The time-delay problem, which is introduced by the response time of hardware for correction, is a critical and non-ignorable problem of adaptive optics (AO) systems. It will result in significant wavefront correction errors while turbulence changes severely or system responses slowly. Predictive AO is proposed to alleviate the time-delay problem for more accurate and stable corrections in the real time-varying atmosphere. However, the existing prediction approaches either lack the ability to extract non-linear temporal features, or overlook the authenticity of spatial features during prediction, leading to poor robustness in generalization. Here, we propose a mixed graph neural network (MGNN) for spatiotemporal wavefront prediction. The MGNN introduces the Zernike polynomial and takes its inherent covariance matrix as physical constraints. It takes advantage of conventional convolutional layers and graph convolutional layers for temporal feature catch and spatial feature analysis, respectively. In particular, the graph constraints from the covariance matrix and the weight learning of the transformation matrix promote the establishment of a realistic internal spatial pattern from limited data. Furthermore, its prediction accuracy and robustness to varying unknown turbulences, including the generalization from simulation to experiment, are all discussed and verified. In experimental verification, the MGNN trained with simulated data can achieve an approximate effect of that trained with real turbulence. By comparing it with two conventional methods, the demonstrated performance of the proposed method is superior to the conventional AO in terms of root mean square error (RMS). With the prediction of the MGNN, the mean and standard deviation of RMS in the conventional AO are reduced by 54.2% and 58.6% at most, respectively. The stable prediction performance makes it suitable for wavefront predictive correction in astronomical observation, laser communication, and microscopic imaging.

Digital holography records the entire wavefront of an object, including amplitude and phase. To reconstruct the object numerically, we can backpropagate the hologram with Fresnel–Kirchhoff integral-based algorithms such as the angular spectrum method and the convolution method. Although effective, these techniques require prior knowledge, such as the object distance, the incident angle between the two beams, and the source wavelength. Undesirable zero-order and twin images have to be removed by an additional filtering operation, which is usually manual and consumes more time in off-axis configuration. In addition, for phase imaging, the phase aberration has to be compensated, and subsequently an unwrapping step is needed to recover the true object thickness. The former either requires additional hardware or strong assumptions, whereas the phase unwrapping algorithms are often sensitive to noise and distortion. Furthermore, for a multisectional object, an all-in-focus image and depth map are desired for many applications, but current approaches tend to be computationally demanding. We propose an end-to-end deep learning framework, called a holographic reconstruction network, to tackle these holographic reconstruction problems. Through this data-driven approach, we show that it is possible to reconstruct a noise-free image that does not require any prior knowledge and can handle phase imaging as well as depth map generation.

In optical scanning holography, one pupil produces a spherical wave and another produces a plane wave. They interfere with each other and result in a fringe pattern for scanning a three-dimensional object. The resolution of the hologram reconstruction is affected by the point spread function (PSF) of the optical system. In this paper, we modulate the PSF by a spiral phase plate, which significantly enhances the lateral and depth resolution. We explain the theory for such resolution enhancement and show simulation results to verify the efficacy of the approach.