Abstract
A three dimensional (3D) pupil is an optical element, most commonly implemented on a volume hologram, that processes the incident optical field on a 3D fashion. Here we analyze the diffraction properties of a 3D pupil with finite lateral aperture in the 4-f imaging system configuration, using the Wigner Distribution Function (WDF) formulation. Since 3D imaging pupil is finite in both lateral and longitudinal directions, the WDF of the volume holographic 4-f imager theoretically predicts distinct Bragg diffraction patterns in phase space. These result in asymmetric profiles of diffracted coherent point spread function between degenerate diffraction and Bragg diffraction, elucidating the fundamental performance of volume holographic imaging. Experimental measurements are also presented, confirming the theoretical predictions.
Highlights
The use of volume holographic (VH) pupils in imaging systems includes applications such as hyper-spectral image acquisition [1], profilometric imagers [2, 3], unhindered imaging capability under broadband illumination, and multi-focal microscopic imaging [4, 5]
The 3D pupil implemented by VH was located in the Fourier plane based on Fig. 1(c)
Thickness of the 3D pupil in the point spread function (PSF) measurements was ~1.2mm with θs = 68, and Bragg-matched operation wavelength was 532nm (Millennia, SpectraPhysics)
Summary
The use of volume holographic (VH) pupils in imaging systems includes applications such as hyper-spectral image acquisition [1], profilometric imagers [2, 3], unhindered imaging capability under broadband illumination, and multi-focal microscopic imaging [4, 5]. Utilizing holographic recording techniques and advances in material [5], the 3D VH imaging pupil can be further functionally engineered to achieve wavelength-coded [8] and phase-coded [9] VH imaging gratings. We are interested in phase space (i.e. space-spatial frequency) information transport [13] between the object and image planes through the 3D pupil. We derive basic volume holographic properties of angular selectivity in phase space as well as phase space information of diffracted beams at various locations along the VH pupil, we analyze of the relationship between the response of 3D pupils in phase space and point spread function as it impacts imaging performance we compare; the simulation results with experiments under different aperture conditions validating the theory
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