Analytical form of the refocused images from correlation plenoptic imaging

Correlation plenoptic imaging (CPI) is emerging as a promising approach to light-field imaging (LFI), a technique for concurrently measuring light intensity distribution and propagation direction of light rays from a 3D scene. LFI thus enables single-shot 3D imaging, offering rapid volumetric reconstruction. The optical performance of traditional LFI, however, is limited by a micro-lens array, causing a decline in resolution as 3D capabilities improve. CPI overcomes these limitation by measuring photon number correlations on two photodetectors with spatial resolution, in a lenslet-free design, so that the correlation function can be decoded in post-processing to reconstruct high-resolution images. In this paper, we derive the analytical expression of CPI images reconstructed through refocusing, addressing the previously unknown mathematical relationship between object shape and its final image. We show that refocused images are not limited by numerical aperture-induced blurring, as in conventional imaging. Rather, the image features of CPI can be explained through an analogy with imaging systems illuminated by spatially coherent light.