Optical three-dimensional refocusing from elemental images based on a sifting property of the periodic δ-function array in integral-imaging

We propose a novel approach to optically refocus three-dimensional (3-D) objects on their real depth from the captured elemental image array (EIA) by using a sifting property of the periodic δ-function array (PDFA) in integral-imaging. By convolving the PDFAs whose spatial periods correspond to each object's depth with the sub-image array (SIA) transformed from the EIA, a set of spatially filtered-SIAs (SF-SIAs) for each object's depth can be extracted. These SF-SIAs are then inverse-transformed into the corresponding versions of the EIAs, and from these, 3-D objects with their own perspectives can be reconstructed to be refocused on their depth in the space. The feasibility of the proposed method has been confirmed through optical experiments as well as ray-optical analysis.