# Fabrication of Random Microlens Array for Laser Beam Homogenization with High Efficiency
## 3 Fabrication of Random Microlens Array (rMLA)
### Preparation of Chemical Etching Solution  
In the experiment, ultra-white glass was selected as the substrate material, which has a transmittance of 91.5% in the visible regime. The main component of the selected substrate is SiO\({}_{2}\), with a content of 73%. The contained impurities mainly involve Al\({}_{2}\)O\({}_{3}\), Fe\({}_{2}\)O\({}_{3}\), CaO, MgO, Na\({}_{2}\)O and K\({}_{2}\)O. Among them, CaO and Na\({}_{2}\)O occupy a relatively high proportion, which are 11% and 15%, respectively. The other impurities are low, at about 0.15%, which were not considered as key factors in this experiment. During chemical etching, three different chemical etching solutions were fabricated. The compositions of the chemical etching solution included deionized water, hydrofluoric acid solution (HF solution) (40%) and ammonium fluoride particles (NH\({}_{4}\)F), which was called the fundamental chemical etching solution. The proportion of ingredients was 10:3:1. Meanwhile, the units of deionized water and HF solution were \"mL\", while the unit of NH\({}_{4}\)F was \"g\". The HF solution is able to react with various oxides of ultra-white glass [32], and the chemical reaction formulas are expressed as Equations (4)-(6)  
\[\mathrm{SiO}_{2}+4\mathrm{HF}\rightarrow\mathrm{SiF}_{4}+2\mathrm{H}_{2} \mathrm{O} \tag{4}\]  
\[\mathrm{CaO}+2\mathrm{HF}\rightarrow\mathrm{CaF}_{2}+\mathrm{H}_{2}\mathrm{O} \tag{5}\]  
\[\mathrm{Na}_{2}\mathrm{O}+2\mathrm{HF}\rightarrow\mathrm{2 NaF}+\mathrm{H}_{2} \mathrm{O} \tag{6}\]  
where SiF\({}_{4}\) will continue to react with the generated fluoride, which can be expressed by Equations (7) and (8). Among these, the reaction rate of CaF\({}_{2}\) is slow and will be residues  
\[\mathrm{SiF}_{4}+\mathrm{CaF}_{2}\rightarrow\mathrm{CaSiF}_{6} \tag{7}\]  
\[\mathrm{SiF}_{4}+2\mathrm{NaF}\rightarrow\mathrm{Na}_{2}\mathrm{SiF}_{6} \tag{8}\]  
where SiF\({}_{4}\) will react with the NH\({}_{4}\)F added in the chemical etching solution, expressed as Equation (9), to accelerate the etching rate of the glass. \[\mathrm{SiF}_{4}+2\mathrm{NH}_{4}\mathrm{F}\rightarrow(\mathrm{NH}_{4})_{2} \mathrm{SiF}_{6} \tag{9}\]  
In the process of a reaction between the etching solution and glass substrate, the generated impurities CaF\({}_{2}\) and Na\({}_{2}\)SiF\({}_{6}\) with low solubility would adhere to the surface of the glass and prevent further etching. Although the chemical etching solution was continuously oscillated during the experiment to prevent impurities from adhering to the glass surface, the surface of the fabricated rMLA is not smooth, with a roughness of 106 nm, as shown in Figure 2. Thereby, a lot of stray light is generated during the beam homogenization process, which seriously affects the uniformity of the homogenized light spot. Figure 2: The rMLA fabricated by the fundamental chemical etching solution. It was necessary to consider adding other chemical reagents to react with the generated impurities of the fundamental chemical etching to dissolve it in the etching solution. In this paper, the concentrated sulfuric acid (H\({}_{2}\)SO\({}_{4}\)) was selected to prepare the H\({}_{2}\)SO\({}_{4}\) chemical etching solution. The components of the H\({}_{2}\)SO\({}_{4}\) chemical etching solution were deionized water, HF solution (40%), and H\({}_{2}\)SO\({}_{4}\) (95-98%). The proportion of ingredients was 5:2:2, and their units were \"mL\". The diluted H\({}_{2}\)SO\({}_{4}\) is able to react with the generated fluoride, which can be expressed as Equation (10):  
\[\mathrm{H_{2}SO_{4}+CaF_{2}\to CaSO_{4}+2 HF} \tag{10}\]  
As can be seen from Equation (10), H\({}_{2}\)SO\({}_{4}\) is able to react with CaF\({}_{2}\). The produced CaSO\({}_{4}\) will dissolve to some extent, but the remaining impurities still adhered to the glass surface. Although the chemical etching solution was also oscillated in the experiment, the impurities still hindered any further etching of the glass.