are central to modern optical applications, yet conventional projective tomography requires multi‐step measurements that severely limit efficiency, particularly for complex fields. Here, a fast high‐dimensional tomography technique based on spatial correlation is presented, which directly retrieves modal amplitudes from the central intensity of Fourier‐domain correlation patterns and enables single‐shot estimation of intermodal phases from the surrounding interference fringes. This correlation‐based approach eliminates the need for phase‐shifting interference and reduces the required number of measurements for an ‐dimensional state from to , a total reduction of . By exploiting the polarization insensitivity and kilohertz‐level modulation capability of digital micromirror devices (DMDs), rapid and accurate reconstruction of complex structured light composed of multiple LG modes is experimentally demonstrated. The method provides a scalable platform for high‐throughput optical field characterization with broad applications in optical metrology, high‐speed imaging, and the analysis of both quantum and classical states of light.