A method for reconstructing an electromagnetic wave, comprising the steps of: a) illuminating a specimen mounted in a hole in a 2 dimensional occluding plane at an output plane; b) measuring at a diffraction plane the amplitude distributions of a plural number N of diffraction patterns, each of the diffraction patterns resulting from the application of a different phase filter of known phase shift at or near the output plane; and characterized by iteratively: c) beginning the first iterative algorithm cycle in the diffraction plane by selecting an amplitude distribution corresponding to one particular filter; d) combining a first estimate of the phase distribution with the selected amplitude distribution to yield a first estimate of the complete wave function for the particular filter in the diffraction plane; e) inverse Fourier-transforming the estimate of the complete wave function from each of the diffraction patterns to produce an estimate of the filtered specimen wave at the output plane; f) applying an inverse phase filter to the estimate of the filtered specimen wave to cancel the effect of the application of the particular filter, yielding a first raw estimate of the specimen phase and amplitude distributions; g) repeating steps (c) through (f) for each of the N diffraction patterns to determine N raw estimates of the specimen phase and amplitude distribution; h) adding the N raw estimates of the specimen phase and amplitude distribution and dividing each sum by N to provide an average specimen phase and amplitude distribution; and i) setting to zero the values of those elements of the average specimen phase and amplitude distribution corresponding to locations outside of the hole of the 2 dimensional occluding plane to provide an estimate of the wave function in the occluding plane; and thereby, on the basis of the transformed diffraction patterns and the known characteristics of the filters estimating the wave functions at the diffraction and specimen planes, including the amplitude and phase at previously unmeasured points. a) illuminating a specimen mounted in a hole in a 2 dimensional occluding plane at an output plane; b) measuring at a diffraction plane the amplitude distributions of a plural number N of diffraction patterns, each of the diffraction patterns resulting from the application of a different phase filter of known phase shift at or near the output plane; and characterized by iteratively: c) beginning the first iterative algorithm cycle in the diffraction plane by selecting an amplitude distribution corresponding to one particular filter; d) combining a first estimate of the phase distribution with the selected amplitude distribution to yield a first estimate of the complete wave function for the particular filter in the diffraction plane; e) inverse Fourier-transforming the estimate of the complete wave function from each of the diffraction patterns to produce an estimate of the filtered specimen wave at the output plane; f) applying an inverse phase filter to the estimate of the filtered specimen wave to cancel the effect of the application of the particular filter, yielding a first raw estimate of the specimen phase and amplitude distributions; g) repeating steps (c) through (f) for each of the N diffraction patterns to determine N raw estimates of the specimen phase and amplitude distribution; h) adding the N raw estimates of the specimen phase and amplitude distribution and dividing each sum by N to provide an average specimen phase and amplitude distribution; and i) setting to zero the values of those elements of the average specimen phase and amplitude distribution corresponding to locations outside of the hole of the 2 dimensional occluding plane to provide an estimate of the wave function in the occluding plane; and