Speckle-correlation-assisted phase alignment for scattering matrix reconstruction

Optical scattering severely distorts optical fields propagating through complex media, posing fundamental challenges for imaging and wavefront control. Transmission-matrix-based approaches provide a deterministic framework for compensating such distortions; however, reference-free, intensity-only schemes suffer from inter-row phase ambiguities that prevent reconstruction of a globally phase-consistent scattering matrix. Here we introduce a speckle-correlation-assisted phase alignment method that resolves this limitation by incorporating intrinsic speckle correlations as physically motivated convolutional constraints within an iterative phase-retrieval framework. The proposed approach enables fully reference-free reconstruction of a globally phase-consistent scattering matrix using intensity measurements alone. As an experimental validation of the reconstructed matrix, we demonstrate high-fidelity projection of optical vortex beams and user-defined, continuously distributed complex fields through different scattering media, including ground glass and zinc oxide. These results confirm the accuracy and robustness of the method for deterministic complex field control in strongly scattering environments.