Symmetric-anchored transport-of-intensity phase retrieval with adaptive gradient refinement

Quantitative phase imaging via the transport-of-intensity equation (TIE) enables label-free phase measurement, but its accuracy degrades under large defocus, where the underlying nonlinearity becomes pronounced. We propose SA-RAdam, a symmetric-anchored, rectified-Adam-refined framework for high-fidelity TIE phase retrieval. A symmetric two-plane architecture yields a second-order accurate derivative prior at a virtual mid-plane, anchored to the reference plane via angular-spectrum propagation. An adjoint gradient of the forward model, combined with rectified adaptive momentum and line search, then recovers nonlinear high-frequency phase details typically lost in linear solvers. Simulations and experiments on binary and biological phase targets show consistent convergence, elimination of boundary overshoot, and RMSE reductions of over 60% relative to existing iterative solvers, substantially extending the practical defocus range of TIE-based phase retrieval.