A General Purpose Fiber-Optic Hydrophone Made of Castable Epoxy

A General Purpose Fiber-Optic Hydrophone Made of Castable Epoxy 

Steven L. Garrett, David A. Brown, B. L. Beaton(a), K. Wetterskog(a), and J. Serocki(a) 

Naval Postgraduate School, Physics Department, Code PH/Gx 

Monterey, CA 93943 

ABSTRACT 

A fiber-optic, interferometric, flexural disk hydrophone cast from an epoxy resin is described. This 

hydrophone is designed in the shape of an enclosed, hollow cylinder with pairs of flat, spiral wound coils 

of optical fiber embedded in each sensing plate. An all-fiber Michelson interferometer is used to detect the 

optical phase shift which results from pressure induced strains in the optical fiber. The sensing coils are 

positioned in the plates in a manner to enhance the acoustic response and provide cancelation of 

acceleration induced signals. An epoxy resin was chosen for its relatively high tensile strength, its low 

Young's modulus, and its ability to cure at room temperature. The acoustic sensitivity of this sensor in 

both air and water was measured to be 0.277 0.005 rad/Pa (-131.2 dB re radfliPa) which corresponds to 

a normalized sensitivity 4/p = a1n4/ap 

= -297 dB re 1 iPa1 below 1 .0 kHz. This measured result is in 

excellent agreement with simple elastic theory and the measured epoxy elastic constants. The normalized 

acceleration sensitivity is 3/4aa = ln/aa -163 dB re g1. The acceleration-to-acoustic sensitivity ratio 

(figure-of-merit) of -134 dB re g4tPa is the largest reported to date for any fiber-optic hydrophone. 

1. INTRODUCTION 

Optical fibers alone are neither intrinsically sensitive nor selective, hence it can be difficult to design a 

fiber-optic hydrophone which is sensitive to acoustic pressure while rejecting variations in ambient 

pressure and temperature, platform vibration, flow noise, or other environmental quantities1. Most of the 

published hydrophone research has involved the use of one coating to increase sensitivity to the measurand 

of interest for one on the interferometer legs and a different coating or decoupling scheme to desensitize the 

other interferometer leg which acts as a reference2'3. We feel that a better way to overcome the selectivity 

problem and to increase sensitivity to the measurand of interest is to design fiber-optic interferometric 

sensors in which both legs of the interferometer are active and respond to the measurand field with strains 

(i.e., changes in optical path-length) of opposite sign. Since the interferometer generates a signal in 

response only to differences in the optical path lengths in the two arms, the interferometer automatically 

provides common-mode rejection of the unwanted influences. The fact that the optical path-length in both 

arms change in the opposite direction also doubles the sensitivity (+6 dB) of the hydrophone over that of 

one having an identical construction (i.e., same materials, fiber length, etc.) but employing an "ideal" 

reference arm. The success of this strategy has been documented in the open literature by both the Naval 

Postgraduate Schoo1418 and Litton Guidance and Control19'2° and has produced the first fiber-optic 

sensor whose detection threshold was limited by its own temperature21. 

SPIE Vol. 1367 Fiber Optic and Laser Sensors VIII (1990) / 13

2. DUAL FLEXURAL PLATE HYDROPHONE ELEMENT DESIGN 

2 . 1 Pressure and Acceleration Response 

When .a thin circular plate is subject to a pressure differential across its surface, it will deform and 

therefore experience a surface strain which is compressive on one side and expansive on the other. This 

fact has been used previously to develop a hydrophone element using piezoelectric polymer films as the 

strain transducers22'23. We have applied this strategy to fiber-optic hydrophone designs by bonding flat 

spiral coils of optical fiber to both surfaces12 14,17, 1 8 jf the two coils act as the two legs of an 

interferometer, the plate becomes the transduction mechanism in a push-pull fiber-optic hydrophone. 

A single-plate hydrophone will also sense accelerations in the direction normal to the plate surface 

because the mass of the plate is not zero. Such an acceleration would produce a deflection which is equal 

to that produced by a pressure differential given by the product of the plate mass and its acceleration 

divided by the surface area of the plate. The acceleration sensitivity can be reduced by using two identical 

plates and four coils as shown schematically in Figures 1 and 2. When the element is subjected to an 

excess external pressure, both plates are displaced inward toward the air gap. This deformation causes the 

length ofboth Al and A2 to decrease while both Bi and B2 increase producing a "push-pull" enhancement 

of the optical path length change due to the applied pressure excess. The signs of these changes would 

reverse for a pressure reduction. This doubles the element's sensitivity to pressure over a single plate 

hydrophone of identical design. 

- If the entire sensor element is accelerated in a direction which is normal to the plate surface, then the 

two plates move in unison and the length of Al and B2 would increase while the length of A2 and Bl 

would decrease. The signs of these changes would reverse for a reversal in the direction of acceleration. 

Since the coils in each arm of the interferometer ideally experience no net change in length in either arm, 

AA1 + L\A2 = AB1 + EB2 = 0, the element is, in principal, immune to accelerations. If the plates, and the 

location of the fiber-optic coils in each plate, are not identical, the cancelation will not be optimized, so 

careful attention has been paid in the fabrication process to make these elements as symmetric as possible 

about both the air gap and the rotation axis. 

Al 

A2 

3 dB 

Bl 52 

Fig. 1. Fiber-optic Michelson interferometer. Each sensing leg consists of two flat spiral coils 4.50m in 

length and 4.0 cm in diameter. The two coils labeled Al and A2 are placed on the outer surfaces of the 

sensing plates and the two coils B 1 and B2 are placed on the inner surfaces which face the air gap. 

14 / SPIE Vol. 1367 Fiber Optic and Laser Sensors VIII (1990)

ATMOSPHERIC PRESSURE 

Sensing Plate 1 

(a) 

Fiber Coils 

:: r5::::e: Air Gap 

AirGap 

Sensing Plate 2 

(a) 

PRESSURE RESPONSE 

1 

(b) 

Sensing Plates 

(b) 

TEST DEPTH 

(C) 

(C) 

Fig. 2. (Left) Schematic representation of the four-coil, dual-plate hydrophone element showing a crosssectional 

view (a) with the dimensions of the plates, air gap, and stem (coupler housing). The location of 

the fused evanescent wave directional coupler and the fiber coils is shown in cross-section in (b) and in 

plan view in (c). 

Fig. 3. (Right) Static pressure response of a dual-plate flexural disk hydrophone. Cross-sectional views 

show the position of the plates and the air gap at (a) atmospheric pressure, (b) operating pressure, and (c) 

maximum operating depth where the plates touch. 

2.2 Dynamic Flexural Plate Theory 

We have previously constructed and tested several flexural plate hydrophone designs using 6061-T6 

aluminium and have found that their measured sensitivity and their theoretical sensitivity, based on the 

elastic properties of the plate material and the boundary conditions, are in excellent agreement for both 

hydrostatic and acoustic pressure fie1ds1214'17. The sensitivity, M = (a/P), of the dual-plate, fourcoil 

hydrophone element, assuming that the perimeter of the plate is rigidly clamped, can be expressed in 

terms of the length of the optical fiber in one leg, L, the elastic properties of the plate material, and the plate 

and fiber coils' physical dimensions. 


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)

The reader is reminded that M is the acoustic sensitivity as defined in equation (1). This result is useful in 

the determination of how successful the dual-plate design has been in canceling the acceleration induced 

forces. An ideal acceleration canceling hydrophone would have a measured Macc which would be 

identically zero. This, however, is very difficult to achieve since the physical dimensions, the plate 

boundary condition, the plate mass, and the length of fiber in each coil and their distance from the plate's 

neutral axis would all have to be identical for both sensing plates. 

2 . 2 Static Flexural Plate Theory 

In any hydrophone application one has also to consider the response to changes in operating depth. 

Because this design is "air backed", it is important to limit the deformation of the plates for two reasons. 

The first is simply structural. If the plate is constructed from a material with a yield strength, Tyjeld, the 

maximum operating pressure, m' must be limited to4, 

max 16h2 Tyjeld (5) 

3a 

The second reason the plate deformation must be limited is unique to fiber-optic hydrophones and is due to 

the fact that the maximum strain which can be tolerated by the typical glass fiber with breakage17 is 

approximately 0.5%. 

If one chooses not to employ pressure compensation techniques25 to equilibrate the static pressure 

inside and outside the hydrophone element due to the added complexity or degradation of the low 

frequency response, 1max a function of the plate dimensions and material and is inversely proportional 

to the hydrophone sensitivity. Equations (1) and (5) can be combined to produce an approximate 

expression for the normalized sensitivity of a hydrophone element of this flexural plate design. 

I M = = aln Tyjeld 

n 

4E max 

ap , A. 

ap 

(6) 

Approximations involved in deriving equation (6) include assuming a clamped boundary condition, letting 

a = b >> c, and setting factors such as (1 - 2), which are close to one, equal to one. Equation (6) 

suggests that the optimum material for this style of hydrophone element would be one which has the 

greatest ratio of yield strength to Young's modulus. Plastics tend to be about five times better than 

aluminum based on that criterion22 although the temperature dependance of their Young's modulus is 

significantly larger2 and the resulting resonance frequency and bandwidth is also lowered. 

By Hooke's Law, the maximum stresses can be related to the maximum strains and hence,17 the 

maximum strain in the optical fiber occuring at max' can be expressed using the same 

approximations as used in equation (6), for a clamped disk as 

(AL) max 

Tyjeld 

SPIE Vol 1367 Fiber Optic and Laser Sensors VIII (1990) / 17

Since the normalized sensitivity is proportional to AL/L, the sensitivity of a hydrophone element based on 

the integrated strain on the surfaces of a flexural plate will also be proportional to the ratio of yield strength 

to Young's modulus. 

It is possible to use the size of the air gap in the dual-plate hydrophone element to control the maximum 

strain experienced by the glass fiber and to provide support at depths which are greater than those given be 

equation (5)23. This is accomplished, as shown in Figure 3, by choosing the plate spacing provided by 

the air gap to be twice the displacement of a single plate at the maximum operating pressure. The 

displacement of the center of a thin clamped plate, z, is given26 as 

3(1 - 

zc= 

128Eh3 

(8) 

With the plates in contact, the hydrophone element will be protected from catastrophic failure at the 

expense of becoming acoustically insensitive until the pressure is once again reduced below 1max 

3.1 Material Selection 

3. HYDROPHONE ELEMENT CONSTRUCTION 

A castable epoxy was chosen as the capsule material so that the fiber coils could be cast directly into 

the sensing plates of the hydrophone. This also facilitated the fabrication of plates which were of uniform 

thickness. Casting the sensor capsule as a single unit also ensures that the boundary conditions at the wall 

were well matched and reproducible for both plates. 

TABLE 1. Measured Material Properties of E-CAST F-28 

Property 

Mass density 

Dynamic Young's modulus (E) 

Dynamic shear modulus (G) 

Thermal coefficient of dynamic elasticity (lnE/aT) 

Thermal coefficient of dynamic elasticity ()lnG/aT) 

Static Young's modulus (Estat) 

Tensile strength (Tyjeld) 

Poisson's ration () 

Strength-to-modulusratio (TyjeidE) 

Value 

1.15 

3.4 0.2 

1.15 0.09 

0.41 0.2 

0.39 0.2 

3.0 0.2 

6.8 0.4 

0.39 

0.02 

Units 

gm/cm3 

iO Pa 

10 Pa 

%/°C 

%/°C 

10 Pa 

10 Pa 

The process which led to the selection of E-CAST F-28 with 215 hardner27 as the hydrophone 

element body and plate material involved the testing of seventeen different room temperature castable 

epoxy compounds and composites to determine their static Young's modulus, yield strength, and dynamic 

shear and Young's moduli as a function of temperature in the range from 0°C to 25°C and for frequencies 


on the order of one kilohertz. The results of these measurements, on all seventeen materials, will be 

reported separately28 as well as the method29 and apparatus3° which was developed to automate the 

measurements of the dynamic shear and Young's moduli as a function of temperature. The static Young's 

modulus and tensile strength were determined by conventional techniques31. The measured properties of 

the E-CAST F-28 are listed in Table 1. This was the only epoxy material used in the construction of the 

capsule so in all subsequent discussion the term epoxy will be understood to refer to E-CAST F-28. 

3 . 2 Resonance Frequency 

The gravest resonance frequency of the capsule sets an upper limit on the hydrophone bandwidth and 

also provides insight into the actual boundary conditions experienced by the plates. The theoretical 

resonance frequency of the sensing plates can be calculated from equation (3). Assuming ideally clamped 

plate boundary conditions, a resonance frequency of 1 1 .0 kHz was predicted for each plate. If the 

boundary was simply supported, rather than clamped, the resonance frequency would be 5.3 kHz. The 

actual resonance frequencies for both plates were measured by tapping on the plates and recording the 

resulting free decay response with a microphone and digital storage oscilloscope. Based on the period of 

twenty cycles, the resonance frequency of the top and bottom plates was determined to be 7.79 0.03 

kHz and 7.77 0.01 kHz respectively. Since the measured resonance frequencies fall between the two 

ideal cases, the boundary conditions were considered to be a compromise between ideally clamped and 

simply supported. 

To further investigate the modes of vibration, a finite element model of the capsule was generated. 

That model predicted a resonance frequency of 7. 14 kHz which was within eight percent of the measured 

result. That small difference may be due to the perturbations induced by fiber coils and the attachment of 

the stem which housed the coupler, neither of which were included in the model. The modal shape is 

shown in the upper portion of Figure 4. It is interesting to note that a slight deformation of the outer wall 

occurs and hence the boundary condition is truly elastic33. The resonant mode for an acceleration induced 

response occurs at 8.95 kHz and is shown in the lower portion of Figure 5. If the plates are identical, this 

mode produces no net change in the interferometer's optical path length and therefore, it can be employed 

to evaluate the effectiveness of the acceleration canceling design. 

3 . 3 Interferometer Fabrication 

The objective of this sensor design was to provide a means of fabrication that was relatively simple, 

yet integrates delicate fiber optic components into a single, rugged capsule that is suitable for sustained 

underwater use. The first step in the fabrication process was the construction of the all-fiber, Michelson 

interferometer. 

The flat spiral optical fiber coils were wound by hand between two lucite plates separated by a washer 

with a thickness of approximately 300 .tm. This allowed the optical fiber which had an acrylate coating 

with an outer diameter of 250 m to pass between the plates but prevented the individual turns from 

sliding over each other during the winding process. Each coil consisted of 4.50 meters of fiber with 

approximately one centimeter of fiber between the coil pairs. The coils were bonded with thin strips of 

rubber adhesive before they were removed from the winding jig to prevent unwinding prior to their 

attachment to the sensing plates. 


After the coils were wound, the input lead of the coupler34 was spliced to a pigtailed Hitachi HL83 12G 

laser diode35. A Litton Model 87B Fiber Optic Sensor Demodulator36 was used to power to the laser 

diode, modulate the laser output wavelength by modulating the diode current, and monitor the output of 

the interferometer. A 20 kHz current modulation was applied to the laser diode. By monitoring the optical 

output of the interferometer, the fiber ends were cleaved to achieve an optimal path length difference 

between the two interferometer legs for demodulation purposes and to maximize the modulation depth 

(i.e., fringe visibility). The result was a difference in length of 2.4 cm. This was small enough to ensure 

operation within the coherence length of the laser diode and large enough to avoid the use of an 

unacceptably high laser diode current modulation amplitude. At this point the cleaved ends were protected 

by using an adhesive to bond plastic sleeves over the ends of the fiber. 

Fiber leads 7 

from couplerf 

L 

Wax disk 

Fiber coils 

(a) 

(a) 

Inner Core 

Thin epoxy layer 

Outer 

Capsule 

Shell 

Walls of sensor 

(b) 

Fig. 4. (Left) Finite element model of capsule mechanical resonances. a) Fundamental pressure 

response resonant mode. b) Fundamental acceleration response resonant mode. 

Fig. 5. (Right) Sensor inner core construction. a) Exploded view of "sandwich. b) Inner core within 

completed epoxy capsule. 

20 / SPIE Vol. 1367 Fiber Optic and Laser Sensors V/Il (1990)

3 .4 Capsule Fabrication 

The task of packaging the four interconnected fiber-optic coils and their coupler in a compact unit with 

an air gap of controlled size is not trivial. Since the two sensing coils are connected by the delicate fibers, 

the capsule can not be easily molded in two sections and later bonded into a single unit. The solution to 

this problem was to pour the capsule in one step as a single unit and create the air gap with parafin' wax 

using the "lost wax" technique. 

An inner core was constructed by making the "sandwich" shown schematically in Figure 5. The inner 

spacing disks were used to maintain an equal spacing between the coils in each plate. The circular wax 

disk was formed by pouring melted paraffin in a mold. Two 2-56x 1/4" machine screws were set into the 

wax disk to provide "feet" for the inner core shown in Figure 6. These screws provided for alignment of 

the sensor when standing upright in the outer shell mold and also provided two ducts for the removal of 

the wax after the assembled capsule had cured. 

Fig. 6. Photograph of an assembled inner core showing coupler at the left and machine screw "feet" at the 

right. 

Fig. 7. Photograph of the completed capsule. 

SPIE Vol. 1367 Fiber Optic and Laser Sensors V/il (1990) / 21

The inner core was placed in a lucite mold which could then be filled with epoxy to form the capsule. 

After the epoxy had cured, the capsule was removed from the mold and the two machine screws were 

removed from the capsule. The capsule was then placed in a vacuum oven and heated for approximately 

twelve hours at 500 C to remove the wax and post-cure the epoxy. Before encapsulation, both screw holes 

were filled with epoxy, but at this stage only one hole was filled so that the other hole could be used to 

connect the capsule to a vacuum rig for static pressure sensitivity calibration. A photograph of the 

completed capsule is shown as Figure 7. 

4. HYDROPHONE CALIBRATION AND COMPARISON TO THEORY 

The results reported in this section were obtained by the comparison technique39 in air and in water 

near atmospheric pressure in the calibrators which were small compared to the acoustic wavelengths of 

interest since the hydrophone was compact'0 (i.e., small compared to the wavelengths of interest) and its 

response is expected to be omnidirectional The hydrophone was tested in water over the range of 

temperatures from 7.5 °C to 45 °C, at ambient pressure. 

The acoustical and vibration sensitivities were measured by a fixed phase shift techniquel8 which 

involved the adjustment of a sinusoidal excitation (acoustic pressure or acceleration) until the output of the 

interferometer, observed on an oscilloscope, corresponded to an identifiable amount of optical phase shift 

(integer multiples of 2it radians per half-cycle of excitation). This technique can provide results which 

were accurate to better than and agreed with the Bessel function zero-crossing technique4'5 also to 

better than 1 %. The results reported here are therefore demodulator independent. The normalized 

sensitivity, M, was obtained from the measured sensitivities by subtracting 20 log10 (2nkL) from the 

measured sensitivities expressed in decibels. The factor of two appears due to the "double pass" in a 

Michelson interferometer. For this hydrophone, n = 1.48, A = 830 nm, and L = 9.0 m, which 

corresponds to a normalization factor is 166 dB. 

4 . 1 Comparison Calibration Standards 

Measurements of acoustic pressure sensitivity in air were made between 60 Hz and 900Hz using a 1- 

inch laboratory standard condenser microphone (Brüel & Kjer Model 4132, S/N 172894) as a transfer 

standard. The calibration of this microphone with its associated pre-amplifier (Brüel & Kjer Model 

2660), cable, and power supply (BrUel & Kjer Model 2807) was checked using a pistonphone (Brüel & 

Kjer Model 4220) for acoustic calibration prior to and immediately after use. This calibration was verified 

with a high precision reciprocity calibration of the 1-inch microphone using the BrUel & Kjer Type 4143 

Reciprocity Calibration Apparatus and two additional BrUel & Kjar 1-inch reference microphones. The 

measured sensitivity was 48.3 mV/Pa. 

Measurements of acceleration sensitivity were made between 40 Hz and 1 kHz using a piezoelectric 

accelerometer (BrUel & Kjar Type 4382) followed by a voltage pre-amplifier (Ithaco Model 1201). The 

calibration of the accelerometer, cable, and amplifier were checked 159 Hz using a calibration exciter 

(Brüel & Kjar Type 4294) which was itself check by comparison to the "chatter" method based on the 

magnitude if the Earth's gravitational acceleration41. The two calibrations were found to agree to within 

2%. 


Acoustic calibrations in water were made between 14 Hz and 300 Hz in a water-filled compliant tube 

calibrator2. A Brüel & Kjar Type 8103 hydrophone followed by an Ithaco Model 1201 pre-amplifier 

served as the reference hydrophone. The hydrophone, cable, and pre-amplifier were calibrated in air using 

a BrUel & Kjer Type 4223 Calibrator. 

4 . 2 Acoustic Sensitivity 

The acoustical sensitivity of the hydrophone capsule measured in water and air near room temperature 

are summarized in Figure 8, and yield an average sensitivity from 14 Hz to 900 Hz of 0.277 0.005 

radians/Pa (±0.16 dB), for peak acoustic pressure amplitudes in the range of 1 1 to 95 Pa in air and 45 to 

480 Pa in water. As expected, the sensitivities measured in air and water are identical. The corresponding 

normalized acoustic sensitivity is d/dp = a1n4/ap = -297 dB re 1 pPa1. The predicted sensitivity based 

on equation (1) is 0.263 radians per Pascal, where we have set n = 1.48, L = 4.5 m, = 0.39, a = 2.0 

cm, b = 0.82 cm, c = 1.96 cm, E = 3.4 x iO Pa, h = t/2 = 0.25 cm, and = 830 nm. 

This excellent agreement between measurement and theory is not fortuitous! Although the assumption 

underlying equation (1) is that of an ideally clamped boundary condition, the prefactor for equation (2), 

which expresses the sensitivity in terms of the fiber properties and the flexural plate resonance frequency, 

is insensitive to the specific boundary condition. For the perfectly clamped case it is 0.52 and for the 

simply supported case it is 0.48. If we take the intermediate case prefactor to be 0.5 and include a 10% 

increase in the fiber diameter (250 tim) to allow for wrapping and adhesive, the measured resonance 

frequency (7.8 kHz) yields a boundary condition independent sensitivity of 0.29 radians per Pascal. 

4 . 3 Static Pressure Sensitivity 

As shown in Table 1, the static Young's modulus of the plate material was measured to be 12% lower 

than the dynamic Young's modulus which suggests, based on equation (1), that the static pressure 

sensitivity should be 1 2% greater than the acoustic sensitivity. This was measured by evacuating the air 

gap within capsule through one of the wax drainage ducts and recording the optical fringes on a strip chart 

recorder while the pressure was slowly equilibrated. The static sensitivity, fl radians per Pascal 

can be expressed as 

Mstatic = 1.856 x i0 -u--- (9) 

AP 

where N is the number of interferometric fringes produced while the pressure is changed by an amount, 

Al?, expressed in inches of mercury. The prefactor in (9) arises from the fact that a "fringe" corresponds 

to 2it radians of optical phase shift and 1013 mbar equals 29.92 inches Hg. 

The capsule was evacuated to 0. 1 in Hg and was allowed to leak at an initial rate of 0.6 in Hg per 

minute. Three thousand two hundred ninety-two fringes were counted when the pressure reached 20.0 

0.2 in Hg. This produced a static sensitivity of 0.305 radians per Pascal which is about 10% higher than 

the acoustic measurements. This result very close to what would be expected since the measured 

differences between the static and dynamic Young's moduli differ by 12%. 


C. 5 

C-. 

Ct 

D.. — 

P 

> 

C.3— 

am 4t am ,v,. - - 

cL 'p w' 

Cs) 

a) 

Li) 

0 

0.2 

U) 

C 

0 

100 

Freouenc, hertz 

DOD 

Fig. 8 Measured acoustic sensitivity of the hydrophone capsule in air and water. The solid line represents 

a best fit to the measured data and has a value of 0.277 0.005 rad/Pa. The water measurements are 

represented by the filled circles and were made at 23° C. The air measurements are represented by the 

open diamonds and were made at 22° C. 

4 . 4 Temperature Coefficient of Acoustic Sensitivity 

The hydrophone capsule was calibrated in water over the temperature range from 7.5° C to 45° C 

(45.5° F to 1 1 3° F) and the sensitivity was found to change at the rate of +1 .1% /°C . That is, the 

sensitivity of the capsule increases with increasing temperature (+0. 10 dB/°C). This result includes the 

correction for the temperature coefficient of the sensitivity of the Bruel and Kjer Type 8103 which is given 

by the manufacturer as -0.03 dB/°C. 

Based on the modulus measurements of the epoxy18'23 shown in Table 1, one would expect a 

temperature coefficient of acoustic sensitivity that was equal to the measured temperature coefficient of the 

Young's modulus which was only +0.4 %/°C. In an attempt to check this result, the temperature 

coefficient of the elastic moduli were remeasured using a variation of technique and reaffirmed the original 

results. 

At the present time, the best available explanation for this discrepency is that the temperature 

dependance of the Young's modulus of the epoxy also effected the boundary conditions (and the 

resonance frequency) and therefore had a greater effect than would be predicted from consideration of 

equations (1) or (2). The finite element model in Figure 5a tends to reinforce this hypothesis since the 

elastic response of the junction of the two plates is clearly also flexing. Further studies will be attempted 

to resolve and quantify this discrepancy. 

24 / SPIE Vol. 1367 Fiber Optic and Laser Sensors V/li (1990)

4 . 5 Acceleration Sensitivity and Cancelation Figure-of-Merit 

The hydrophone capsule was mounted on the surface of an APS 120S shaker table using a support 

ring with two BrUel and Kjar Type 4382 piezoelectric accelerometers as shown in Figure 9. The use of 

two accelerometers ensured that the acceleration experienced by the hydrophone capsule mounted between 

the two accelerometers was uniform. The results of these measurements for accelerations in the direction 

normal to the sensor plate surfaces is shown in Figure 10. The filled dots represent the measurement 

when the capsule stem was supported and show an average acceleration sensitivity between 70 Hz and 900 

Hz of 1.4 0.6 rad/g (-163 dB re 1 g1), where g is the acceleration due to gravity (9.8 m/sec2). For 

comparison, the predicted single-plate, dual-coil acceleration sensitivity, based on equation (4) is shown as 

a solid line at 7.4 rad/g. The X's represent the measured acceleration sensitivity of the capsule when the 

stem containing the coupler and about 1 .5 cm of optical fiber is not supported on the shaker table. It is 

clear that the stem has a cantilever flexural resonance at about 300 Hz which would significantly degrade 

the acceleration response if neglected. The transverse acceleration sensitivity was measured by mounting 

the capsule on the shaker table with the stem pointing upward. The average acceleration sensitivity in this 

orientation, between 250 Hz and 1 kHz was determined to be 1 .8 0.7 rad/g (-161 dB re 1 g1), again 

with the stem unsupported. 

To estimate the success of the acceleration canceling design, one can form the ratio of the acceleration 

output when the two plates are "wired" to enhance acceleration sensitivity44 (and cancel pressure) to the 

output when the plates are in their acceleration canceling configuration. If both plates were used to 

measure acceleration the sensitivity would be twice the single plate sensitivity or 14.8 rad/g. Since the 

average measured acceleration sensitivity was 1.4 rad/g, the design can be said to provide slightly better 

than 20 dB of acceleration rejection independent of any additional vibration isolating mounting. 

Figure 9. Photograph of the hydrophone capsule mounted on the shaker table with two piezoelectric 

accelerometers. 


ic.D 

> 

.-) 

C 

Cr) 

C 

0 

.-) 

0 

a) 

a) 

0 

e. 

6.0 

4.0 

2.0 

liii ZI1II 1ZI ZI 1. 

x 

xXZ) 

. 

--;-;- 

T 

0.0 

40 ido 

. 

> 

Figure 10. Axial acceleration sensitivity. The filled dots represent the measurement when the capsule 

stem was supported and show an average acceleration sensitivity between 70 Hz and 900 Hz of 1.4 0.6 

rad/g, represented by the dashed line. For comparison, the predicted single-plate, dual-coil acceleration 

sensitivity, based on equation (4) is shown as a solid line at 7.4 rad/g. The X's represent the measured 

acceleration sensitivity of the capsule when the stem containing the coupler and about 1.5 cm of optical 

fiber is not supported on the shaker table. 

In a vibrationally noisy environment, the ratio of the acceleration sensitivity to the acoustic sensitivity 

to is a good figure-of-merit for comparison of their noise-limited performance. Since this ratio removes 

the output parameter (volts or radians), it is also useful for comparing fiber-optic hydrophones to 

piezoelectric hydrophones. Reporting this ratio in decibels, the hydrophone capsule discussed in this 

paper has a figure-of-merit is -134 dB re g/Pa. This is 43 dB better than the Naval Research 

Laboratory's planar flexible fiber-optic interferometric hydrophone and 57 dB better than the piezoelectric 

polymer (PVF2) hydrophone of similar geometry3. An overall comparison of the NRL and NPS designs 

is given in Table 2. 

TABLE 2. NPS and NRL Planar Hydrophones 

Performance measurement NRL NPS NPS Advantage 

Normalized acoustic sensitivity (dB re: lpPa1) -321 -297 

Normalized acceleration sensitivity (dB re: lj.iPa1) -144 -163 

Acoustic-to-acceleration FOM (dB re: g/jiPa) -177 -134 

x 

Table 2. The NPS flexural disk hydrophone is 16 times more sensitive to pressure and 9 time less 

sensitive to acceleration than the NRL spiral3 giving the NPS design a factor of 43 dB improvement over 

the spiral in a vibrationally noisy application. 

. 

>( 

Freauenc, Kertz 

. 

: 

iiiIziiziizI Iz1 1ZI I 11 1 

cT . 

: 

1000 

(dB) 

+24 

+19 

+43 

26 1 SPIE Vol. 1367 Fiber Optic and Laser Sensors VIII (1990)

5. DISCUSSIONOF RESULTS 

The results reported here represent the highest normalized sensitivity ever reported for a fiber-optic 

hydrophone designed to operate under conditions of static pressure higher than 500 psi. It also represents 

the best acceleration cancellation figure of merit for any fiber-optic hydrophone. One additional feature of 

the design which should be considered equally important is that its performance is in excellent agreement 

with simple elastic theory so that hydrophone designers can scale these results as necessary for other 

applications requiring differing materials, bandwidth, depth tolerance, etc., with a good deal of 

confidence. 

The fact that this hydrophone capsule can be fabricated as a single unit cast out of epoxy suggests that 

its cost for mass production may be significantly lower that other hydrophone designs requiring machined, 

thin, air-backed, cylindrical mandrils which may require subsequent fabrication steps that make internal 

access for fiber winding, and thus push-pull performance impractical. 

Thus far, the discussion of acoustic performance has concentrated on the normalized sensitivity. That 

parameter provides a comparison between design strategies on a meter-for-meter basis. We would like to 

conclude this discussion with comparison of the NPS flexural disk and NRL flexible planar designs which 

also introduces the effects of "winding density" since this allows comparison of the actual available phase 

modulation (i.e., signal). The overall available phase modulation amplitude determines the detection 

threshold if one assumes a given demodulator detection threshold. Similarly, one could use an acoustic 

basis to set the detection threshold and allow the hydrophone sensitivity to dictate the required demodulator 

performance, which then determines the cost and complexity of the demodulator, laser diodes, etc. 

6. ACKNOWLEDGEMENTS 

Over the past six years this work has been supported by the Office of Naval Research - Physics 

Division, the Office of Naval Technology, the Space and Naval Warfare Systems Command, the Naval 

Sea Systems Command, and the Naval Postgraduate School Direct Funded Research Program. 

7. REFERENCES 

a) Lieutenant, U. S. Navy 

1 . T. G. Giallorenzi, A. Dandridge, and A. D. Kersey, "Interferometric and intensity sensors become 

more sophisticated" Laser Focus World 27(7), 137-143 (July, 1989). 

2. N. Lagakos, A. Dandridge, and J. A. Bucaro, "Optimizing fiber coatings for interferometric acoustic 

sensing (U)", U. S. Navy J. Underwater Acoustics 37(3), 233-254 (July,1987). 

3 . N. Lagakos, P. Ehrenfeuchter, T. R. Hickman, A. Tveten, and J. A. Bucaro, "Planar flexible fiberoptic 

interferometric acoustic sensor", Opt. Lett. 13(9), 788-790; OFC '90 Tech. Digest (22-26 Jan 

1990, San Francisco, CA) p. 46; N. Lagokos, J. A. Bucaro, P. A. Ehrenfeuchter, T. R. Hickman, 

A. B. Tveten, and A. Dandridge, "Planar-conformal fiber optic acoustic sensing element", in Fiber 

Optic Smart Structures and Skins II, Proc. Soc. Photo-Optical Instrumentation Eng. (SPIE) 1170, 

472-477, (1989). 


4. G. B. Mills, S. L. Garrett, and E. F. Carome, "Fiber optic gradient hydrophone", in Fiber Optic and 

Laser Sensors II, Proc. Soc. Photo-Optical Instrumentation Eng. (SPIE) 478, 98-103 (1984). 

5 . G. B. Mills, "Fiber optic gradient hydrophone", Master's thesis, Naval Postgraduate School (June, 

1984), DTIC Report No. A 143 975. 

6. G. E. MacDonald, "Fiber optic gradient hydrophone construction and calibration for sea trials", 

Master's thesis, Naval Postgraduate School (March, 1985), DTIC Report No. A 156 469. 

7 . P. A. Feldmann, "Construction of a fiber optic gradient hydrophone using a Michelson 

configuration", Master's thesis, Naval Postgraduate School (March, 1986), DTIC Report No. A 167 

892. 

8. D. L. Gardner, T. Hofler, S. R. Baker, R. K. Yarber, and S. L. Garrett, "A fiber-optic 

interferometric seismometer", J. Lightwave Tech. 5(7), 953-960 (1987). 

9. D. L. Gardner, and S. L. Garrett, "Fiber optic seismic sensor", in Fiber Optic and Laser Sensors V, 

Proc.Soc. Photo-Optical Instrumentation Eng. (SPIE) 838, 27 1 -278 (1987). 

10. D. L. Gardner, "A fiber-optic interferometric seismic sensor with hydrophone applications", Ph.D. 

thesis, Naval Postgraduate School (September, 1987), DTIC Report No. B 1 12 487 

1 1 . D. L. Gardner and S. L. Garrett, "High sensitivity fiber-optic compact directional hydrophone (U)", 

U. S. Navy J. Underwater Acoust. 38(1), 1-23 (1988). 

12. D. A. Brown, T. Hofler, and S. L. Garrett, "Fiber optic flexural disk microphone", in Fiber Optic 

and Laser Sensors IV, Proc. Soc. Photo-Optical Instrumentation Eng. (SPIE) 985, 172-182 (1988). 

1 3 . D. A. Brown, "A fiber-optic flexural disk hydrophone", Master's thesis, Naval Postgraduate School 

(March, 1989), DTIC Report No. B 132 243. 

14. J. A. Flayharty and B. M. Fitzgerald, "Design and fabrication of a fiber optic acceleration canceling 

hydrophone", Master's thesis, Naval Postgraduate School (September, 1989), DTIC Report No. B 

136 179. 

1 5. D. A. Danielson and S. L.Garrett, "Fiber-optic ellipsoidal flextensional hydrophones", J. Lightwave 

Tech. 7(12), 1995-2002 (1989). 

16. D. A. Brown, S. L. Garrett, and D. A. Danielson, "Fiber-optic oblate flextensional hydrophone", in 

Fiber Optic and Laser Sensors VII, Proc. Soc. Photo-Optical Instrumentation Eng. (SPIE) 1169, 

240-248 (1989). 

17. D. A. Brown, T. Hofler, and S. L. Garrett, "High sensitivity, fiber-optic, flexural disk hydrophone 

with reduced acceleration response", Fiber and Integrated Optics 8(3), 169-191 (1989). 

1 8. K. Wetterskog, B. L. Beaton, and J. Serocki, "A fiber-optic acceleration canceling hydrophone made 

of a castable epoxy", Master's thesis, Naval Postgraduate School (June, 1990). 

19. M. R. Layton, B. A. Danver, J. D. Lastofka, D. P. Bevan, and E. F. Carome, "A practical fiber 

optic accelerometer", in Fiber Optic and Laser Sensors V, Proc. Soc. Photo-Optical Instrumentation 

Eng. (SPIE) 838, 279-284 (1987). 

20. M. R. Layton, A. D. Meyer, D. P. Bevan, and J. S. Bunn, "Multiplexed fiber optic hydrophones", 

DOD Fiber Optics Conference '88 (22-25 Mar 1988, McLean, VA) p. 85. 

21. T. J. Hofler and S. L. Garrett, "Thermal noise in a fiber optic sensor", J. Acoust. Soc. Am. 84(2), 

471-475 (1988); J. Acoust. Soc. Am. 87(3), 1362-1365 (1990). 

22. T. Sullivan and J. Powers, "Piezoelectric polymer flexural disk hydrophone", J. Acoust. Soc. Am. 

63(5), 1396-1401 (1978). 


23. D. Ricketts, "Model for a piezoelectric polymer flexural plate hydrophone", J. Acoust. Soc. Am. 

70(4), 929-935 (1981). 

24. S. Timoshenko and S. Woinowsky-Kreiger, Theory of Plates and Shells, 2nd edition (McGraw- 

Hill, 1959), pp. 51-58. 

25. C. L. LeBlanc, Handbook of Hydrophone Element Design Technology, (Naval Underwater 

Systems Center Technical Document 5813, 1 1 October 1978), 

26. A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity, 4th edition (Dover, 1944), p. 

484. 

27. United Resin Corporation, 2730 S. Harbour Blvd., Santa Ana, CA 92704. 

28. S. L. Garrett, D. A. Brown, J. Serocki, K. Wetterskog, and B. L. Beaton, "Elastic moduli of 

castable epoxies", submitted to the U. S. Navy Journal of Underwater Acoustics. 

29. S. L. Garrett, "Resonant acoustic determination of elastic moduli", J. Acoust. Soc. Am. 88(1), 210- 

221 (1990). 

30. Mechanical Measurement Devices, Model 3012A Dynamic Modulus Measurement System, P. 0. Box 

8716b, Monterey, CA 93943. 

3 1 . ASTM D 638, 1989 Annual Book ofASTM Standards,(American Society for Testing and Materials, 

1989), Section 8, Plastics, volume 08.01, pp. 156-166. 

32. Coming Glass Works, Telecommunications Prothicts Division, Coming, NY 14831. 

33. A. W. Leissa, Vibration ofPlates, NASA Tech Doc: SP-160-N70-18461 (1969), 

34. Interfuse 945 Series single mode coupler, Amphenol Corp., Lisle, IL 60532. 

3 5 . Seastar Optics, Model PT-450, Sidney, B .C., Canada V8L 31. 

36. Litton Guidance and Control Systems, Woodland Hills, CA 91367. 

37. Hexcel Corporation, Chemical Products Division, Chatsworth, CA 91311. 

38. International Transducer Corporation, Goleta, CA 93117. 

39. R. J. Bobber, Underwater Acoustic Measurements, (Naval Research Laboratory, 1970). 

40. J. Lighthill, Waves in Fluids, (Cambridge University Press, 1978), 

41. J. D. Ramboz, "Calibration of pickups", in Shock and Vibration Handbook, 2nd ed., C. M. Harris 

and C. E. Crede, editors (McGraw-Hill, 1976), pg. 18-14. 

42. M. B. Johnson, "Reciprocity calibration in a compliant cylindrical tube", Master's Thesis, Naval 

Postgraduate School, Monterey, CA, June, 1985; DTIC Report No. A158-998. 

43. D. A. Brown and S. L. Garrett, "An interferometric fiber optic accelerometer", in Fiber Optic and 

Laser Sensors VIII, Proc. Soc. Photo-Optical Instrumentation Eng. (SPIE) 1367-34, (1990), in 

press.

A General Purpose Fiber-Optic Hydrophone Made of Castable Epoxy

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?