On Phase Retrieval Algorithm Based On Transport Of Intensity Equation

Phase is an intrinsic property of the wave field, some researches show that about a quarter of the information in amplitude, and about three-quarters of the information is in the phase. In practice, with the existing detector equipment, only the intensity of the wave field can be measured directly, the phase of the wave field can not be. The lost phase information is critical in the surface renewal, microscopy, the position detection and the depth measurement. Obtained the lost phase information by using the intensity knowned information, this is phase retrieval technique, it has extremely important implication in different branches of physics and engineering applications.At present, phase retrieval technology mainly includes the deterministic algorithm that based on the intensity transport equation(TIE) and Gerchberg-Saxton-Fienup iterative algorithm. As the TIE method can reconstruct the wave spatial phase by solving the second order differential equations(that is, use non-iterative deterministic algorithm) which only need to measure two or three planes intensities that perpendicular to the optical axis, overcomes the uncertainty and poor antinoise of the iterative algorithm. This thesis concentrate on the research of deterministic phase retrieval technology base on the intensity measurement. This thesis is focus on research and analysis of the multigrid algorithm, the phase solution recovered fromed the intensity information is the extact solution. The main research work and contributions as follows:(1) This thesis discusses the deterministic phase retrieval algorithm based on TIE. Four kind of classic algorithm for solving the TIE is summarized, such as Fourier method, Green function method, Zernike polynomial method and Multigrid method. And mathematical calculation of multiple grid is described.(2) The thesis concentrate on the research of deterministic phase retrieval technology of Multigrid algorithm base on the intensity measurement, and made some improvement. The main idea of this method is that:stared from the coarsest grid, given a initial value, then got a solution by calculating, regard the calculated solution as the finest initial value, got an approximate solution by calculating, then calculate its residual, restricted it to coarser grid and solving, until it to the coarsest grid, followed with the correction step by step of the solution of a fine grid layer. Finally, we eliminate different frequency error components by looping in different degree of the grid layer, so get the accurate solution.We verify the algorithm using simulation experiments, and examine the algorithm performance of noise immunity. We find that the improved multi-grid algorithm improves the accuracy of phase retrieval. And we build the image data acquisition platform, use it shoot real defocus image and make real experiment with the algorithm. The simulation and real experiments show that the multigrid algorithm can better take true phase objects from the intensity image.(3) We research multigrid algorithm by using multiple defocus images to solve the TIE. We discuss important parameters calculate in solving the TIE process, that is calculation of the intensity differential, and use it in improved multigrid algorithm. And use simulation experiment verify the method, the results shows that it improve the algorithm performance of noise immunity further. The author make real experiment by using the platform, which can better retrieval the actual phase of the object from the intensity image.(4) We make detail introduce for the developed phase retrieval system, the system contains four classical algorithms used in solve TIE, and we introduce how to handle Multigrid algrorithms manily. The system software interface is simple, intuitive, easy and simple to handle. The author has applied software copyright.