Developments in primary calibration
The demand for traceable hydrophone calibrations at very low frequencies in support of ocean monitoring applications requires primary standard methods that are able to realise the acoustic pascal at such frequencies. The primary standard realisation is then disseminated by use of calibrated hydrophones, devices that respond to pressure in water.
In this project, two primary methods for calibration of hydrophones have been developed by the project partners: (i) use of a calculable laser pistonphone to cover frequencies from 0.5 Hz to 200 Hz; (ii) use of the coupler reciprocity calibration method. Both these methods are pressure calibrations methods, where the hydrophone is exposed to an oscillating pressure in an enclosed chamber or coupler. The basic methodologies for the methods are described in IEC 60565-2: 2019.
Laser pistonphone method
The laser pistonphone is the basis of an absolute calibration method that enables a calculable sound pressure to be generated in a coupler of fixed volume by the motion of a piston that creates a well-defined volume velocity. In the laser pistonphone, the volume velocity is determined through measurement of the dynamic displacement of the piston using laser interferometry. The sound pressure applied to the sensor under test is calculated based on knowledge of the acoustic transfer impedance of the coupler and the piston displacement, assuming a rigid piston and a known piston surface area. The sensor to be calibrated is exposed to this known sound pressure, and its output voltage is measured. The sensitivity modulus, MH is then calculated from:
where UH is the hydrophone voltage, ΔV is the volume change, V0 is the total volume, p0 the static pressure and γ is the ratio of specific heats for the gas.
An implementation of the method at NPL uses a pre-stressed piezoelectric stack to drive a piston to create a varying pressure in an air-filled enclosed cavity, the dimensions of the front cavity being designed to allow the calibration of reference hydrophones, but the system may also be used to calibrate microphones. This implementation has demonstrated the feasibility of this method for calibrating hydrophones in air in the frequency range from 0.5 Hz to 200 Hz, achieving measurement uncertainties of 0.XX dB for sensitivity modulus. The method has been validated by comparison to independent methods at other NMIs using microphones as the transfer standard, showing agreement with 0.YY dB, and to the method of coupler reciprocity with agreement 0.ZZ dB in the frequency range X Hz to Y Hz.
Coupler reciprocity method
The coupler reciprocity method, based on the use of closed couplers, is routinely employed by national metrology institutes (NMIs) for microphone calibration. Described in IEC 60565-2, it has been developed in a number of NMIs for hydrophone calibration [ref Slater et al] and previously has been typically used in the frequency range from 20 Hz to 2 kHz.
In the most usual configuration, the pressure reciprocity method requires three hydrophones, at least one of which is reciprocal. The three hydrophones are coupled using a fluid-filled coupler (typically the fluid is deionised, degassed water). A projector, P, a reciprocal transducer, T, and a hydrophone, H, are wholly or partially inserted into the chamber (in practice, both P and T are reciprocal). As in microphone reciprocity, the transducers may be paired off in three measurement stages, at each stage one device being used as a transmitter and the other as a receiver. For each pair a measurement is made of the electrical transfer impedance (eg ZPT), that is, the ratio of the voltage detected at the receiving transducer to the current flowing into the transmitting device. By use of the reciprocity principle, as applied to the reciprocal transducer, the sensitivity of any of the three devices in the chamber can be determined from these purely electrical measurements and from analytical calculation of the acoustic transfer admittance of the coupler system. Unlike for air acoustics, where the gaseous medium dominates the acoustic compliance, for a fluid-filled hydrophone coupler, there are contributions from the fluid, the coupler chamber and the transducers, and soft compliant materials such as rubber and (most important) gas bubbles must be eliminated. To avoid the need to know the compliance of the coupler with the hydrophone under test, two of the transducers (designated as reference transducers) are designed without any compliant encapsulant and are maintained for use in the coupler. By measuring the electrical transfer impedance between the reference transducers without the hydrophone inserted into the coupler, the required compliance for the coupler with all three devices inserted may be calculated in terms of the compliance of the reference coupler configuration only, where the inclusion of soft compliant material is eliminated. This method is termed the “reference transfer” method [ref Zalesak, IEC 60565-2]. The sensitivity modulus, MH, of the hydrophone to be calibrated is given by:
where the total compliance Ct of the reference coupler is given by:
where ρf is the density and cf is the sound speed in the fluid, and ΔC is the compliance of the reference coupler additional to the fluid (coupler walls, reference transducers…). The value of ΔC is minimised by the design and is calculated analytically from material properties or from finite element analysis.
Implementations of the method at Tubitak-MAM have demonstrated the feasibility of the method for the frequency range 10 Hz to 500 Hz (?) with uncertainties ranging from 0.X dB to 0.Y dB. Figure X shows an image of the system at Tubitak-MAM and results of a calibration of a reference hydrophone.
One of the benefits of coupler reciprocity with a fluid-filled coupler is that the coupler may be pressurised to simulate water depth, and operated over a range of water temperatures. The system at Tubitak-MAM is able to operate to static pressures of 10 MPa (equivalent to 1000 m ? of ocean depth) and over a modest temperature range of 8 °C to 25 °C ?
There are considerable challenges in lowering the lower frequency limit including:
the decreasing signal-to-noise ratio as frequency decreases, especially for measurement of drive current for the high impedance reference transducers;
ensuring the reference transducers do not have any electrically conductive path through the water medium, thus creating a high pass filter effect with the transducer capacitance and introducing a low frequency roll-off (replacing the water with the less conducting castor oil has been tried by other researchers, but that is a less practical solution due to the tendency to trap gas bubbles)
The primary standard methods developed in the Infra-AUV project will enable the partners to submit CMC entries to the BIPM Key Comparison Database, and one of the partners (NPL) will facilitate the organisation of a new low-frequency key comparison under the auspices of the CCAUV.
References
IEC 60565 – 2: 2019 Underwater acoustics — Hydrophones — Calibration of hydrophones Part 2: Procedures for low frequency pressure calibration, IEC Geneva.
Barham, Ford, Malcher, Robinson, Cheong, Bridges, Rodrigues, Ward. “A calculable pistonphone for the absolute calibration of hydrophones in the frequency range from 0.5 Hz to 200 Hz” Metrologia, submitted 2023.
Malcher, F., Ford, B., Barham, R., Çorakçi, C., Biber, A., Robinson, S., Cheong, S.-H., Ablitt, J., and Wang, L. “Low-frequency standards for hydroacoustics in the Infra-AUV project”, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-5620, doi.org/10.5194/egusphere-egu23-5620 2023.
Freya Malcher, Richard Barham, Ben Ford, Emily Webster, Stephen Robinson, Justin Ablitt, Sei Him Cheong, Lian Wang. “Low frequency primary pressure calibration techniques at NPL”, Proceedings of UACE 2023.
Robinson, S.P., Ward, J. “Low frequency hydrophone calibration with a laser interferometer”, Proceedings of the 5th Underwater Acoustics Conference and Exhibition, UACE2019, Crete, p 33-40, June 2019
Slater W H, Crocker S E, and Baker S R. “A primary method for the complex calibration of a hydrophone from 1 Hz to 2 kHz”, Metrologia 55 (2018) 84–94