Realizing Fresnel Incoherent Correlation Holography as a Coded Aperture Imaging System using Advanced Computational Algorithms

Fresnel incoherent correlation holography (FINCH) also called as incoherent digital holography. In FINCH, a self-interference Fresnel hologram is created when light from an object point is split into two, modulated using two different quadratic phase masks and interfered. At least three such holograms are needed with phase shifts
$0,2\pi /3$
and
$4\pi /3$
and combined to remove the twin image and bias terms during computational reconstruction involving Fresnel backpropagation. When the FINCH setup is engineered to achieve the same beam diameter for the two interfering beams, a super lateral resolution which is 1.5 times that of a direct imaging system for the same numerical aperture, is obtained. FINCH has a low temporal and axial resolution and low light throughput when compared to the direct imaging system. In this study, FINCH is enhanced and realized as a coded aperture imaging (CAI) system using three computational algorithms: Transport of Amplitude into Phase based on Gerchberg Saxton Algorithm (TAP-GSA), Lucy-Richardson-Rosen algorithm (LRRA) and computational point spread function engineering (CPSFE) technique. The PSF is recorded for FINCH in the first step as in CAI and used as the reconstruction function. The TAP-GSA was used to improve the design of phase masks and achieve a high light throughput. The CPSFE was used to shift the lateral resolution limit from the diameter of the pinhole which is used for recording the PSF to the limit of FINCH. The LRRA was used for the reconstruction of FINCH holograms. Optical experimental results of CAI-inspired ‘perfect’ FINCH are promising for applications in fluorescence microscopy.