Analysis of practical sampling and reconstruction from Fresnel fields

We present an analysis of the different aspects involved with the sampling and reconstruction of Fresnel field distribution. Fresnel fields, describing a propagating optical wave, are digitally recorded in many optical applications. The recording process involves discretization of the continuous Fresnel field using a sampling sensor. Typical nonideal sensors induce degradation of the optical information due to finite spatial sampling rate, finite aperture size, and finite detector element size (finite fill factor). In this work, we investigate the condition and limitation of the reconstruction of Fresnel fields sampled with nonideal sampling sensors. We also analyze the propagation of measurement and reconstruction noise through the reconstruction process. In our analysis, we distinguish between continuous (optical) and numerical (computational) reconstructions. We focus on the different reconstruction conditions and limitations, depending on whether the reconstruction is performed in a continuous space or numerically.