Physics-Informed Sequential Reconstruction of Scanning Probe Microscopy Images with Calibrated Uncertainty
Scanning probe microscopy (SPM) has become a mainstay of materials science, condensed matter physics, nanotechnology, biology, and semiconductor metrology. An SPM image, however, is acquired sequentially as the probe traverses the surface under closed-loop feedback while thermal drift, feedback dynamics, tip state, mechanical disturbances, and electronic noise evolve during the experiment. Image correction has therefore become an intrinsic part of SPM data analysis. Classical approaches rely on line leveling, filtering, registration, interpolation, and explicit models of tip or scanner distortions, whereas recent work increasingly uses neural networks trained to map corrupted images to corrected ones. Here, we explore a different formulation in which SPM reconstruction is treated as a Bayesian sequential state-estimation problem. The hidden state represents surface height and its low-order evolution along the slow-scan direction; an artifact-dependent quality score continuously modifies the observation likelihood; a forward Kalman pass provides the causal estimate and innovation diagnostics; and a Rauch-Tung-Striebel (RTS) backward pass incorporates information from the complete acquisition. The result is a reconstructed surface, a relative posterior uncertainty map, and line-resolved diagnostic signals. The recursion is computationally lightweight and scales linearly with the number of image pixels, while the physical parameters can in principle be initialized from instrument characterization or from priors learned during previous operation, an extension not exercised here. We organize the method as a multi-axis family of models so that the contributions of state representation, artifact recognition, lateral coupling, and acquisition redundancy can be evaluated independently.