Free-field three-transducer spherical-wave reciprocity calibration for hydrophone at hydrostatic pressure of 10 MPa

Free-field three-transducer spherical-wave reciprocity method has been reviewed and employed to calibrate the hydrophone of TC4033 in a high hydrostatic pressure vessel. To reduce the measurement uncertainty, a reciprocal calibration bracket and reciprocal transducers were designed and developed. The calibration bracket can locate the transducers in the high hydrostatic pressure vessel. The reciprocal transducer can reduce the errors caused by the deviation of reciprocity. A correcting sensitivity method based on complex electrical impedance measurement has been described, which can obtain the original open-circuit sensitivity of a hydrophone. It is more accurate than correcting method based on the measurement of extension cable capacitance especially near the resonant frequency range. The TC 4033 hydrophone was calibrated in the one-third octave frequency points from 2 kHz to 200 kHz at a high hydrostatic pressure of 10 MPa. The calibration results were analyzed, and the measurement uncertainty was estimated to be 0.5 dB (k=2).


Introduction
With the development of the marine industry, deep-water transducers are widely used in the ocean oceanographic engineering.The characteristics of transducers will vary with hydrostatic pressure which changes with immersed depth of water.In general, parameters measured in low hydrostatic pressure are not valid at great depths in the ocean.They can hardly be accurately obtained through theoretical calculation.To solve the problems of electroacoustic parameter measurement in great depth-ocean, calibration facilities need to be established to measure high hydrostatic pressure which ensures the availability and stability of transducers in deep-ocean [1,2].
Hydrophones, as receiving transducers, can obtain sound information in the ocean, and they are widely used in ocean sound detection.The sensitivity is the main response parameter of hydrophones.However, with the same transducers, the impact of hydrostatic pressure on the sensitivity of hydrophones cannot be ignored in the ocean condition of large depths.To correctly obtain the sensitivity of hydrophones in the deep ocean with high hydrostatic pressure, many measurement methods and facilities have been performed all over the world.The most widely used method is the coupler reciprocity method in a low-frequency range below 2 kHz [3][4][5][6].In addition, the ocean simulation and acoustic calibration vessel were established in the Underwater Sound Reference Division (USRD) [7,

Calibration method
The traditional free-field three-transducer spherical-wave reciprocity calibration method can be used at high hydrostatic pressure conditions.The theoretical principle of the reciprocity calibration method is the electroacoustic reciprocity theory, which is derived from the acoustic field reciprocity theory and the electromechanical reciprocity theory of a linear reciprocal transducer [6,7].
In the reciprocity calibration, there must be three transducers.An auxiliary projector F (projector) is only used for transmitting sound waves, a hydrophone J is only used for receiving sound waves, and a reciprocal transducer H is used for both transmitting and receiving sound waves.The principle of reciprocity calibration in free-field is carried out in three steps as shown in Figure 1.
Schematic of free-field three-transducer spherical-wave reciprocity calibration principle and procedure.
First, the amplitude of transfer impedance ZFH between the transducer pair of auxiliary projector F and the reciprocal transducer H is measured.Then, the auxiliary transducer F and the receiving hydrophone J are combined into a transducer pair, and their amplitude of transfer impedance ZFH is measured.Finally, the reciprocal transducer H and the receiving hydrophone J are combined as a transducer pair, and their amplitude of transfer impedance ZHJ is measured.The transfer impedances of three transducer pairs can be expressed as follows: where IF is the electrical current flowing through the projector F, and IH is the electrical current flowing through the reciprocal transducer H. UFH is the output voltage of the reciprocal transducer H in the sound field produced by the projector F, UFJ is the output voltage of the hydrophone J in the sound field produced by the projector F, and UHJ is the output voltage of the hydrophone J in the sound field produced by the reciprocal transducer H. SF is transmitting the response to the current of the projector F, and SH is transmitting the response to the current of the reciprocal transducer H. MH is the sensitivity of the reciprocal transducer H, and MJ is the sensitivity of the hydrophone J. dFH is the distance between the projector F and the reciprocal transducer H, dFJ is the distance between the projector F and the hydrophone J, and dHJ is the distance between the reciprocal transducer H and the hydrophone J.
According to the reciprocity theory, the sensitivity of hydrophone can be expressed as follows: where ρ is the density of water, and f is frequency.

Correcting technique of complex electrical impedance
In the process of calibration at high hydrostatic pressure, the added extension cables are used to connect the hydrophone and the calibration facility instruments.The addition of an extra length of extension cable will change the overall electrical impedance of the hydrophone, and the sensitivity of the hydrophone will change as well.A traditional correction for added extension cable is often performed by measuring the capacitances of the hydrophone and extension cable, which is accurate enough at a low-frequency range, especially 1 kHz or lower.However, as the frequency increases towards the resonant frequency range, this correction method of capacitance measurement is significantly in error.
In the correcting technique of complex electrical impedance for added extension cable, the hydrophone and the added extension cable can be considered as a two-port electrical network.The hydrophone and its original cable can be considered as a combination, and the added extension cable will change the impedance of this combination.The method requires the measurement of the complex electrical impedance of both the hydrophone-cable combination and the added extension cable respectively.The equivalent electrical circuit of the hydrophone-cable combination and the added extension cable is shown in Figure 2. In Figure 2(a), the open circuit sensitivity of the hydrophone-cable combination is M0, and the sound pressure is PS.The impedance of the hydrophone-cable combination is ZH, where the current flow through impedance is I0 with the open circuit voltage of UH at the terminal of the combination.The overall sensitivity of the combination with the added extension cable is MC, which can be measured directly at the terminal of the added extension cable through Equation (3).The overall current is IE and the open circuit voltage is UE at the overall terminal.The overall impedance ZE of the hydrophone-cable combination and the added extension cable can also be measured when the sound pressure around the hydrophone is zero (Ps=0), which is described in Equation ( 3), and its equivalent electrical circuit is shown in Figure 2(b).The open-circuit impedance of the added extension cable is ZOC, and the short-circuit impedance of it is ZSC.
Here, the overall sensitivity of the hydrophone-cable combination with the added extension cable MC can be measured directly at the terminal of the added extension cable.The relationship between the sensitivity of the hydrophone-cable combination MH and the overall sensitivity of the hydrophone-cable combination with the added extension cable MC can be expressed as ( )

High hydrostatic anechoic pressure vessel and calibration bracket
The hydrophone needs to be calibrated in an anechoic water vessel, and the high hydrostatic anechoic pressure vessel, calibration bracket and transducers are shown in Figure 3.The vessel is designed as a cylinder body with hemispherical ends at both sides of the cylinder, and the vessel is placed horizontally.
In order to produce a sound field environment close to the free field, the sound-absorbing materials are laid inside the vessel to eliminate the reflecting sound wave from the boundary and reduce reverberation during the measurement.The temperature and hydrostatic pressure control system is equipped on the periphery of the vessel, which can control the temperature and hydrostatic pressure of the water in the vessel.
The calibration bracket consisting of a lifting and rotating system is installed on the top cover of the high hydrostatic pressure vessel.It works under hydrostatic pressure, and the maximum hydrostatic pressure is 10 MPa (simulating depth of 1000 meters).Below the calibration bracket, the hydrophone, projector, and transducer are located in the center of the vessel through carbon fiber rods which are fixed on the calibration bracket by universal joints to ensure that the three positioning rods are vertically downward.A counterweight is installed on the carbon fiber rod to ensure that it has enough gravity to avoid moving underwater.The positioning mechanism can fine-tune the position of the underwater transducers, and the hydrophone to ensure that the spherical centers of the three transducers are in the same straight line.

Calibration Instruments and procedures
The free-field reciprocity calibration facility at high hydrostatic pressure is shown in Figure 4.The calibration can be performed automatically through the computer, and the instruments are controlled by the computer through the IEEE 488 bus.Before measurement, it was necessary to fix the projector, reciprocal transducer, and hydrophone on the calibration bracket.To ensure that the acoustic centre of the projector, reciprocal transducer and hydrophone was horizontal and on the same straight line, the laser beam was used to adopt the position of the projector, hydrophone, and transducers.After the installation of the projector, hydrophone, and reciprocal transducer, the calibration bracket was installed in the vessel.In the measurement of transfer impedance ZFJ, the calibrated direction of the hydrophone was aimed at the projector, and received the sound wave transmitted by the projector, which is shown in Figure 5(a).The computer controlled the signal generator to produce a discrete single-frequency tone-burst signal.The tone-burst signal was amplified by a power amplifier and used to drive the projector to transmit the sound wave in the vessel.The signal of electrical current flowing through the projector was detected by the current sensor, and the output of the current sensor and open-circuit voltage of the hydrophone was in connection with the switch.These signals were separately amplified and filtered by amplifier and filter, and measured by oscilloscope.In the measurement of transfer impedance ZHJ, the calibrated direction of the hydrophone rotated and aimed at the reciprocal transducer shown in Figure 5(a), and the transfer impedance can be measured in the same procedure described above.In the measurement of transfer impedance ZFH, the hydrophone needs to be lifted through the calibration bracket to avoid the scattering and reflecting of the hydrophone which is shown in Figure 5(b).In this step, the reciprocal transducer was used as a receiver to receive sound waves, and the transfer impedance was measured in the same procedure.

Sensitivity correction caused by added extension cable
The end of the hydrophone-cable combination needs to be extended to the laboratory by an added extension cable in the measurement.Before measurement, it was necessary to measure the parameters of the added extension cable as described in Equation (3).The correct sensitivity deviation caused by the added extension cable can be calculated through Equation (5).The frequency response curve of sensitivity correction calculated through Equation ( 5) in one-third octave frequency points from 2 kHz to 200 kHz is shown in Figure 6.It can be observed from that figure that compared with the constant value calculated through the capacitance correcting method, the correcting method of complex electrical impedance can obtain the frequency response of the correction value.At the resonant frequency range, the correction value exceeded 3.5 dB. (

Calibration results
The Reson TC 4033 was chosen as the measured hydrophone, and it was calibrated using the free-field three-transducer spherical-wave reciprocity method at a high hydrostatic pressure vessel of 10 MPa.The sensitivity level can be expressed as where the reference value of the sensitivity level is 1 V/μPa.The sensitivity level of the hydrophone TC 4033 in one-third octave frequency points from 2 kHz to 200 kHz is shown in Table 1.

Measurement uncertainty
The measurement uncertainty of the free-field three-transducer spherical-wave calibration performed at high hydrostatic pressure of 10 MPa needs to be estimated by considering the calibration method, the calibration facility, and calibration results.The uncertainty components are evaluated by either statistical means (type A) or other non-statistical means (type B).The type A components of uncertainty represent the repeatability or precision and were obtained from a series of independent repeated measurements.The type B components of uncertainty, which represent the possibility of measurement bias, cannot be assessed statistically.They include components that remain constant when the measurements are repeated, and sources of uncertainty are listed in Table 2.The expanded uncertainty of free-field threetransducer spherical-wave reciprocity calibration at high hydrostatic pressure is estimated to be 0.5 dB (k=2).

Conclusion
The free-field three-transducer spherical-wave reciprocity calibration method and facility of hydrophone at high hydrostatic pressure of 10 MPa are described.To obtain sensitivity accurately, a calibration bracket installed on the cover of the hydrostatic pressure vessel has been developed, and the transducers and hydrophone need to be located accurately through it.To avoid the deviation of calibration caused by the added extension cable, the correcting technique of complex electrical impedance has been researched, and it can obtain the original sensitivity of the hydrophone.The TC 4033 hydrophone was chosen as the measured hydrophone, and the calibration experiment was performed in the high hydrostatic pressure vessel.The measurement uncertainty was analyzed and estimated.
The calibration results and measurement uncertainty show that the method and facility described can realize the accurate free-field calibration of hydrophones at high hydrostatic pressure.The calibration is more accurate in the resonant frequency range.The maximum hydrostatic pressure can reach 10 MPa, and the frequency range is 2 kHz~200 kHz.The measurement uncertainty is estimated to be 0.5 dB (k=2).

Figure 2 .
Figure 2. Electrical equivalent circuit of the hydrophone-cable combination and the added extension cable.

Figure 3 .
Figure 3. Schematic of high hydrostatic anechoic pressure vessel and calibration bracket.

Figure 4 .
Figure 4. Schematic of calibration facility at high hydrostatic pressure vessel.

Figure 5 .
Figure 5. Schematic of the relative position of projector, hydrophone, and reciprocal transducer during the calibration.

Table 1 .
Sensitivity of Reson TC 4033 hydrophone in one-third octave frequency points from 2 kHz to 200 kHz.

Table 2 .
Sources of uncertainty of type B based on the free-field three-transducer spherical-wave reciprocity method at high hydrostatic pressure of 10 MPa.