# Correlation Plenoptic Imaging: An Overview
## 1 Introduction
We perform \"spatial\" and \"directional\" measurements on two separate sensors: one gives the image of the scene of interest, while the other one gives the image of the focusing element responsible for image formation (e.g., the camera lens of standard PI). The correlation measurement combines such structured information to provide the same kind of information acquired by a conventional plenoptic camera, but without losing image resolution. In fact, the retrieval of the directional information is exactly the same as in standard PI, namely, it is obtained by joining \"points\" of the image of interest with \"points\" of the image of the focusing element. We have theoretically shown that CPI can be achieved by exploiting the correlation properties of both chaotic light [39; 40] and entangled photons from spontaneous parametric down-conversion (SPDC) [41]. We have also performed the first experimental proof of CPI with chaotic light [42], and we are currently generalizing the experimental demonstration to entangled photons. The results suggest that CPI can improve the power of plenoptic imaging, opening the way to promising applications, especially in fields like microscopy and 3D imaging where fast acquisition must be combined with high resolution. In addition, entangled photons from SPDC provide the possibility to perform CPI by correlating photons of different wavelengths in the two arms of the setup: light illuminating the object in one arm is not required to have the same wavelength as light remotely detected in the other arm [43; 44; 45]. This feature is interesting both in view of applications requiring specific illumination wavelengths for the object and to optimize the detection efficiency. Entanglement has the further advantage of enabling high signal-to-noise ratio (SNR) images at low photon fluxes [46; 47; 48], which is particularly interesting when radiation damage of the sample is an issue (e.g., in biomedical microscopy). Unlike previous fundamental demonstrations [49; 50; 51], CPI exploits the simultaneous momentum and position correlation of light to address intrinsic limitations affecting practical imaging system, such as the resolution versus DOF compromise. Compared to other 3D imaging techniques based on the simultaneous detection of both the spatial distribution and the propagation direction of light, CPI does not require either delicate interferometric techniques, as in digital holographic microscopy [52], or phase retrieval algorithms, as in Fourier ptychography [53]. Furthermore, similar to standard PI, CPI does not require fast pulsed light, as Time-Of-Flight (TOF) imaging [54; 55; 56; 57; 58; 59; 26], and, compared to confocal microscopy [60], offers the advantage of being a scanning-free imaging modality. In this paper, we review the main aspects of CPI, and present different schemes we have so far developed. We start, in Section 2, with the first proposed CPI setup, where an adequate modification of lensless ghost imaging is employed to retrieve the plenoptic ghost image of the object. In Section 3,we report the first experimental realization of this CPI scheme. In Section 4, we present an alternative CPI scheme, where the image of the object is directly focused on one sensor, while ghost imaging (i.e., correlation measurements) is employed to image the focusing element in order to gain the required directional information; the practical advantages of this scheme will also be discussed. In Section 5, we present CPI based on entangled photon pairs generated by SPDC.