PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Validation of Reflectance-based Fiber-Optic Hydrophones
Samuel HOWARD1; Claudio ZANELLI2
1

Onda Corporation, United States of America

2

Onda Corporation, United States of America

ABSTRACT
Reflectance-based fiber-optic hydrophones are frequently used for high pressure ultrasound measurements.
Often, damage to the fiber forces the user to re-cleave the fiber-top, necessitating a means of re-validating thecalibration over a broad frequency range. A previous study proposed a validation method utilizing a stable,
calibrated pulse ultrasound source operating at moderate diagnostic levels (about 6 MPa pk-pk.). This
presentation will briefly review this approach, adding new results in support of the overall calibration
scheme: (a) comparison of the calibration-check from the pulsed source to a conventional swept-frequency
substitution method of calibration (b) recent experimental measurements of the effective aperture from 2 to
15 MHz (c) recently compiled long-term stability data for a proposed implementation of the pulsed
check-source.
Keywords: optical, hydrophone, calibration

1. INTRODUCTION
Reflectance-based fiber-optic hydrophones (FOHs) are widely used for the measurement of HIFU
and lithotripsy fields, primarily because they are easily repairable by a user simply re -cleaving thefiber tip whenever it is damaged. These devices work by measuring changes in the optical intensity
reflection coefficient at the tip of a glass fiber immersed in water, due to the pressure dependence ofwater’s refractive index [1].
The theory of operation of FOHs has been extensively described before [1-3]. Fig. 1 shows asketch of an FOH. An optical fiber is cleaved and the bare tip is immersed in water. An incident
acoustic pressure wave changes the index of refraction of both the water and (to a lesser extent) theglass at the tip. The change in reflected light is recorded as a change of voltage by the photoamplifier,which typically has both DC and AC output circuits (which we can denote as V DC and VAC (t)) and a
specified relative Gain between the two.
If δR(t) denotes the variation in the reflection coefficient of optical intensity,
δR(t)/ R0 = [GVAC(t) / (VDC- V0)]
(1)
where V DC is the voltage output of the photoamplifier under quiescent conditions (i.e., no acoustic
wave is incident) and R 0 is the optical intensity’s reflection coefficient under ambient temperature andpressure. The term V 0 accounts for stray light and is measured by an initial measurement with thefiber’s tip immersed in a fluid which has an optical index matched to glass or, alternatively, in a seriesof fluids with refractive index close to glass, followed by a fitting procedure.Thus, two or more initialstatic measurements, one in water and at least one in an index-matched fluid, are sufficient tonormalize further measurements of the voltage output to calculate the fractional change in reflection
coefficient δR(t)/ R0 in Eq. (1).
For a typical multi-mode fiber, the optical reflection coefficient may be calculated assuming an
optical plane wave impinging normally on the glass-water interface, and may therefore be readily
calculated from the index of optical refraction for water and of the glass of the fiber. As these material
properties of glass and water are well-known functions of temperature and pressure, it is therefore
possible to invert these functions to determine the pressure at the tip at a given ambient temperature,taking into account the non-linear aspects of water [3,4].
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sh@ondacorp.com

Optical Dump

Laser Diode
Photo amplifier

To waterFigure 1 Schematic of a Reflectance-based Fiber-Optic Hydrophone

The pressure at the fiber tip is a superposition of the free-field pressure and the wave diffracted at thetip, and it is therefore necessary to correct for the diffracted wave in order to determine the free -fieldpressure of an incident wave. As this effect is frequency-dependent, a deconvolution procedure isnecessary, utilizing a “deconvolution kernel” which accounts for both the magnitude and phase of thediffraction over a wide bandwidth (usually > 50 MHz) because of the high -frequency harmonics
usually present in the incident pressure waveform. Because of the difficulty of direct measurement, thedeconvolution kernels have often been based on a model. To first order the deconvolution kernel may
be modeled by utilizing classical formulas for the average pressure from a normally incident wave
scattered by a rigid cylinder [2]. A further refinement accounted for the fact that the fiber averages thepressure only over its optical core, obtaining the deconvolution kernel from a closed -form integral [5].
A more recent refinement accounted for the elasticity of the fiber by calculatin g the diffraction kernel
from a Finite Element Analysis (FEA), obtaining good experimental agreement with results measured
with a membrane hydrophone [3].
Calibration has therefore usually assumed that a previously validated calibration (whetherexperimentally or from a model) is still valid, even after a fiber has been re -cleaved. To address thisconcern, we previously proposed the use of a “Pulsed Check Source” (PCS) as a broadband check of
the accuracy of an FOH, obtaining good experimental agreement between an FOH and a calibrated
membrane hydrophone [3] when 8192 averages are performed to filter out noise from an Onda
PCS-1000. Figure 2 shows a comparison of the deconvolved averaged FOH waveform to themembrane hydrophone. Fig. 3 shows the corresponding spectral comparison.
PCS waveform (8192 averages) deconvolved to pressure waveform
6FO (HFO 690)
Membrane Hydrophone (HMA0200)

54MPa

32
10-1-2

00.5

11.5

2
sec

2.5

33.5

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Figure 2 PCS waveform
PCS Pressure Spectrum (Deconvolved)
0FO (HFO 690)
Membrane Hydrophone (HMA0200)-10-20dB re pk-30-40-50
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4050
MHz

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Figure 3 PCS Spectrum
The present paper validates this concept further, with the following results:
 comparison of the calibration-check from the pulsed source to a conventional swept-frequency
substitution method of calibration
 recent experimental measurements of the effective aperture from 2 to 15 MHz
 recently compiled long-term stability data for a proposed implementation of the pulsed
check-source

2. Comparison Between PCS Measurement and Swept-Frequency Calibration
Most conventional hydrophone calibration schemes employ pressure amplitudes that are relatively
low for the typical FOH. The Onda HFO-690, for example, has sensitivity of around 7 mV/MPa and anoise equivalent pressure (NEP) of about 0.5 MPa for 100 MHz bandwidth. Calibration therefore
requires extensive averaging and therefore good stability over time in a calibration setup. Recently, thesensitivity of an Onda HFO-690 was measured in Onda’s standard swept-frequency calibration setup,in the range of 1-20 MHz. The setup utilizes a 2.54 cm diameter F/10 broadband PVDF transducer, asdescribed in [6]. The transducer was driven with a 60 micro-second tone-burst while the frequency wasstepped from 1 MHz to 20 MHz in increments of 50 kHz. Pressures varied from approximately 40 kPato 110 kPa throughout the frequency range. An Onda HMA0200 piezopolymer membrane hydrophone,which was calibrated at National Physical Laboratory (UK) was placed in the tank as a reference inorder to determine the frequency-dependent sensitivity of the HFO-690, following procedures
described in [7]. Fig. 4 shows a comparison between the swept-frequency calibration, the theoretical
FEA-based calibration of the hydrophone, and the sensitivity prediction based on the pulsed checksource following the method of [3] Excellent agreement was obtained between the three methods
below 20 MHz, where the HMA calibration is expected to be most accurate. The discrepancies above
20 MHz may be due to errors in the model, in the HMA calibration or in the PCS measurement (e.g.,
spatial averaging effects). It is planned to extend the range of conventional calibration of the HFO-690
by using the harmonic comparison method per [7] with an unfocused source; hopefully this will
provide insight into this question.

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18
Swept Frequency Calibration
PCS comparison
FEA model

16nV/Pa

141210860102030MHz40

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Figure 4: HFO-690 sensitivity from theoretical calibration compared to check with PCS, and to
swept-frequency calibration

3. Measurements of Directivity and Effective Aperture
The setup used for swept-frequency calibration was also used to perform directivity measurementsof the HFO-690. Results were previously reported in [8] and will therefore only be summarized here.
Measurements were performed over +/- 90 degrees at 2.25, 3.5, 5, 7.5, 10, and 15 MHz. Several
models were evaluated to find the effective radius a eff which best fit the data at each frequency. The
first model evaluated was the standard “Jinc” function [7]:DRB (k , )  2 J 1 (kaeff sin( )) / kaeff sin( )(2)which corresponds to a rigid baffle (RB) assumption for the fiber, and where θ = angle of incidence, k= 2π / λ, λ = wavelength, and a eff = the effective radius of the hydrophone sensitive element. The
value of aeff was chosen by minimizing the mean square difference between the model and the data .
As frequency increased, the best-fit result for aeff converged to the geometric radius of the fiber core
(designated as ag and equal to 52.5 micro-meters). However, at lower frequencies a eff became muchlarger than ag for the RB model of Eq. (1). Additional models were evaluated: (i) an “unbaffled model”(UB) where the standard Jinc function is multiplied by a factor of (1+cos(θ))/2 (ii) a “soft baffled”(SB) model where the Jinc function is multiplied by a factor of cos(θ) and (iii) a “rigid piston model”(RP), which is provided as an integral formula in [5] and was evaluated numerically. As shown in Fig.
5, the RP model corresponds to a consistent effective radius close to the nominal value. It is expectedthat this is because it provides the most physically realistic representation of the boundary conditions.

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Figure 5 – Effective radius based on fit to different directivity models

4. Stability of the Pulsed Check Source
Previous work [9] has summarized the short-term repeatability and stability of the PCS-1000
pulsed check source. Temperature stability of output power is within 0.4% per deg C in the 19 deg C to25 deg C temperature range, and variations in hydrophone measurements are primarily due tovariations in alignment, which typically result in a few percent of variation.
Figure 6 shows the long-term stability of a PCS-1000, by plotting the output powers over ten yearsof time for a typical unit. Periodic measurements made with a radiation force balance (RFB) at Onda
are shown, along with measurements at the German National Laboratory PTB. There is a long-term
ageing effect on the order of one to two percent over the course of the first two to three years, whichthen slows down, although this trend is within measurement uncertainties.
80
Onda Measurements
PTB

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Power (mW)

7776
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Figure 6 – Power output over time for a typical PCS-1000, with error bars1022

5. Conclusions
The results presented here further validate the theoretical model used to calibrate the HFO-690
fiber-optic hydrophone. In addition, the PCS-1000 pulsed check source has been shown to provide aconsistent, stable check for the HFO-690.
Further work is planned to check the theoretical model by performing harmonic calibrations tohigher frequencies.

REFERENCES
1. Staudenraus, J., Eisenmenger, W. Fiber-optic probe hydrophone for ultrasonic and shock-wave
measurements in water, Ultrasonics, Vol. 31, No. 4, 1993, p. 267-273.
2. Wang, Z., Lauxmann, P., Wurster, C., Kohler, M., Gompf, B., Eisenmenger. "Impulse response of a fiber
optic probe hydrophone determined with shock waves in water," Journal of Applied Physics, Vol 85,
Number 5, March 1999, pp. 2514-2516.
3. Howard, S. Calibration of reflectance-based fiber-optic hydrophones Proc. IEEE Ultrasonics Symposim(IUS) 2016.
4. Arvengas, K., Davitt, K. Caupin, F. Fiber optic probe hydrophone for the study of acoustic caviation inwater, Review of Scientific Instruments, 82, 034904, 2011.
5. Krucker, J. F., Eisenberg, A., Krix, M., Lotsch, R., Pessel, M. Trier, H.G., Rigid piston approximation forcomputing the transfer function and angular response of a fiber-optic hydrophone, J. Acoust. Soc. Am.,
vol. 197 no. 4 pp 1994-2003, April, 2000.
6. Selfridge, A., Lewin, P., Wideband spherically focused PVDF acoustic sources for calibration ofultrasound hydrophone probes, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency
Control, Vol. 47, No. 6, p. 1372-1382, November 2000.
7. IEC 62127-2, Ultrasonics-hydrophones-part 2: Calibration for ultrasonic fields up to 40 MHz, 2013.
8. Wear, K. and Howard, S., Directivity and frequency-dependent effective sensitive element size of areflectance-based fiber optic hydrophone: predications from theoretical models compared withmeasurements. IEEE Transactions on Ultrasonics, Frerroelectrics, and Frequency Control, Vol. 65, No.
12, 2018.
9. Howard, S., Stoft, D. Chen, X. Morris, H. and Zanelli, C. Evaluataon of stability and repeatability of apulsed check source, Proceedings of Advanced Metrology for Ultrasound in Medicine, Teddington, UK.
May 2010.

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