# Integrated Double-Sided Random Microlens Array Used for Laser Beam Homogenization
## 4 D-rMLA Testing  
The experimental optical paths are constructed on the basis of the fabricated D-rMLA to test the laser beam homogenization and verify the applicability of the lasers with different wavelengths. Firstly, the divergence angles of the homogenized spots generated by the D-rMLA of different wavelengths are measured. In the experiment, the laser beams with wavelengths of 650 nm (R), 532 nm (G), and 405 nm (B) were irradiated to the D-rMLA, respectively. The powers of the sources of RGB laser radiation are 100 mW, 100 mW, and 30 mW, respectively. The transverse mode of the RGB laser radiation is near TEM\({}_{00}\), which has high coherence. By the phase modulation of the D-rMLA the homogenized spots were obtained. The propagation distance \(Z\) between the Charge Coupled Device (CCD, the resolution of 4896 \(\times\) 3248 and pixel size of 7.4 \(\upmu\)m \(\times\) 7.4 \(\upmu\)m) and D-rMLA was measured as 20 mm, and the incident spot size T\({}_{0}\) was 4 mm. Therefore, if the size of the homogenized spot T can be measured, the half divergence angle \(\theta\) of the homogenized spot at different wavelengths can be calculated by Equation (6). \[\theta=\arctan\frac{\text{T}-\text{T}_{0}}{2\text{Z}} \tag{6}\]  
The homogenized spots of different wavelengths were captured by CCD, and the sizes of the homogenized spots were calculated by numerical analysis software MATLAB. The energy of the homogenized spots attenuates to \(1/\text{e}^{2}\) is counted as T, which can be obtained by multiplying the number of pixels of the spot by the pixel size. For the laser beam with wavelength of 650 nm (R), the pixel number of homogenized spots is accounted as 2093, and the T and the full divergence angle were calculated as 15.5 mm and 32\({}^{\circ}\), respectively. For the laser beam with wavelength of 532 nm (G), the pixel number was 1929, and the T and the full divergence angle were calculated as 14.3 mm and 29\({}^{\circ}\). For the laser beam with wavelength of 405 nm (B), the pixel number was 1799, and the T and the full divergence angle were calculated as 13.3 mm and 26\({}^{\circ}\). For the fabricated D-rMLA, the central zero order strong intensity will not be produced by the incident beams with different wavelengths. The divergence angle of the homogenized spot will change when different wavelength beams are incident. According to the grating equation (\(d\times sin\)\(\theta\) = \(\lambda\)), the longer the wavelength is, the larger the diffraction angle is. Secondly, the uniformity of homogenized spots was tested. The homogenized spots of the laser with different wavelengths were captured after laser homogenization, as shown in Figure 8. The uniformity was calculated by Equation (7). The uniformity of 650 nm (R), 532 nm (G), and 405 nm (B) was 91%, 89%, and 90%, respectively. It can be seen that the uniformity of the homogenized spots for different wavelengths is very high with a little difference. Comparing the homogenization results of simulation and experiment, it  
Figure 7: Profile Comparison between the fabricated microlens with ideal sphere. is found that the homogenized spot is no longer composed of strong diffraction orders, the energy of the homogenized spot of the D-rMLA is more discrete and uniform. The experimental and simulation results are consistent. Finally, the energy utilization rate is tested. The power of the incident and outgoing laser beams is measured by the power meter (accuracy of 1 \(\mu\)W) and the energy utilization rate is calculated by Equation (8). The power \(\mathrm{P_{in}}\) of the incident beam of 650 nm (R) is 0.98 mW, and the outgoing power \(\mathrm{P_{out}}\) is 0.87 mW. The energy utilization rate is calculated as 89%. The power \(\mathrm{P_{in}}\) of the incident beam of 532 nm (G) is 2.05 mW and the outgoing power \(\mathrm{P_{out}}\) is 1.8 mW. The energy utilization rate was calculated as 87%. The power \(\mathrm{P_{in}}\) of the incident beam of 405 nm (B) is 4 mW, and the outgoing power \(\mathrm{P_{out}}\) is 3.44 mW.