Analyzing digital holographic systems with the LCT

Abstract

Digital holography is an electronic means of measuring the complex amplitude of an optical wavefield using CCD or CMOS arrays. With an appropriate reconstruction algorithm the intensity values registered by the pixels produce images of a particular (object) scene. These holographic systems are very sensitive to even small vibrations or deformations of an object, mainly due to the phase information that is also recovered by the measurement. Hence these systems are useful in a wide array of different metrology problems. It is important that we somehow quantify the information that can be recovered with such a detection scheme; better if we can provide a theoretical framework to optimize an optical system design for a given metrology problem. In this manuscript we show how the Linear Canonical Transform can fulfill this role and can optimally match the space-bandwidth product (SBP) of a signal to be measured with the SBP of a CCD/CMOS detector array. We provide formulae that determine the performance of generalized holographic optical systems (containing lenses and sections of free space), taking into account the finite extent of the CCD array, the size of the pixels, and the spacing between them. Some illustrative examples are presented, with associated numerical simulations.