## 2 Plenoptic Imaging with Correlations: From Working Principle to Recent Advances  
Quantum plenoptic cameras promise to offer the advantages of plenoptic imaging, primarily ultrafast and scanning-free 3D imaging and refocusing capability, with performances that are beyond reach for the classical counterpart. State-of-the-art plenoptic imaging devices are able to acquire multi-perspective images in a single shot [5]. Their working principle is based on the simultaneous measurement of both the spatial distribution and the propagation direction of light in a given scene. The acquired directional information translates into refocusing capability, augmentable depth of field (DOF), and parallel acquisition of multi-perspective 2D images, as required for fast 3D imaging. In state-of-the-art plenoptic cameras [32], directional detection is achieved by inserting a microlens array between the main lens and the sensor of a standard digital camera (see Figure 1a). The sensor acquires composite information that allows identification of both the object point and the lens point where the detected light is coming from. However, the image resolution decreases with inverse proportionality to the gained directional information, for both structural (use of a microlens array) and fundamental (Gaussian limit) reasons; plenoptic imaging at the diffraction limit is thus considered to be unattainable in devices based on simple intensity measurement [5]. Recently, the INFN group involved in Qu3D has proposed a novel technology, named Correlation Plenoptic Imaging (CPI), that enables overcoming the resolution drawback of current plenoptic devices, while keeping their advantages in terms of refocusing capability and 3D reconstruction [1; 16; 33]. CPI is based on either intensity correlation measurement or photon coincidence detection, according to the light source: actually, CPI can be based on the spatio-temporal correlations characterizing both chaotic sources [16; 33] and entangled photon beams [34] to encode the spatial and directional information on two disjoint sensors, as shown in Figure 1b. CPI with chaotic light is based on the measurement of the correlation function  
\[\Gamma(\mathbf{\rho}_{a},\mathbf{\rho}_{b})=\langle I_{a}(\mathbf{\rho}_{a})I_{b}(\mathbf{ \rho}_{b})\rangle-\langle I_{a}(\mathbf{\rho}_{a})\rangle\langle I_{b}(\mathbf{\rho}_ {b})\rangle, \tag{1}\]  
where \(\langle\dots\rangle\) denotes the average on the source statistics, and \(I_{i}\mathbf{\rho}_{j}\) (\(j=a,b\)) are the intensities propagated by the beam \(j\) and registered in correspondence of point \(\mathbf{\rho}_{j}\) on the sensor D\({}_{j}\). Experimentally, the statistical averages are replaced by time averages, obtained by retrieving a collection of frames, simultaneously acquired by the two detectors. In CPI  
Figure 1: **(a)** the scheme of a conventional plenoptic imaging (PI) device: the image of the object is focused on a microlens array, while each microlens focuses an image of the main lens on the pixels behind. Such a configuration entails a loss of spatial resolution proportional to the gain in directional resolution; **(b)** shows the scheme of a correlation plenoptic imaging (CPI) setup, in which directional information is obtained by correlating the signals retrieved by a sensor on which the object is focused with a sensor that collects the image of the light source. The image in **(a)** is reproduced with the permission from Ref. [16], copyright American Physical Society, 2017.  
devices, the correlation function encodes combined information on the distribution of light on two reference planes, one of which corresponds to the \"object plane\" that would be focused on the sensor in a standard imaging setup, placed at a distance \(s_{0}\) from the focusing element.