Measuring the Oscillation Frequency beyond the Diffraction Limit

High-resolution array detectors are widely used in single-particle tracking, but their performance is limited by excess noise from background light and dark current. As pixel resolution increases, the diminished signal per pixel exacerbates susceptibility to noise, degrading tracking accuracy. To overcome this limitation, we use spatial-mode demultiplexing (SPADE) as a noise-robust approach for estimating the motion characteristics of an optical pointlike source. We show that SPADE efficiently concentrate the information into a few key spatial modes, drastically reducing the number of detectors while maintaining high estimation precision. Furthermore, we enhance the robustness of the estimation against excess noise by elaborately designing the modes to be decomposed. We demonstrate, both theoretically and experimentally, that a SPADE with two specific modes outperforms direct imaging in estimating the microoscillation frequency of an optical point source in the presence of excess noise.