Crosstalk-free large aperture electromagnetic 2D micromirror for LiDAR application

This paper presents a novel design of a 2D electromagnetic micromirror without crosstalk. The proposed micromirror uses a flexible printed circuit board (FPCB) and four layers of coils embedded in the polyimide layers. The insulated layers of the coil allow for independent actuation of the mirror plate to rotate about two orthogonal axes. The diamond shaped micromirror uses a hyperbola-shaped magnetic field on the coils under the mirror plate and a 45-degrees magnetic field on the coils embedded in the FPCB frame to eliminate the mechanical crosstalk. Finite element analysis was used to predict the novel 2D micromirror’s behavior. The novel 2D micromirror prototype is used in scanning LiDAR, The results indicate that the crosstalk-free pattern yielded significantly clearer results, particularly for detecting object boundaries and reducing barrel distortion. The experimental test has verified the novel crosstalk-free 2D micromirror working principle and showed good scanning quality: no crosstalk and an improvement in the horizontal field of view up to 19% But with the cost of reducing the vertical field of view by up to 12%. The novel 2D micromirror prototype has a large aperture of 19 × 19 mm2, which is very suitable for coaxial scanning LiDAR.


Introduction
Two-dimensional (2D) micromirrors has been successfully developed for various applications such as projection display [1], [2] AR-display(augmented reality display) [3] medical imaging [4] and LiDAR applications [5] during the past two decades. A conventional 2D electromagnetic micromirror has a gimbal structure, in which the mirror plate rotates about two orthogonal axes, i.e., the rotation about a vertical axis * Author to whom any correspondence should be addressed.
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
(normally resonant vibration and named as inner rotation or mirror rotation.) and the rotation about a horizontal axis (normally quasi-static rotation and named as outer rotation or frame rotation).
Thus far, 2D electromagnetic actuation micromirrors draw a lot of attention out of the four MEMS actuation technologies, i.e., electrostatic [6], thermal [7], electromagnetic [1] and piezoelectric [8] driving mechanisms due to the large force generated using electromagnetic driving [2,[9][10][11]. One of the main problems with traditional electromagnetic 2D micromirrors is the crosstalk between the two rotations about the orthogonal axes [12]. Crosstalk is the undesired outer rotation caused by the signal driving the inner plate resonant rotation. Consequently. A pure inner plate resonant vibration cannot be achieved, i.e., undesired outer rotation always exists once the inner plate resonant vibration is generated, consequently, when the 2D micromirror is used to scan a laser beam, the reflected laser beam cannot form a horizontal straight trajectory due the existence of the outer rotation caused by the inner plate resonant vibration. Instead, only an elliptical trajectory can be formed when only driving the inner plate resonant vibration. When using a traditional electromagnetic 2D micromirror scan laser beam, the crosstalk makes the scanning pattern uneven and then increases the position sensing error if the laser scanning is used for measuring distance.
There are two causes leading to crosstalk, i.e., electrical and mechanical causes [12,13]. In an electromagnetic 2D gimbal micromirror, there are two groups of coils, one group of coils are used for generating torque for the inner plate resonant vibration. This group of coils is called hereafter inner coils. The other group of coils is for generating torque for outer vibration. This group of coils is called outer coils hereafter in this paper. In most of the traditional electromagnetic 2D micromirrors, the two groups of coils are electrically connected in series and use a superimposed driving signal. Electrical crosstalk mostly occurs in micromirrors that use a single layer of coil using electroplating manufacturing process [10,14].
The mechanical crosstalk is usually related to the design of the mirror supported by a 2D gimbal structure. In order to generate the inner plate resonant vibration, the inner coil is subjected to a driving current to generate Lorentz forces. However, in traditional 45-degrees magnetic field designs [15,16], since the magnetic field applied to the inner coil has a direction not perpendicular to the inner rotation's axis (named as vertical axis previously), about which the inner rotation is, the direction of the torque for driving inner rotation is not along the inner rotation axis. The direction is between the inner rotation axis and outer rotation axis (figure 1). Thus, the torque generated for driving the inner resonant rotation can always be decomposed into components along both the inner rotation axis and outer rotation axis, which causes both inner rotation and outer rotation. This paper proposes a novel design of a 2D electromagnetic micromirror, which can eliminate crosstalk. Using flexible printed circuit board (FPCB), four layers of coil has been used in the design of this micromirror. Four layers of coil under the mirror responsible for vertical axis actuation are completely isolated from the two layers of coil under the frame responsible for the horizontal axis actuation. Using four layers of coil not only increases the current path length and Lorentz force, but also it eradicates the electrical crosstalk by separating the current path of the outer and inner coils. The general concept of this micromirror was first presented at IEEE MEMS 2023 conference [17] but the performance of the micromirror were not thoroughly examined. In this paper the electromechanical characteristics of the mirror was refined using finite element analysis (FEA) and a prototype was built and used in a LiDAR system to verify the performance.
The paper is organized as follows. Section 2 presents the detailed design of the novel 2D electromagnetic micromirror. Simulations of the novel design are introduced in section 3. Prototyping and testing are given in sections 4 and 5. Conclusions and discussion are presented in sections 6 and 7.

Design
The author's group proposed FPCB micromirror technology in 2016 [18] and started to develop the FPCB micromirror since then [11,[19][20][21]. The fatigue life of FPCB micromirrors has been examined using multiple designs and a promising result of 0.8 billion cycles was achieved in a previous study [22]. An exploded view of the 2D gimbal mirror presented in this paper is shown in figure 2(a). An FPCB micromirror consists of external permanent magnets, an FPCB structure which in this case contains four layers of copper coil (figure 2(b)) sandwiched in between polyimide layers, and finally a gold coated silicon layer that acts as a mirror plate.
The mirror is specifically designed to generate a crosstalkfree raster pattern. The four layers of the mirror coil are isolated from the two layers of the frame coil. Separate current paths allow independent actuation of the mirror or the frame which eliminates the electrical crosstalk. Figure 3(a) shows the design using a traditional 45-degrees magnetic field. Although the electrical crosstalk is eliminated in figure 3(a), the torsion axis of the Lorentz force generated on the mirror current path has 45 degrees deviation from the torsional beam. This deviation causes a decomposition of the mirror torsion (T m ) into T my and T mx which are effective on the mirror and frame torsional beam respectively. The Lorentz force generated on the outer coil generates T fx which is only effective on the frame torsional beam. While T my and T fx are the desired torques, responsible for the horizontal and vertical actuations, T mx is the main cause of mechanical crosstalk. Figure 3(b) shows the same design using two extra magnets on the mirror coil i.e. the novel 2D micromirror design. The four magnets on the mirror coil provide a hyperbola shaped magnetic field which generates Lorentz force on all four quarters of the mirror coil. The Lorentz forces generated with this  method will generate torque around a torsion axis parallel to the mirror torsional beam. The extra Lorentz forces on the mirror contribute to the torque on the mirror torsional beam (T my ) but cancel the undesired torque on the frame torsional beam (T mx ) and eliminate the mechanical crosstalk.

Modal analysis
Ansys modal analysis was done to determine the resonant frequency of the design and also see the other undesired modal shape results ( figure 4). Dimensions of the design can be found in table 1.
Since the micromirror is designed for raster scanning, the mirror will be actuated at near resonance frequency (mode 2: 46.03 Hz) and the frame will actuate at a quasi-static frequency of 1-2 Hz.

Magnetostatic analysis
In order to determine the magnetic field distribution and consequently Lorentz force on the coils, Magnetostatic analysis was done on the design. Figures 5(a) and (b) shows the magnetic flux density on the inner coil in magnetic orientations similar to figures 3(a) and (b) respectively.

Static structural analysis
In this study, the Lorentz forces calculated in the Magnetostatic analysis were applied to the design in an ANSYS static structural analysis. The resulting deflection of the mirror was plotted as a function of applied current, ranging from 10 to 60 mA in figure 6. The experimental and FEA results indicate a trade-off between the horizontal and vertical maximum angles. Based on the experimental results, incorporating two additional magnets enhances the horizontal maximum angle by 19%. However, this improvement comes at the cost of generating resistive Lorentz force within the inactive portion of the outer coil, resulting in a reduction of up to 12% in the vertical maximum angle.

Fabrication
A prototype of the design was fabricated and tested for performance. The prototype consisted of four main components: (1) a FPCB with four layers of the embedded coil, which was fabricated by a commercial PCB manufacturer, (2) a goldcoated silicon layer produced in an ISO class 7 cleanroom, using an evaporation technique to deposit a 100 nm gold layer on a 200 µm thick silicon wafer, which was subsequently diced into 19 mm × 19 mm squares using a silicon dicing saw, (3)  six block magnets made of N52 neodymium, and (4) a 3Dprinted case structure. These components were assembled to create the prototype shown in figure 7. Resistance of the inner coil and outer coil of the prototype are 83.2 Ω and 53.8 Ω respectively.

Testing
As the first experimental test, the quasi-static angle of actuation was measured at 1 Hz and compared to FEA results ( figure 6). The deviation of the experimental result can be due to the simplification of the FEA model and the estimated   figure 8(b) is due to crosstalk. In contrast, the laser line generated using the setup with six magnets shown in figure 8(a) is a single line, as predicted and desired. Additionally, figure 8(c) presents a raster pattern generated while the micromirror was actuated in both horizontal and vertical direction directions with an AC voltage of 8 mA at 45 Hz and 37 mA at 1 Hz respectively.
The micromirror was subsequently integrated into a LiDAR setup, as shown in figure 9. Benewake TF03 [23] was used as the single point LiDAR. A position sensing prototype that was previously developed by the author was used for the angle  measurement. The angle measurement system uses one 1D PSD on the backside of the mirror that receives parts of the scanning pattern and interpolates the scanning pattern based on Lagrange interpolation method for quasi-static actuation and timing measurement method for resonance actuation [24]. Figures 10(a) and (b) depict the setup and scene of the LiDAR scan respectively, while figures 11(a) and (b) illustrate the resulting 3D point cloud generated from two setups using baseline model and zero-crosstalk model, respectively. The mirror was actuated at 40 Hz, 13 mA and 2 Hz, 50 mA.
The crosstalk due to using only four magnets resulted in a 3D point cloud which had two major problems. The most significant issue with the baseline model is the barrel distortion of the 3D point cloud which shows flat surfaces as curved structures [25]. This distortion is significantly higher in the four magnets configuration comparing to six magnets configuration. The second issue is differentiating the boundaries of the objects in the scene. Crosstalk introduces irregularities in the angular resolution by disrupting the distribution of points in a raster pattern. Consequently, the absence of  crosstalk enables the detection of the general rectangular shape of objects with greater clarity. Another issue is with the position sensing mechanisms. While the Lagrange interpolation algorithm used for the position sensing in this paper worked accurately with both baseline model and zero-crosstalk model, the crosstalk can cause significant error in position sensing using other angle measurement methods [26]. Table 2 shows a comparison of characteristics of large aperture micromirrors based on a figure of merit (FoM) proposed by Wang et al [5] in equation (1).

Summary and discussion
where θ is the effective optical FoV (rad) which is the geometric mean of the horizontal and vertical optical angle (rad), f is the effective resonance frequency (kHz) which is the geometric mean of the horizontal and vertical resonance frequency, and d is the effective dimension of the mirror plate (mm). Although the presented design has a significant advantage over equivalent micromirrors in terms of aperture size, its low resonance frequency noticeably affects the total FoM, resulting in a lower value compared to three of the cases. Nonetheless, the design still outperforms the two larger micromirrors, highlighting its potential for practical applications. Moreover, the crosstalk-free scanning pattern is the main advantage of this design.
Although the current design's low resonance modes make it suitable for low-vibration applications such as ground robotics, modifications are necessary to enable its usage in more dynamic environments that require more robustness.
This micromirror was designed with consideration of its intended use on the Benewake TF03, which has a maximum sampling rate of 10 kHz. Considering the resonance actuation at approximately 40 Hz, each horizontal scanning line in the mirror generates only about 250 points per scan, significantly reducing the angular resolution. Although the crosstalk-free concept can be applied to micromirrors with higher resonance frequencies, for these experiments, the resonance frequency and field of view of the micromirror were deliberately limited to ensure compatibility with the Benewake TF03.
Further analysis done by the authors indicates that adding a 200 µm silicon layer to the entire structure via a one-step etching method [31] and reducing the number of inner coil layers from 4 to 2 can raise the first mode's resonance frequency to as high as 180 Hz allowing it to be used in a vast variety of applications.

Conclusion
This paper presented a novel design of a 2D electromagnetic micromirror which is able to eliminate the crosstalk that traditional 2D electromagnetic micromirrors suffer from. The paper analytically proved the principle of the novel design and also experimentally verified it. In addition, the novel 2D micromirror has been applied to construct 3D LIDAR by integrating it with a single point LIDAR and comparing the result with the base model. The unique orientation of the magnets on the mirror and the use of isolated layers for inner and outer actuation, increased the horizontal field of view by 19% and eliminated any mechanical and electrical crosstalk but it also decreased the vertical field of view by 12%. The large aperture size of the mirror makes it suitable for use in LiDAR applications in the field of robotics and sensor technology.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).