## 2 Materials and Methods
### Hot Embossing of the Microlens Array  
The hot embossing process included presetting, heating, embossing, cooling, and demolding (See Figure 2). We used SZU's PGMM30 glass molding machine (Shenzhen, China) (See Figure 3) to complete the molding process. It basically consists of five subsystems including the moulding machine, vacuum system, nitrogen system, cooling water, and control system. First, the mold and sleeves were pre-fixed on the platform, and the  
Figure 1: Aspheric microlens array mold design and processing. (**a**) Design of aspheric microlens array with basic geometric parameters, (**b**) mold processing, and (**c**) characterization of microlens array mold.  
dust-free PMMA ball was carefully placed at the center of the 10 \(\times\) 10 array mold. Then, the lower mold was manually servo-positioned upwards to leave a gap of 1-3 mm between the upper mold and PMMA and moved upwards with a smaller torque force and speed (100 N and 10 mm/s) through the torque positioning of the lower mold until its position was no longer changing. Next, the PMMA ball was heated (SZU's PGMM30 transfers heat to the upper and lower molds through infrared induction heating. Then it is connected to the control system through the temperature sensor to form a controllable closed loop system to set the mold temperature.) and the lower mold was compressed by a constant pressure between 300 and 500 N. When the PMMA ball was in a viscoelastic state, it could deform easily so that the filling process could be achieved within time with the lower mold in the proper position. After hot embossing, the PMMA was held at a holding pressure of 200 N, and the holding pressure was removed at 50-90 \({}^{\circ}\)C. Finally, demolding could be performed at room temperature.  
During the hot embossing process, process parameters such as compressing temperature, compressing pressure, holding temperature, holding pressure, and cooling rate greatly influence the deformation behavior and replication quality of the hot-embossing microstructure. Thus, we designed an orthogonal experiment to investigate the effect of hot-pressing temperature, hot-pressing pressure, and holding temperature on microstructures.  
The temperature range in the work was set according to the flow behavior of PMMA during the hot embossing process. At about 104 \({}^{\circ}\)C, PMMA changes from the glass state  
Figure 3: (**a**) Schematic diagram of molding machine system and (**b**) SZU’s PGMM30.  
Figure 2: Process diagram of hot press forming and time history of force and temperature.  
to the elastic rubber state, in which state plastic flow does not exist because the memory effect of the thermoplastic polymer makes it challenging to maintain the formed shape. Above 120 \({}^{\circ}\)C, PMMA is in a typical viscoelastic state, a plastic state, which exhibits viscoelasticity and plastic flow. It is an appropriate state for hot embossing [26]. Therefore, the temperature range was set as 110-150 \({}^{\circ}\)C. In the experiment, at the lowest molding temperature of 110 \({}^{\circ}\)C, holding temperature of 80 \({}^{\circ}\)C, and hot-pressing pressure of 300 N, the microlens structure with the basic replicated morphology could be processed. Table 2 shows the final range of process parameters.