# Sixty-Nine-Element Voice Coil Deformable Mirror for Visible Light Communication
## 3 Design and Optimization
### Optimization of Micro VCA  
To realize the compact VCDM, the pitch of actuators must be small enough. The geometrical shape of the VCA array as shown in Figure 2 is square with a pitch of 2.5 mm. In addition, the diameter of the micro VCA is less than 2.5 mm. The geometrical model of VCA is built and analyzed with Ansys software. The initial geometrical sizes for the micro VCA are defined as follows: (1) the permanent magnet with a radius of 1 mm and height of 0.1 mm; (2) the coil with an inner diameter of 0.2 mm, the outer diameter of 2.2 mm, and a height of 1 mm. When the permanent magnet moves to the side close to the coil, it is necessary to avoid touching the coil, that is, the height of the air gap should be larger than the mechanical stroke of the micro VCA. So, the initial size of the air gap is 50 \(\upmu\)m. The permanent magnet is made of NdFe35. The parameters that need to be optimized are listed in Table 2. \begin{table}
\begin{tabular}{c c} \hline
**Serial Number** & **Component** \\ \hline
1 & Front shell \\
2 & Thin mirror \\
3 & O-ring \\
4 & Springs \\
5 & Struts \\
6 & Spring fixing plate \\
7 & Permanent magnets \\
8 & Voice coils \\
9 & Substrate \\
10 & Back shell \\ \hline \end{tabular}
\end{table} 
Table 1: The composition of compact VCDM. Figure 2: 3D drawing of VCDM. Front shell 1, thin mirror 2, O-ring 3, springs 4, struts 5, spring fixing plate 6, permanent magnets 7, voice coils 8, substrate 9, back shell 10. For two different magnetization directions of permanent magnets, the effect of electromagnetic force as a function of current is shown in Figure 3. The results indicate that there is a linear relationship between the electromagnetic force and the inputted current for permanent magnets with both axial magnetization (black square in Figure 3) and radial one (red triangle in Figure 3), which could be explained with Equation (2). For the same current, the force under radial magnetization is larger than that under axial one. Additionally, the former is larger by a factor of 1.5. Figure 4a,b show the electromagnetic force and efficiency \(\varepsilon\) as a function of magnet radius and height, respectively. The larger the magnet radius and magnet height are, the larger the electromagnetic force and efficiency would be. Their differences are the curve slopes of the electromagnetic force and efficiency. It should be noted that the permanent magnet is the mover of VCA, and increasing the permanent magnet's volume will reduce the response speed of VCA. Therefore, the optimized radius of the magnet is selected as 1 mm and its optimized height is selected as 0.2 mm. The results in Figure 4c indicate that as the inner diameter of the coil increases, both the electromagnetic force and the efficiency decrease. Therefore, the optimized inner diameter of the coil is 0.2 mm. Similarly, according to Figure 4d, the optimized outer diameter of the coil is 2 mm. The change of force and efficiency in Figure 4e is slightly different from the others. Although the electromagnetic force increases with the height of the coil, its efficiency first increases and then decreases. It is because the wire far away from the permanent magnet contributes less to the electromagnetic force. Considering the efficiency of the actuator, the optimized coil height is 0.4 mm. Figure 4f shows that the larger the air gap is, the smaller the electromagnetic force and efficiency are. Therefore, the optimized air gap of the micro VCA is 50 \(\upmu\)m. In summary, after optimization, the micro VCA has a diameter of 2 mm and a height of 0.65 mm.