The Transport-of-Intensity Equation (TIE) stands out as a prominent method for quantitative phase imaging and phase retrieval. Its strength lies in directly recovering the quantitative phase distribution of an optical field through intensity measurements taken at different focus planes. This deterministic and non-interferometric approach bypasses the complexities of interferometry. However, current TIE solvers often rely on strict preconditions, such as specific boundary conditions, a clearly defined closed region, and a near-uniform in-focus intensity distribution. These conditions are challenging to meet simultaneously in real-world experiments, limiting the accuracy and applicability of existing methods.
To overcome these limitations, we introduce a universal Solution Transport method for TIE that ensures high accuracy, guaranteed convergence, and applicability to regions of any shape. This method also simplifies both implementation and computation. By employing a “maximum intensity assumption,” we initially transform the TIE into a standard Poisson equation. Solving this equation provides an initial estimate of the phase. This preliminary solution transport is then iteratively refined. In each iteration, we solve the same Poisson equation, effectively circumventing instability problems arising from division by zero or small intensity values, as well as significant intensity variations.
The effectiveness and versatility of our proposed method have been validated through simulations and experiments. These tests encompassed diverse scenarios, including arbitrary phase profiles, varied aperture shapes, and non-uniform intensity distributions. The results consistently demonstrate the robustness and broad applicability of this universal solution transport approach, marking a significant advancement in phase retrieval techniques.
