Feature engineering with neural networks in Shack–Hartmann wavefront sensing

Wavefront sensing in conventional Shack–Hartmann wavefront sensors (SHWSs) relies on sequential centroiding and wavefront slope fitting algorithms, which are computationally demanding and whose accuracy is limited by wavefront sampling. In this work, we propose hybrid machine learning (ML) strategies combining feature selection and extraction with artificial neural networks (ANNs) that enhance both the wavefront sensing accuracy and computational efficiency. The ML models proposed for use in a SHWS (8×8 lenslets) are compared against a robust traditional wavefront sensing algorithm. Using a numerically simulated dataset of 10000 SHWS images, we evaluated three approaches: (1) manual feature selection (MFS) with ANNs, (2) random forest (RF)–based feature selection with ANNs, and (3) principal component analysis (PCA)–based feature extraction with ANNs. These methods achieved an average wavefront root-mean-square (RMS) error lower than the traditional algorithm, while maintaining sub-millisecond wavefront sensing time. To evaluate the models’ performance under realistic conditions, we introduced a simulated Gaussian readout noise with a standard deviation of 15 ADU for a 12-bit camera. Evaluations using both noise-free models and those explicitly trained on noisy data confirmed that the proposed ML frameworks remain robust to readout noise. All the simulations and neural network training were performed on a personal laptop without a dedicated GPU or high-performance computing resources. These results demonstrate that integrating feature engineering with ANNs offers significant potential for accurate and computationally efficient SH wavefront sensing.