30 September 2013 A theoretical comparison of Fresnel based digital holography and phase retrieval from the transport of intensity equation
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Abstract
Optical systems that can recover both the amplitude and phase of a scattered wave eld are important for a range of di erent practical imaging and metrology applications. In this manuscript we examine two di erent 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 eld 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 eld is required and should overlap, and interfere, with the scattered eld 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 eld. In system (B) no reference eld is needed, which is a signi cant advantage from a practical implementation point of view. Rather, the intensity of the scattered wave eld 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 nite extent of CCD array, (ii) the nite 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), e ect the imaging performance of each system by varying the spatial frequency extent of the scattered wave eld. We nd that system A has superior performance compared to system B.
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Damien P. Kelly, Damien P. Kelly, Lysann Megel, Lysann Megel, Thomas Meinecke, Thomas Meinecke, Stefan Sinzinger, Stefan Sinzinger, } "A theoretical comparison of Fresnel based digital holography and phase retrieval from the transport of intensity equation", Proc. SPIE 8833, Tribute to H. John Caulfield, 88330G (30 September 2013); doi: 10.1117/12.2024855; https://doi.org/10.1117/12.2024855
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