Time-delay spectrometry measurement of magnitude and phase of hydrophone response

Nominal Versus Actual Spatial Resolution: Comparison of Directivity and Frequency-Dependent Effective Sensitive Element Size for Membrane, Needle, Capsule, and Fiber-Optic Hydrophones

Frequency-dependent effective sensitive element radius [Formula: see text] is a key parameter for elucidating physical mechanisms of hydrophone operation. In addition, it is essential to know [Formula: see text] to correct for hydrophone output voltage reduction due to spatial averaging across the hydrophone sensitive element surface. At low frequencies, [Formula: see text] is greater than geometrical sensitive element radius a_g . Consequently, at low frequencies, investigators can overrate their hydrophone spatial resolution. Empirical models for [Formula: see text] for membrane, needle, and fiber-optic hydrophones have been obtained previously. In this article, an empirical model for [Formula: see text] for capsule hydrophones is presented, so that models are now available for the four most common hydrophone types used in biomedical ultrasound. The [Formula: see text] value was estimated from directivity measurements (over the range from 1 to 20 MHz) for five capsule hydrophones (three with [Formula: see text] and two with [Formula: see text]). The results suggest that capsule hydrophones behave according to a "rigid piston" model for k a _g ≥ 0.7 ( k = 2π /wavelength). Comparing the four hydrophone types, the low-frequency discrepancy between [Formula: see text] and a_g was found to be greatest for membrane hydrophones, followed by capsule hydrophones, and smallest for needle and fiber-optic hydrophones. Empirical models for [Formula: see text] are helpful for choosing an appropriate hydrophone for an experiment and for correcting for spatial averaging (over the sensitive element surface) in pressure and beamwidth measurements. When reporting hydrophone-based pressure measurements, investigators should specify [Formula: see text] at the center frequency (which may be estimated from the models presented here) in addition to a_g .

Hydrophone Measurements for Biomedical Ultrasound Applications: A Review

This article presents basic principles of hydrophone measurements, including mechanisms of action for various hydrophone designs, sensitivity and directivity calibration procedures, practical considerations for performing measurements, signal processing methods to correct for both frequency-dependent sensitivity and spatial averaging across the hydrophone sensitive element, uncertainty in hydrophone measurements, special considerations for high-intensity therapeutic ultrasound, and advice for choosing an appropriate hydrophone for a particular measurement task. Recommendations are made for information to be included in hydrophone measurement reporting.

Spatiotemporal Deconvolution of Hydrophone Response for Linear and Nonlinear Beams-Part II: Experimental Validation

This article reports experimental validation for spatiotemporal deconvolution methods and simple empirical formulas to correct pressure and beamwidth measurements for spatial averaging across a hydrophone sensitive element. The method was validated using linear and nonlinear beams transmitted by seven single-element spherically focusing transducers (2-10 MHz; F /#: 1-3) and measured with five hydrophones (sensitive element diameters d_g : 85-1000 [Formula: see text]), resulting in 35 transducer/hydrophone combinations. Exponential functions, exp( -αx ), where x = d_g /( λ₁F /#) and λ₁ is the fundamental wavelength, were used to model focal pressure ratios p'/p (where p' is the measured value subjected to spatial averaging and p is the true axial value that would be obtained with a hypothetical point hydrophone). Spatiotemporal deconvolution reduced α (followed by root mean squared difference between data and fit) from 0.29-0.30 (7%) to 0.01 (8%) (linear signals) and from 0.29-0.40 (8%) to 0.04 (14%) (nonlinear signals), indicating successful spatial averaging correction. Linear functions, Cx + 1, were used to model FWHM'/FWHM, where FWHM is full-width half-maximum. Spatiotemporal deconvolution reduced C from 9% (4%) to -0.6% (1%) (linear signals) and from 30% (10%) to 6% (5%) (nonlinear signals), indicating successful spatial averaging correction. Spatiotemporal deconvolution resulted in significant improvement in accuracy even when the hydrophone geometrical sensitive element diameter exceeded the beam FWHM. Responsible reporting of hydrophone-based pressure measurements should always acknowledge spatial averaging considerations.

Optical phase contrast imaging for absolute, quantitative measurements of ultrasonic fields with frequencies up to 20 MHz

The technique of phase contrast imaging, combined with tomographic reconstructions, can rapidly measure ultrasonic fields propagating in water, including ultrasonic fields with complex wavefront shapes, which are difficult to characterize with standard hydrophone measurements. Furthermore, the technique can measure the absolute pressure amplitudes of ultrasonic fields without requiring a pressure calibration. Absolute pressure measurements have been previously demonstrated using optical imaging methods for ultrasonic frequencies below 2.5 MHz. The present work demonstrates that phase contrast imaging can accurately measure ultrasonic fields with frequencies up to 20 MHz and pressure amplitudes near 10 kPa. Accurate measurements at high ultrasonic frequencies are performed by tailoring the measurement conditions to limit optical diffraction as guided by a simple dimensionless parameter. In some situations, differences between high frequency measurements made with the phase contrast method and a calibrated hydrophone become apparent, and the reasons for these differences are discussed. Extending optical imaging measurements to high ultrasonic frequencies could facilitate quantitative applications of ultrasound measurements in nondestructive testing and medical therapeutics and diagnostics such as photoacoustic imaging.

A Comparison of Different Calibration Techniques for Hydrophones Used in Medical Ultrasonic Field Measurement

The acoustic output characterization of medical ultrasonic equipment requires regular calibration of the hydrophones used to ensure the reliability of measurements. Such hydrophone calibration is offered as a service by several institutions. Various calibration techniques using a variety of ultrasonic excitation pressure waveforms comprising different pressure amplitude ranges and frequency compositions as well as different reference measurement systems have been proposed and applied over the past decades. Currently, four different setups for hydrophone calibration are available at the Physikalisch-Technische Bundesanstalt (PTB). This internal comparison study addresses the consistency of all four methods, including direct primary calibration and substitution calibration using reference hydrophones. The methods apply single-frequency tonebursts and swept tonebursts in the kPa amplitude range of quasi-linear acoustics as well as impulse excitation including nonlinear propagation. In recent years, a new primary calibration setup using a high-frequency vibrometer has been implemented at PTB, enabling the characterization of hydrophone frequency responses in modulus and phase and extending the upper frequency limit to up to 100 MHz. For the comparison in the frequency range from 0.5 MHz to 60 MHz, two passive membrane hydrophones with well-known characteristics gained from many years of measurements were used. Another membrane hydrophone with a nominal diameter of 0.2 mm and an integrated preamplifier was applied to address the frequency range up to 100 MHz. The results obtained with the different setups showed good agreement with average root-mean-square (rms) deviations of 3% (primary calibrations, 1-60 MHz) and 4% (1-100 MHz). The consistency of the implementations was thus verified in this comparison.

Correction for Hydrophone Spatial Averaging Artifacts for Circular Sources

This article reports an investigation of an inverse-filter method to correct for experimental underestimation of pressure due to spatial averaging across a hydrophone sensitive element. The spatial averaging filter (SAF) depends on hydrophone type (membrane, needle, or fiber-optic), hydrophone geometrical sensitive element diameter, transducer driving frequency, and transducer F number (ratio of focal length to diameter). The absolute difference between theoretical and experimental SAFs for 25 transducer/hydrophone pairs was 7% ± 3% (mean ± standard deviation). Empirical formulas based on SAFs are provided to enable researchers to easily correct for hydrophone spatial averaging errors in peak compressional pressure ( p_c ), peak rarefactional pressure ( p_r ), and pulse intensity integral. The empirical formulas show, for example, that if a 3-MHz, F /2 transducer is driven to moderate nonlinear distortion and measured at the focal point with a 500- [Formula: see text] membrane hydrophone, then spatial averaging errors are approximately 16% ( p_c ), 12% ( p_r ), and 24% (pulse intensity integral). The formulas are based on circular transducers but also provide plausible upper bounds for spatial averaging errors for transducers with rectangular-transmit apertures, such as linear and phased arrays.

Investigation of the repeatability and reproducibility of hydrophone measurements of medical ultrasound fields

Accurate measurements of acoustic pressure are required for characterisation of ultrasonic transducers and for experimental validation of models of ultrasound propagation. Errors in measured pressure can arise from a variety of sources, including variations in the properties of the source and measurement equipment, calibration uncertainty, and processing of measured data. In this study, the repeatability of measurements made with four probe and membrane hydrophones was examined. The pressures measured by these hydrophones in three different ultrasound fields, with both linear and nonlinear, pulsed and steady state driving conditions, were compared to assess the reproducibility of measurements. The coefficient of variation of the focal peak positive pressure was less than 2% for all hydrophones across five repeated measurements. When comparing hydrophones, pressures measured in a spherically focused 1.1 MHz field were within 7% for all except 1 case, and within 10% for a broadband 5 MHz pulse from a diagnostic linear array. Larger differences of up to 55% were observed between measurements of a tightly focused 3.3 MHz field, which were reduced for some hydrophones by the application of spatial averaging corrections. Overall, the major source of these differences was spatial averaging and uncertainty in the complex frequency response of the hydrophones.

Considerations for Choosing Sensitive Element Size for Needle and Fiber-Optic Hydrophones-Part I: Spatiotemporal Transfer Function and Graphical Guide

The spatiotemporal transfer function for a needle or reflectance-based fiber-optic hydrophone is modeled as separable into the product of two filters corresponding to frequency-dependent sensitivity and spatial averaging. The separable hydrophone transfer function model is verified numerically by comparison to a more general rigid piston spatiotemporal response model that does not assume separability. Spatial averaging effects are characterized by frequency-dependent "effective" sensitive element diameter, which can be more than double the geometrical sensitive element diameter. The transfer function is tested in simulation using a nonlinear focused pressure wave model based on Gaussian harmonic radial pressure distributions. The pressure wave model is validated by comparing to experimental hydrophone scans of nonlinear beams produced by three source transducers. An analytic form for the spatial averaging filter, applicable to Gaussian harmonic beams, is derived. A second analytic form for the spatial averaging filter, applicable to quadratic harmonic beams, is derived by extending the spatial averaging correction recommended by IEC 62127-1 Annex E to nonlinear signals with multiple harmonics. Both forms are applicable to all hydrophones (not just needle and fiber-optic hydrophones). Simulation analysis performed for a wide variety of transducer geometries indicates that the Gaussian spatial averaging filter formula is more accurate than the quadratic formula over a wider range of harmonics. Additional experimental validation is provided in Part II. Readers who are uninterested in hydrophone theory may skip the theoretical and experimental sections of this paper and proceed to the graphical guide for practical information to inform and support selection of hydrophone sensitive element size (but might be well advised to read the Introduction).

Considerations for Choosing Sensitive Element Size for Needle and Fiber-Optic Hydrophones-Part II: Experimental Validation of Spatial Averaging Model

Acoustic pressure can be measured with a hydrophone. Hydrophone measurements can underestimate incident acoustic pressure due to spatial averaging effects across the hydrophone sensitive element. The spatial averaging filter for a nonlinear focused beam is a low-pass filter that decreases monotonically from 1 to 0 as frequency increases from 0 to infinity. Experiments were performed to test an analytic model for the spatial averaging filter. Nonlinear pressure tone bursts were generated by three source transducers with driving frequencies ranging from 2.5 to 6 MHz, diameters ranging from 19 to 64 mm, and focal lengths ranging from 38 to 89 mm. The nonlinear pressure fields were measured using four needle hydrophones with nominal geometrical sensitive element diameters of 200, 400, 600, and [Formula: see text]. The average root-mean-square difference between theoretical and experimental spatial averaging filters was 5.8% ± 2.6%.

Directivity and Frequency-Dependent Effective Sensitive Element Size of a Reflectance-Based Fiber-Optic Hydrophone: Predictions From Theoretical Models Compared With Measurements

The goal of this work was to measure the directivity of a reflectance-based fiber-optic hydrophone at multiple frequencies and to compare it to four theoretical models: rigid baffle (RB), rigid piston (RP), unbaffled (UB), and soft baffle (SB). The fiber had a nominal 105- [Formula: see text] diameter core and a 125- [Formula: see text] overall diameter (core + cladding). Directivity measurements were performed at 2.25, 3.5, 5, 7.5, 10, and 15 MHz from ±90° in two orthogonal planes. Effective hydrophone sensitive element radius was estimated by least-squares fitting the four models to the directivity measurements using the sensitive element radius as an adjustable parameter. Over the range from 2.25 to 15 MHz, the average magnitudes of differences between the effective and nominal sensitive element radii were 59% ± 49% (RB), 10% ± 5% (RP), 46% ± 38% (UB), and 71% ± 19% (SB). Therefore, the directivity of a reflectance-based fiber-optic hydrophone may be best estimated by the RP model.

Directivity and Frequency-Dependent Effective Sensitive Element Size of Needle Hydrophones: Predictions From Four Theoretical Forms Compared With Measurements

Directivity is a hydrophone specification that describes response as a function of angle of incidence. The goal of this study was to compare, in the context of needle hydrophones, the commonly used rigid baffle model for hydrophone directivity to three alternative models: soft baffle, unbaffled (UB), and rigid piston (RP). Directivity measurements were performed at 1, 2, 3, 4, 6, 8, and 10 MHz from ±7° in two orthogonal planes for two ceramic and two polymer needle hydrophones with nominal geometrical sensitive element diameters of 200, 400, 600, and 1000 . Effective hydrophone sensitive element radius was estimated by least-squares fitting the four models to directivity measurement data using the sensitive element radius (a) as an adjustable parameter. For > 4 (where and = wavelength), the RP model outperformed the other three models. For , the average error in estimated sensitive element radius was 7% [95% confidence interval (CI): 3%-12%] for the RP model while the lowest average error by the other three models was 46% (95% CI: 38%-54%) for the UB model.

Broadband characterization of plastic and high intensity therapeutic ultrasound phantoms using time delay spectrometry-With validation using Kramers-Kronig relations

Time delay spectrometry (TDS) is extended for broadband characterization of plastics (low-density polyethylene, LDPE) and tissue-mimicking material (TMM). The results suggest that TDS and the conventional broadband pulse method give comparable measurements for frequency-dependent attenuation coefficient and phase velocity near the center frequency, where signal-to-noise ratio is high. However, TDS measurements show enhanced bandwidth for attenuation coefficient of 30%-40% (LDPE) and 89%-100% (TMM) and for phase velocity of 43% (LDPE) and 36% (TMM) for a single transmitter/receiver pair. In addition, TDS provides measurements of dispersion that are consistent with predictions based on the Kramers-Kronig relations to within 5 m/s over the band from 2 to 12 MHz in LDPE and to within 1 m/s in TMM over the band from 0.5 to 29 MHz.

Pressure Pulse Distortion by Needle and Fiber-Optic Hydrophones due to Nonuniform Sensitivity

Needle and fiber-optic hydrophones have frequency-dependent sensitivity, which can result in substantial distortion of nonlinear or broadband pressure pulses. A rigid cylinder model for needle and fiber-optic hydrophones was used to predict this distortion. The model was compared with measurements of complex sensitivity for a fiber-optic hydrophone and three needle hydrophones with sensitive element sizes ( ) of 100, 200, 400, and . Theoretical and experimental sensitivities agreed to within 12 ± 3% [root-mean-square (RMS) normalized magnitude ratio] and 8° ± 3° (RMS phase difference) for the four hydrophones over the range from 1 to 10 MHz. The model predicts that distortions in peak positive pressure can exceed 20% when and spectral index (SI) >7% and can exceed 40% when and SI >14%, where is the wavelength of the fundamental component and SI is the fraction of power spectral density contained in harmonics. The model predicts that distortions in peak negative pressure can exceed 15% when . Measurements of pulse distortion using a 2.25 MHz source and needle hydrophones with , 400, and agreed with the model to within a few percent on the average for SI values up to 14%. This paper 1) identifies conditions for which needle and fiber-optic hydrophones produce substantial distortions in acoustic pressure pulse measurements and 2) offers a practical deconvolution method to suppress these distortions.

Variation of High-Intensity Therapeutic Ultrasound (HITU) Pressure Field Characterization: Effects of Hydrophone Choice, Nonlinearity, Spatial Averaging and Complex Deconvolution

Reliable acoustic characterization is fundamental for patient safety and clinical efficacy during high-intensity therapeutic ultrasound (HITU) treatment. Technical challenges, such as measurement variation and signal analysis, still exist for HITU exposimetry using ultrasound hydrophones. In this work, four hydrophones were compared for pressure measurement: a robust needle hydrophone, a small polyvinylidene fluoride capsule hydrophone and two fiberoptic hydrophones. The focal waveform and beam distribution of a single-element HITU transducer (1.05 MHz and 3.3 MHz) were evaluated. Complex deconvolution between the hydrophone voltage signal and frequency-dependent complex sensitivity was performed to obtain pressure waveforms. Compressional pressure (p₊), rarefactional pressure (p_-) and focal beam distribution were compared up to 10.6/-6.0 MPa (p₊/p_-) (1.05 MHz) and 20.65/-7.20 MPa (3.3 MHz). The effects of spatial averaging, local non-linear distortion, complex deconvolution and hydrophone damage thresholds were investigated. This study showed a variation of no better than 10%-15% among hydrophones during HITU pressure characterization.

The Practicalities of Obtaining and Using Hydrophone Calibration Data to Derive Pressure Waveforms

This paper considers the means by which calibration data are used to convert hydrophone output voltage into pressure. Hydrophone frequency responses are complex-valued quantities, and only by correcting for the magnitude and phase variations, is it possible to accurately recover the original pressure waveform. The limitations of current hydrophone calibration techniques are discussed, and a new method of obtaining hydrophone phase data is presented. Magnitude and phase information is measured via both coarse increment (1 MHz) and fine increment (50 kHz) calibration techniques for three exemplar hydrophones (0.5 mm needle, 0.2 mm needle, and 0.4 mm membrane). Frequently hydrophone calibration data are available at frequency increments that do not match that required by the deconvolution process. Therefore, a variety of methods to interpolate the calibrated system response to obtain correctly spaced data are considered, and two spline interpolation methods are found to offer best performance. Data preconditioning and filtering to address artifacts above and below the 1 to 40 MHz bandwidth of the coarse frequency increment calibration are also investigated, and a simple procedure for selecting an appropriate low-pass filter is presented. The revised calibration data are used to deconvolve the hydrophone frequency response for experimentally derived waveforms. Standard ultrasonic output parameters (such as peak compressional and peak rarefactional pressures, pulse intensity integral, and temporal peak and pulse average acoustic intensities) are calculated from these waveforms. Although the three hydrophones used in this paper are of different types and have a range of active element sizes, all output parameters derived from the deconvolved waveforms have <5% variation from their respective population means (with the majority being within <2%).

Primary reciprocity-based method for calibration of hydrophone magnitude and phase sensitivity: complete tests at frequencies from 1 to 7 MHz

A primary reciprocity-based method for calibration of hydrophone magnitude and phase sensitivity is proposed. The method starts determining the transmit transfer function of an auxiliary transducer, based on the self-reciprocity method and using a stainless steel cylinder as reflecting target. Afterwards, the hydrophone, to be calibrated, is positioned facing the auxiliary transducer. The pressure field waveform, calculated at the hydrophone spot and based on the transmit transfer function of an auxiliary transducer, is used together with the output end of cable voltage waveform signal from the hydrophone to yield the calibrated hydrophone sensitivity. The method was tested with two similar membrane hydrophones, at frequencies within the 1.0-7.0 MHz range, in steps of 1.0 MHz. Results for magnitude sensitivity agree, within a confidence level of 95%, with those from previous calibration of same hydrophones at the National Physical Laboratory, in the UK (Enor⩽1.0). Phase sensitivity results agree with literature reported ones concerning the achieved uncertainty. Additionally, the phase sensitivities measured at 5.0 MHz for two similar hydrophones and employing two distinct auxiliary transducers presented no statistical significant difference. The method yielded a relative expanded uncertainty (p=0.95) for the sensitivity magnitude ranging between 6.6 and 7.0%, and an expanded uncertainty (p=0.95) ranging between 12° and 17° for the phase sensitivity. The results obtained so far lead to conclude that the proposed hydrophone calibration method is a validated alternative to the different existing methods.

Correction for frequency-dependent hydrophone response to nonlinear pressure waves using complex deconvolution and rarefactional filtering: application with fiber optic hydrophones

Nonlinear acoustic signals contain significant energy at many harmonic frequencies. For many applications, the sensitivity (frequency response) of a hydrophone will not be uniform over such a broad spectrum. In a continuation of a previous investigation involving deconvolution methodology, deconvolution (implemented in the frequency domain as an inverse filter computed from frequency-dependent hydrophone sensitivity) was investigated for improvement of accuracy and precision of nonlinear acoustic output measurements. Timedelay spectrometry was used to measure complex sensitivities for 6 fiber-optic hydrophones. The hydrophones were then used to measure a pressure wave with rich harmonic content. Spectral asymmetry between compressional and rarefactional segments was exploited to design filters used in conjunction with deconvolution. Complex deconvolution reduced mean bias (for 6 fiber-optic hydrophones) from 163% to 24% for peak compressional pressure (p+), from 113% to 15% for peak rarefactional pressure (p-), and from 126% to 29% for pulse intensity integral (PII). Complex deconvolution reduced mean coefficient of variation (COV) (for 6 fiber optic hydrophones) from 18% to 11% (p+), 53% to 11% (p-), and 20% to 16% (PII). Deconvolution based on sensitivity magnitude or the minimum phase model also resulted in significant reductions in mean bias and COV of acoustic output parameters but was less effective than direct complex deconvolution for p+ and p-. Therefore, deconvolution with appropriate filtering facilitates reliable nonlinear acoustic output measurements using hydrophones with frequency-dependent sensitivity.

Introducing S-parameters for ultrasound-based structural health monitoring

Scattering parameters (S-parameters) are the most common tools for characterizing microwave devices and high-frequency systems but have not been used for ultrasoundbased structural health monitoring (SHM) so far. In this paper, we present the theory, signal processing algorithms, and experimental results to demonstrate the applications of S-parameters for three common ultrasound-based SHM techniques, i.e., ultrasound pitch-catch, pulse-echo, and impedance/admittance measurements. The concept of the S-parameters is first introduced, followed by the discussions of extracting the time-domain ultrasound signals from the frequency-domain Sparameter measurements. The time-domain signals calculated from the measured S-parameters were compared with the oscilloscope measurements. Excellent agreements between these two sets of measurements were achieved. In addition, time-frequency analysis of the ultrasound inspection system based on the S-parameter measurements has also been performed. This work demonstrated that the S-parameters can serve as a versatile tool for ultrasound-based SHM.

Improved measurement of acoustic output using complex deconvolution of hydrophone sensitivity

The traditional method for calculating acoustic pressure amplitude is to divide a hydrophone output voltage measurement by the hydrophone sensitivity at the acoustic working frequency, but this approach neglects frequency dependence of hydrophone sensitivity. Another method is to perform a complex deconvolution between the hydrophone output waveform and the hydrophone impulse response (the inverse Fourier transform of the sensitivity). In this paper, the effects of deconvolution on measurements of peak compressional pressure (p+), peak rarefactional pressure (p_), and pulse intensity integral (PII) are studied. Time-delay spectrometry (TDS) was used to measure complex sensitivities from 1 to 40 MHz for 8 hydrophones used in medical ultrasound exposimetry. These included polyvinylidene fluoride (PVDF) spot-poled membrane, needle, capsule, and fiber-optic designs. Subsequently, the 8 hydrophones were used to measure a 4-cycle, 3 MHz pressure waveform mimicking a pulsed Doppler waveform. Acoustic parameters were measured for the 8 hydrophones using the traditional approach and deconvolution. Average measurements (across all 8 hydrophones) of acoustic parameters from deconvolved waveforms were 4.8 MPa (p+), 2.4 MPa (p_), and 0.21 mJ/cm(2) (PII). Compared with the traditional method, deconvolution reduced the coefficient of variation (ratio of standard deviation to mean across all 8 hydrophones) from 29% to 8% (p+), 39% to 13% (p_), and 58% to 10% (PII).

Challenges and regulatory considerations in the acoustic measurement of high-frequency (>20 MHz) ultrasound

This article examines the challenges associated with making acoustic output measurements at high ultrasound frequencies (>20 MHz) in the context of regulatory considerations contained in the US Food and Drug Administration industry guidance document for diagnostic ultrasound devices. Error sources in the acoustic measurement, including hydrophone calibration and spatial averaging, nonlinear distortion, and mechanical alignment, are evaluated, and the limitations of currently available acoustic measurement instruments are discussed. An uncertainty analysis of acoustic intensity and power measurements is presented, and an example uncertainty calculation is done on a hypothetical 30-MHz high-frequency ultrasound system. This analysis concludes that the estimated measurement uncertainty of the acoustic intensity is +73%/-86%, and the uncertainty in the mechanical index is +37%/-43%. These values exceed the respective levels in the Food and Drug Administration guidance document of 30% and 15%, respectively, which are more representative of the measurement uncertainty associated with characterizing lower-frequency ultrasound systems. Recommendations made for minimizing the measurement uncertainty include implementing a mechanical positioning system that has sufficient repeatability and precision, reconstructing the time-pressure waveform via deconvolution using the hydrophone frequency response, and correcting for hydrophone spatial averaging.