Mitigating the effect of noise in the hybrid input-output method of phase retrieval

Here a modification to the hybrid input-output (HIO) method of phase retrieval is presented which aides in mitigating the negative effects of low signal-to-noise ratios (SNRs). Various type of interferometers measure diffraction patterns which are used to determine the Fourier transform modulus of an objective. Interferometry often suffers from very low SNRs making phase retrieval difficult because of the sensitivity of most phase retrieval algorithms to local minima. Here we analyze the effect of noise on the HIO method. The result is used as a rationale for the proposed modification to the HIO method. The algorithm presented here introduces a filtering scheme which removes much of the Fourier modulus noise. Examples are shown and the results are compared to the HIO method with and without the proposed modification. Comparisons are also made to other methods of filtering the Fourier modulus noise.