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

Abstract

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 (RB) model for hydrophone directivity to three alternative models: soft baffle (SB), unbaffled (UB), and rigid piston (RP). Directivity measurements were performed at 1, 2, 3, 4, 6, 8, and 10 MHz from ±70° in two orthogonal planes for two ceramic and two polymer needle hydrophones with nominal geometrical sensitive element diameters of 200, 400, 600, and 1000 μm. 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 ka < 4 (where k = 2π/λ and λ = wavelength), the RP model outperformed the other three models. For ka = 1, the average error in estimated sensitive element radius was 7% (95% Confidence Interval: 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.

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

“…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). The decline of a eff with frequency is consistent with reported measurements for needle [35, 39, 45], fiber optic [45], and membrane [42] hydrophones. (Recall that k is directly proportional to frequency.…”

“…Alternative methods for directivity measurement include a pulsed near-field method [37], a harmonic-based approach [35, 38] a time-delay-spectrometry (TDS) based method [39], and a method based on using a photoacoustic source consisting of a blackened planar surface illuminated by a laser [40, 41].…”

“…However, Wear et al . subsequently demonstrated good agreement between the RP model and experimental measurements of sensitivity of needle and reflectance-based fiber optic hydrophones (12% ± 3% root-mean-square difference in normalized sensitivity [29]) and directivity of needle hydrophones (7% ± 5% accuracy in measurement of geometrical sensitive element radius [35]).…”

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

“…The numerator and denominator of the ratio should be calculated based on the hydrophone effective sensitive element radius a eff (f), which is a function of frequency and can differ from the geometrical radius, a g [50]. Functional forms for a eff (f) have been reported for needle and fiber optic hydrophones [50,67,68]. The spatial averaging filter may be written as [50]…”

“…A formula for the frequency-dependent effective sensitive element size [50], which is required for (5), can be derived from a rigid piston model [73,74] that has been previously validated for sensitivity [75,76] and directivity [67] of needle hydrophones and sensitivity [76] and directivity [68] of fiber optic hydrophones.…”