# Flexible Construction of a Partially Coherent Optical Array
## 3 Results and Discussion
A clear lattice distribution of the SCLs can be observed (see Figure 4(d1,d2)), with a higher transverse coherence width because the Gaussian terms  
Figure 3: Density plots of (**a1–d1**) and (**a3–d3**), the normalized intensity distribution \(\mathrm{I}(\rho)/\mathrm{I}(\rho)_{\mathrm{max}}\), and (**a2–d2**) and (**a4–d4**), the square modulus of the CDOC of the focused USCLs and NUSCLs, at several propagation distances z, with \(\delta_{0}=1\) mm and \(\mathrm{M}=30\). play a main role in the CDOC functions. The influence of the modulation parameter \(m\) is smaller with a higher transverse coherence width. This proves that we can not only manipulate its spatial coherence structure to achieve beam shaping, but also adjust its transverse coherence width to achieve beam shaping for the partially coherent optical array that we have constructed. And this undoubtedly increases the flexibility of regulation. To prove the feasibility of our approach, we utilized the experimental schematic shown in Figure 5. A linear polarized laser beam with a wavelength of \(\lambda\) = 532 nm from a Nd:YAG laser is expanded by a beam expander (BE), and modulated by a spatial light modulator (SLM) with a computer-generated hologram (CGH). Figure 5 illustrates the CGH used to generate the SCLs after passing through a beam splitter (BS). The generated beam from the SLM is then emitted to dynamic scattering, e.g., a rotating ground glass disk (RGGD), producing an incoherent light field, after being collimated and filtered by the thin lens L\({}_{2}\) (\(f_{2}=\)150 mm) and Gaussian amplitude filter (GAF). This generates the SCLs source, and the distance from the RGGD to the thin lens L\({}_{2}\) is 15 cm. The transverse coherence width can be adjusted utilizing the distance from the thin lens L\({}_{1}\) to RGGD. A neutral density filter (NDF) is used to adjust the amplitude of the laser beam. The generated SCLs are then split into two parts, with the transmitted part passing through a 4\(f\) image system, consisting of thin lenses L\({}_{3}\) and L\({}_{4}\) with a focal length of \(f_{3}=f_{4}=f\) = 150 mm, and are then recorded by a charge-coupled device (CCD\({}_{1}\)). The reflected part is focused by a thin lens L\({}_{5}\) and then received by a charge-coupled device (CCD\({}_{2}\)) which is located at a distance z from the thin lens L\({}_{5}\). The recorded frames from the CCDs are used to measure the intensity and the square modulus of the CDOC in the source plane and propagated plane, respectively. For the measurement of the square modulus of the CDOC of the partially coherent optical array, we can refer to Equation (14). Figure 6 shows our experimental results of the normalized intensity distribution and the square modulus of the CDOC of the USCLs and NUSCLs at several propagation distances z with M = 30 and \(\delta_{0}=\) 1 mm. By using CCD camera, we obtained its intensity distribution, and by performing calculations on the intensity correlation, we obtained the square modulus of the CDOC of the SCLs. Consistent with our theoretical simulation, the intensity distribution of SCLs gradually evolves from a Gaussian distribution to a coherent lattice during propagation, and the square modulus of the CDOC gradually rotates during propagation and eventually evolves into a Gaussian distribution when reaching the far field. Usually, we approximate the focal plane after it has been focused by a lens as a far-field plane. The results of the measurements are in good agreement with the simulation results shown in Figure 3, whether for intensity distribution or the square modulus of the CDOC distribution. This also confirms the correctness of our method. Figure 4: Density plots of the normalized intensity distribution \(\mathrm{I}(\rho)/\mathrm{I}(\rho)_{\mathrm{max}}\) of the focused (**a1–d1**) USCLs and (**a2–d2**) NUSCLs in the focal plane with M = 30 for different transverse coherence widths \(\delta_{0}\). Figure 7 shows the experimental measurement of the intensity distribution of the USCLs and NUSCLs in the focal plane.