Developments in secondary calibration

Basics

Only some transducers for infrasound measurements can be primary calibrated with the methods described in the previous section. Particularly, devices commonly applied in field and on-site use, such as microbarometers and sound level meters can currently not be directly calibrated in primary calibration facilities. The purpose of secondary calibration facilities is to bridge this gap and provide a traceable calibration for such measurement devices and, more generally, to disseminate the traceability to the SI without the need for primary calibration of all transducers.

The main secondary calibration principle is calibration by comparison. For the audible frequency range, this principle is standardized in IEC 61094-5 [1] [IEC 2016]. A device under test (DUT) and a reference sensor (e.g., laboratory standard microphone) are subjected to the same sound field and the DUT is calibrated by comparing the output signals. While it is difficult to achieve highly reproducible infrasound pressure levels in a free field, high sound pressure levels with a good signal-to-noise ratio can be generated in sealed chambers, using pistons or loudspeakers as excitation sources.

The reference sensor and the DUT are either subjected to the sound field one after the other (sequential excitation) or they are mounted close to each other and are subjected to the sound field at the same time (simultaneous excitation). At infrasound frequencies with corresponding wavelengths in the order of several meters, the sound field in a sealed chamber of a size that can  accommodate two or more sensors, can be regarded as homogeneous. For this reason, two sensors mounted in such a chamber close to each other are subjected to the same sound pressure level and, thus for infrasound frequencies the preferred calibration principle is simultaneous excitation.

Because the sensitivity of infrasound sensors depends on the working frequency, the calibration has to be conducted at every frequency of interest. When the reference and the DUT are subjected to the same sinusoidal sound pressure with a complex amplitude  and frequency , the amplitudes of the output voltages depend on the respective complex sensitivities  and  and amount to

,

,

 has been determined by the primary calibration of the reference sensor. The sensitivity of the DUT is then determined as

.

Note that consideration of complex quantities enables both the magnitude and phase components of the sensitivity to be characterised.

Calibration setups

Within the Infra-AUV project four partners (CEA, DFM, LNE and PTB) developed and / or improved their secondary calibration facilities. All of these calibration facilities are based on comparison by simultaneous excitation in a sealed chamber.

The sound tube constructed at PTB [Rust et al 2023] consists of an acrylic tube with an outer diameter of 30 cm and a height of 115 cm. At the bottom a subwoofer is placed as the sound source. The top of the tube is closed by a lid which contains several different mounting options for devices to be calibrated. As reference sensors, microphones of various types calibrated with different primary calibration methods are employed.

A sound tube following a similar design has been established at DFM.

LNE’s laser pistonphone [Rodrigues et al 2022], which has been constructed as a primary calibration facility, can also be employed as secondary calibration facility. For a secondary calibration, microphones of type Brüel & Kjær 4193 and static pressure sensors of type SETRA 278 are utilized.

CEA’s calibration bench also utilizes a piston as excitation source. Up to 8 microbarometers can be calibrated simultaneously. As reference sensors, microphones of type Brüel & Kjær 4193 or barometers of type Keller PAA33X are employed. By varying the static pressure inside the calibration chamber in a range from 600 to 1100 hPa, a variable altitude between 4000 m to -500 m can be simulated.

 The following table compares the secondary calibration setups.

In addition to the abovementioned facilities, the extension of the reciprocity calibration method to 25 mHz has also enabled HBK to extend the frequency range of already existing calibration system, Brüel & Kjær Type 9757, to 25 mHz to 250 Hz.

References

International Electrotechnical Commision. IEC 61094-5:2016 Electroacoustics - Measurement microphones - Part 5: Methods for pressure calibration of working standard microphones by comparison. 2016.

Rust M, Kling C, and Koch C. Novel methods and services for microphone calibration at infrasound frequencies. Forum Acusticum 2023, Torino, Italy, Sept. 2023.

Rodrigues D, Vincent P, Barham R, Larsonnier F and Durand S 2022 A laser pistonphone designed for absolute calibration of infrasound sensors from 10 mHz up to 20 Hz. Metrologia 60 015004.