A theoretical comparison of Fresnel based digital holography and phase retrieval from the transport of intensity equation

摘要

Optical systems that can recover both the amplitude and phase of a scattered wave field are important for a range of different practical imaging and metrology applications. In this manuscript we examine two different techniques: (A) Fresnel based digital holography and (B) Teague's transport of intensity phase retrieval technique, using a special analytical function that serves to act as the scattered wave field we would like to recover. Nowadays both systems use modern CCD or CMOS arrays to make the necessary intensity measurements. In system (A) an ideal plane wave reference field is required and should overlap, and interfere, with the scattered field at at the CCD plane. The resulting intensity distribution recorded by the CCD is a digital hologram. If several captures are recorded, where the phase of the reference has been changed (stepped) between captures, it is possible to recover an approximation to the complex amplitude of the scattered wave field. In system (B) no reference field is needed, which is a significant advantage from a practical implementation point of view. Rather, the intensity of the scattered wave field has to be measured at two axially displaced planes. We expect that the performance of both systems will be fundamentally limited by at least three separate factors, (ⅰ) the finite extent of CCD array, (ⅱ) the finite extent of the CCD pixels which average the light intensity incident upon them, and (ⅲ) the sampling operation which occurs because the intensity is recorded at a set of uniformly displaced discrete locations. In this manuscript, we examine how factors (ⅰ) and (ⅲ), effect the imaging performance of each system by varying the spatial frequency extent of the scattered wave field. We find that system A has superior performance compared to system B.