Wavefront Estimation from Pyramid Type Wavefront Sensors Using a Convolutional Neural Network

Images of astronomical objects and orbiting satellites captured by ground-based telescopes are blurred by atmospheric turbulence. Adaptive optics systems correct this blurring using wavefront sensors to measure distortions and deformable mirrors to apply corrections. Among these sensors, the pyramid wavefront sensor is particularly effective. In its basic form, it consists of a four-sided glass prism placed at the focal plane of a telescope, with relay optics that re-image the pupil through the prism onto a detector. The pyramid wavefront sensor can be extended to an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex>-sided prism, including 3-sided, 6-sided, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\infty$</tex>-sided configurations. Traditionally, aberration estimation with the pyramid wavefront sensor relies on Least Squares reconstruction. With advancements in machine learning, this paper explores the use of a convolutional neural network to predict wavefront aberrations directly from noiseless pyramid wavefront sensor and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex>-sided sensor data, expressed in terms of Zernike coefficients. Numerical simulation results demonstrate that the convolutional neural network offers significant improvement over the LS approach in wavefront reconstruction.