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

Abstract

The goal of this work was to measure 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 μm diameter core and a 125 μm 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 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, directivity of a reflectance-based fiber-optic hydrophone may be best estimated by the RP model.

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

“…The rigid piston (RP) model [49, 50] has been validated for predicting sensitivity [51, 52] and directivity [53] of many needle hydrophones and sensitivity [52] and directivity [54] of a reflectance-based fiber optic hydrophone. One RP model expresses spatiotemporal response in the form of an integral that may be evaluated numerically [50].…”

“…The present paper investigates the validity of the separable form of the spatiotemporal response through comparison to a theoretical rigid piston hydrophone spatiotemporal response [49, 50] that does not assume separability and has been validated for predicting sensitivity [51, 52] and directivity [53] of needle hydrophones and sensitivity [52] and directivity [54] of reflectance-based fiber-optic hydrophones. This paper is relevant to reflectance-based fiber optic hydrophones that measure changes in a fluid refractive index caused by pressure changes [20, 25, 54-57]. This paper does not consider fiber optic displacement sensors [58].…”

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.…”

“…The values chosen for the present investigation were A = 1.85 and B = 1.05, corresponding to |θ| < 30°. This formula applies to needle hydrophones and reflectance-based fiber optic hydrophones that measure changes in a fluid refractive index caused by pressure changes [27,30,31,68,77,78]. It does not apply to fiber optic displacement sensors [79], Fabry-Perot interferometric fiber optic hydrophones [57,[80][81][82][83], other Fabry-Perot sensors [84,85], or other fiber optic designs [86][87][88].…”