Rigid piston approximation for computing the transfer function and angular response of a fiber-optic hydrophone

The transfer function of a fiber-optic hydrophone (FOH) is computed for various fiber core radii. The hydrophone is modeled as a rigid disk, with plane waves impinging at normal or oblique incidence. The total sound field is written as the sum of the incident field and the field diffracted from the hydrophone. The diffracted field is approximated by the field generated by a vibrating planar piston in an infinite rigid baffle. For normal incidence and a pointlike fiber core, an analytical solution is presented. For finite fiber core radii, and for oblique incidence, the transfer functions are computed numerically. The calculated transfer functions exhibit an oscillatory frequency dependency that is most pronounced for small fiber cores. The solution for a core radius of 2.5 microm can be very well approximated by the analytical solution for a pointlike core at frequencies of up to 30 MHz. The results for normal incidence can be directly employed to deconvolute ultrasonic pressure signals measured with an FOH. From the transfer functions for oblique incidence, the angular response of the hydrophone is calculated. The angular response obtained here differs significantly from the model commonly used for piezoelectric hydrophones. The effective hydrophone radius derived from the angular response shows a strong frequency dependency. For low frequencies, it is found to be larger than the outer fiber radius, whereas it generally lies between the outer radius and the fiber core radius for frequencies above 10 MHz.