Computational three-dimensional reconstruction in diffraction grating imaging by convolution with periodic δ-function array

Abstract

In this paper, we propose a new 3-D computational reconstruction method in diffraction grating imaging. Diffraction grating imaging has advantages in terms of system complexity in generating a parallax image array (PIA) for 3-D imaging. In general, a computational reconstruction of 3-D images isś implemented with a back-projection algorithm of PIA. Therefore, the PIA obtained by a camera array and a lens array based system requires the process of defining and extracting the individual parallax image region in advance. However, since the PIA in a diffraction grating imaging is generated by a single optical element, so there is no suitable method to detect the region of individual parallax images from captured PIA. In addition, it is almost impossible to extract individual parallax image regions when parallax images of different orders overlap each other in the PIA. As a 3-D computational reconstruction method that solves this problem in diffraction grating imaging, we propose a method of extracting a spatially filtered PIA from an original PIA. The proposed method theoretically derives the periodicity and intensity of a PIA by optically analyzing the acquisition process of a PIA. Reconstruction of 3-D object image is realized through the superposition by convolution of parallax images with the same period. The proposed 3-D computational reconstruction may be an optimized method for diffraction grating imaging because it does not require the extraction of individual parallax image regions. The proposed theoretical analysis and computational reconstruction verified the usefulness in 3-D imaging through the optical experimental results.