Fast modal broadband phase retrieval via spatial-spectral compression

Broadband phase retrieval technology overcomes the limitations of light sources, offering a highly flexible and versatile method for wavefront measurement. To address the challenge of repetitive multi-wavelength forward propagation, we propose a joint spatial-spectral compression model. This method utilizes Zernike orthogonal basis modes to fit the complex amplitude of the pupil, with complex polynomial coefficients expanded along the spectral dimension. Leveraging the linear nature of diffraction propagation, the point spread function is represented as a weighted sum of propagated Zernike mode fields at different wavelengths. The weights are determined by a spectral basis coefficient matrix, whose dimensionality is independent of the number of wavelengths. In the diffraction model, the Zernike-mode propagation responses are spatially separable and invariant across iterations, enabling precomputation and caching. This eliminates the repeated Fourier propagations required in conventional phase retrieval technology, markedly improving computational efficiency while preserving reconstruction accuracy. This strategy provides an effective modeling and reconstruction framework for broadband phase retrieval.