Primary calibration for airborne infrasound utilizing the vertical gradient of the ambient pressure

The demand for reliable and traceable measurements of airborne infrasound has risen, one major application being the International Monitoring System run by the Comprehensive Nuclear-Test-Ban Treaty Organization. However, the current calibration methods do not sufficiently cover the infrasound frequency range. In this paper, we present a calibration method for microphones in this frequency range and its implementation as a measurement setup. The method is based on the vertical gradient of the ambient pressure as a stimulus. A DUT is subjected to an alternating pressure by periodically changing its altitude. The measurement setup realizes such a periodic altitude change by means of a vertically rotating disk and is capable of calibrating measurement microphones in a frequency range from 0.1 Hz to 5 Hz with a planned extension to 10 Hz. A measurement uncertainty of 0.07 dB at maximum could be realized. Particular attention was paid to the mechanics of the measurement setup to ensure that the DUT moves in a precisely determined orbit. We present example calibrations and an uncertainty budget for a Brüel & Kjær 4193 measurement microphone in the frequency range from 0.1 Hz to 5 Hz. Finally, we demonstrate the performance of the calibration method by comparing the acquired results to other calibration techniques showing an agreement better than 0.1 dB.


Introduction
Infrasound is emitted by a large number of natural phenomena, such as earthquakes, volcanic activity, or wind, and also by man-made sources, for example, nuclear explosions. Infrasound plays a major role in characterizing, assessing, and monitoring these phenomena. When considering nuclear * Author to whom any correspondence should be addressed.
Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. explosions which are banned by the Comprehensive Nuclear Test-Ban Treaty (CTBT), infrasound measurements are an important part of the International Monitoring System (IMS) that is in place to detect and locate such events. For all of these purposes, the sensors used to detect and quantify lowfrequency sound have to yield precise and reliable results.
The transition to renewable energy production often requires the use of energy generators which unintentionally emit low-frequency noise and infrasound. People living near those devices often express their concern that the infrasound emission may lead to health concerns and annoyance. To assess and moderate these concerns, a quantitative analysis of the situation is indispensable. Such an analysis relies on accurate and traceable sound measurements.
To date, traceability to the SI for airborne sound at low frequencies has been realized through the pressure reciprocity calibration method according to IEC 61094-2 (IEC 61094-2+AMD1:2022 [1]). This method is currently only available with high uncertainty below 10 Hz and only realized in experimental setups below 2 Hz. The limitations are mainly caused by leakages of the couplers used to connect the transmitter and receiver microphones with a known volume during a calibration procedure. An additional reason for the low-frequency limitations is the modeling of heat conduction necessary to calculate the acoustical transfer impedance of the microphonecoupler-microphone arrangement. Another limitation is the selection of microphones which can be used for pressure reciprocity calibration. Currently, only selected laboratory standard microphones of type LS1P according to IEC 61094-1 (IEC 61094-1:2000 [2]) can be reliably calibrated at such low frequencies using the reciprocity method.
As an alternative method, laser pistonphones are used to calibrate microphones at low frequencies. These devices work by creating an alternating pressure in a closed chamber using a piston. The displacement of the piston is measured by a laser interferometer. In combination with the known geometry of the chamber, the alternating pressure in the chamber can be calculated from the piston displacement and is used as a reference. To date, multiple laser pistonphones have been realized as calibration facilities for infrasound sensors [3][4][5][6]. Apart from laser interferometers, the displacement of the piston can also be measured by other means such as a linear variable differential transformer [7].
The laser pistonphone developed at the UK's National Physical Laboratory (NPL) has been part of the CCAUV.A-K2 key comparison, which compared the primary calibration facilities for LS1P microphones at low frequencies [8]. The participants of this comparison reported on the sensitivity of two LS1P microphone cartridges, Brüel & Kjaer type 4160, which were circulated between the participating laboratories. Except for NPL, which used a laser pistonphone as a calibration system for frequencies up to 31.5 Hz, all participants employed setups based on the pressure reciprocity method for calibration. The comparison covered a frequency range from 2 Hz to 250 Hz, with two laboratories reporting sensitivity values for the optional frequency of 1 Hz. At the lowest commonly used frequency of 2 Hz, the measurement uncertainties reported by the participants were the highest and ranged from 0.09 dB to 0.99 dB. The degrees of equivalence for each participant, computed as the difference from the key comparison reference value, were lower than the corresponding uncertainties for all participants except for NPL's laser pistonphone. This suggests that there may be systematic differences between the pistonphone method and the pressure reciprocity method at low frequencies.
In the later CCAUV.A-K5 key comparison [9], all participants employed calibration setups based on the pressure reciprocity method. Two LS1P microphones, Brüel & Kjaer type 4160, were used as travelling standards. The frequency range covered in this key comparison was 2 Hz to 10 000 Hz. The infrasound frequency range below 20 Hz was optional, and some participants did not submit results for this frequency range. Furthermore, the comparison optionally included the phase of the sensitivity, which was reported by most participating laboratories. For the sensitivity level, the data reported by all participants passed the consistency test and no reported values were excluded from the calculations of the key comparison reference value. At the lowest frequency of 2 Hz, the participants reported uncertainty values between 0.06 dB to 0.27 dB. The degree of equivalence was lower than the corresponding uncertainty for all participants. Because all participants employed setups based on the same basic method, any systematic uncertainties concerning the method in general would not have been noticed.
One important aspect of the pressure reciprocity method is the calculation of the acoustical transfer impedance of the microphone-coupler-microphone arrangement. Especially the heat conduction in the system must be considered. Before the latest amendment to IEC 61094-2 in 2021, two models were proposed to cover dissipation by heat conduction and to correct the obtained values, which yielded conflicting results in the infrasound frequency range [10]. This issue has been resolved with the amendment. The fact that the correction model has a significant influence on the result and that all laboratories are now required to use the same standardized model highlights the need for an independent verification by alternative calibration methods.
To establish traceability to the SI for monitoring facilities, such as the IMS run by the Preparatory Commission for the CTBT Organization (CTBTO), the Infra-AUV research project 'Metrology for low-frequency sound and vibration' within the European Metrology Programme for Innovation and Research (EMPIR) aims to develop primary calibration procedures. These methods are based on multiple different physical principles for airborne infrasound in the frequency range of 0.04 Hz to 20 Hz [11]. Furthermore, methods and facilities for the dissemination of the traceable standards realized by these primary calibration methods are developed within the Infra-AUV project. The primary calibration techniques developed in this project exploit the improvement and extension of already existing calibration principles to lower frequencies, such as the pressure reciprocity method or laser pistonphones. Other techniques include the evaluation of alternative physical principles for their implementation as calibration setups for infrasound calibration. One of these alternative physical principles utilizes the relationship between sound pressure and the refractive index to determine sound pressure using a Fabry-Pérot interferometer. Another method directly determines sound pressure in a coupler using a water manometer.
The calibration method and setup presented in this paper utilize the vertical gradient of the ambient pressure as a stimulus and expose a device under test (DUT) to an alternating pressure by changing its altitude. This method was first proposed by Ole-Herman Bjor (Norway, former member of IEC TC29 'Electroacoustics', WG5 'Measurement microphones') to be used on a linearly exciting long stroke shaker. In this work, it is realized in a measurement setup using a rotating wheel, which inspired the colloquial term 'carousel method'. In contrast to the other methods mentioned above, the carousel method is not based on the characterization of a sound field in a closed cavity, but rather utilizes a free-field pressure difference as a stimulus. For this reason, the carousel method does not rely on the modeling of the acoustic and thermodynamic properties of such a cavity. Moreover, the correction of the dissipation of energy into the device walls by heat conduction or the impedance of the volume do not need to be taken into account. Furthermore, the carousel method relies only on very basic model assumptions for the determination of the amplitude of the stimulus, thereby reducing the systematic uncertainty introduced by such assumptions.
The measurement setup presented in this paper implements the carousel method and is currently capable of reliably calibrating measurement microphones in the frequency range of 0.1 Hz to 5 Hz. An extension of the upper frequency limit to 10 Hz is possible if issues regarding aerodynamic effects and vibrations in the measurement setup are resolved. An extension to frequencies below 0.1 Hz is possible, provided that the environmental conditions are stable enough. However, calibration at these frequencies is out of the scope of the intended application.
This paper is organized as follows: In section 2, the theoretical foundations of the carousel method are presented. The measurement setup implementing the carousel method is described in section 3. The results obtained and challenges faced during microphone calibrations by means of the microphone carousel, including potential solutions, are discussed in section 4. Finally, the measurement uncertainty for the microphone carousel and the results acquired and compared to a laser-pistonphone calibration are outlined in section 5.

Theory
When calibrating a measurement microphone, the measurand to be determined is the sensitivity amplitude of the microphone to the sound field, measured in V Pa −1 . For some applications, the sensitivity phase measured in • or rad is also of interest. It describes the phase relation between the output signal of the DUT and the sound field the DUT is exposed to. In these cases, the sensitivity can be expressed as a complex value S, consisting of the sensitivity amplitude S and the sensitivity phase ϕ. Determining the sensitivity of a DUT can be accomplished by exposing the DUT to an alternating pressure of a known frequency and amplitude and acquiring the output voltage response from the DUT. In this paper, a method is presented that utilizes the vertical gradient of the ambient pressure to realize such an alternating pressure which can be applied as a stimulus. The idea to use the hydrostatic pressure gradient for this purpose, as proposed by Ole-Herman Bjor, has to date not been implemented as a measurement setup.
The static pressure of the ambient air decreases with increasing altitude following an exponential course [12]. The vertical gradient of this static pressure amounts to dp dh = −ρ · g (1) with air density ρ and gravity g. As neither air density nor gravity change significantly for height differences of a few meters, the exponential function can be linearized for small height differences. For a given height difference ∆h the pressure difference amounts to Gravity g is monitored worldwide through the International Gravity Reference System [13]. This reference system yields a value with an uncertainty much lower than required in this application.
Air density ρ can be determined analytically from climate measurements (temperature, humidity, static ambient pressure) using the CIPM-2007 model for the density of moist air [14]. To determine ρ with a relative uncertainty of 3.5 · 10 −4 , the temperature has to be measured with an uncertainty of 0.05 K, the humidity has to be measured with an uncertainty of 2%, and the static ambient pressure has to be measured with an uncertainty of 10 Pa. All of these measurements are possible with readily available measurement equipment.
At laboratory conditions (temperature t = 23 • C, relative humidity h = 50%, ambient pressure p = 1013.25 hPa) and at standard gravity g = 9.81 m s −2 , the gradient amounts to dp/dh = −11.64 Pa m −1 . This means that changing the height of a DUT by 1 m subjects this device to a pressure change of ∆p = 11.64 Pa. A vertical sinusoidal movement with a peakto-peak value of 1 m (and thus an amplitude of 0.5 m) therefore subjects a DUT to a sinusoidal alternating pressure with a root-mean-square (RMS) value of 4.12 Pa, which results in an unweighted sound pressure level of 106.3 dB (re 20 µPa). Therefore, with small height variations, an alternating pressure can be applied to a DUT with a level which is typical of standard calibration setups. This alternating pressure does not represent a real sound wave but is rather caused by the change of the microphone position.
This alternating pressure with an amplitude which can be determined analytically is applied to calibrate a DUT. While the DUT is moved up and down periodically, the output voltage of the DUT is measured and its amplitude is determined. In the case of a harmonic oscillation with complex amplitudes p for the alternating pressure and U of the output voltage, the complex sensitivity S consisting of the sensitivity amplitude and phase is calculated as According to (2), the time course of the alternating pressure is proportional to the time course of the alternating height with opposite polarity. In case of a harmonic oscillation with complex variables U and p, this results in a phase shift of π between the alternating height and the alternating pressure.
Since the height of the DUT as a whole is changed during a calibration, the equalization vent of the DUT is always subjected to the sound field. This is different to the pressure reciprocity method, where the equalization vent of the microphone is outside the sound field. It is also unlike the laser pistonphone, where the positioning of the equalization vent inside or outside the sound field can be controlled individually, at least for back-vented microphones. The positioning of the vent in regard to the sound field greatly influences the sensitivity of the DUT at low frequencies, because the vent acts as an acoustical high-pass filter when subjected to the sound field [15]. For this reason, it is important to note whether the vent is subjected to the sound field and to calibrate a microphone the way it is intended to be used later.
The cutoff frequency (−3 dB) of the acoustical high-pass filter due to the vent is on the order of 0.01 Hz to 0.05 Hz for microphones specifically designed for infrasound measurements, such as the Brüel & Kjaer type 4193 [16]. For the laboratory standard microphone Brüel & Kjaer type 4160, the lower frequency limit is between 1 Hz and 2 Hz [17].

Construction
A measurement setup implementing the method described in section 2 was constructed. A sinusoidal height change was realized by a vertically rotating disk, hence the colloquial name 'microphone carousel' for the setup. When the disk rotated at a constant speed, a DUT mounted eccentrically perpendicular to the disk surface experienced a sinusoidal height change and therefore an alternating pressure (see figure 1). The frequency of the alternating pressure was defined by the rotation speed of the disk. To mount a DUT, the disk was equipped with mounting holes with a diameter of 20 mm, which had distances of 15 cm, 20 cm, and 25 cm from the rotational axis of the disk. The distance defined the radius of the rotation and thus the amplitude of the alternating height. The disk was precisely machined, and the locations of the mounting holes were carefully measured to ensure that the maximum deviation of the actual radius from the nominal radius was below 50 µm for every mounting hole.
A DUT was mounted on the disk with the aid of 3D-printed self-adjusting mounting clamps, which positioned the DUT exactly in the center of the mounting hole and perpendicular to the disk surface. A similar technique connected the disk to the rotation axis of the motor, where central and perpendicular mounting is particularly critical. The axis itself was adjusted parallel to the ground with a precision spirit level directly mounted on the bearing block guiding the axis. The whole assembly was directly driven by a DC motor which was connected to the axis assembly via an elastomer coupling to reduce vibrations on the axis. A custom-designed slip ring transferred all electrical connections of the DUT on the rotating disk to the power supply on the stationary frame. Three 7pin LEMO connections could be transferred through the slip ring without signal degradation, and up to three measurement microphones can be mounted on the disk simultaneously. To reduce vibrations during the rotation, the mass imbalance of the rotating disk was compensated for with brass weights that were bolted to the back of the disk. Figure 2 shows a side view of the axis assembly.
The air density ρ was computed as described in section 2 from measurements of temperature, humidity and static ambient pressure. For the measurements of temperature and humidity an Ahlborn type ZAD936RAK sensor was used. The static ambient pressure was measured with a  (1), the self-centering clamping set for mounting the disk on the axis (2), the slip ring for transmission of the electrical signals from the rotating axis (3), the bearing block with a spirit level holding the axis (4), the elastomer coupling reducing vibrations from the motor (5), and the motor (6). precision pressure indicator of type Druck PACE1000. All devices were calibrated in-house at PTB with traceability to national standards.
The local value of gravity g is known to a high accuracy at PTB, as there are multiple gravimetric measurement stations on the campus [18]. The local value of g changes with height with a gradient of about −3 µm (s 2 m) −1 in free air. The difference in height between the gravimetric measurement stations and the calibration setup was in the order of 10 m. Even without a relative correction for the height difference to the station, these values acquired by the stations are accurate enough to serve as reference values, and a value of g = 9.8125 m s −2 with an uncertainty of ±0.0001 m s −2 was used.
To ensure the disk was rotating with the correct speed for a given calibration frequency, the actual rotation speed was measured with an optical encoder mounted directly on the motor. This encoder delivered 1000 pulses per full revolution of the disk and was connected to a frequency counter. The measurement values acquired from the frequency counter determined the actual angular velocity of the disk and thus the calibration frequency.
To obtain the absolute phase information of the excitation signal, the optical encoder also provided a reference pulse once per rotation. The pulse triggered the start of a measurement with a fixed phase for the excitation signal. This allowed the determination of the phase sensitivity of the DUT in addition to the amplitude sensitivity.
The output signal of the DUT was recorded in the time domain by an analog-to-digital converter of type Data Translation DT9857E and stored for an offline evaluation.
Friction between the rotating disk and the air directly above the surface of the disk causes an outward air stream due to centrifugal forces [19]. To avoid disturbances, there should not be any obstructions near the disk in the plane of the disk because these obstructions would disturb the outward air stream and cause turbulence near the DUT. For this reason, there was no enclosure around the microphone carousel, and the DUT was directly subjected to the ambient air. This caused background noise to directly influence the measurement. Therefore, a microphone mounted stationarily next to the microphone carousel was used as a background microphone to actively suppress this background noise. This procedure is described in detail in section 4.1.

Evaluation
During a microphone measurement in the setup described in section 3.1, a set of voltage waveforms, one for each calibration frequency, was obtained. These waveforms were sampled and stored as a digital signal for the evaluation.
To determine the amplitude sensitivity of the DUT in V Pa −1 , the amplitude of the sinusoidal output voltage resulting from the sinusoidal pressure change was computed for each calibration frequency from the corresponding time course. The measurement system itself was not shielded against background noise, which can have high sound pressure levels at low frequencies. For this reason, an evaluation determining the RMS level of the output voltage of the DUT was not applicable because the signal would have been severely disturbed by noise. A narrow-band evaluation was thus applied to reduce the influence of noise and increase the signal-to-noise ratio (SNR).
In the measurement setup presented in this paper, the amplitude and phase of the sine signal were computed from the corresponding coefficients of a discrete Fourier series. The Fourier coefficient for the specific calibration frequency f is given by with the sampled time course x f with sample count N sampled at a sample rate of f s . The amplitudeÛ and phase ϕ of the sine signal were determined asÛ The pure sine signal u(t) that only contains the spectral component at frequency f was reconstructed from the amplitude and phase as This method is identical to computing the discrete Fourier transform (DFT) of the time course without a window function (thus using a rectangular window) and picking out the bin corresponding to the calibration frequency. Therefore, this method only yields the correct results when the length of the acquired time course is an integer multiple of the period 1/f of the calibration signal. In all other cases, spectral leakage occurs, and the computed amplitude is smaller than the actual amplitude of the voltage signal. For this reason, the acquired time course was truncated to an integer multiple of the period of the actual calibration frequency before the Fourier coefficient was computed. To allow a fine resolution for the truncation, a sample rate of f s = 2 kHz was used to digitize the voltage signal of the DUT. This sample rate was much higher than necessary for an accurate representation of the output voltage of the DUT in the frequency range of interest, but ensured that a truncation to a length sufficiently close to an integer multiple of the period could be accomplished. Figure 3 illustrates the evaluation process by showing a raw data signal (top), the reconstructed pure sine wave according to (7) (middle), and the residual signal from the DUT as the difference between the raw signal and the reconstructed sine signal (bottom). Furthermore, the signal of a background microphone placed next to the measurement setup is shown. This microphone was of the same type as the DUT and was subjected only to the background noise, not to the calibration stimulus. Its time signal shows a course very similar to the residual waveform, which means that the main disturbances during the measurement came from background noise. The properties and limitations of such a background microphone measurement for active noise suppression will be discussed in section 4.1.

Background noise
In contrast to other infrasound calibration methods, such as the laser pistonphone, the microphone carousel is an open system in which the DUT is always subjected to the ambient air. For this reason, ambient noise directly disturbs a calibration since there is no additional shielding as there would be in a closed chamber.
To assess the impact of background noise, a second microphone was used as a background microphone. This microphone was placed next to the rotating disk, so that it was subjected to the same noise as the DUT. At the same time, the height of the background microphone was not varied during a measurement, so it was not subjected to the calibration stimulus. In the evaluation process, the signal of the background microphone was subtracted from the signal of the DUT, thereby suppressing the background noise. Because the sensitivities of the DUT and the background microphone differed slightly, the quality of the noise suppression was improved by taking the difference in phase and amplitude sensitivity into account. This difference in sensitivity was measured in a relative comparison measurement, where both the DUT and the background microphone were simultaneously exposed to an acoustical calibration signal in a closed chamber. As this measurement was only relative, there was no need for an absolute reference at this stage. Figure 4(a) shows the Fourier spectrum of a carousel measurement without compensation, with generic compensation which does not take the sensitivity difference into account, and with an individual compensation by a background microphone. To assess the quality of the compensation, the Fourier spectrum of the background microphone is included and figure 4(b) shows the magnitude squared coherence of the signals of the DUT and the background microphone. Apart from the calibration frequency of 0.51 Hz and its multiples, the coherence is close to 1 which suggests that background noise is the dominating noise source in this case. Since the stimulus is only present at the DUT the coherence at the calibration frequency is low. For higher calibration frequencies, wind-induced noise became the dominating noise source and the coherence between DUT and background microphone signal was lower.
When the individual compensation is employed, the SNR can be improved by up to 25 dB, which increases the repeatability of a calibration. This is especially true of the lower end of the frequency range of the microphone carousel, where the sound pressure level of the background noise due to wind and other sources is highest.

Wind-induced noise
At frequencies of about 3 Hz and higher, wind-induced noise due to the movement of the DUT during the rotation becomes prevalent. There are two major air streams that affect the DUT during a measurement. First, there is the headwind in the direction of movement of the microphone. The amplitude v of the velocity of the headwind is directly related to the calibration frequency f and the radius r the microphone is mounted on and amounts to v = 2πrf.  For a calibration on the lowest radius on the microphone carousel (r = 0.15 m), the speed of the headwind amounts to 0.94 m s −1 for a frequency of 1 Hz and to 9.4 m s −1 for a frequency of 10 Hz. Moreover, there is a radial wind stream flowing outward at the boundary layer of the rotating disk. This wind stream was avoided by not mounting the microphone with the membrane flush to the rotating disk surface, but rather having it protruding a few centimeters from the surface, which is the standard measurement configuration.
To further mitigate the headwind-induced noise, strategies to pass the air stream by the microphone tip were applied. A 90 • nose cone inspired by commercially available nose cones for wind shielding in wind tunnels was constructed and manufactured on a 3D printer (see figure 5(a)). Figure 5(b) shows a carousel calibration result at a frequency of 6.31 Hz with and without this nose cone. With the nose cone, the wind-induced noise was reduced by about 20 dB, which increased the SNR and thereby the repeatability of the measurements.
One inherent problem of the presented nose cone construction arises from its geometry. The orbit at which the microphone moved was inevitably curved but the nose cone was straight and had a length of 103 mm. For this reason, the angle of incidence of the headwind was different at the tip of the nose cone compared to the position of the microphone itself. The deviation between these angles of incidence increases when the radius of the orbit decreases. Tests with a deliberately rotated nose cone showed that the noise suppression capabilities started to degrade when the angle of incidence of the headwind on the tip was greater than 25 • . For a tangentially oriented nose cone of these dimensions, this results in a minimum radius of 0.11 m. Below this radius, the angles of incidence at the tip of the nose cone and at the microphone differ by more than 25 • .
Although the nose cone was very effective in reducing the wind-induced noise at higher rotation speeds, it should be noted that it was only a first attempt with a simple geometry. To better understand the working principle and to improve the performance of the nose cone are issues of further investigation.

Asymmetry of a DUT
The mounting setup presented in section 3.1 does not consider the spatial extent of the microphone membrane and models the microphone as a point receiver located in the geometric center of the membrane. Since the outermost part of the microphone membrane, seen from the rotation axis, actually moves in an orbit with a slightly larger radius than the innermost part of the membrane, the actual alternating pressure acting on these parts of the membrane also slightly differs. The assumption that the DUT is a point receiver located in the geometric center of the mounting hole only holds completely true if the sensitivity distribution over the microphone membrane area is radially symmetrical with the symmetry axis located in the center of the microphone. While this assumption seems likely to be true due to the radially symmetric construction of the standard measurement microphones, some parts, for example the equalization vent, still introduce a geometric asymmetry. This may in turn influence the location of the acoustical center of the microphone. Furthermore, material irregularities of the membrane or contaminations on it might also introduce an asymmetry to the microphone. Another factor is a deviation in the geometry of the preamplifier. An asymmetry of the DUT would cause deviations of the measured sensitivity depending on the rotational alignment of the DUT in the mounting clamp.
To test the assumption of rotational symmetry, multiple measurements were conducted with a 1/2 ′′ measurement microphone, where the microphone was rotated by 90 • around its symmetry axis after each measurement cycle. The microphone was mounted on the disk at a distance of 150 mm from the rotational axis. Figure 6 shows the deviation of each measurement cycle to the average of all four measurement passes. The rotational angle was defined from an arbitrary but fixed starting point. The measurement passes deviate by up to 0.1 dB from the average, with rotational positions that are 180 • apart yielding approximately opposite deviations for frequencies below 5 Hz. These deviations were reproducible across multiple measurement cycles. This suggests that the assumption of rotational symmetry of the DUT is not justified in all cases. Further tests with different combinations of microphone cartridges and preamplifiers revealed that the main aspect introducing an asymmetry is the preamplifier of the DUT.
Although not every microphone tested showed such behavior, a potential asymmetry still has to be taken into account for an unknown microphone to be calibrated. To eliminate errors of the actual orbit radius of a DUT, it is advisable to conduct multiple measurement passes and rotate the DUT between each pass by a fraction of a full rotation, for example, by 90 • . The sensitivity of the microphone can then be determined as the average of these measurement passes, where a deviation caused by an asymmetry of the DUT is reduced.

Uncertainty analysis
To assess the quality of calibrations conducted in the microphone carousel, the measurement uncertainty was analyzed following the Guide to the Expression of Uncertainty in Measurement [20]. Since the carousel method is a primary calibration method, several further calibration procedures are necessary before a calibrated device is applied in the field. All these calibration procedures increase the measurement uncertainty of the complete calibration process for a DUT; thus, the uncertainty of the primary calibration should be as low as possible. In the current uncertainty budget, the main contributions stem from mechanical issues of the measurement setup and, at higher frequencies, from wind noise due to the movement of the DUT.
It is likely that additional effects arise in the frequency range above 5 Hz, in which the microphone carousel currently does not yield reliable results. Table 1 lists all uncertainty contributions with their relative uncertainty. These contributions are explained in detail in the paragraphs below. Because the individual contributions can be regarded as statistically independent, the resulting total measurement uncertainty of the amplitude sensitivity S in dB is calculated as u(S) = 20 · log 10 N n=0 u 2 rel,n (9) from the N individual relative uncertainty contributions u rel . Because the amplitude of the alternating pressure applied to the DUT is directly proportional to the amplitude of the mechanical height change, the mechanical properties of the measurement setup directly affect the measurement uncertainty. The uncertainty of the base radius (row 1) of the orbit at which the microphone moves is determined by the distance between the center of the disk as the rotational axis and the microphone mounting point. These distances were measured after manufacturing the disk on a coordinate measurement machine and deviate less than 50 µm from the nominal values. The rotational axis itself has to be parallel to the ground. A small angular error of the rotational axis (row 2) only has marginal influence on the effective radius of the orbit of the microphone. This is because the effective radius is proportional to the cosine of the error angle of the rotational axis.
Furthermore, mounting the disk on the shaft introduces an eccentricity error (row 3) and an angular error (row 4) between the disk and the rotational axis, which both influence the effective radius of the orbit the microphone is traveling on. Both deviations were measured with the disk rotating slowly using a dial gauge. The eccentricity was found to be below 100 µm, and the angular error of the disk to the axis was found to be below 0.1 • .
Another source of uncertainty is the attachment of the microphone to the disk. As the microphone membrane has a distance of approximately 5 cm from the disk, any angular error of the microphone in the disk (row 5) also affects the effective radius of the microphone orbit. The angular error of the microphone to the disk was found to be below 0.4 • .
At higher rotation speeds, the measurement setup starts to vibrate. The dynamic displacement of the axis vertical to the ground was measured with an acceleration sensor and found to be below 5 µm at 10 Hz and even lower for lower calibration frequencies (row 6).
The last mechanical uncertainty contribution originates in the mechanics of the DUT. As described in section 4.3, some measurement microphones exhibited different sensitivities when rotated inside the mounting clamp on the disk. This suggests that there is an asymmetry in these microphones. The observed asymmetries (row 7) lead to level differences of less than 0.15 dB. To reduce the uncertainty originating from this effect, four measurements taken with the DUT rotated inside the mounting clamp in 90 • increments were averaged. With the rotational positions of the DUT inside the mounting clamp accurate to ±4 • , the averaging reduces the uncertainty from the asymmetry by a factor of 10.

Calculation of air density.
The density of the ambient air is needed to calculate the gradient of the ambient pressure. In combination with the amplitude of the circular motion it is used to determine the amplitude of the alternating pressure that the DUT was exposed to. According to (2), this amplitude is directly proportional to the air density. As the air density is computed from climate measurements using the CIPM-2007 model [14], the uncertainties of the climate parameter measurements (rows 8 to 11) directly affect the uncertainty of the calibration itself. The temperature was measured with an uncertainty of 0.05 K, and the humidity was measured with an uncertainty of 2%. Furthermore, the static ambient pressure was measured with an uncertainty of 10 Pa. For the required precision, a direct measurement of the CO 2 content of the ambient air was not necessary. Instead, the CO 2 content was assumed to be between 0 ppm and 1000 ppm. As the laboratory was regularly ventilated and only rarely frequented by humans, this range was a valid assumption. In addition to the input parameters of temperature, humidity, static ambient pressure, and CO 2 content, the CIPM-2007 model itself (row 12) contributes a relative uncertainty of 22 · 10 −6 to the overall measurement uncertainty.
Another input parameter for the calculation of the amplitude of the alternating pressure is the gravity (row 13). The gravity at the location of the measurement setup is determined from nearby measurement stations [18] and a value of g = 9.8125 m s −2 with an uncertainty of ±0.0001 m s −2 was used.

Electrical contributions.
The electrical output signal of a DUT is transmitted from the rotational axis to the static frame of the measurement setup through a slip ring (row 14). This slip ring is therefore located in the electrical measurement part, although it is not part of a DUT, and its influence must be considered in the uncertainty budget. Measurements comparing the slip ring at different rotation speeds to a normal cable showed no difference apart from a very slightly raised noise floor. A relative uncertainty of 50 · 10 −6 is assumed for the slip ring.
On the stationary side of the measurement setup, the analog voltage signal of the DUT is digitized using an A/D converter of type Data Translation DT9857E (row 15). This A/D converter has been adjusted in offset and gain and was compared to a traceably calibrated Keysight multimeter of type 3458A in direct current voltage (DCV) sampling mode. The maximum deviation of any channel of the DT9857E from the 3458A multimeter in the frequency range of 0.1 Hz to 20 Hz was below 0.002 dB.
Another electrical component influencing the measurement result is the polarization voltage applied to the microphone (row 16). The sensitivity of an externally polarized measurement microphone is approximately proportional to the applied polarization voltage, so any deviation from the nominal value of 200 V directly influences the determined sensitivity. For DUTs which do not include their own polarization voltage source, the polarization voltage was provided by a Keysight precision voltage source of type B2961B with a maximum deviation of 0.1 V. 5.1.4. Acoustical contributions. The movement of the DUT on the disk causes wind-induced noise (row 17). This noise is detected together with the stimulus by the DUT and is prevalent for frequencies of 5 Hz and higher. Furthermore, background noise directly reaches the DUT (row 18). Both effects lower the SNR of the calibration measurement, which in turn increases the measurement uncertainty for a calibration.
For the uncertainty analysis, both noise mechanisms are assumed to have a broadband character with random phase and that they are incoherent with respect to the stimulus. The Fourier coefficient X f as computed in (4) contains an additional noise component which is random in phase. The relation between the level of the signal component and the noise component is given by the SNR and was estimated by comparing the DFT bin containing the signal to the adjacent bins. For a given SNR in dB, the relative uncertainty u rel introduced by the noise amounts to To separate the contribution of the background noise from the contribution of the wind-induced noise, the signal of the background microphone was used as reference for the background noise level. At a calibration frequency of 0.1 Hz, the wind-induced noise can be neglected with respect to the background noise. An SNR of 45 dB for the background noise was assumed for the uncertainty analysis.
At 1 Hz, the wind-induced noise can still be neglected with respect to the background noise. The background noise was lower compared to the background noise at 0.1 Hz and an SNR of 60 dB was assumed for the uncertainty analysis.
At 5 Hz, the wind-induced noise was the dominating noise source and an SNR of 45 dB was assumed for the uncertainty analysis. The level of the background noise was comparable to the level at 1 Hz.

Comparison to laser pistonphone
The measurement setup described in section 3.1 was used to calibrate a microphone set consisting of an infrasound microphone cartridge of type Brüel & Kjaer 4193 mounted on a lowfrequency preamplifier of type GRAS 26AI. The microphone set was supplied with a polarization voltage of 200 V for the cartridges and a symmetrical supply voltage of ±50 V for the preamplifier. To improve the SNR, a background microphone was set up in front of the microphone carousel at a distance of approximately 50 cm and the DUT was equipped with a nose cone as described in section 4.2. Furthermore, to eliminate the influence of a potential asymmetry of the DUT, four measurement passes with different orientations of the DUT were conducted and averaged as described in section 4.3. The calibration was conducted in the frequency range from 0.1 Hz to 10 Hz in third-octave band steps. The same microphone set was calibrated at the Laboratoire national de métrologie et d'essais (LNE) in France in a laser pistonphone [5] in the frequency range from 0.01 Hz to 20 Hz. In the overlapping frequency range, these calibrations can be compared to mutually validate the two calibration methods. Figure 7 shows the results of both calibrations. The calibration results are plotted as absolute values and as the difference to a frequency response obtained by a model of the calibrated microphone set consisting of two first-order high-pass filters connected in series. The first filter describes the low frequency behavior of the microphone cartridge with its vent exposed to the sound field. Its cutoff frequency was set to 0.02 Hz, which is in agreement with the specifications given by the manufacturer. The second filter models the electrical high-pass behavior of the microphone cartridge's capacitance combined with the preamplifier's input impedance. For a given capacitance C of the microphone cartridge and input impedance R of the preamplifier, the cutoff frequency f c of the electrical high-pass filter amounts to For the microphone set used, the cartridge capacitance is C = 19.1 pF and the preamplifier input impedance is R = 40 GΩ, which results in a cutoff frequency of f c = 0.21 Hz. The purpose of the model is to provide a detailed view of the differences between the calibration methods. It is not part of the further evaluation.
The sensitivity values determined in the microphone carousel and in the LNE laser pistonphone are in very good agreement for frequencies of 5 Hz and below. Above 5 Hz, the sensitivity determined in the microphone carousel starts to rise and significantly deviates from the values determined in the laser pistonphone and those obtained by the high-pass model.
Vibrations within the measurement setup could be a likely reason for this behavior. At frequencies above 5 Hz, the microphone carousel started to vibrate, which seemed to affect the radius of the orbit the microphone was moving in. This in turn influences the determined sensitivity. Another possible reason might be aerodynamic effects caused by the dynamic pressure due to the headwind acting on the microphone during rotation. All in all, the comparison to the LNE laser pistonphone validates the determined sensitivities for frequencies up to 5 Hz, but demonstrates the need for further research on the carousel method when it is applied at higher frequencies.

Discussion
The carousel method, implemented by the setup described in this paper, was shown to be suitable in principle for the calibration of measurement microphones. A DUT was mounted on a disk rotating around a horizontal axis, which moved the device up and down periodically and subjected it to an alternating pressure. The amplitude of the alternating pressure was determined from measurements of the ambient temperature, humidity, and static pressure combined with a defined amplitude of the movement. This measurement setup was shown to yield reliable results for the calibration of measurement microphones in the frequency range below 5 Hz. Compared to the established pressure reciprocity calibration method, the carousel method is based on completely different physical principles, and it promotes a mutual validation of the acquired results. However, in the microphone carousel, multiple issues concerning the calibration in different frequency ranges were identified.
At the lower end of the frequency range, background noise poses a potential problem, as the microphone carousel cannot completely be shielded acoustically from the environment. This results in a high background noise level and consequently a low SNR. Shielding the setup from outside noise with an enclosure was not possible because the radial air stream caused by the rotation of the disk would have been blocked by the walls of an enclosure. The knock-on effect of the resulting low SNR on the uncertainty budget can, however, be mitigated by active compensation with the aid of a background microphone as shown in section 4.1. This microphone only captures the outside noise, which can be subtracted from the DUT's signal. While the active compensation by direct subtraction presented in this paper already provides good results, the usage of comprehensive coherent subtraction techniques could further improve the effectiveness of this compensation [21].
An extension to frequencies lower than 0.1 Hz is possible, but further challenges will be faced. As discussed in section 2, the amplitude of the stimulus the DUT is subjected to depends on the air density, which is influenced by the ambient temperature, humidity and static pressure. For this reason, these ambient conditions must be kept stable during the measurement duration. Especially the ambient temperature and static pressure have a strong influence on the air density. For example, a deviation from the standard conditions of 2.5 K in temperature or 1 kPa in static pressure changes the air density and thus the amplitude of the stimulus by 1%. At low frequencies, the measurement duration can reach several hours for a calibration at a single frequency. It would therefore be necessary to tightly control the ambient conditions over a long timespan to conduct calibrations at very low frequencies.
At the upper end of the frequency range, wind-induced noise caused by the movement of the DUT is a significant issue. Furthermore, with increasing frequency, the air stream around the microphone starts to influence the calibration result. The impact of the wind-induced noise can be partly mitigated if a nose cone as presented in section 4.2 is mounted on the DUT. While this nose cone improves the SNR, further research is necessary to understand the operation of such a device and to improve its performance. Aerodynamic effects of this wind stream beyond wind-induced noise should also be researched further.
One aspect affecting the whole frequency range is the asymmetry of some DUTs. A deviation of the acoustical center of the microphone from the symmetry axis causes a systematic deviation of the effective radius of the orbit, although the mechanical radius remains unchanged. While the reasons for such an asymmetry are to date not completely understood, they can be mitigated by the rotation of the DUT between measurement cycles as described in section 4.3. This mitigation should always be performed because an asymmetry should always be expected for an unknown DUT.
With the aid of all these mitigation strategies, the comparison of the results acquired in the microphone carousel to those acquired in the LNE laser pistonphone show a very good agreement in the frequency range below 5 Hz. For frequencies above 5 Hz, there is a significant deviation of the results and further research is needed.
While the investigations in this paper mainly concern the determination of the pressure sensitivity level, the carousel method is in principle also suitable for the determination of the sensitivity phase. This, however, is currently not fully implemented in the setup presented here but can easily be introduced by a precise determination of the rotation position of the disk.
In the future, the measurement setup presented in this paper will serve as a primary calibration method for environmental infrasound in the frequency range from 0.1 Hz to 5 Hz with a planned extension to 10 Hz. This will then extend the frequency range covered by national standards for infrasound. In the frequency range from 2 Hz to 5 Hz, covered by both the carousel method and the established reciprocity method, the existence of two distinct calibration methods will be used for a mutual validation of the calibration facilities.