In the co-phasing techniques applied to the segmented telescope, a Shack–Hartmann wavefront sensor cannot accurately detect the piston error of the segment. Although the phase diversity (PD) algorithm can detect the piston error of each segment, it fails to reconstruct the wavefront quickly, and its dynamic range is small. Other technologies, such as prisms or micro-lens arrays, will significantly increase the complexity and construction cost of the optical system. Moreover, they may also introduce non-common path errors. In this study, we propose an approach to address this challenging problem via curvature sensing. This method uses multi-wavelength to eliminate the influence of $2\pi $ ambiguity and improve the capture range of co-phasing detection. However, curvature sensing is easily influenced by atmospheric seeing. We propose a wavelet support vector machine optimized via particle swarm optimization (PSO-WSVM) method to deal with this problem, and to improve the application scope of curvature sensing. We reshape SVM with a wavelet kernel function, and improve the PSO algorithm. We train the SVM to build a prediction model to distinguish the piston error range of each pair of adjacent segments and surpass $2\pi $ ambiguity. First, we obtain defocused images by means of the convolution technique. Second, we propose a prediction model based on SVM. We select the correlation coefficient between the sampling signal and the template signal at different wavelengths as the input vector, and we choose a wavelet basis function as the kernel function of SVM. Third, we improve the PSO algorithm with the exponential decreasing inertia weight (EDIW) to tune the parameters of SVM. Finally, we perform a simulation experiment on a real optical system model based on the Keck telescope. The results indicate that the performance of this method is better than that of other state-of-the-art SVM-based classifiers, and it works rapidly during the observation.

Optical systems suffer from wavefront aberrations due to complex atmospheric environments and system component errors, leading to systematic aberrations and significantly degrading optical field quality. Therefore, the detection and correction of optical aberrations are crucial for efficient and accurate observations. To fully utilize the capabilities of observation equipment and achieve high-efficiency, accurate imaging, it is essential to develop wavefront correction technologies that enable ultra-precise wavefront control. The application of data-driven techniques in wavefront correction can effectively enhance correction performance and better address complex environmental challenges. This paper elaborates on the research progress of data-driven methods in wavefront correction from three aspects: principles, current research status, and practical applications. It analyzes the performance of data-driven methods in diverse real-world scenarios and discusses future trends in the deep integration of data-driven approaches with optical technologies. This work provides valuable guidance for advancing wavefront correction methodologies.

Wavefront reconstruction and correction under strong turbulence has become a crucial issue for adaptive optics systems. An approach using a plenoptic sensor has attracted high attention recently. However, the existing reconstruction and correction algorithms based on the plenoptic sensor are sometimes unsatisfactory. Therefore, we propose a modified approach based on the checkerboard algorithm to reconstruct the wavefront. By means of a weighted summation, the reconstruction accuracy is clearly increased. We propose using the direct-gradient method to correct the disturbed wavefront after reconstruction, and our experimental results demonstrate the effectiveness with only one correction step.

Single-pixel imaging is a computational optical imaging technique that uses a single-pixel detector to obtain scene information and reconstruct the image. Compared with traditional imaging techniques, single-pixel imaging has the advantages of high sensitivity and a wide dynamic range, etc., which make it have broad application prospects in special frequency band imaging and scattering media imaging. This paper mainly introduces the history of development and the characteristics of the single-pixel detector, focuses on the typical applications of single-pixel imaging in coded aperture, transverse scanning, and longitudinal scanning systems, and gives an account of the application of deep learning technology in single-pixel imaging. At the end of this paper, the development of single-pixel imaging is summarized and future trends forecasted.

The ability to detect pistons with high accuracy over a wide range is paramount to the co-phasing of sparse aperture optical systems. This paper proposes a global piston error modulation method for sparse aperture mirrors based on convolutional neural networks. The efficacy of this approach is demonstrated by the introduction of a convolutional block attention module (CBAM) with a data generalization mechanism, which facilitates the rapid and accurate learning of key features from actual co-phasing sensor images. This is achieved with less labelled data, thereby enabling the accurate detection of piston error distribution. The experimental results demonstrate that the method exhibits high prediction accuracy, enhances the piston error detection efficiency and sensing range, and facilitates global fine phase correction (<λ/80) under closed-loop conditions. The technique demonstrates considerable potential for application in the field of simplifying the wavefront sensing and modulation process of large segmented telescopes.

Large survey telescopes are vital for mapping dark energy and dark matter in the deep universe. This study presents a fiber-linked internal motion metrology system that aligns the mirrors and large lenses in the telescopes to enhance alignment accuracy by improving the image quality at a lower weight, volume, power, and cost. The internal motion system comprises a photonic laser beam projector capable of projecting multiple Gaussian beams onto the detector of the telescope. The specific spatial frequency aberration component is determined by combining Gaussian beam location and the geometry model of the telescope. Furthermore, integrating the proposed system with the curvature-sensing wavefront system enables more precise alignment and camera sensing. In the experimental tests, the location precision was within 10 μm, and the rotation precision improved to 5 arcsecs, fulfilling the alignment and motion monitoring requirements of large survey telescopes. The results of this study can be used as a reference to improve the performance of closed-loop bandwidth systems and active camera optics.