# Investigation of Electromagnetic Angle Sensor Integrated in FR4-Based Scanning Micromirror
## 1 Introduction  
Scanning micromirrors are essential core elements in various optical microsystems (e.g., barcode reader, endoscopic probe, and LiDAR) [1; 2; 3; 4]. Especially, a large-aperture and low-frequency micromirror is required for a broad range of applications, such as fluorescence microscopes [5], laser projection [6; 7], micro-spectrometers [8; 9; 10], etc. However, conventional Si-based MEMS (microelectromechanical systems) micromirrors cannot meet the requirements because large-aperture and low-frequency Si micromirrors are fragile, and cannot survive the environmental shocks and vibrations [8; 11]. In comparison, flame retardant 4 (FR4)-based micromirrors are more promising, due to the inherent flexibility of FR4 [7; 12; 13; 14]. Until now, FR4 is the most widely used material for printed circuit boards (PCBs). Thus, commercial PCB technology, with low cost and a short process cycle, can be employed to fabricate the flexure and driving parts. After that, a mirror plate fabricated by dicing an aluminum-coated Si wafer is bonded to achieve large aperture and high surface quality. In general, the micromirror must scan the optical beam at a specific optical scan angle in practical applications. However, the current FR4 micromirror with a simple open-loop control cannot guarantee it, owing to the relatively poor stability of FR4 [12; 15]. Therefore, an angle sensor is highly desired to monitor the scan angle in real time, and further form a feedback control.  
External optical sensors may be a good solution to provide a real-time feedback signal [4; 16; 17]. However, this requires a complex assembly, and inevitably increases the system's volume and cost.  
Another simple, yet highly effective alternative, is the integrated angle sensor. Several corresponding sensing methods have already been proposed and applied in MEMS micromirrors, such as piezoresistive [18; 19], capacitive [20], piezoelectric [21; 22], and electromagnetic [9; 23]. Among these methods, electromagnetic angle sensing is more suitable to be integrated in the aforementioned FR4 micromirror, due to its excellent process compatibility. In our previous work [15], we presented a FR4-based electromagnetic scanning micromirror monolithically integrated with an electromagnetic angle sensor. However, it focused more on basic prototyping, driving performance, and reliability of the micromirror. As a continuation of previous work, this paper performed accurate modeling and detailed tests of the integrated angle sensor. Particularly, we study the coupling effect between the driving coil and sensing coil, which has not been reported by other groups, up to now. Finally, a simple closed-loop control circuit is developed to further verify the angle sensor's good feasibility for providing a real-time feedback signal.  
This paper is organized as follows. Section 2 introduces the working principle of the electromagnetic angle sensor integrated in the FR4 micromirror, and presents the modeling. Section 3 discusses the test results and compares it with model results. Furthermore, the frequency response and phase-frequency characteristics of the angle sensor, and the closed-loop control, are also described in this section. The conclusion is summarized in Section 4.