Phase retrieval wavefront sensing for space adaptive optics using one significantly defocused image

A wavefront sensing method based on a single-frame, significantly defocused point spread function is proposed for retrieving higher-order Zernike aberration coefficients in space optical systems. Unlike conventional phase retrieval algorithms, the proposed approach eliminates the requirement for beam splitters and multiple defocus adjustments. Consequently, system complexity and potential errors arising from misalignment are effectively reduced. In this method, a single PSF image acquired at a predetermined large-defocus position is employed for accurate reconstruction of higher-order wavefront aberrations. A two-stage solution strategy, consisting of an initial coarse estimation followed by refined iterative optimization, is implemented to retrieve the aberration coefficients. Additionally, an enhanced BFGS optimization algorithm is applied to further improve the convergence efficiency of the reconstruction. Robustness to imaging noise was evaluated through Monte Carlo simulations under PSNR levels ranging from 20 to 50 dB. Across 100 trials per noise level, the algorithm consistently converged with root-mean-square wavefront errors below 0.011<i>λ</i> at 30-50 dB. Even under the challenging 20 dB condition, the average error remained within 0.0218<i>λ</i>. Additionally, experimental validation under representative optical misalignments demonstrated that the proposed method achieves high reconstruction accuracy, yielding an average RMS wavefront error of 0.0163<i>λ</i> across multiple test cases. The reconstructed wavefronts exhibit strong agreement with interferometric measurements, verifying the effectiveness and feasibility of this method for space-based optical systems utilizing active wavefront sensing.