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Abstract
In this article, a fiber optic accelerometer based on a Fabry-Perot interferometer is presented and prepared by micromachining on a silicon substrate. The inertial sensing structure of the accelerometer is built by a center block mass and four folded springs with a high thickness-to-width ratio, providing an in-plane resonance vibration. The miniature-sized sensor has large flexibility in structural design and its acceleration response can be predicted by theoretical estimation and finite element simulation. Experimental results show that the proposed sensor’s sensitivity is over 161 rad/g in frequency range of 1 to 63 Hz. It also achieved a low average noise level of 67.4 ng/Hz1/2 on the working band. The sensor’s transverse crosstalk is less than 1.38%, proving its potential ability in low frequency vibration detection applications.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Acceleration sensing plays an irreplaceable role in our everyday life and industrial activities such as machine condition surveillance [1,2], structural health monitoring [3,4], seismic detection [5,6], and so on. Therefore, various kinds of accelerometers have been developed in the past decades. In comparison with traditional accelerometers based on large machining structures, sensors involving micromachining technology have attractive advantages like flexible design, light weight, miniature size, and mass production, which draw much attention from many researchers. Since many sensing applications mentioned above are closely related to low frequency signal sensing, narrow function space, and harsh environment, an accelerometer design of high sensitivity, low noise, and compact size is of great significance.
In the signal readout, with either electric or optic modulation and demodulation techniques, acceleration sensing can be achieved with high precision. For electric accelerometers, capacitive [7], piezoresistive [8], and silicon micro-resonant [9] methods are adopted in signal modulation-demodulation. There are also highly integrated optical accelerometers with VCSEL, photodetector, and electrostatic implants [10–15] to achieve compact design. These electrical components and inevitable circuit embedding require complex micromachining process, making it difficult for the sensor to endure harsh environment since the sensing performance can be easily influenced by temperature and electromagnetic (EM) interference. As a possible solution to these problems, passive optical accelerometers are free of electric parts, featuring EM wave immunity, stable chemical nature, and low power consumption, which show a promising prospect in high precision acceleration sensing. In the structural design, a spring-mass oscillator is fundamental to acceleration transduction, which usually converts vibrational signals into displacement and stress of the sensing structure in the micromachined sensors. For commonly practiced designs, micromachined diaphragms [16,17] and mass block with cantilevers [18,19] are used as the spring-mass oscillator. In these cases, the direction of light propagation and the direction of spring-mass vibration are the same, being perpendicular to the substrate plane where the acceleration-sensitive structure is etched, which brings a larger sensor package volume. These out-of-plane oscillating structures’ sensitivity and design flexibility are also restricted because of limited processing thickness of the substrate using micromachining techniques. Furthermore, large diaphragms and thin long cantilevers are usually necessary for higher sensitivity, increasing the difficulty of structural fabrication and reducing yield. As an alternative, in-plane oscillating structures are used to lower fabrication complexity and enhance sensitivity. For example, photonic crystal structures are etched on the spring-mass for light modulation [20,21]. The sensing structure’s mechanical displacement alters the resonance of the optical resonant cavity resulting in a wavelength shift of the transmitted light, achieving high sensitivity and low noise sensing, but with a very limited dynamic range due to its subtle optical resonant structure and coupling fiber tapers. In-plane meshed cantilever [22] is reported to have high sensitivity, but the theoretical optimization of its mechanical design is hardly explored. Furthermore, the fabrication process and the dynamic range of the sensing system can be further improved.
To solve the problems mentioned above, both the signal readout and the inertial structure design are studied. Instead of using intensity modulation [10–15,23,24] or wavelength modulation [20,21] which is vulnerable to light power fluctuation and temperature, phase modulation method [25–27] that uses passive interferometers is applied for high precision acceleration detection. Particularly, Fabry-Perot (FP) interferometer is proposed for its compact size and simple structure, and its short interference light path is beneficial to noise resistance. In this article, spring-mass structures are carved on a single crystal silicon substrate with an in-plane fundamental vibration mode in our research. Without any implant of micro electric devices, the sensor’s passive nature makes it not susceptible to complex EM surroundings. The proposed acceleration-sensitive structure is comprised of four folded spring cantilevers and a rectangular block mass. FP interference is formed between a lead-in fiber facet and the side wall of the movable block mass. The folded spring structures extended the effective length of the spring beams so that high sensitivity can be realized with ease. A large thickness-to-width ratio of the spring beam is chosen to isolate the sensor’s fundamental vibration mode from higher vibrational modes and increase the transverse stiffness of the spring, decreasing the interaxial crosstalk of the accelerometer. In addition, a heavy center mass and a low damping are beneficial to the suppression of thermomechanical noise level of the sensor. By theoretical calculation and finite element simulation, signal response performance of the sensing structure is predicted with accuracy. The proposed scheme provides tremendous design flexibility for the spring-mass oscillator. Using deep reactive ion etching (DRIE) process, the fabrication of the acceleration sensing structure is greatly simplified compared with thin films or mass-cantilevers. During the experiment, the micro-fabricated accelerometer exhibits main axis sensitivity over 161 rad/g in frequency range of 1 to 63 Hz, and the crosstalk of the transverse axes is below 1.38% and 1.17%. The sensor also achieves an average noise floor of 67.4 ng/Hz1/2 on the working band, and its acceleration sensing dynamic range is 140 dB. On the whole, the proposed sensor has advantages of small size, low noise, and large dynamic range, making it applicable for low frequency vibration sensing areas.
2. Sensor design and fabrication
The proposed passive accelerometer based on the FP optic interferometer in our study is shown in Fig. 1(a). The acceleration-sensitive component of the sensor includes a flat cuboid mass and four folded elastic springs symmetrically distributed around the mass. Unlike diaphragms and mass-cantilevers whose acceleration response movement is perpendicular to their substrate plane, the mechanical construction of our research provides a zero-order vibration mode that converts the acceleration signal into an in-plane displacement. The folded spring beams can enhance the acceleration sensitivity while their transverse sensitivity is suppressed. Generally, the proposed design can significantly increase the flexibility of structural parameter selection and decrease fabrication complexity.
Fig. 1. (a) The schematic of the proposed sensing structure. (b) The theoretical deformation analysis of the folded spring.
In the sensor’s light path setup, a single mode fiber is inserted through a fiber insertion groove on the silicon substrate that leads the way to one of the side walls of the center mass. The side wall of the mass block and the input fiber end facet serve as two reflective mirrors of the FP cavity. These two surfaces are expected to offer proper reflectivity which meets the two-beam interference requirement of the FP structure.
In the sensor’s mechanical configuration, it is important to analyze the sensing structure’s response to acceleration excitations. The designed structure is theoretically composed of a sensor mass M, an equivalent spring stiffness coefficient K, and a total damping C, which fits the spring-mass oscillator model. Due to the inertia, the movement of the sensor mass and the outer substrate frame will not be synchronous. Thus the relationship between their relative displacement Δz and the input acceleration a can be utilized for acceleration sensitivity deduction in the FP interferometric setup, expressed by
Similarly, when a force F is applied to the spring in the transverse directions (x and y axes), the corresponding deformations of the spring can also be calculated. Then, the total stiffness coefficients of the proposed sensing structure on its three axes Kz, Kx, and Ky are concluded as
By Eq. (1) and Eq. (3), a thinner spring beam width bi allows the efficient enhancement of sensitivity on all three axes of the sensor due to the inverse relationship between the spring’s stiffness coefficient and sensitivity. For the sake of size reduction of the sensor, half the length of the spring beam l1 and the number of spring period N are restricted, although they can also be made longer and larger to increase the sensitivity. With varied b1, the sensor configuration is proved by finite element analysis (FEA) as well, which shows little difference from the numerical estimation in Fig. 2(a). The theoretical calculation and FEA give us a research basis of good reliability in the structural parameters selection.
Fig. 2. (a) The theoretical calculation (short dash) and finite element analysis (solid) results of the sensor’s frequency response curves under different spring beam widths b1. (b) The estimation of the acceleration sensitivity and the transverse crosstalk of insensitive axes under different spring thicknesses h.
For a single-axis accelerometer, it is crucial to enlarge the differences between the sensitivity in the sensitive direction Sz and the transverse directions Sx and Sy, making the sensor insensitive to lateral vibration signals. A transverse movement of the mass can bring unexpected light phase or power changes on the sensitive axis, causing crosstalk in the actual use. In this regard, the effect of the thickness of the spring beam h is studied. In the frequency region much lower than the sensor resonance, with different thicknesses h applied, the ratios of the sensor’s transverse sensitivities to the main axis sensitivity are calculated as the transverse crosstalk. Exhibited in Fig. 2(b), a thicker spring beam suppresses the transverse crosstalk on the out-of-plane direction (x axis) of the sensor, while the crosstalk on the transverse in-plane direction (y axis) is much smaller and remains unchanged. Considering the influence of the spring width bi and thickness h, increasing the thickness-to-width ratio of the springs is a practical way to isolate the main resonant mode of the sensor from its high-order lateral vibrating patterns, lower the transverse crosstalk, and maintain high main axis sensitivity. A thicker spring beam also contributes to a stronger structural strength against large signal input, expanding the dynamic range of the sensor. It is noteworthy that the unlimited thickening of the spring beam is not recommended since the sensitivity of the main axis will go down and the change of the x-axis crosstalk will become slower as the h increases according to the result in Fig. 2(b). The etching process in sensor fabrication will also be more difficult if the spring beam is too thick, introducing more uncertainty of structural parameters and stress accumulation that damages the sensing performance.
The influence of the total damping C is discussed for noise calculation. Although the total damping hardly alters the sensor’s response sensitivity on the working band that is much lower than the resonant frequency, it will have impact on the thermomechanical noise of the sensor, estimated by
In general, the configuration of the sensor parameters is mainly based on the simplification of the sensing structure fabrication process, while ensuring high sensitivity and low transverse crosstalk. The resonant frequency of the sensor is higher than 100 Hz so that a low-frequency working band can be covered. The main parameters of the proposed accelerometer are shown in Table 1.
Table 1. Main parameters of the proposed accelerometer
With the given parameters, the proposed design has theoretical acceleration sensitivity above 160.9 rad/g and its resonant frequency is around 112 Hz. The finite element simulation gives the nearest rocking mode frequency and lateral vibration mode frequency of 599.85 Hz and 727.03 Hz respectively, which are more than 5 times the zero-order mode frequency, shown in Fig. 3(a) and (b). The high-order mode frequency separation is beneficial to the transverse crosstalk suppression as discussed. The sensor also shows a low thermal noise level of about 24 ng/Hz1/2, which is ideal for small signal detection of low frequency.
Fig. 3. (a) The spring rocking mode of the sensing structure. (b) The lateral vibration mode of the sensing structure.
The proposed passive sensing structure is fabricated by micromachining techniques, shown in Fig. 4(a). First, a set of grooves is etched for the fiber insertion on a 700 µm thick silicon substrate. Then the pattern of the block mass and the folded springs are outlined by photolithography process and silicon dioxide (SiO2) deposition. The SiO2 layer is effective for structural protection during the substrate deep etching. Using DRIE, the substrate is etched to the designed depth so that the spring-mass geometry emerges. Then, DRIE is applied to the back of the substrate to form a 280 µm back cavity and release the sensing structure. Finally, the SiO2 protection layer is removed. Figure 4(b) shows a photo of the fabricated on-chip sensing structure. The sensing units are processed on a 6-inch silicon substrate and the size of each chip unit is 18 mm × 10 mm × 0.7 mm. The whole procedure is rather simple and the manufacturing cost can be further reduced in batch production.
Fig. 4. (a) The fabrication process of the proposed sensor structure. (b) The picture of the fabricated sensor chip before inserting the fiber. (c) The reflected signal of the FP interferometer of the accelerometer and its two-beam interference fitting.
The prepared sensor chip is significantly shrunk in size and weight in contrast with sensors based on machining. The high accuracy micromachining procedure reduces fabrication error, decreasing the deviation of experimental results from our theoretical design. The in-plane design also avoids subtle structure etching of thin diaphragms or cantilevers, which is more controllable in practice.
The light path setup of the sensor is accomplished with the help of a three-dimensional precise adjuster. The input fiber moves back and forth along the groove on the silicon substrate to adjust the interference cavity length, and the fiber is fixed by commonly used epoxy. The reflectivity of the mass side wall and the fiber facet are tested to be about 16% and 3.5%. Reflected signal of the built-in FP interferometer is observed by a spectrometer through an optical circulator during the calibration of the FP cavity length. It can be seen from Fig. 4(c) that the reflected light of the accelerometer matches well with the two-beam interference fitting, and the spectrum is of high contrast which benefits the following signal demodulation.
3. Sensor calibration and characterization
After the on-chip optic accelerometer is fabricated, its sensing properties are tested in laboratory environment, including dynamic acceleration response, transverse crosstalk, and minimum detectable acceleration (MDA).
In the frequency response test of the proposed sensor, the white light demodulation method is adopted to recover the acceleration signal. The sensing system is exhibited in Fig. 5. The proposed sensor chip and a standard electric accelerometer (YMC 271A01) are mounted on a vibration table (YMC VT-500), and their sensitive axes are coaxial with the direction of acceleration excitation. An amplified spontaneous emission source (ASE, BGM3C130FA, Beogold Technology) with a flat power output wavelength around the conventional band serves as a broadband source to light up the proposed sensor. The FP interference takes place in the optical sensor and the reflective optic signal is recorded by a spectrum interrogator (I-MON 512HS, Ibsen Photonics) with a time sampling rate up to 17 kHz. Then the phase variation of the proposed sensor can be extracted from the spatial frequency peak of the FP cavity by Fourier transformation of the sensor output spectrum. A data acquisition card (DAQ, Brüel & Kjaer 3160-A-022) is set to generate sinusoidal signals that drive the vibration table. The DAQ is also used for the output collection of the standard accelerometer. Both the DAQ control and the white light demodulation of the proposed sensor are processed by a personal computer (PC). During the experiment, the demodulation result of the optic sensor is calibrated by the output of the electric accelerometer under a set of acceleration signals so that the frequency response curve is obtained.
Shown in Fig. 6(a), the sensitivity data of the proposed accelerometer under different vibration frequencies is marked by dots and is compared with the theoretical calculation and FEA results. The sensor features a flat response in low frequency region of 1 Hz to 63 Hz, and the sensitivity varies within 3 dB in this frequency band. Due to a low-pass filter in the standard accelerometer readout of the DAQ, the amplitude of acceleration becomes smaller than the actual value, which causes a slightly higher sensitivity of the proposed sensor below 1 Hz in the calibration. The overall acceleration sensitivity is above 44.16 dB re rad/g (161.4 rad/g) on the sensor’s working band. The resonant frequency of the proposed sensor is tested to be around 112.7 Hz. proving the feasibility of the theoretical prediction of the sensor’s mechanical properties. In the fitting curve of the inset of Fig. 6(a), the total damping C is also considered, which will be discussed later. With the assistance of the large block mass and the folded springs, the acceleration sensitivity of the demonstrated sensor chip is largely enhanced, according to the experimental result. A linear response test is also conducted to show good linearity of the proposed accelerometer. Under the signal input of 25 Hz, the linearity is 0.998, shown in Fig. 6(b). In our experiment, the maximum acceleration applied to the sensor is limited by the vibration table, which is about 0.69 g (g = 9.8 m/s2).
Fig. 6. (a) The frequency response performance of the proposed sensor. (b) The linearity test result of the sensor at 25 Hz.
Low transverse crosstalk is of great importance to a single-axis accelerometer. To observe the crosstalk performance, the sensor is fixed on the vibration table and the sensitivity is calibrated as the acceleration signal is applied to the lateral axes (x and y axes) of the sensor. Figure 7(a) exhibits the frequency-dependent sensitivities of the three axes. Then the crosstalk of the transverse axes can be obtained. From the collected data, the crosstalk of the transverse x axis and y axis are calculated to be below 1.38% and 1.17%, respectively. The tested transverse crosstalk fluctuations with frequency and the deviation from theoretical analysis in Section 2 are most likely caused by installation inaccuracy and environmental noise, although the crosstalk value is expected to be frequency-independent. Including these systematic errors, the proposed accelerometer still presents low transverse sensitivity, which is quite appropriate for multi-axis signal sensing.
Fig. 7. (a) The sensitivity of the sensor’s sensitive axis and transverse axes. (b) The consistency test result of the acceleration sensor chips. The light green area covers the working band of the sensor.
As a micromachining-based acceleration sensing chip, its consistency is also verified by experiment. Several sensors are prepared and their sensitivity response curves are drawn in Fig. 7(b). The sensitivity difference in the operating frequency range of these accelerometers is less than 0.54 dB. The good consistency of the sensor chips indicates that the fabrication process is well controlled and the symmetrical designed sensing structure is stable enough for mass production.
In the noise characterization, the proposed sensors are placed on a vibration isolation platform in the lab to record their demodulation output during the test period. By coherent method [28], the noise level of the sensors’ output is acquired. It is worth noting that the good consistency of the sensor chips made this testing method applicable. Combined with the calibrated sensitivity data, the minimum detectable acceleration (MDA) can be obtained, shown in Fig. 8(a). On the working band of 1-63 Hz, the demonstrated sensing scheme has an average MDA of 67.4 ng/Hz1/2. In this case, the proposed accelerometer has a large dynamic range of 140 dB. The ringdown curve of the sensor is also tested for the mechanical Q factor calculation. As the sensor returns to its thermal equilibrium state from a resonant oscillation, the square of the vibrating amplitude of the sensing structure will experience an exponential decay related to the damping property [29]. In Fig. 8(b), the fitting of data reveals a structural Q factor of 224.9 which corresponds to low total damping C = 1.38 × 10−4 kg/s and thermomechanical noise ath = 1.1 ng/Hz1/2. According to the theory and experiment, the total damping has no obvious effect on the sensor’s sensitivity on the working band. The ath is lower than the experiment result because of the additional noise that comes from the demodulation system and the lab environment. In the system noise reduction, the presented short-cavity FP interferometer design will diminish the influence of temperature and phase jitter of the light source to some extent. Furthermore, the sensing structure can be processed by vacuum capsulation to cut off acoustic influence and lower the system damping.
Fig. 8. (a) The minimum detectable acceleration of the sensor chip. (b) The ringdown curve of the sensing structure.
The main properties of the proposed accelerometer are listed in Table 2. The fabrication of the sensor is rather simple and controllable. In comparison with other reported acceleration sensors involving micromachining techniques, the whole noise of the sensor chip is at a low level owing to the sensor’s low system noise and high sensitivity, which is suitable for low-frequency acceleration sensing. Moreover, the folded spring-mass structure with large spring thickness and wide gaps between the spring beams provide more space for structural deformation, and can withstand relatively stronger vibration input, achieving larger dynamic range.
Table 2. The performance of the accelerometers reported by researchers
4. Conclusions
In summary, a passive silicon optic accelerometer based on a built-in FP interferometer is demonstrated by both theory and experiments. Compared with commonly seen out-of-plane structures such as thin membranes and mass-cantilevers, the proposed in-plane vibrating mass and folded springs ensure high acceleration sensitivity and the structure is easier to be achieved with simple micromachining techniques. The sensing performance of the accelerometer is analyzed and predicted by theoretical calculation and finite element analysis with proper selected structural parameters. In the characterization of the proposed scheme, the sensor shows an acceleration sensitivity of 161.4 rad/g on the 1-63 Hz operation band. The minimum detectable acceleration is as low as 67.4 ng/Hz1/2, and the sensor’s transverse crosstalk is better than 1.38%. The research also indicates that the sensor is of good consistency and has a large dynamic range of over 140 dB in vibration detection. The acceleration sensor chip has the advantages of compact size, robust structure, and low noise, which guarantees a broad prospect in structural health monitoring and seismic sensing applications.
Funding
National Natural Science Foundation of China (62275096); NSFC-RS Exchange Programme (62111530153); Science Fund for Creative Research Groups of the Nature Science Foundation of Hubei (2021CFA033); Science, Technology and Innovation Commission of Shenzhen Municipality (2021Szvup089); The Royal Society International Exchanges 2020 Cost Share of United Kingdom (IEC\NSFC\201015).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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