RESUMEN
In general, the problem of reconstructing an object from its Fourier modulus has no solution when the Fourier modulus is contaminated by noise. Therefore a quasi solution, which we call the ideal estimate of the object to be reconstructed, is defined here based on the concept of territories of the convergence objects of the error-reduction algorithm, and a method that attempts to find that solution is presented. Keeping in mind that the ideal estimate is one of the output-stagnation objects of the hybrid input-output algorithm, we modify the hybrid input-output algorithm so that the output-stagnation objects can be located even when the value of the feedback parameter is not infinitesimally small, and this modified algorithm is combined with the hybrid input-output algorithm itself. The results of computer simulations carried out to test the performance of the proposed method are shown.
RESUMEN
We show that a small-scale wave front can be reconstructed by an algebraic procedure from its intensity distribution in the focal plane, except for the ambiguities of the piston phase and the point-symmetrical solution of the complex conjugate. Details of the reconstruction procedure for a 3 x 3 wave front are presented, and the effectiveness of this procedure for a contaminated case is shown by computer simulation. A method for overcoming the ambiguity problem resulting from the point-symmetrical solution is also suggested.