Measuring the Phase of an Optical Field from Two Intensity Measurements: Analysis of a Simple Theoretical Model

Figure 1

Depiction of phase retrieval setup for an idealized phase retrieval experiment, OFT: optical Fourier transform. A set of point sources with known amplitude and unknown phase are present in the input plane. This distribution is Fourier-transformed by the lens and the intensity of the resulting distribution in the Fourier plane is recorded. We assume that we can measure this intensity distribution over an infinite extent and with extremely high spatial resolution so that we can ignore the numerical effects of sampling due to the CCD/CMOS pixels. We show how this intensity distribution is processed using a second Fourier transform, this time calculated numerically, and we examine its properties in the “analysis plane” (as depicted above). We show how to determine the phase values of the point sources in the input plane.