1. Introduction

A typical MEMS mirror consists of a metalized plate connected to a support structure with springs allowing the mirror to move in a tip-tilt and/or piston mode. Tip-tilt mirrors are widely used in optical communications [1–5], 3D scanning (i.e. LIDAR) [6–8], optical switches [9], and biomedical imaging [10–12]. Such mirrors can work as scanners in which the mirror continuously moves or as galvos which operate quasi-statically, moving from one fixed angle to another [13]. Generally MEMS mirrors are small, light and inexpensive, offering a ubiquitous technical solution for beam steering.

Designing a micromirror is always a compromise between angular range and speed [14]. To achieve larger tilt angles engineers can take advantage of high quality factor (Q) systems and the gains from driving a mirror at resonance. It is common for resonant mirrors to have a Q greater than 100, leading to large angles upwards of ±80° optical [15]. However, moving a high Q mirror via a step causes it to ring, with a settling time proportional to Q. For quasi-static applications, the mirror is effectively useless until it stops ringing. Another path to large tilt angles uses softer springs and a large external force. Softening the springs however decreases the resonant frequency and therefore increases the response time of the system. The mirror may be capable of large angular galvo motion but at the expense of speed. Increasing the angular range of MEMS mirrors is an ongoing area of research [16–18]. A typical commercial micromirror can tilt ±15° optical, however current research achieves optical angles upwards of ±60° [19], and one can use additional optics to amplify the angle [16, 20]. One dimensional mirrors can achieve extreme angles and can be used in a dual mirror design to produce a 2D scan; however, despite the mirrors’ large 1D angle, in general these designs are limited in their 2D coverage [21]. A highly sought after goal is a device that enables full hemispheric optical coverage at reasonable speeds. In other words, with a laser beam focused on the mirror from the zenith, the device could direct the beam anywhere in a hemisphere. Such a MEMS device would require a mechanical angular range of at least ±45° about two orthogonal axes.

 

Fig. 1 Overview of MEMS Mirror Design. (a) False color SEM image of the MEMS magnet mirror comprising four bimorphs that lift a polysilicon platform 450 μm off the substrate. A 250 μm cube N50 magnet is attached to the platform using a custom pick-and-place micro-gluing technique and a gold plated mirror is glued on top of the magnet using the same gluing technique. The image has been edited to remove debris and excess glue from the device. (b) False color SEM image of the MEMS magnet mirror from a different angle. To achieve this angle the die is mounted 90° in the SEM. The mirror tilt seen in this figure is due to gravity. (c) Illustration of the experimental setup with the N-S axis of the magnet orthogonal to the substrate. The MEMS mirror assembly is positioned between a pair of electromagnets configured to generate a controllable uniform magnetic field to steer the mirror. A microscope is used for the static measurements and a position sensitive detector (PSD) and laser for the dynamic measurements.

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In this paper, we describe such a device and a driving algorithm that minimizes the negative consequences of our design choices. We believe this approach, with the device and algorithm designed together, will considerably open the phase space for MEMS micromirror applications. Figures 1(a) and 1(b) show false color scanning electron microscope (SEM) images of our device. It comprises a 250 μm cube N50 neodymium magnet (100 μg), glued between a 375 μm diameter gold mirror and a 400 μm diameter polysilicon platform which is attached to four polysilicon springs. To provide clearance for the mirror to rotate, the mirror-spring system is raised off the substrate by four gold-polysilicon bimorphs. The combination of a highly compliant spring system and a strong micro-magnet allow the mirror to reach mechanical angles beyond ±45° quasi-statically with magnetic fields on the order of 50 μT. The final piece of our solution is a control algorithm that moves the mirror much faster than the resonant frequency would suggest. All three elements are key to our device: a compliant spring system, a method of micro-gluing released MEMS and an engineered algorithm that moves the mirror at high speed.

2. Methods

2.1. Device fabrication

The magnet mirror is fabricated using a combination of the MEMSCAP PolyMUMPs process [22] and a custom micro-gluing procedure. The platform comprising four gold-polysilicon bimorphs, four serpentine springs, and a 400 μ

m diameter polysilicon plate is designed in-house and fabricated by MEMSCAP. A layer of protective photoresist is stripped with acetone for 15 minutes at 70° C, and released in hydrofluoric acid for 8 minutes. Using a probe station, tethers are cut that anchor the bimorphs to the substrate. The device is then placed on a hot plate at 250° C for 2 minutes to anneal the bimorphs, which lifts the platform 450 μm off the substrate. A similiar micro-gluing technique was designed and used previously to assemble micro-sized objects on post-released MEMS devices [23]. In this work, vacuum is drawn in a glass micropipette with a 45° articulation near the aperture. The pipette is fastened to a micromanipulator by a 3D-printed coupler and is coarsely moved in plane so that the aperture is positioned over a N50 neodymium cube micro-magnet with 250 μm side length. North is oriented upward toward the aperture face. The magnet is picked up and dipped in a UV curable epoxy (NOA81). It is then centered above the platform plate under a microscope and lowered until contact is made. The device is held and radiated with UV light. The device is then balanced against Earth’s field by an external magnet. Vacuum is removed and the pipette is pulled away from the device. The pipette is then positioned over a separate released MEMS die with a mirror attached by four polysilicon springs. The mirror design consists of a 375 μm diameter, 500 nm thick gold layer deposited on a 400 μm diameter, 3.5 μm thick polysilicon plate. The mirror uses two layers of polysilicon to prevent the mirror from deforming like the bimorphs. The pipette is evacuated on the mirror surface and lifted off, breaking the tethers. The same gluing, placing and UV radiating procedures are followed to secure the mirror on the top face of the magnet. The device is then held at 50°C overnight to fully cure the epoxy according to manufacturer recommendations. The pick-and-place technique allows us to precisely position a wide range of micro-scale structures. We have subsequently created a similar device with a 1 mm diameter mirror and future work could use other mirror designs, such as a single-crystal-silicon mirror for improved optical quality.

 

Fig. 2 (a) Normalized simulation of the magnetic field generated by four electromagnet in a configuration similar to the experimental setup. The color map and arrows represent the amplitude and direction of the B field respectively. All four electromagnets are powered equally and in this configuration provide a uniform B field in the center pointing towards the northwest corner of the figure. (b) Optical image of the MEMS die and coils used during the experiments. (c) Close-up view of the 2 mm x 2 mm area centered around the micro-magnet in Fig. 2(a). Figure 2(c) illustrates how the the mirror/micro-magnet assembly (at scale) tilts to align its magnetic moment, M, with the imposed B field. The uniformity of the field in Fig. 2(c) is characterized by an amplitude range of 0.17 |B|_max to 0.18 |B|_max and a direction range of 40° to 50°.

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2.2. Test setup

Figures 1(c) and 2(a)-(c) show the experimental setup. The mirror is placed between a pair of electromagnets, with radius R, connected in a configuration similar to a Helmholtz pair. Instead of using coils with air cores separated by R, our setup uses electromagnets with iron cores separated by 2R. Due to symmetry, a uniform magnetic field is generated at the point on the coils’ axis centered between the two coils. The amplitude of the magnetic field, B, is proportional to the current, I, through the coils. Assuming the serpentine springs are linear, the relationship between the mirror’s angular position and electromagnetic current is,

The mirror is sensitive to both the earth’s magnetic field as well as 60 Hz magnetic noise that is presumably generated from the laboratory power lines. With no power to the electromagnets, the mirror rotates towards magnetic north approximately 50° - 60° mechanical depending on the orientation. There are two methods we used to shield the mirror from these external sources, (1) an active method and (2) a passive method. The active method uses the electromagnets to offset the external fields. We increase the current applied to the coils until the mirror is parallel to the substrate. This value is the zero point for the angle and the adjusted current in Fig. 3(b). This DC current is combined with a 60 Hz input to minimize the response from the 60 Hz noise in the room. The active method is used for collecting all data presented in this article. In addition to the active method, we can shield the mirror passively by placing the MEMS inside a Mu-metal enclosure. A hole in the lid is used for optical access to the mirror. The high permeability Mu-metal draws external magnetic fields away from the mirror. By using this enclosure we no longer need to apply current to the electromagnets to zero the mirror or cancel any 60 Hz fields.

 

Fig. 3 Quasi-Static Response. (a) Series of images of the mirror from an optical microscope is used to measure the angle and direction of the mirror. In each image, with the exception of the center, the mirror is tilted more than 45° in its respective direction. (b) Plot of tilt angle versus the adjusted current. The angles are measured by analyzing images similar to those shown in a. The black line fits the data to the equation displayed. The inset data is collected while driving the Y coils and the angle is measured via a more conventional approach using a PSD. (c) Polar plot of the mirror’s angle (radial dimension) and steering direction (angular dimension) using the same data presented in Fig. 3(b). The blue and orange data represent positions by only controlling the X and Y coils, whereas the green data uses a combination of the two to steer to an off-axis position.

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2.3. Microscope static measurements

We characterize the static response of the device using an optical microscope to take a series of images of the mirror while actuating the coils, as shown in Fig. 1(c). We use the active shielding method described above to protect the mirror from external magnetic fields. The voltage levels are adjusted, an image of the mirror is captured and the voltage and current are recorded. Examples of the images are shown in Fig. 3(a). The projection of a circle, radius R, onto an surface at angle (θ) relative to the circle’s original plane will result in an ellipse Fig. 3(a) with major radius R and minor radius $R\cos \theta$. The mirror is accurately circular and therefore by fitting an ellipse to the mirror we can deduce the tilt angle. The orientation of the ellipse’s axes indicates the direction of the tilt.

2.4. PSD dynamic and quasi-static measurements

While the imaging technique allows us to measure extreme deflection angles, we also measure over a smaller angular range via a position sensitive detector (PSD). Such a conventional approach can measure in situ with much higher resolution but is limited to a 15° mechanical (30° optical) range due to geometric limitations of our optical setup. The PSD also allows us to measure the dynamics of the device. Figure 1(c) illustrates our setup with a laser focused onto the mirror and reflecting onto a PSD. To calibrate the PSD, we first take an angular measurement on a wall a known distance away. Without adjusting driving parameters, we move the PSD into the beams path. The PSD outputs a voltage proportional to the beams position. This provides an angle/voltage conversion. A few different methods are used to produce the dynamic drives. We use a summing circuit to combine the active shielding and the signals to control the mirror. The quasi-static data in the inset of Fig. 3(b) uses a function generator to produce a 0.3 Hz triangle wave to sweep over a 15° mechanical range. The frequency sweep in Fig. 4 uses a function generator to produce a sinusoidal input and a lock-in amplifier to measure the PSD output. The step and advanced drives are generated with a digital pulse generator and an oscilloscope to measure the PSD output. The data presented in the Fig. 3(b) inset and Figs. 5(a)-(c) are an average of approximately 100 scans to reduce external noise.

 

Fig. 4 The frequency response by driving only the Y coils using a sinusoidal input and sweeping the frequency from 5 to 250 Hz. The plot has been normalized to the Y tilt amplitude at 5 Hz. The inset is a closer look at the frequency range near the resonant peak.

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Fig. 5 Step response and advanced drives. (a) The blue and orange solid lines are the X and Y responses to a step to the Y coils. The gold and green dotted lines are the X and Y response to a double step to the Y coils. (b) Closer look at the response from a single step input, a double step input and a one sided overdrive. The vertical dashed lines are added to guide the eye to half the period of the system in orange and the response time of the double step and overdrive in green and purple. The responses in Figs. 5(a) and 5(b) are normalized to the Y steady state angles, corresponding to approximately 5° optical for the single step and 10° optical for the double step and overdrive. (c) The input drives for the responses in Fig. 5(b). The voltages are normalized to the steady state voltage which are approximately 5 - 10 mV.

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3. Results

3.1. Static

Examples of the static images are shown in Fig. 3(a), which also highlight the steering capability of the mirror. In each image, the mirror is tilted more than 45° mechanical in its respective direction. The mirror angles measured using this technique are shown in Fig. 3(b). In this figure we plot the mirror angle versus adjusted current. The earth’s field imparts a torque on the mirror resulting in an angular offset. We use the electromagnets to actively shield the micro-magnet from the earth’s effect and bring the mirror parallel to the substrate. We have found that shielding can also be achieved passively by placing the MEMS into a Mu-metal enclosure. For this plot we offset the current such that 0° tilt angle corresponds to 0 mA. The black line fits the data to Eq. (1). The reason for the discrepancy between the fit and data is not known at this time but could be due to a number of factors such as asymmetries in the device, non-linearity of the springs, or non-uniformity in the magnetic field to name a few. While this imaging technique allows us to measure extreme deflection angles, we also measure over a smaller angular range via a PSD shown in the Fig. 3(b) inset. A large angle quasi-static circular scan and raster scan are demonstrated in Visualization 1 and Visualization 2 respectively. The full hemispheric coverage is demonstrated in a polar plot featured in Fig. 3(c). This plot shows the tilt angle and direction the mirror is facing. When driving only the X or Y coils the mirror steers along the respective axis. This is the same data presented in Fig. 3(b). When controlling both coils, the mirror can steer in any off-axis direction, demonstrated by the diamonds. As we see in the plot, the X and Y directions are not completely independent in this design. This could be due to a number of factors such as those mentioned above. This setup is designed to more easily characterize and highlight the MEMS mirror; however, one of the limitations is that in some azimuthal orientations the geometry of the electromagnets block the reflected beam beyond ±

45° optical. Realizing a fully hemispheric beam would require generating a uniform magnetic field at the mirror with the electromagnets below the plane of the device.

3.2. Dynamic

To accurately measure the dynamics of the system we use the PSD setup. Figure 4 shows the frequency response of both axes while driving only the Y coils. The plots have been normalized by the Y tilt amplitude at 5 Hz. As the frequency increases we see two peaks in Y tilt, a small peak at 66 Hz, which corresponds to the X resonant frequency, and a large peak at 71 Hz corresponding to the Y resonant frequency. The double peak, in addition to the response of the X direction, indicates a coupling between the X and Y modes [24]. Based on the frequency response we calculate the Q of the mirror to be ∼70. Due to the symmetric nature of the device, the frequency response driving the X coils would look similar to Fig. 4,except the peak at 66 Hz would be larger than the peak at 71 Hz.

The step response in Fig. 5(a) demonstrates the inherent drawback of using a high Q mirror as a galvo. The solid blue and orange lines show the X and Y responses to a step input to the Y coils. It takes approximately 1.35 s for the device to settle within 2% of the final position with a step input. The Y response follows a classic harmonic oscillator response, however there is a 5 Hz beating frequency in both the X and Y due to coupling between the modes. It is well known that two loosely coupled oscillators have a response similar to the step response shown in Fig. 5(a) [24]. When one oscillator is driven by a step input the oscillation energy transfers back and forth between the two oscillators. Each oscillator rings at its respective natural frequency but the ringing beats at a frequency equal to the difference between the two oscillators. This agrees with the frequency response in Fig. 4, where the difference between the X and Y peaks is 5 Hz.

By using an advanced open-loop drive [14, 25] we can improve the settling time by a factor of 300. Figure 5(a) includes the X and Y response to a double step, shown by the dotted gold and green lines. By adding a second step to the input we can drastically reduce the oscillation in both the X and Y axes. The step response of an underdamped system is known to overshoot its final position. We take advantage of this by first giving a smaller step, typically a half step, which peaks at our desired position. At this point in time the mirror is at the final desired position with zero velocity and by applying the full force, we effectively catch the mirror at its final position with no ringing. The exact amplitude and timing of the step depend on the relative damping of the system and has been calculated by Imboden et al. [14]. In this system the double step improves the settling time from 1.35 s to 7 ms. Visualization 3 compares the single and double step responses of another magnetic mirror using a high speed camera. The video is recorded at 6000 fps and played back at 30 fps. A closer look at the Y response is shown in Fig. 5(b). Here we compare the step response to the double step, as well as a unipolar overdrive [14, 25] which further improves the settling time to 4.5 ms. The unipolar overdrive follows a similar principle as the double step except it uses a precisely timed, full force pulse to generate the initial momentum instead of the half step. The input signals for these responses are shown in Fig. 5(c) and we see that they match the above descriptions. The double step input consists of a half step followed by another step to the full voltage, whereas the overdrive input consists of a precisely timed full voltage pulse, followed by a zero voltage pulse, and then a final step to the full voltage.

4. Conclusion

In this paper we have presented results on a MEMS magnet mirror that can access quasi-static mechanical tilt angles of ±60° (±120° optical) about two rotation axes. This micromirror enables greater than full hemispheric optical coverage operating as either a scanner (continuously moving) or galvo (quasi-static). As shown, these large tilt angles do not come at the expense of speed with a settling time of 4.5 ms. Our solution comprises three pieces of technology: a) a carefully engineered spring and mounting system capable of large tilt angles, b) a pick-and-place micro-gluing technique that allows the assembly of complex, post release MEMS devices and c) a set of engineered drive algorithms that enables high Q systems to step and settle in millisecond time scales even though the open-loop ringing decay time is 1.35 seconds. This mirror will enable many new applications for tilting MEMS micromirrors previously unrealized due to its novel design and driving methods.