A LINE ARRAY OF DIRECTIONAL HYDROPHONES FOR IMPROVED DETECTION OF EMERGENCY LOCATOR BEACONS

The U.S Navy’s system for locating black boxes from downed aircraft is the Towed Pinger Locator 25 (TPL-25). The TPL-25 is a kite-shaped fiberglass shell that is towed behind a surface vessel while its single omnidirectional hydrophone listens for the signal being transmitted from the emergency beacon on one of the aircraft’s black boxes. Recovery of the black boxes is critical to an accident investigation yet the window in which to locate the black box is short, typically only 30 days, and the success of the TPL-25 is limited as evidenced by the unsuccessful search for Malaysia Airlines Flight 370 in 2014. This thesis explores how replacing the TPL-25’s single omnidirectional hydrophone with a device that has an increased directivity index, specifically with a linear array of directional multimode hydrophones, can increase the detection range of the TPL-25.

iii ACKNOWLEDGMENTS As my thesis work comes to an end, I would like to express my deepest gratitude to those who supported me throughout this journey.
To my major professor Dr. Harold Vincent who taught many of my courses, served as my advisor, and inspired me by his enthusiasm for acoustics.
To my professor Dr. Steven Crocker who gave me the idea for my initial study and later helped me when I was struggling with three-dimensional plots in MATLAB.
To the professors at the Naval Post Graduate School who taught my first graduate level courses and introduced me to acoustics. To the DeSantis Foundation for the generous donation that allowed me to purchase the materials I needed.
And finally, to my family -my husband Bruce, our children Kyle and Evan, and my parents Merrill and Pat Louks -for their patience, understanding and support throughout the many years it took me to complete my degree, and most importantly for always believing in me. To them, I dedicate this work.      x

Background
A towed pinger locator is a towed underwater platform used to locate cockpit voice recorders and flight data recorders -commonly referred to as black boxesfrom downed aircraft. The towed pinger locator's hydrodynamic shell is connected by a cable and winch to a surface vessel, and towed across the search area. An acoustic listening device mounted under the towed pinger locator listens for the acoustic signal ("ping") being transmitted by an acoustic transmitter that is fitted to the aircraft's black boxes. These acoustic transmitters -commonly referred to as emergency beacons, pingers, or underwater locator beacons (ULBs) -transmit at a frequency of around 37.5 kHz (BEA, 2011). Figure 1 contains a pictorial of a towed pinger locator being used in a search for a flight recorder.

The Emergency Beacon's Transmission Signal
In August 2011, the Bureau d'Enquêtes et d'Analyses pour la sécurité de l'aviation civile (translated as "Bureau of Enquiry and Analysis for civil aviation safety") called for the measurement of aircraft emergency beacons. Six Dukane DK 120 and six Benthos ELP 362 D emergency beacons were included in this test. The beacons and the hydrophones were immersed to 10 m with a separation distance of 3.75 m. Table 1 shows the results of the measurement, and is included to provide additional details regarding the beacon's transmission signal.

The Towed Pinger Locator 25
The U.S Navy's system for locating black boxes from downed aircraft is the Towed Pinger Locator 25 (TPL-25). The TPL-25, which was first fielded in 2010, is shown in Figure 2. It is the Navy's fourth generation towed pinger locator -the first  The TPL-25 consists of a tow fish (a 70-lb fiberglass shell, 30 inches in length and 35 inches in diameter 2 ), tow cable, winch, hydraulic power unit, generator, and topside control console. It is towed behind a vessel at slow speeds, generally from 1 to 5 knots, depending on the depth. The TPL-25 contains a single omnidirectional hydrophone (listening device) within a 1-standard atmosphere titanium housing rated for a maximum depth of 6,100 meters (Sasse, 2014). The TPL-25 therefore has a maximum operating depth of 6,100 meters or 20,000 feet. Recovery of a downed aircraft's black boxes is critical to an accident investigation because the information they provide is essential to determining the cause of the accident. However, the window in which to locate the black boxes is short. The typical battery on a black box's emergency beacon begins to fade after 35 days and loses meaningful output after 38 to 40 days (Bloomberg, 2014).

Significance
One way to increase the chances of locating the emergency beacons during this window of time is to increase the detection range of the TPL-25. Designing an improved sonar system for the TPL-25, one that that will increase the TPL-25's detection range, is the goal of this thesis.

Initial Study
In 2015, a preliminary analysis of the performance of the existing TPL-25 system and the performance of an upgraded design that incorporated a linear array of 32 omnidirectional hydrophones was conducted (Alvanas, 2015).

Hypothesis
Detection range ( ) can be predicted through the Transmission Loss (TL) parameter (Urick p. 17, 1983) of the passive sonar equation which is defined by Urick (p. 22, 1983) as: This equation is discussed in more detail later in the thesis. For now, it is only necessary to understand that, based upon this equation, Transmission Loss (TL), and therefore detection range ( ), can be increased if Directivity Index (DI) is increased.
The hypothesis of this thesis is that if, as shown in the initial study, replacing the TPL-25's single omnidirectional hydrophone with a linear array of omnidirectional hydrophones can affectedly increase the detection range ( ) of the TPL-25, then replacing the single hydrophone with a linear array of directional hydrophones (which has a higher Directivity Index (DI) than a linear array of omnidirectional hydrophones) will increase the detection range ( ) even more dramatically.

Methodology
The use of multimode technology as a means to increase the directionality of a transducer was first researched.
This multimode technology was then applied to a single-cylinder hydrophone prototype. The theoretical directivity (beam pattern and directivity index) of the single-cylinder multimode hydrophone prototype was predicted, the prototype was fabricated, the prototype was tested in an acoustic test tank, the data collected in the tank was processed using MATLAB, and the actual directivity was compared to the predicted directivity.
The multimode technology was then applied to a multi-cylinder linear hydrophone array. The array was designed using SOLIDWORKS. And again, the theoretical directivity (beam pattern and directivity index) of the linear hydrophone array was predicted, the array was fabricated, the array was tested in an acoustic test tank, the data collected in the tank was processed using MATLAB, and the actual directivity was compared to the predicted directivity.
Finally, detection ranges were estimated for the existing TPL-25 system and for the TPL-25 with the proposed multi-cylinder multimode linear hydrophone array.

Thesis Outline
The thesis contains thirteen chapters. Chapter 2 provides an overview of the This chapter includes an overview of the technology that was researched and applied in the following chapters. A number of the terms introduced in this chapter are applicable to both projectors (transmitting transducers) and hydrophones (receiving transducers), however, they are defined here, and used later, primarily in the context of hydrophones.

Spherical Coordinate System
The spherical coordinate system shown in Figure 5 is the coordinate system that is used throughout this thesis to describe the direction of arrival of a sound wave relative to an acoustic aperture. The acoustic aperture is positioned in the coordinate system so that its acoustic center is located at point x=y=z=0 and its length extends along the y-axis. The vector points to the sound wave's direction of arrival. The angle phi, ∅, is considered the azimuthal angle, and the angle theta, , is considered the elevation angle.

Directionality
Directionality of an acoustic aperture refers to its ability to focus in a particular direction. Directionality increases sensitivity in the direction of interest, and reduces the noise arriving from directions that are not of interest, therefore increasing the overall signal-to-noise ratio (SNR). There are a number of ways to quantify directionality including beam pattern, directivity index and beam width -these terms are introduced in the following sections.

Beam Pattern
Beam pattern describes the response of an acoustic aperture as a function of direction. For hydrophones, beam pattern is a function of phi and theta, and is the mean-square voltage produced by an array of unit response when sound of unit pressure is incident on it in the direction of phi, theta (Urick p. 54, 1983). Beam pattern is the voltage response at each arrival angle, normalized so that its maximum value is 1, and then squared.
At times within this text, there are references to three-dimensional (3-D) beam patterns, and at other times there are references to two-dimensional (2-D) beam patterns. A 3-D beam pattern is a function of both azimuthal angle phi and elevation angle theta and is referred to as (∅, ). A 2-D beam pattern can exist in either the xy plane, where it is a function of the azimuthal angle phi and is referred to as (∅), or it can exist in the xz plane, where it is a function of the elevation angel theta and is referred to as ( ).

The 2-D beam pattern at elevation angle is simply the 3-D beam pattern
averaged over all azimuthal angles (Ellis, 2006): Likewise, the 2-D beam pattern at azimuthal angle ∅ is simply the 3-D beam pattern averaged over all elevation angles (Ellis, 2006): One of the beam patterns discussed in this thesis is the beam pattern for a continuous linear aperture of length L and wavelength . The 2-D beam pattern is given by Urick (p. 43, 1983) as: Another beam pattern that is addressed in this thesis is the beam pattern for a linear array of N equally spaced elements. This beam pattern is a derivation of the array factor, which is the spatial Fourier transform of the element excitations and is defined by Balanis (2005) as: where is the excitation coefficient of each element is the wavenumber, 2 ⁄ is the acoustic wavelength is the distance between elements For uniform element excitation (the case in this thesis), can be set to 1/N for each element and the array factor becomes: The 3-D array factor is: The beam pattern is the magnitude squared of the array factor. The 2-D and 3-D beam patterns are defined respectively as:

Product Theorem
The product theorem states that the beam pattern of an array of identical, equally spaced directional hydrophones is the product of (1) the pattern of each hydrophone alone, and (2) the pattern of an identical array of nondirectional hydrophones (Urick p. 60, 1983). In this thesis, the product theorem is used to determine the beam pattern for a linear array of equally spaced cylinders.
The 2-D beam pattern for a linear array of equally spaced cylinders is the product of the beam pattern for a cylinder and the beam pattern for a linear array of N equally spaced elements: Likewise, the 3-D beam pattern is the following product:

Array Gain
Array gain (AG) is the ratio of the signal-to-noise ratio of the array to the signalto-noise ratio of a single element of the array, and is defined in decibels by Urick (p. 34, 1983) as: When the signal is a unidirectional plane wave and is therefore perfectly coherent, array gain can be reduced to the ratio of the noise power out of one element to the noise power out of the array (Burdic, 1991): where is a solid angle given by ∅ and (∅, ) is the beam pattern of the array

Directivity Index
When the noise is isotropic such that (∅, ) = 1, the array gain of Equation (14) can be further reduced to a quantity called directivity index (Urick p. 42, 1983): If the beam pattern has rotational symmetry and is nondirectional in elevation, then the Directivity Index (DI) can be reduced to (Urick p. 42, 1983): Likewise, if the beam pattern has rotational symmetry and is nondirectional in azimuth, then the directivity index can be reduced to: The above directivity indexes are referred to in this text as 3-D directivity indexes because they are measures of a 3-D beam pattern. Often, however, a 3-D beam pattern is not available. If a hydrophone is rotated vertically and directivity measurements are taken, a 2-D vertical beam pattern can be created. If the hydrophone is then rotated horizontally and directivity measurements are taken, a 2-D horizontal beam pattern can be created. In these cases, when there are one or more 2-D beam patterns but not a 3-D beam pattern, only the 2-D directivity indexes can be calculated as follows: Directivity index is defined by Nuttall and Cray (2001) as "a decibel measure of the improvement in the SNR that a beamformed array provides in an ideal isotropic noise field with a perfectly correlated signal, relative to an omnidirectional array element in the free field".

Beam Width
Beam width is the angle between the points on each side of the main response axis where the sound pressure level is at some specified level relative to the main response level. A standard beam width level is -3 dB, because this is the half power level. The beam width is a measure of the sharpness of the main lobe of the beam pattern.

Multimode Transducer Technology
Multimode transducer technology is a technology that exploits the fundamental vibration modes of a transducer in order to create a particular directional transmit or receive pattern. An overview of this technology as it applies to the cylindrical hydrophone (the subject of this thesis) and the specific goal of increased directivity is provided in the following sections.

Multimode Beam Patterns
A multimode beam pattern is created by combining the beam patterns associated with the natural vibration modes of the device shape. The focus of this section (and throughout this paper) is the creation of the multimode cardioid beam pattern through the combination of the first two extensional modes of vibration of the cylinder, the omnidirectional (n=0) mode and the dipole (n=1) mode ( Figure 6).

Omni Beam Pattern
The omni (or omnidirectional) mode is the fundamental extensional "breathing" mode, where the expansion is uniform and in phase at all locations along the circumference of the cylinder. The cylinder vibrates in the radial direction as a single mass as a result of the expansion and contraction of the circumference (Sherman and Butler, 2007). The 2-D omni beam pattern is given by the following equation: and is shown in Figure 7(a). When this beam pattern is plugged into Equation (18), the resulting 2-D directivity index is 0 dB. The beam width is considered to be 360 degrees.

Dipole Beam Pattern
The dipole mode has a figure eight beam pattern where the two lobes have the same magnitude of expansion but are 180 degrees out of phase, so that when one half of the cylinder is expanding, the other half is contracting. According to Sherman & Butler (2007), the dipole has a 3-D DI of 4.8 dB, a 90 degree beam width, and a 2-D beam pattern given by the following equation: When this beam pattern is plugged into Equation (18), the resulting 2-D directivity index is 3.0 dB. The dipole 2-D beam pattern is shown in Figure 7(b).

Cardioid Beam Pattern
When the omni and dipole beam patterns are combined with equal weight, a cardioid (heart-shaped) beam pattern is created. 3 This cardioid is sometimes referred 3 Other weights can be applied to the dipole to generate variations of the cardioid such as the supercardioid (or maximum-DI cardioid). These variations are not considered in this work. to as the optimum-null cardioid. According to Sherman & Butler (2007), the cardioid has a 3-D DI of 4.8 dB (same as the dipole), a 131 degree beam width, and a 2-D beam pattern given by the following equation: When this beam pattern is plugged into Equation (18) The cardioid 3-D beam pattern is shown in Figure 8. This is the 3-D beam pattern for a true cardioid sensor.

Multimode Cylinders
The type of multimode transducer that is the focus of this thesis is the 4-quadrant striped cylinder. The particular cylinder is manufactured by Steiner & Martins, Inc.
(STEMiNC). It has an outside diameter of 26mm, inside diameter of 22mm and length of 13mm. It is radially poled, and has a single electrode on the outside, and four electrodes (also referred to as quadrants) on the inside. When the cylinder is wired, each quadrant produces a separate voltage output that is proportional to that quadrant's deformation. The cylinder is shown in Figure 9.  Table 3. This cylinder has a fundamental resonance frequency of 42 kHz. This is the resonance frequency of the n=0 or omni mode of vibration, and is defined by Sherman & Butler (2007) as: where c is the sound speed in the cylinder D is the mean diameter of the cylinder For the next mode of vibration, the n=1 or dipole mode, the cylinder's resonance frequency is defined by Sherman & Butler (2007) as: For this cylinder, the dipole mode resonance frequency is 59.4 kHz.
Dividing the inside electrode of a typical piezoelectric cylinder into four (4) or more separate electrodes results in two notable changes in behavior.
The first notable change is the increased prominence of higher modes of vibration in the cylinder. This phenomenon was described in a paper by Hing Leung Li, Jun Hui Hu and Helen Lai Wah Chan (2002) titled "Finite Element Analysis on Piezoelectric Ring Transformer". In it, through both finite element method (FEM) and experimental measurements, they showed that creating multiple concentric electrodes along the thickness of a PZT ring increased the relative level of the higher extensional modes of vibration. The study shows that a ring with a single electrode responds the most to the frequency of its 1 st and 2 nd radial extensional modes of vibration, a ring with two concentric electrodes responds the most to the frequency of its 3 rd radial extensional mode of vibration, and a ring with three concentric electrodes responds most to the frequency of its 4 th radial extensional mode of vibration. Figure 10 shows rings with 3 and 2 concentric electrodes respectively. This behavior is explained as a decoupling of the compressive and tensile stress regions by splitting the electrode according to the stress distribution.
Figure 10 PZT cylinders electrode for 3 rd and 4 th radial extensional modes of vibration (Li et al., 2002) The nodal points for a particular mode of vibration are the locations where the displacement is always zero. On adjacent sides of a nodal point, the forces are in opposite directions. A single electrode resists these opposite forces. But splitting the electrode at the nodal points reduces the resistance and allows for increased elongation in one electrode and increased compression in the next. , in their U.S. Patent titled "Multimode synthesized beam transduction apparatus", describe a PZT cylinder with eight separate electrodes spaced around the inside of the cylinder. They measure the response of the first 3 extensional modes of vibration. This response is shown in Figure 11. This further illustrates how when operating a multimode cylinder at its fundamental breathing resonance frequency, there also exist components of the higher extensional modes of vibration. Figure 11 Multimode cylinder transmitting response for the three separate modes of vibration  The second notable change when the inside electrode of a typical piezoelectric cylinder is divided into four (4) or more separate electrodes is that the cylinder now functions as a combination of a pressure hydrophone and a pressure gradient hydrophone. The magnitude of the multimode cylinder's omni mode response provides a measure of pressure. The multimode cylinder's dipole mode of vibration is a response to a difference in pressure between one half of the cylinder and the other half, and the magnitude of this dipole mode response is proportional to the pressure gradient.

Multimode Signal Processing
The paper titled "A tri-modal directional transducer" by Butler, Butler and Rice (2001) contains a detailed description on how to use multimode cylinders to transmit cardioid beam patterns. Another paper titled "A low-frequency directional flextensional transducer and line array" by Butler, Butler, Butler and Cavanagh (1997) contains additional details on how to transmit cardioid beam patterns.
When a multimode cylinder is used as a projector, an actual cardioid shape beam pattern is transmitted. This is done by applying a specific complex voltage to each electrode so that the resulting vibration has a cardioid shape -no displacement at the point on the cylinder that corresponds to the null of the cardioid, and maximum displacement at the opposite side of the cylinder that corresponds to the cardioid's main response axis. The applied complex voltages are determined by combining the voltages required to generate an omni beam pattern and the voltages required to generate a dipole beam pattern.
In contrast, when a multimode cylinder is used as a hydrophone, the cylinder does not physically vibrate in this cardioid shape. Instead, the voltages generated at each electrode (the output voltages) are processed in a manner that produces a cardioid receive pattern.
For a multimode cylinder with eight (8) inner electrodes connected in pairs, Butler, Butler and Rice (2004) define the basic voltage distribution that is required to excite the omni and dipole modes of vibration. This voltage distribution is shown in Table 4, where 1 , 2 , 3 and 4 are the complex voltages applied to electrode pairs 1, 2, 3 and 4, respectively.
is the omnidirectional complex voltage -the sum of the 4 quadrants' complex voltages.
is the dipole complex voltage -the difference between a) the sum of quadrant 1 and 2 complex voltages and b) the sum of quadrant 3 and 4 complex voltages.
Butler, Butler and Cavanagh (1997) explain that when transmitting a cardioid beam pattern, the applied dipole voltage must be adjusted so that the resulting on-axis pressure amplitude and phase of the dipole beam pattern match that of the omni beam pattern. This creates a dipole pattern that has one lobe with the same pressure magnitude and phase as the omni pattern, and one lobe with the same pressure magnitude but the opposite phase of the omni pattern, so that the one lobe adds to the omni pattern and the other lobe cancels, yielding a null at one side and a pressure increase on the other side. Although the equations used to accomplish this do not translate directly to a multimode cylindrical hydrophone, the general premise was used to arrive at the following equation for a four quadrant multimode hydrophone: where is the cardioid complex voltage is the complex ratio of omni and dipole voltages is defined so that the cardioid receive pattern has a null at 180 degrees. In other words, is defined so that the following condition is met: Combining Equations 28 and 29 gives: This results in the following definition for : The magnitudes squared of these complex voltages at each angle create the omni, dipole and cardioid beam patterns as defined respectively below: These equations are used later in the thesis to process the data that is collected during the tank tests.

Budget Driven Decisions
A donation of $1000 was received to purchase materials for this project. The most significant design decision -how many elements to include in the linear arraywas based entirely on this budget. There was enough money to purchase 16 cylinders.
One of these 16 was allocated to the single-cylinder hydrophone prototype that would be built and tested first. Therefore, the array would include 15 cylinders.
The second design decision that was influenced by budget was how to assemble the cylinders into a linear array. While soliciting design ideas from colleagues, one colleague located an obsolete hydrophone frame that was the perfect size. It comprised six stainless steel rods, 24 inches in length and 1/8 inch in diameter, arranged in parallel, and held in place by 2 cylindrical brass endcaps. The interior space created by the arrangement of the rods was just large enough for the cylindrical transducers to fit into. This frame (shown in Figure 12) was donated to the project and became the backbone of the linear array design. Figure 12 Array frame

Element Spacing
The next design decision was the array element spacing. Given the parameters in Table 5, Equations (11) and (18) were used to calculate the horizontal beam pattern and directivity index for a linear array of 15 cylinders with the distance between cylinders, d, set to 1/2 wavelength, 3/4 wavelength, 7/8 wavelength and 1 wavelength.
The results are shown in Figure 13. A decision was made to proceed with 7/8 wavelength spacing because it generated the highest directivity index, a horizontal DI of 15.8 dB.  cylinders. This can be seen in Figure 14 for a linear array with 7/8 wavelength spacing between elements. Figure 14 Beam patterns for a linear array of 15 point receivers, a single cylinder, and a linear array of 15 cylinders (for 7/8 wavelength spacing)

Final Array Design
The cylinders are free-flooded (oil filled) for deep submergence. The rubber rings are used to isolate the cylinders from the stainless steel rods (Figure 15). The rest of the design decisions incorporate standard linear array technology. Figure 15 Cylinder and rubber ring The final multimode linear hydrophone array design is illustrated in Figure 16.

Single-Cylinder Multimode Prototype
To calculate the 3-D beam pattern of a multimode (cardioid) sensor, the product theorem is applied to the 3-D beam pattern for a true cardioid from Equation (23) and the 3-D beam pattern for the cylinder from Equation (5) This 3-D beam pattern is shown in Figure 17. Applying Equation (15) gives a cardioid cylinder 3-D directivity index of 5.2 dB.
Note that the beam pattern and directivity index for the cardioid cylinder are only slightly different than those for a true cardioid (Figure 8), because the cylinder is almost omnidirectional.
Taking a slice of the above 3 D shape at theta equal to 90 degrees provides the horizontal beam pattern. Likewise, taking a slice at phi equal to zero degrees provides the vertical beam pattern. These beam patterns and their respective 2-D directivity indexes are shown in Figure 18.

Multimode Linear Hydrophone Array
The theoretical 3-D beam pattern for a linear array of 15 multimode cylinders, according to the product theorem, is the product of the 3-D beam pattern for the multimode cylinder which is given by Equation (35) and shown in Figure 17, and the 3-D beam pattern for a linear array of 15 isotropic sensors which is given by Equation (10) and shown in Figure 19.

degrees) IN-AIR CHARACTERIZATION
When fabricating acoustic apertures, it is common practice to first perform in-air characterizations of the individual transducers. The purpose for doing so is to establish a baseline of performance and to identify any variation that may exist from one element to the next. Typical in-air measurements include admittance, blocked capacitance, leakage resistance and dissipation factor.
For this thesis, in-air admittance, blocked capacitance, leakage resistance and dissipation factor measurements were made on each of the four quadrants of each of the 15 cylinders that were used in the array. In this chapter, these measurements are presented, and compared to the manufacturer's specification when available.

Admittance
Admittance, Y, is the ratio of input current to applied voltage with the output open-circuited. "Open-circuit" implies that the mechanical side is constrained, or clamped, so that it is not free to move, and the displacement, and therefore the strain in the material, is zero. This is achieved with a static applied voltage or with a low frequency applied sinusoidal voltage (Burdic, 1991).
The admittance of each quadrant of each of the 15 cylinders was measured using an Admittance Gain Phase Analyzer. The measurements were made over a range of frequencies near the cylinder's in-water resonance frequency of 42 kHz. Figure 22 shows the measured admittance magnitude in milliSiemens (10 -12 Siemens) and phase in degrees for all four quadrants of one cylinder (typical of each cylinder). Figure 23 shows the measured admittance magnitude and phase for one quadrant (typical of each quadrant) for all 15 cylinders. From the plots, it can be seen that there is not much variance from one quadrant to another on a given cylinder, but there is a slight variance from one cylinder to another. Admittance magnitude peaks at the resonance frequency of the transducer. From the plots it can be seen that the measured in-air resonance frequencies range from 45.5 kHz to 46.5 kHz, slightly higher than the manufacturer's specified in-water resonance frequency of 42 kHz.

Blocked Capacitance
Blocked capacitance, also referred to as the clamped or static capacitance, is the capacitance in a piezoelectric material under the clamped condition, when no strain (deformation) is permitted. The manufacturer specifies a blocked capacitance of 6600 pF +/-20% @ 1kHz. Blocked capacitance of each quadrant of each of the 15 cylinders was measured with an LCR Meter at 1 kHz. Figure 24 shows the measured blocked capacitance in picoFarads (10 -12 Farads) for all four quadrants of each of the 15 cylinders.  Figure 24 In-air blocked capacitance for all cylinders and segments

Leakage Resistance
Leakage resistance, also referred to as insulation resistance, is the extent to which a dielectric material resists leakage current. In piezoelectric ceramics, a high number such as 10 Gigaohms is desired. The leakage resistance of each quadrant of each of the 15 cylinders was measured with a Megohmmeter. Figure 25 shows the measured leakage resistance in Gigaohms (10 9 Ohms) for all four quadrants of each of the 15 cylinders.

Dissipation Factor
Dissipation factor is a measure of the losses in a capacitor and is sometimes called the "loss tangent". It is the ratio of the equivalent series resistance to the capacitive reactance, and is usually expressed as a percentage. The reciprocal of the dissipation factor is called the "Q", or quality factor. The manufacturer specifies a dissipation factor at 1 kHz of 0.5%. The dissipation factor of each quadrant of each of the 15 cylinders was measured at 1 kHz with an Inductance, Capacitance, and Resistance (LCR) Meter. Figure 26 shows the measured dissipation factor percentage for all four quadrants of each of the 15 cylinders.

CHAPTER 6 HYDROPHONE PROTOTYPE FABRICATION
As previously mentioned, a single-cylinder hydrophone prototype was first fabricated. Table 7 lists the materials used to build the single-cylinder hydrophone. The single-cylinder hydrophone prototype was constructed as follows: A hollow was machined in the Delrin plastic rod, leaving ¼ inches of material on the sides and on one end. A 7/16" threaded hole was machined into the closed end, and the 5-pin connector was screwed into the hole. The four signal wires were soldered to the four inside electrodes of the piezoelectric cylinder. The ground wire was soldered to the outside of the cylinder. The cylinder and wires were pushed into the Delrin housing and the cylinder was centered. The potting compound was poured into the housing while taking care to keep the cylinder centered. The potting compound was cured at room temperature. Figure 27 includes photos of the inprocess product. Figure 28 includes a photo of the final product. The purpose of the test was two-fold: 1) to characterize the performance of a single-cylinder multimode hydrophone, and 2) to provide data that could be used to test the MATLAB code being written to generate the cardioid beam pattern from the four channels of measured voltages.

Test Facility
The OTF is one of the six measurement facilities maintained by the Underwater Sound Reference Division (USRD) which serves as the U.S. standardizing activity in the area of underwater acoustic measurements. The USRD is part of NUWC Division Newport's Sensor and Sonar Systems Department.
The OTF is a fresh water facility. The tank is an indoor concrete tank, 4.57 meters wide, 4.57 meters deep and 9.14 meters long.

Figure 30 NUWC Open Tank Facility photo
The test equipment is described below in Table 8. The 5 pin connector on the hydrophone was connected to the mating 5 pin connector on the cable. The hydrophone was then mounted to a 1-inch diameter hollow stainless steel pole which was attached to a rolling carriage with a turntable, and lowered into the tank to the same depth as the projector, 90 inches below the water surface. The hydrophone was positioned 2 meters from the projector.
For each test, the projector transmitted an acoustic signal at a specified frequency, and in response, the hydrophone generated four analog low-level voltage signals (one for each of the multimode cylinder quadrants) proportional to the acoustic pressure acting upon the hydrophone. An analog-to-digital (A/D) converter converted the analog signals into digital signals which were recorded and processed by the test set.
In order to prevent reflections from the water surface and side of the tank from interfering with the measurements, pulsed continuous waves were transmitted by the projector, and receive gates were used by the test set to exclude the reflections.
The specific environmental conditions and test set parameters are described below in Table 9.

Test Procedure
Free field voltage sensitivity (FFVS) readings were first taken. Free field voltage sensitivity is one of the measurements used to predict the performance of an acoustic aperture. Free field voltage sensitivity is the ratio of the complex voltage output by the aperture to the complex pressure acting on the aperture when in the presence of an undisturbed sound pressure wave in a free field. Free field voltage sensitivity is therefore a complex quantity with both a magnitude and a phase.
"Free field" implies that the sound may propagate free from any form of obstruction. The basic requirements for "free field" measurements are (1) enough space so that interference from boundary reflections can be eliminated by pulsing techniques, anechoic boundaries, or spreading losses due to long distances, (2) a low ambient noise level, and (3) a water medium that is relatively free of anything that will cause refraction and scattering (Bobber, 1988).
The THAMES test set computes free field voltage sensitivity using a comparison replacement calibration method in which a calibrated reference standard hydrophone with known free field voltage sensitivity is used to determine the sound pressure level in the water, then the hydrophone with unknown sensitivity is subjected to the known sound pressure level and computations are performed to deduce its free field voltage sensitivity (Acoustical Society of America, 2012). The THAMES test set computes the FFVS magnitudes expressed in decibels relative to one volt per micropascal (e.g. dB re 1V/uPa), but does not compute the FFVS phases.
For the first set of tests the hydrophone was mounted vertically to the pole (Figure 31).
Using the turntable, the hydrophone was rotated about its central axis. These measurements are referred to herein as the hydrophone vertical measurements.
While the hydrophone was stationary, FFVS measurements were taken over a range of transmit frequencies from 10 kHz to 100 kHz.
Then the hydrophone was rotated and FFVS measurements were taken at each bearing for the operating frequency of 37.5 kHz. FFVS measurements were made for each of the 4 hydrophone quadrants. For the second set of tests, the hydrophone was mounted horizontally to the pole ( Figure 32). Using the turntable, the hydrophone was rotated about its acoustic center.
The same measurements were taken as for the previous orientation. These measurements are referred to herein as the hydrophone horizontal measurements.

Free Field Voltage Sensitivity
Free field voltage sensitivity (FFVS) magnitudes were provided by the test set for each of the four quadrants over a range of frequencies. Figure 33 contains a plot of the FFVS magnitudes for each quadrant for frequencies from 10 kHz to 60 kHz.
FFVS plots typically peak at the resonance frequency. For this cylinder, the resonance frequency is 42.0 kHz. The plot shows a peak slightly below this resonance frequency and closer to the operating frequency of 37.5 kHz.
Figure 33 FFVS magnitude vs. frequency for single-cylinder hydrophone Table 10 lists the FFVS magnitudes for each of the hydrophone's four quadrants at the operating frequency of 37.5 kHz.

Vertical Directivity
From the voltage time series data that was recorded for each quadrant while the hydrophone was rotated in its vertical orientation, the test set calculated the complex voltage (magnitudes and phase) for each quadrant, at each angle of arrival. Figure 34 shows how the voltage magnitudes and phases varied from one quadrant to the next as the hydrophone was rotated. The actual (measured) omni, dipole and cardioid beam patterns for this vertical rotation are compared to the theoretical (predicted) beam patterns in Figure 35 The actual plots in Figure 35(a)-(c) are not identical to the theoretical plots but are close. It appears that the asymmetry of the actual beam patterns is the result of the hydrophone not being rotated precisely about its central axis. There is evidence of this in the voltage magnitude plot in Figure 34: the dip in all four magnitudes near 215 degrees, the increase in all four magnitudes near 325 degrees, and the wide variation in the quadrant 2 magnitudes all indicate that the hydrophone was not rotated exactly about its central axis.
From the beam patterns, the actual 2-D vertical omni, dipole and cardioid directivity indexes were calculated using Equation (19), and the respective beam widths were measured. Table 11 displays the actual values next to the theoretical values. As with the beam patterns, the actual directivity indexes and beam widths are very close to the respective theoretical values.

Horizontal Directivity
From the voltage time series data that was recorded for each quadrant while the hydrophone was rotated in its horizontal orientation, the test set calculated the complex voltage (magnitudes and phase) for each quadrant, at each angle of arrival.
The plan had been to process the horizontal measurements in the same manner as the Theoretical Actual vertical measurements. However, when the horizontal measurements were taken, the hydrophone was not oriented so that the line separating quadrant 1 and quadrant 2 was facing the transmitter. That particular orientation -where the elevation angle theta equals 90 degrees -is the orientation of the theoretical beam pattern, and the only orientation that results in the horizontal cardioid beam pattern.
Therefore, the only horizontal actual vs. theoretical beam pattern comparison that can be made is the omnidirectional beam pattern comparison. This comparison is shown in Figure 36. From Figure 36, it can be seen that the actual horizontal beam pattern does not match the theoretical beam pattern. However, a probable explanation for the nulls that occur at roughly 60 and 120 degrees is that they were caused by interference from the fixture (shown in Figure 32). Furthermore, the arrival angles that matter are the broadside angles of 0 degrees and 180 degrees, and the values at these angles match almost exactly.

Conclusion
Based upon the minimal differences between the theoretical and actual (vertical and horizontal) prototype beam patterns, directivity indexes and beam widths, it has been determined that this prototype served its intended purpose and demonstrated that cardioid receive beam patterns could be generated by a single four-quadrant multimode cylinder. ARRAY FABRICATION Next, the 15-cylinder linear hydrophone array was fabricated. Table 12 contains the material list. The array was constructed in the following manner in the order described: The rubber rings were glued to the outside of the cylinders with a single small amount of instant adhesive. One of the six steel rods was removed from the frame so that the cylinders could be inserted. One of the remaining five steel rods was marked  The five wires were cut so that they were long enough to extend just beyond the brass cylinder at the end of the frame. Heat shrink tubing was attached to the last few inches of the wires to prevent the bare wires from touching each other or the frame.
These now shielded wires were brought through the hole in the brass cylinder at the end of the frame. The wires of the 5-pin connector were brought through the single hole in the first Delrin plug and the 5-pin connector was screwed into the plug. The 5 wires from the array were then soldered to the 5 wires of the 5-pin connector, and the solder joints were covered with additional heat shrink tubing ( Figure 39).

Figure 39 Photo 3 of array fabrication
The above assembly was slid into the rubber tubing (referred to as a boot). One clamp was placed around the rubber boot at the location of the brass cylinder and tightened. A second clamp was placed around the rubber boot at the location of the Delrin plug and tightened.
The booted array was filled with castor oil through the hole in the brass cylinder at the end opposite the 5-pin connector. When the oil had reached the brass cylinder, a second Delrin plug, this one with two small holes drilled through it, was inserted into the rubber boot about an inch above the brass cylinder. Again, one clamp was placed around the rubber boot at the location of the brass cylinder and tightened, and a second clamp was placed around the rubber boot at the location of the Delrin plug and tightened.
The area between the brass cylinder and the second Delrin plug was filled with castor oil through one of the holes in the plug -the other hole allowed the air to escape. Sealing screws were used to seal the two holes.  The same test equipment was used.
This time the distance between the transmitter and array was increased from 2 meters to 6 meters to ensure far-field plane wave propagation. The following equation for the minimum separation distance for far-field water tank measurements for a linear array (Bobber, 1991) was used to determine the required separation: where d is the distance between the transmitter and the acoustic center of the array L is the length of the linear array = ⁄ is the wavelength is the sound speed is the operating frequency The same cable assembly that had been used to test the single-cylinder hydrophone was used, but because the array was now further from the transmitter, a 1.2 meter, a 1.6 m and a 1.8 meter RG-58 cable extension had to be added to each of the four cables.
The same tests that were previously run for the single-cylinder hydrophone prototype were repeated for the array. The test conditions are described in Table 13.  Figure 41 was used.

CHAPTER 11 PROCESSING THE ARRAY TEST RESULTS
In this chapter, a quadrant refers collectively to the particular quadrant of all 15 cylinders, and a quadrant's data originates from the single wire attached to the particular quadrant of all 15 cylinders.

Free Field Voltage Sensitivity
As with the single-cylinder hydrophone, free field voltage sensitivity (FFVS) magnitudes were provided by the test set for each of the four quadrants over a range of frequencies. Figure 42 contains a plot of the FFVS magnitudes for each quadrant for frequencies from 10 kHz to 50 kHz.

Vertical Directivity
From the voltage time series data that was recorded for each quadrant while the array was rotated in its vertical orientation, the test set calculated the complex voltage (magnitudes and phase) for each quadrant, at each angle of arrival. Figure 43 shows how the voltage magnitudes and phases varied from one quadrant to the next as the array was rotated.
The actual (measured) omni, dipole and cardioid beam patterns for this vertical rotation are compared to the theoretical (predicted) beam patterns in Figure 44 From the beam patterns, the actual 2-D vertical omni, dipole and cardioid directivity indexes were calculated using Equation (19), and the respective beam widths were measured.

Horizontal Directivity
From the voltage time series data that was recorded for each quadrant while the array was rotated in its horizontal orientation, the test set calculated the complex voltage (magnitudes and phase) for each quadrant, at each angle of arrival. As with the horizontal measurements of the single-cylinder hydrophone, when the horizontal array measurements were taken, the array was not oriented so that the line separating quadrant 1 and quadrant 2 was facing the transmitter (again, the orientation of the theoretical beam pattern, and the only orientation that results in the horizontal cardioid beam pattern). So, again, the only horizontal actual vs. theoretical beam pattern comparison that can be made is the omnidirectional beam pattern comparison. This comparison is shown in Figure 45. The beam patterns are not a perfect match, but there is nothing about the actual beam pattern that indicates a problem. The following quantitative comparison between theoretical and actual directivity indexes and beam widths provides more conclusive information.
From the actual horizontal beam pattern, the actual directivity index was calculated using Equation (18), and the beam width was measured.

Conclusion
The minimal differences between the theoretical and actual (

Performance Analysis of Existing TPL-25 System
The below ambient noise limited passive sonar equation was used to analyze the performance of the system (Urick p. 22, 1983):

Source Level (SL)
Source Level ( ) was given to be 160 dB.

Noise Level (NL)
From the Urick fig. 7. 5 (1983) Wenz curve, given frequency of 37.5 kHz and Sea State of 3, the Ambient Noise Level ( ) is determined to be 35 dB.

Transmission Loss (TL)
From Urick fig. 5.5 (1983), the absorption coefficient at zero depth α 0 for the given frequency of 37.5 kHz, water temperature of 4℃, salinity of 35 ppt, and pH of 8 is determined to be 8 dB/kyd. When α 0 of 8 dB/kyd and search depth of 9843 feet (3000 meters) are plugged into the following equation (Urick p. 108, 1983), the absorption coefficient α is determined to be 6.5 dB/kyd.

Directivity Index (DI)
Given that the single hydrophone used in the TPL 25 is omnidirectional (Sasse, 2014), the beam pattern is given by: When the beam pattern is plugged into Equation (16), the resulting Directivity Index ( ) is 0 dB.

Detection Threshold (DT)
From the Urick fig. 12.7 (1983) ROC curve, given desired Probability of Detection of 50% and desired Probability of False Alarm of .01%, the detection index, , is determined to be 16. For the case of known signal wave shape (frequency, time of occurrence and duration), Urick (p. 394, 1983) gives the following equation for Detection Threshold (DT): However, when the integration time is not "matched" to the signal duration, an additional term must be added to the equation as follows (Urick p. 394, 1983): When detection index ( ), signal duration ( ) and integration time ( ) are plugged into Equation (45) (Hodges p. 20, 2010). FOM is therefore calculated by setting the signal excess to zero and solving the sonar equation for Transmission loss (Hodges p. 21, 2010). For a passive sonar system, FOM is defined by Urick (p. 23, 1983) as follows:   Summary of Performance analysis for existing TPL-25 system Table 17 contains a summary of the performance analysis for the existing TPL-25 system.

Directivity Index (DI)
Directivity Index ( ) of 18.35 dB is being used for the 15-cylinder multimode linear hydrophone array (Section 11.4).

Figure of Merit (FOM)
When Source Level ( ), Noise Level ( ), Directivity Index ( ) and Detection Threshold ( ) are plugged into Equation (46) Table 19 compares FOM and detection range ( ) between the existing TPL-25 system and the proposed design: Table 19 Comparison of FOM and detection range

Summary
This thesis explored how replacing the TPL-25's single omnidirectional hydrophone with a device that has an increased directivity index, specifically with a linear array of directional multimode hydrophones, could increase the detection range of the TPL-25.
The use of multimode technology as a means to increase the directionality of a transducer was researched and this research was presented in Chapter 2. This multimode technology was first applied to a single-cylinder hydrophone prototype.
The theoretical directivity of the single-cylinder multimode hydrophone prototype was predicted (Chapter 4), and the prototype was fabricated (Chapter 6) and then tested in an acoustic test tank (Chapter 7). The data collected in the tank was processed with multimode signal processing, a cardioid beam pattern was successfully created, and the prototype's calculated horizontal and vertical directivity indexes were shown to be comparable to the predicted values (Chapter 8).
The multimode technology was then applied to a 15-cylinder linear hydrophone array. The array was designed (Chapter 3), and the theoretical directivity of the multimode linear hydrophone array was predicted (Chapter 4). The array was fabricated (Chapter 9), and then tested in the acoustic test tank (Chapter 10). The data collected in the tank was processed with multimode signal processing, and the calculated horizontal and vertical beam patterns and directivity indexes were shown to be comparable to those predicted (Chapter 11).
The theoretical 3-D Directivity Index ( ) of the 15-cylinder multimode linear hydrophone array was calculated to be 18.35 dB (Chapter 4), and this DI was used in the passive sonar equation to determine the predicted Figure of Merit ( ) and detection range ( ) of the multimode linear hydrophone array (Chapter 12).

Conclusion
When the 15-cylinder multimode linear hydrophone array's theoretical Directivity  The multimode array's detection range ( ), based upon this increased FOM, was calculated to be 4510 meters -this detection range is 1913 meters (73.7%) greater than the detection range calculated for the current TPL-25 system.
This thesis, which researched, designed, fabricated and tested the application of multimode technology to a linear hydrophone array, concludes that a linear array of 15 multimode cylinders would be able to increase the detection range of the TPL-25 -the system currently used by the U.S. Navy to locate the black boxes from downed aircraft -by 73.7%.

Areas of Future Research
One area of future research would be to calculate the Area Coverage Rate (ACR) for both the existing TPL-25 system and the multimode linear hydrophone array based upon the detection ranges and other relevant factors.