Citation
Acoustic Application of Pressure-Sensitive Paint

Material Information

Title:
Acoustic Application of Pressure-Sensitive Paint
Creator:
VIRGIN, CHRISTOPHER ALLEN
Copyright Date:
2008

Subjects

Subjects / Keywords:
Acoustic noise ( jstor )
Audio frequencies ( jstor )
Electric potential ( jstor )
Frequency response ( jstor )
Microphones ( jstor )
Oxygen ( jstor )
Plane waves ( jstor )
Predetermined motion time systems ( jstor )
Signals ( jstor )
Waveguides ( jstor )
City of Gainesville ( local )

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright Christopher Allen Virgin. Permission granted to University of Florida to digitize and display this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Embargo Date:
4/17/2006
Resource Identifier:
77078666 ( OCLC )

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Full Text












ACOUSTIC APPLICATION OF PRESSURE-SENSITIVE PAINT


By

CHRISTOPHER ALLEN VIRGIN


















A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


2005

















To my family.















ACKNOWLEDGMENTS

The author would like to thank the supervisory committee chairman, Dr. Bruce

F. Carroll, for his continued guidance, support, and encouragement. Gratitude is also

addressed to Dr. Louis Cattafesta for his advice and guidance. The author would

like to thank the other supervisory committee members, Dr. Mark Sheplak, Dr. Kirk

Schanze, and Dr. Martin Morris, for their support. The author would also like to

acknowledge all family and friends who have helped make this possible.















TABLE OF CONTENTS
page

ACKNOWLEDGMENTS ................... ...... iii

LIST OF TABLES ...................... ......... vi

LIST OF FIGURES ................... ......... viii

LIST OF SYMBOLS AND ABBREVIATIONS ................. x

ABSTRACT . . . . . . . . xiii

CHAPTER

1 INTRODUCTION ......... .......... ......... 1

PSP Physics ............................ .... 1
Previous W ork .. .. ... .. .. .. .. ... .. .. .. ... .. .. 4
Motivation ................... .............. 9

2 EXPERIMENTAL APPARATUS ................ .... 10

Plane Wave Tube ............................... 10
Temperature Effects of Acoustic Waves ............... 12
Photodetector Description ......... .......... .... 12
PSP Applied to Detector ......... .................. 14

3 EXPERIMENTAL SETUP AND PROCEDURE . . .24

Standing Wave Ratio Test ............... ....... ..24
PSP Static Calibration ............... ......... ..26
Photomultiplier Frequency Response ........ ............ 27
Acoustic Testing ..... ...................... 27

4 EXPERIMENTAL RESULTS ........................ 29

Standing Wave Ratio Results ..... ........... .... 29
PSP Calibration ..... ...................... 29
Photodetector Frequency Response ................ .... 30
Noise in Experimental Setup ................ ... ... .. 33
PSP Behavior ............... .............. ..34
PSP Linearity ............... .............. ..36
Thermal Response ............... ........... ..38
Time Resolution of Optical Signal ................ ...... 39









Uncertainty Analysis ............. . . .... 41
PSP Static Calibration Uncertainty ................. .. 41
Frequency Response Errors .................. .. 42

5 CONCLUSIONS ............... ........... .. 45

APPENDIX

A DERIVATIONS OF ACOUSTIC RELATIONS . 47

Temperature C!( ,ii,i. of a Small Isentropic Compression . ... 47
Derivation of the One-Dimensional Wave Equation . . 48
Derivation of the Cutoff Frequency .................. ... 50
Derivation of the Waveguide Equations .................. .. 52
Derivation of the Rectangular Waveguide Equation . ... 52
Derivation of the Cylindrical Waveguide Equation . ... 55
Normal Incidence Sound Reflection and Transmission . .... 57

B STANDING WAVE RATIO METHOD ........ . . 60

Standing Wave Ratio Calculations .................. .. 60
Standing Wave Ratio Figures .................. .... .. 63

C TABULATED EXPERIMENTAL RESULTS . . ..... 66

D EXPERIMENTAL RESULTS FIGURES ................. .. 75

LIST OF REFERENCES ........... . ......... .. 83

BIOGRAPHICAL SKETCH .............. . .. 86















LIST OF TABLES


SWR Data Collection Settings . .....

SW R Results . ..............

PSP Static Calibration Settings . ....

PMT FRF Acquisition Settings . ....

PMT FRF Acquisition Settings . ....

Linearity Data Acquisition Settings . ..

Single Time Series Data Acquisition Settings .

PSP Static Calibration Results . ....

PMT Frequency Response Results . ...

PSP Linearity Results . .........


C-4 115 dB SPL Frequency Response Data


5 115 dB

6 119 dB

7 119 dB

8 122 dB

9 122 dB

10128 dB

11128 dB

12134 dB

13134 dB

14140 dB

15140 dB

16140 dB


SPL Frequency Response Normalized Error

SPL Frequency Response Data . .

SPL Frequency Response Normalized Error

SPL Frequency Response Data . .

SPL Frequency Response Normalized Error

SPL Frequency Response Data . .

SPL Frequency Response Normalized Error

SPL Frequency Response Data . .

SPL Frequency Response Normalized Error

SPL Frequency Response Data . .

SPL Frequency Response Normalized Error

SPL Frequency Response in N2 Data .


Estimates .



Estimates .



Estimates .



Estimates .



Estimates .



Estimates .


Table

31

41

42

43

44

45

46

C-

C-1

C-


page

25

29

30

31

37

38

41

66

67

67

68

68

69

69

70

70

71

71

72

72

73

73

74









C-17140 dB SPL Frequency Response in N2 Normalized Error Estimates 74















LIST OF FIGURES
Figure page

1-1 Schematic of a Typical PSP Layer .... . .... 2

1-2 Comparison of the Amplitude Response of Winslow's Model and 1/2,
1st, and 2"d Order Systems ............. . 6

1-3 Comparison of the Phase Response of Winslow's Model and 1/2, 1st,
and 2"d Order Systems... ............ ........ 7

2-1 Schematic of a Cylindrical Waveguide Modes ............. .11

2-2 Schematic of a Side-On PMT .................. ..... 13

2-3 Equivalent Circuit Representation of a Photodetector . ... 15

2-4 Desirable C'!. im .I Properties of a PSP Coating . ..... 20

2-5 Minimum Detectable Radiant Flux of Detectors ........... .21

2-6 Minimum Detectable SPL of Detectors ................ 22

3-1 Schematic of Experimental Setup for Standing Wave Ratio Testing .25

3-2 Schematic of Experimental Setup for Acoustic Testing . ... 28

4-1 PSP Static Calibration Results ................ ...... 31

4-2 PMT Frequency Response ............... .... 32

4-3 Experimental Noise Comparison ................ .... 34

4-4 PSP Coating Relative Frequency Response . . 35

4-5 PSP Coating Phase Response ................ . .36

4-6 Linearity of Optical System ................ .... 37

4-7 Coating Response in Air and Nitrogen ............... .. 39

4-8 Comparison of Unfiltered PMT Output, Filtered PMT Output, and
Microphone Output ... ............ ..... .. 40

A-1 Schematic of a Square Duct ................ .... 52

A-2 Schematic of a Cylindrical Duct .................. .. 55









A-3 Sound Reflection and Transmission at a Normal Incidence Surface

B-1 Microphone Voltage vs. Xcor for 600 Hz Excitation .........


B-2 Microphone Voltage vs. Xcor for 1000 Hz Excitation

B-3 Microphone Voltage vs. X ,, for 1400 Hz Excitation

B-4 Microphone Voltage vs. X ,, for 1800 Hz Excitation

D-1 PMT Power as a Function of SPL .. ........

D-2 Mic-PMT Coherence as a Function of SPL .....

D-3 Response, Relative Response, and Phase Response o


at 115 dB SPL .. .......

D-4 Response, Relative Response, and
at 119 dB SPL .. .......

D-5 Response, Relative Response, and
at 122 dB SPL .. .......

D-6 Response, Relative Response, and
at 128 dB SPL .. .......

D-7 Response, Relative Response, and
at 134 dB SPL .. .......

D-8 Response, Relative Response, and
at 140 dB SPL .. .......


Phase Response o


Phase Response o


Phase Response o


Phase Response o


Phase Response o


f Optical System


f Optical System


f Optical System


f Optical System


f Optical System


f Optical System














LIST OF SYMBOLS AND ABBREVIATIONS

a Width/Diameter of Waveguide [m]

co Speed of Sound [m/s]

e C'i irge of an electron [1.60E-19C

f, Cutoff Frequency of mode (m,n)[Hz]

1ishot Shot Noise [A]

itpl Anode current due to the illumination from the acoustic signal [A]

(ispi),,,, Minimum Detectable Anode Current due to Acoustic Signal [A]

k Boltzmann's Constant [1.38E-23J/K]

k' Wavenumber

uf Velocity

t Time [sec]

x Distance [m]

S1/4 Scale Reading with microphone at 1st minimum [mm]

xor Correction Factor [mm]

x.2m Scale reading with microphone touching face of specimen [mm]

Xobs Observed scale reading [mm]

xjf Observed scale reading with probe touching specimen [mm]

z/pc Impedance Ratio

A Area of PSP Coating [m2]

B System Bandwidth [Hz]

C Capacitance [Farad]

GC, C1 Temperature dependant constants

F Device Noise Figure []









G Gain

1 Photodetector Current [A]

lby Anode current due to the mean background illumination [A]

Id Dark Current = Id, + GId [A]
I,9 Dark current subject to gain (from photocathode) [A]

Ids Dark current not subject to gain (from anode) [A]

Iph Total anode current due to incident light = isp + Iby [A]
In Johnson (Thermal) Noise [A]

J, Derivative of Bessel Function of order m

Kq Rate Constant for Oxygen Quenching

L Radiant Flux of Dye [W]

AL Fluctuating emission level from PSP [W]

L,,,, PSP emission in the absence of oxygen [m]

N Total Noise Present at Anode [A]

P Pressure [Pa]

R Resistance [Ohms]

S Henry's Law Sorption Coefficient

Se Entropy

Sp, Cathode Radiant Sensitivity [A/W]
T Temperature [K]

a nth zero of J

a, Normal Incidence Sound Absorption Coefficient

7 Ratio of Specific heats
I Pressure Reflection Coefficient Magnitude

Tr Irradiance of the PSP Coating [W/m22] (r = L/A)
C( Tube Attenuation Constant

0 Pressure Reflection Coefficient Phase [degrees]









A Wavelength [m]

n(A) Cathode Quantum Efficiency

p Density

o phase [radians]

S Quantum Yield of dye at Pressure P

S PSP quantum yield in the absence of oxygen

Yo2 Mole Fraction of Oxygen (in the medium)
1w Radian Frequency [radians/sec]

APD Avalanche Photodiode

CE Anode Collection Efficiency

NEP Noise Equivalent Power

PMT Photomultiplier Tube

SPL Sound Pressure Level [dB]

S WR Standing Wave Ratio

PSP Pressure-Sensitive Paint
















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

ACOUSTIC APPLICATION OF PRESSURE-SENSITIVE PAINT

By

Christopher Allen Virgin

December 2005

Chair: Bruce F. Carroll
Major Department: Mechanical and Aerospace Engineering

This thesis describes the effort to experimentally verify the response of "traditional"

Pressure-Sensitive Paint (PSP) to low amplitude pressure fluctuations such as those common in

acoustic measurements. Pressure-sensitive paint utilizes molecular quenching of fluorescent

compounds in the presence of oxygen to discern the pressure field at a given point on a surface.

A 0.1 meter diameter by 1.0 meter long plane wave tube is utilized to create a planar acoustic

field at the surface of a PSP sample. The response of the paint is measured using a

Photomultiplier Tube (PMT). The plane wave tube is driven through a function generator and an

audio amplifier.

Frequency response, linearity, and temperature effects of the coating are evaluated.

Frequency response measurements show the paint to behave similar to a "1/2"-order system, i.e.,

a -45 phase and -10 dB/decade attenuation. This is in agreement with previous research

conducted at the University of Florida. Using a numerical model, the optical system (coating and

detector) is estimated to have a noise floor of 115 dB SPL. This is quite high for an acoustic

detection scheme and is the result of the PSP and PMT fundamental characteristics. Experimental

results show the noise floor to be in the region of 119 to 115 dB SPL. The optical system









is shown to be linearly related to the sound pressure at the face of the specimen

through both frequency response and direct tests of the coating response versus ap-

plied acoustic pressure. The response of PSP can vary strongly with temperature

depending upon the specific paint formulation. In this instance, the temperature

fluctuations associated with the acoustic waves are experimentally shown to have

negligible impact on the response of the coating.

The interests of this research lie in applying unsteady pressure measurement

tools to high-speed hydrodynamic pressure fluctuations such as those seen in tur-

bulent boundary l -Vr-. PSP is currently being evaluated in several forms in hopes

of attaining sufficient sensitivity to be applicable in this regime. The ability of ob-

taining real-time measurements of comparatively small pressure fluctuations also has

potential impact in medical and environmental fields.















CHAPTER 1
INTRODUCTION

This chapter presents some background information on pressure-sensitive paint,

commonly referred to as PSP. Reviews of recent studies in the dynamic response of

PSP are also presented. It is shown that the dynamic response of several different

types of PSP are currently being investigated. Recent studies focus on the dynamic

response of newer types of PSP due to their faster response times. This study in-

vestigates the dynamic behavior of a PSP and primer l -1--r applied directly to an

aluminum substrate.

PSP Physics

Pressure-Sensitive Paint is a measurement technique based on the oxygen quench-

ing of fluorescent molecules in a polymer binder. A schematic of a typical PSP 1I-vr

is shown in Figure 1-1. Shown is a PSP l-1-,-r applied directly to a substrate. The

process begins with Excitation of the luminophore molecules. This is accomplished

with a light source having strong intensity in the blue to UV portion of the spectrum

(A = 300-500 nm). Lasers, halogen lamps, LED's and strobe lights are often employ,

in this task. Luminophore molecules absorb energy from the source and transition

to a higher vibrational energy level [Kose, 2005]. Once at its higher energy level, the

luminophore has three routes to the ground state. One possible mode of decay is for

the luminophore to release its energy to the surrounding polymer matrix in the form

of thermal energy [Schanze et al., 1997, Winslow, 2001]. This process is not favored in

most PSP formulations. The second route of decay is known as i i ,. decay or

luminescence. This route encompasses both fluorescence and phosphorescence. Fluo-

rescence is the process of absorbing a photon and emitting a photon of lower energy.

Phosphorescence is a quantum process involving the change in the spin multiplicity











Excitation Light




*


Luminescence


Oxygen Molecule



Polymer Binder %I i


Substrate / ygen uenchi
/ Luminophore / yg

Figure 1-1: Schematic of a Typical PSP L v.-r

of a molecule. Ruthenium-based PSP's exhibit fluorescence, while platinum-based
paints display phosphorescence [Winslow, 2001]. Both processes result in the emis-
sion of a photon of lower energy (i.e., longer wavelength) than the absorbed photon.
The emitted photon is in the red to orange color of the spectrum (A = 550-650 nm).
The third and distinctive feature of PSP is that a luminophore may release
its energy to an oxygen molecule that has permeated the polymer binder. This
process is known as ..::i.- -: qi, ii, n!p,11 [Schanze et al., 1997, Winslow et al., 2001].
Luminescence and oxygen quenching are the primary routes of decay for a PSP. The
partial pressure of oxygen in the binder 1-v.-r is directly dependant on the partial
pressure of oxygen directly above the 1livr and the mass diffusivity of the polymer(s)
used in the binder. The luminophores in the binder exhibit the behavior of either
emitting a red-shifted photon or interacting with oxygen. In this manner, it can be
shown that the observed intensity of the emission of the PSP is inversely proportional
to the oxygen concentration surrounding the luminophores. This behavior is governed









by the Stern-Volmer relation [Winslow et al., 2001]

1Vac Lvac
1 = + KqSxoP (1.1)
) L

The Stern-Volmer Equation relates the emission intensity (radiant flux) of the PSP

in the absence of oxygen, Lac, to the emission, L, at an absolute pressure, P. In aero-

dynamic applications, it is often not feasible to measure the intensity in the absence

of oxygen, so Eqn(1.1) is often related to the intensity at some reference pressure

(typically Patm) [Virgin et al., 2005]. This yields the more familiar rodynamic

testing; form of the Stern-Volmer relation [Liu et al., 1997]


= Co (T) + C1 (T) L- (1.2)
Po L

This form is commonly used in applications of PSP as it allows one to use any reference

condition to infer the pressure at some other condition of interest. As indicated, the

constants Co and C1 vary with temperature. More exact descriptions of PSP behavior

are provided by Winslow [2001] and Kose [2005].

Many variables influence the specific behavior of a PSP 1I- r. The procedure

of application influences the uniformity of the luminescence of the 1-ri v. One may

increase the observed luminescence of a li- -r by first applying a white primer l1-,-r to

the substrate, however this may adversely impact the response time of the l-1-, r due

to oxygen degassing between the paint and primer [Liu et al., 1997]. Thicker paint

l-i. r~s result in increased luminescence due to a larger population of luminophores.

However, thicker lI. rs also result in slower response time due to the increased length

which oxygen must diffuse into the binder. There also exists a limit, above which the

luminophores will begin to "self-quench" [C'!ii i et al., 1999], which greatly degrades

the measurable response.









Previous Work

Many studies have been performed using PSP in steady pressure fields. Bell

et al.(2001),Liu et al.(1997), and Lu et al.(2000) provide adequate reviews of the

literature. The various flow fields which have been investigated include both subsonic

and supersonic loads on aircraft models, turbomachinery such as fans and compressors

and automobile wind tunnel testing.

Cox and Dunn [1986] were the first to apply PSP to an unsteady flow field.

They investigated oxygen transport within a poly(dimethyl siloxane) (PDMS) l-i~v-r

doped with 9,10-diphenyl anthracene (9,10-D) as a Function of time using a static

calibration. They developed an analytical model for oxygen concentration within the

li. r derived from the 1-D diffusion equation. However, the li--r was viewed from

the side in this application so the intensity was the integrated intensity of the entire

I-,--i -r.

Mills and Chang [1992] were the first to look at the dynamic response of optical

film sensors, now known as PSP. The inverse of the PSP emission intensity was com-

pared to the pressure as it was quickly changed from a near vacuum to atmospheric

pressure. A model was developed which treated the paint as a first-order dynamic

system. The time constants and term weights were determined using nonlinear least

squares curve fits. The model developed by this method was found to strongly agree

with experimental results.

Both Engler [1995] and Carroll et al. [1995] introduced concurrent studies on the

response of PSP to periodic pressure fields. Engler subjected the PSP to frequencies

over the range of 0.1 to 50 Hz. The main goal was to characterize the pressure reso-

lution and dynamic range of the coating. No dynamic compensation or exploration

of the dynamics of the system were attempted. Carroll et al. presented experiments

of similar character. Much of the analysis was performed in the frequency domain.








It was shown that the PSP di-p1 II an amplitude response of a first-order dynamic
system although the phase response did not agree with expected results.
Winslow et al. [1996] developed a linearized dynamic model for PSP given in
Eqn.(1.3). This model has frequency response characteristics of a "1/2-order" system:
an amplitude response of -10 dB/decade beyond the cutoff frequency, and a phase
shift of -45. Winslow et al. then developed a dynamic compensator by performing
an inverse Fourier transform on the inverse of the frequency domain response. The
compensator was of the same form as a six term FIR filter. Applying this compensator
to the PSP response for a 1 Hz sawtooth wave yielded a corrected signal considerably
more accurate than the PSP measurement alone. This was the first application of a
dynamic compensator to PSP data.

A (, 0.1551 + 0.8449
( T[ + /1f( ) +
(1.3)

S(w) = -1/2 tan-1 (wr) 1+0.811 .94

where

1.423 2 (1.4)
S_ (log( )2)2 (t. 4)

This model demonstrated behavior similar to that of a "1/2" order system as shown
in Figure 1-2 and Figure 1-3. Winslow et al. also showed that the frequency response
of the paint was invariant to the pressure field. It was shown that coating thickness
effects the frequency response. This is due to the necessary mass diffusion through the
polymer binder. It was concluded that the developed model did not fully explain the
PSP behavior due to interactions with the primer l1 -r. However, the break points
and values of mass diffusivity agree with results of a study conducted by Carroll et al.
concerning the response of PSP to a step pressure change. Winslow et al. [2001]
developed three dynamic models for PSP. The first model, an empirical model in the
form of a transfer Function was applied to the signal from a high-frequency pressure














-20 -- -"... "
-20


S-40
0
o \

S-60

E
< -80-

1/2 Order System
-100 ....... 1st Order System
2nd Order System
Model System
1 2 0 ***** * ** *
10-2 10-1 100 101 102 103
Frequency [rad/sec]

Figure 1-2: Comparison of the Amplitude Response of Winslow's Model and 1/2,
1st, and 2nd Order Systems


transducer to model the output pressure. This model showed reasonable agreement

with data, but the coefficients developed were dependant on the thickness of the PSP

-1v-r and thus the model was only well suited to single sample usage. Diffusion-based

models with a linear and a stern-volmer calibration were both proposed and shown

to conform quite well to experimental observations.

Schairer [2002] Performed a numerical study on the influence of coating thick-

ness on the frequency response of a PSP 1iv, r. Using the one-dimensional diffusion

equation and a small sinusoidally varying pressure signal, it was shown that the op-

timum coating thickness for unsteady measurements is that which results in a -1.25

dB attenuation of the unsteady pressure signal i.e. PspI/Pp, = 0.866. This coat-

ing thickness corresponds to a maximum in the signal-to-noise ratio. The optimum












0

-20

-40 .

S-60
_0
-80 -
o \
0\
w -100

2 -120
-- \
-140- 1/2 Order System
.... 1st Order System \
-160 2nd Order System
Model System
-180 ........ .....
10-2 10-1 100 101 102 103
Frequency [radians/sec]

Figure 1-3: Comparison of the Phase Response of Winslow's Model and 1/2, 1st, and
2nd Order Systems


thickness was shown to decrease with increasing frequency. Above frequencies of 10

Hz, the greatest factor in determining the optimum thickness is the mass diff' I-i llii.

In recent years, several new types of PSP have been developed for better dynamic

response. PSP has been applied to anodized aluminum, TLC (thin-l-i- r chromatog-

raphy) plates and hard ceramic particles have been added to the polymer binder

(Gregory et al.(2002); Gregory(2004)). The porous surfaces serve to increase the

dynamic response time by enabling faster oxygen diffusion into the polymer binder.

Baron et al. [1993] first demonstrated that submillisecond response times may

be achieved using commercial TLC plates. Sakamura et al. [2005] showed that time-

resolved measurements of a pressure distribution are possible using PSP on a TLC









substrate in a two-dimensional Laval nozzle. TLC plates are easy to prepare and pro-

duce bright emission, however they are limited to use on flat plates and are relatively

fragile.

Several studies have been performed on anodized aluminum PSP [Sakaue and

Sullivan, 2000, 2001, Kameda et al., 2004]. This is made by anodizing the surface of

an aluminum body and dipping this body in a luminophore solution. The anodized

surface is very porous and serves to greatly enhance the oxygen diffusion and thus

the dynamic response of the PSP. The exact behavior of this type of PSP is still a

subject of investigation.

The suitability of PSP for detecting large pressure fluctuations has been demon-

strated. Currently, there is an interest in the smallest dynamic pressure which may

be detected using PSP. This is facilitated by an interest in hydrodynamic turbulent

pressure fluctuations of airborne bodies. Demonstration of non-invasive, direct de-

tection of turbulent noise on bodies would greatly decrease design cycle time of new

airframes.

McGraw et al. [2003] presented a proof of concept experiment for acoustic PSP

measurements. A single point measurement in a plane wave tube was performed

using a PMT and a traditional PSP formulation on a TLC substrate. McGraw et al.

reported the ability to collect valid signals for sound pressure levels (SPL) from 110

(AP = 6 Pa) to 137 dB (re 20/Pa) at a mean pressure of 101.5 kPa and frequencies

up to 3500 Hz. Significant damping of the signal was present at frequencies above

1000 Hz. In their work, signal averaging of the periodic sinusoidal output was used to

improve signal-to-noise ratio. Time accurate direct detection was not demonstrated

in this work and full field measurements were not attempted. Optimization of the

PSP formulation for the acoustic case was not attempted. An important result of

this work was the determination that temperature fluctuations due to the acoustic









pressure variations did not adversely impact the accuracy of the measurement due to

the large thermal mass of the substrate.

Motivation

Previous work has studied the dynamic response of newer types of PSP. Tra-

ditional PSP (i.e. an active and primer 1I- -r applied directly to a substrate) has

been shown to be able to detect large pressure fluctuations on the order of 0.1 atm.

[Carroll et al., 1995, 1996, Winslow et al., 1996, 2001]. This study investigates the

suitability of traditional PSP to detecting pressure fluctuations on the order of typical

acoustic signals. Diffusion limiting factors are reduced by restricting the PSP to a

thin coating. Traditional PSP possess the advantages of less cost, durability, and well

studied behavior as compared to the new variants now under scrutiny.















CHAPTER 2
EXPERIMENTAL APPARATUS

This chapter introduces the equipment used in this study. The behavior and

limitations of the plane wave tube used in this study are explored. The performance

of the tube driver is limited by the cutoff frequency of the tube to retain a planar sound

field. The photodetector, a Hamamatsu H9306-02 PMT module, is also introduced

and discussed. The performance of the detector and PSP were modelled in order to

predict a minimum pressure detection floor of the optical system, i.e., considering

the PSP and photodetector setup as a complete system. The experimental setup and

data collection systems are explained.

Plane Wave Tube

The plane wave tube used in this study is a cylinder of clear lexan and has a

diameter of 0.1 meters and length of 1.0 meter. The tube is actually a composite

structure of a lexan tube and an aluminum chamber to which a driver is mounted.

However, for the purposes of this study, the waveguide can be treated as a simple

cylinder. In this instance, the performance of the waveguide is limited by the cutoff

frequency (Eqn.(A.53)).(See Appendix A)

fc iamnCO
,n. 27a (2.1)
27ra

The cutoff frequency is the lower limit at which higher-order modes may propagate

down the waveguide. The first modes to propagate are the (1,0) and (2,0) modes,

followed by the (0,1) mode il\!,,ie and Ingard, 1987]. The mode notation is (r,O),

where the number indicates the number of 1/2 wavelengths present in each direction.

The behavior of the first 2 modes in each direction is illustrated in Figure 2-1. Below

their respective cutoff frequencies each higher-order mode is evanescent, which means









R0 Spinning) Modes


(1.0) Mode (0,1) Mode


(2,0) Mode (0,2) Mode

Figure 2-1: Schematic of a Cylindrical Waveguide Modes

it decays exponentially with distance from the source. If the waveguide is operated

below the first cutoff frequency, which is calculated as 2016 Hz, then the acoustic

field will be completely planar, i.e., the pressure at any station of the waveguide is

only a Function of time.

By operating the waveguide below the cutoff frequency, the PSP sample is en-

sured to receive a uniform pressure signal over its entire surface. Above the cutoff,

the pressure would vary with r and 0 over the surface of the sample. Since the pho-

todetector used has no innate spatial resolution, this would degrade the detectable

optical signal.


Radial Modes









Temperature Effects of Acoustic Waves

The acoustic waves manifest themselves as oscillatory isentropic compressions

of the medium. In addition to an increase in pressure (and density), there is also a

temperature perturbation. This temperature effect is relevant because temperature

can p1 i,- a substantial role in the behavior of PSP. The temperature perturbation of

an ideal gas due to a small amplitude acoustic wave is given by Swift [1988] and is

derived in Appendix A to be

7- ldP
dT Tf-,, P (2.2)
7 Po

where T,,f is the ambient temperature (298 K), 7 = 1.4 and Po is the ambient pressure

(101 kPa).

For a 140 dB acoustic wave, Eqn.(2.2) predicts a corresponding temperature

change of 0.1669 K. The PSP formulation used in this experiment has a fractional

change in intensity of -0.53'/K. [Kose, 2005] If the temperature change permeates

the PSP liv-r, this would induce a 0.08870 change in the PSP emission. Thus, the

temperature effects of the acoustic waves seem to be negligible. This result was also

confirmed experimentally by McGraw et al. [2003].

Photodetector Description

A Photomultiplier Tube (PMT) is an extremely sensitive photodetector. PMTs

have been commercially available for nearly 40 years and have become commonly

used in chemical, medical, and astronomical equipment. The extreme sensitivity

of PMTs is due to a large internal gain, typically ranging from 104 to 107. There

are two 1i i, ri" types of PMTs, side-on and head-on. In head-on PMTs the viewing

window and cathode are located at the head (end) of the tube whereas side-on PMTs

have the cathode and viewing window placed on the side of the tube. Both types

work on the same basic principles: Light enters the PMT through a viewing window.

The photons interact with the cathode material, releasing photoelectrons (electrons).









The photoelectrons are steered to the first dynode stage where they cause more

photoelectrons to be created by means of secondary electron emission. This process

continues along successive dynode stages (PMTs can have 10 or more dynode stages).

At each successive dynode, the incoming photoelectrons are multiplied again and

sent towards the next dynode. At the end of the tube, the anode collects all of the

photoelectrons [Corp., September, 2005]. This process is shown in the schematic of a

side-on PMT below in Figure 2-2. PMTs are able to obtain such large internal gain

Incoming Photon
















Meter




Power Supply

Figure 2-2: Schematic of a Side-On PMT


through the use of a large input voltage, typically on the order of 1000 Volts or larger.

This voltage is successively stepped up from perhaps 1 Volt at the first dynode, to

1000 Volts or more at the final dynode, resulting in more secondary photoelectron

emission at each succeeding dynode. Due to the large input voltage required by PMTs

it has become common practice for PMTs to be offered as complete PMT modules,

in which a more reasonable input voltage, such as 10 Volts, is stepped up by internal









circuitry within the module and then supplied to the PM tube to minimize the hazards

to people and equipment, and to eliminate the need for high voltage external power

supplies. The anode current is converted to a voltage by a conversion factor (typically

of the same order as the PMT gain) and this signal, plus noise, is the output of the

PMT.

One drawback of photomultiplier tubes is their relatively low Quantum Efficiency

(QE). The QE is the likelihood that an incoming photon will be converted to a

photoelectron and be detected by the device. There are typically two properties that

determine the overall QE of a PMT. The cathode QE, often noted as n(A), where

A is the wavelength of the incident light, is the likelihood that an incoming photon

will generate a photoelectron at the cathode. The anode Collection Efficiency (CE)

is the percentage of photoelectrons that are collected by the anode. The product

of theses two terms gives the overall QE of a PMT. The value of n(A) can range

from 0.01 4070, while the CE can be as high as 80 9070. However, the overall

QE of a PMT is typically 3070 or less [Corp., September, 2005]. This low QE results

in decreased sensitivity of the PMT and more noise resulting from the undetected

photons.

PSP Applied to Detector

We now turn to estimating the expected response of the optical system. This

may be accomplished by approximating the behavior of the PMT module and the

calibrated behavior of the PSP sample. In this instance, the signal of interest is

a fluctuating light signal (PSP reaction to an acoustic wave) superimposed onto a

large background signal (PSP emission due to Patm). Obviously, this shall serve to

complicate detection of the PSP response and yields pertinent criteria for evaluating

photodetectors for future experiments. One may pose a photodetector as an electrical

circuit. The detector then acts as a current source, where I = SpLG. The bandwidth



















+





Figure 2-3: Equivalent Circuit Representation of a Photodetector

of the detector is then evaluated as

1
B = (2.3)
2rRC

In general the bandwidth of the detector may be reduced by the addition of a low

pass (or bandpass) filter to the output of the detector. As we will find, reducing the

bandwidth has a positive impact on the system noise.

The gain of the photodetector is defined as the ratio of the current present after

amplification to that prior to amplification. For a PMT this is the anode current

divided by the photocathode current.

G = ot (2.4)
iin

We will now address the several sources of noise present in a PMT. One of the more

predictable noise sources of a PMT is thermal or Johnson noise. In order to maintain

the high sensitivity of PMTs, the materials used in the photocathodes and dynodes

have high work Functions, which means it takes very little energy to for them to

release an electron into a vacuum. This results in the materials emitting thermal

electrons due to being at room temperature. [Corp., September, 2005]









The Johnson noise appears as an AC current at the anode.


4kTB
-R R


(2.5)


The Johnson noise depends only on the temperature and internal features of the

PMT, so it is not directly subject to the gain.

The other 1i ii ,i source of noise in the PMT output is shot noise. Shot noise

arises from the statistical fluctuations of the interactions between photons and pho-

toelectrons inside the PMT. Other sources of noise include current leakage of the

circuitry, noise caused by the electric fields of the dynodes when the PMT is oper-

ated at high gain, external noise, and impedance mismatches in the experimental

wiring. These noise sources will be accounted for by specifying a dark current for the

device. The dark current is the current present at the anode when the PMT is in a

darkened environment, it thus implies an independence of the light signal. The dark

current however, is subject to gain because of the action of the dynodes and cathode

in its creation. There is also a noise contribution of the background light, this will

be considered in the shot noise of the device.


The dark current, denoted as Id, is composed of two separate currents.

Id Dark current subject to gain (from photocathode)

Ids Dark current not subject to gain (from anode)

Id Total Dark Current = Id + GIld

The signal current at the anode also has 2 contributions

Ib Anode current due to the mean background illumination

ispl -Anode current due to the illumination from the acoustic signal

ph Total anode current due to incident light = ipl + Iby









Comparing the acoustic and atmospheric pressures, it is seen that the acoustic pres-

sure is very small compared to Patm. For an acoustic wave of 140 dB, the pressure

change is 200 Pa. Even this unusually large acoustic pressure is only 0.2%7 of Patm,

which is 101,000 Pa. Thus, the fluctuating signal, isp is a small ac current super-

imposed on a mean background current, Iby. The total shot noise of the detector is

given by

i hot 2e (isp + + Idb ) BG2F + 2elIdB (2.6)

The total noise present at the anode is the sum of the Johnson and shot noises

N = /Ip+ sho
(2.7)
= 2e(i~pl + by + Idg)BG2F + 2elIdB + kTB

The signal of interest is the anode is the fluctuating signal isp. This signal is the

product of the cathode radiant sensitivity and the incident light flux. Mathematically

this is stated as ispi = Sp(rpl)AG. This enables us to state a fundamental signal-to-

noise ratio in terms of the anode current

S ispl (2.8)
/\ 2e~ddB 4kTB
N 2e (ispl + Ibgy I dg) BF+ + RG

The minimum detectable signal is the condition of S/N=1. We shall state this con-

dition as (ispl)min.

/ 2eladB 4kTB
(ip n 2 ((ispi)min + Iby + d) BF + 2 (2.9)

One should note that (ispi)min < (Ibg + Idg) and that isp = Sp(lspl)AG. We may

substitute these relations into Eq.(2.9) above. This will yield the minimum detectable

light flux from the PSP. This is termed the Noise Equivalent Power, or NEP.

/2 ((ispl)mln + bg + Idg) BFG2 + 2eIdB + 4k
NEP = (Tspl)nin SA (2.10)
m~n S, AG









We are now left with the NEP in terms of the irradiant flux of the PSP 1I, r. We shall

invoke the Stern-Volmer relations (Eqns(1.1),(1.2)) to correlate the photodetector and

PSP behaviors. The Stern-Volmer Equation is restated for convenience.

wVac Lvac
Vac- Lu = 1 + KqSXo2P (2.11)
L

The rodynamic testing form of the Stern-Volmer equation (Eqn.(1.2)) is created

by applying Eqn.(2.11) at two pressures, P and Po. The ratio of these two states

yields the rodynamic testing" form of the equation.

SCo (T) + C1 (T) L- (2.12)
po L

where

L (Ib + isp)/Sp = Radiant intensity at the acoustic pressure p

Lo = Ib/Sp = Radiant intensity at the background pressure po



The coefficients, Co(T) and CI(T) are given by

Co (T) 1
KSXo2po (2.13)
C, (T) = +KSXo2PO
c1() KSXo2p0

We may now state Eqn.(2.12) in terms of the acoustic pressure and radiant flux of

the PSP. Differentiating Eqn.(2.12) with respect to radiant flux (L) and assuming the

reference state Po is Patm gives

(A)min dp ClpoLo 1 -CC P (2.14)
(AL) in dL L2 Lo

Applying this relation to Eqn.(2.10) allows us to state the minimum detectable pres-

sure

POSpAG /2 ((isp)in + by + Id) BFG2 + 2eIB + kTB
APpmin = -Ci S G (2.15)
Ibgq SpAG









For the case of interest where background light noise dominates over dark current

and Johnson noise, Eqn.(2.15) reduces to

-Cipo -2eBF
Pmin (2.16)
V'b9 S A

One may state this as the minimum detectable sound pressure level (SPL) as


(SPL)min 20logl, (A2 ) (2.17)
2E-5 [Pa]

The first term on the right-hand side of Eqn.(2.16), CJpo/0Tib, is related to the chem-

ical composition of the luminescent sensor (PSP) and the mean operating pressure,

while the second term, /2eBF/SA, is related to the characteristics of the photode-

tector. With a goal of minimizing the minimum detectable signal we see that we

must use minimal bandwidth, B, minimize the excess noise factor, F, and maximize

the radiant sensitivity at the cathode, S,. In terms of PSP parameters, we seek to

minimize the parameter Cipo/ o. Using Eqn.(2.11) applied at a reference state, Po,

and the expression for C1 in Eqn.(2.13) yields

Cip0 (1 + KSXoPo) /2 (2.8)
Vo K SXo

as the parameter that must be minimized in the PSP formulation. Lowering KSXo,

is desirable in terms of minimizing the detectable pressure level. This is due to the

nature of C1, the slope of the linear PSP calibration, as defined in Eqn.(2.13). As

KqSXo2 goes to zero, this forces C1 to oo. Clpo//-qo (for a O.lm dia. circle) is plotted
versus KqSXo, for an atmospheric reference pressure (Po=lOlkPa) in Figure 2-4. A

minimum of Cipo/ To appears at KqSXo= 2/Po = 2E-5 Pa-'. This corresponds to

a minima of C1 and is thus a desirable value for KqSXo2 to achieve maximum coat-

ing sensitivity for an atmospheric mean pressure. The analysis was applied to two

photodetectors, a Hamamatsu H9306-02 PMT module, which utilizes a R6352 PMT

and a Hamamatsu C5460-01 Avalanche Photodiode (APD) Module, which utilizes










x 105
12





91 : : : : : : : : : : : : : ': -
10

9-

-0 8-

7

0 6-

5-

4-

3-

2 -I
10-6 10-5 10-4 10-3
KSX02

Figure 2-4: Desirable C('! im Id Properties of a PSP Coating


an S3884 APD for comparison. The analysis was applied assuming that the PSP lu-

minescent output was at a wavelength matched to the peak sensitivity wavelength of

each photodetector, 450 nm and 800 nm for the PMT and APD, respectively. Arbi-

trary radiant flux levels up to the point of maximum light input level were considered,

1.67E-6 watts and 6.OE-6 watts for the PMT and APD, respectively.

Figure 2-5 shows the minimum detectable radiant flux for a 0.lm diameter sur-

face for the two photodetectors. The curves for both the APD and PMT have a noise

floor where the thermal noise dominates. The PMT has an inherently lower noise

floor making it better for very low light level detection. As light levels increase, the

shot noise becomes a dominate noise source with the shot noise increasing as light

levels increase. At the higher light levels, the APD is seen to have slightly better

performance than the PMT, i.e., it can detect a lower light level at given background










illumination level. The minimum detectable SPL is shown in Figure 2-6. The goal is


- e APD C5460-01
: E-- PMT H9306-02









- -o- -e e -


10-11



10-12


10-13


in-141


10-15 10 10-5
Incident Light Power [W]

Figure 2-5: Minimum Detectable Radiant Flux of Detectors


to minimize the minimum detectable SPL. We observe that as background light level

(PSP background emission) increases, the minimum detectable pressure decreases.

Sound pressure levels as low as 115 dB are possible with the PMT and 106 dB with

the APD. As shown in Eqn. (2.16), for two photodetectors with identical bandwidth

and background illumination levels, the minimum detectable pressure is proportional

to F/Sp which has values of 21.67 and 7.96 for the PMT and APD, respectively.

The typical APD has significantly better radiant sensitivity (Sp) than the typical

PMT with only moderately higher excess noise factor (F). Another implication of

Equation(2.16) is that for two photodetectors with equivalent F/S,, one should se-

lect the detector with the higher maximum allowable light input. A lower gain may

be used to avoid saturating the device.


Typical PMT Application


Typical APD Application










As shown in Figure 2-5 and Figure 2-6, the PMT di-l, '1' higher sensitivity at

lower light levels due to the high device gain. There exists a limit near ~ 10-9 Watts

where the shot noise of the PMT becomes a limiting factor. At higher light levels, the

APD is seen to perform better due to its greater quantum efficiency and higher radiant

sensitivity. A PSP coating with maximum pressure sensitivity, C1, and maximum

total emission, Lo shall produce a lower detectable SPL. If possible, it is also desirable

to operate at lower mean pressure (Po) as this increases the background emission,

however this would also effect the SPL of the incident acoustic wave. Although not

explicitly considered, a coating with high dynamic response is also desired. There


250




co
0.
R 200


0.
U)



S150
C,


100
10-15


10-10
Incident Light Power [W]


Figure 2-6: Minimum Detectable SPL of Detectors


are a few assumptions in this analysis that should be noted. The presented noise

characteristics of the photodetector assume that there is no noise present in the data

acquisition system. Also, the detector performance has been assumed at the peak


\ e APD C5460-01
S PMT H9306-02


Typical APD Application


Typical PMT Application









sensitivity wavelength (A = 420nm), while in reality measurements will be conducted

at A = 650nm. Measurements not at the peak sensitivity wavelength suffer from

pronounced degradation of the quantum efficiency (QE) and the radiant sensitivity

of the detector. [Corp., August, 2005,J] The reduction of both S, and QE may have a

large effect on the actual minimum detectable signal. The cathode radiant sensitivity

is given in the PMT datasheet, Corp. [August, 2005], however there is no readily

apparent data on the behavior of the anode radiant sensitivity, Sp, as a Function of

incident light wavelength. As a result, S, is assumed to be wavelength independent

with respect to wavelength, yielding a minimum detectable signal of 115 dB.

Finally, the dynamic characteristics of the PSP have been ignored. The response

of the PSP system is inherently limited by the diffusion of oxygen within the PSP

coating. Reducing the coating thickness or increasing the mass diffusivity of the

coating can improve the PSP frequency response but typically will simultaneously

reduce the signal radiant intensity. The assumption has been made in this analysis

that sufficient PSP illumination levels and coating thicknesses are present to supply

the required background illumination levels (Ib = SpLo). In terms of PSP chemistry,

it would be desirable to customize the formulation to match the peak luminescent

wavelength to the photodetector peak sensitivity wavelength. It may also be possible

to design PSP formulations with increased sensitivity (dP/dPo) near atmospheric

pressure levels. This may result in reduced background emission Po and increased

signal emission AL.















CHAPTER 3
EXPERIMENTAL SETUP AND PROCEDURE

This chapter explains the experimental setups and procedures used in data col-

lection. The same general setup is used for all experiments however a probe connected

to a microphone must be installed in the plane wave tube for the standing wave ra-

tio tests. PSP static calibration is accomplished with the use of a vacuum chamber

and pressure transducer. Two separate data collection systems are utilized in the

experiment. An Agilent VXI system is utilized for static calibration and noise floor

measurements, while a Stanford Research Systems SR785 dynamic signal analyzer is

used for frequency response measurements.

Standing Wave Ratio Test

For testing of the Standing Wave Ratio (SWR), also known as the 2 Microphone

Method, the end cap of a 0.1m diameter, 1.0 m long lexan plane wave tube is replaced

with a specially designed cap. As shown in Figure 3-1 this specially designed cap is

fitted with a probe capable of translating along a limited distance (0.25 m). A Briiel

& Kjaer type 4138 condenser microphone, noted as \ !i rophone 1" in Figure 3

1, is attached to the probe via flexible tubing. This apparatus allows for direct

measurement of the acoustic signal at various locations inside the tube. A 2nd Briiel

& Kjaer type 4138 microphone is placed at the face of the aluminum piston at the

end of the tube, this is denoted as \ !, rophone 2" in Figure 3-1. Comparisons of

the output of microphones 1 and 2 allows for the calculation of the SWR, pressure

reflection coefficient (F) and other properties of the sample. The plane wave tube

is excited using a JBLPro 2490H driver. This driver is operated by a waveform

generator (HP/Agilent E1441A) passed through a Crown International K1 amplifier.

Data collection is accomplished with the use of an HP/Agilent VXI data acquisition









Driver

Probe

Microphone 2





PSP ample Plane Wave Tube
Microphone 1

Figure 3-1: Schematic of Experimental Setup for Standing Wave Ratio Testing


system (E1432A). The data collection parameters are outlined below in Table 3-1.

To perform the SWR test, the waveform generator is set at the specified frequency

Table 3-1: SWR Data Collection Settings

Value Parameter
10240 Sampling Frequency (f,) [Hz]
20 Data Blocks
4096 Samples/block
AC C(! .i,,,, I Coupling
100 C('i! i,, I Coupling Frequency [Hz]
Uniform Window
0.1 C('i inn. I Range [V]


and an output level of 300 mVPP. The amplifier attenuation is set to zero, this

setting corresponds to 126.9 dB SPL at 1000 Hz. The probe is advanced as close

to the sample face as possible. The signals of both microphones are recorded. The

probe is retracted 5mm from the sample face and the microphone signal is again

recorded. This procedure is repeated for four frequencies, 600 Hz, 1000 Hz, 1400 Hz,

and 1800 Hz. The microphone outputs are then analyzed as outlined in Appendix B.

The Standing Wave Ratio (SWR) is simply a ratio of the maximum and minimum

microphone voltage near the face of the sample. The magnitude of this ratio can be

analyzed to decipher acoustic properties of the specimen.









When analyzing the data, a correction factor must be applied to the microphone

location because the geometric and acoustic centers are not typically coincident. This

correction factor is a Function of the wavelength of the sound being tested and other

variables as outlined in Appendix B.

PSP Static Calibration

The PSP coating is statically calibrated using a pressure chamber and an H9306-

02 PMT module. The PSP sample is inserted into the chamber and aligned with

the photodetector. The sample is focused onto the PMT by an optical lens. The

sample is illuminated using two tungsten-halogen lamps fitted with 400/80 nm filters

(03FIB002, Melles Griot). The gain of the PMT is set such that the device is operating

at 9i1'. maximum output signal. This is to ensure proper detection of the PSP

intensity. The lamps are then turned off and the setup is left in the dark for 30

minutes in order to stabilize the PMT dark current. After 30 minutes, the dark

output signal is recorded (this will be subtracted from all subsequent measurements).

The PMT signal is acquired and the average rms value is computed and recorded.

The PMT signal is first acquired at P,,t,, this will serve as the reference pressure

for subsequent measurements. The pressure is changed and the system is left to

equilibrate. Measurements are conducted over a small range about Pt,, as this is

the anticipated pressure environment of the plane wave tube. After all experiments

are conducted, the pressure chamber is again brought to Pat, and left to settle. The

PMT output is compared to the initial measurement in order to ensure nothing has

changed in the setup.

In analyzing the calibration data, the dark current is first subtracted from all

pressure measurements. Each pressure and PMT output is then compared to the

reference state in order to yield a calibration of the same form as Eqn.(1.2).









Photomultiplier Frequency Response

To test the frequency response of the PMT an optical chopper and fiber optic

light source are utilized. The PMT is equipped with a 650/40 optical filter (\ !!.-

Griot 03FIV048). A fiber optic light source (Fiber-Lite series 180 High-Intensity

Illuminator, Dolan-Jenner Industries) is positioned in front of the detector and far

enough away as to not saturate the device. An optical chopper (300 CD Miniature

Optical C('! i.' II, Scitec Instruments Ltd.) is positioned in front of the light source to

create a fluctuating signal. The chopper used is available with several discs which al-

low for different chopping frequency ranges. The chopper is equipped with a 5 bladed

chopping disc. This disc allows for for chopping frequencies of dc to approximately

2700 Hz to be applied to the optical detector.

Acoustic Testing

The face of an aluminum piston is painted with a primer li,-.r made by dissolving

90 mg of poly(tBS-co-TFEM)(3: I'.) [poly-(tert-Butylstyrene-co-trifluoroethyl-

methacrylate)] and 100 mg of CR-800 titanium dioxide pigment (CR-800, Kerr-

McGee Corporation) in 4 mL of dichloromethane. This primer is applied to increase

the detectable response of the active l- r, which is composed of 0.75 mg of Plat-

inum meso-Tetra(pentafluorophenyl) porphrine [PtTFPP] and 30 mg of poly(tBS-co-

TFEM)(3: ') dissolved in 3 mL of dichloromethane. Both l-vr -i are applied to the

4" diameter piston, which is then installed into the plane wave tube. The PSP sample

is excited using two tungsten-halogen lamps fitted with 400/80 nm filters (03FIB002,

Melles Griot). The tube is made of clear lexan allowing optical Excitation through

the tube side walls. A microphone is co-located with the PSP sample (type 4138,

Briiel & Kjaer), enabling validation of the sound pressure field present at the PSP

surface and to test the frequency response of the PSP formulation. A photodetector

is mounted outside of the plane wave tube and focused on the PSP sample. Optical

detection is accomplished via a 650/40 optical filter ('\. II. Griot 03FIV048), and an










optical lens array. The lens array allows for the full sample surface to be focused on

the viewing window of the detector. The experimental setup is shown schematically

in Figure 3-2. The tested frequency range varies from 500-2100 Hz and is limited

by the performance envelope of the driver (2490H, JBL Professional) used to excite

the tube and the cutoff frequency of the tube. Two separate data acquisition sys-

Halogen Lamp


Photodetector
Driver (Harmamatsu
450 nm Excitaton (JBL 2490H) H9306-02)




650 nm
Luminwsne s


SPSP Sample m
Microphone \ Optical
B&K type 4138) Plane Wave Tube Lenses

Figure 3-2: Schematic of Experimental Setup for Acoustic Testing


teams are utilized. A two-channel dynamic signal analyzer (SR785, Stanford Research

Systems) is utilized for frequency response measurements and measurements over the

entire acoustic spectrum. The analyzer contains both a source and two acquisition

channels, which enables the module to control the complete experimental setup. The

analyzer source signal is passed through an amplifier (K1, Crown International) and

then routed to the JBL driver. For detector linearity measurements, the system is ex-

cited through the use of a waveform generator (E1441A, HP/Agilent) which is passed

through the amplifier, which is in turn connected to the driver. Data collection in this

case is accomplished through the use of another data acquisition system (E1432A,

HP/Agilent). Both setups allow sound pressure levels (SPL) of up to 164 dB to be

applied to the PSP sample.















CHAPTER 4
EXPERIMENTAL RESULTS

Standing Wave Ratio Results

The results of the Standing Wave Ratio testing are tabulated below in Table 4-1.

The results of the SWR tests show that the PSP sample/substrate may be treated

Table 4-1: SWR Results
Property 1800 Hz 1400 Hz 1000 Hz 600 Hz
F 0.9979 0.9959 0.9878 0.9957
0 14.22 10.86 -1.73 2.52
a 4.19E-3 7.98E-3 2.43E-2 8.64E-3
z/pc 0.675+j7.963 0.2238+j10.52 23.13-j56.82 4/45+j45.07
SWR(0) 959.9 498.8 162.7 461.1
SWR(0) [dB] 59.64 53.96 44.23 53.28


as a sound-hard surface due to the large pressure reflection coefficient, F (also known

as R), and standing wave ratio at the sample face, SWR(0). (for explanation see

Appendix A.)

These results are as expected because the substrate is an aluminum piston, which

should act as a sound hard surface when compared to air. Since the substrate is sound

hard, this means that there is a pressure doubling at the face of the PSP sample, so

that the sound pressure experienced by the PSP is nearly twice the sound pressure

at any other location in the tube. This pressure doubling allows for the high SPL at

the face of the sample. This signifies that the acoustic energy is concentrated at the

sample face and not allowed to propagate through the substrate medium and out of

the system.

PSP Calibration

The PSP static calibration results are shown below in Figure 4-1 and Table C

1. Data is acquired with settings specified in Table 4-2. These results show the









PSP behaves as predicted by Eqn.(1.2). A linear regression was performed to fit a

relationship to the data points. The resulting relationship is shown as a red line in

Figure 4-1 and is given by the equation

Vo 0.8687 P\
v 0.8687 1 + 0.13108 (4.1)
V (Po/

The linear relation has a correlation coefficient (r2) value of 0.9989 and a standard

error of 5.04E-4. This shows that the PtTFPP responds linearly to small changes in

pressure, and is expected to retain this behavior when exposed to fluctuating pressures

within the plane wave tube. Figure 4-1 shows error bars which are depicted as the

95% confidence interval.

Table 4-2: PSP Static Calibration Settings

Value Parameter
8192 Sampling Frequency (f,) [Hz]
50 Data Blocks
8192 Samples/block
AC C(! .i,,,, I Coupling
100 C('i! i,, I Coupling Frequency [Hz]
Uniform Window
10 PMT C('! i,, I Range [V]


Photodetector Frequency Response

The PMT frequency response results are shown in Figure 4-2 and Table C-2.

(note: the SR785 is capable of auto-ranging the acquisition channels, eliminating the

need to set a voltage range) Results show that the photodetector response may be

considered to be flat over the range of 100 to 2200 Hz, and thus it does not impact

the measured response of the PSP coating.

Data acquisition was accomplished with the SR785 dynamic ,i ,iv. r. Pertinent

data acquisition settings are listed in Table 4-3. The magnitude and phase responses

are shown in Figure 4-2. The magnitude response of the detector is erratic although

there is no visible cutoff frequency and the magnitude remains within 0.1 dB of the







31



1.025

1.02-

1.015-

1.01 -

0 1.005 -

1

0.995-

0.99-

0.985

0.98 '
0.98 0.985 0.99 0.995 1 1.005 1.01 1.015 1.02 1.025
P/P,


Figure 4-1: PSP Static Calibration Results


reference at 500 Hz, showing that the PMT has negligible influence on the frequency

response measurement of the PSP coating. The noise in the measurement is due to

the low gain setting of the PMT. Due to the high intensity of the fiber optic light

source, the PMT gain signal was set at 0.23 Vdc. The usable range for the gain signal

is 0 to 1.25 Vdc. At such a low gain setting, the thermal noise has a larger influence

on the device output signal. The reference signal output of the optical chopper was

Table 4-3: PMT FRF Acquisition Settings

Value Parameter
3.2 kHz Span
1.6 kHz Center Freq.
16 Hz FFT Line Width
1000 Vector Averages
Uniform Window


used as the reference signal for the frequency response measurements. This signal is








32

a constant amplitude square wave of the same frequency as the motor which drives

the chopping disc. Knowing the motor frequency and the number of blades on the

disc yields the chopping frequency.

The phase response is flat at approximately -10. This plot of phase response

can be used for qualitative results only because the phase difference of the PMT and

optical chopper is unknown. As shown in Appendix C, the phase delay is approx.

-9. This offset has been removed in Figure 4-2 as this is a constant phase difference

in the chopping motor and the reference output signal. For the shown results, the

disc was mounted to the chopping motor and all experiments were conducted without

moving the disc. Thus, the phase relationship between the disc and motor is unknown

but constant, enabling one to discern any phase roll off of the PMT over the tested

range.


1.25
1

-0.6

- -0.8

a -1
C,
S-1.2

-1.4
1


0 0 0 0 00
S O0
0 000 0
S: : : :0 0 0

S: : : :

02 103




0 0 : 0
S: : : : : 00

000



02 103
Frequency [Hz]


Figure 4-2: PMT Frequency Response









Noise in Experimental Setup

The noise present in the experimental setup is shown in Figure 4-3. This figure

is a comparison of the dark noise, background noise, and the VXI DAQ system noise.

Data was collected using settings specified in Table 4-5. The DAQ system noise is

the noise present in collecting data with no device connected to the DAQ board.

This is a Function of the influence of external noise sources. One sees that this noise

is largely dominated by 60 Hz line noise, however connecting a device to the DAQ

channel reduces this noise source.

The dark noise is the PMT output with the speaker and Excitation lights turned

off. This is an indication of the external light which leaks into the enclosure which

surrounds the experimental setup. The dark noise is seen to be roughly 2 orders of

magnitude below the background noise, showing that a minimum of external light is

entering the enclosure and that the dark noise of the PMT has minimal influence on

the device output once it is subjected to a reasonable light signal. This curve shows

a spike at 120 Hz, however this influence may be eliminated by proper grounding

of the detector. The dark noise can be seen to be white noise across the entire

span. One should note that an estimate of the true dark noise of the PMT would

be a measurement of the device output with the viewing window covered. The dark

noise mentioned here is a measure of the influence of external light sources and the

dark noise of the detector on the output signal. It was assumed that due to the

comparatively high light levels, the dark noise of the detector would be somewhat

negligible when compared to the shot noise present.

The background noise is due to the PSP luminescence at Patm, i.e., Excitation

source on, but no acoustic input signal. This is also seen to be white noise. Since

there is no temporal pressure signal the PSP emission is constant and there is no

dominant frequency component present. Both the background and dark noises are









dominated by the shot noise of the detector. Any acoustic signal supplied to the PSP

will show up as a spike among the background noise.


10-6


10-8

10-10


9 10-12


0 10-14

10-16


10-18


500 1000 1500 2000 2500 3000
Frequency [Hz]


3500 4000 4500


Figure 4-3: Experimental Noise Comparison


PSP Behavior

The dynamic behavior of the PSP is now addressed. The frequency response

is measured using the SR785 dynamic analyzer. Data acquisition parameters are

outlined in Table 4-4. The frequency response of the optical system is measured at

140, 134, 128, 122, 119, and 115 dB SPL. In all cases the optical system is shown to

behave as a "l/2"-order system (-10dB/decade attenuation, 450 phase delay) which

is in agreement with previously reported results. [Winslow et al., 1996] The behavior

of a "1/2"-order system is shown by dashed lines in Figure 4-4 and Figure 4-5. The

behavior at all SPL is consistent, however the higher SPL are better behaved due to

the decreased noise content of the signal.


1 jjj jj.... jA_L.i.hhp.wLhIJ&s.J.~.L.D.L,k.-d&.J..


10-20 L
0













S 0O 0 o O 140dBSPL
S-1 .O 0 134dBSPL
o O O 128 dB SPL
O -2- : x 122dBSPL
U D O x 119 dB SPL
S-3- x 115 dBSPL
o x no
-4- x x


o ..
-5-

-6 .
N

-8 -













There is seen to be measurable response of the coating at 122 and 119 dB SPL.

This indicates that the wavelength dependance of the anode radiant sensitivity of the

PMT, Sp, may not be proportional to the cathode radiant sensitivity as discussed

in Ch pter 2. The relative and phase response of the optical system are shown

in Figure 4-4 and Figure 4-5 (note: uncertainties have been omitted for clarity).

Tabulated data with uncertainties are located in Appendix C and plots of the response

magnitude, relative magnitude, phase, and coherence for each SPL are located in

Appendix D.







PMT power are seen to scale somewhat linearly with SPL. The noise floor is seen
-10 I---------------------































PMT power are seen to scale somewhat linearly with SPL. The noise floor is seen












-ILJ
O 140 dB SPL
S134 dB SPL
O 128 dB SPL
-20 -
122 dB SPL
x 119 dB SPL
S x 115 dB SPL
-30 -
0)

Sxx


0 Q: g O 0-----
a 0 :0 0 0
L7.1 x 0 .:
U-50 -
0
: : x x -




-60 -



-70 x0
-70 ..-----'--------------
103
Frequency [Hz]


Figure 4-5: PSP Coating Phase Response


graphically in figures Figure D 1 and Figure D-2 for the curves of 122, 119, and 115

dB SPL. Above 122 dB SPL the coherence and power seem to scale linearly with SPL.

Below 122 dB there is a decreased relationship with SPL, this indicates the increased

influence of noise on the measurement.

As seen in Figure 4-4 at 119 dB SPL, the optical system is still capable of

detecting the acoustic signal, however 115 dB SPL seems to be at or below the noise

floor of the system. This agrees well with the previously predicted noise floor of 115

dB SPL. (ref C'! plter 2)

PSP Linearity

To test for linearity of the system the HP/Agilent E1441A waveform generator

and E1432A DAQ system are utilized. SPL was varied from 145 to 157 dB at 540 Hz.

Data Acquisition settings are defined in Table 4-5. The square root of the amplitude







37

Table 4-4: PMT FRF Acquisition Settings

Value Parameter
1.6 kHz Span
1.3 kHz Center Freq.
16 Hz FFT Line Width
1000 Vector Averages
Uniform Window
0.44 Vdc PMT Gain Control
5.3 E-4 V/Pa Calibrated Mic. Sensitivity


of the PMT power spectrum at the Excitation frequency of 540 Hz for each SPL

was recorded and is di- i'. '1 in Figure 4-6 and in Table C-3 in Appendix C, which

shows a linear relationship between the acoustic pressure and the response of the

active l-I-1r, as predicted by Eqns.(1.2),(4.1). The linear equation fit to the data is

given below.


11

10-

9-

8

7

6

5

4

3-

2-

1
200


400 600 800 1000 1200 1400 1600
Acoustic Pressure [Pa]


Figure 4-6: Linearity of Optical System







38

Table 4-5: Linearity Data Acquisition Settings

Value Parameter
8192 Hz fs
8192 Data Points/Block
50 Data Blocks
100 Hz Coupling Freq.
Uniform Window
0.1 V PMT C'I .111,, I Range
0.44 Vd PMT Gain Control
5.3 E-4 V/Pa Calibrated Mic. Sensitivity


V = 6( :':.V-6 (Pa) + 2.1627E-4

r2 = 0.999 (4.2)

Std.Error = 6.511E-5

Thermal Response

The temperature influence on the response of the PSP l-v. r is investigated. As

discussed in C'! lpter 2 there is a temperature change associated with an acoustic

wave. Due to the properties of the PSP formulation, this effect was estimated to

have a minimal effect on the response of the coating. To verify this assumption,

the oxygen must be removed from the interior of the plane wave tube in order to

isolate the influence of the temperature oscillation on the PSP emission. Two holes

are drilled into the end cap of the plane wave tube, one for the addition of industrial-

grade nitrogen and one for venting. The PSP sample is removed from the end of

the tube and the tube washed with nitrogen for 20 minutes. The sample is then

re-inserted into the plane wave tube and the tube is washed with nitrogen for an

additional 5 minutes. The nitrogen hose is removed and the fittings in the end cap of

the tube are replaced with plugs. Care should be exercised as to not overpressure the

tube with respect to Patm as the pressure differential across the speaker diaphragm

may damage it. The driver is then operated at 140 dB SPL and frequency response

measurements are taken. A comparison of the coating response in air and nitrogen







39

is shown below in Figure 4-7. The results are tabulated in Appendix C with the

frequency response data of other sound pressure levels. The results show that the


SO 0 140 dB SPL-Air
0 140 dBSPL-N2
4


3-


2-


1


0mr [Q w E M o [0 m] m M

0-1r--------- --o---:------0-----U-n 9-

-1e e I
103
Frequency [Hz]


Figure 4-7: Coating Response in Air and Nitrogen


response of the coating to the temperature fluctuation are negligible compared to the

response in the presence of oxygen.

Time Resolution of Optical Signal

In addition to measurements in the frequency domain, the optical system has

shown the ability to resolve the time series data of the PSP response without the use

of data averaging as shown in Figure 4-8, provided the SPL is high enough. Using

the HP/Agilent waveform generator and DAQ system, the JBL driver was excited

at 540 Hz and 160 dB SPL. Data was collected using the parameters in Table 4-6.

The resulting data is di-pi'l 1 in Figure 4-8. In part a) of Figure 4-8 the PMT

signal di- 1 pl, a faint similarity to the microphone, however the signal is significantly







40



S 1 a)

0 0
I-

-1
0.18 0.185 0.19 0.195 0.2 0.205



1
0



0.18 0.185 0.19 0.195 0.2 0.205



0-


-1
0.18 0.185 0.19 0.195 0.2 0.205
Time [sec]


Figure 4-8: Comparison of Unfiltered PMT Output, Filtered PMT Output, and
Microphone Output


corrupted by noise. This noise is a result of the several noise sources present in

the PMT (thermal, background, dark, shot). The thermal, background, and dark

noise are manifested as broadband noise in the PMT output which degrades the

signal-to-noise ratio and hampers data collection. One may reduce the impact of

this background noise by reducing the bandwidth of the measurement. This may

be accomplished by reducing the sampling rate or by applying a bandpass filter to

the signal. Reducing the sampling rate is straightforward; however this results in a

loss of data quality due to the reduced number of data points available to describe

the photodetector output. Applying a filter, either analog or digital, to the detector

output allows sampling at a higher frequency and thus retention of more signal detail,

while also allowing the ability to choose filter parameters to suit the situation at hand.









To improve the resolution of the time series data, a digital filter was applied using

Table 4-6: Single Time Series Data Acquisition Settings

Value Parameter
6.4 kHz Span
8192 Data Points/Block
1 Data Blocks
100 Hz Coupling Freq.
Uniform Window
0.1 V Range
0.44 Vdc PMT Gain Control
5.3 E-4 V/Pa Calibrated Mic. Sensitivity


Matlab. A 6th order Butterworth bandpass filter centered at 540 Hz with cutoff

frequencies of +/- 50 Hz was applied to both the microphone and PMT data, the

filtered PMT signal is di-,i'l 1 in part b) of Figure 4-8. In this case, much of the

noise present in the unfiltered signal has been removed and the filtered signal has

clearly resolved the acoustic signal as referenced by the filtered microphone output in

plot c). The amplitude modulation apparent in part b) of Figure 4-8 is due to noise

which has passed through the filter and characteristics of the filter.

Uncertainty Analysis

PSP Static Calibration Uncertainty

We will now compute the uncertainty of the static calibration test. The static

calibration of the coating was found to follow Eqn. (4.1), restated here for convenience.

Vo P\
V- 0.8687 +0.13108 (4.3)
V Po

Solving the above Equation for V yields

7.63VoPo
V (4.4)
Po + 6.627P

We shall compute the uncertainty as the square root of the sum of the squares. We

must first solve for the uncertainties of the measured voltage and pressure. This is









summarized as
U = B2 + (,


B = B (4.5)
i-i


P

where Bi and Pi are the bias and precision errors respectively of each measurement

and t,95 is the student's t-distribution for 95'7 confidence (v number of samples).

For greater than 30 samples, the standard confidence interval, i.e., t,,95 is 2. For

the reference condition, ,, we shall use the standard deviation of the mean, 2 The

uncertainty in the measured voltage is taken to be the standard deviation, denoted as

a, given in Table C 1. For the pressure uncertainty, we will use the average standard

deviation of the pressure 1 i11,i- 5E-4. The pressure and voltage uncertainties are

substituted into (4.6) for the total uncertainty of the output voltage given below.

The resulting PMT output level is the mean voltage due to the PSP response to a

steady pressure. Thus, the uncertainty of interest is the standard deviation of the

mean, 2 The resulting uncertainties are listed in Table C 1 as ui, and shown as

error bars in Figure 4-1.


U, 1( UVo + ( U p2 + UP)2 (4.6)
,V9 OP 9Po

The resulting uncertainty for each pressure is listed in Table C 1 and shown graphi-

cally in Figure 4-1.

Frequency Response Errors

The frequency response errors are self-contained measurements performed by the

SR785 analyzer. As such, it is subject to errors and uncertainties which are based on

the spectral measurements used to calculate the frequency response. It is now useful

to introduce notation typically used in dealing with random, periodic signals. The









frequency response measurements are subject to both bias and precision errors. We

shall denote a bias error as b[x] and a precision error as c[x], where x is the quantity

being examined. We shall denote the estimated quantities as x. The quantities

measured are in fact estimates of the true values, hence, they are subject to errors.

If the true values were known then no error analysis would be necessary.

We shall first look at the coherence of the frequency response. The coherence

between signals x and y is denoted as ? and is defined as [Bendat and Piersol, 2000]


(f) W G(4.7)
xx yy

The coherence Function is a method to describe the correlation between the output,

y, and input signal, x. The coherence can vary from 0 to 1, with 1 being perfect

correlation between the two signals. High coherence values lead to less errors in

spectral measurements. The normalized bias and precision coherence errors are given

as [Bendat and Piersol, 2000]


b[2] 1 (i 2(4.8)

[r^29] V 2 *1-- )1-

where nd is how many times the data is averaged (number of data blocks).

For the frequency response itself, the bias of the magnitude is proportional to the

amount of noise in the measurement. The measurement signal is typically specified as

Gxx = G, + G,, where Gn is the noise magnitude and G,, is the signal magnitude.

In tables in Appendix C, Gix is the magnitude of the signal at the specified frequency

and GT is the observed average magnitude of the noise in the signal (response at

other frequencies). The normalized bias and precision errors of the frequency response









are given as [Bendat and Piersol, 2000]


b "J] [Guu+Gnn


L(4.9)




Then the total uncertainty for each measured quantity (magnitude, phase, coherence)

is then given by Eqn.(4.5). For a large number of samples, the standard 9570 con-

fidence interval is 2U. This is used to generate the confidence interval shown in

figures for each SPL in Appendix D.

Errors for each SPL tested are tabulated in Appendix C. One sees that for the

lower SPL the errors in the frequency response become considerable. This is due

to the very low coherence of the microphone-PSP signal. At levels of 128 dB SPL

and higher the typical magnitude errors become 10%0 or less. To further decrease the

errors, one must increase the number of averages (data blocks) gathered as the errors

scale as 1. Appendix C also contains magnitude and phase plots with error bars

of the response of the optical system at each SPL.















CHAPTER 5
CONCLUSIONS

The research described in this thesis successfully investigated the response of

PtTFPP in poly(tBS-co-TFEM)(3:i I.) to acoustic pressure fluctuations. The research

showed that the coating responds in the manner of a "1/2"-order system. The coating

was shown to have a noise floor similar to the predicted value of 115 dB SPL.

Frequency response measurements showed the optical detector to have negligible

(flat) response over the applicable frequency range. It was also shown that the optical

coating response scales linearly with the applied acoustic pressure to the lower limit

of the noise floor of the system. The noise floor was numerically estimated to be 115

dB SPL. Subsequent experimental data revealed the actual noise floor to be within

5% of this value. The temperature dependance of the coating due to the acoustic

waves was assumed and verified to be negligible compared to the pressure response.

The optical system was also shown to have the ability of direct temporal resolution

of the PSP emission. Adequate filtering of the PMT signal removes the significant

noise component and reveals a clear correlation of the PSP emission to a microphone

located at the coating surface.

Although the research conducted in this thesis is complete, there is future work to

be conducted. The application of other photodetectors to this experimental method

may allow resolution of lower sound pressure levels. Avalanche photodiodes and high-

speed CCD cameras are two detectors which may prove useful in this area of study.

With the use of high-speed phase locked CCD cameras, it may prove possible to

directly image the surface of a PSP sample in a fluctuating pressure field, thereby

gaining an optical record of the exact pressure distribution, similar to results achieved

using PSP in wind tunnels.







46

The upper frequency applied to the coating in this research was limited by the

cutoff frequency of the plane wave tube. Future work should utilize apparatus with

higher cutoff frequencies in order to better characterize the response of the coating(s).

The chemistry of a PSP formulation defines its properties and was ultimately

the limiting factor in terms of noise floor in this research. New PSP formulations are

the subject of continual research. Discovery of new binder-luminophore formulations

which promote increased oxygen diffusion and greater sensitivity near atmospheric

pressure levels will enable further reduction of the noise floor in dynamic pressure

applications.














APPENDIX A
DERIVATIONS OF ACOUSTIC RELATIONS

Temperature Change of a Small Isentropic Compression

First, we assume that temperature is a Function of pressure and entropy. An

acoustic wave (or any small, isentropic compression) can be treated as a perturbation

about a mean.
dT dT
To + t' -To P' + T'+ 0 (2) (A.1)

where 0(e2) are higher order terms that may be neglected for the time being.

Since we have assumed the compression process to be isentropic, we may make

use of the isentropic relations for pressure and temperature.


p 1 (A.2)
To Po(

where 7 = C,/C,.

Substituting these relations into Eq.(A.1), we are left with

dP TP '- 1P P
T' = P' To (-P' (A.3)


Which, after some manipulation yields


T' To (A.4)


We may now set T and P to be any arbitrary temperature and pressure. We shall

choose the quiescent values, To and Po. This gives us the final form of the temperature

change of an isentropic compression.


T' To 1) To 1) P2 (A.5)
S7 PO 7 Poco









Derivation of the One-Dimensional Wave Equation

We shall begin by examining a homogenous medium at rest.

P Po

p = po (A.6)
= 0

We will assume that any disturbances to this medium are small compared to the value

of the static properties Po and po. This is known as the small signal approximation.

Thus, we have the properties of a small disturbance initiated in the medium at rest:

16pI < po
\6PI < Po = poce (A.7)

IUl < Co

We will use the above quantities to linearize the conservation equations. We first

examine the 1-D Continuity equation:


Pt + (pu), 0 (A.8)

We will define 16p| = P- po as the change in density from the equilibrium state to the

disturbed state. It is somewhat straightforward to substitute this relation for density

into Eq.(A.8)

S p+po (A.9)

Pt +, '", + Px = (6p + po)t + (6p + po) u + (6p + po) u = 0

Seeing that po is constant leaves us with

6pt + 6, ',,, + pou, + 6pfu = 0
(A.10)
0o (E) + O (E2) + O (E) + O (E2)= 0








The 2nd and 4th terms are of second order and thus can be neglected. Removing these
terms leaves us with the linearized conr lii,, i equation for a homogeneous medium

6pt + pox = 0 (A.11)

We will now approach the momentum equation in the same manner. We will start
with the 1-D momentum equation

p (ut + uuX) + PX = 0 (A.12)

Making the same assumption of the change in density as above leaves

(6p + po) (ut + uuX) + P 0
6,n, + 6,,,.,, + pout + ,,,,.", + P= 0 (A.13)
o (2) + O (E3) + (E)+O (2) + ()

Neglecting higher-order terms leaves us with the linearized momentum equation

pout + P 0 (A.14)

Using the Taylor expansion of the ideal gas law,P = 6pc, and continuity and mo-
mentum, Eqs.(A.11),(A.14) we may deduce the linear wave equation. First we will
eliminate density
6p= ,
co (A.15)
(.O)t+,.,,,,, -0
We may remove the pressure terms from Eqs(A.14) and (A.15)

(pout + p- 0) d +,-. =
t !-(( t 0)
Poutt =0 + .. =0
Co (A.16)
PXt = utt = C0Uzz = PtX = 0









This leaves us with the linearized 1-D wave equation

1
Uxx -utt 0 (A.17)
CO

If one chooses to eliminate u rather than P in Eq.(A.16), the result is the wave

equation in terms of pressure
1
Pxx P=0 (A. 18)
Co
In 3-D/vector notation, we are left with the more familiar form of the wave equation

Blackstock [2000]

V2P Ptt 0 (A.19)
Co

Derivation of the Cutoff Frequency

Let us first define what is meant by Group V l.. Hil and Phase V l1.. IH,:

Group Velocity

The group velocity is the progress of the "center of ,ii ,ii- of a group of waves of

different frequencies. This may be thought of as the average speed of a group of

vehicles on a highway.

Phase Velocity

Phase velocity, CO, is the velocity at which the phase angle, w(t x/c6), of harmonic

waves of the same frequency propagates down the waveguide. This can be likened to

the speed of a school bus full of children (harmonic waves) travelling down a highway.

How We Get Phase Velocity

We begin with the phase of a harmonic acoustic wave


; = (wt k'x) (A.20)


where

k /o) 2 (A.21)


is known as the wave number.









We may differentiate Eqn.(A.20)

d( = wdt kdx (A.22)


where k' is the wave number for the nth mode. In Eqn A.22 we see that for constant

phase one is left with

(d) (A.23)

This expression is denoted c%, and is known as the phase velocity. We may now

substitute the frequency from the nth mode from the derivation of the waveguide

equation, 7 = nry/a, which gives us


c=P c (A.24)
k _22)
kln (nw)2 1i


This relation shows that waveguides are dispersive because the phase speed is a

Function of frequency. By graphing Eqn. A.24, one will see that the phase velocity

will increase with frequency until a point where


f = o f (A.25)
2a

At which point c oo. This point is known as the cutoff frequency. We may

rephrase the phase speed in terms of the cutoff frequency as


S co (A.26)
c2


Below the cutoff frequency, the wave number is imaginary. This means that the

acoustic waves are evanescent and decay exponentially with distance. Above the

cutoff frequency, the acoustic waves are real and propagate down the tube. One will

alv--i- have acoustic waves however, as ko = 0 corresponds to plane waves. Any value

of n greater than zero is indicative of higher order modes.









Derivation of the Waveguide Equations

In this section We will derive the equations governing the behavior of both rec-

tangular and cylindrical waveguides.

Derivation of the Rectangular Waveguide Equation

If A > a then sound will propagate down a waveguide as a plane wave. The

acoustic signal can be described as


P'(x, t) f(x ct) + g(x + ct) (A.27)


This is a solution to the 3-D Wave Equation(A.19)


V2P Ptt = 0 (A.28)


We will consider a rigid walled duct as shown in Figure A-1. By inspection, one may

deduce the boundary conditions of no flow into the walls of the duct. Mathematically

stated, the boundary conditions are

i = 0 at x = 0, a
(A.29)
y = 0 at y = a

There are no evident boundary conditions in the z-direction as this is the propagation

y










a
z


Figure A-1: Schematic of a Square Duct









direction of the tube and no information is given concerning the source. This may

not be necessary and it will be addressed as needed.

We see that Eq.(A.19), the three-dimensional wave equation, is a f(x,y,z,t) as

shown in Figure A-1. This equation can be solved through the use of separation of

variables by assuming a solution of the form Morse and Ingard [1987]

P'(x,y, z, t) f(x)g(y)h(z)ejwt (A.30)

where f,g,h are Functions of only x,y,z respectively. Separating Eq. (A.30) and solving

for f,g,h yields

at2 g ,9J a2 J Jt)
(A.31)
a fr' fg" hew a fgh"eJtC

Substituting these relations into the Wave Equation (Eq.(A.18)) yields

-W2f h ghf" f hg" f gh" jw 2 f/ g" h"
O = 0 (A.32)
fghejit c f g h

which may be rewritten as
f g" h" w2
f h -(A.33)
f g h C2
This shows us that a Function of x equals a Function of y and z. This is true only if

both sides are equal to a constant. We may now separate and solve the equation for

each direction, starting with f(x).

f -a or f"+a f 0 (A.34)
f I

This homogenous, 2nd order ODE has roots of ja, thus the solution has the form

f = Alcos(aix) + Bisin(aix). Invoking the boundary condition of no flow normal
to the wall gives us

df 0 =- B1 0,aO1 (A.35)
dx z=O,a a









Thus, f = Alcos(mwx/a). Repeating the above procedure for g(y) yields a solution
of the same form, g = A2cos(nO y/a).

We are now left with the behavior of the propagation direction (z). To solve for

this behavior, we shall substitute the solutions for f(x) and g(y) into Eq.(A.33) and

solve for h(z).
f" _-Al C -OS x 2 T2
S A2 cos ( (A.36)
f Acos(m7x) a2
-A2 (nS ) _2 _2
g a22 cos (A.37)
g A2cos( ) aa2 )
Substitution into Eq.(A.33) gives us

h" + n- (m2 )2) h= 0 (A.38)

The coefficient of h is made up of constant values. This quantity will be denoted as k2

and is known as the Dispersion Equation. One now sees that Eq.(A.38) is of the same

form as Eq.(A.34). For Eq.(A.34) the geometric form was chosen to emphasize the

shape of the Function. In this case we will use the exponential form of the solution

since this equation describes the propagation of a wave:

h = Ce-kmz + '_, (A.39)

The constant k has been written as kmn to remind us of its dependence on the values
of m and n. We now have assembled solutions for all components of P'(x,y,z,t) that

were assumed in Eq.(A.30) and we may assemble the final solution, which is simply

a matter of superposition.

P'(x, y, z, t)= f Ji, '* = (cos (m ) cos ( ) (Cle-kmnZ +C, )) e
a a (A.40)
P'(x, y, z, t) cos (mx) cos (w t) (Aej (wt-kmn) + B pnej(wt+kmnz)

where Am, and Bmn are constants determined by source conditions which can be

stated as P(x, y, 0, t) = F(x, y ',. <[Blackstock, 2000]









The 2 indices, m and n, are the mode numbers. Physically these numbers

represent the number of 1/2 wavelengths present in the x and y directions, with

(m 0,n 0) representing the plane wave mode which has uniform pressure in both x
and y. [Schultz, 2004]

Derivation of the Cylindrical Waveguide Equation

Having tackled the rectangular waveguide equation, we will now approach the

cylindrical waveguide in much the same manner. We will consider a cylindrical

waveguide of radius a as shown in Figure A-2. Again, we begin with the wave











Figure A-2: Schematic of a Cylindrical Duct


equation,

V2P tPU 0 (A.41)

In cylindrical coordinates, the Laplacian operator (V2) has the form

S() () 1 t 2 02
r + + z (A.42)
r Or Or ) r2 902 OZ2

We have the same boundary condition as before,


iUr a = 0 (A.43)

We will assume a separable solution of the same form as above,


P'(r, 0, z, t) = R(r)O(0)Z()ejWt


(A.44)









Substitution into Eq(A.19) and simplifying leaves

R" R' 0" Z" w2
+ + + (A.45)
R rR r26 Z c (A.45)

We will let w2/c = k2. This bears some resemblance to Eq.(A.33) however the r's

apparent in this case must be dealt with. We may first address the Z term. We will

equate this to a constant and solve.

Z/
-k (A.46)
Z

The form of this equation should be familiar to the reader. We may assume a solution

of the form as above

Z(z) = Aejkzz + Be-jkzz (A.47)

Returning to Eq.(A.45), we are left with

R" R' ("1
-+ + k2 k- k (A.48)
R rR r2( z

We will define a constant, k,, such that k2 = k2 + k2. This leaves

R" R' ("
+ -+ +k2 0 (A.49)
R rR r2( )

Multiplying by r2 enables us to remove the component.

O"
S-m2 (A.50)


This form has a solution of 0(0) = As cos(mO) + Bo sin(mO) where m is an integer.

We are now left with only Functions of r. Multiplying the remaining quantity of

Eq.(A.45) by R gives
1
R" + -R' + (r2k n2) R 0 (A.51)

This is a Bessel Equation of order m. Thus, the solution is R(r) = ArJ(krr) +

BrNm(krr). However, the Neumann Function (also known as Bessel Function of

2"d kind) (Nm(krr)) is unbounded as r 0 so it is not physically realizable for a









cylindrical waveguide. However, this term should be retained when dealing with an

annular waveguide. Combining the r, z, and O solutions yields us


P'(r, 0, z, t) = Jm(krr) (cos(m0) + sin(m0)) (Amnej(wt+kz) + Bemnne(w-k)) (A.52)


As in the rectangular waveguide the m and n indices give an indication of the number

of 1/2 wavelengths present, although in this case they represent the r and 0 directions.

The first modes to propagate are the (1,0) and (2,0) modes, followed by the (0,1) mode

[\!i e and Ingard, 1987]. For a cylindrical waveguide, the cutoff frequency has the

form
fc amnCO
Tfn 27a (A.53)

where amn is the nth zero of J,. The cutoff frequency of a mode is the minimum

frequency at which that mode can propagate down the waveguide. For the waveguide

used in this study, the 2 lowest cutoff frequencies are 2016 Hz and 3344 Hz. Below

2016 Hz the acoustic field within the waveguide is planar.

Normal Incidence Sound Reflection and Transmission

Let us examine the pressure field at a normal incidence surface between two ideal

fluids, shown below in Figure A-3, where indicated pressures are given by We will

Incident Wave p+= p+(t x/cl)
Reflected Wave p- = p-(t + x/c)
Transmitted Wave pt pt'(t x/c2)


now define a reflection coefficient, F


F = (A.54)


We will also define a transmission coefficient,


T (A.55)
p+









Medium 1
Zi--pIcl



p+ ------









p"


Medium 2
Z2=p2c2








Sptr


Figure A-3: Sound Reflection and Transmission at a Normal Incidence Surface

We shall assume the interface is stationary, which leads to


p+ + p- = pt


(A.56)


dividing by p+ and manipulation shows us that


1+R T


(A.57)


In addition to pressure, velocity must be continuous across the interface. Using the

same notation as pressure, it is straightforward to deduce that u+ + u- = ut. We

would like to know the boundary condition in terms of F and T. To do this we will

use the characteristic impedance of each medium (Z pc) since the acoustic waves in

each media are by definition travelling at the acoustic speed, or u=c. Substitution

leaves us with
O+ O- ptr
p p (A.58)
ZI Z1 Z2









Multiplication by Zi/p+ yields
Z1
1 R = -T (A.59)
Z2
Solving Eqn.(A.59) and (A.57) gives the following relations


R = 2 Z (A.60)
Z2 + ZI

2Z2
T 22 (A.61)
Z2 + ZI
We will now examine three conditions of a normal incidence surface. First, let us

consider an interface at which Z2 < Z1. In this case, Eqn.(A.60) R = -Z1/Z1 = -1,

which means there is perfect reflection 1800 out of phase. Then, pt 0 so that p+

-p-, so that the pressure at the interface tends to zero while the velocity doubles,

from Eqn.(A.57). This situation is known as a sound soft boundary and occurs at

the end of a tube or for an acoustic wave travelling from water into air.

Next, consider what happens if Z2 > Z1. In this case, R 1, or p+ = p. This

tells us that pt = 0. At the interface, since p+ and p- are reflected in phase, they are

additive, interface = p+ + p- = 2p. Also, since the pressure signal can not penetrate

into medium 2, neither does the velocity signal, ut = 0, or u+ = u-. So there is

a pressure doubling in medium 1 at the interface and zero velocity at the interface.

This is known as a sound hard boundary and occurs for a wave travelling from air

into water, or from air into another suitable medium with a much greater impedance,

such as a block of aluminum.

Thirdly, what if the media are identical, or at least have identical impedance. In

this case Z1 = Z2, so that R 0. There is perfect transmission across the interface,

which is intuitively satisfying. [Blackstock, 2000]















APPENDIX B
STANDING WAVE RATIO METHOD

Standing Wave Ratio Calculations

The Standing Wave Ratio/2 Microphone Method is a commonly used proce-

dure for determining the impedance ratios and normal incidence sound absorption

coefficients of acoustical materials.

A plane wave travelling down a waveguide impinges on the end of the tube and

is reflected back in the opposite direction. In this process, a standing wave pattern

is produced which can be measured using a microphone. Using the standing wave

ratio (SWR) at the face of a test specimen placed at the end of the tube, the normal

incidence sound absorption coefficient, a,, pressure reflection coefficient, F, and other

properties can be calculated. The method prescribed below is that of the AST\

C384-98 Standard [of Testing and ASTM] and is valid only for planar sound fields,

i.e., it is only valid below the cutoff frequency of a waveguide. The Standing Wave

Ratio is defined as

SWR(x)= () (B.1)
Vmin (X)
where V(x) is the output voltage of the microphone at station x of the waveguide.

To discern the standing wave pattern within the tube, the exact location of the

microphone with respect to the sample face must be known. This is accomplished by

the use of a millimeter scale attached to the bottom of the waveguide. This enables the

distance from the specimen to the microphone to be known at all times. A correction

factor must be applied to the location of the microphone because the acoustic and

geometric centers of the probe are not necessarily coincident. The correction factor









is defined as

cor m (B.2)

where

xcor = Correction Factor

X1/4 = Scale Reading with Microphone at 1st minimum

xmr = Scale reading with microphone touching face of specimen

When making measurements, scale readings at each frequency should be corrected as

follows:

S= (Xobs Xsf) Xcor (B.3)

where

x =True distance from specimen [mm]

Xobs = Observed scale reading [mm]

xsf = Observed scale reading with probe touching specimen [mm]

If possible, it is desired to adjust the scale such that xsf=0



Following data collection, the microphone signal can be graphed as shown below

in Figure B 1, Figure B-2, Figure B-3, and Figure B-4 to yield the voltage as a

Function of xcor. This data is then used to determine the properties of the sample.

Data reduction is performed differently according to the nature of the available data.

If two or more minima are present, the maximum voltage nearest the sample face

is taken to be Vmax(0). Vmi,(0) is then found by using the following formula


V..min(0) V (x) V (2)- V (X) (B.4)
X2 X1

If one minima and one maxima are present, one uses the available maxima as Vmax (0),

and the tube attenuation, (, must be called upon to discern Vmi,(O). ( may be









estimated as

( =0.02203- (B.5)
2aco

where

f = Driver Frequency [Hz]

a = Tube radius

co = Speed of Sound

Using ( one may calculate Vmin(O) using


Vmin (0) = V (xi) (XiVmax (0) (B.6)


One may now calculate the Pressure Reflection Coefficient, F. For an infinitely rigid

surface F = 1 which means that the entirety of the acoustic energy is reflected back

into the medium. Obviously, an infinitely rigid surface does not exist, but it is

possible to generate F's which are very nearly 1. F is a complex quantity and has

both a magnitude and phase

ipi SWR(0)-1
SSWR(0)+1 (B.7)
0 =720 () 180

where x, is the distance from the specimen to the first minimum.

One may also calculate the Normal Incidence Sound Absorption Coefficient, aO,

and the impedance ratio, z/pc


a, = 1 P|2
(B.8)
z l+r
pc 1-F








63


Standing Wave Ratio Figures


x 10-3 Microphone Voltage vs. Distance from Piston Face
61-----


01 1 I I-E ----I-I-I 1-1
-250 -200 -150 -100 -50 0 50
Corrected Distance from Piston Face (Xco) [mm]


Figure B-1: Microphone Voltage vs. xcor for 600 Hz Excitation


5

"(i
E
> 4

C-

S3
CL
"c
O. 3
O




1



















Cn


0


0
0
0 1
t-
t-
o
O


64



x 10-4 Microphone Voltage vs. Distance from Piston Face


01
-150 -100 -50 0 50 100 150
Corrected Distance from Piston Face (Xco) [mm]


Figure B-2: Microphone Voltage vs. Xcor for 1000 Hz Excitation


Microphone Voltage vs. Distance from Piston Face
0.012



0.01 -



0.008



0.006



0.004



0.002



0
-100 -50 0 50 100 150 200
Corrected Distance from Piston Face (Xco) [mm]


Figure B-3: Microphone Voltage vs. Xcor for 1400 Hz Excitation


























x 10-5 Microphone Voltage vs. Distance from Piston Face
7


6-








2-4
S4
0





-50 0 50 100 150 200 250





Corrected Distance from Piston Face (Xc) [mm]
Figure B4: Microphone Voltage vs. for 1800 Hz Excitation
F 2





0
-50 0 50 100 150 200 250
Corrected Distance from Piston Face (Xcor [mm]


Figure B-4: Microphone Voltage vs. x... for 1800 Hz Excitation















APPENDIX C
TABULATED EXPERIMENTAL RESULTS

Table C 1: PSP Static Calibration Results


P/PO
/o 1
0 -'-1I

1.000
1.0 10
1.020


Vr-rs
8.526
8.472
8.387
8.310
8.251
1.09E-2


a
0.066
0.C' .
0.074
0.0. I:.
0.067
2.40E


V V'dark
8.515
8.461
8.376
8.299
8.240


13/V
0 .-,17
0 *'*
1.000
1.01('
1.0165


(Note: In the following tables the Coherence (between the microphone and PMT)


is denoted by its common symbol, 7'2)


P Ipsial
14.346
14.457
14.617
14.766

dark


it,
7.21E-
7.18E-
7.10E
7.04E
6.98E











Table C-2:

Freq. [Hz]

106
204
,: I ;


608
704


10 ,-,
1104
1200
1 < t' ,
1 : I -,
1504
1600


1904
2000
2096
*-. '


PMT Frequency Response Results

Mag. [] Mag. [dB] Phase (o)


1.164
1.167
1.164
1.166
1.165
1.167
1.161
1.161
1.163
1.158
1.160
1.1, :;
1.1". I
1.165
1.163
1.167
1.166
1.164
1.160
1.159
1.158
1.163


1.319
1.341
1.319
1.334
1.327
1.341
1.297
1.297
1.312
1.274
1 '-: "

1.312
1.319
1.327
1.312
1.341
1.334
1.319


1.274
1.312


-9.85
-9.92
-9.93
-10.14
-9.92
-10.08
-9.82
-10.04
-10.03
-10.02
-10.1

-10.13
-9 *!I.
-10.13
-10.08
-9.81
-9.9
-10.14
-10.21
-10.07
-10.18


Table C-3: PSP Linearitv Results


Pressure [Pa]
356.23
497.55
631.89
762.64

1011.51
1129.06
1245.66
1357.55
1 i,-_-.62


SPL [dB]
145.01
147.92
149.99
15 i .
1 ,:2 -,
154.08
155.03
155.89
156.63
157.32


PMT Power [pV2]
6.02
12.08
17.97

33.83
44.70
55.35
64.80
79.58
? ..19


VP TPower [mV]
2.45
3.48
4.24
5.12
5.82
6.69
7.44
8.05
8.92
9.65













F_
5(

7(
8
9:
10
11
1:
13
1 .
14
15
17
17
1'
20
[1


115 dB SPL F..- ::-. -y i-.onse Data


- i Gxx GRe Resp. Rel. Mag Phase -72 SPL
00 4.546 0.15 5.571 0.000 -30.33 19.60 115.1. :1.
;. 2.324 0.15 4.195 -2.464 -56.63 9.70 115.185
00 2.304 0.15 3.975 -2.932 -47.30 9.31 115.614
04 2.41 0.15 4.213 -2.427 -48.35 10.27 115.301
24 1.424 0.15 -4.721 -19.82 5.65 115.319
04 -. 0.15 4.1 -2.468 -56.13 10.40 115.57
00 2.301 0.15 4.0-. -2 c..*5 -37.86 9.0'" 115.372
i 1 1.591 0.15 3.329 -4.472 -33 ";; 6 4, 115.548
00 3.050 0.15 4.559 -1.741 -. : )1 12.63 115.644
1.185 0.15 '" "' -5.611 -41.24 1 ,. 115.408
92 1.187 0.15 2.913 -5.632 -65.06 4.652 115.437
96 0.7 :, 0.15 :"' -7.351 -(. ::, 2.951 115.048
00 0.579 0.15 1.944 -9.145 -42.94 2.330 11 .1
1.003 0.15 2.710 -6.259 -48.97 4.174 115.333
0.779 0.15 _- '.,I -7.351 -56.73 3.148 115.328
20 1.072 0.15 2.821 -5.911 -49.25 4.377 115.273
[z] [n ,U [n Vj [, V/Pa] [dB] [deg. [*10-] [dB re -/. Pa]




Table C-5: 115 dB SPL Frequency Response Normalized Error Estimates


Mag. Random
0.158
( I ,
0.231
0.220
0.297
0.218
0.233
0.273
0.198
( *
0.327
0.411
0.463
0.345
0 :- .
0.337


Phase Random
0.158
0.226
0.231
0.220
0.297
0.218
0.233
0.273
0.1' .
( I .
0.327
0.411
0.463
0.345

0.337


Mag. Bias
-0.032
-0.061
-0.061
-0.059
-0 i
-0.056
-0.061
-I 1 1 1
-0.047
-0.113
-0. 112
-0.171
-( _-'I ,
-0.130
-0.162
-0.123


2 Bias
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
O.Oot


,2 Random
0.313
0.450
0.459
0.437
0(I _'
0.434
0.465
0.543

0.654
0.653
0.821
0 -4
0., '1
0.795
0.673


Table C-4:











a119 dB SPL F..I -. : ,.y R i.onse Data


500

700
804
932
1020
1100
1:01
1300
1 -., i.
1492
1620
1700
1828
1892
2020
[l[z]


CGxx
5.966
5.797
3.995
4. -.' I
2.375
3.476
2.912
5.160
- .. I

3.138
2. :1.
2.827
2.947
1.922
1.872
[o2-2 J


G0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.[15
In V^s] I


Table C-7: 119 dB SPL Trequency Response Normalized Error Estimates


Mag. Random
1.450
0.148
0.174
0.162
0.232
0.1' .
0.211
0.159
0.246
0.179
0.175
0.307
0.226
0.192
0 :', ,
0.321


Phase Random
1.450
0.148
0.174
0.162
0.232
0.1' .
0.211
0.159
0.246
0.179
0.175
0.307
0 _. -
0.192
0.321
0.321


2 Bias
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
O.Oot


/2 Random

( "'2
0.344
0.320
0.462

0.420
0.316
0.4'!-
0.355
0.348
0.612
0.450
0 ..: '
0.736
0.640


Resp.
4 '- ,
: : ,
3 !,-.
3.564
2.897
3.238
2.953
2.739
2.512
2.492
2.522
2.517
2.516
2.527

2.227
[pV/Pa]


Rel. Mag
0.000
t -. ,
-1.465
-1.213
-3.012
-2.046
-2.846
-3.500
-4.251
-4.320
-4.217
-4.234
-4.237
-4.199
-4.' .
-5.297
[dB]


Phase
- .. 43
-34.02
-42.46
-37.25
_'- 48
-47. .,
-55.84
-47.55
-26.04

-41.54
- '.60
-I";, "7
-41.01
- ,. 1i6
-54.07
[deg.]


,.2
xy


16.330
18.7 ,,
9.199
13 '
11. (''i
19 '
8. ','
15.370
16.1 I,
;-. t
9.(.

3.662
4.843
[*W0-3]


SPL
119.482
119.655
119.211
119.532
119.444
119.187
119.216
119.651
119.531
119 ',
119.212
119.511
119.447
119., 1 4,.
119.255
119.7 : .
[dB re ',. Pa]


Mag. Bias
-0.025
-0.025
-0.0 :.
-0.032
-0.059
-0.041
-0.049
-0.028
-0.062
-0.060
-0.046
-0.050
-0.050
-0.048
-0.072
-0.074


Table C-6:













F_
5(

7(
8
9
10
11
1
13
1 *
14
16
17
18
1i
20
[H


122 dB SPL F..i-:,. iy R i..onse Data


S Gxx GR Resp. Rel. Mag Phase -2 SPL
00 15.530 0.15 4.666 0.000 -44.09 ) 122.515
,. 13.090 0.15 4.343 -0.623 -4(. '1 24 -1 i" :'' 2
00 12.240 0.15 4.17 -0.976 -3- 22.370 122.452
04 9.920 0.15 3';'; -1.346 -49.91 4 1 122.348
32 11.610 0.15 3.976 -1.390 -39.02 22..! : 1-'-' '
28 8.854 0.15 3.678 -2.'.i. -48.99 15 .,,' 122.137
08 6.8 0.15 3.462 -2.592 -,:,. 47 16.7'' 122.412
ii 6.894 0.15 3 i -3.024 -48.34 12.840 122.554
00 6.634 0.15 3.149 -3.415 -;: I '.' I. 122.232
6. :, 0.15 ".' -3.594 -45.75 12.310 122.711
92 6.277 0.15 3.003 -_, 11.730 122.li_2
20 5.976 0.15 2.812 -4.. -45.09 11..I: 122.539
00 4.403 0.15 2.527 -5.327 -41.34 9.151 122.367
28 5.953 0.15 2.417 -5.713 .72 -1 122.291
5.' 0.15 2.332 -6.024 -48.63 10.720 122.322
20 -. 0.15 2.213 -6.479 -41.62 11.630 122.399
z] [n [nV,,] [,pV/Pa] [dB] [deg.] [*10 [dB re -'. Pa]




Table C-9: 122 dB SPL frequency Response Normalized Error Estimates


Mag. Random
0.130
0.140
0.148
0.106
0.148
0.179
0.171
0. 1" C
0.198
0.200
0.205
0.207
0.233
0.237
0.215
0.206


Phase Random
0.130
0.140
0.148
0.106
0.148
0.179
0.171
O.1";";
0.1 "
0. 1 -

0.205
(' 117
0.233

0.215
I I 'I H,


Mag. Bias
-0.010
-0.011
-0.012
-0.015
-0.013
-0.017
-0.021
-0.021
-0.022
-0.023
-(* _' ;
-0.024
-0.033
-0.025
-0.026
-0.022


2 Bias
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
O.Oot


,2 Random
0.256
0.276
0.292

0 -" '
0.355
0.339
0.390

0 .' :!
0. i -.
0.413
0 .'! 1 :
0.471
0.427
0.410


Table C-8:











128 dB SPSL F .. ,. l ny Response Data


516

708
804
932
1012
1124
1 l i
1300
1 -., I .
1492
1620
1700
1828
l !I r
2020
[11z]


Gxx
4 > >8
66.82
50.53
49.53
30.96
32.67
41.19

37.48
'.i- 1 ;3
28.91
22.93
21.15
19.90
15.12
14.415
[o/-2 J


Gatt
0.16
0.16
0.16
0.16
0.16
0.16
0.16
0.16
0.16
0.16
0.16
0.16
0.16
0.16
0.16
0.16
[n V?,as


Resp.
4.489
4.339
4.241
4.203
4.159
4.055
3.932
3.732
;: .''

3.078
2.32

2.552
2.1.
2.387
[pV/Pa]


Rel. Mag
0.000

-0. iI 1
-0.572
-0.663
-( I
-1.151
-1.604
-1.'. 8
2.4 :,
-3.278
-3.937
-4.451
-4.905
-5.179
-5.,i -
[dB]


Phase
-35.17
-32.3
-33.26
-46.48
- i. '11
-54.31
-40.79
-40.66
-50.40
-41.45
-46.10
-46.67
-48.01
-51.54
-33.49
-45.11
[deg.]


Table C-11:

Mag. Bias
-0.003
-0.002
-0.003
-0.003
-0.005
-0.005
-0.004
-0.004
-0.005
-0.004
-0.006
-0.007
-0.008
-0.0 ,.
-0.010
-0.011


128 dB SPL Frequency Response Normalized Error Estimates


Mag. Random
0.067
0.066
0.075
0.076
0.C',.

0.082
0.086
0.097
0.095
0.099
0.113
0.116
0.122
0.136
0.130


Phase Random
0.067
0.0' .,.
0.075
0.(1, ,
0.096
0.094

0 0;
0.097
0.095
(I 1 *
0.113
0.116
0.122
0.1, .
0.130


-2
Sxy
100.70
103.40
81.49
79.60
51.14
53.18
68.44
63.11
52.62
50.58
48.90
37.71
36.09
32.70
26.50
28.64
[*10-3]


SPL
1 753
128.535
1 ,--. "
128.251
1 .
128.184
1_'- 11
128.408
128.254
: 74
128.824
1 : 42
128.476
12. ':1

128.597
[dB re 'v. Pa]


2 Bias
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
O.Oot


2 Random
0.127
0.125
0.144
0.146
0.188
0.184
0.159
0.167
0.185
0.189
0.192
0.222
0.227
0 :'
0.267
0.257


Table C-10:











134 dB SPTL F.. il. ,ny Response Data


FP. .
516

708
804
932
1012
1108
1t i1
1300
1 -., >.
1492
1620
1700
17'- .

2020
[l[z]


Table C-13:

Mag. Bias
-0.001
-0.001
-0.001
-0.001
-0.001
-0.001
-0.001
-0.001
-0.001
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002
-0.002


134 dB SPL Frequency Response Normalized Error Estimates


Mag. Randomi
0.033
0.0 :
O.C 2.
0.043
0.045
0.048
0.045
0.048
0.048
0.051
0.051
0.052
0.055
0.059
0.056
0.059


Phase Random
0.033
0.0( ':
0.040
0.043
0.045
0.048
0.045
0.048
0.048
0.051
0.051
0.052
0.055
0.059
0.059 -,
0.059


Gxx
247.8
181.6
165.9
152.2
1.;:,, 1
117.3
133.5
121.8
120.0
109.9
112.9

90.8



. 2
[oL ,j,]


Gatt
0.17
0.17
0.17
0.17
0.17
0.17
0.17
0.17
0.17
0.17
0.17
0.17
0.17
0.17
0.17
0.17
[nV?, ,s


Resp.
4.808
4.194
3.970
3.787
3.603
3 .1-*
3.465
3.347
3.310
3.219
3. '
2.973
' -;7
2.757
_' V'a

[pV/Pa]


Rel. Mag
0.000
-1.187
-1.663
-2.073
-2.506
-3 0-"
-2.845
-3.146
-3.243
-3.485
:. :
-4.175
-4..i : I
-4.831
-5.031
-5.326
[dB]


Phase
- :'. ;3
-37.10
-35.34
-40.30
-38.47
-48.79
-41.43
-42.15
-43.55
-43.47
-41.39
-44.05
-50.35
-43.46
-45.38
-42.63
[deg.]


,f2
Ixy
311.2
248.3
: .3
211.4
197.8
175.9
195.2
177.1
179.5
162.2
l : ,
157.7
14 1.8
124.3
136.5
127.0
[*10-o]


SPL
134.283
134.118
134.203
134 .*
134.1;t
134.122
131. 122 -
134.1. -.
134.343
134.376
1311 ':
134.1 ,-;
13z1 :4.1
134.350
134.271
133.923
134.445
[dB re ,. Pa]


2 Bias
0.000
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001


S2 Random
0.055
0.067
0.070
0.077
0 0.1
I0 II


0 0.7
0 i0;7
0.

0.095
0.102
0.111
0.105
0.110


Table C-12:














1 il dB SPL FI .i::. ny F, onse Data


1-r ., ( (7 B. .i. IThi-f


516

708
804
948
1108
I _'_ i
1300

1 I i

1700
[Hz]


0
928.9


, : i.7

515.9
509.8
487.2
473.3
:- .3
[ni 5


0.155
0.155
0.155
0.155
0.155
0.155
0.155
0.155
0.155
0.155
0.155
0.155
0nW12


4.744
4.648
4.263
4.174

3. 1
3. I',

3.331

3.01' '
3.018
[pV/Pa]


0.000
-0.178
-0.929
-1.112
-1.567
-2.654
-2.870
-3.061
-3.071
-, '' "
-3.7;- .

[dB]


-37., !

-38.49
-43.60
-43.25
-41.42
-41.20
-47.83
-43.56
-44.03
-42.79
-43.65
[deg.]


649.80
636.10
610.90
494.30
567.20
503.50
499.70
477.00
465.50
476.70
404.50
410.70
[*10-3]


C'1 TT
140.38
140.316
140.324
1 -. )4
140.415
140.519
140.203
140.595
140. ,1,
140.41
140.043
140.189
[dB re -I; Pa]


Table C 15:


0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000


1 i1 dB SPL Fr.-ii-r..-- Response Normalized Error Estimates


0.016
0.017
0.018
0.O -
0.020
0.022
0.022
(I0 :
0.024
(I0 :
0.027
0.027


P 1 ... R .. ,. 1 .....
0.016
0.017
0.018
0.023
0 22
0.022
0.022

0.024
0 i :9
0.027
0.027


0.000
? r;. .-


0.000
0.000
0.000
0.000
0.000
0.000
0.000

0.000
0.000
0.000


0.019
0.020
0.022
0.032
0 0 _.1
0.031
0.032
0.034
0.0 .
0.034
0.042
0.041


Table C 14:














140 dB SPL Frequency Response in -'. Data


220
165.5
176.4
629
111.3
322.6

25.66
457.9
822.8
73.07
[*10-3]


140.672
140.458
140.267
140.12
140.392
140.21
140. :,, .
140.294
140.768
140.324
140.373
140.041
[dB re 20pPa]


Table C 17: 140 dB SPL Frequency Response in iV. Normalized Error Estimates


Mag. Random
1.299
1.507
1 .', 1 ,
1.683
0.891
2.119
1.245
2.516
4.414
1.045
0.779
2.616


Phase Random
1.299
1.507
1 .'. -,
1.683
0.891
2.119
1.245
2.516
4.414
1.045
0.779
2.616


0.00
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001


7~2 Random
2.599
3.014
3.476
3.367
1.782
/I 4 .' I
2. -i
5.032
8.828
2.089
1.558
5.231


F.. |
516
50^4
708

948
1108
1 -,
1300


1620
1700
[Hz]


92.07
95.06
,-.40
63 "
73.70
88.40
103.20
86.40
65.36
104.73
92.92
82.37
[plJms


0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
[0.20
[pV2


1. -i,.
23.91
20.37

5.674
11.14
16.08
31. 1'
14.42
7.21
33.06
23.6
13.01
[nV//Pa]


T 1. ,_
0.000
-1 -'2
-2.1;,.
-12.494
-6.634
-3.446
2.392
-4. 12
-10.413
2.814
-0.113
-5.286
[dB]


-77.14
99.37
98.25
5-- .-1
-165.8
-43.21
113.6
- 1. 19
56.86
107.1
-82.73
68.91
[deg.]


Mag. Bias
-0.002
-0.002
-0.002
-0.003
-0( IiII
-0.002
-0.002
-0.002
-0.003
-0.002
-0.002
-0.002


Table C 16:


















APPENDIX D
EXPERIMENTAL RESULTS FIGURES


! !. .i! . . . .
........................:: :: :: :0 0


. . . .


















rA : : :A ;
. . . .[ [.. :. .

. . . . . i ~i i


. . i


S.. . . . . .

; .: .. x . ..-. .
. . . .. . . .




............. .. X X x
.IORF

.......... ... ........ X. 1 d B S.. F. .
:;:::j:;............... : I o 140BS


103




102




E 10




100
a
|- 10o




10-1




10-2


Frequency [Hz]


0 134 dB SPL
O 128 dB SPL
122 dB SPL
x 119 dB SPL
* 115 dB SPL
S140 dB SPL-N


Figure D 1: PMT Power as a Function of SPL


AAA: AAAll^ ^ !
A..............::......
.... ........................


. . . . .


L
'I



































.. .. .. .

OO -


: : : : : : : : : :



n D


.. . . .. :. . .

K : : :: q : : : : : : : : : :



x
. .. .. .


0 140 dB SPL
0 134 dB SPL
0 128 dB SPL
122 dB SPL


.. .. ... ... .. ...... x 119 dB S P L
S! 115dB SPL



S0. 0 . . . . . . .
000
. :.0.. ...... 0 .0 -..



S. . X. .
:x x


x x
S : : : : : : : : : : : x : : : : : : : : : x: : :
. . ... . . . . . ..
.. . . . . . .
. .. .. .. .. .. .. ... .. .. .. .. .. .


103
Frequency [Hz]



Figure D-2: Mic-PMT Coherence as a Function of SPL


. . . . ..
X
. . . . .
. f . . . . ..


























10





101
10 3



-5- i []




S00-


103


1005 I I I


3.05 1--I-I


Frequency [Hz]


Figure D-3: Response, Relative Response, and Phase Response of Optical System at
115 dB SPL


co



0
V,
Co
Co
01
a
0)









-a


Q-


a)

C, 0
o


O-
0
0


i i : i :I ( i
































10





0-
103


: : :D O
-5-


-10
103
0


-50


.100
103

0.04 i

0.02

03I


Frequency [Hz]



Figure D-4: Response, Relative Response, and Phase Response of Optical System at
119 dB SPL


CO

Q.
0



0)
C,

Co
a


m
a

0)


co


Co
0)
C)
-a

o


o
Cu






-c

0
























10





0
103



-3 n ion,------------
o :: :

-5 -


-10-
103
0



-50s |


100 '
103
0.1





-0.1
103
Frequency [Hz]


Figure D-5: Response, Relative Response, and Phase Response of Optical System at
122 dB SPL


cu


C,
a
a
C,

m
-a
0)
Cu

c,
Cu


C,
-a


Co



a
0)
















1 m .. '- tI

0

-100


103
Frequency [Hz]


Figure D-6: Response, Relative Response, and Phase Response of Optical System at
128 dB SPL


II i~


" m m ,~ mmmmm m~~"~




















I6

S4

o 2
0
. 0
0)
CO
2 -5
S-10
10 -l


-20

-40

-60 0 3
103
0.4

0.2
f2- m i 1l


Frequency [Hz]


Figure D-7: Response, Relative Response, and Phase Response of Optical System at
134 dB SPL


I I I I I I I I


PPiPliiijiiy

























4-

3-

2
103

0 0E

2-
10


00
41 I OpD C






103
103
1, Frequency [Hz]


CO







-2
I,
Co
a
0














o -
o
co,






-2

(,
a



-6







0


Figure D-8: Response, Relative Response, and Phase Response of Optical System at
140 dB SPL


Mi ; D B D D



103
Frequency [Hz]


m m3


5















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N.A. Winslow, B.F. Carroll, and A.J. Kurdila. Model development and analysis of
the dynamics of pressure-sensitive paints. AIAA Journal, 39(4):660-666, 2001.















BIOGRAPHICAL SKETCH

('!i i-l1.! ih. r Allen Virgin was born on February 23, 1981, in Kankakee, IL. Upon

graduating from Bradley-Bourbonnais Community High School in 1999, ('!~!- at-

tended Bradley University where he was awarded a bachelor of science degree in

mechanical engineering in 2003. During his final year at Bradley University, C('lo:-

considered pursuing a career as a developmental engineer with the United States

Air Force. In April of 2003, ('!!i i decided to attend graduate school to change his

career focus to aerospace engineering. C('!ii sought employment with Butler Interna-

tional working at the Caterpillar Mossville Engine Assembly Center while applying

to graduate schools. After evaluating his options, ('C!ii moved to Gainesville, FL, to

attend the University of Florida where he received a Master of Engineering degree in

aerospace engineering in 2005.




Full Text

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ACOUSTIC APPLICATION OF PRESSURE-SENSITIVE PAINT By CHRISTOPHER ALLEN VIRGIN A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2005

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Theauthorwouldliketothankthesupervisorycommitteechairman,Dr.BruceF.Carroll,forhiscontinuedguidance,support,andencouragement.GratitudeisalsoaddressedtoDr.LouisCattafestaforhisadviceandguidance.Theauthorwouldliketothanktheothersupervisorycommitteemembers,Dr.MarkSheplak,Dr.KirkSchanze,andDr.MartinMorris,fortheirsupport.Theauthorwouldalsoliketoacknowledgeallfamilyandfriendswhohavehelpedmakethispossible. iii

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page ACKNOWLEDGMENTS ............................. iii LISTOFTABLES ................................. vi LISTOFFIGURES ................................ viii LISTOFSYMBOLSANDABBREVIATIONS ................. x ABSTRACT .................................... xiii CHAPTER 1INTRODUCTION .............................. 1 PSPPhysics .................................. 1 PreviousWork ................................ 4 Motivation ................................... 9 2EXPERIMENTALAPPARATUS ...................... 10 PlaneWaveTube ............................... 10 TemperatureEectsofAcousticWaves ................... 12 PhotodetectorDescription .......................... 12 PSPAppliedtoDetector ........................... 14 3EXPERIMENTALSETUPANDPROCEDURE ............. 24 StandingWaveRatioTest .......................... 24 PSPStaticCalibration ............................ 26 PhotomultiplierFrequencyResponse .................... 27 AcousticTesting ............................... 27 4EXPERIMENTALRESULTS ........................ 29 StandingWaveRatioResults ........................ 29 PSPCalibration ............................... 29 PhotodetectorFrequencyResponse ..................... 30 NoiseinExperimentalSetup ......................... 33 PSPBehavior ................................. 34 PSPLinearity ................................. 36 ThermalResponse .............................. 38 TimeResolutionofOpticalSignal ...................... 39 iv

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............................. 41 PSPStaticCalibrationUncertainty .................. 41 FrequencyResponseErrors ....................... 42 5CONCLUSIONS ............................... 45 APPENDIX ADERIVATIONSOFACOUSTICRELATIONS .............. 47 TemperatureChangeofaSmallIsentropicCompression .......... 47 DerivationoftheOne-DimensionalWaveEquation ............ 48 DerivationoftheCutoFrequency ..................... 50 DerivationoftheWaveguideEquations ................... 52 DerivationoftheRectangularWaveguideEquation ......... 52 DerivationoftheCylindricalWaveguideEquation .......... 55 NormalIncidenceSoundReectionandTransmission ........... 57 BSTANDINGWAVERATIOMETHOD ................... 60 StandingWaveRatioCalculations ..................... 60 StandingWaveRatioFigures ........................ 63 CTABULATEDEXPERIMENTALRESULTS ................ 66 DEXPERIMENTALRESULTSFIGURES .................. 75 LISTOFREFERENCES ............................. 83 BIOGRAPHICALSKETCH ............................ 86 v

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Table page 3{1SWRDataCollectionSettings ...................... 25 4{1SWRResults ................................ 29 4{2PSPStaticCalibrationSettings ..................... 30 4{3PMTFRFAcquisitionSettings ...................... 31 4{4PMTFRFAcquisitionSettings ...................... 37 4{5LinearityDataAcquisitionSettings ................... 38 4{6SingleTimeSeriesDataAcquisitionSettings .............. 41 C{1PSPStaticCalibrationResults ...................... 66 C{2PMTFrequencyResponseResults .................... 67 C{3PSPLinearityResults ........................... 67 C{4115dBSPLFrequencyResponseData .................. 68 C{5115dBSPLFrequencyResponseNormalizedErrorEstimates ..... 68 C{6119dBSPLFrequencyResponseData .................. 69 C{7119dBSPLFrequencyResponseNormalizedErrorEstimates ..... 69 C{8122dBSPLFrequencyResponseData .................. 70 C{9122dBSPLFrequencyResponseNormalizedErrorEstimates ..... 70 C{10128dBSPLFrequencyResponseData .................. 71 C{11128dBSPLFrequencyResponseNormalizedErrorEstimates ..... 71 C{12134dBSPLFrequencyResponseData .................. 72 C{13134dBSPLFrequencyResponseNormalizedErrorEstimates ..... 72 C{14140dBSPLFrequencyResponseData .................. 73 C{15140dBSPLFrequencyResponseNormalizedErrorEstimates ..... 73 C{16140dBSPLFrequencyResponseinN2Data .............. 74 vi

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. 74 vii

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Figure page 1{1SchematicofaTypicalPSPLayer .................... 2 1{2ComparisonoftheAmplitudeResponseofWinslow'sModeland1/2,1st,and2ndOrderSystems ....................... 6 1{3ComparisonofthePhaseResponseofWinslow'sModeland1/2,1st,and2ndOrderSystems ......................... 7 2{1SchematicofaCylindricalWaveguideModes .............. 11 2{2SchematicofaSide-OnPMT ...................... 13 2{3EquivalentCircuitRepresentationofaPhotodetector ......... 15 2{4DesirableChemicalPropertiesofaPSPCoating ............ 20 2{5MinimumDetectableRadiantFluxofDetectors ............ 21 2{6MinimumDetectableSPLofDetectors ................. 22 3{1SchematicofExperimentalSetupforStandingWaveRatioTesting .. 25 3{2SchematicofExperimentalSetupforAcousticTesting ......... 28 4{1PSPStaticCalibrationResults ...................... 31 4{2PMTFrequencyResponse ........................ 32 4{3ExperimentalNoiseComparison ..................... 34 4{4PSPCoatingRelativeFrequencyResponse ............... 35 4{5PSPCoatingPhaseResponse ...................... 36 4{6LinearityofOpticalSystem ....................... 37 4{7CoatingResponseinAirandNitrogen ................. 39 4{8ComparisonofUnlteredPMTOutput,FilteredPMTOutput,andMicrophoneOutput .......................... 40 A{1SchematicofaSquareDuct ....................... 52 A{2SchematicofaCylindricalDuct ..................... 55 viii

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.. 58 B{1MicrophoneVoltagevs.xcorfor600HzExcitation ........... 63 B{2MicrophoneVoltagevs.xcorfor1000HzExcitation .......... 64 B{3MicrophoneVoltagevs.xcorfor1400HzExcitation .......... 64 B{4MicrophoneVoltagevs.xcorfor1800HzExcitation .......... 65 D{1PMTPowerasaFunctionofSPL .................... 75 D{2Mic-PMTCoherenceasaFunctionofSPL ............... 76 D{3Response,RelativeResponse,andPhaseResponseofOpticalSystemat115dBSPL ............................. 77 D{4Response,RelativeResponse,andPhaseResponseofOpticalSystemat119dBSPL ............................. 78 D{5Response,RelativeResponse,andPhaseResponseofOpticalSystemat122dBSPL ............................. 79 D{6Response,RelativeResponse,andPhaseResponseofOpticalSystemat128dBSPL ............................. 80 D{7Response,RelativeResponse,andPhaseResponseofOpticalSystemat134dBSPL ............................. 81 D{8Response,RelativeResponse,andPhaseResponseofOpticalSystemat140dBSPL ............................. 82 ix

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a Width/DiameterofWaveguide[m] e Chargeofanelectron[1:60E19C] (ispl)min k Boltzmann'sConstant[1:38E23J=K] t Time[sec] x Distance[m] A AreaofPSPCoating[m2] B SystemBandwidth[Hz] C Capacitance[Farad] F DeviceNoiseFigure[] x

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Gain I PhotodetectorCurrent[A] L RadiantFluxofDye[W] L N TotalNoisePresentatAnode[A] P Pressure[Pa] R Resistance[Ohms] S Henry'sLawSorptionCoecient T Temperature[K] PressureReectionCoecientMagnitude xi

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n() CathodeQuantumEciency APD AvalanchePhotodiode CE AnodeCollectionEciency NEP NoiseEquivalentPower PMT PhotomultiplierTube SPL SoundPressureLevel[dB] SWR StandingWaveRatio PSP Pressure-SensitivePaint xii

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xiii Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science ACOUSTIC APPLICATION OF PRESSURE-SENSITIVE PAINT By Christopher Allen Virgin December 2005 Chair: Bruce F. Carroll Major Department: Mechanic al and Aerospace Engineering This thesis describes the effort to experiment ally verify the response of "traditional" Pressure-Sensitive Paint (PSP) to low amplitude pressure fluctuations such as those common in acoustic measurements. Pressure-sensitive pain t utilizes molecular quenching of fluorescent compounds in the presence of oxygen to discern the pressure field at a given point on a surface. A 0.1 meter diameter by 1.0 meter long plane wave tube is utilized to create a planar acoustic field at the surface of a PSP sample. The response of the paint is measured using a Photomultiplier Tube (PMT). The plane wave tube is driven through a function generator and an audio amplifier. Frequency response, linearity, and temperatur e effects of the coating are evaluated. Frequency response measurements show the paint to behave similar to a "1/2"-order system, i.e., a -45 phase and -10 dB/decade attenuation. This is in agreement with previous research conducted at the University of Florida. Using a numerical model, the optical system (coating and detector) is estimated to have a noise floor of 115 dB SPL. This is quite high for an acoustic detection scheme and is the result of the PSP and PMT fundamental characte ristics. Experimental results show the noise floor to be in the region of 119 to 115 dB SPL. The optical system

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Theinterestsofthisresearchlieinapplyingunsteadypressuremeasurementtoolstohigh-speedhydrodynamicpressureuctuationssuchasthoseseenintur-bulentboundarylayers.PSPiscurrentlybeingevaluatedinseveralformsinhopesofattainingsucientsensitivitytobeapplicableinthisregime.Theabilityofob-tainingreal-timemeasurementsofcomparativelysmallpressureuctuationsalsohaspotentialimpactinmedicalandenvironmentalelds. xiv

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Thischapterpresentssomebackgroundinformationonpressure-sensitivepaint,commonlyreferredtoasPSP.ReviewsofrecentstudiesinthedynamicresponseofPSParealsopresented.ItisshownthatthedynamicresponseofseveraldierenttypesofPSParecurrentlybeinginvestigated.RecentstudiesfocusonthedynamicresponseofnewertypesofPSPduetotheirfasterresponsetimes.Thisstudyin-vestigatesthedynamicbehaviorofaPSPandprimerlayerapplieddirectlytoanaluminumsubstrate.PSPPhysics 1{1 .ShownisaPSPlayerapplieddirectlytoasubstrate.TheprocessbeginswithExcitationoftheluminophoremolecules.ThisisaccomplishedwithalightsourcehavingstrongintensityinthebluetoUVportionofthespectrum(=300-500nm).Lasers,halogenlamps,LED'sandstrobelightsareoftenemployedinthistask.Luminophoremoleculesabsorbenergyfromthesourceandtransitiontoahighervibrationalenergylevel[ Kose 2005 ].Onceatitshigherenergylevel,theluminophorehasthreeroutestothegroundstate.Onepossiblemodeofdecayisfortheluminophoretoreleaseitsenergytothesurroundingpolymermatrixintheformofthermalenergy[ Schanzeetal. 1997 Winslow 2001 ].ThisprocessisnotfavoredinmostPSPformulations.Thesecondrouteofdecayisknownas\radiative"decayorluminescence.Thisrouteencompassesbothuorescenceandphosphorescence.Fluo-rescenceistheprocessofabsorbingaphotonandemittingaphotonoflowerenergy.Phosphorescenceisaquantumprocessinvolvingthechangeinthespinmultiplicity 1

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Figure1{1: SchematicofaTypicalPSPLayer ofamolecule.Ruthenium-basedPSP'sexhibituorescence,whileplatinum-basedpaintsdisplayphosphorescence[ Winslow 2001 ].Bothprocessesresultintheemis-sionofaphotonoflowerenergy(i.e.,longerwavelength)thantheabsorbedphoton.Theemittedphotonisintheredtoorangecolorofthespectrum(=550-650nm). ThethirdanddistinctivefeatureofPSPisthataluminophoremayreleaseitsenergytoanoxygenmoleculethathaspermeatedthepolymerbinder.Thisprocessisknownas\oxygenquenching"[ Schanzeetal. 1997 Winslowetal. 2001 ].LuminescenceandoxygenquenchingaretheprimaryroutesofdecayforaPSP.Thepartialpressureofoxygeninthebinderlayerisdirectlydependantonthepartialpressureofoxygendirectlyabovethelayerandthemassdiusivityofthepolymer(s)usedinthebinder.Theluminophoresinthebinderexhibitthebehaviorofeitheremittingared-shiftedphotonorinteractingwithoxygen.Inthismanner,itcanbeshownthattheobservedintensityoftheemissionofthePSPisinverselyproportionaltotheoxygenconcentrationsurroundingtheluminophores.Thisbehaviorisgoverned

PAGE 17

bytheStern-Volmerrelation[ Winslowetal. 2001 ] Vac TheStern-VolmerEquationrelatestheemissionintensity(radiantux)ofthePSPintheabsenceofoxygen,Lvac,totheemission,L,atanabsolutepressure,P.Inaero-dynamicapplications,itisoftennotfeasibletomeasuretheintensityintheabsenceofoxygen,soEqn( 1.1 )isoftenrelatedtotheintensityatsomereferencepressure(typicallyPatm)[ Virginetal. 2005 ].Thisyieldsthemorefamiliar\aerodynamictesting"formoftheStern-Volmerrelation[ Liuetal. 1997 ] p0=C0(T)+C1(T)L0 ThisformiscommonlyusedinapplicationsofPSPasitallowsonetouseanyreferenceconditiontoinferthepressureatsomeotherconditionofinterest.Asindicated,theconstantsC0andC1varywithtemperature.MoreexactdescriptionsofPSPbehaviorareprovidedby Winslow [ 2001 ]and Kose [ 2005 ]. ManyvariablesinuencethespecicbehaviorofaPSPlayer.Theprocedureofapplicationinuencestheuniformityoftheluminescenceofthelayer.Onemayincreasetheobservedluminescenceofalayerbyrstapplyingawhiteprimerlayertothesubstrate,howeverthismayadverselyimpacttheresponsetimeofthelayerduetooxygendegassingbetweenthepaintandprimer[ Liuetal. 1997 ].Thickerpaintlayersresultinincreasedluminescenceduetoalargerpopulationofluminophores.However,thickerlayersalsoresultinslowerresponsetimeduetotheincreasedlengthwhichoxygenmustdiuseintothebinder.Therealsoexistsalimit,abovewhichtheluminophoreswillbeginto\self-quench"[ Chanetal. 1999 ],whichgreatlydegradesthemeasurableresponse.

PAGE 18

Belletal. ( 2001 ), Liuetal. ( 1997 ),and Luetal. ( 2000 )provideadequatereviewsoftheliterature.Thevariousoweldswhichhavebeeninvestigatedincludebothsubsonicandsupersonicloadsonaircraftmodels,turbomachinerysuchasfansandcompressorsandautomobilewindtunneltesting. CoxandDunn [ 1986 ]werethersttoapplyPSPtoanunsteadyoweld.Theyinvestigatedoxygentransportwithinapoly(dimethylsiloxane)(PDMS)layerdopedwith9,10-diphenylanthracene(9,10-D)asaFunctionoftimeusingastaticcalibration.Theydevelopedananalyticalmodelforoxygenconcentrationwithinthelayerderivedfromthe1-Ddiusionequation.However,thelayerwasviewedfromthesideinthisapplicationsotheintensitywastheintegratedintensityoftheentirelayer. MillsandChang [ 1992 ]werethersttolookatthedynamicresponseofopticallmsensors,nowknownasPSP.TheinverseofthePSPemissionintensitywascom-paredtothepressureasitwasquicklychangedfromanearvacuumtoatmosphericpressure.Amodelwasdevelopedwhichtreatedthepaintasarst-orderdynamicsystem.Thetimeconstantsandtermweightsweredeterminedusingnonlinearleastsquarescurvets.Themodeldevelopedbythismethodwasfoundtostronglyagreewithexperimentalresults. Both Engler [ 1995 ]and Carrolletal. [ 1995 ]introducedconcurrentstudiesontheresponseofPSPtoperiodicpressureelds. Engler subjectedthePSPtofrequenciesovertherangeof0.1to50Hz.Themaingoalwastocharacterizethepressurereso-lutionanddynamicrangeofthecoating.Nodynamiccompensationorexplorationofthedynamicsofthesystemwereattempted. Carrolletal. presentedexperimentsofsimilarcharacter.Muchoftheanalysiswasperformedinthefrequencydomain.

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ItwasshownthatthePSPdisplayedanamplituderesponseofarst-orderdynamicsystemalthoughthephaseresponsedidnotagreewithexpectedresults. Winslowetal. [ 1996 ]developedalinearizeddynamicmodelforPSPgiveninEqn.( 1.3 ).Thismodelhasfrequencyresponsecharacteristicsofa\1=2-order"system:anamplituderesponseof10dB/decadebeyondthecutofrequency,andaphaseshiftof45. Winslowetal. thendevelopedadynamiccompensatorbyperforminganinverseFouriertransformontheinverseofthefrequencydomainresponse.ThecompensatorwasofthesameformasasixtermFIRlter.ApplyingthiscompensatortothePSPresponsefora1HzsawtoothwaveyieldedacorrectedsignalconsiderablymoreaccuratethanthePSPmeasurementalone.ThiswastherstapplicationofadynamiccompensatortoPSPdata. 1+0:8115e0:0943(1.3) where Thismodeldemonstratedbehaviorsimilartothatofa\1/2"ordersystemasshowninFigure 1{2 andFigure 1{3 Winslowetal. alsoshowedthatthefrequencyresponseofthepaintwasinvarianttothepressureeld.Itwasshownthatcoatingthicknesseectsthefrequencyresponse.Thisisduetothenecessarymassdiusionthroughthepolymerbinder.ItwasconcludedthatthedevelopedmodeldidnotfullyexplainthePSPbehaviorduetointeractionswiththeprimerlayer.However,thebreakpointsandvaluesofmassdiusivityagreewithresultsofastudyconductedby Carrolletal. concerningtheresponseofPSPtoasteppressurechange. Winslowetal. [ 2001 ]developedthreedynamicmodelsforPSP.Therstmodel,anempiricalmodelintheformofatransferFunctionwasappliedtothesignalfromahigh-frequencypressure

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Figure1{2: ComparisonoftheAmplitudeResponseofWinslow'sModeland1/2,1st,and2ndOrderSystems transducertomodeltheoutputpressure.Thismodelshowedreasonableagreementwithdata,butthecoecientsdevelopedweredependantonthethicknessofthePSPlayerandthusthemodelwasonlywellsuitedtosinglesampleusage.Diusion-basedmodelswithalinearandastern-volmercalibrationwerebothproposedandshowntoconformquitewelltoexperimentalobservations. Schairer [ 2002 ]Performedanumericalstudyontheinuenceofcoatingthick-nessonthefrequencyresponseofaPSPlayer.Usingtheone-dimensionaldiusionequationandasmallsinusoidallyvaryingpressuresignal,itwasshownthattheop-timumcoatingthicknessforunsteadymeasurementsisthatwhichresultsina-1.25dBattenuationoftheunsteadypressuresignali.e.Pspl=Ppsp=0:866.Thiscoat-ingthicknesscorrespondstoamaximuminthesignal-to-noiseratio.Theoptimum

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Figure1{3: ComparisonofthePhaseResponseofWinslow'sModeland1/2,1st,and2ndOrderSystems thicknesswasshowntodecreasewithincreasingfrequency.Abovefrequenciesof10Hz,thegreatestfactorindeterminingtheoptimumthicknessisthemassdiusivity. Inrecentyears,severalnewtypesofPSPhavebeendevelopedforbetterdynamicresponse.PSPhasbeenappliedtoanodizedaluminum,TLC(thin-layerchromatog-raphy)platesandhardceramicparticleshavebeenaddedtothepolymerbinder( Gregoryetal. ( 2002 ); Gregory ( 2004 )).Theporoussurfacesservetoincreasethedynamicresponsetimebyenablingfasteroxygendiusionintothepolymerbinder. Baronetal. [ 1993 ]rstdemonstratedthatsubmillisecondresponsetimesmaybeachievedusingcommercialTLCplates. Sakamuraetal. [ 2005 ]showedthattime-resolvedmeasurementsofapressuredistributionarepossibleusingPSPonaTLC

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substrateinatwo-dimensionalLavalnozzle.TLCplatesareeasytoprepareandpro-ducebrightemission,howevertheyarelimitedtouseonatplatesandarerelativelyfragile. SeveralstudieshavebeenperformedonanodizedaluminumPSP[ SakaueandSullivan 2000 2001 Kamedaetal. 2004 ].Thisismadebyanodizingthesurfaceofanaluminumbodyanddippingthisbodyinaluminophoresolution.TheanodizedsurfaceisveryporousandservestogreatlyenhancetheoxygendiusionandthusthedynamicresponseofthePSP.TheexactbehaviorofthistypeofPSPisstillasubjectofinvestigation. ThesuitabilityofPSPfordetectinglargepressureuctuationshasbeendemon-strated.Currently,thereisaninterestinthesmallestdynamicpressurewhichmaybedetectedusingPSP.Thisisfacilitatedbyaninterestinhydrodynamicturbulentpressureuctuationsofairbornebodies.Demonstrationofnon-invasive,directde-tectionofturbulentnoiseonbodieswouldgreatlydecreasedesigncycletimeofnewairframes. McGrawetal. [ 2003 ]presentedaproofofconceptexperimentforacousticPSPmeasurements.AsinglepointmeasurementinaplanewavetubewasperformedusingaPMTandatraditionalPSPformulationonaTLCsubstrate. McGrawetal. reportedtheabilitytocollectvalidsignalsforsoundpressurelevels(SPL)from110(4P=6Pa)to137dB(re20Pa)atameanpressureof101.5kPaandfrequenciesupto3500Hz.Signicantdampingofthesignalwaspresentatfrequenciesabove1000Hz.Intheirwork,signalaveragingoftheperiodicsinusoidaloutputwasusedtoimprovesignal-to-noiseratio.Timeaccuratedirectdetectionwasnotdemonstratedinthisworkandfulleldmeasurementswerenotattempted.OptimizationofthePSPformulationfortheacousticcasewasnotattempted.Animportantresultofthisworkwasthedeterminationthattemperatureuctuationsduetotheacoustic

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pressurevariationsdidnotadverselyimpacttheaccuracyofthemeasurementduetothelargethermalmassofthesubstrate.Motivation Carrolletal. 1995 1996 Winslowetal. 1996 2001 ].ThisstudyinvestigatesthesuitabilityoftraditionalPSPtodetectingpressureuctuationsontheorderoftypicalacousticsignals.DiusionlimitingfactorsarereducedbyrestrictingthePSPtoathincoating.TraditionalPSPpossesstheadvantagesoflesscost,durability,andwellstudiedbehaviorascomparedtothenewvariantsnowunderscrutiny.

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Thischapterintroducestheequipmentusedinthisstudy.Thebehaviorandlimitationsoftheplanewavetubeusedinthisstudyareexplored.Theperformanceofthetubedriverislimitedbythecutofrequencyofthetubetoretainaplanarsoundeld.Thephotodetector,aHamamatsuH9306-02PMTmodule,isalsointroducedanddiscussed.TheperformanceofthedetectorandPSPweremodelledinordertopredictaminimumpressuredetectionooroftheopticalsystem,i.e.,consideringthePSPandphotodetectorsetupasacompletesystem.Theexperimentalsetupanddatacollectionsystemsareexplained.PlaneWaveTube A.53 )).(SeeAppendix A ) Thecutofrequencyisthelowerlimitatwhichhigher-ordermodesmaypropagatedownthewaveguide.Therstmodestopropagatearethe(1,0)and(2,0)modes,followedbythe(0,1)mode[ MorseandIngard 1987 ].Themodenotationis(r,),wherethenumberindicatesthenumberof1=2wavelengthspresentineachdirection.Thebehavioroftherst2modesineachdirectionisillustratedinFigure 2{1 .Belowtheirrespectivecutofrequencieseachhigher-ordermodeisevanescent,whichmeans 10

PAGE 25

Figure2{1: SchematicofaCylindricalWaveguideModes itdecaysexponentiallywithdistancefromthesource.Ifthewaveguideisoperatedbelowtherstcutofrequency,whichiscalculatedas2016Hz,thentheacousticeldwillbecompletelyplanar,i.e.,thepressureatanystationofthewaveguideisonlyaFunctionoftime. Byoperatingthewaveguidebelowthecutofrequency,thePSPsampleisen-suredtoreceiveauniformpressuresignaloveritsentiresurface.Abovethecuto,thepressurewouldvarywithrandoverthesurfaceofthesample.Sincethepho-todetectorusedhasnoinnatespatialresolution,thiswoulddegradethedetectableopticalsignal.

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Swift [ 1988 ]andisderivedinAppendix A tobe P0(2.2) whereTrefistheambienttemperature(298K),=1:4andP0istheambientpressure(101kPa). Fora140dBacousticwave,Eqn.( 2.2 )predictsacorrespondingtemperaturechangeof0.1669K.ThePSPformulationusedinthisexperimenthasafractionalchangeinintensityof0:53%=K.[ Kose 2005 ]IfthetemperaturechangepermeatesthePSPlayer,thiswouldinducea0:088%changeinthePSPemission.Thus,thetemperatureeectsoftheacousticwavesseemtobenegligible.Thisresultwasalsoconrmedexperimentallyby McGrawetal. [ 2003 ].PhotodetectorDescription

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Thephotoelectronsaresteeredtotherstdynodestagewheretheycausemorephotoelectronstobecreatedbymeansofsecondaryelectronemission.Thisprocesscontinuesalongsuccessivedynodestages(PMTscanhave10ormoredynodestages).Ateachsuccessivedynode,theincomingphotoelectronsaremultipliedagainandsenttowardsthenextdynode.Attheendofthetube,theanodecollectsallofthephotoelectrons[ Corp. September,2005 ].Thisprocessisshownintheschematicofaside-onPMTbelowinFigure 2{2 .PMTsareabletoobtainsuchlargeinternalgain Figure2{2: SchematicofaSide-OnPMT throughtheuseofalargeinputvoltage,typicallyontheorderof1000Voltsorlarger.Thisvoltageissuccessivelysteppedupfromperhaps1Voltattherstdynode,to1000Voltsormoreatthenaldynode,resultinginmoresecondaryphotoelectronemissionateachsucceedingdynode.DuetothelargeinputvoltagerequiredbyPMTsithasbecomecommonpracticeforPMTstobeoeredascompletePMTmodules,inwhichamorereasonableinputvoltage,suchas10Volts,issteppedupbyinternal

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circuitrywithinthemoduleandthensuppliedtothePMtubetominimizethehazardstopeopleandequipment,andtoeliminatetheneedforhighvoltageexternalpowersupplies.Theanodecurrentisconvertedtoavoltagebyaconversionfactor(typicallyofthesameorderasthePMTgain)andthissignal,plusnoise,istheoutputofthePMT. OnedrawbackofphotomultipliertubesistheirrelativelylowQuantumEciency(QE).TheQEisthelikelihoodthatanincomingphotonwillbeconvertedtoaphotoelectronandbedetectedbythedevice.TherearetypicallytwopropertiesthatdeterminetheoverallQEofaPMT.ThecathodeQE,oftennotedasn(),whereisthewavelengthoftheincidentlight,isthelikelihoodthatanincomingphotonwillgenerateaphotoelectronatthecathode.TheanodeCollectionEciency(CE)isthepercentageofphotoelectronsthatarecollectedbytheanode.TheproductofthesestwotermsgivestheoverallQEofaPMT.Thevalueofn()canrangefrom0:0140%,whiletheCEcanbeashighas8090%.However,theoverallQEofaPMTistypically30%orless[ Corp. September,2005 ].ThislowQEresultsindecreasedsensitivityofthePMTandmorenoiseresultingfromtheundetectedphotons.PSPAppliedtoDetector

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Figure2{3: EquivalentCircuitRepresentationofaPhotodetector ofthedetectoristhenevaluatedas 2RC(2.3) Ingeneralthebandwidthofthedetectormaybereducedbytheadditionofalowpass(orbandpass)ltertotheoutputofthedetector.Aswewillnd,reducingthebandwidthhasapositiveimpactonthesystemnoise. Thegainofthephotodetectorisdenedastheratioofthecurrentpresentafteramplicationtothatpriortoamplication.ForaPMTthisistheanodecurrentdividedbythephotocathodecurrent. WewillnowaddresstheseveralsourcesofnoisepresentinaPMT.OneofthemorepredictablenoisesourcesofaPMTisthermalorJohnsonnoise.InordertomaintainthehighsensitivityofPMTs,thematerialsusedinthephotocathodesanddynodeshavehighworkFunctions,whichmeansittakesverylittleenergytoforthemtoreleaseanelectronintoavacuum.Thisresultsinthematerialsemittingthermalelectronsduetobeingatroomtemperature.[ Corp. September,2005 ]

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TheJohnsonnoiseappearsasanACcurrentattheanode. R(2.5) TheJohnsonnoisedependsonlyonthetemperatureandinternalfeaturesofthePMT,soitisnotdirectlysubjecttothegain. TheothermajorsourceofnoiseinthePMToutputisshotnoise.Shotnoisearisesfromthestatisticaluctuationsoftheinteractionsbetweenphotonsandpho-toelectronsinsidethePMT.Othersourcesofnoiseincludecurrentleakageofthecircuitry,noisecausedbytheelectriceldsofthedynodeswhenthePMTisoper-atedathighgain,externalnoise,andimpedancemismatchesintheexperimentalwiring.Thesenoisesourceswillbeaccountedforbyspecifyingadarkcurrentforthedevice.ThedarkcurrentisthecurrentpresentattheanodewhenthePMTisinadarkenedenvironment,itthusimpliesanindependenceofthelightsignal.Thedarkcurrenthowever,issubjecttogainbecauseoftheactionofthedynodesandcathodeinitscreation.Thereisalsoanoisecontributionofthebackgroundlight,thiswillbeconsideredintheshotnoiseofthedevice. Thedarkcurrent,denotedasId,iscomposedoftwoseparatecurrents.

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Comparingtheacousticandatmosphericpressures,itisseenthattheacousticpres-sureisverysmallcomparedtoPatm.Foranacousticwaveof140dB,thepressurechangeis200Pa.Eventhisunusuallylargeacousticpressureisonly0:2%ofPatm,whichis101,000Pa.Thus,theuctuatingsignal,isplisasmallaccurrentsuper-imposedonameanbackgroundcurrent,Ibg.Thetotalshotnoiseofthedetectorisgivenby ThetotalnoisepresentattheanodeisthesumoftheJohnsonandshotnoises R(2.7) Thesignalofinterestistheanodeistheuctuatingsignalispl.Thissignalistheproductofthecathoderadiantsensitivityandtheincidentlightux.Mathematicallythisisstatedasispl=Sp(spl)AG.Thisenablesustostateafundamentalsignal-to-noiseratiointermsoftheanodecurrent N=ispl G2+4kTB RG2(2.8) TheminimumdetectablesignalistheconditionofS/N=1.Weshallstatethiscon-ditionas(ispl)min. (ispl)min=r G2+4kTB RG2(2.9) Oneshouldnotethat(ispl)min(Ibg+Idg)andthatispl=Sp(spl)AG.WemaysubstitutetheserelationsintoEq.( 2.9 )above.ThiswillyieldtheminimumdetectablelightuxfromthePSP.ThisistermedtheNoiseEquivalentPower,orNEP. R

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WearenowleftwiththeNEPintermsoftheirradiantuxofthePSPlayer.WeshallinvoketheStern-Volmerrelations(Eqns( 1.1 ),( 1.2 ))tocorrelatethephotodetectorandPSPbehaviors.TheStern-VolmerEquationisrestatedforconvenience. The\aerodynamictesting"formoftheStern-Volmerequation(Eqn.( 1.2 ))iscreatedbyapplyingEqn.( 2.11 )attwopressures,PandP0.Theratioofthesetwostatesyieldsthe\aerodynamictesting"formoftheequation. p0=C0(T)+C1(T)L0 where L=(Ibg+ispl)=Sp=Radiantintensityattheacousticpressurep WemaynowstateEqn.( 2.12 )intermsoftheacousticpressureandradiantuxofthePSP.DierentiatingEqn.( 2.12 )withrespecttoradiantux(L)andassumingthereferencestateP0isPatmgives (p)min dL=C1p0L01 ApplyingthisrelationtoEqn.( 2.10 )allowsustostatetheminimumdetectablepres-sure Ppmin=C1p0SpAG Ibgq R

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ForthecaseofinterestwherebackgroundlightnoisedominatesoverdarkcurrentandJohnsonnoise,Eqn.( 2.15 )reducesto pmin=C1p0 SpA(2.16) Onemaystatethisastheminimumdetectablesoundpressurelevel(SPL)as (SPL)min=20log10(p)min Thersttermontheright-handsideofEqn.( 2.16 ),C1p0=p 2.11 )appliedatareferencestate,P0,andtheexpressionforC1inEqn.( 2.13 )yields astheparameterthatmustbeminimizedinthePSPformulation.LoweringKSo2isdesirableintermsofminimizingthedetectablepressurelevel.ThisisduetothenatureofC1,theslopeofthelinearPSPcalibration,asdenedinEqn.( 2.13 ).AsKqSo2goestozero,thisforcesC1to1.C1p0=p 2{4 .AminimumofC1p0=p

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Figure2{4: DesirableChemicalPropertiesofaPSPCoating anS3884APDforcomparison.TheanalysiswasappliedassumingthatthePSPlu-minescentoutputwasatawavelengthmatchedtothepeaksensitivitywavelengthofeachphotodetector,450nmand800nmforthePMTandAPD,respectively.Arbi-traryradiantuxlevelsuptothepointofmaximumlightinputlevelwereconsidered,1:67E6wattsand6:0E6wattsforthePMTandAPD,respectively. Figure 2{5 showstheminimumdetectableradiantuxfora0.1mdiametersur-faceforthetwophotodetectors.ThecurvesforboththeAPDandPMThaveanoiseoorwherethethermalnoisedominates.ThePMThasaninherentlylowernoiseoormakingitbetterforverylowlightleveldetection.Aslightlevelsincrease,theshotnoisebecomesadominatenoisesourcewiththeshotnoiseincreasingaslightlevelsincrease.Atthehigherlightlevels,theAPDisseentohaveslightlybetterperformancethanthePMT,i.e.,itcandetectalowerlightlevelatgivenbackground

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illuminationlevel.TheminimumdetectableSPLisshowninFigure 2{6 .Thegoalis Figure2{5: MinimumDetectableRadiantFluxofDetectors tominimizetheminimumdetectableSPL.Weobservethatasbackgroundlightlevel(PSPbackgroundemission)increases,theminimumdetectablepressuredecreases.Soundpressurelevelsaslowas115dBarepossiblewiththePMTand106dBwiththeAPD.AsshowninEqn.( 2.16 ),fortwophotodetectorswithidenticalbandwidthandbackgroundilluminationlevels,theminimumdetectablepressureisproportionaltop 2.16 )isthatfortwophotodetectorswithequivalentF=Sp,oneshouldse-lectthedetectorwiththehighermaximumallowablelightinput.Alowergainmaybeusedtoavoidsaturatingthedevice.

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AsshowninFigure 2{5 andFigure 2{6 ,thePMTdisplayshighersensitivityatlowerlightlevelsduetothehighdevicegain.Thereexistsalimitnear109WattswheretheshotnoiseofthePMTbecomesalimitingfactor.Athigherlightlevels,theAPDisseentoperformbetterduetoitsgreaterquantumeciencyandhigherradiantsensitivity.APSPcoatingwithmaximumpressuresensitivity,C1,andmaximumtotalemission,L0shallproducealowerdetectableSPL.Ifpossible,itisalsodesirabletooperateatlowermeanpressure(P0)asthisincreasesthebackgroundemission,howeverthiswouldalsoeecttheSPLoftheincidentacousticwave.Althoughnotexplicitlyconsidered,acoatingwithhighdynamicresponseisalsodesired.There Figure2{6: MinimumDetectableSPLofDetectors areafewassumptionsinthisanalysisthatshouldbenoted.Thepresentednoisecharacteristicsofthephotodetectorassumethatthereisnonoisepresentinthedataacquisitionsystem.Also,thedetectorperformancehasbeenassumedatthepeak

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sensitivitywavelength(=420nm),whileinrealitymeasurementswillbeconductedat=650nm.Measurementsnotatthepeaksensitivitywavelengthsuerfrompronounceddegradationofthequantumeciency(QE)andtheradiantsensitivityofthedetector.[ Corp. August,2005 J ]ThereductionofbothSpandQEmayhavealargeeectontheactualminimumdetectablesignal.ThecathoderadiantsensitivityisgiveninthePMTdatasheet, Corp. [ August,2005 ],howeverthereisnoreadilyapparentdataonthebehavioroftheanoderadiantsensitivity,Sp,asaFunctionofincidentlightwavelength.Asaresult,Spisassumedtobewavelengthindependentwithrespecttowavelength,yieldingaminimumdetectablesignalof115dB. Finally,thedynamiccharacteristicsofthePSPhavebeenignored.TheresponseofthePSPsystemisinherentlylimitedbythediusionofoxygenwithinthePSPcoating.ReducingthecoatingthicknessorincreasingthemassdiusivityofthecoatingcanimprovethePSPfrequencyresponsebuttypicallywillsimultaneouslyreducethesignalradiantintensity.TheassumptionhasbeenmadeinthisanalysisthatsucientPSPilluminationlevelsandcoatingthicknessesarepresenttosupplytherequiredbackgroundilluminationlevels(Ibg=SpL0).IntermsofPSPchemistry,itwouldbedesirabletocustomizetheformulationtomatchthepeakluminescentwavelengthtothephotodetectorpeaksensitivitywavelength.ItmayalsobepossibletodesignPSPformulationswithincreasedsensitivity(dP=dP0)nearatmosphericpressurelevels.ThismayresultinreducedbackgroundemissionP0andincreasedsignalemissionL.

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Thischapterexplainstheexperimentalsetupsandproceduresusedindatacol-lection.Thesamegeneralsetupisusedforallexperimentshoweveraprobeconnectedtoamicrophonemustbeinstalledintheplanewavetubeforthestandingwavera-tiotests.PSPstaticcalibrationisaccomplishedwiththeuseofavacuumchamberandpressuretransducer.Twoseparatedatacollectionsystemsareutilizedintheexperiment.AnAgilentVXIsystemisutilizedforstaticcalibrationandnoiseoormeasurements,whileaStanfordResearchSystemsSR785dynamicsignalanalyzerisusedforfrequencyresponsemeasurements.StandingWaveRatioTest 3{1 thisspeciallydesignedcapisttedwithaprobecapableoftranslatingalongalimiteddistance(0.25m).ABruel&Kjrtype4138condensermicrophone,notedas\Microphone1"inFigure 3{1 ,isattachedtotheprobeviaexibletubing.Thisapparatusallowsfordirectmeasurementoftheacousticsignalatvariouslocationsinsidethetube.A2ndBruel&Kjrtype4138microphoneisplacedatthefaceofthealuminumpistonattheendofthetube,thisisdenotedas\Microphone2"inFigure 3{1 .Comparisonsoftheoutputofmicrophones1and2allowsforthecalculationoftheSWR,pressurereectioncoecient()andotherpropertiesofthesample.TheplanewavetubeisexcitedusingaJBLPro2490Hdriver.Thisdriverisoperatedbyawaveformgenerator(HP/AgilentE1441A)passedthroughaCrownInternationalK1amplier.DatacollectionisaccomplishedwiththeuseofanHP/AgilentVXIdataaquisition 24

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Figure3{1: SchematicofExperimentalSetupforStandingWaveRatioTesting system(E1432A).ThedatacollectionparametersareoutlinedbelowinTable 3{1 .ToperformtheSWRtest,thewaveformgeneratorissetatthespeciedfrequency Table3{1: SWRDataCollectionSettings ValueParameter 10240SamplingFrequency(fs)[Hz]20DataBlocks4096Samples/blockACChannelCoupling100ChannelCouplingFrequency[Hz]UniformWindow0:1ChannelRange[V] andanoutputlevelof300mVPP.Theamplierattenuationissettozero,thissettingcorrespondsto126.9dBSPLat1000Hz.Theprobeisadvancedasclosetothesamplefaceaspossible.Thesignalsofbothmicrophonesarerecorded.Theprobeisretracted5mmfromthesamplefaceandthemicrophonesignalisagainrecorded.Thisprocedureisrepeatedforfourfrequencies,600Hz,1000Hz,1400Hz,and1800Hz.ThemicrophoneoutputsarethenanalyzedasoutlinedinAppendix B .TheStandingWaveRatio(SWR)issimplyaratioofthemaximumandminimummicrophonevoltagenearthefaceofthesample.Themagnitudeofthisratiocanbeanalyzedtodecipheracousticpropertiesofthespecimen.

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Whenanalyzingthedata,acorrectionfactormustbeappliedtothemicrophonelocationbecausethegeometricandacousticcentersarenottypicallycoincident.ThiscorrectionfactorisaFunctionofthewavelengthofthesoundbeingtestedandothervariablesasoutlinedinAppendix B .PSPStaticCalibration ThePMTsignalisacquiredandtheaveragermsvalueiscomputedandrecorded.ThePMTsignalisrstacquiredatPatm,thiswillserveasthereferencepressureforsubsequentmeasurements.Thepressureischangedandthesystemislefttoequilibrate.MeasurementsareconductedoverasmallrangeaboutPatm,asthisistheanticipatedpressureenvironmentoftheplanewavetube.Afterallexperimentsareconducted,thepressurechamberisagainbroughttoPatmandlefttosettle.ThePMToutputiscomparedtotheinitialmeasurementinordertoensurenothinghaschangedinthesetup. Inanalyzingthecalibrationdata,thedarkcurrentisrstsubtractedfromallpressuremeasurements.EachpressureandPMToutputisthencomparedtothereferencestateinordertoyieldacalibrationofthesameformasEqn.( 1.2 ).

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opticallensarray.Thelensarrayallowsforthefullsamplesurfacetobefocusedontheviewingwindowofthedetector.TheexperimentalsetupisshownschematicallyinFigure 3{2 .Thetestedfrequencyrangevariesfrom500-2100Hzandislimitedbytheperformanceenvelopeofthedriver(2490H,JBLProfessional)usedtoexcitethetubeandthecutofrequencyofthetube.TwoseparatedataacquisitionsysFigure3{2: SchematicofExperimentalSetupforAcousticTesting temsareutilized.Atwo-channeldynamicsignalanalyzer(SR785,StanfordResearchSystems)isutilizedforfrequencyresponsemeasurementsandmeasurementsovertheentireacousticspectrum.Theanalyzercontainsbothasourceandtwoacquisitionchannels,whichenablesthemoduletocontrolthecompleteexperimentalsetup.Theanalyzersourcesignalispassedthroughanamplier(K1,CrownInternational)andthenroutedtotheJBLdriver.Fordetectorlinearitymeasurements,thesystemisex-citedthroughtheuseofawaveformgenerator(E1441A,HP/Agilent)whichispassedthroughtheamplier,whichisinturnconnectedtothedriver.Datacollectioninthiscaseisaccomplishedthroughtheuseofanotherdataacquisitionsystem(E1432A,HP/Agilent).Bothsetupsallowsoundpressurelevels(SPL)ofupto164dBtobeappliedtothePSPsample.

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4{1 .TheresultsoftheSWRtestsshowthatthePSPsample/substratemaybetreated Table4{1: SWRResults Property1800Hz1400Hz1000Hz600Hz 0.99790.99590.98780.995714.2210.86-1.732.524:19E37:98E32:43E28:64E3z=c0.675+j7.9630.2238+j10.5223.13-j56.824/45+j45.07SWR(0)959.9498.8162.7461.1SWR(0)[dB]59.6453.9644.2353.28 asasound-hardsurfaceduetothelargepressurereectioncoecient,(alsoknownasR),andstandingwaveratioatthesampleface,SWR(0).(forexplanationseeAppendix A .) Theseresultsareasexpectedbecausethesubstrateisanaluminumpiston,whichshouldactasasoundhardsurfacewhencomparedtoair.Sincethesubstrateissoundhard,thismeansthatthereisapressuredoublingatthefaceofthePSPsample,sothatthesoundpressureexperiencedbythePSPisnearlytwicethesoundpressureatanyotherlocationinthetube.ThispressuredoublingallowsforthehighSPLatthefaceofthesample.Thissigniesthattheacousticenergyisconcentratedatthesamplefaceandnotallowedtopropagatethroughthesubstratemediumandoutofthesystem.PSPCalibration 4{1 andTable C{1 .DataisacquiredwithsettingsspeciedinTable 4{2 .Theseresultsshowthe 29

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PSPbehavesaspredictedbyEqn.( 1.2 ).Alinearregressionwasperformedtotarelationshiptothedatapoints.TheresultingrelationshipisshownasaredlineinFigure 4{1 andisgivenbytheequation P0+0:13108(4.1) Thelinearrelationhasacorrelationcoecient(r2)valueof0.9989andastandarderrorof5:04E4.ThisshowsthatthePtTFPPrespondslinearlytosmallchangesinpressure,andisexpectedtoretainthisbehaviorwhenexposedtouctuatingpressureswithintheplanewavetube.Figure 4{1 showserrorbarswhicharedepictedasthe95%condenceinterval. Table4{2: PSPStaticCalibrationSettings ValueParameter 8192SamplingFrequency(fs)[Hz]50DataBlocks8192Samples/blockACChannelCoupling100ChannelCouplingFrequency[Hz]UniformWindow10PMTChannelRange[V] 4{2 andTable C{2 .(note:theSR785iscapableofauto-rangingtheacquisitionchannels,eliminatingtheneedtosetavoltagerange)Resultsshowthatthephotodetectorresponsemaybeconsideredtobeatovertherangeof100to2200Hz,andthusitdoesnotimpactthemeasuredresponseofthePSPcoating. DataacquisitionwasaccomplishedwiththeSR785dynamicanalyzer.PertinentdataacquisitionsettingsarelistedinTable 4{3 .ThemagnitudeandphaseresponsesareshowninFigure 4{2 .Themagnituderesponseofthedetectoriserraticalthoughthereisnovisiblecutofrequencyandthemagnituderemainswithin0:1dBofthe

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Figure4{1: PSPStaticCalibrationResults referenceat500Hz,showingthatthePMThasnegligibleinuenceonthefrequencyresponsemeasurementofthePSPcoating.ThenoiseinthemeasurementisduetothelowgainsettingofthePMT.Duetothehighintensityoftheberopticlightsource,thePMTgainsignalwassetat0.23Vdc.Theusablerangeforthegainsignalis0to1.25Vdc.Atsuchalowgainsetting,thethermalnoisehasalargerinuenceonthedeviceoutputsignal.Thereferencesignaloutputoftheopticalchopperwas Table4{3: PMTFRFAcquisitionSettings ValueParameter 3.2kHzSpan1.6kHzCenterFreq.16HzFFTLineWidth1000VectorAveragesUniformWindow usedasthereferencesignalforthefrequencyresponsemeasurements.Thissignalis

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aconstantamplitudesquarewaveofthesamefrequencyasthemotorwhichdrivesthechoppingdisc.Knowingthemotorfrequencyandthenumberofbladesonthediscyieldsthechoppingfrequency. Thephaseresponseisatatapproximately1.ThisplotofphaseresponsecanbeusedforqualitativeresultsonlybecausethephasedierenceofthePMTandopticalchopperisunknown.AsshowninAppendix C ,thephasedelayisapprox.9.ThisosethasbeenremovedinFigure 4{2 asthisisaconstantphasedierenceinthechoppingmotorandthereferenceoutputsignal.Fortheshownresults,thediscwasmountedtothechoppingmotorandallexperimentswereconductedwithoutmovingthedisc.Thus,thephaserelationshipbetweenthediscandmotorisunknownbutconstant,enablingonetodiscernanyphaserolloofthePMToverthetestedrange. Figure4{2: PMTFrequencyResponse

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4{3 .Thisgureisacomparisonofthedarknoise,backgroundnoise,andtheVXIDAQsystemnoise.DatawascollectedusingsettingsspeciedinTable 4{5 .TheDAQsystemnoiseisthenoisepresentincollectingdatawithnodeviceconnectedtotheDAQboard.ThisisaFunctionoftheinuenceofexternalnoisesources.Oneseesthatthisnoiseislargelydominatedby60Hzlinenoise,howeverconnectingadevicetotheDAQchannelreducesthisnoisesource. ThedarknoiseisthePMToutputwiththespeakerandExcitationlightsturnedo.Thisisanindicationoftheexternallightwhichleaksintotheenclosurewhichsurroundstheexperimentalsetup.Thedarknoiseisseentoberoughly2ordersofmagnitudebelowthebackgroundnoise,showingthataminimumofexternallightisenteringtheenclosureandthatthedarknoiseofthePMThasminimalinuenceonthedeviceoutputonceitissubjectedtoareasonablelightsignal.Thiscurveshowsaspikeat120Hz,howeverthisinuencemaybeeliminatedbypropergroundingofthedetector.Thedarknoisecanbeseentobewhitenoiseacrosstheentirespan.OneshouldnotethatanestimateofthetruedarknoiseofthePMTwouldbeameasurementofthedeviceoutputwiththeviewingwindowcovered.Thedarknoisementionedhereisameasureoftheinuenceofexternallightsourcesandthedarknoiseofthedetectorontheoutputsignal.Itwasassumedthatduetothecomparativelyhighlightlevels,thedarknoiseofthedetectorwouldbesomewhatnegligiblewhencomparedtotheshotnoisepresent. ThebackgroundnoiseisduetothePSPluminescenceatPatm,i.e.,Excitationsourceon,butnoacousticinputsignal.Thisisalsoseentobewhitenoise.SincethereisnotemporalpressuresignalthePSPemissionisconstantandthereisnodominantfrequencycomponentpresent.Boththebackgroundanddarknoisesare

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dominatedbytheshotnoiseofthedetector.AnyacousticsignalsuppliedtothePSPwillshowupasaspikeamongthebackgroundnoise. Figure4{3: ExperimentalNoiseComparison 4{4 .Thefrequencyresponseoftheopticalsystemismeasuredat140,134,128,122,119,and115dBSPL.Inallcasestheopticalsystemisshowntobehaveasa\1/2"-ordersystem(-10dB/decadeattenuation,45phasedelay)whichisinagreementwithpreviouslyreportedresults.[ Winslowetal. 1996 ]Thebehaviorofa\1/2"-ordersystemisshownbydashedlinesinFigure 4{4 andFigure 4{5 .ThebehavioratallSPLisconsistent,howeverthehigherSPLarebetterbehavedduetothedecreasednoisecontentofthesignal.

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Figure4{4: PSPCoatingRelativeFrequencyResponse Thereisseentobemeasurableresponseofthecoatingat122and119dBSPL.ThisindicatesthatthewavelengthdependanceoftheanoderadiantsensitivityofthePMT,SP,maynotbeproportionaltothecathoderadiantsensitivityasdiscussedinChapter 2 .TherelativeandphaseresponseoftheopticalsystemareshowninFigure 4{4 andFigure 4{5 (note:uncertaintieshavebeenomittedforclarity).TabulateddatawithuncertaintiesarelocatedinAppendix C andplotsoftheresponsemagnitude,relativemagnitude,phase,andcoherenceforeachSPLarelocatedinAppendix D LocatedinAppendix D areplotsofthecoherenceandPMTpowervsfrequencyforthevariousSPL.Theseguresillustratethatthedelityoftheopticalsystemisproportionaltothemagnitudeofthepressureuctuation,asthecoherenceandPMTpowerareseentoscalesomewhatlinearlywithSPL.Thenoiseoorisseen

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Figure4{5: PSPCoatingPhaseResponse graphicallyinguresFigure D{1 andFigure D{2 forthecurvesof122,119,and115dBSPL.Above122dBSPLthecoherenceandpowerseemtoscalelinearlywithSPL.Below122dBthereisadecreasedrelationshipwithSPL,thisindicatestheincreasedinuenceofnoiseonthemeasurement. AsseeninFigure 4{4 at119dBSPL,theopticalsystemisstillcapableofdetectingtheacousticsignal,however115dBSPLseemstobeatorbelowthenoiseoorofthesystem.Thisagreeswellwiththepreviouslypredictednoiseoorof115dBSPL.(refChapter 2 )PSPLinearity 4{5 .Thesquarerootoftheamplitude

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Table4{4: PMTFRFAcquisitionSettings ValueParameter 1.6kHzSpan1.3kHzCenterFreq.16HzFFTLineWidth1000VectorAveragesUniformWindow0.44VdcPMTGainControl5.3E4V/PaCalibratedMic.Sensitivity ofthePMTpowerspectrumattheExcitationfrequencyof540HzforeachSPLwasrecordedandisdisplayedinFigure 4{6 andinTable C{3 inAppendix C ,whichshowsalinearrelationshipbetweentheacousticpressureandtheresponseoftheactivelayer,aspredictedbyEqns.( 1.2 ),( 4.1 ).Thelinearequationttothedataisgivenbelow. Figure4{6: LinearityofOpticalSystem

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Table4{5: LinearityDataAcquisitionSettings ValueParameter 8192Hzfs8192DataPoints/Block50DataBlocks100HzCouplingFreq.UniformWindow0.1VPMTChannelRange0.44VdcPMTGainControl5.3E4V/PaCalibratedMic.Sensitivity 2 thereisatemperaturechangeassociatedwithanacousticwave.DuetothepropertiesofthePSPformulation,thiseectwasestimatedtohaveaminimaleectontheresponseofthecoating.Toverifythisassumption,theoxygenmustberemovedfromtheinterioroftheplanewavetubeinordertoisolatetheinuenceofthetemperatureoscillationonthePSPemission.Twoholesaredrilledintotheendcapoftheplanewavetube,onefortheadditionofindustrial-gradenitrogenandoneforventing.ThePSPsampleisremovedfromtheendofthetubeandthetubewashedwithnitrogenfor20minutes.Thesampleisthenre-insertedintotheplanewavetubeandthetubeiswashedwithnitrogenforanadditional5minutes.Thenitrogenhoseisremovedandthettingsintheendcapofthetubearereplacedwithplugs.CareshouldbeexercisedastonotoverpressurethetubewithrespecttoPatmasthepressuredierentialacrossthespeakerdiaphragmmaydamageit.Thedriveristhenoperatedat140dBSPLandfrequencyresponsemeasurementsaretaken.Acomparisonofthecoatingresponseinairandnitrogen

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isshownbelowinFigure 4{7 .TheresultsaretabulatedinAppendix C withthefrequencyresponsedataofothersoundpressurelevels.Theresultsshowthatthe Figure4{7: CoatingResponseinAirandNitrogen responseofthecoatingtothetemperatureuctuationarenegligiblecomparedtotheresponseinthepresenceofoxygen.TimeResolutionofOpticalSignal 4{8 ,providedtheSPLishighenough.UsingtheHP/AgilentwaveformgeneratorandDAQsystem,theJBLdriverwasexcitedat540Hzand160dBSPL.DatawascollectedusingtheparametersinTable 4{6 .TheresultingdataisdisplayedinFigure 4{8 .Inparta)ofFigure 4{8 thePMTsignaldisplaysafaintsimilaritytothemicrophone,howeverthesignalissignicantly

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Figure4{8: ComparisonofUnlteredPMTOutput,FilteredPMTOutput,andMicrophoneOutput corruptedbynoise.ThisnoiseisaresultoftheseveralnoisesourcespresentinthePMT(thermal,background,dark,shot).Thethermal,background,anddarknoisearemanifestedasbroadbandnoiseinthePMToutputwhichdegradesthesignal-to-noiseratioandhampersdatacollection.Onemayreducetheimpactofthisbackgroundnoisebyreducingthebandwidthofthemeasurement.Thismaybeaccomplishedbyreducingthesamplingrateorbyapplyingabandpassltertothesignal.Reducingthesamplingrateisstraightforward;howeverthisresultsinalossofdataqualityduetothereducednumberofdatapointsavailabletodescribethephotodetectoroutput.Applyingalter,eitheranalogordigital,tothedetectoroutputallowssamplingatahigherfrequencyandthusretentionofmoresignaldetail,whilealsoallowingtheabilitytochooselterparameterstosuitthesituationathand.

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Toimprovetheresolutionofthetimeseriesdata,adigitallterwasappliedusing Table4{6: SingleTimeSeriesDataAcquisitionSettings ValueParameter 6.4kHzSpan8192DataPoints/Block1DataBlocks100HzCouplingFreq.UniformWindow0.1VRange0.44VdcPMTGainControl5.3E4V/PaCalibratedMic.Sensitivity 4{8 .Inthiscase,muchofthenoisepresentintheunlteredsignalhasbeenremovedandthelteredsignalhasclearlyresolvedtheacousticsignalasreferencedbythelteredmicrophoneoutputinplotc).Theamplitudemodulationapparentinpartb)ofFigure 4{8 isduetonoisewhichhaspassedthroughthelterandcharacteristicsofthelter.UncertaintyAnalysis PSPStaticCalibrationUncertainty 4.1 ),restatedhereforconvenience. P0+0:13108(4.3) SolvingtheaboveEquationforVyields Weshallcomputetheuncertaintyasthesquarerootofthesumofthesquares.Wemustrstsolvefortheuncertaintiesofthemeasuredvoltageandpressure.Thisis

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summarizedas whereBiandPiarethebiasandprecisionerrorsrespectivelyofeachmeasurementandtv;95isthestudent'st-distributionfor95%condence(v=numberofsamples). Forgreaterthan30samples,thestandardcondenceinterval,i.e.,tv;95is2.Forthereferencecondition,v0weshallusethestandarddeviationofthemean,2 C{1 .Forthepressureuncertainty,wewillusetheaveragestandarddeviationofthepressurereading,5E4.Thepressureandvoltageuncertaintiesaresubstitutedinto( 4.6 )forthetotaluncertaintyoftheoutputvoltagegivenbelow.TheresultingPMToutputlevelisthemeanvoltageduetothePSPresponsetoasteadypressure.Thus,theuncertaintyofinterestisthestandarddeviationofthemean,2 C{1 asuv,andshownaserrorbarsinFigure 4{1 @V @V0UV02+@V @PUP2+@V @P0UP02(4.6) TheresultinguncertaintyforeachpressureislistedinTable C{1 andshowngraphi-callyinFigure 4{1 .FrequencyResponseErrors

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frequencyresponsemeasurementsaresubjecttobothbiasandprecisionerrors.Weshalldenoteabiaserrorasb[x]andaprecisionerroras[x],wherexisthequantitybeingexamined.Weshalldenotetheestimatedquantitiesas^x.Thequantitiesmeasuredareinfactestimatesofthetruevalues,hence,theyaresubjecttoerrors.Ifthetruevalueswereknownthennoerroranalysiswouldbenecessary. Weshallrstlookatthecoherenceofthefrequencyresponse.Thecoherencebetweensignalsxandyisdenotedas^2xyandisdenedas[ BendatandPiersol 2000 ] ^2xy(f)=jGxy(f)j2 ThecoherenceFunctionisamethodtodescribethecorrelatinbetweentheoutput,y,andinputsignal,x.Thecoherencecanvaryfrom0to1,with1beingperfectcorrelationbetweenthetwosignals.Highcoherencevaluesleadtolesserrorsinspectralmeasurements.Thenormalizedbiasandprecisioncoherenceerrorsaregivenas[ BendatandPiersol 2000 ] wherendishowmanytimesthedataisaveraged(numberofdatablocks). Forthefrequencyresponseitself,thebiasofthemagnitudeisproportionaltotheamountofnoiseinthemeasurement.ThemeasurementsignalistypicallyspeciedasGxx=Gnn+GuuwhereGnnisthenoisemagnitudeandGuuisthesignalmagnitude.IntablesinAppendix C ,GxxisthemagnitudeofthesignalatthespeciedfrequencyandGnnistheobservedaveragemagnitudeofthenoiseinthesignal(responseatotherfrequencies).Thenormalizedbiasandprecisionerrorsofthefrequencyresponse

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aregivenas[ BendatandPiersol 2000 ] Thenthetotaluncertaintyforeachmeasuredquantity(magnitude,phase,coherence)isthengivenbyEqn.( 4.5 ).Foralargenumberofsamples,thestandard95%con-denceintervalis2U.ThisisusedtogeneratethecondenceintervalshowninguresforeachSPLinAppendix D ErrorsforeachSPLtestedaretabulatedinAppendix C .OneseesthatforthelowerSPLtheerrorsinthefrequencyresponsebecomeconsiderable.Thisisduetotheverylowcoherenceofthemicrophone-PSPsignal.Atlevelsof128dBSPLandhigherthetypicalmagnitudeerrorsbecome10%orless.Tofurtherdecreasetheerrors,onemustincreasethenumberofaverages(datablocks)gatheredastheerrorsscaleas1 C alsocontainsmagnitudeandphaseplotswitherrorbarsoftheresponseoftheopticalsystemateachSPL.

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TheresearchdescribedinthisthesissuccessfullyinvestigatedtheresponseofPtTFPPinpoly(tBS-co-TFEM)(30%)toacousticpressureuctuations.Theresearchshowedthatthecoatingrespondsinthemannerofa\1/2"-ordersystem.Thecoatingwasshowntohaveanoiseoorsimilartothepredictedvalueof115dBSPL. Frequencyresponsemeasurementsshowedtheopticaldetectortohavenegligible(at)responseovertheapplicablefrequencyrange.Itwasalsoshownthattheopticalcoatingresponsescaleslinearlywiththeappliedacousticpressuretothelowerlimitofthenoiseoorofthesystem.Thenoiseoorwasnumericallyestimatedtobe115dBSPL.Subsequentexperimentaldatarevealedtheactualnoiseoortobewithin5%ofthisvalue.Thetemperaturedependanceofthecoatingduetotheacousticwaveswasassumedandveriedtobenegligiblecomparedtothepressureresponse.TheopticalsystemwasalsoshowntohavetheabilityofdirecttemporalresolutionofthePSPemission.AdequatelteringofthePMTsignalremovesthesignicantnoisecomponentandrevealsaclearcorrelationofthePSPemissiontoamicrophonelocatedatthecoatingsurface. Althoughtheresearchconductedinthisthesisiscomplete,thereisfutureworktobeconducted.Theapplicationofotherphotodetectorstothisexperimentalmethodmayallowresolutionoflowersoundpressurelevels.Avalanchephotodiodesandhigh-speedCCDcamerasaretwodetectorswhichmayproveusefulinthisareaofstudy.Withtheuseofhigh-speedphaselockedCCDcameras,itmayprovepossibletodirectlyimagethesurfaceofaPSPsampleinauctuatingpressureeld,therebygaininganopticalrecordoftheexactpressuredistribution,similartoresultsachievedusingPSPinwindtunnels. 45

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Theupperfrequencyappliedtothecoatinginthisresearchwaslimitedbythecutofrequencyoftheplanewavetube.Futureworkshouldutilizeapparatuswithhighercutofrequenciesinordertobettercharacterizetheresponseofthecoating(s). ThechemistryofaPSPformulationdenesitspropertiesandwasultimatelythelimitingfactorintermsofnoiseoorinthisresearch.NewPSPformulationsarethesubjectofcontinualresearch.Discoveryofnewbinder-luminophoreformulationswhichpromoteincreasedoxygendiusionandgreatersensitivitynearatmosphericpressurelevelswillenablefurtherreductionofthenoiseoorindynamicpressureapplications.

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dPSeP0+dT dSePT0+O"2(A.1) whereO(2)arehigherordertermsthatmaybeneglectedforthetimebeing. Sincewehaveassumedthecompressionprocesstobeisentropic,wemaymakeuseoftheisentropicrelationsforpressureandtemperature. P0= 0T T0=P P01 where=Cp=Cv. SubstitutingtheserelationsintoEq.( A.1 ),weareleftwith dPSeP0=T01 P(A.3) Which,aftersomemanipulationyields T0P0 WemaynowsetTandPtobeanyarbitrarytemperatureandpressure.Weshallchoosethequiescentvalues,T0andP0.Thisgivesusthenalformofthetemperaturechangeofanisentropiccompression. 47

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WewillassumethatanydisturbancestothismediumaresmallcomparedtothevalueofthestaticpropertiesP0and0.Thisisknownasthesmallsignalapproximation.Thus,wehavethepropertiesofasmalldisturbanceinitiatedinthemediumatrest: Wewillusetheabovequantitiestolinearizetheconservationequations.Werstexaminethe1-DContinuityequation: Wewilldenejj=0asthechangeindensityfromtheequilibriumstatetothedisturbedstate.ItissomewhatstraightforwardtosubstitutethisrelationfordensityintoEq.( A.8 ) Seeingthat0isconstantleavesuswith

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The2ndand4thtermsareofsecondorderandthuscanbeneglected.Removingthesetermsleavesuswiththelinearizedcontinuityequationforahomogeneousmedium Wewillnowapproachthemomentumequationinthesamemanner.Wewillstartwiththe1-Dmomentumequation Makingthesameassumptionofthechangeindensityasaboveleaves (+0)(ut+uux)+Px=0ut+uux+0ut+0uux+Px=0O("2)+O("3)+O(")+O("2)+O(")(A.13) Neglectinghigher-ordertermsleavesuswiththelinearizedmomentumequation UsingtheTaylorexpansionoftheidealgaslaw,P=c20,andcontinuityandmo-mentum,Eqs.( A.11 ),( A.14 )wemaydeducethelinearwaveequation.Firstwewilleliminatedensity c20;P c20t+0ux=0(A.15) WemayremovethepressuretermsfromEqs( A.14 )and( A.15 ) dt(0ut+Px=0)d dxP c20t+0ux=00utt+Pxt=0Ptx

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Thisleavesuswiththelinearized1-Dwaveequation IfonechoosestoeliminateuratherthanPinEq.( A.16 ),theresultisthewaveequationintermsofpressure In3-D/vectornotation,weareleftwiththemorefamiliarformofthewaveequation Blackstock [ 2000 ] where isknownasthewavenumber.

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WemaydierentiateEqn.( A.20 ) wherek0nisthewavenumberforthenthmode.InEqn A.22 weseethatforconstantphaseoneisleftwith dt'=! k0n(A.23) Thisexpressionisdenotedcn,andisknownasthephasevelocity.Wemaynowsubstitutethefrequencyfromthenthmodefromthederivationofthewaveguideequation,=ny=a,whichgivesus k0n=c0 c02ny a2=c0 ThisrelationshowsthatwaveguidesaredispersivebecausethephasespeedisaFunctionoffrequency.BygraphingEqn. A.24 ,onewillseethatthephasevelocitywillincreasewithfrequencyuntilapointwhere Atwhichpointcn!1.Thispointisknownasthecutofrequency.Wemayrephrasethephasespeedintermsofthecutofrequencyas Belowthecutofrequency,thewavenumberisimaginary.Thismeansthattheacousticwavesareevanescentanddecayexponentiallywithdistance.Abovethecutofrequency,theacousticwavesarerealandpropagatedownthetube.Onewillalwayshaveacousticwaveshowever,ask0=0correspondstoplanewaves.Anyvalueofngreaterthanzeroisindicativeofhigherordermodes.

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Thisisasolutiontothe3-DWaveEquation( A.19 ) WewillconsiderarigidwalledductasshowninFigure A{1 .Byinspection,onemaydeducetheboundaryconditionsofnoowintothewallsoftheduct.Mathematicallystated,theboundaryconditionsare FigureA{1: SchematicofaSquareDuct

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directionofthetubeandnoinformationisgivenconcerningthesource.Thismaynotbenecessaryanditwillbeaddressedasneeded. WeseethatEq.( A.19 ),thethree-dimensionalwaveequation,isaf(x,y,z,t)asshowninFigure A{1 .Thisequationcanbesolvedthroughtheuseofseparationofvariablesbyassumingasolutionoftheform MorseandIngard [ 1987 ] wheref,g,hareFunctionsofonlyx,y,zrespectively.SeparatingEq.( A.30 )andsolvingforf,g,hyields SubstitutingtheserelationsintotheWaveEquation(Eq.( A.18 ))yields c20ghf00fhg00fgh00ej!t whichmayberewrittenas ThisshowsusthataFunctionofxequalsaFunctionofyandz.Thisistrueonlyifbothsidesareequaltoaconstant.Wemaynowseperateandsolvetheequationforeachdirection,startingwithf(x). Thishomogenous,2ndorderODEhasrootsofj,thusthesolutionhastheformf=A1cos(1x)+B1sin(1x).Invokingtheboundaryconditionofnoownormaltothewallgivesus dxx=0;a=0)B1=0;1=m a(A.35)

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Thus,f=A1cos(mx=a).Repeatingtheaboveprocedureforg(y)yieldsasolutionofthesameform,g=A2cos(ny=a). Wearenowleftwiththebehaviorofthepropagationdirection(z).Tosolveforthisbehavior,weshallsubstitutethesolutionsforf(x)andg(y)intoEq.( A.33 )andsolveforh(z). a a=m22 a a=n22 SubstitutionintoEq.( A.33 )givesus Thecoecientofhismadeupofconstantvalues.Thisquantitywillbedenotedask2andisknownastheDispersionEquation.OnenowseesthatEq.( A.38 )isofthesameformasEq.( A.34 ).ForEq.( A.34 )thegeometricformwaschosentoemphasizetheshapeoftheFunction.Inthiscasewewillusetheexponentialformofthesolutionsincethisequationdescribesthepropagationofawave: Theconstantkhasbeenwrittenaskmntoremindusofitsdependenceonthevaluesofmandn.WenowhaveassembledsolutionsforallcomponentsofP'(x,y,z,t)thatwereassumedinEq.( A.30 )andwemayassemblethenalsolution,whichissimplyamatterofsuperposition. acosny aC1ekmnz+C2ekmnzej!tP0(x;y;z;t)=cosmx acosny aAmnej(!tkmnz)+Bmnej(!t+kmnz)(A.40) whereAmnandBmnareconstantsdeterminedbysourceconditionswhichcanbestatedasP(x;y;0;t)=F(x;y)ej!t.[ Blackstock 2000 ]

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The2indices,mandn,arethemodenumbers.Physicallythesenumbersrepresentthenumberof1=2wavelengthspresentinthexandydirections,with(m=0,n=0)representingtheplanewavemodewhichhasuniformpressureinbothxandy.[ Schultz 2004 ]DerivationoftheCylindricalWaveguideEquation A{2 .Again,webeginwiththewave FigureA{2: SchematicofaCylindricalDuct equation, Incylindricalcoordinates,theLaplacianoperator(r2)hastheform 1 Wehavethesameboundaryconditionasbefore, Wewillassumeaseparablesolutionofthesameformasabove,

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SubstitutionintoEq( A.19 )andsimplifyingleaves Wewilllet!2=c20=k2.ThisbearssomeresemblancetoEq.( A.33 )howeverther'sapparentinthiscasemustbedealtwith.WemayrstaddresstheZterm.Wewillequatethistoaconstantandsolve. Theformofthisequationshouldbefamiliartothereader.Wemayassumeasolutionoftheformasabove ReturningtoEq.( A.45 ),weareleftwith Wewilldeneaconstant,kr,suchthatk2=k2r+k2z.Thisleaves Multiplyingbyr2enablesustoremovethecomponent. 00 Thisformhasasolutionof()=Acos(m)+Bsin(m)wheremisaninteger.WearenowleftwithonlyFunctionsofr.MultiplyingtheremainingquantityofEq.( A.45 )byRgives ThisisaBesselEquationoforderm.Thus,thesolutionisR(r)=ArJm(krr)+BrNm(krr).However,theNeumannFunction(alsoknownasBesselFunctionof2ndkind)(Nm(krr))isunboundedasr!0soitisnotphysicallyrealizablefora

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cylindricalwaveguide.However,thistermshouldberetainedwhendealingwithanannularwaveguide.Combiningther,z,andsolutionsyieldsus Asintherectangularwaveguidethemandnindicesgiveanindicationofthenumberof1=2wavelengthspresent,althoughinthiscasetheyrepresenttheranddirections.Therstmodestopropagatearethe(1,0)and(2,0)modes,followedbythe(0,1)mode[ MorseandIngard 1987 ].Foracylindricalwaveguide,thecutofrequencyhastheform wheremnisthenthzeroofJ0m.Thecutofrequencyofamodeistheminimumfrequencyatwhichthatmodecanpropagatedownthewaveguide.Forthewaveguideusedinthisstudy,the2lowestcutofrequenciesare2016Hzand3344Hz.Below2016Hztheacousticeldwithinthewaveguideisplanar.NormalIncidenceSoundReectionandTransmission A{3 ,whereindicatedpressuresaregivenbyWewill IncidentWavep+=p+(tx=c1)ReectedWavep=p(t+x=c1)TransmittedWaveptr=ptr(tx=c2) nowdeneareectioncoecient, =p Wewillalsodeneatransmissioncoecient,

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FigureA{3: SoundReectionandTransmissionataNormalIncidenceSurface Weshallassumetheinterfaceisstationary,whichleadsto dividingbyp+andmanipulationshowsusthat 1+R=T(A.57) Inadditiontopressure,velocitymustbecontinuousacrosstheinterface.Usingthesamenotationaspressure,itisstraightforwardtodeducethatu++u=utr.WewouldliketoknowtheboundaryconditionintermsofandT.Todothiswewillusethecharacteristicimpedanceofeachmedium(Z=c)sincetheacousticwavesineachmediaarebydenitiontravellingattheacousticspeed,oru=c.Substitutionleavesuswith

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MultiplicationbyZ1=p+yields 1R=Z1 SolvingEqn.( A.59 )and( A.57 )givesthefollowingrelations Wewillnowexaminethreeconditionsofanormalincidencesurface.First,letusconsideraninterfaceatwhichZ2Z1.Inthiscase,Eqn.( A.60 )R=Z1=Z1=1,whichmeansthereisperfectreection180outofphase.Then,ptr=0sothatp+=p,sothatthepressureattheinterfacetendstozerowhilethevelocitydoubles,fromEqn.( A.57 ).Thissituationisknownasasoundsoftboundaryandoccursattheendofatubeorforanacousticwavetravellingfromwaterintoair. Next,considerwhathappensifZ2Z1.Inthiscase,R=1,orp+=p.Thistellsusthatptr=0.Attheinterface,sincep+andparereectedinphase,theyareadditive,pinterface=p++p=2p.Also,sincethepressuresignalcannotpenetrateintomedium2,neitherdoesthevelocitysignal,utr=0,oru+=u.Sothereisapressuredoublinginmedium1attheinterfaceandzerovelocityattheinterface.Thisisknownasasoundhardboundaryandoccursforawavetravellingfromairintowater,orfromairintoanothersuitablemediumwithamuchgreaterimpedance,suchasablockofaluminum. Thirdly,whatifthemediaareidentical,oratleasthaveidenticalimpedance.InthiscaseZ1=Z2,sothatR=0.Thereisperfecttransmissionacrosstheinterface,whichisintuitivelysatisfying.[ Blackstock 2000 ]

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Aplanewavetravellingdownawaveguideimpingesontheendofthetubeandisreectedbackintheoppositedirection.Inthisprocess,astandingwavepatternisproducedwhichcanbemeasuredusingamicrophone.Usingthestandingwaveratio(SWR)atthefaceofatestspecimenplacedattheendofthetube,thenormalincidencesoundabsorptioncoecient,n,pressurereectioncoecient,,andotherpropertiescanbecalculated.ThemethodprescribedbelowisthatoftheASTMC384-98Standard[ ofTestingand ASTM ]andisvalidonlyforplanarsoundelds,i.e.,itisonlyvalidbelowthecutofrequencyofawaveguide.TheStandingWaveRatioisdenedas whereV(x)istheoutputvoltageofthemicrophoneatstationxofthewaveguide. Todiscernthestandingwavepatternwithinthetube,theexactlocationofthemicrophonewithrespecttothesamplefacemustbeknown.Thisisaccomplishedbytheuseofamillimeterscaleattachedtothebottomofthewaveguide.Thisenablesthedistancefromthespecimentothemicrophonetobeknownatalltimes.Acorrectionfactormustbeappliedtothelocationofthemicrophonebecausetheacousticandgeometriccentersoftheprobearenotnecessarilycoincident.Thecorrectionfactor 60

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isdenedas where Whenmakingmeasurements,scalereadingsateachfrequencyshouldbecorrectedasfollows: where x=Truedistancefromspecimen[mm] Ifpossible,itisdesiredtoadjustthescalesuchthatxsf=0 Followingdatacollection,themicrophonesignalcanbegraphedasshownbelowinFigure B{1 ,Figure B{2 ,Figure B{3 ,andFigure B{4 toyieldthevoltageasaFunctionofxcor.Thisdataisthenusedtodeterminethepropertiesofthesample.Datareductionisperformeddierentlyaccordingtothenatureoftheavailabledata. Iftwoormoreminimaarepresent,themaximumvoltagenearestthesamplefaceistakentobeVmax(0).Vmin(0)isthenfoundbyusingthefollowingformula Ifoneminimaandonemaximaarepresent,oneusestheavailablemaximaasVmax(0),andthetubeattenuation,,mustbecalledupontodiscernVmin(0).maybe

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estimatedas where f=DriverFrequency[Hz] a=Tuberadius UsingonemaycalculateVmin(0)using OnemaynowcalculatethePressureReectionCoecient,.Foraninnitelyrigidsurface=1whichmeansthattheentiretyoftheacousticenergyisreectedbackintothemedium.Obviously,aninnitelyrigidsurfacedoesnotexist,butitispossibletogenerate'swhichareverynearly1.isacomplexquantityandhasbothamagnitudeandphase wherex1isthedistancefromthespecimentotherstminimum. OnemayalsocalculatetheNormalIncidenceSoundAbsorptionCoecient,n,andtheimpedanceratio,z=c n=1jj2z c=1+ 1(B.8)

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MicrophoneVoltagevs.xcorfor600HzExcitation

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FigureB{2: MicrophoneVoltagevs.xcorfor1000HzExcitation FigureB{3: MicrophoneVoltagevs.xcorfor1400HzExcitation

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FigureB{4: MicrophoneVoltagevs.xcorfor1800HzExcitation

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TableC{1: PSPStaticCalibrationResults P[psia]P=P0 66

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TableC{2: PMTFrequencyResponseResults Freq.[Hz]Mag.[]Mag.[dB]Phase() 1061.1641.319-9.852041.1671.341-9.923041.1641.319-9.934001.1661.334-10.144961.1651.327-9.926081.1671.341-10.087041.1611.297-9.828001.1611.297-10.048961.1631.312-10.0310081.1581.274-10.0211041.1601.289-10.112001.1631.312-9.9512961.1641.319-10.1314081.1651.327-9.9615041.1631.312-10.1316001.1671.341-10.0816961.1661.334-9.8118081.1641.319-9.919041.1601.289-10.1420001.1591.282-10.2120961.1581.274-10.0722081.1631.312-10.18 TableC{3: PSPLinearityResults Pressure[Pa]SPL[dB]PMTPower[V2]p 356.23145.016.022.45497.55147.9212.083.48631.89149.9917.974.24762.64151.6326.205.12888.68152.9533.835.821011.51154.0844.706.691129.06155.0355.357.441245.66155.8964.808.051357.55156.6379.588.921469.62157.3293.199.65

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TableC{4: 115dBSPLFrequencyResponseData Freq.GxxGnnResp.Rel.MagPhase2xySPL 5004.5460.155.5710.000-30.3319.60115.6365962.3240.154.195-2.464-56.639.70115.1857002.3040.153.975-2.932-47.309.31115.6148042.4080.154.213-2.427-48.3510.27115.3019241.4240.153.235-4.721-19.825.65115.31910042.5360.154.193-2.468-56.1310.40115.5711002.3010.154.085-2.695-37.869.098115.37212041.5910.153.329-4.472-33.966.682115.54813003.0500.154.559-1.741-63.9112.63115.64413961.1850.152.920-5.611-41.244.632115.40814921.1870.152.913-5.632-65.064.652115.43715960.7300.152.390-7.351-62.362.951115.04817000.5790.151.944-9.145-42.942.330115.83117961.0030.152.710-6.259-48.974.174115.33319080.7790.152.390-7.351-56.733.148115.32820201.0720.152.821-5.911-49.254.377115.273 [Hz][nV2rms][nV2rms][V=Pa][dB][deg.][103][dBre20Pa] TableC{5: 115dBSPLFrequencyResponseNormalizedErrorEstimates Mag.BiasMag.RandomPhaseRandom2xyBias2xyRandom -0.0320.1580.1580.0010.313-0.0610.2260.2260.0010.450-0.0610.2310.2310.0010.459-0.0590.2200.2200.0010.437-0.0960.2970.2970.0010.592-0.0560.2180.2180.0010.434-0.0610.2330.2330.0010.465-0.0860.2730.2730.0010.543-0.0470.1980.1980.0010.393-0.1130.3280.3280.0010.654-0.1120.3270.3270.0010.653-0.1710.4110.4110.0010.821-0.2060.4630.4630.0010.924-0.1300.3450.3450.0010.689-0.1620.3980.3980.0010.795-0.1230.3370.3370.0010.673

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TableC{6: 119dBSPLFrequencyResponseData Freq.GxxGnnResp.Rel.MagPhase2xySPL 5005.9660.154.0980.000-36.430.238119.4825965.7970.153.961-0.295-34.0222.360119.6557003.9950.153.462-1.465-42.4616.330119.2118044.5640.153.564-1.213-37.2518.760119.5329322.3750.152.897-3.012-28.489.199119.44410203.4760.153.238-2.046-47.3613.280119.18711002.9120.152.953-2.846-55.8411.090119.21612045.1600.152.739-3.500-47.5519.280119.65113002.2660.152.512-4.251-26.048.193119.53113962.3590.152.492-4.320-35.2815.370119.20214923.1380.152.522-4.217-41.5416.000119.21216202.8360.152.517-4.234-39.605.280119.51117002.8270.152.516-4.237-36.879.683119.44718282.9470.152.527-4.199-41.0113.350119.40618921.9220.152.389-4.687-36.863.662119.25520201.8720.152.227-5.297-54.074.843119.738 [Hz][nV2rms][nV2rms][V=Pa][dB][deg.][103][dBre20Pa] TableC{7: 119dBSPLFrequencyResponseNormalizedErrorEstimates Mag.BiasMag.RandomPhaseRandom2xyBias2xyRandom -0.0251.4501.4500.0012.899-0.0250.1480.1480.0010.292-0.0360.1740.1740.0010.344-0.0320.1620.1620.0010.320-0.0590.2320.2320.0010.462-0.0410.1930.1930.0010.383-0.0490.2110.2110.0010.420-0.0280.1590.1590.0010.316-0.0620.2460.2460.0010.490-0.0600.1790.1790.0010.355-0.0460.1750.1750.0010.348-0.0500.3070.3070.0010.612-0.0500.2260.2260.0010.450-0.0480.1920.1920.0010.382-0.0720.3690.3690.0010.736-0.0740.3210.3210.0010.640

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TableC{8: 122dBSPLFrequencyResponseData Freq.GxxGnnResp.Rel.MagPhase2xySPL 50015.5300.154.6660.000-44.0928.820122.51559613.0900.154.343-0.623-46.9224.990122.39270012.2400.154.17-0.976-38.8222.370122.4528049.9200.153.996-1.346-49.9142.380122.34893211.6100.153.976-1.390-39.0222.430122.63910288.8540.153.678-2.067-48.9915.360122.13711086.8390.153.462-2.592-36.4716.799122.41212046.8940.153.294-3.024-48.3412.840122.55413006.6340.153.149-3.415-36.3512.630122.23213966.4360.153.085-3.594-45.7512.310122.71114926.2770.153.003-3.828-45.0911.730122.40216205.9760.152.812-4.399-45.0911.480122.53917004.4030.152.527-5.327-41.349.151122.36718285.9530.152.417-5.713-39.728.853122.29119085.5980.152.332-6.024-48.6310.720122.32220206.5490.152.213-6.479-41.6211.630122.399 [Hz][nV2rms][nV2rms][V=Pa][dB][deg.][103][dBre20Pa] TableC{9: 122dBSPLFrequencyResponseNormalizedErrorEstimates Mag.BiasMag.RandomPhaseRandom2xyBias2xyRandom -0.0100.1300.1300.0010.256-0.0110.1400.1400.0010.276-0.0120.1480.1480.0010.292-0.0150.1060.1060.0010.208-0.0130.1480.1480.0010.292-0.0170.1790.1790.0010.355-0.0210.1710.1710.0010.339-0.0210.1960.1960.0010.390-0.0220.1980.1980.0010.393-0.0230.2000.2000.0010.398-0.0230.2050.2050.0010.408-0.0240.2070.2070.0010.413-0.0330.2330.2330.0010.463-0.0250.2370.2370.0010.471-0.0260.2150.2150.0010.427-0.0220.2060.2060.0010.410

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TableC{10: 128dBSPLFrequencyResponseData Freq.GxxGnnResp.Rel.MagPhase2xySPL 51660.580.164.4890.000-35.17100.70128.75359666.820.164.339-0.295-32.3103.40128.53570850.530.164.241-0.494-33.2681.49128.46480449.530.164.203-0.572-46.4879.60128.25193230.960.164.159-0.663-46.0151.14128.357101232.670.164.055-0.883-54.3153.18128.184112441.190.163.932-1.151-40.7968.44128.311120438.620.163.732-1.604-40.6663.11128.408130037.480.163.579-1.968-50.4052.62128.254139630.830.163.395-2.426-41.4550.58128.274149228.910.163.078-3.278-46.1048.90128.824162022.930.162.853-3.937-46.6737.71128.642170021.150.162.689-4.451-48.0136.09128.476182819.900.162.552-4.905-51.5432.70128.231190815.120.162.473-5.179-33.4926.50128.200202014.450.162.387-5.486-45.1128.64128.597 [Hz][nV2rms][nV2rms][V=Pa][dB][deg.][103][dBre20Pa] TableC{11: 128dBSPLFrequencyResponseNormalizedErrorEstimates Mag.BiasMag.RandomPhaseRandom2xyBias2xyRandom -0.0030.0670.0670.0010.127-0.0020.0660.0660.0010.125-0.0030.0750.0750.0010.144-0.0030.0760.0760.0010.146-0.0050.0960.0960.0010.188-0.0050.0940.0940.0010.184-0.0040.0820.0820.0010.159-0.0040.0860.0860.0010.167-0.0050.0970.0970.0010.185-0.0040.0950.0950.0010.189-0.0060.0990.0990.0010.192-0.0070.1130.1130.0010.222-0.0080.1160.1160.0010.227-0.0080.1220.1220.0010.239-0.0100.1360.1360.0010.267-0.0110.1300.1300.0010.257

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TableC{12: 134dBSPLFrequencyResponseData Freq.GxxGnnResp.Rel.MagPhase2xySPL 516247.80.174.8080.000-36.83311.2134.283596181.60.174.194-1.187-37.10248.3134.118708165.90.173.970-1.663-35.34239.3134.203804152.20.173.787-2.073-40.30211.4134.239932136.10.173.603-2.506-38.47197.8134.1861012117.30.173.369-3.089-48.79175.9134.1221108133.50.173.465-2.845-41.43195.2134.1681204121.80.173.347-3.146-42.15177.1134.3431300120.00.173.310-3.243-43.55179.5134.3761396109.90.173.219-3.485-43.47162.2134.2341492112.90.173.199-3.539-41.39163.5134.408162096.50.172.973-4.175-44.05157.7134.360170090.80.172.887-4.430-50.35141.8134.350179685.50.172.757-4.831-43.46124.3134.271190888.20.172.694-5.031-45.38136.5133.923202093.50.172.604-5.326-42.63127.0134.445 [Hz][nV2rms][nV2rms][V=Pa][dB][deg.][103][dBre20Pa] TableC{13: 134dBSPLFrequencyResponseNormalizedErrorEstimates Mag.BiasMag.RandomPhaseRandom2xyBias2xyRandom -0.0010.0330.0330.0000.055-0.0010.0390.0390.0010.067-0.0010.0400.0400.0010.070-0.0010.0430.0430.0010.077-0.0010.0450.0450.0010.081-0.0010.0480.0480.0010.088-0.0010.0450.0450.0010.081-0.0010.0480.0480.0010.087-0.0010.0480.0480.0010.087-0.0020.0510.0510.0010.093-0.0020.0510.0510.0010.093-0.0020.0520.0520.0010.095-0.0020.0550.0550.0010.102-0.0020.0590.0590.0010.111-0.0020.0560.0560.0010.105-0.0020.0590.0590.0010.110

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TableC{14: 140dBSPLFrequencyResponseData Freq.GxxGnnResp.Rel.MagPhase2xySPL 516982.00.1554.7440.000-37.86649.80140.38596928.90.1554.648-0.178-38.80636.10140.316708783.60.1554.263-0.929-38.49610.90140.324804607.30.1554.174-1.112-43.60494.30138.994948690.70.1553.961-1.567-43.25567.20140.4151108550.60.1553.495-2.654-41.42503.50140.5191204515.90.1553.409-2.870-41.20499.70140.2031300509.80.1553.335-3.061-47.83477.00140.5951396487.20.1553.331-3.071-43.56465.50140.4071492473.30.1553.282-3.200-44.03476.70140.411620380.30.1553.069-3.783-42.79404.50140.0431700380.50.1553.018-3.929-43.65410.70140.189 [Hz][nV2rms][nV2rms][V=Pa][dB][deg.][103][dBre20Pa] TableC{15: 140dBSPLFrequencyResponseNormalizedErrorEstimates Mag.BiasMag.RandomPhaseRandom2xyBias2xyRandom 0.0000.0160.0160.0000.0190.0000.0170.0170.0000.0200.0000.0180.0180.0000.0220.0000.0230.0230.0000.0320.0000.0200.0200.0000.0260.0000.0220.0220.0000.0310.0000.0220.0220.0000.0320.0000.0230.0230.0000.0340.0000.0240.0240.0000.0350.0000.0230.0230.0000.0340.0000.0270.0270.0000.0420.0000.0270.0270.0000.041

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TableC{16: 140dBSPLFrequencyResponseinN2Data Freq.GxxGnnResp.Rel.MagPhase2xySPL 51692.070.2023.910.000-77.14296140.67259695.060.2020.37-1.39299.37220140.45870885.400.2018.59-2.18698.25165.5140.26780463.800.205.674-12.49455.36176.4140.1294873.700.2011.14-6.634-165.8629140.392110888.400.2016.08-3.446-43.21111.3140.211204103.200.2031.492.392113.6322.6140.363130086.400.2014.42-4.392-83.1978.96140.294139665.360.207.21-10.41356.8625.66140.7681492104.730.2033.062.814107.1457.9140.324162092.920.2023.6-0.113-82.73822.8140.373170082.370.2013.01-5.28668.9173.07140.041 [Hz][pV2rms][pV2rms][nV=Pa][dB][deg.][103][dBre20Pa] TableC{17: 140dBSPLFrequencyResponseinN2NormalizedErrorEstimates Mag.BiasMag.RandomPhaseRandom2xy2xyRandom -0.0021.2991.2990.0012.599-0.0021.5071.5070.0013.014-0.0021.7381.7380.0013.476-0.0031.6831.6830.0013.367-0.0030.8910.8910.0011.782-0.0022.1192.1190.0014.239-0.0021.2451.2450.0012.489-0.0022.5162.5160.0015.032-0.0034.4144.4140.0018.828-0.0021.0451.0450.0012.089-0.0020.7790.7790.0011.558-0.0022.6162.6160.0015.231

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FigureD{1: PMTPowerasaFunctionofSPL 75

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FigureD{2: Mic-PMTCoherenceasaFunctionofSPL

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FigureD{3: Response,RelativeResponse,andPhaseResponseofOpticalSystemat115dBSPL

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FigureD{4: Response,RelativeResponse,andPhaseResponseofOpticalSystemat119dBSPL

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FigureD{5: Response,RelativeResponse,andPhaseResponseofOpticalSystemat122dBSPL

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FigureD{6: Response,RelativeResponse,andPhaseResponseofOpticalSystemat128dBSPL

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FigureD{7: Response,RelativeResponse,andPhaseResponseofOpticalSystemat134dBSPL

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FigureD{8: Response,RelativeResponse,andPhaseResponseofOpticalSystemat140dBSPL

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A.E.Baron,J.D.S.Danielson,M.Gouterman,J.R.Wan,andJ.B.Callis.Sub-millisecondresponsetimesofoxygen-quenchedluminescentcoatings.ReviewofScienticInstruments,64(12):3394{3402,1993. J.H.Bell,E.T.Schairer,L.A.Hand,andR.D.Mehta.Surfacepressuremeasurementsusingluminescentcoatings.AnnualReviewofFluidMechanics,33:155{206,2001. J.S.BendatandA.G.Piersol.RandomData:AnalysisandMeasurementProcedures.WileyInterscience,NewYork,NY,3rdedition,2000. D.T.Blackstock.FundamentalsofPhysicalAcoustics.JohnWileyandSons,NewYork,NY,2000. B.F.Carroll,A.Winslow,J.Abbitt,K.Schanze,andM.Morris.Pressuresensitivepaint:Applicationtoasinusoidalpressureuctuation.Proceedingsofthe16thICIASF,pages35.1{35.6,1995. B.F.Carroll,J.D.Abbitt,E.W.Lukas,andM.J.Morris.Stepresponseofpressure-sensitivepaints.AIAAJournal,34(3):521{526,1996. C.-M.Chan,M.-Y.Chan,M.Zhang,W.Lo,andK.-Y.Wong.Theperformanceofoxygensensinglmswithruthenium-absorbedfumedsilicadispersedinsiliconerubber.TheAnalyst,124:691{694,1999. HamamatsuCorp.S3884datasheet.OntheWWW, S/S2381 etc.pdf HamamatsuCorp.R6352datasheet.OntheWWW, R/R6352.pdf HamamatsuCorp.Photoncountingusingphotomultipliertubes.OntheWWW, photoncounting.pdf M.E.CoxandB.I.Dunn.Oxygendiusioninpoly(dimethylsiloxane)usinguo-rescencequenching.i.measurementtechniqueandanalysis.JournalofPolymerScience,PartA:PolymerChemistry,24(4):621{636,1986. R.H.Engler.Furtherdevelopmentsofpressuresensitivepaint(opms)fornon-atmodelsinsteadytransonicowandunsteadyconditions.16thICIASFRecord,16:33.1{33.8,1995. 83

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ChristopherAllenVirginwasbornonFebruary23,1981,inKankakee,IL.UpongraduatingfromBradley-BourbonnaisCommunityHighSchoolin1999,Chrisat-tendedBradleyUniversitywherehewasawardedabachelorofsciencedegreeinmechanicalengineeringin2003.DuringhisnalyearatBradleyUniversity,ChrisconsideredpursuingacareerasadevelopmentalengineerwiththeUnitedStatesAirForce.InAprilof2003,Chrisdecidedtoattendgraduateschooltochangehiscareerfocustoaerospaceengineering.ChrissoughtemploymentwithButlerInterna-tionalworkingattheCaterpillarMossvilleEngineAssemblyCenterwhileapplyingtograduateschools.Afterevaluatinghisoptions,ChrismovedtoGainesville,FL,toattendtheUniversityofFloridawherehereceivedaMasterofEngineeringdegreeinaerospaceengineeringin2005. 86