Adaptive wavelength calibration for robust multi-plane phase retrieval

Multi-plane phase retrieval reconstructs complex wavefronts from axially scanned diffraction patterns. However, laser instability or calibration errors can cause the experimental wavelength to deviate from the nominal value, resulting in cumulative phase errors and resolution loss. Here, we propose an adaptive wavelength calibration (AWC) algorithm to compensate for wavelength deviations by adjusting axial propagation distances during iteration. Utilizing the wavelength-distance equivalence in Fresnel diffraction, the algorithm dynamically adjusts axial spacing by minimizing structural similarity differences between simulated and actual diffraction patterns. The enhanced particle swarm optimization automatically determines the optimal axial correction for each plane, achieving sub-nanometer wavelength accuracy even under large deviations. Experiments on resolution targets, phase objects, and biological samples confirm its robustness against coupled errors from wavelength drift and stage misalignment. This approach relaxes strict wavelength stability requirements, enabling high-fidelity phase imaging with low-cost laser sources.