# Correlation Plenoptic Imaging: An Overview
## 2 Correlation Plenoptic Imaging with Chaotic Light--First Scheme
### Depth-of-Field Improvement
Hence, the physical quantities that generally define the directional and spatial resolution of correlation plenoptic imaging are the source-to-object distance \(z_{b}\) and the quantities \(a\) and \(d\) that characterize the object transmission function. Figure 7c shows, in a density plot, the visibility of the images of double slits with center-to-center distance \(d\) and width \(a=d/2\), evaluated in the experimental setting described in Section 3. The plot tests the reliability of the geometrical prediction in Equation (16), and also reveals the real (wave-optics) limits of resolution and depth of field in CPI. Oscillations that can be observed in the density plot are due to the coherent nature of correlation plenoptic imaging. Figure 7: Visibility of double-slit masks in the case of standard imaging (**a**), standard plenoptic imaging with \(N_{u}=3\) (**b**) and CPI (**c**). The compared devices are characterized by the same numerical aperture of the focusing element employed in the experiment reported in Section 3. The distance \(d=2a\) between slits is measured in units of the focused image resolution \(\Delta x^{f}\). Points labeled by A, B and C identify the scenarios implemented in the experiment, and the corresponding results are reported in Figures 8 and 9a,b. In (**c**), the (white) dashed line indicates the limit of perfect refocusing, according to the geometrical prediction of Equation (16) [42]. Reproduced with the permission from [42], copyright American Physical Society, 2017. To compare CPI with both standard imaging and standard PI, we consider imaging devices having the same NA as the light source in our scheme, and report in Figure 7,b the visibility they achieve. In such cases, the quantity \(z_{b}-z_{a}\) is the difference between the actual position of the object and the position of the plane focused on the detector by the imaging lens. We have considered the  
Figure 3:0 Experimental demonstration of CPI as obtained in the setup of Figure 3:1 The out of focus image of the object (element 3 of group 2 of a positive USAF-1951 test target) is reported in the left panel, while the refocused image is represented in the right panel. This experimental scenario, labelled by B in Figure 7, is characterized by \(z_{b}-z_{a}=21\) mm. The experimental data are retrieved with a pixel size \(\delta_{x}=7.2\) μm, coinciding with the resolution limit, as determined by diffraction; the effective pixel size of the refocused image is scaled by a factor \(z_{b}/z_{a}\), in line with Equation (12). After correlation measurement, the uncorrelated background has been removed by combining a Gaussian low-pass filter with thresholding in the Fourier domain (experimental results originally published in Ref. [42]). Reproduced with the permission from [42], copyright American Physical Society, 2017. Figure 3:2 CPI images obtained in the experimental settings A and C of Figure 7, with the setup reported in Figure 3:3 The experimental data are taken with a pixel size at the diffraction limit (\(\delta_{x}=7.2\) μm), while the refocused images are characterized by an effective pixel size scaled by a factor \(z_{b}/z_{a}\), in line with Equation (12). After correlation measurement, low-pass Gaussian filtering and thresholding in the Fourier domain was applied to remove an uncorrelated background. Experimental results were originally published in supplementary material of Ref. [42]. Reproduced with the permission from [42], copyright American Physical Society, 2017.  
case \(N_{u}=3\) (namely, \(3\times 3\) resolution cells on the focusing element) in the case of standard PI, in order to gain directional information without hindering too much spatial resolution. Comparing the three plots in Figure 7, we can observe that CPI combines in an optimal way the advantages of standard imaging and plenoptic imaging, since diffraction-limited resolution is preserved and DOF is increased beyond the typical values achieved in standard PI.