# Design Study of a Large-Angle Optical Scanning System for MEMS LIDAR
## 3 Scanning Optical System Design  
The design was implemented by ZEMAX software, which works by ray tracing [22]. The laser source in this work is a tunable semiconductor from NewFocus, which is suitable for FMCW LIDAR. Its center wavelength is 1550 nm, the wavelength scanning range is from 1520 nm to 1570 nm, the maximum beam divergence angle is 1.5 mrad and the maximum output power is 50 mW. To simulating this laser source, in the normal column setting of ZEMAX software, the aperture type is selected as object space numerical aperture (NA), the value is 0.00075, the apodization type is Gaussian, and the factor is 1. This design uses the MEMS mirror model S40919 manufactured by Mirrorcle. The effective diameter of the mirror is 5 mm, and the rotation range is \(\pm\)5\({}^{\circ}\). It works based on the principle of electrostatic driving. The relationship between the driving voltage and the tilt angle provided by the mirror manufacturer is shown in Figure 3. The parameters are listed in Table 1.  
As shown in Figure 2, the laser beam emitted by the semiconductor laser should first be focused by a positive lens to completely illuminate the effective mirror surface without causing beam leakage. A double cemented lens L\({}_{0}\) with a focal length of 80 mm is used to eliminate spherical aberration. The object distance between the laser source and L\({}_{0}\) is 1207 mm. Therefore, the image height D of the spot incident on the c  
Figure 2: Schematic diagram of MEMS scanning system. exceed 2 mm, which can ensure that all the laser beams passing through L\({}_{0}\) focusing on the MEMS mirror surface. A flat mirror is adding between the doublet lens and the MEMS mirror to change the propagation direction of the light path and improve the utilization of the actual system internal assembly space. For _f-\(\theta\)_ lens, ideally, the image height \(h\) and the scanning field angle \(\gamma\) of the MEMS mirror should have a linear relationship. In order to meet the linear scanning requirements of the scanning system, the _f-\(\theta\)_ lens needs to bring a certain amount of barrel distortion. When the scanning angle of the MEMS mirror gradually increases, the ideal image height should be smaller than the actual image height, and their difference is:  
\[\Delta h=f_{1}{}^{\prime}tan\gamma-f_{1}{}^{\prime}\gamma=f_{1}{}^{\prime}(tan \gamma-\gamma) \tag{4}\]  
It is impossible to fully meet the linearity requirements. Generally, the relative distortion is required to not exceed 0.5%, so the relative distortion should meet:  
\[\delta=\frac{h-f_{1}{}^{\prime}\gamma}{f_{1}{}^{\prime}\gamma}\times 100\%<0.5\% \tag{5}\]  
The _f-\(\theta\)_ lens should introduce barrel distortion, and because of its larger field of view, the off-axis aberrations should be corrected, such as astigmatism and field curvature. The lenses were optimized by The ZEMAX software using the optimization function, in which field curvature and distortion were optimized with the help of FCUR and DIST operands. The optimization function is set to the RMS spot radius, and FCUR and DIST operands are inserted and set to target 0 and weight 1. The two-dimensional structure of the cemented lens L\({}_{0}\) and _f-\(\theta\)_ lens L\({}_{1}\) designed in ZEMAX is shown in Figure 4. Scanning beams with different angles are in different colours, 0\({}^{\circ}\) in blue, 1\({}^{\circ}\) in green, 2\({}^{\circ}\) in red, 3\({}^{\circ}\) in gray, 4\({}^{\circ}\) in purple, and 5\({}^{\circ}\) in wathet. The _f-\(\theta\)_ lens is consist of 5 lenses with a focal length of 35 mm. \begin{table}
\begin{tabular}{c c} \hline
**Device Parameters** & **Value** \\ \hline Actuator & Gimbal-less Dual-Axis Quasistatic \\ Mirror Size & 5.0 mm \\ Maximum Mech. Angle-X Axis & 5.1928\({}^{\circ}\) \\ Maximum Mech. Angle-Y Axis & 5.2236\({}^{\circ}\) \\ Driver Bias Voltage & 90 V \\ Low pass filter Cutoff Frequency & 120 Hz \\ \hline \end{tabular}
\end{table} 
Table 1: MEMS mirror parameters of S40919. Figure 3: The relationship between drive voltage and tilt angle.