Sparse aperture optical systems employ separated subapertures to achieve equivalent large aperture high resolution imaging, but they are also more susceptible to the combined effects of cophase errors and polarization aberrations, which lead to point spread function distortion and image quality degradation. To address this problem, this paper proposes a Polarization Phase Diversity (PPD) method for cophase errors and polarization aberrations in sparse aperture optical systems. Based on the Jones pupil theory, a unified imaging model incorporating both cophase errors and polarization aberrations is established. By combining focused and defocused images acquired under different analyzer directions, a polarization multichannel observation framework is constructed to jointly retrieve piston, tilt, diattenuation, and retardance parameters. Numerical simulations are mainly carried out on a Golay3 sparse aperture optical system, and additional Gaussian-noise and Golay6 simulations are performed to evaluate the robustness and extensibility of the proposed framework. The results show that, except for the phase-equivalent ambiguity of the piston term, the proposed method can accurately recover the cophase and polarization-aberration parameters under noise-free conditions. Compared with conventional methods considering only cophase errors, the proposed method achieves better image restoration performance in terms of image sharpness, detail recovery, PSNR, and SSIM. The noise experiments further demonstrate that the full-parameter restoration maintains clear advantages under noisy observations, and the Golay6 results indicate that the framework can be extended to sparse aperture configurations with more subapertures. The proposed method provides an effective approach for error sensing and image restoration in sparse aperture optical systems.
Liu et al. (Thu,) studied this question.