Directivity and Frequency-Dependent Effective Sensitive Element Size of Membrane Hydrophones: Theory Versus Experiment

Abstract

It is important to know hydrophone frequency-dependent effective sensitive element size in order to account for spatial averaging artifacts in acoustic output measurements. Frequency-dependent effective sensitive element size may be obtained from hydrophone directivity measurements. Directivity was measured at 1, 2, 3, 4, 6, 8, and 10 MHz from ±60° in two orthogonal planes for 8 membrane hydrophones with nominal geometrical sensitive element radii (a g) ranging from 100 to 500 μm. The mean precision of directivity measurements (obtained from four repeat measurements at each frequency and angle) averaged over all frequencies, angles, and hydrophones was 5.8%. Frequency-dependent effective hydrophone sensitive element radii a eff (f) were estimated by fitting the theoretical directional response for a disk receiver to directivity measurements using the sensitive element radius (a) as an adjustable parameter. For the 8 hydrophones in aggregate, the relative difference between effective and geometrical sensitive element radii, (a eff-a g) / a g , was fit to C / (ka g) n where k = 2π/λ and λ = wavelength. The functional fit yielded C = 1.89 and n = 1.36. The root mean square difference between data and model was 34%. It was shown that, for a given value for a g , a eff (f) for membrane hydrophones far exceeds that for needle hydrophones at low frequencies (e.g., < 4 MHz when a g = 100 μm). This empirical model for a eff (f) provides information required for compensation of spatial averaging artifacts in acoustic output measurements and is useful for choosing an appropriate sensitive element size for a given experiment.

Solvability for Photoacoustic Imaging with Idealized Piezoelectric Sensors

“…The directional response for plane waves derived in section 3 and displayed in Figure 2 matches the experimental measurements carried out by other researchers [44,40,41,11]. Specifically, design considerations concerning the mechanical and electrical properties of the piezoelectric film and backing layer play a role in the appearance of critical angles where the sensitivity of the sensor vanishes.…”

“…They measure a surrogate for pressure that depends on the actual transducer mechanism. The most common mechanisms for ultrasound applications are based on the piezoelectric effect [44,40,41], on Fabry-Perot interferometry [9,14,50,22] or on fiber-optic refractometry [43,42,45]. In [3] we formulated a model specifically tailored to the Fabry-Perot sensor design.…”

“…Hence, we do not account for resolution limitations due to the finite size of sensing elements. See [47,23,36,29,40,41] for investigations concerning this issue. We also assume that the domain to be imaged is fully enclosed by the detection surface.…”

Correction for Spatial Averaging Artifacts in Hydrophone Measurements of High-Intensity Therapeutic Ultrasound: An Inverse Filter Approach

“…The spatial averaging filter requires knowledge of the frequency-dependent hydrophone effective sensitive element radius, which can obtained from a rigid piston model for needle and fiber optic hydrophones [50] or from empirical data for membrane hydrophones [107].…”

Localized Measurement of a Sub-Nanosecond Shockwave Pressure Rise Time

“…There are multiple approaches to measure these transient signals, like piezoelectric sensor [9], [10], PVDF membrane [11]- [13] or needle hydrophone [14], [15] and fiber optic hydrophone [16]- [18], all with their own advantages and drawbacks. In the case considered here, i. e. measurement of shockwave emitted during laser induced breakdown in water, the fiber optic probe hydrophone comes with a key advantagethe ability to measure and withstand very quick changes of very high positive or negative pressures that are generated during breakdown [19].…”