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).