Non-recursive transport of intensity phase retrieval with the transport of phase

The transport of intensity equation (TIE) is a non-interferometric phase retrieval method that originates from the imaginary part of the Helmholtz equation and is equivalent to the law of conservation of energy. From the real part of the Helmholtz equation, the transport of phase equation (TPE), which represents the Eikonal equation in the presence of diffraction, can be derived. The amplitude and phase for an arbitrary optical field should satisfy these coupled equations simultaneously during propagation. In this work, the coupling between the TIE and TPE is exploited to improve the phase retrieval solutions from the TIE. Specifically, a non-recursive fast Fourier transform (FFT)-based phase retrieval method using both the TIE and TPE is demonstrated. Based on the FFT-based TIE solution, a correction factor calculated by the TPE is introduced to improve the phase retrieval results.