Determination of frequency response of MEMS microphone from sound field measurements using optical phase-shifting interferometry method
Introduction
Performance of the microelectromechanical systems (MEMS) microphone has been improved [1], [2]. The development of the material, structural design, and fabrication technology yields a MEMS microphone with a wide operating frequency range, better signal-to-noise ratio (SNR), and high sensitivity in a small package [3]. These improvements have extended its applicability in acoustics such as multimedia system, acoustic imaging [4], [5], energy harvesting system [6] as well as measurement instruments [7], [8]. The MEMS microphone is the key enabling technology for the development of future acoustical devices.
Microphone sensitivity is an important parameter to build a reliable acoustical device. This sensitivity represents the ratio of the output voltage to a given input pressure with the unit of millivolt per Pascal (mV/Pa) or decibel relative to 1 V/Pa (dB re. 1 V/Pa). As an example, a far-field application such as a smart speaker requires a high-sensitivity microphone to pick up sound from a distance. In contrast, a high-sensitivity microphone is not suitable for near-field devices such as cellular devices because the signal will be clipped and produces a distortion in the output signal. Sensitivity varies with frequency, which is represented by the frequency response of the microphone. This frequency response is determined by performing a calibration. However, a standard calibration method for the MEMS microphone has not yet been established because its geometry is different from a conventional condenser microphone. Therefore, a new calibration method applicable to the MEMS microphone needs to be developed.
The implementation of conventional condenser microphone calibration methods has been proposed for MEMS microphone calibration. For example, Wagner et al. implemented the reciprocity calibration method [9]. According to IEC 61094-2 and IEC 61094-3, this method requires a reciprocal microphone that is configured as a pair of transmitter and receiver [10], [11]. The input pressure is estimated from a mathematical model of sound propagation that requires precise measurement of the microphone’s front cavity [12], [13], [14]. In this method, an adapter was developed to attach the MEMS microphone with a diameter of inch to fit the reciprocity calibration apparatus. The MEMS microphone was configured only as of the receiver, and the front cavity of the MEMS microphone was estimated by implementing an iterative fitting method. Prato et al. proposed the implementation of the pressure field microphone comparison method [15]. In this method, a reference and microphone under test are interchanged at the same position from a sound source, and thereby both microphones experience the same sound field [16]. An adapter was developed to provide the MEMS microphone geometry to be the same as the conventional condenser microphone, and the calibration was performed according to the IEC 61094-5 [17].
Another solution to calibrate the MEMS microphone is based on the measurement of the sound pressure applied on the MEMS microphone and its output voltage. In this approach, the sound pressure is measured rather than estimated from the sound propagation model, which has geometrical dependencies. This method has advantages in that it can be implemented for calibration regardless of the geometry of the microphone under test. Therefore, it is suitable for calibrating the MEMS microphone, which is available with various geometries.
Near-field sound pressure measurement can be realized using an optical method. To our knowledge, there are two available optical methods for measuring sound. The first method is based on the relation between sound pressure and particle velocity. In this method, the sound pressure at a particular point in space is estimated from the measurement of acoustic particle velocity using the laser Doppler shift technique [18], [19] as well as photon correlation spectroscopy (PCS) [20], [21]. The implementation of this method for the MEMS microphone has been reported in the literature [22]. The second method is based on the acousto-optic effect that describes the relationship between the sound and phase of light. According to this principle, the light phase shift corresponds to the integrated sound pressure along the optical path. Measurement of phase modulation by sound can be implemented using an optical interferometer such as laser Doppler vibrometer (LDV) [23], [24], [25], [26]. A tomography technique is applied by performing parallel scanning of the laser beam to reconstruct the sound field in the measurement area [27], [28].
In this paper, we propose a MEMS microphone calibration method by using an acousto-optic-based sound pressure measurement. Parallel phase-shifting interferometry (PPSI) was used to measure the phase of the light, and the tomography technique was applied to reconstruct the sound field applied to the MEMS microphone. By using the PPSI, the phase of the light is extracted directly from the captured interferogram without the usage of the seeding particle or integration process in the measurement. The tomography technique can also be implemented using PPSI without the need for performing parallel laser beam scanning. The proposed calibration procedure consists of three steps: initialization, measurement of phase, and data processing. Validation of the sensitivity result was conducted by calibrating the MEMS microphone under test by using the microphone substitution method.
Section snippets
Acousto-optic principle
Phase of light propagating through a sound field can be approximated by using geometrical optics aswhere is wave number of the light, n is air refractive index and is the path following by the beams of the light in the Euclidean space [27], [29]. By assuming the adiabatic condition and linear process, the connection between air refractive index and sound pressure can be derived from the Gladstone–Dale relation [30], [31] as follows:where
Initialization step
The proposed method consists of three steps: initialization step, phase measurement step, and data processing. The initialization step determines the signal generator’s output voltage setting to generate a reference sound source that will be used in the measurement process and provide the pressure measurement traceability. The instrument configuration for the initialization step is shown in Fig. 3. Absorbing materials were installed on the walls to reduce the reflection of the sound. A
Experiment result
The MEMS microphone datasheet provides the free field response in the frequency range of 100 Hz to 10000 Hz that we used as the reference to check the performance of the substitution method and the proposed method. In practice, there were two difficulties in the low-frequency range: (1) maintaining the stability of the generated low-frequency sound pressure by our sound source system, and (2) low signal-to-noise ratio of the phase measurement in the low-frequency range using our PPSI system.
Discussion
According to the datasheet, the typical sensitivity for the MEMS microphone under test is dBV/Pa at frequency 1000 Hz with the tolerance of dBV/Pa. By the implementation of the substitution method, the determined sensitivity of the MEMS microphone under test was dBV/Pa with a measurement standard deviation of dBV/Pa. We obtained the discrepancy between the substitution method result, and the typical sensitivity value was 1 dBV/Pa at 1000 Hz and increased as the frequency
Conclusions
We have presented a method to determine the sensitivities of the MEMS microphone based on the direct measurement of sound pressure and voltage. The measurement of sound pressure based on the acousto-optic effect principle was realized by using a PPSI instrument and implementing the tomography reconstruction technique. The free-field frequency response of a MEMS microphone under test has been determined in the frequency range of 1000 Hz to 12000 Hz and validated using the microphone substitution
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
The research work is supported by the Scholarship Program for Research and Innovation in Science and Technologies (RISET-Pro), Ministry of Research, Technology and Higher Education, Republic of Indonesia.
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