The conventional Broyden–Fletcher–Goldfarb–Shanno (BFGS) method used to solve the cost function of a phase diversity (PD) algorithm converges to a global optimum only when the cost function is convex. We present a modified BFGS method, which has fine global convergences for both convex and nonconvex functions, guarantees that the solutions will converge to the global minimum, corresponding to the actual wavefront coefficients, and apply it to minimize the PD cost function to co-phase the segmented active optics system and recover the unknown object under different noise levels. The noise amplification effect on the accuracy of the algorithm is removed by our proposed estimated strategy of the regularization parameter for the PD problem. The vast contrast results demonstrate that the modified method has a much higher accuracy than the conventional BFGS method for the nonconvex condition even under a considerably high noise level.

Aimed at the slow detection speed and low measurement accuracy of wavefront aberration in current wavefront sensorless adaptive optic technology, different convolution neural networks (CNNs) are established to detect the turbulence wavefront, including an ordinary convolutional neural network, a ResNet network, and an EfficientNet-B0 network. By using the nonlinear fitting ability of deep neural networks, the mapping relationship between Zernike coefficients and focal degraded image can be established. The simulation results show that the optimal network model after training can quickly and efficiently predict the Zernike coefficients directly from a single focal degraded image. The root-mean-square errors of the wavefront detection accuracy of the three networks are 0.075 λ , 0.058 λ , and 0.013 λ , and the time consumed for predicting the wavefront from the single degraded image are 2.3, 4.6, and 3.4 ms, respectively. Among the three networks presented, the EfficientNet-B0 CNN has obvious advantages in wavefront detection accuracy and speed under different turbulence intensities than the ordinary CNN and ResNet networks. Compared with the traditional method, the deep learning method has the advantages of high precision and fast speed, without iteration and the local minimum problem, when solving wavefront aberration.

Wavefront sensorless (WFSless) adaptive optics (AO) systems have been widely studied in recent years. To reach optimum results, such systems require an efficient correction method. This paper presents a fast wavefront correction approach for a WFSless AO system mainly based on the linear phase diversity (PD) technique. The fast closed-loop control algorithm is set up based on the linear relationship between the drive voltage of the deformable mirror (DM) and the far-field images of the system, which is obtained through the linear PD algorithm combined with the influence function of the DM. A large number of phase screens under different turbulence strengths are simulated to test the performance of the proposed method. The numerical simulation results show that the method has fast convergence rate and strong correction ability, a few correction times can achieve good correction results, and can effectively improve the imaging quality of the system while needing fewer measurements of CCD data.

The misalignment between recorded in-focus and out-of-focus images using the Phase Diversity (PD) algorithm leads to a dramatic decline in wavefront detection accuracy and image recovery quality for segmented active optics systems. This paper demonstrates the theoretical relationship between the image misalignment and tip-tilt terms in Zernike polynomials of the wavefront phase for the first time, and an efficient two-step alignment correction algorithm is proposed to eliminate these misalignment effects. This algorithm processes a spatial 2-D cross-correlation of the misaligned images, revising the offset to 1 or 2 pixels and narrowing the search range for alignment. Then, it eliminates the need for subpixel fine alignment to achieve adaptive correction by adding additional tip-tilt terms to the Optical Transfer Function (OTF) of the out-of-focus channel. The experimental results demonstrate the feasibility and validity of the proposed correction algorithm to improve the measurement accuracy during the co-phasing of segmented mirrors. With this alignment correction, the reconstructed wavefront is more accurate, and the recovered image is of higher quality.

Low light level (LLL) images, which were captured by Intensified CCD (ICCD) camera equipped with an image intensifier, suffer low spatial resolution and contrast due to noise and dispersion. By dividing the integration time into intervals short enough, we obtain photon images where photon formed spots were nearly nonoverlapping. In order to enhance LLL images, we propose a Multi-layer slicing (MLS) photon localization algorithm based on photon images. The photon image is sliced by different planes. Photon spatial distribution (PSD) information is acquired by using projected area ratio, circularity and the number of slices. The enhanced LLL image is obtained by accumulating time-domain correlated PSD images. Experimental results show that the visual effects, spatial frequencies and contrast of the enhanced image are significantly improved.