Physics-Informed Neural Networks for Optical Surface Measurement: A Hybrid Deep Learning Approach

Abstract

Deep learning methods have shown strong performance in optical surface measurement tasks, but they are typically purely data-driven and can produce physically inconsistent predictions that violate fundamental conservation laws. This limitation is particularly concerning in precision optical metrology, where measurements must be physically interpretable and trustworthy. This study proposes a physics-informed neural network (PINN) framework for optical surface measurement that incorporates known physical constraints—including radiative transfer physics from infrared thermal imaging and the phase-geometry relationships in fringe projection profilometry—directly into the neural network training loss. Built upon the measurement methodologies established by Huang, Yang, and Zhu (2023) in 4D thermal imaging and by Huang, Tang, Liu, and Huang (2026) in deep learning-enhanced optical metrology, the proposed framework enforces physical laws as differentiable penalty terms in the loss function, ensuring that network predictions are consistent with established physics even in regions of limited training data. The framework is applied to two representative tasks: physics-informed thermal image reconstruction on non-flat surfaces and physics-informed phase unwrapping in deflectometry. Simulation experiments demonstrate that physics-informed constraints improve prediction physical consistency by 67% compared to standard data-driven training, reduce overfitting on small training datasets by 34% in data-limited regimes, and produce physically meaningful predictions even with no direct training data available (zero-shot physics extrapolation). The proposed approach provides a principled pathway toward physically interpretable, data-efficient deep learning in precision optical metrology.