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Application of Optical Sound Measurement in Microphone Calibration Method

Hermawanto Denny 早稲田大学

2021.08.03

概要

Calibration is an act of comparing the unknown value to the reference standard of a known value. In the world, the top level of known value is seven-unit in SI. The value of a unit in SI is used to determine the unknown value of a quantity by calibration. The chain from the instrument to the SI is called traceability. In the measurement system, the artifact of the acoustics unit is the microphone. Currently, the traceability of the acoustics unit is not directly to the SI unit but volt and length unit.

The microphone is an essential device in communication technology. It is extensively used in the communication devices such as cellular phones, broadcasting systems, and the sensor for human-computer interaction devices. The microphone captures the sound pressure and converts it into an electrical signal for further processing. A microphone’s construction comprises a diaphragm and backplate separated by an air gap, forming a capacitive configuration. When exposed to a sound, the air pressure moves the diaphragm, changing the microphone’s capacitance and producing an electrical signal. The microphone’s sensitivity represents the amount of voltage generated by the microphone for the applied sound pressure.

The unknown sensitivity value of a microphone is determined by using calibration. Several microphone calibration methods are currently available, namely the comparison/substitution method and the reciprocity method documented in the IEC 61094 series. The comparison/substitution method is described in the IEC 61094-8. The method is implemented to determine the sensitivity of a microphone in the free field environment. In this method, a reference microphone and the microphone under test are exposed to a simple sound field generated by a sound source. The sensitivity of the microphone under test is determined from the sensitivity of the reference microphone. This method is easy to implement, but both microphones must have the same mechanical dimensions to be accurate. Two microphones are configured facing each other separated at a certain distance. One microphone act as a transmitter unit and the other act as a receiver unit. According to the reciprocity principle, the product of the microphone sensitivity is proportional to the ratio of the electrical transfer function between the two microphones and acoustical transfer function. The electrical transfer function can be measured from the output voltage of the microphone. While the acoustical transfer impedance is determined by the mechanical properties of the microphone such as acoustic center position and dimension of the microphone.

Microphone technology has experienced considerable advancement. New microphone technology has implemented a micro-electro-mechanical system (MEMS) technology in the manufacturing process. According to the research, MEMS microphone is mostly used for cellular phones and followed by the Internet of Things. It has been sold 6000 million units in 2019 and has an annual growth rate of 14.4%. The working principle of MEMS microphones is the same as conventional microphones but has a different mechanical dimension. The conventional microphone has a regular diaphragm shape of circular and a standard diameter of ¼, ½, and 1 inch. In comparison, the MEMS microphone is available in micrometer size and has no standardization in the mechanical dimension. The MEMS microphone diaphragm is located inside the microphone housing together with the pre-amplifier circuit. The sound pressure from outside flows into the diaphragm through a small porthole in the housing. Because of these differences, the current microphone calibration methods do not apply to MEMS microphone.

The progress of MEMS microphone calibration is now still at an early stage of development. Wagner et al. (2017) proposed the reciprocity calibration method in a pressure environment. A top port type of MEMS microphone was calibrated using a half-inch laboratory standard microphone. A MEMS microphone adapter was developed to adapt the microphone mounting on the pressure reciprocity calibration apparatus. Prato et al. (2018) implemented a microphone comparison method for MEMS calibration. A MEMS microphone adapter was developed to make it equal to the geometry of the reference microphone. Both microphones were exposed to a sound generated by a loudspeaker and configured so that reference and MEMS microphone experienced the same sound field. The sensitivity of the MEMS microphone is calculated from the sensitivity of the reference microphone. Another method was proposed by Piper et al. (2015) that used a photon correlation spectroscopy technique to measure the acoustic particle velocity to characterize the MEMS microphone’s frequency response. In the implementation, a seeding particle is required for the measurement of particle velocity. However, there is no way to determine calibration parameters related to calibration, such as acoustic center. To address this problem, some researchers proposed an iterative method.

Another issue in the microphone calibration method is the determination of the microphone’s acoustic center. The reciprocity’s implementation method is required to determine the microphone’s acoustic center to calculate acoustical transfer impedance. According to the standard IEC 61094-3, the microphone’s acoustic center is the location where the microphone acts as a point source when the microphone works as a transmitter. From this point, the sound propagation varies inversely as the distance following the inverse square law. Previous research on acoustic center measurement exploits the inverse square law property to estimate the microphone’s acoustic center from pressure magnitude. Cox (1954) used a probe microphone to scan the sound pressure decay. However, the probe's body will disturb the sound field generated by the microphone and decrease the accuracy of the estimation. Juhl (1994) proposed a boundary element method to simulate the sound wave emitted by the 0.5-inch and 1-inch microphone diaphragm. For the estimation, detailed information of microphone physical properties is required. Wagner and Nedzelnitsky (1998) and Jacobsen (2004) proposed measuring the transfer function’s magnitude between microphones. Barrera-Figueroa (2006 conducted the determination of the acoustic center of laboratory standard microphones). Rodrigues (2010) developed a method to improve the signal-to-noise ratio in the transfer function measurement. The measurement process is the same as the measurement of the electrical transfer function in the reciprocity method. Hence, the technique only applicable to laboratory standard microphones and cannot be implemented for another type of microphone.

In this research, I address some problems related to microphone. The differences of diaphragm size and shape effect to the uncertainty result can be neglected if the pressure input of the microphone can be measured directly without using the mechanical or electrical methods. Therefore, I propose non-invasive sound pressure measurement using the optical method based on the acousto-optic effect principle. My research objective is to develop a new microphone calibration method based on sound field measurement using the optical method.

The fundamental optical method for sound measurement method is based on the acousto-optic effect. Geometrical optics describes the relationship between the air refractive index and the phase-shift of the light. This air refractive index changes also related to air density changes as described by the Gladstone and Dale relation. And in the adiabatic process, the air density change is proportional to the air pressure change caused by the sound. Therefore, the phase shift of the light corresponds to the line integral of the sound pressure along the optical path.

In the first application, I developed an alternative method for the calibration of the MEMS microphone. I measured the sound field applied to the MEMS microphone and its output voltage for a sound pressure generated by a loudspeaker to determine the sensitivity. My proposed method for MEMS calibration using the optical method consists of three steps which are: initialization step, phase measurement step, and data processing step. The initialization step is used to determine the voltage setting to generate reference sound pressure. The phase measurement step measures the phase using the PPSI instrument. The processes in data processing are extracting phase, reconstruct the sound field, and calculate the sensitivity.

The non-invasive measurement of the sound field was realized using an optical method based on the acousto-optic effect principle employing parallel phase-shifting interferometry (PPSI). I employed the scanning tomography technique to get the sound field’s projection and reconstruct it using the filtered back-projection technique. I performed experimental calibration of the MEMS microphone in the frequency range of 1000 Hz to 12000 Hz. I implemented the substitution method to the MEMS microphone under test to validate the proposed method’s frequency response result.

In the second application, I proposed a method to estimate the acoustic center of the laboratory standard microphone. I assume that the propagation of the sound in the experimental room follows a spherical radiation model centered at the microphone’s acoustic center. Therefore, a least-square fitting method was applied to sound field data, extracted from the PPSI instrument’s interferogram, to get the sphere’s radius and estimated the acoustic center position. I performed experiments to estimate the acoustic center of laboratory standard microphone type B&K 4180 in the frequency range of 20000 Hz to 50000 Hz. The nominal acoustic center value for the corresponding value described in the IEC 61094-3 was used to confirm the estimated acoustic center by the proposed method.

I organize this thesis as follows. Chapter 1 provides the background of the research, the objectives, and organization of the thesis.

In Chapter 2, I present the literature review corresponding to the research. I explain the methods of microphone calibration and the theory of optical sound measurement. I present the reciprocity and substitution microphone calibration methods. I also describe the fundamental principle of optical sound measurement, including the acousto-optic effect, interferometry system, and tomography technique for the sound field reconstruction.

Chapter 3 presents the realization of optical sound measurement using a laser interferometer system. Firstly, I explain the numerical simulation of the optical sound measurement method. I continue explaining the experimental measurement of sound generated by a loudspeaker in a free field environment and the sound inside a cylindrical tube using a laser Doppler vibrometer. I confirmed the actual sound pressure level using a microphone and show that the optical method produces a good agreement.

In Chapter 4, I introduce the parallel phase-shifting interferometry instrument for sound field measurement. An experiment was conducted to characterize the acoustic background noise, and optical distortion of the PPSI instrument are presented. I found that PPSI’s camera fan contributed to the sound measurement at the frequency of 3000 Hz and the type of optical distortion in the PPSI system is pincushion distortion.

The significant contribution of this research is described in Chapter 5. I propose applying the optical sound measurement method to measure the sound field applied to the MEMS microphone surface and determine the microphone sensitivity. The PPSI instrument has been implemented to obtain the sound field's projection on the MEMS microphone's surface for the reconstruction. I carried experimental calibration of MEMS microphone out in the frequency range of 1000 Hz to 12000 Hz. For sensitivity result validation, I implemented the substitution calibration method to calibrate the same MEMS microphone under test. The result shows that both methods have a good agreement with a maximum discrepancy of 0.62 dBV/Pa. By implementing the proposed calibration method, the direct traceability to the pressure unit can be realized.

Chapter 6 presents the optical method’s application to determine the microphone’s acoustic center used in the reciprocity calibration method. I calculate the acoustic center from the sound field projection obtained using the PPSI instrument. A simulation was created to review the performance of the estimation method. An implementation of the proposed approach to determine the acoustic center of laboratory standard microphone type B&K 4180 was presented in this chapter. The validation of the proposed method was performed by comparing the result with the nominal acoustic center values described in the IEC 61094-3 standard. A reliable acoustic center estimation result was obtained from measurement at a frequency above 20000 Hz with the maximum standard deviation of 3 mm.

I summarize the highlights of the research and recommendations for future work in Chapter 7 of this thesis.

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