Acta Optica Sinica, Volume. 29, Issue 6, 1514(2009)
Phase Retrieval Using Transport of Intensity Equation Solved by Full Multigrid Method
The computation of the basic multigrid method is started with an arbitrary approximation on the finest grid. When the basic multigrid method is used to solve the transport of intensity equation(TIE) for phase retrieval, the retrieved phase distribution is sensitive to the initial values on the finest grid. To mitigate the above-mentioned problem, a full multigrid method (FMG) solving the TIE for phase retrieval is presented. Instead of starting with an arbitrary approximation on the finest grid, the first approximation is obtained by interpolating from a coarse grid solution. The coarsest grid is created based on the finest grid using the restrain operators, and the solution on the coarsest grid is gotten. Then the initial value of the fine grid can be obtained through prolongation operator, and the Ⅴ-cycle is adopted to solve the equation on this fine grid. Based on this nested iteration technique, the exact solution to the TIE is obtained. The simulation experiments show that this method can retrieve the complicated phase distributions with high accuracy, and has fast convergence speed.
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Xue Bindang, Zheng Shiling, Jiang Zhiguo. Phase Retrieval Using Transport of Intensity Equation Solved by Full Multigrid Method[J]. Acta Optica Sinica, 2009, 29(6): 1514