Application of Machine Learning Methods for Identifying Wave Aberrations from Combined Intensity Patterns Generated Using a Multi-Order Diffractive Spatial Filter

A multi-order combined diffraction spatial filter, integrated with a set of Zernike phase functions (representing wavefront aberrations) and Zernike polynomials, enables the simultaneous formation of multiple aberration-transformed point spread function (PSF) patterns in a single plane. This is achieved using an optical Fourier correlator and provides significantly more information than a single PSF captured in focal or defocused planes—all without requiring mechanical movement. To analyze the resulting complex intensity patterns, which include 49 diffraction orders, a convolutional neural network based on the Xception architecture is employed. This model effectively identifies wavefront aberrations up to the fourth Zernike order. After 80 training epochs, the model achieved a mean absolute error (MAE) of no more than 0.0028. Additionally, a five-fold cross-validation confirmed the robustness and reliability of the approach. For the experimental validation of the proposed multi-order filter, a liquid crystal spatial light modulator was used. Optical experiments were conducted using a Fourier correlator setup, where aberration fields were generated via a digital micromirror device. The experimental results closely matched the simulation data, confirming the effectiveness of the method. New advanced aberrometers and multichannel diffractive optics technologies can be used in industry for the quality control of optical elements, assessing optical system alignment errors, and the early-stage detection of eye diseases.