# Fabrication of Random Microlens Array for Laser Beam Homogenization with High Efficiency
## 4 Experiments  
Based on the fabricated honeycomb random microlens array (rMLA) and rectangular rMLA, an optical setup was constructed to test the uniformity of the homogenized light spots generated by the two types of rMLAs, as shown in Figure 10a. The rMLA was illuminated by a laser beam with a wavelength of 650 nm and diameter of 5 mm. After the incident light was modulated by the rMLA, a homogenized light spot was able to be obtained. The charges coupling device (CCD) was then used to collect and record the intensity of the homogenized light spot, as shown in Figure 10a. In order to characterize the divergence angle of the reconstructed light spot, the sagittal heights and the apertures of the fabricated rMLA needed to be measured. Subsequently, the divergence angle could be calculated by Equations (1)-(3). Using the theoretical equations, the divergence angle of the rectangular rMLA could be obtained. However, it was difficult to measure the sagittal heights and the apertures due to the irregularity of the structure parameters of the honeycomb rMLA, resulting in the divergence angle of the honeycomb rMLA not being directly calculated by the theoretical Equations (1)-(3). Therefore, the geometric calculation method was performed to calculated the divergence angle of the honeycomb rMLA, which would be described as follows. As could be seen from Figure 10b, the propagation distance \(Z\), the size of the incident light \(T_{0}\) and the reconstructed light spot \(T\) were able to be measured. Therefore, the geometric relationship of these four parameters (\(\theta\), \(T_{0}\), \(T\) and \(Z\)) can be expressed as Equation (12). \[\theta=tan^{-1}\frac{T-T_{0}}{2Z} \tag{12}\]  
The measured \(T_{0}\) was 5 mm and \(Z\) was 27 mm, the homogenized light spot size \(T\) was calculated based on the MATLAB (version 7.1, MathWorks, Natick, MA, USA) numerical analysis software. At the edge of the spot, the dimension when the energy drops to \(1/e^{2}\) is recorded as \(T\), which can be obtained by multiplying the number of pixels occupied by the light spot and the pixel size of the CCD. For the honeycomb rMLA, the number of pixels occupied by a circular light spot was 1177 at the central cross section, and the pixel size of the CCD was 7.4 \(\upmu\)m. Therefore, the calculated \(T\) was about 8.7 mm. On the basis of the geometric calculation method, according to Equation (12), the divergence angle of the circular light spot could be obtained, which was about 7.8\({}^{\circ}\). For the rectangular rMLA, the aperture and depth of sub lenses in multiple rMLA were measured by the step profilometer (Stylus Profiler System, Dektak XT, Bruker, Karlsruhe, Germany), according to Equations (1)-(3), the average value of departure divergence was about 22\({}^{\circ}\). Meanwhile, the geometric calculation method was also performed to calculated the divergence angle of the rectangular rMLA. According to the experimental  
Figure 10: Experimental measurement: (**a**) the experimental setup; and (**b**) the diagram of geometric calculation method. measurement, the number of pixels occupied by the rectangular light spot was 2161 at the central cross section and the calculated \(T\) was 16 mm. Therefore, according to Equation (12), it could be calculated that the divergence angle of the rectangular light spot was about 23\({}^{\circ}\), which is basically consistent with the average divergence angle calculated by the theoretical Equations (1)-(3). Subsequently, the uniformity and energy utilization of the homogenized light spot were tested. The incident light was an uneven light spot with a wavelength of 650 nm, as shown in Figure 11a. A circular homogenized light spot was generated by a honeycomb rMLA, as shown in Figure 11b, and a rectangular homogenized light spot was generated by a rectangular rMLA, as shown in Figure 11c. The uniformity of the light spot was calculated by using Equation (13), where the uniformities of the circular spot and the rectangle spot were about 81% and 88%, respectively.