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Bayesian Optimization and Convolutional Neural Networks for Zernike-Based Wavefront Correction in High Harmonic Generation

Guilherme Grancho D. Fernandes, Duarte Alexandrino, Eduardo Silva, João Matias, Joaquim Pereira

TL;DR

This work tackles aberration-induced beam quality degradation in high-harmonic generation by applying machine-learning-based aberration correction via an SLM. It compares Bayesian optimization, which provides a structured, interpretable baseline via sequential Zernike-mode optimization, with a CNN that learns a direct PSF-to-Zernike mapping to predict correction coefficients from focal-spot images. The CNN achieved 80.39% test accuracy on a small dataset (506 images), illustrating the potential for real-time aberration correction, while Bayesian optimization demonstrates feasibility but is limited by single-objective optimization and mode interactions. The study identifies the dataset size as a primary constraint and outlines future work including additional Zernike modes, closed-loop adaptive optics, transfer learning, multi-objective optimization, and hybrid approaches to combine interpretability with rapid predictions.

Abstract

High harmonic generation (HHG) is a nonlinear process that enables table-top generation of tunable, high-energy, coherent, ultrashort radiation pulses in the extreme ultraviolet (EUV) to soft X-ray range. These pulses find applications in photoemission spectroscopy in condensed matter physics, pump-probe spectroscopy for high-energy-density plasmas, and attosecond science. However, optical aberrations in the high-power laser systems required for HHG degrade beam quality and reduce efficiency. We present a machine learning approach to optimize aberration correction using a spatial light modulator. We implemented and compared Bayesian optimization and convolutional neural network (CNN) methods to predict optimal Zernike polynomial coefficients for wavefront correction. Our CNN achieved promising results with 80.39% accuracy on test data, demonstrating the potential for automated aberration correction in HHG systems.

Bayesian Optimization and Convolutional Neural Networks for Zernike-Based Wavefront Correction in High Harmonic Generation

TL;DR

This work tackles aberration-induced beam quality degradation in high-harmonic generation by applying machine-learning-based aberration correction via an SLM. It compares Bayesian optimization, which provides a structured, interpretable baseline via sequential Zernike-mode optimization, with a CNN that learns a direct PSF-to-Zernike mapping to predict correction coefficients from focal-spot images. The CNN achieved 80.39% test accuracy on a small dataset (506 images), illustrating the potential for real-time aberration correction, while Bayesian optimization demonstrates feasibility but is limited by single-objective optimization and mode interactions. The study identifies the dataset size as a primary constraint and outlines future work including additional Zernike modes, closed-loop adaptive optics, transfer learning, multi-objective optimization, and hybrid approaches to combine interpretability with rapid predictions.

Abstract

High harmonic generation (HHG) is a nonlinear process that enables table-top generation of tunable, high-energy, coherent, ultrashort radiation pulses in the extreme ultraviolet (EUV) to soft X-ray range. These pulses find applications in photoemission spectroscopy in condensed matter physics, pump-probe spectroscopy for high-energy-density plasmas, and attosecond science. However, optical aberrations in the high-power laser systems required for HHG degrade beam quality and reduce efficiency. We present a machine learning approach to optimize aberration correction using a spatial light modulator. We implemented and compared Bayesian optimization and convolutional neural network (CNN) methods to predict optimal Zernike polynomial coefficients for wavefront correction. Our CNN achieved promising results with 80.39% accuracy on test data, demonstrating the potential for automated aberration correction in HHG systems.

Paper Structure

This paper contains 20 sections, 2 equations, 11 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Motivation
  3. Experimental Apparatus
  4. Bayesian Optimization
  5. The bayesopt Function
  6. Optimizing The Peak Intensity
  7. Results and Discussion
  8. Fourier Transform and Harmonic Wavelengths
  9. New Camera
  10. Applying the Fourier Transform
  11. Neural Network
  12. Motivation
  13. Dataset Script
  14. Neural Network Structure
  15. Hyperparameters and Training
  16. ...and 5 more sections

Figures (11)

  • Figure 1: Final setup for HHG with SLM. The gas cell contains krypton. Filters remove all wavelengths from the beam post-HHG (represented in pink), except those corresponding to high-order harmonics in the XUV range (represented in purple). The dashed orange lines represent unwanted diffracted orders from the SLM, which are blocked by an iris.
  • Figure 2: Total HHG signal as a function of oblique astigmatism coefficient.
  • Figure 3: Intensity map for oblique astigmatism coefficient of 0.18.
  • Figure 4: Harmonic signal acquired with the ALEX-i camera.
  • Figure 5: Two-dimensional spatial Fourier transform of the harmonic signal.
  • ...and 6 more figures