Combined hydrophone secondary calibration and

directional response measurement setup

Volker Wilkens Martin Weber
Ultrasonics working Group Department of Physics
Physikalisch-Technische Bundesanstalt University of Helsinki
Braunschweig, Germany Helsinky, Finland
volker.wilkens@ptb.de martin.weber@helsinki.fi

Jennifer Twiefel Georg Dietrich

Gesellschaft für Angewandte Gesellschaft für Angewandte
Medizinische Physik und Technik mbh Medizinische Physik und Technik mbh
Braunschweig, Germany Merseburg, Germany
jennifer.twiefel@ptb.de georg.dietrich@gampt.de

Abstract—A combined measurement setup was developed towards further working hydrophones for daily measurement
for secondary hydrophone sensitivity calibration and tasks. The configuration can also be used to efficiently
hydrophone directional response measurements. The Setup characterize the directional response of hydrophones to
comprises a mechanical hydrophone positioning and scanning derive their effective size. The system developed may also be
system with five motorizes axes, a water basin, a pulse applied to the secondary calibration and spot checking of
generator, a positioning controller, ultrasonic transducers and special hydrophones used for high intensity focused
a computer with software. Sensitivity calibrations are based on ultrasound (HIFU) field characterization, like robust HIFU
comparison of the device under test with a reference membrane hydrophones or fiber-optical hydrophones [7].
membrane hydrophone calibrated primarily beforehand.
Measurements at high output levels pose an increased risk of
Nonlinear broadband ultrasonic pulses are applied for
characterization in wide frequency ranges from 1 MHz to 50
damaging the hydrophone. The setup can be used to perform
MHz. To simplify the rotational axis alignment needs for spot checks of each hydrophone before and after the use to
directional response measurements, an iterative rotational axis verify that the hydrophone still works correctly and that the
mismatch compensation method was developed. Hydrophone sensitivity did not alter. The presented calibration system
characterization examples are provided and the results are uses an electrical excitation signal of a pulse generator that
compared with independent measurements. For sensitivity, was optimized in connection with the source transducer to
good agreement was found with deviations below 0.5 dB. create a short and powerful pressure waveform. The
Hydrophone effective sizes were determined preferably in the secondary sensitivity calibrations are based on comparison
far field of a planar source transducer rather than in a focused with a reference hydrophone in a substitution arrangement.
field. The reference hydrophone in turn needs to be formerly
calibrated. The calibration process is automated and requires
Keywords—ultrasound exposimetry, hydrophones, secondary only a few actions of the user.
hydrophone calibration, directional response, effective size
II. EXPERIMENTAL METHODS
I. INTRODUCTION
Ultrasound exposimetry requires the selection of A. Measurement setup
adequate hydrophone types and sizes and hydrophone The compact setup comprises a pulse generator, a
calibration ranges depending on the specific output positioning controller, a digital oscilloscope, a mechanical
measurement situation [1]. Reliable acoustic pressure data positioning system with motorized axes, a water basin, and
and further parameters derived from that, like pressure ultrasonic transducers as shown in Fig. 1. The setup is
derived intensities or mechanical indices (MI), can be controlled by a computer. A primarily calibrated hydrophone
obtained when the individual calibration data and spatial is used as reference for the secondary calibration.
averaging corrections according to the individual effective
hydrophone size are considered within the measurement and
data evaluation procedures [2]-[5]. Usually, hydrophones are
shipped to calibration laboratories for appropriate
characterization [6], and are then applied to acoustic output
measurements by the user. Additionally, uncalibrated
hydrophones may be used for daily measurement tasks.
Sometimes the output signals of uncalibrated hydrophones
are just compared with measurements using a calibrated
hydrophone to roughly estimate the sensitivity. To support
user’s flexibility and efficiency in appropriate hydrophone Fig. 1. Setup for secondary hydrophone calibration and directional
characterization and calibration of larger varieties of response measurement.
hydrophones on site, a universal setup for secondary
sensitivity calibration of hydrophones and additional A motorized 5-axis positioning system was designed for
effective diameter determination was developed. This alignment of the hydrophones in the ultrasonic field. For the
measurement setup can be used to transfer calibrations from secondary sensitivity calibration, a focusing transducer with
hydrophones calibrated externally at calibration laboratories nominal focal length of 50 mm and 12 mm diameter is
excited by short electrical spike pulses [8],[9]. The same beam profile in the distance of measurement needs to be
transducer can be used for directional response measured beforehand with the setup [9]. This line scan
measurements in the focus as well or, alternatively, a plane should be performed with a hydrophone that is significantly
source transducer (diameter: 6 mm) with the hydrophone smaller than the typical variations of the field. The sensitivity
being positioned in the far field. The characterization is of the hydrophone to be calibrated is then given by:
performed using broadband ultrasonic pulses. This excitation
technique allows a wide frequency range being tested within U hyd ( f ) Fhyd ( f )
just one measurement cycle which speeds up the M hyd ( f ) = M ref ( f ) (1)
measurement on the one hand and provides full spectral U ref ( f ) Fref ( f )
information in amplitude and phase on the other hand. The
excitation signal was optimized to produce a high amplitude C. Compensation of rotational axis mismatch
leading to high frequency components in the signal due to To perform the hydrophone directional response
the nonlinear wave propagation in water, and to realize a measurements, generally it is important that the center of the
short pulse duration to minimize the existence of any sensitive element is exactly on the axis of rotation to ensure
periodic signal components. the same portion of the sound field being measured during
The software developed consists of the measurement data rotation. However, to keep the mechanical system simple,
acquisition (MDA) tool and the data evaluation (DE) tool. provision of additional precise translation stages to adjust the
The software guides the operator throughout all steps of the hydrophones to the rotational axes were dispensed with in
calibration procedure to ensure reliable results. The this setup. Instead, a compensation method for any mismatch
measurement procedure is automized to simplify the between the rotational axis and the hydrophone sensitive
operation. element was implemented enabling the calibration of
different hydrophone types.
B. Secondary hydrophone calibration If the center of the rotation does not coincide with the
The secondary calibration method applied here has been center of the hydrophone element, the distance between
described earlier [10] and is based on substitution. A transducer and hydrophone varies during rotation resulting in
primarily calibrated broadband membrane hydrophone is a variation of the time-of-flight (TOF). The compensation
used as reference. The hydrophone under test is then exposed adjustment is performed after each angular step motion with
to the same ultrasonic pressure field. For this substitution it the Cartesian positioning stages for the hydrophone [11]. The
must be ensured that both subsequent measurements are corrections ∆x and ∆y required in x- and y-direction can be
performed within the very same ultrasonic field, e.g. stable computed utilizing the distances dx and dy between the two
electrical signal generation and pressure pulse excitation as centers in x- and y-direction:
well as stable water quality and temperature conditions are
necessary during the complete set of measurements. To ∆x = xH,o − xH,n (2)
evaluate the sensitivity of the hydrophone under test Mhyd(f)
by means of secondary calibration, the following steps are
performed:
(
−∆y = ( −1) ⋅ yH,n − yH,o ) (3)

At first, the reference hydrophone is positioned in the where xH,o and yH,o are the coordinates of the original position
ultrasonic field. The distance between the transducer and the of the center of the hydrophone, and xH,n and yH,n are the new
hydrophone has to specifically be adjusted by observing the coordinates of the center of the hydrophone element rotated
time-of-flight of the received signal relative to the excitation by ϕ around the z-axis. Those are given by:
pulse of the transducer. The lateral position is adjusted to
receive the maximum signal amplitude. After aligning the xH,n = dx cos (ϕ ) − dy sin (ϕ ) (4)
hydrophone, the time domain signal uref(t) of the reference
hydrophone is captured by the oscilloscope. yH,n = dy cos (ϕ ) + dx sin (ϕ ) (5)
Afterwards, the reference hydrophone is exchanged with Utilizing the change of TOF, dx and dy can be estimated.
the hydrophone under test, and the same adjustment It is obvious from Fig. 2 that the TOF is changing due to the
procedure is performed again. Now the hydrophone signal change of the distance ∆s between the transducer and the
uhyd(t) is acquired. Both signals are transferred into the hydrophone. Due to the relatively small α value the vector
frequency domain by means of the Fourier transformation to from transducer to receiver has a dominant x-component.
become Uref(f) and Uhyd(f). The hydrophone sensitivity Mref(f)
The induced change ∆s can be estimated for any ϕ. With t0 as
of the reference hydrophone in the frequency domain is
known from the calibration certificate. TOF reference for ϕ0 and tH,n for any other angle it is given
by:
Finally, a spatial averaging correction is applied for each
measurement. This correction is necessary as the sound ∆s = ( tH,n − t0 ) c (6)
pressure of the focused field may not be constant over the
finite sensitive area of the hydrophone. The hydrophone with the speed of sound c. Taking into account that ∆x is
signal is proportional to the average sound pressure over the nearly ∆s, neglecting the effect of α, a quadratic function
sensitive area, and to obtain a hydrophone signal related to
based on (2) and (4) can be derived:
the peak pressure, the spatial averaging correction is
performed. For the reference, the spatial averaging correction
is Fref(f), and for the hydrophone under test it is Fhyd(f). To  ϕ2  ϕ2
∆s (ϕ ) ≈ dx − dx 1 −  + dyϕ = dx + dyϕ (7)
calculate the spatial averaging corrections, a lateral ultrasonic  2  2
 
Here, a Taylor series up to the quadratic terms was used to D. Determination of the effective radius
approximate sin and cos. This function can be fitted to a To determine the effective radius, the directional
measured ∆s vs. ϕ curve. The result of the fit are response has to be measured according to IEC 62127-3 [12].
approximated values for dx and dy, the distances between the The presented setup uses an iterative process for
rotational axis and the center of the hydrophone element. compensating misaligned positions (cf. II.C.). During a
Experience shows that the quality of the estimated dx and dy directivity measurement the hydrophones are excited either
values can be significantly improved by running the by a focusing source transducer at focus or by a plane source
estimation in several (two to three) iterations, see Fig. 3, with transducer in the far field. The effective size is then
the offsets dx and dy from the previous run considered within calculated from the measured directivity data D of the final
each iteration. To perform the process, an interaction of the compensated directivity measurement by fitting the rigid
MDA tool and the DE tool is necessary. With successful baffle model function in the angular range extending to
compensation, the TOF is nearly constant over ϕ, see Fig. 4 the -6 dB drop compared to the central maximum, but no
for an example. To compensate the mismatch for the second more than +/- 35° at most [12]:
rotational axis, the same procedure applies to the coordinates
x and z. 2 J1 ( ka sin(ϕ ) )
D ( a, k , ϕ ) = (8)
ka sin(ϕ )

where a is the radius of the sensitive element, ϕ is the angle

of rotation, J1 is the Bessel function of the first order, and k
= 2πλ/f the wavenumber calculated from the ultrasound
frequency f and wavelength λ. The latter is temperature
dependent through the speed of sound in water. The water
temperature is monitored regularly during the measurement
and handed over with the measurement data file. The data
evaluation procedure of the DE tool uses the speed of sound
determined according to [13].

III. RESULTS

Fig. 2. Geometry and simplification for rotational axis mismatch compen-

A. Sensitivity calibration
sation calculation. For the example presented in this work, a backed membrane
hydrophone with nominal diameter of 100 µm and pvdf-foil
thickness of 4.5 µm (GAMPT MH46) was primarily
calibrated and then used as reference hydrophone [9]. A
nominal 200 µm diameter membrane hydrophone with pvdf-
foil thickness of 11 µm (PTB RS072), was then calibrated
against the reference hydrophone. A focusing source
transducer was used for the secondary calibration
measurement. The result of the RS072 is compared to the
result of an additionally performed primary calibration of the
same hydrophone in Fig. 5. Good agreement was found in
the frequency range from 2 MHz to 25 MHz, while small
deviations up to 0.5 dB at maximum can be observed
between 25 MHz and 50 MHz.

Fig. 3. Iterative process to obtain optimum displacement compensation.

Fig. 4. Voltage-time signal distribution versus angle of the membrane Fig. 5. Sensitivity level for a nominal 200 µm hydrophone (RS072)
hydrophone RS078 without (left) and including rotational axis mismatch measured with the secondary calibration setup and with a primary
compensation (right). calibration method for comparison [9]; uncertainties for 95 % coverage.
B. Effective size determination however, a planar source transducer and measurement in the
The measurements were performed for two directions, far field should be applied. The narrow beam profile at focus
the rotational axis parallel to the leads of the hydrophone otherwise causes a violation of the local plane wave
element spot and perpendicular to it. The value of the assumption and an underestimation of the effective size since
obtained radius in the direction parallel to the leads is the outer element regions are insonified with lower
displayed in Fig. 6 for the example of a membrane amplitude and thus contribute to the diffraction by smaller
hydrophone (PTB RS078). In addition to the result obtained amounts.
from measurements with a planar source transducer (green
ACKNOWLEDGMENT
line), measurements were performed using the same focusing
source transducer as for the sensitivity calibrations (blue This work was supported by the German Federal
line) for comparison. Furthermore, the result obtained from Ministry for Economic Affairs and Climate Action, grant
measurements at the reference setup for directivity number TransMeT 2019-1_2, within the “Transfer of
measurements at PTB [14] (black line) is shown in Fig. 6 for Metrological Technology” program.
comparison. Good agreement is found between the results
obtained with the planar source transducer and the reference REFERENCES
measurement. Systematic deviations occur when using the
[1] G. R. Harris S. M. Howard, A. M. Hurrell, P. A. Lewin, M. E.
focusing transducer at frequencies beyond 20 MHz. Fig. 6 Schafer, K. A. Wear, V. Wilkens, and B. Zeqiri., “Hydrophone
also shows the results for a second membrane hydrophone measurements for biomedical ultrasound applications: A review,”
example with larger effective size (PTB 42). Here, the IEEE Trans. Ultrason., Ferroelectr., Freq. Control, vol. 70, no. 2, pp.
differences when using a focusing source transducer are 85–100, Feb. 2023.
much more pronounced. [2] Ultrasonics—Hydrophones—Part 1: Measurement and characteri-
zation of medical ultrasonic fields, International Standard IEC 62127-
1, Ed. 2, 2022.
[3] Ultrasonics—Field Characterization—Test Methods for the
Determination of Thermal and Mechanical Indices Related to
Medical Diagnostic Ultrasonic Fields, International Standard IEC
62359:10+AMD1:2017, CSV Ed.2.1, 2017.
[4] K. A. Wear, “Hydrophone spatial averaging correction for acoustic
exposure measurements from arrays—Part I: Theory and impact on
diagnostic safety indexes,” IEEE Trans. Ultrason., Ferroelectr., Freq.
Control, vol. 68, no. 3, pp. 358–375, Mar. 2021.
[5] K. A. Wear, A. Shah, A. M. Ivory, and C. Baker, “Hydrophone spatial
averaging correction for acoustic exposure measurements from
arrays—Part II: Validation for ARFI and pulsed Doppler waveforms,”
IEEE Trans. Ultrason., Ferroelectr., Freq. Control, vol. 68, no. 3, pp.
376–388, Mar. 2021.
[6] M. Weber and V. Wilkens, “A comparison of different calibration
techniques for hydrophones used in medical ultrasonic field
measurement,” IEEE Trans. Ultrason., Ferroelectr., Freq. Control,
vol. 68, no. 5, pp. 1919–1929, May 2021.
[7] G. Xing, V. Wilkens, P. Yang, “Review of field characterization
techniques for high intensity focused ultrasound,” Metrologia, vol.
58, 022001, DOI: 10.1088/1681-7575/abe02e, Feb. 2021.
[8] V. Wilkens and C. Koch, “Amplitude and phase calibration of
hydrophones up to 70 MHz using broadband pulse excitation and an
Fig. 6. Effective radius for two membrane hydrophones, PTB RS078 and optical reference hydrophone,” J. Acoust. Soc. Am., vol. 115, no. 6,
PTB 42 measured in the direction of the electrodes with the hydrophone pp. 2892–2903, June 2004.
calibration setup using different source transducers.
[9] M. Weber and V. Wilkens, “Using a heterodyne vibrometer in
combination with pulse excitation for primary calibration of
IV. CONCLUSIONS ultrasonic hydrophones in amplitude and phase,” Metrologia, vol. 54,
no. 4, pp. 432–444, June 2017.
The optimized pulse generation equipment provides an [10] V. Wilkens, S. Sonntag, and M. Weber, “Secondary Complex-valued
almost nonperiodic acoustic pulse resulting in a very Hydrophone Calibration up to 100 MHz Using Broadband Pulse
homogenous probing spectrum and a usable frequency range Excitation and a Reference Membrane Hydrophone,” Proc. of 2019
from about 1 MHz to 50 MHz for sensitivity calibrations of IEEE Ultrasonics Symposium – Paper WeH5.2, 0246.pdf, pp. 1846-
hydrophones with effective element sizes up to 0.5 mm 1849, Oct 2019.
diameter. A membrane hydrophone was calibrated against a [11] E. G. Radulescu, P. A. Lewin, A. Nowicki, and W. A. Berger,
“Hydrophones’ effective diameter measurements as a quasi-
reference membrane hydrophone by usage of the developed continuous function of frequency,” Ultrasonics, vol. 41, no. 8, pp.
setup and by a primary calibration for comparison. For the 635–641, Nov. 2003.
0.2 mm membrane hydrophone, the deviation between [12] Ultrasonics—Hydrophones—Part 3: Properties of hydrophones for
primary and secondary calibration data was below ±5 % in ultrasonic fields, International Standard IEC 62127-3, Ed. 2, 2022.
the frequency range from 1 MHz to 40 MHz. Directional [13] V. A. Belogol'skii, S. S. Sekoyan, L. M. Samorukova, S. R. Stefanov,
response measurements were performed, also using pulse and V. I. Levtsov, “Pressure dependence of the sound velocity in
excitation, to determine hydrophone’s effective size for distilled water,” Measurement Techniques, vol. 42, no. 4, pp. 406–
413, Apr. 1999.
frequencies up to 50 MHz. Comparison with results obtained
in a reference setup shows good agreement of the determined [14] V. Wilkens and W. Molkenstruck, “Broadband PVDF membrane
hydrophone for comparisons of hydrophone calibration methods up to
sizes for a nominal 0.2 mm membrane hydrophone up to 140 MHz,” IEEE Trans. Ultrason., Ferroelectr., Freq. Control, vol.
20 MHz when using a focusing source transducer. For larger 54, no. 9, pp. 1784–1791, Sep. 2007.
effective sizes and characterization beyond 20 MHz,