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We present an electromagnetic biaxial vector-graphic scanning micromirror. In contrast to conventional electromagnetic actuators using linear magnetic field, proposed device utilizes a radial magnetic field and uniquely designed current paths to enable the 2 degree-of-freedom scanning motion. As the radial field is generated by concentrically assembled magnets placed under the scanner die, large driving torque can be generated without the aid of hermetic packaging and relatively small device volume can be achieved. Mechanical half scan angle of 6.43° and 4.20° have been achieved at DC current of 250mA and 350mA for horizontal and vertical scans, respectively. Forced actuation along both scan axes has been realized by feedback control.
© 2016 Optical Society of America
1. Introduction
Nowadays, technological trend of miniaturizing electronic devices is gaining more research momentum and is affecting wider spectrum of applications. Electrically-driven or electronically-controlled sensors and actuators with smaller size and lighter weight are being developed to keep pace with the market needs. Biaxial MEMS (Micro-Electro-Mechanical Systems)-based microscanners are good examples of microfabrication technology combined with conventional optics to provide enhanced or new capabilities for applications such as laser-based projection display [1–6], head-up-display [7, 8], motion tracking [9, 10] and ranging [11]. MEMS scanners can be applied to these applications due to small size and weight, low production cost, high energy efficiency and high performance.
Previously, a 2-dimensional (2-D) galvano optical scanner with two isolated driving coils has been proposed for biaxial operation of microscanner [1]. As the typical characteristics of the MEMS vector-graphic scanner mimics those of the conventional galvanometric mirror, MEMS version of the device can be a replacement for galvanometric mirrors in applications such as barcode scanners [12, 13], medical imaging [14, 15], and LiDAR (Light Detection And Ranging) [11, 16].
In this research, we present a new type of 2-D vector-graphic microscanner using radial magnetic field. Previously, Ji et al. have proposed a 2-D raster scanner based on radial magnetic field, but the requirement for resonance mode actuation have limited the utilization of proposed actuation mechanism in vector-graphic scanning applications [17]. In this research, we have proposed unique current paths and gimbal geometry to provide independent 2-DOF (degree-of-freedom) actuation capability and large scan angle without resorting to mechanical resonance. Also, dimensions and geometry of the concentric magnet assembly have been optimized to maximize the driving torque. With the fabricated device, static and dynamic characteristics have been analyzed and forced actuation of the microscanner has been implemented using feedback control of the device.
2. Design
Figure 1 shows the schematic diagram of the proposed microscanner. A 1.2mm-diameter micromirror is connected to inner and outer gimbals through torsion beams. Driving coils for horizontal and vertical scans are formed on inner and outer gimbals, respectively. The microscanner has been fabricated with 80μm-thick device layer of a silicon-on-insulator (SOI) substrate except for the 20μm-thick torsion beams for the outer gimbal. Coils are formed with 10μm-thick electroplated copper and 2μm-thick underlying aluminum interconnections. A two-step electroplating process has been used to realize a 3μm-thick copper feed-line on top of torsion beams.
Figure 2(a) shows the electromagnetic actuation scheme widely used in conventional motors and previously reported micromirrors. Yalcinkaya et al. have proposed a 2-DOF raster scanner by combining the raster and forced mode actuation schemes with single coil [3]. To achieve a 2-DOF static motion using the operation principle shown in Fig. 2(a), a rather complicated allocation of multiple permanent magnets is required to utilize locally distributed magnetic fields, which inevitably increases the total device volume due to increased permanent magnet footprint. In the magnet geometry shown in Fig. 2(b), a radial magnetic field is generated by concentric magnet assembly and a uniform force is produced around the coil circumference. As the two independent driving coils for each axes share the same magnetic field distribution and as the magnet assembly is positioned under the coil, and thus under the micromirror die, complexity of the device packaging and overall volume of the device can be reduced substantially.
Fig. 2 Comparison of the electromagnetic actuation methods: (a) conventional actuation scheme (I: driving current, H: magnetic field intensity, F: force, T: torque), (b) actuation scheme using radial magnetic field (M1, M2: magnetization, I: driving current, T: torque)
Driving coils are formed on two semicircular inner gimbals and an outer gimbal [Fig. 3]. Coil design for y-axis rotation is shown in Fig. 3(a), where two half-turn windings are formed on the outer gimbal. Dotted lines are redundant current paths which do not contribute to the torque generation. These redundant paths have no effect as the current direction is parallel to the field direction. Coil design for x-axis rotation is shown in Fig. 3(b). Inner gimbal has been divided into two semicircular gimbals to meet the following requirements; 1) radius of the gimbal should be as large as possible for high driving torque, 2) length of the torsion beam supporting the inner gimbal should be compatible with that of the torsion beam for outer gimbal, 3) inner gimbal structure should support a coil routing that minimizes the crosstalk between two scan axes. Two separate current paths which detour the mirror region have been designed. Dotted lines are redundant current paths and only solid lines contribute to the torque generation. Although not shown in the schematics, total number of turns for the inner gimbal is five, in contrast to the single turn coil for the outer gimbal.
Fig. 3 Schematic diagram of the coil geometry: (a) coil geometry of the outer gimbal, (b) coil geometry of the inner gimbal
Proposed microscanner can be described as torsional single or double spring-mass system depending on the scan axis, as shown in Fig. 4. The equations of motion for the proposed rotational spring-mass system can be written as follows.
where J1 is the moment of inertia of both the mirror and inner gimbal for the horizontal scan, J2 is the moment of inertia of the outer gimbal for horizontal scan, J3 is the moment of inertia of the mirror and inner and outer gimbals for vertical scan, k1 is the torsional spring constant of inner torsion beams, k2 is the rocking mode spring constant of the outer torsion beams, k3 is the torsional spring constant of the outer torsion beams. θ1 is the angular deflection of mirror along horizontal scan axis, θ2 is the angular deflection of the inner gimbal along horizontal scan axis, and θ3 is the angular deflection of entire body along vertical scan axis. Thorizontal is the driving torque for mirror rotation along x-axis and Tvertical is the driving torque for mirror and gimbal rotation along y-axis.Fig. 4 (a) schematic diagram of components related with x-axis rotation, (b) rotational double spring-mass system for x-axis rotation, (c) schematic diagram of components related with y-axis rotation, (d) rotational spring-mass system for y-axis rotation
Using the Laplace transform, above equations can be rewritten as follows.
Equations (2a) and (2b) can be rewritten using a transfer matrix.
From Eq. (2c) and (3), angular deflection of each part of the microscanner can be obtained as follows.
Analytic modeling result has been verified by FEA (Finite Element Analysis) using Ansys Workbench. Moment of inertia of each component has been estimated with solid modeling tool (SolidWorks) and torsional spring constant has been extracted from the static deflection angle analysis using Ansys Workbench. Table 1 shows the list of dimensional parameters of the designed scanner. Figure 5 shows the modal analysis result of the designed scanner. First mode is the vertical scanning mode where the outer gimbal of the scanner rotates around the y-axis at 609.2Hz. In the second mode, mirror and inner gimbal rotate in phase around the torsion beam supporting the inner gimbal at 832.1Hz, as shown in Fig. 5(b).
Table 1. Dimensions of the designed scanner
Figure 6 shows the frequency response of the designed scanner obtained with FEA and analytic model. For the harmonic analysis using Ansys Workbench, averaged directional deformation in z-direction has been obtained at the mirror edge [Fig. 6(a)]. Figure 6(b) shows the comparison between the frequency response obtained with equations of motion and harmonic analysis result obtained by simulation. Discrepancy in resonance frequency for horizontal scan is 0.47% and that for vertical scan is 0.69%. Constant damping ratio of 0.000645 has been used in the harmonic analysis.
Fig. 6 Frequency response of the designed scanner: (a) measurement location (directional deformation in z-direction) for harmonic analysis using Ansys Workbench, (b) comparison of bode plots obtained with equations of motion (top) and harmonic analysis (bottom)
As only driving torque for x-axis rotation benefits from multiple winding turns, initial design of the magnet assembly, consisting of two concentric magnets and a pole piece [18], has been modified to further increase the driving torque for y-axis rotation. Magnetic field analysis using a 2-D axisymmetric finite element analysis has been performed and additional concentric pole piece on top of the outer permanent magnet has proven to be effective in further increasing the radial magnetic field [Fig. 7(a)]. Figure 7(b) shows the radial magnetic field intensity (H) distribution at various inner radii of the pole piece. Only horizontal component of the total magnetic field intensity is considered in radial field intensity. As the driving torque is proportional to the square of coil radius (R2) and radial field intensity (H) [18], value of R2H has also been compared. As shown in Fig. 7(c), increase of driving torque is more pronounced at outer gimbal region where the coil for y-axis rotation is formed. Considering the size of the gimbal and gap between the mirror die and magnet, inner radius and thickness of the additional pole piece on the permanent magnet have been set to 2.3mm and 0.37mm, respectively. Gap between the mirror die and magnet assembly is 0.37mm, which matches the thickness of the pole piece on top.
Fig. 7 Magnetic circuit design: (a) axisymmetric simulation result, (b) simulated radial magnetic field intensity (H) distribution at various inner radii of the upper pole piece (Rp), (c) torque component (R2H) distribution at various inner radii of the upper pole piece (Rp)
3. Experimental results and discussion
Device has been fabricated with SOI (silicon-on-insulator) substrate using Senplus’ proprietary metal process which enables the realization of multiple thickness single crystalline silicon structure with two metal layers on top (Senplus Inc., Gyeonggi-do, Korea) [19]. Structural layer of the device has been fabricated with 80μm-thick device layer except for the 20μm-thick torsion beam as shown in Fig. 8. Windings have been formed with 10μm-thick electroplated copper. A two-step electroplating process has been used to form 3μm-thick copper line on top of the torsion beam region. Multi-turn winding has been realized using additional aluminum layer (2μm-thick) under the winding as shown in the inset of Fig. 8.
After the die separation, a flexible printed circuit board (FPCB) has been attached directly to the interconnection pads formed on the scanner die using anisotropic conductive film (ACF) bonding process. Silicon die and magnet has been aligned passively and assembled inside a fluorocarbon-based polymer housing [Fig. 9]. Total volume of the packaged device measures 0.53cm3.
Angular deflection of the micromirror has been measured using experimental setup shown in Fig. 10(a). The MHSA (Mechanical Half Scan Angle) of the scanner, which is a quarter of the optical full scan angle, has been estimated by measuring the scan pattern length. MHSA of the x-axis and y-axis rotation are 6.43° and 4.20° at DC current of 250mA and 350mA, respectively [Fig. 10(b)]. Scan angle of the micromirror has been increase by 20.0% for y-axis rotation and 3.7% for x-axis rotation by addition of concentric pole piece on the top side. Measured resistances of the inner and outer coils were 6.8Ω and 4.1Ω, respectively.
Fig. 10 Deflection angle measurement: (a) experimental setup, (b) measurement results (subscript “New” denotes result with additional pole piece on the top side and “Old” denotes result with pole piece only at the bottom of the permanent magnets)
To demonstrate an independent forced actuation along both scan axes, a rectangular test pattern has been generated with scanned beam. To draw a rectangular test pattern, input current with 90° phase difference has been fed to each driving coil, as shown in Fig. 11(a). To implement this experiment, FPGA (Field Programmable Gate Array) module and LabView have been utilized. To generate sufficient amount of driving torque, driving current in the range of 100-300mA is required. As the maximum value of the output current from FPGA is 50mA, class B push-pull amplifier has been used for amplification. As the class B amplifier can only amplify half of the signal, a push-pull configuration has been used. Typical amplification efficiency for this type of amplifier is very high, but the distortion of output signal is relatively larger than that of other types of amplifiers [20]. Even if the input current is high enough to generate the driving torque required to draw a rectangle, scanned pattern still suffers a non-negligible amount of distortion due to the ringing effect caused by the moment of inertia of the micromirror, as shown in Figs. 11(b) and 11(c).
Fig. 11 (a) Input currents for each driving axis of the microscanner to draw a rectangular test pattern, (b) ringing effect at 1Hz, (c) ringing effect at 2.5Hz
To reduce this effect, closed loop feedback control has been utilized as shown in Fig. 12(a). Deflection angle of the mirror has been measured with PSD (Position Sensitive Device) sensor. Part of the reflected beam from the microscanner has been fed to PSD using beam splitter as shown in Fig. 10(a). Firstly, a low pass filter (LPF) has been used to eliminate high frequency components of the vibration generated by oscillation of the micromirror. As the overshoot consists of high frequency components, especially the harmonics of resonance frequency, cutoff frequency of the low pass filter has been set to be near the resonance frequency. Used cutoff frequencies were 717Hz and 530Hz for horizontal and vertical scans, respectively. Although substantial amount of overshoot has been reduced with the aid of LPF [Fig. 12(b)], perfect rectangular pattern could not be generated.
Fig. 12 (a) block diagram of the closed loop feedback system, (b) rectangular test pattern after LPF, (c) rectangular test pattern after PID control
To fully remove the remainders of the ringing, a PID (Proportional-Integral-Derivative) controller has been utilized whose governing equation can be expressed as,
where Kp is the proportional constant, Ki is the integral constant, Kd is the derivative constant, e(t) is the error between set point and process variable, and u(t) is the output of PID controller.The set points for PID controller are provided with atmega128 which are identical to the current functions shown in Fig. 10(a). PSD sensor measures the actual deflection angle of the micromirror and provides process variable to the PID controller. As the current level of the PSD exceeds the capability of FPGA, a 25MΩ-resistor is added to PSD in series. Digital LPFs are also added to reduce the noise of the output signal from PID. Cutoff frequencies are 1,478Hz and 1,730Hz for the x and y scans, respectively. The output current of PID controller has been modified gradually while estimating the difference between the set point and actual current value. As shown in Fig. 12(c), substantial amount of ringing effect has been removed from the rectangular test pattern, which still requires further optimization. Experimentally determined proportional constant (Kp) and derivative constant (Kd) are 1.67969 and 48.5078 for the x-axis rotation and 1.71875 and 24.9844 for the y-axis rotation.
4. Conclusion
A new type of biaxial vector-graphic microscanner using radial magnetic field has been designed, fabricated, and tested. Self-aligned concentric magnet assembly placed under the silicon-fabricated scanner die enables a compact non-hermetic microscanner package without compromising the driving torque. Scan angle increase of up to 20.0% has been achieved for the y-axis rotation by further optimization of the magnetic circuit. Maximum mechanical half scan angle of the x-axis and y-axis rotation are 6.43° and 4.20° at DC current of 250mA and 350mA, respectively. Although differences in the scan angle for each axis require further optimization, biaxial scanning capability has been demonstrated successfully. Furthermore, we have successfully implemented an independent forced actuation along two perpendicular scan axes. A rectangular test pattern has been generated where scan pattern distortion from ringing effect has been reduced substantially with the aid of LPF, class B amplifier, and PID controller. Further optimization of PID control parameters for each axis is required to completely eliminate the ringing.
Acknowledgments
Authors would like to thank Byung-Min Yoon, Seung Lee, and Taeha Kim of Senplus Inc., for the device fabrication and support with the characterization. This work was supported by the industrial technology innovation program (No.10047785) funded by the Ministry of Trade, Industry and Energy (MI, Korea), by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2014R1A1A2057721), by the EU Framework Program of the National Research Foundation (NRF) funded by the Ministry of Science, ICT & Future Planning (2014K1B1A1073720), and by the Center for Integrated Smart Sensors as GFP (CISS-2012M3A6A6054204).
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