# Effects of Atmospheric Turbulence on Lensless Ghost Imaging with Partially Coherent Light
## 4 Experimental Measurement of the Ghost Image through Monostatic and Bistatic Turbulence in the Lab  
In this section, we carry out the lensless GI experiment through thermally-induced turbulence in the laboratory. The schematic for the experiment setup is shown in Figure 6.  
A He-Ne laser beam operated at \(\lambda~{}=~{}632.8\) nm is reflected by the mirror M\({}_{1}\), then focused onto a rotating ground glass disk (RGGD) by the lens \(L_{1}\), then passes through the collimation lens \(L_{2}\) and the Gaussian amplitude filter (GAF), which are used to collimate the light from RGGD and shape the intensity distribution of the light into the Gaussian profile, respectively. The beam emerging from the GAF can be regarded as the GSM source, the second-order correlations of the electric fields of which are described by Equation (12). The beam width and the coherence width are determined by the transmission radius of the GAF and the beam spot size on the RGGD, respectively. Note that the GSM source is not the unique source for realizing ghost imaging. Light sources with low spatial coherence such as sunlight and halogen lamps can serve as the illuminations in ghost imaging systems [49; 50]. Perhaps, the light generated by a superluminescent diode is also a good candidate [51]. The generated source is split into two paths by the intensity beam splitter (BS). The transmitted beam is received by the detector \(D_{1}\) after being reflected by the mirror \(M_{3}\), and the reflected beam is received by the detector \(D_{2}\). An object is placed against \(D_{2}\). The output signals from \(D_{1}\) and \(D_{2}\) are sent to a computer to measure the FOCF. A \(35\) cm \(\times\)\(50\) cm hot plate is located in two paths to produce the thermally-induced turbulence. The strength of the turbulence is controlled by the temperature of the hot plate \(T\). As seen in Figure 6, the distance between two paths after \(M_{3}\) and \(M_{4}\) is \(l\). In our experiment, we modulate the distance \(l\) to control the monostatic or bistatic turbulence. If \(l=0\), the two optical paths from source to \(D_{1}\) and from source to \(D_{2}\) experience the same turbulence exactly. Therefore, the statistics of the turbulence is correlated, belonging to monostatic turbulence. When \(l\) is large enough, the correlation of the turbulence between two paths degrades, which means the statistics of turbulence in two paths are independent, degenerating to bistatic turbulence. In the experiment, the object we used is a double slit with slit width \(a~{}=~{}0.6\) mm and the distance of two slits \(d~{}=~{}1.2\) mm, corresponding to the numerical simulation in Figure 2. The beam width and the coherence width of the source measured from the experiment are \(\sigma_{I}~{}=~{}4.0\) mm and \(\sigma_{g}~{}=~{}0.3\) mm, respectively. The distance from the source plane to \(D_{1}\) or \(D_{2}\) is about \(1.0\) m. In our experiment, \(D_{1}\) and \(D_{2}\) recorded 3000 frames with the frames per second (FPS) being 30, respectively, and then, the data were used to reconstruct the ghost image using the MATLAB software. The total time for obtaining one  
Figure 6: Experimental setup for the lensless ghost imaging (GI) system through thermal-induced turbulence. M\({}_{1}\)-M\({}_{4}\), mirrors; \(L_{1}\), \(L_{2}\), thin lenses; RGGD, rotating ground glass dishes; GAF, Gaussian amplitude filter; BS, intensity beam splitter; \(D_{1}\), \(D_{2}\), detectors; PC, computer. ghost image was about 140 s. Figure 7 presents the experiment results of the ghost image of the double slit with several different \(l\) and temperature \(T\).