# Manufacturing of Micro-Lens Array Using Contactless Micro-Embossing with an EDM-Mold
## 4 Results and Discussion
### Fabrication of Micro-Lens Array  
The height ratios of the micro-lens array change with different processing parameters. It is worth mentioning that the profile of micro-lens array can be replicated randomly by controlling the embossing conditions. The three processing parameters had significant effects on the deformation of the micro-lens array. The results indicated that the flow behaviors of PMMA were much better with the increase of embossing temperature. In addition, the increasing holding pressure and time can reduce the recovery deformation of micro-lens array. The height ratios of micro-lens array became larger as the embossing force rose.  
Figure 7 shows the embossed PMMA microstructure under different processing parameters. The aspect ratios of the microstructure changed with different processing parameters. Much like the profile of micro-lens array, the profile of microstructure can also be replicated randomly by controlling the embossing conditions. With the increase of temperature, the depth of the replicated structures increased, and their recovery deformation decreased. The defects occurred on the edge of the microstructures, due to the mold quality, because the edge of mold machined by EDM appeared with some defects affecting the replication quality. In the future studies, the problem of fabrication quality will be solved by polishing or coating.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**No.** & **Temp\(J\)\({}^{\circ}\)C** & **Force/N** & **ID/mm** & **OD/mm** & **T/mm** \\ \hline
1 & 90 & 3000 & 5.21 & 13.26 & 3.10 \\
2 & 90 & 3000 & 4.66 & 13.85 & 2.75 \\
3 & 90 & 3000 & 2.34 & 14.66 & 3.96 \\
4 & 105  
The ContourGT-X 3D Optical Profiler (Bruker, Germany) was used to observe the surface morphology and profile shape. Figure 8 shows the measurement results of different embossing processing parameters, and the 3D profile and shape of the formed micro-lens array (with diameter \(\approx 300\) um, and height \(\approx 10\) um) corresponding to Figure 7a. Figure 8b shows the profile shape of the micro-lens array (with diameter \(\approx 300\) um, and height \(\approx 33\) um) by filtering. It can be concluded that embossing temperature and force are the important factors on the contactless hot embossing process.  
The stress inside the microstructure affected the optical quality of the embossed micro-lens because of temperature gradient during cooling. The simulation can be used to investigate the evolution mechanism of residual stress during hot embossing. Figure 9 shows the [PERSON] stress and friction shear stress of the micro-lens array from FE simulation. The maximum stress focused on the edge of the microstructure, and the lowest stress took place around the center of microstructure. The deformation characteristic of the PMMA during hot embossing is dependent on temperature. The stress concentrated in the contact edge region of the lens, during thermal loading process, which led to large plastic deformation in the region. Stress concentration and shear flow led to the defects and strain hardening of the micro-lens, affecting the optical quality. The friction coefficient had a great effect on the shear deformation. To reduce the stress concentration and shear stress, we increased the temperature of mold in the certain range.