A General Purpose Fiber-Optic Hydrophone Made of Castable Epoxy

M=a
8icnL
2
- b2 - c2)
(1)
Here 4 represents the optical pathlength in radians and P is the applied excess acoustic pressure. E and
are the Young's modulus and Poisson's ratio of the plate material, 2h is the plate thickness, and a,b, and
c, are the radius of the plate and the maximum and minimum spiral coil radii respectively. The wavelength
of light in vacuum is , and n is the effective index of refraction of the optical fiber core. The derivation of
this result and similar results for simply supported plates with bonded optical fiber spirals have been
published elsewhere13'16'17.
It is conventional to normalize this sensitivity to provide a comparison with other fiber-optic
hydrophones that may use different mechanical designs, fiber lengths, optical wavelengths, and glasses
with different indices of refraction. The normalized sensitivity, M = = is
determined by dividing the acoustic sensitivity by the optical path length (in radians of phase) of one leg of
the sensor. This convention has been used because most early interferometric sensors use one leg as a
reference leg. The sensitivity can be expressed in a particularly simple form for two plates totally wrapped
on each side with optical fiber and having ideal clamped boundary conditions as
M=O.52—
(2)
Hence, the product of the sensitivity and the square of the fundamental plate resonance frequency, f02, is a
constant which depends only upon the wavenumber of the light in the fiber, kg 2ltflIX, the density of the
plate material, p, and the outside diameter of the optical fiber, D. For the simply supported case, the prefactor
in (2) is equal to 0. 125 (5 + c)/(1 + ). When 0.27, the pre-factors for both cases are identical.
The fundamental resonance frequency of the plate is given by
f0=A2J1—4F E (3)
ita2 V 12(1-&)p
where A2 = 10.2 for a clamped plate. For a simply supported plate, A2 4.9, and is a very weak function
of Poisson's ratio.
By Newton's Second Law, the acceleration, a, of a plate normal to its surface produces a force which
is the product of the mass of the plate and its acceleration. That force, divided by the area of the plate,
produces an equivalent acceleration induced pressure. One can use this "equivalence" to write an
expression for the acceleration sensitivity, Ma, for a plate of mass m = 2itpha2.
M=2.=2Mhp
(4)
16 / SP/E Vol. 1367 Fiber Optic and Laser Sensors Vii (1990)