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A large piston-displacement electrothermal micromirror with closed-loop control of both piston scan and tilting of the mirror plate is demonstrated for use in a miniature Fourier transform spectrometer. Constant scan velocity in an ultra large piston scan range has been demonstrated by the proposed closed-loop piston control scheme which can be easily implemented without considerably increasing system complexity. The experimental results show that the usable linear scan range generated by the micromirror has been extended up to 505 μm. The measured spectral resolution in a compact spectrometer reaches 20 cm−1, or 0.57 nm at 532 nm wavelength. Compared to other presented systems, this microspectrometer will benefit from the closed-loop thermal actuator approach utilizing both the piston servo and tilt control to provide more consistent spectral response, improved spectral resolution and enhanced robustness to disturbances.
© 2016 Optical Society of America
1. Introduction
Fourier transform spectroscopy in infrared (IR) or near infrared (NIR) is well known for its capabilities of providing high resolution and large spectral range without the need of expensive IR/NIR detector arrays. It is preferred in a wide range of biochemical analysis applications in both laboratory and field environments due to its high throughput and multiplexing advantages [1–3]. The core of a Fourier transform spectrometer (FTS) is a Michelson interferometer with a fixed mirror and a movable mirror respectively placed in the two optical arms. Miniaturization of a FTS utilizing a MEMS scanning mirror as the movable mirror enables rapid on-site detection and analysis of chemical and biological samples [4,5]. Currently, micromirrors with different actuation mechanisms, such as electromagnetic, electrostatic, piezoelectric, and electrothermal, have been widely reported in literature [6–11]. Among them, electrothermally-actuated bimorph micromirrors can provide large linear travel range without the need of operating at resonance [12]. This advantage makes these electrothermal micromirrors well suited for use in miniature FTS instruments.
One of the key performance parameters of a FTS is the optical path difference (OPD) between the two optical arms of the interferometer, which is the double of the physical scan range produced by the movable mirror. The larger the usable scan range, the higher the achievable spectral resolution. Although, for miniature FTS, the large-piston electrothermal bimorph actuation is preferred over other actuation mechanisms, there exists a relatively large tilting of the mirror plate during the piston scan, which limits the usable range and deteriorates the interferogram signals and thus lowers the spectral resolution [12]. In our previous work, the tilting of the mirror plate during large-piston scanning has been reduced dramatically with a closed-loop tilting control approach [13], in which the usable travel range scanned by the moving electrothermal micromirror is increased significantly, up to 356.4 μm. However, the linear piston scan is still in open-loop drive operation, which results in non-uniform scan velocity and poor robustness to disturbances and environmental changes. Furthermore, scanning the movable mirror at constant velocity has been the traditional method in commercial FTS instruments [1]. If the mirror moves exactly at a constant velocity, the radiation from a monochromatic source will form a perfectly sinusoidal interferomgram, leading to a single sinc function in the recovered spectrum. On the other hand, if the mirror velocity varies, the interferogram will have a varying fringe density, resulting in uneven data sampling, i.e., denser fringe regions will have less sampling points per fringe. This effect not only increases the complexity of the data processing but also reduces the overall signal-to-noise ratio (SNR) of the FTS system [14,15].
In this work, we propose a closed-loop piston position control scheme that allows the velocity of the moving mirror to be controlled accurately. An electrothermal micromirror with an ultra large piston scan range, up to 505 μm, has been developed for Fourier transform microspectrometers. The piston servo control provides accurate position tracking and improved robustness against external disturbances. Meanwhile, the previously-demonstrated tilting control loop [13] is also implemented in this proposed system. Experimental results conducted on a miniature FTS setup have validated the effectiveness of this dual closed-loop control approach. Compared to our previous works, the constant-velocity scan system exhibits more consistent spectral response, improved spectral resolution and enhanced robustness.
This paper is organized as follows. The design and characteristics of the electrothermal micromirror is introduced in section 2. Then the closed-loop piston control is described in section 3. The FTS setup with the dual closed-loop controlled MEMS mirror and the corresponding FTS experimental results are presented in section 4.
2. Electrothermally actuated micromirror
The electrothermal micromirror to be used as the movable mirror of the miniature FTS is shown in Fig. 1. In our bimorph actuator design depicted in Fig. 1(a), Pt is used as the thin film heater, and Al and SiO2 are used as the two active bimorph layers with large difference in their thermal expansion coefficients which will lead to large actuation range. The bimorph actuator consists of two segments of silicon-backed rigid frames and three segments of Al/SiO2 bimorphs. Such a configuration yields large vertical displacement with lateral-shift-free (LSF) actuation [16]. The LSF micromirror is fabricated using a combined bulk and surface micromachining process [12]. One fabricated device is shown in Fig. 1(b), where the 1.0 mm × 1.0 mm Al-coated mirror plate is attached to the substrate on the two opposite sides by two arrays of LSF bimorph actuators. Characterization of the mirror has been performed with the drive voltage varying from 0 to 6.5 V, as shown in Fig. 1(c), where the static displacement without control reaches 629 μm at 6.5 V, but the corresponding tilt angle is as large as 0.11°. The mirror tilt mainly results from the small discrepancy between the two bimorph actuators, which is caused mostly by fabrication variations. For instance, the resistances of the two actuators are slightly different, which are 346.6 Ω and 349.4 Ω, respectively. Fortunately, using the closed-loop tilt control approach known as dynamic alignment, the tilting angle can be reduced below ± 0.0015° throughout the entire drive voltage range [13], as shown in Fig. 1(d) where the drive voltage range is set from 0.3 to 6.5 V and its frequency at 0.2 Hz. Maintaining very small tilting is critical to ensure high quality interferograms when the micromirror is used as the movable mirror in a miniature FTS.
Fig. 1 Electrothermal micromirror: (a) Scanning mirror with LSF bimorph actuation. (b) SEM of a fabricated device. (c) Measured static actuation and tilt angle versus drive voltage. (d) Residual mirror tilt angle using closed-loop tilting control.
In most conventional FT-IR spectrometers, the moving mirror travels at a constant velocity during each scan [1], which greatly simplifies signal acquisition and processing and ensures a uniform spectral resolution. Thus, accurate control of the mirror velocity has a significant impact on the spectrometer performance. However, as can be seen in Fig. 1(c), the static displacement-voltage curve of the electrothermal micromirror is highly nonlinear. This means the responsivity of the bimorph actuator varies nonlinearly with the drive voltage, which is a challenging issue in designing a closed-loop piston scan control system. Moreover, when traditional open-loop scan operation in the form of a triangular drive voltage is applied, the movable mirror travels at a varying scan velocity [13], which results in an interferogram with a wide frequency range even when a monochromatic optical beam is passed through the interferometer. Although the pre-shaped open-loop drive by using special input waveforms is helpful to generate roughly constant linear velocity scan profile, the residual speed error is relatively large [17]. Moreover, the open loop drive is sensitive to various disturbances, such as environmental vibrations and ambient temperature fluctuations. On the other hand, closed-loop controlled MEMS devices have many advantages such as improvements in system precision, stability and robustness [18]. This suggests that a closed-loop control should be applied to the micromirror to obtain a constant scan velocity and consequently consistent spectral response.
3. Closed-loop linear scan control
The proposed closed-loop piston scan scheme is illustrated in Fig. 2, in which a He-Ne laser (632.8 nm) is coupled into an interferometer with an MEMS mirror (MM) in one of the arms. When the MEMS mirror scans, an interferogram is picked up by the photodetector (PD), which is a sinusoidal signal, Vz, that crosses zero twice for every 316.4 nm (half wavelength of the laser) piston displacement of the movable mirror. The zero-crossing pulses are detected by a zero-crossing detector circuit (ZCD) and subsequently acquired by a Capture Unit (CU) on a control-optimized DSP (TMS320F28335) board. So the OPD change during the mirror traveling is extracted by counting each pulse in real time. Besides the linear piston scan control, the tilting angle of the mirror plate is also sensed by a position-sensing detector (PSD) and fed back to an 18-bit A/D converter. Both the piston servo and tilting control are realized in the DSP-based digital controller at a sampling frequency of 10 kHz. By superimposing the tilting control voltage (Vc) on the piston control signal (Vb), two drive voltages, Vb + Vc and Vb-Vc, are generated and applied on the two bimorph actuators in a differential fashion. The mirror scan speed is set by the gradient of the waveform of the piston input signal, Zref, while the reference input for the tilting control loop is fixed at zero, i.e., θref = 0. Since only the ZCD is added to the hardware of the original tilting control system [13], the proposed dual piston (z) and tilting (θ) control can be readily implemented without considerably increasing system complexity.
Fig. 2 Schematic of the closed-loop controlled electrothermal micromirror with both piston (z) servo and tilting (θ) control.
Similar to the fitted tilting motion model reported in [13], the piston motion of the electrothermally-actuated micromirror device, which experiences the electrical to thermal, thermal to stress, and stress to motion conversion processes, can also be represented approximately by a fourth-order transfer function model together with a drive voltage-dependent loop gain, i.e.,.
where is the drive voltage-dependent gain of the bimorph actuator, m and bz represent the mass and air damping coefficient of the mirror plate, Kz is the mechanical stiffness of the bimorph actuators, and are three time constants corresponding to the thermal response of the micromirror. The two poles associated with τ1 and τ2 correspond to the two thermal capacitances stemmed from the silicon frames and bimorph actuators, respectively. Considering the temperature dependent resistance of the embedded heater, the maximum power dissipated in each bimorph actuator is 91 mW when operated at its upper drive voltage limit of 6.5 V.A simplified block diagram of the closed-loop piston servo control system is shown in Fig. 3, where Gm(s) denotes the micromirror model given in Eq. (1) and Gc(s) is the feedback controller to be designed. The photodetector-based position sensor is modeled as a scale factor, Kp. Based on the measured frequency response of the micromirror device [12], the micromirror model parameters in Eq. (1) are extracted through curve fitting. The fitted model is plotted as the dashed lines in Fig. 4, showing the first piston mode frequency (ωr) at 162 Hz and the low frequency drop at 2.5 Hz which is attributed to relatively large thermal capacitance of the bimorph actuator introduced by the thick silicon frames [13].
Fig. 4 Open-loop frequency responses of the uncompensated (Gm) and compensated (GmGc) micromirror systems by setting Vb = 3.0V.
The piston feedback controller is similar to the controller for the tilting control but with some modified design parameters by considering that the measured piston resonant frequency is much smaller than that of the tilting [13]. The piston controller is a cascade of a lag compensator GLC(s), a three-order low-pass filter GLPF(s) and a notch filter GNF(s) in the form of a six-order transfer function, i.e.,
Figure 4 shows the open-loop frequency responses of the uncompensated and compensated systems by setting Vb = 3.0 V. It is shown that the compensated system exhibits a cross-over frequency (ωc) at 25.5 Hz and a phase margin of 35.4 °. This cross-over frequency is over ten times higher than the cutoff frequency of the uncompensated system. The position servo system has a relatively large bandwidth of 52.2 Hz in which constant scan velocity can be maintained in the presence of environmental disturbances. In principle, the higher the bandwidth, the better the accuracy of the constant velocity. In this LSF electrothermal micromirror, the servo bandwidth is limited mainly by its first-order piston resonant frequency, i.e. 162 Hz, as stated above.
Furthermore, since the nonlinear relationship between the loop gain and the drive voltage, Ka(Vb) in Eq. (1), can be obtained by fitting the slope of the measured displacement-voltage curve as shown in Fig. 1(c), a drive voltage-based gain compensation is also utilized and realized in the DSP-based digital controller to provide more consistent response over a wide drive voltage range. In this case, the controller in Eq. (2) becomes
Figure 5(a) shows the measured time response of the closed-loop controlled micromirror where Zref is a periodic ramp input signal at a constant slope of 820 μm/s. After a short initial transient period, the controlled micromirror tracks accurately the reference position input at the preset scan velocity. Figure 5(b) shows the position tracking error during the entire scan where the settling time is 65 ms and overshoot is less than 10%. In comparison, the open-loop operation of a similar MEMS mirror led to a rise time of 200 ms [12]. So, the closed-loop system exhibits much faster dynamic response than the open-loop drive. Moreover, Fig. 5(b) indicates that the tracking error is less than 1.1 μm during the steady-state scan and stays almost at the same level across the entire range, regardless of the nonlinear bimorph actuator responsivity, as depicted in Fig. 1(c).
Fig. 5 Measured time response of the closed-loop controlled micromirror: (a) Drive voltage and displacement. (b) Position tracking error.
In order to evaluate the robustness of the micromirror piston servo loop, an equivalent disturbance excitation, Vd, is superimposed on the piston control voltage (Vb) before being applied on the two bimorph actuators. For a comparison of the disturbance rejection performance, the MEMS mirror was firstly driven in the open-loop mode using a triangular wave drive signal. Figures 6(a) and 6(b) show the measured open-loop responses where Vb varies linearly from 0.8 V to 6.5 V while Vd is superimposed on Vb as a sinusoidal disturbance voltage signal at 0.2 V and 4 Hz. Figure 6(b) is the deviation of the physical displacement of the mirror plate due to the disturbance, which is as large as 10 μm. It is also clear that the frequency of the disturbance appears in the scan response. Figures 6(c) and 6(d) show the measured closed-loop responses with the same disturbance input, indicating the dynamic displacement deviation is reduced down to within 0.7 μm. Hence, much increased disturbance rejection, over 10 times, is achieved by the proposed closed-loop piston control approach.
Fig. 6 Comparison of mirror scanning responses by applying a sine disturbance input: (a) Open-loop drive signal, position response and (b) position tracking error. (c) Closed-loop drive signal, position response and (d) position tracking error.
4. Experimental results in a miniature FTS
A miniature FTS setup used in the initial characterization of the closed-loop controlled micromirror is constructed on an optical bench, as sketched in Fig. 7, to demonstrate the spectrometer performance at constant scan velocity. The reference laser light source (LS-R) and testing light source (LS-G) are combined by the first beam splitter (BS1) and directed into the second beam splitter (BS2), where the combined light beam is split into two beams which are reflected respectively from a fixed mirror (FM) and the movable MEMS mirror (MM) and then re-combined as a single beam by the BS2. After that, the third beam splitter (BS3) directs half of the optical power to the first photodetector (PD-T) which picks up the interferogram of the combined light; BS3 directs the other half to a dichroic filter which only lets the red reference laser pass through to the second photodetector (PD-R). The red laser here is introduced as the reference light for both the spectral calibration and detection of the MEMS mirror travel. When the FTS system starts to run after optical alignment, the raw interferograms of the reference light and the testing light are picked up concomitantly by the two PDs and then digitalized by a data acquisition module (DAQ) with 14-bit A/D resolution. The acquired data is processed in a PC using the same data processing algorithm reported in [11] to recover the spectrum. Both the closed-loop piston servo and tilt control systems are employed to drive and control the MEMS mirror in order to keep the desirable constant speed scan trajectory in the position tracking mode. In this case, the mirror plate tilting is dramatically reduced down to within ± 0.0015°, as indicated in Fig. 1(d), which can largely increase the modulation index of the interference fringes.
For demonstration purpose, a red He-Ne laser (632.8 nm) is used as the reference light, and a green semiconductor laser (532 nm) combined with the red laser together is used as the testing light to be measured. The drive voltage is limited within its allowable range of 0.4-6.5 V during the piston scanning. The raw interferograms of the reference light and the testing light are sampled by the DAQ at 20 kHz.
For a comparison of the scan response and spectral performance, the MEMS mirror was firstly driven in an open-loop mode using a ramp drive voltage signal to generate the piston scan motion [13]. Note that this piston scan is open loop but the tilt is already compensated with a closed-loop control. As shown in Fig. 8(a), the maximum OPD is 0.940 mm at a scan time duration of 2.0 s. It is clear that the scan velocity is uneven due to the strong nonlinear response at the low drive voltage range. It is also found that there exists a considerable discrepancy in the achievable OPD, about 5% during multiple scans. Figure 8(b) shows the signal frequency of the acquired reference interferogram in which a moving average filter is used to smooth the noisy frequency data. In each scan, the reference signal frequency varies greatly from 33 to 1145 Hz. Figure 8(c) also shows a raw interferogram signal of the testing light in a wide frequency range. The higher the drive voltage, the higher the signal frequency. This results in a varying fringe density and an uneven data sampling. In order to recover the spectrum from the raw interferogram, a data processing algorithm is used to calibrate the uneven scan velocity so that the interferogram signal is converted from the temporal domain into the spatial domain at equal intervals of retardation. Finally, the corresponding spectrum of the testing light is recovered and plotted in Fig. 8(d). The spectral peaks of the testing light, which is a combination of the He-Ne laser and the green laser, are detected at 15800 cm−1 and 18790 cm−1, respectively. The measured spectral resolution, i.e., full-width at half-maximum (FWHM), is 21.7 cm−1.
Fig. 8 FTS experimental results with open-loop (left-side) and closed-loop (right-side) scan drives: (a) and (e) Drive voltages and generated OPDs. (b) and (f) Signal frequency of the reference light interferogram vs. scan time. (c) and (g) Acquired interferogram signals of the testing light in time domain. (d) and (h) Recovered spectra of the testing light at 18790 cm−1.
In contrast, Figs. 8(e)-8(h) show the experimental results for the closed-loop piston scan controlled micromirror by setting a scan rate of 0.255 mm/s and the same time duration of 2.0 s. As shown in Fig. 8(e), the actual velocity of the MEMS mirror travel is constant over 96.7% of the full scan range, which leads to a uniform fringe density of the interferogram signal and a uniform data sampling in the temporal domain. It is also noted that the closed-loop drive yields a slightly increased OPD (1.01 mm per scan), which means the actual displacement of the mirror plate reaches up to 505 μm during a single scan cycle. Moreover, the observations show a much improved OPD repeatability with about only 0.2% maximum variation during multiple scans. The signal frequency and acquired interferogram shown in Figs. 6(f) and 6(g) indicate that the interferogram signal exhibits a uniform signal frequency of approximately 804.7 Hz after the initial transient response, benefiting from the constant scan velocity. The recovered spectrum of the testing light is shown in Fig. 6(h). The measured FWHM of the testing light is improved to 20 cm−1, corresponding to a spectral resolution 0.57 nm at 532 nm wavelength. Note that the interferogram is transformed into a spectrum with the assumption that the middle of the scan range corresponds to the zero path difference (ZPD) of the FTS system. When a Gaussian window is used for apodization, the theoretical FWHM resolution is given by 2.03/OPD [1], i.e., 19.9 cm−1 for this FTS setup. The measured FWHM is in good agreement with the theoretical limit. In addition, it is expected that the resolution will reach 10 cm−1 if a single-sided scan starting from the ZPD is applied in broadband FTS systems.
In a continuous-scanning FTS, the sampling of the interferogram at an equal time interval can be easily implemented, but this usually requires an accurate mirror drive because the mirror scan speed variation causes variable space intervals in the OPD domain. Sampling errors induce artifacts, such as spectral ghosts, and in general increase the spectral noise [19]. Thus, the recovered spectrum of the velocity signal is helpful to evaluate the characteristics of the micromirror drive system. As shown in Fig. 9, the open-loop drive generates a reference interferogram with a frequency varying from a few Hz to 1.145 kHz whereas the closed-loop drive exhibits a uniform signal frequency at a peak of 804.7 Hz, which is only 70.3% of the maximum signal frequency generated by the open-loop drive. Although the open-loop drive can produce roughly constant velocity using the generated drive voltage by the closed-loop system, as shown in Fig. 8(e), this method is susceptible to any environmental disturbances and/or device characteristics of drifting over time.
A performance comparison between the two micromirror drive methods is shown in Table 1. Compared to the open-loop scan with active tilt control only, the proposed dual tilt and piston closed-loop control ensures the MEMS mirror to exhibit not only constant scan velocity and greatly increased robustness to disturbances but also increased spectral resolution and enhanced repeatability.
Table 1. Comparison between the Open Loop and Closed-loop Scan Operations
Theoretically, the resolution is inversely proportional to the usable OPD range in which the interferogram fringe modulation does not have significant loss. It is important to note that the achievable scan range, 505 μm in Fig. 8(e), is about 80.3% of the maximum static piston displacement of the micromirror. Apart from relatively large thermal response time (~200 ms) of this LSF type micromirror [12], the temperature rise of the mirror plate due to continuous scan drive plays an important impact on the electrothermal actuation range. In order to maximize the OPD, it is essential to reduce the average power consumption of the bimorph actuators. This can be realized by further optimizing the scan profile in one full cycle. A proposed unidirectional scan drive signal versus time curve is plotted in Fig. 10(a), where each scan cycle consists of two time periods: T1 and T2. During T1, the mirror scans forward at a preset speed by the closed-loop piston control, while during T2, the mirror returns back rapidly and rests at the initial position waiting for the next forward scan. Here, properly choosing the time interval T2 allows the bimorph actuators to dissipate heat and also reduce the average drive power, which can increase the attainable OPD by minimizing the temperature of the bimorph actuators at t2 as well as the temperature rise of the mirror plate.
Fig. 10 (a) A proposed unidirectional scanning scheme with two time segments, the forward scan T1 by closed-loop piston control and retracement T2 at open-loop operation. (b) Measured OPD with different time settings where the upper and lower limits of the drive voltage are Vmax = 6.5 V and Vmin = 0.4 V, respectively.
The measured OPD with different settings for T1 and T2 are shown in Fig. 10(b). It is clear that the achievable OPD increases by extending the scan time (T1). This is in agreement with theoretical predication by considering the large thermal time constant of this LSF micromirror. Moreover, it is also noted that the achievable OPD increases by extending the return and waiting time (T2). However, the maximum OPD virtually no longer increases when T2 > 1.0 s. The experimental results also show that the reversal mirror velocity will slow down to 0.038 mm/s at the moment t2 = T1 + 1.0 s, which is much smaller than the forward scan velocity, e.g., 0.50 mm/s at t1 = 1.0 s. T1 and T2 must be optimized by considering the actual requirements on scan speed and spectral resolution when designing a practical FTS.
5. Conclusion
In comparison to prior tilt-only closed-loop control of the scanning micromirror, the proposed dual piston/tilt closed-loop control ensures the micromirror to have constant scan velocity, fast dynamic response and greatly increased resistance to various disturbances. More importantly, the dual closed-loop mirror-based FTS system offers much more consistent spectral response and slightly increased spectral resolution. This is especially important for electrothermal bimorph MEMS mirror-based FTS devices as the initial position of the mirror plate varies over time and is also very sensitive to the ambient temperature. As the moving speed of the mirror is uniform throughout the entire scan, the sampling with equal spatial intervals is obtained, which greatly simplifies the data processing. Also, because of the uniform scan velocity, the bandpass filter can have a smaller bandwidth and the effective oversampling factor is higher compared to a variable scan velocity system with the same sampling rate, both of which lead to higher SNR and thus better spectral resolution. Future work will focus on realization of the dual closed-loop control approach in a broadband FTS system.
Funding
National Science Foundation (NSF) (1512531 and 1514154); Chinese Scholarship Council (CSC) (201506215006).
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