# Correlation Plenoptic Imaging: An Overview
## 3 Experimental Demonstration of CPI  
The experimental setup employed to demonstrate CPI is represented in Figure 10. The light source is a continuous-wave single-mode laser with wavelength \(\lambda=532\,\)nm and tunable power up to \(5\,\)W (Azur Light Systems ALS-532 nm-SF, Azur Light Systems, Pessac, France). To obtain a controllable chaotic source, the laser beam is expanded to a spot size \(\sigma=1.08\,\)mm, is passed through a polarizer and impinges on a rotating ground glass disk, spinning at \(0.05\,\)Hz, at a distance of about \(4\,\)cm from its center. As depicted in Figure 10, light is then divided by a polarizing beam-splitter (PBS). The combination of polarizer and PBS enables optimizing the SNR by balancing the intensities at the sensors D\({}_{a}\) and D\({}_{b}\), which are different areas of the same scientific complementary metal-oxide semiconductor (sCMOS) sensor (Hamamatsu ORCA-Flash 2.8 camera C11440-10C, Hamamatsu Corporation, Shizuoka Prefecture, Hamamatsu, Japan). The reflected beam passes through the object of interest (ThorLabs 1951 USAF Resolution Test Targets, Newton, NJ, USA), propagates toward a lens (\(L_{b}\)) of focal length \(F=300\,\) mm, and reaches the angular sensor D\({}_{b}\), which lies in the conjugate plane of the source (image has unitary magnification \(M=1\)). The transmitted beam propagates toward a lens (\(L_{a}\)) of focal length \(f_{a}=125\,\)mm, that reproduces on the spatial sensor D\({}_{a}\) the image of the \"ghost-imaging plane\", set at a distance \(z_{a}=92\,\)mm from the source, with a magnification \(M_{a}=1\). In our case, the resolution at focus is \(\Delta x^{f}=\lambda/\)NA\({}^{2}=14\,\)um, where NA is the smaller numerical aperture between the ones of the source and of \(L_{a}\). For objects at the resolution limit, DOF \(=\lambda/\)NA\({}^{2}=0.37\,\)mm. The camera is characterized by a pixel size of \(3.6\,\)um, which is much smaller than both the spatial and the directional resolution. We thus perform a binning of the camera pixels to match the effective pixels \(\delta_{x}\) and \(\delta_{u}\) with the spatial and directional resolutions, respectively. In particular, during data acquisition, we perform a \(2\times 2\) binning to get \(\delta_{x}=7.2\,\)um\(\approx\Delta x^{f}/2\). In post-processing, a further \(10\times 10\) binning is performed on the region of the camera sensor dedicated to the angular measurement, thus getting \(\delta_{u}=72\,\)um\(<\Delta u/2\), with \(\Delta u=\lambda\,z_{b}/a\). The latter is determined, for the chosen values of \(z_{b}\) and object size, by diffraction at the object. The test target mimics small details and allows for easily monitoring the image resolution, both in the out-of-focus and in the refocused image. We acquire 50,000 frames for all measurements at a frame rate of \(45.4\,\) s\({}^{-1}\), with an exposure time \(\tau_{\text{meas}}=21\,\)um approximately 100 times smaller than the chaotic source coherence time. The acquired frames are processed to evaluate the spatio-temporal intensity correlation, which is expected to converge to Equation (2). The CPI images are reported in Figures 8 and 9a,b. In Figure 8, we report the experimental results obtained for element 3 of group 2 of the test target: the three slits have center-to-center distance \(d=0.198\) mm and slit width \(a=d/2\) (measurement B in Figure 7). In the left column, we report the out-of-focus image obtained on D\({}_{a}\) by measuring correlation with the whole detector D\({}_{b}\), when the mask is placed significantly out of focus (\(z_{b}-z_{a}\gtrsim 20\) mm); this is equivalent to the blurred image that any conventional imaging system, characterized by the same NA as our CPI scheme, would retrieve with the same defocusing. In the right column, we report the same image after implementing the CPI refocusing algorithm in Equation (12).