Due to its high precision, phase-shifting interferometry (PSI) is a commonly used optical component detection method in interferometers. However, traditional PSI, which is susceptible to environmental factors, is costly, with piezoelectric ceramic transducer (PZT) being a major contributor to the high cost of interferometers. In contrast, two-frame random interferometry does not require precise multiple phase shifts, which only needs one random phase shift, reducing control costs and time requirements, as well as mitigating the impact of environmental factors (mechanical vibrations and air turbulence) when acquiring multiple interferograms. A novel method for wavefront reconstruction using two-frame random interferometry based on Swin-Unet is proposed. Besides, improvements have been made on the basis of the established algorithm to develop a new wavefront reconstruction method named Phase U-Net plus (PUN+). According to training the Swin-Unet and PUN+ with a large amount of simulated data generated by physical models, both of the methods accurately compute the wrapped phase from two frames of interferograms with an unknown phase step (except for multiples of $\pi$). The superior performance of both methods is effectively showcased by reconstructing phases from both simulated and real interferograms, in comprehensive comparisons with several classical algorithms. The proposed Swin-Unet outperforms PUN+ in reconstructing the wrapped phase and unwrapped phase.

Fourier ptychography (FP) is a computational imaging technique with the advantage that it can obtain large field-of-view (FOV) and high-resolution (HR) imaging. We propose an algorithm for Fourier ptychography based on reweighted amplitude flow (RAF) with regularization by denoising (RED) and deep decoder (DD), which is an untrained deep generative model. The proposed method includes two loops, using reweighted amplitude flow with regularization by denoising as an inner loop for phase retrieval and deep decoder for further denoising as an outer loop in the Fourier ptychography recovery system. The proposed method does not need any training dataset, just adds a little computer time during the image recovery process. The proposed method has no bias due to training images, which is different from other deep learning methods. The experimental results show that the proposed method can improve the reconstruction quality in both PSNR and SSIM.

High-fidelity imaging in extreme low light is challenged by ultra-low signal-to-noise ratios. We propose a hybrid noise modeling framework integrating physical priors with generative adversarial networks (GANs). The method simulates photon shot noise via Poisson distribution and incorporates readout, row, and quantization noise. A multi-layer perceptron (MLP) dynamically maps ISO levels to noise intensities in logarithmic space, followed by a residual U-Net for non-linear refinement. Results on the SID datasets show that our method outperforms state-of-the-art approaches in terms of Average Kullback–Leibler Divergence (AKLD). Denoising networks trained on our synthetic noise achieve performances comparable to those trained on real-world paired datasets.

We present a differentiable, curriculum-based optimization workflow for the engineering-oriented design of large-aperture reflective optical systems. The method integrates physics-informed differentiable ray tracing with a progressive, two-stage optimization strategy that evolves from simple Ritchey–Chrétien (RC) foundations to complex four-mirror architectures. Without relying on pretrained models or large datasets, the workflow optimizes geometric and physical parameters under field-weighted RMS, focal length, and dynamic obscuration constraints while maintaining minimal perturbation to primary and secondary mirrors. Validated through Zemax-based analysis, the optimized systems achieve high imaging quality with improved RMS uniformity and stable convergence across varying aperture scales. This approach provides a practical and scalable pathway for the design and optimization of reflective optical instruments, offering strong robustness and adaptability for diverse imaging applications.