Locating a single point source of light using an analytic estimator enabled by spatial mode demultiplexing

Advances in single-particle tracking (SPT) have heightened the importance of accurately locating a single point source of light. In traditional direct imaging, the optimal method is maximum likelihood estimation, which can attain the Cramér-Rao bound but typically requires iterative methods or grid searches. In this proof-of-principle experiment, we demonstrated that under high signal-to-noise ratio conditions, the analytic estimator enabled by the spatial mode demultiplexing (SPADE) measurement scheme can achieve localization accuracy comparable to that of the maximum likelihood estimator with a single calculation. These results highlight the computational advantage of SPADE, suggesting its potential utility in SPT tasks where both accuracy and efficiency are important.