High-precision intelligent measurement of surface relief grating parameters based on physical knowledge and an improved Tandem model

Abstract

Diffraction gratings are key components in spectroscopy, imaging, and communications. Their performance critically depends on precise parameters such as period, groove depth, and duty cycle. However, conventional measurement techniques face inherent limitations. Purely physics-based models are time-consuming, labor-intensive, and destructive, while data-driven approaches often exhibit physical inconsistency. To address these challenges, this paper proposes PKITM (Physics-Knowledge Improved Tandem Model), a novel non-destructive algorithm for rapid and precision surface relief grating parameters measurement. The PKITM integrates physical priors with an improved tandem neural network architecture. First, to overcome the limitations of pure data-driven models, PKITM establishes the multi-wavelength S-polarized −1st order diffraction efficiency response via rigorous physics-based modeling (Rigorous Coupled Wave Theory). This process augments training data with realistic Gaussian noise to simulate experimental conditions. Second, a pre-trained forward Deep Neural Network (DNN) is employed to learn the complex nonlinear mapping from grating parameters to diffraction efficiency. Finally, to address physical consistency and capture complex spectral correlations, a global Attention Mechanism(AM) is integrated into the Tandem model architecture. This integration enforces physics-informed loss constraints while capturing wavelength-dependent efficiency correlations, thereby achieving robust and physically logical grating parameter measurement. Experimental results demonstrate that PKITM achieves state of the art accuracy and inherent physical consistency. Compared to Support Vector Regression(SVR), Artificial Neural Networks(ANN), and standard Deep Neural Networks(DNN), PKITM achieves Mean Absolute Error(MAE) below 0.02 for duty cycle and 0.01 μm for groove depth in both simulated and experimental measurements, respectively. Moreover, PKITM exhibits superior prediction performance and enhanced robustness. This method provides a novel enabling technology for advanced grating manufacturing, quality assurance, and application deployment.