Ismael Hernández-Capuchin

Fringe projection profilometry (FPP) is established as a dual-role metrological instrument: a calibration source for physics-based analytical models and a validation benchmark for machine learning surrogates of thermoelastic out-of-plane deformation. A three-stage framework is presented with three principal contributions: (i) physics-consistent synthetic data generation via the Kirchhoff–Love plate solution, with boundary condition factor κ calibrated from FPP phase-unwrapping measurements; (ii) comparative training of five baseline surrogates, including four classical regressors and a physics-free multilayer perceptron (MLP), and a physics-informed neural network (PINN) with residual architecture, physics branch, gating mechanism, and curriculum learning, embedding flexural rigidity, thermal bending moment, and the scaling relation α ⋅ Δ T ⋅ L 2 / t as physics-informed inputs; all neural network models were evaluated across five random seeds to report mean ± standard deviation; and (iii) external metrological validation against FPP displacement maps at three thermal states ( Δ T = 65 , 123 , and 172 K ) on an aluminum 1060 plate, with measurement uncertainty explicitly characterized. The first state serves as the κ calibration anchor; the remaining two constitute independent validation points. The PINN achieves RMSE = 2.90 ± 0.26 μ m and MAPE = 1.82 ± 0.16 % (mean ± std over five seeds), outperforming the best classical baseline (Gradient Boosting, RMSE = 5.28 μ m) by 45 % in root mean square error (RMSE) and the physics-free MLP (RMSE = 10.27 ± 3.08 μ m) by 72 % , with the performance gap attributable to physics embedding rather than network capacity. Against FPP measurements, PINN prediction errors are 0.9%, 0.9%, and 18.2% at the three states—closely matching the calibrated analytical model alone (0.87%, 0.85%, 18.16%), and consistently below the errors of an industrial-grade SolidWorks finite element method model (6.0%, 12.9%, 23.4%), used here as a reference without a documented mesh convergence study (section 4.6.2), rather than a fully verified benchmark, at the two lower states. An out-of-distribution generalization experiment confirms that the PINN degrades 50.6 % less than the best tuned classical model in physically demanding extrapolation zones. These results demonstrate that FPP can anchor both calibration and independent validation of physics-informed surrogates on a single specimen and thermal loading configuration, establishing a reproducible methodology for dimensional stability assessment in precision engineering.

Digital fringe projection profilometry (DFPP) is a widely used technique for full-field, non-contact 3D surface measurement, offering precision from the sub-micrometer-to-millimeter scale depending on system geometry and fringe design. This review provides a consolidated synthesis of advances reported between 2022 and 2025, covering projection and imaging architectures, phase formation and unwrapping strategies, calibration approaches, high-speed implementations, and learning-based reconstruction methods. A central contribution of this review is the integration of these developments within a metrological perspective, explicitly relating phase–height transformation, fringe parameters, system geometry, and calibration to dominant uncertainty sources and error propagation. Recent progress highlights trade-offs between sensitivity, robustness, computational complexity, and applicability to non-ideal surfaces, while learning-based and hybrid optical–computational approaches demonstrate substantial improvements in reconstruction reliability under challenging conditions. Remaining challenges include measurements on reflective or transparent surfaces, dynamic scenes, environmental instability, and real-time operation. The review outlines emerging research directions such as physics-informed learning, digital twins, programmable optics, and autonomous calibration, providing guidance for the development of next-generation DFPP systems for precision metrology.