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

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 I: Theory, Spatial-Averaging Correction Formulas, and Criteria for Sensitive Element Size

This article reports spatiotemporal deconvolution methods and simple empirical formulas to correct pressure and beamwidth measurements for spatial averaging across a hydrophone sensitive element. Readers who are uninterested in hydrophone theory may proceed directly to Appendix A for an easy method to estimate spatial-averaging correction factors. Hydrophones were modeled as angular spectrum filters. Simulations modeled nine circular transducers (1-10 MHz; F/1.4-F/3.2) driven at six power levels and measured with eight hydrophones (432 beam/hydrophone combinations). For example, the model predicts that if a 200- [Formula: see text] membrane hydrophone measures a moderately nonlinear 5-MHz beam from an F/1 transducer, spatial-averaging correction factors are 33% (peak compressional pressure or p_c ), 18% (peak rarefactional pressure or p ), and 18% (full width half maximum or FWHM). Theoretical and experimental estimates of spatial-averaging correction factors to were in good agreement (within 5%) for linear and moderately nonlinear signals. Criteria for maximum appropriate hydrophone sensitive element size as functions of experimental parameters were derived. Unlike the oft-cited International Electrotechnical Commission (IEC) criterion, the new criteria were derived for focusing rather than planar transducers and can accommodate nonlinear signals in addition to linear signals. Responsible reporting of hydrophone-based pressure and beamwidth measurements should always acknowledge spatial-averaging considerations.