Learned spatially varying microscopy model with adaptive point spread functions

Spatial variability in fluorescence microscopy, particularly in lensless systems, necessitates precise calibration and modeling of the system. We introduce the learned spatially varying microscopy model (LSVMM), a framework that learns spatially varying point spread functions from randomly distributed bead images, supported by an adaptive warp module. LSVMM offers a practical alternative to traditional stepwise calibration, which requires careful operation using precise motorized stages. We evaluate LSVMM on lensless microscopes with inherent variability, demonstrating its ability to capture rich position-dependent responses and achieve robust modeling accuracy with minimal manual preprocessing. LSVMM outperforms conventional spatially varying models across diverse optical configurations, increasing median peak signal-to-noise ratio by 2-7 dB and median multi-scale structural similarity by 0.02-0.10. As a differentiable forward model, it supports synthetic data generation and integration with deep learning reconstruction pipelines. The LSVMM framework can be applied to spatially varying imaging modalities that traditionally rely on stepwise calibration.