Phase retrieval using multi-grid method based on transport of intensity equation

The multi-grid method is a common method for solving the transport of intensity equation (TIE). Transport of intensity equation can retrieve phase information from the directly measured intensity image. When using multi-grid method to solve the TIE, firstly, the phase distribution is directly solved on the coarsest layer. The solved phase distribution is regard as the initial value on the finest grid layer to increase the convergence speed of the algorithm. Residual error on the finest grid can be obtained, then, using the restrict operators transfer the residual error from finer grid to coarser grid, until the solution on the coarsest grid is obtained. the solution on coarser grid transfer to finer grid by using prolongation operator, until the accurate phase distribution solution obtained on the finest grid. The Simulation experiments show that this method has a better convergence rate and retrieves complicated phase with higher accuracy.