Physics-constrained autofocus in fiber-coupled single-pixel microscopy

Most existing reconstruction-free autofocus methods in single-pixel imaging (SPI) are designed for global focus assessment, whereas many applications require target-selective focusing on designated targets of interest. Addressing the limitations of image-feature-dependent methods, we present a physics-constrained autofocus framework for fiber-coupled SPI. This approach explicitly constrains autofocus with a diffraction-limited, defocus-dependent point spread function evolution model in the measurement domain, so the focus search follows physically admissible energy redistribution rather than scene-dependent sharpness surrogates. By enforcing L1 normalization to ensure energy conservation and exploiting the analytic scaling laws of intensity distribution, we effectively decouple illumination fluctuations from physical defocus blur. Subsequently, the L2 norm is identified as the optimal metric to quantify energy concentration due to its superior peak sensitivity. The focal position is determined directly without image reconstruction. Simulations confirm that the L2 metric yields the narrowest response bandwidth, minimizing focus bias. Experimental validation on resolution targets and biological samples demonstrates exceptional robustness, where precise focal plane determination is achieved even at an extreme sampling rate of 1%. This data-efficient approach offers a robust solution for SPI focusing tasks targeting individual points of interest.