High-precision wavefront reconstruction from Shack-Hartmann wavefront sensor data by a deep convolutional neural network

Abstract

The Shack–Hartmann wavefront sensor (SHWFS) has been widely used for measuring aberrations in adaptive optics systems. However, its traditional wavefront reconstruction method usually has limited precision under field conditions because the weight-of-center calculation is affected by many factors, such as low signal-to-noise-ratio objects, strong turbulence, and so on. In this paper, we present a ResNet50+ network that reconstructs the wavefront with high precision from the spot pattern of the SHWFS. In this method, a nonlinear relationship is built between the spot pattern and the corresponding Zernike coefficients without using a traditional weight-of-center calculation. The results indicate that the root-mean-square (RMS) value of the residual wavefront is 0.0128 μm, which is 0.79% of the original wavefront RMS. Additionally, we can reconstruct the wavefront under atmospheric conditions, if the ratio between the telescope aperture’s diameter D and the coherent length r 0 is 20 or if a natural guide star of the ninth magnitude is available, with an RMS reconstruction error of less than 0.1 μm. The method presented is effective in the measurement of wavefronts disturbed by atmospheric turbulence for the observation of weak astronomical objects.

Shack-Hartmann wavefront reconstruction by deep learning neural network for adaptive optics

“…Hu et al took this a step further, using the raw SHWFS dot patterns to directly reconstruct wavefronts without the need for slope measurements at all. 14 This was done using a ResUNet model architecture, which is the basis for the current research.…”

“…In this paper, a ResUNet CNN, similar to Hu et al, 14 is employed on a set of SHWFS images collected from wind tunnel experiments. The ResUNet architecture is a combination of the well-established ResNet 14 and U-Net, 15 which is an encoder-decoder architecture commonly used in image-to-image applications.…”

“…10 U-Net, on the other hand, extracts feature maps from images at different resolution levels by downsampling using a combination of convolutional and maxpooling layers, and then upsampling the extracted feature maps back to the original resolution. 14 In this encoder-decoder architecture, information at each encoder level is preserved and transferred to its corresponding decoder level, creating dense feature representations without the loss of spatial information commonly associated with successive convolutions. By combining the two model architectures, ResUNet works by passing residual blocks from the encoder layers across to their equivalent decoder layers, where each residual block is composed of concatenated features extracted from the image by using differently-sized convolution kernels, as in.…”

“…By combining the two model architectures, ResUNet works by passing residual blocks from the encoder layers across to their equivalent decoder layers, where each residual block is composed of concatenated features extracted from the image by using differently-sized convolution kernels, as in. 14 The network's U-shape structure, shown in Fig3, reduces the spatial information with each consecutive block while increasing the number of features captured, allowing for detection and preservation of key features that are then expanded back to an image by the decoder.…”

Modal shape reconstruction method for deflectometry based on deep learning

“…Jin et al [23] propose a weights-sharing two-stream network for the prediction of the Zernike coefficient. Gu et al [24] presents a network based on ResNet50+ for reconstructing the wavefront with high accuracy.…”