Work

Predictive alignment system integrating feedforward neural networks with riemann fit for diffraction efficiency enhancement in convex ruling grating

Year: 2025

Type: article

Abstract: • Demonstrates superior robustness across 36 test conditions, especially to noise. • Achieves 0.04032 MSE under high noise conditions - 5x better than traditional methods. • Enables sub-10 μ m point spacing after neural optimization with 0.00941 MSE. • Improves average diffraction efficiency by 16.03 % over conventional methods. • Reaches 92.96 % of theoretical diffraction efficiency at 632.8 nm wavelength. The spectral resolution and signal-to-noise ratio quality of an Offner imaging spectrometer depend on the quality of convex grating. To address issues in current convex grating ruling processes, including the influence of convex-specific sagitta factors, substrate eccentricity errors leading to inconsistent groove profiles, low diffraction efficiency in surface micro-regions, and uneven zonal efficiency distribution, this paper proposes a hybrid algorithm integrating radius-constrained Riemann fitting with feedforward neural network (FFNN) optimization. By introducing radius constraints and Lagrange multipliers to enhance short-arc data point fitting, an eccentricity error model is constructed to train the neural network for optimal center calculation, resulting in improved substrate centering accuracy. Based on the substrate centering position, a diffraction efficiency inversion model is established, achieving closed-loop mapping between alignment parameters and optical performance. Through cyclic comparisons under three initial conditions, namely, the central angle, radius, and noise level, the proposed algorithm achieves computational accuracy comparable to that of traditional algorithms under large central angles and large radii. Moreover, under extreme convex grating ruling conditions, such as a 10 ∘ central angle, 20-mm radius, and a noise level with a standard deviation of 0.2, the proposed algorithm achieves a mean square error (MSE) of 0.04032, which is one order of magnitude higher than that of traditional algorithms, indicating greater robustness. Experiments revealed that the algorithm achieves an MSE of 0.00941 at a central angle of 10 ∘ . After neural network optimization, the fitted point spacing is less than 10 µm. The groove consistency of the ruled convex grating is significantly improved. At a wavelength of 632.8 nm, the average efficiency across measured grating positions increases by 16.03 % compared with traditional alignment methods, and the average diffraction efficiency reaches 92.96 % of the theoretical diffraction efficiency. The proposed algorithm effectively solves the high-precision centering challenge for convex grating substrates with small central angles, establishes a quantitative mapping relationship between the diffraction efficiency and the alignment parameters, enhances convex grating ruling technology, enables the preparation of convex gratings with diffraction efficiency closer to theoretical calculations, and provides reliable technical support for improving the performance of Offner imaging spectrometers.

Source: Results in Engineering

DOI: 10.1016/j.rineng.2025.108432