Uncertainty Quantification for Deep Learning in Optical Surface Metrology: A Bayesian Approach

Abstract

Deep learning methods have demonstrated strong performance in optical surface metrology tasks including phase unwrapping, thermal image reconstruction, and defect detection. However, a critical limitation of standard deep networks is that they produce point predictions without calibrated confidence estimates, making it difficult to assess when to trust their outputs in high-stakes manufacturing inspection scenarios. This study proposes a Bayesian uncertainty quantification framework for deep learning in optical surface metrology, built upon the measurement systems 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 framework employs Bayesian convolutional neural networks with Monte Carlo dropout to produce pixel-wise uncertainty maps alongside prediction outputs, enabling both aleatoric uncertainty (measurement noise) and epistemic uncertainty (model confidence) to be characterized. A comprehensive evaluation is conducted across three representative tasks: thermal image reconstruction on non-flat surfaces, phase unwrapping in deflectometry, and surface defect detection. Simulation and benchmark experiments demonstrate that the proposed framework produces well-calibrated uncertainty estimates—uncertainties correctly identify 91.3% of high-error predictions as uncertain—and reduces failure detection latency by enabling early stopping of unreliable predictions. The framework provides a principled pathway toward trustworthy deep learning deployment in precision optical metrology and quality control.