# A Fourier Transform Spectrometer Based on an Electrothermal MEMS Mirror with Improved Linear Scan Range

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{−1}, or 0.55 nm at 531.9 nm wavelength, is demonstrated in the FTS system, which is a significant improvement on both MEMS design and tilting compensation method compared to the prior work.

## 2. The Principle of Fourier Transform Spectrometer (FTS)

_{max}, is given by [31]

_{max}is the wavenumber of the shortest-wavelength component of the light source under test. If D is 0.1 cm and ν

_{max}is 15,800 cm

^{−1}, a tilt angle no more than 0.002° is desired for no significant resolution degradation. Therefore, when designing MEMS mirrors for FTS, we must consider not only the extension of the scan range, but also the compensation of the tilting effect.

## 3. MEMS Mirror Design & Fabrication

_{b}is the curvature coefficient, which is a constant determined by the properties of the bimorph materials, and l and t are respectively the length and thickness of the bimorph. For high actuation, aluminum (Al) and silicon dioxide (SiO

_{2}) are chosen as the bimorph materials for their large CTE difference [32].

_{1}and R

_{2}), and three Al/SiO

_{2}bimorphs (B

_{1}, B

_{2}and B

_{3}), as shown in Figure 2b. The lengths of R

_{1}and R

_{2}, L

_{R}

_{1}and L

_{R}

_{2}, are equal, and the lengths of the three bimorphs must satisfy the relation L

_{B}

_{2}= L

_{B}

_{1}+ L

_{B}

_{3}. So, to the first order, the tilt and the lateral shift can be compensated, and the angular actuation of the Al/SiO

_{2}bimorphs can be converted into a pure large vertical displacement, ΔH, which is expressed by Equation (5).

_{t}, of the mirror plate can be expressed as

_{2}layer (1 µm thick) deposited with plasma enhanced chemical vapor deposition (PECVD) and patterned with buffered oxide etchant (BOE) (Figure 3a). Then a 150 nm-thick Pt is sputtered and lifted off to form the heater layer, followed by the second thin PECVD SiO

_{2}layer (100 nm) deposited as the isolation (Figure 3b). Before the first Al layer (1 µm) is sputtered and lifted off, a reactive ion etch (RIE) of SiO

_{2}is carried out to make the contact opening between the Pt heater and the Al pads and wiring (Figure 3c). Up to this step, both bimorph materials for the bimorph structures have been formed. After that, the third SiO

_{2}layer (600 nm) is deposited with PECVD and patterned with RIE to define the bimorph actuators and also to serve as the Deep-RIE (DRIE) etching mask in the release step (Figure 3d). Then a second Al layer (200 nm) is deposited and patterned with lift-off to form the mirror surface (Figure 3e). Next, the process turns to the backside of the SOI wafer. A backside silicon DRIE is first performed to etch the silicon all way to the buried oxide (BOX) layer and then the BOX layer is removed by RIE to form the release cavity under the mirror plate (Figure 3f). Finally, a front-side silicon anisotropic DRIE is performed to etch through the device layer (Figure 3g), followed by isotropic DRIE to undercut the silicon underneath the Al/SiO

_{2}bimorphs to complete the device release (Figure 3h).

## 4. Closed-Loop Control of the MEMS

_{ref}(t), which is applied to one of the actuators of the MEMS mirror, i.e., Act.1, leading to a vertical displacement and a tilt of the mirror plate. Via a beam splitter, a laser beam is directed to and reflected off the mirror surface. The laser beam continues to pass through the beam splitter and reach to a position-sensitive device (PSD). The PSD tracks the tilt of the mirror plate by locating the incident position of the laser spot. The output signal of the PSD, P(t), is digitized and compared with a preset voltage, P

_{0}, which corresponds to the target tilt angle. The difference between P(t) and P

_{0}, or the error, e(t), is fed to a PID controller. The output voltage of the PID controller, after being converted into an analog signal, U

_{var}(t), is applied to the other actuator, i.e., Act.2. Here, U

_{ref}(t) applied to Act.1 is a reference waveform while U

_{var}(t) applied to Act.2 is a corrected waveform that is generated by the PID controller. At any instant, U

_{var}(t) is adjusted to make P(t) to converge to P

_{0}. The error, e(t), is a measure of the residual tilting of the mirror plate, which will diminish through the closed loop with the PID controller. According to the classic PID control theory, the proportional term produces an output proportional to e(t) to let P(t) reach P

_{0}rapidly, but the steady-state error may still exist, which can be eliminated by the integral term. Moreover, there may be a fluctuation of e(t) when P(t) is almost equal to P

_{0}, so the derivative term helps to provide a stable response. The gain values, K

_{P}, K

_{I}, and K

_{D}, are tuned based on a basic model identified via the Matlab toolbox, which are K

_{P}= 0.076478, K

_{I}= 2.121529, K

_{D}= −0.000502; respectively. The sampling frequency is set at 10 kHz. According to the step response in this closed-loop control system, the rise time is 16.2 ms and the settling time is 47.2 ms with the overshoot less than 8%.

_{var}(t) is adjusted in real time by the PID controller, the laser beam is stabilized at the preset position

**P**on the PSD, which means the tilting of the mirror plate is compensated effectively during the whole piston motion. Figure 7 shows the residual tilting versus voltage under such a closed-loop control. The tilting angle is significantly reduced down to within ±0.002° in the entire drive voltage range, which meets the mirror tilt requirement of our FTS system. Note that the MEMS mirror has strong nonlinearity and weak response at low voltage as shown in Figure 5a, so the voltage of the reference driving waveform starts from 1 V instead of 0 V to discard the nonlinearity range at low voltage. This leads to only a small loss in the piston scan range.

_{0}## 5. FTS Setup & Experiments

**P**. Attributing to the closed–loop PID control, the FTS system reached a stable operation quickly when the MEMS was actuated, and the mirror plate tilting was kept within ±0.002° during the whole scan voltage range from 1 V to 7 V at 0.1 Hz. The interferogram signals of the reference light and the test light, which were generated in one single stroke of the MEMS scanning, were picked up by PD-R and PD-T, as shown in Figure 9a,b, respectively.

_{0}^{−1}in wavenumber. In FTS spectroscopy, the best resolution in wavelength, δ

_{λ}, is given by Equation (7).

_{max}is the maximum optical scan range. With an 860 μm OPD, the theoretical resolution is 0.33 nm at 531.9 nm. The difference between the theoretical and experimental resolution may result from the residual tilting, external vibrations, and noises. A performance comparison between the former open-loop control method and the closed-loop control method are briefly summarized as Table 3, which clearly indicates that the closed-loop control method provide a great enhancement to the electrothermal MEMS based FTS system.

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 2.**MEMS mirror design: (

**a**) The bimorph structure; (

**b**) The LSF actuator; (

**c**) The basic schematic of LSF MEMS; (

**d**) The LSF MEMS with extended bridge.

**Figure 5.**(

**a**) Quasi-static response curve; (

**b**) Frequency response curve; (

**c**) The tilt angle versus voltage.

**Figure 6.**The block diagram of the closed-loop control. Note: MCU is micro control unit, ADC is analog to digital converter, DAC is digital to analog converter, OPA is operational amplifier, and PSD is position-sensitive device.

**Figure 8.**(

**a**) The schematic of the FTS system with closed-loop control; (

**b**) The experimental setup for demonstration.

Type | Capable Range | Maximum Tilting | Control Method | Compensated Tilting | Usable Range | Utilization |
---|---|---|---|---|---|---|

Wu’s first LSF [23] | 620 μm | 0.7° | None | N/A | N/A | N/A |

Liu’s CCBA [24] | 200 μm | 0.4 | None | N/A | N/A | N/A |

Laddered ISC [25] | 90 μm | 0.25° | None | N/A | N/A | N/A |

Wu’s second LSF [26] | 1000 μm | 2.5° | Optimized Ratio Voltages | 0.06° | 70 μm | 7% |

Meshed ISC [27] | 145 μm | 0.37° | Optimized Ratio Voltages | 0.004° | 48 μm | 33% |

Wang’s LSF [28] | 650 μm | 0.3° (@3.5V) | Open-loop Control | 0.002° | 225 μm | 34% |

Present work | 550 μm | 0.65° | Closed-loop Control | 0.002° | 430 μm | 78% |

Length | Width | Thickness | |
---|---|---|---|

Mirror plate: | 1.1 mm | 1.1 mm | 30 µm |

Extended bridge beam | 1 mm | 150 µm | 31.7 µm ^{1} |

Bimorph beam (B_{1},B_{2},B_{3}) | 150 µm, 300 µm,150 µm | 10 µm | 2.2 µm |

Rigid beam (R_{1},R_{2}) | 1 mm, 1 mm | 160 µm | 31.7 µm ^{1} |

^{1}The extended bridge beams and rigid beams consist of the 30 µm-thick silicon device layer and all of the deposited SiO

_{2}layers which are 1.7 µm in total.

Performance | Open-Loop Control [28] | Closed-Loop Control |
---|---|---|

Rising time | 190 ms | 16.2 ms |

Maximum OPD | 225 µm | 430 µm |

Scan range Utilization | 34% | 78% |

Spectral resolution | 33 cm^{−1} | 19.4 cm^{−1} |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Wang, W.; Chen, J.; Zivkovic, A.S.; Xie, H.
A Fourier Transform Spectrometer Based on an Electrothermal MEMS Mirror with Improved Linear Scan Range. *Sensors* **2016**, *16*, 1611.
https://doi.org/10.3390/s16101611

**AMA Style**

Wang W, Chen J, Zivkovic AS, Xie H.
A Fourier Transform Spectrometer Based on an Electrothermal MEMS Mirror with Improved Linear Scan Range. *Sensors*. 2016; 16(10):1611.
https://doi.org/10.3390/s16101611

**Chicago/Turabian Style**

Wang, Wei, Jiapin Chen, Aleksandar. S. Zivkovic, and Huikai Xie.
2016. "A Fourier Transform Spectrometer Based on an Electrothermal MEMS Mirror with Improved Linear Scan Range" *Sensors* 16, no. 10: 1611.
https://doi.org/10.3390/s16101611