Micro-Oscillation Frequency Estimation of an Optical Point Source Using Spatial Mode Demultiplexing

Abstract: 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 propose to use spatial mode demultiplexing (SPADE) as a noise-robust approach for estimating the motion characteristics of an optical point-like source. Utilizing quantum estimation theory, we show that SPADE efficiently concentrate the point source's positional information into a few key spatial modes, drastically reducing the number of detectors needed while maintaining high estimation precision. We further demonstrate, both theoretically and experimentally, that a SPADE with two elaborately designed modes outperforms direct imaging in estimating the micro-oscillation frequency of an optical point source in the presence of background noise.