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In this Letter, we propose a universal iterative compensation solution to the transport-of-intensity equation (US- TIE) with the advantages of high accuracy, convergence guarantee, applicability to arbitrarily-shaped regions, and simplified implementation and computation. With the “maximum intensity assumption”, we firstly simplified TIE as a standard Poisson equation to get an initial guess of the solution. Then the initial solution is further refined iteratively by solving the same Poisson equation, and thus, the instability associated with the division by zero/small intensity values and large intensity variations can be effectively bypassed. The convergence analysis and effectiveness of the iterative process has been given in detail. Furthermore, simulations with arbitrary phase, arbitrary aperture shapes, and nonuniform intensity distributions verify the effectiveness and universality of the proposed method.
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