.~PLICATION OF OPTICAL FIBERS TO WIDEBAND DIFFERENTIAL INTERFEROMETRY AND MEASUREMENTS OF PULSED WAVES IN LIQUIDS

by

Avinash 0. Garg

Thesis submitted to the Faculty of the

Virginia Polytechnic Institute and State University

in partial fulfillment of the requirements for the degree of

MASTER OF SCIENCE

in

ELECTRICAL ENGINEERING

A?PROVED:

. . . ----------------------------Dr. R. 0. Claus

iJ----------------Dr. L. C. Burton Dr. D. D. Chen

July, 1982 Blacksburg, Virginia

ACKNOWLEDGEMENTS

I would like to thank my advisor, Dr. R. 0. Claus, for

his time, encouragement and unceasing patience. I also wish

to thank my graduate committee, Dr. L. C. Burton and Dr. D.

D. Chen for their comments and suggestions

I am indebted to Tyson Turner and· Dan Dockery for their

help and numerous suggestions. Among those whom I owe spe-

cific gratitude are Vicki Trump and my colleagues Janet

Wade, John Gray and Sam Zerwerkh.

I must include special note of appreciation to my par-

ents for their love and endless patience and moral support.

ii

TABLE OF CONTENTS

ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . ii

Chapter page

I.

I I.

INTRODUCTION

SURFACE ELASTIC WAVES

2.1 Properties of Surface Elastic Waves 2.2 Types of Elastic Waves 2.3 Rayleigh Waves 2.4 Stoneley Waves .....

1

4

4 5 8

10

III. DETECTION OF SURFACE WAVES USING SURFACE DEVICES 12

IV.

v.

VI.

3.1 Transduction ...... . 3.2 Piezoelecetric transducers

3.2.1 Piezoelectricity 3.2.2 Piezoelectric Transducers

3.3 Electromagnetic transducers 3.4 Electrostatic transducers

OPTICAL DETECTION TECHNIQUES

4.1 Interaction of surface waves with optical waves . . . . . . .

4.2 Michelson Interferometer .. 4.3 Stabilized path interferometer 4.4.Differential Interferometer

FIBER DIFFERENTIAL INTERFEROMETER

12 . 13

13 18 22

. 23

28

28 36 42 44

56

5.1 Differential Fiber System . 56 5.2 Maximum permissible DC movement of the

surf ace 60 5.3 Measurements 66 5.4 Results 67

BULK WAVE DETECTION USING DIFFERENTIAL INTERFEROMETRIC TECHNIQUES 69

6.1 Technique for the detection of bulk waves 69 6.2 Two beam differential system for bulk wave

detection . . . . . . . . . . . . . . . 70 6.3 Four beam differential system for detection

of bulk waves 80 6.4 Results ........... 88

iii

VII. CONCLUSIONS AND FURTHER REFINEMENTS ........ 90

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . 94

Appendix page

A. PREPARATION OF SINGLE MODE FIBERS FOR EXPERIMENTS . 98

B. COMPUTER PROGRAM FOR CALCULATING THE POSITIONS OF LENSES FOR VARIOUS SAW FREQUENCIES 105

C. DATA FOR THE DETECTION OF PULSED WAVE IN WATER USING TWO BEAM DIFFERENTIAL SYSTEM 118

D. DATA FOR DETECTION OF THE DIRECTION OF PULSED WAVE IN WATER USING FOUR BEAM SYSTEM 121

VITA 127

ABSTRACT

iv

LIST OF TABLES

Table page

3.1. Types of Crystals and their Constants [11] . 17

6.1. Data values for detection of compressional waves in water (refer figure 6.4) . . 79

6.2. Data values for detection of direction of bulk waves in water (refer figure 6.10) . . 89

v

LIST OF FIGURES

Figure

3.la. Quartz crystal structure

3.lb. Crystal cuts

3.2. Piezoelectric transducer

3.3. Electromagnetic transducer

3.4. Electrostatic transducer .

4.1. Flat plate Fabry-Perot interferometer

4.2. Bulk waves in water .

4.3. Diffraction of light by compressional waves in water

4.4. Michelson interferometer

4.5. Stabilized optical path interferometer

4.6. Differential interferometer .

4.7. Basic differential interferometer geometry

4.8. Narrowband differential interferometry

4.9. Sensitivity of a differential interferometer

4.10. Sensitivity of differential interferometer as a

page

14

15

20

24

25

32

35

37

38

43

4S

47

50

S4

function of spot separation . SS

S.l. Fiber differential interferometer 57

S.2. Remote detection head S9

5.3. Gaussian wavefront in far field 61

5.4. Focussed gaussian beam 62

vi

5.5. Collimated gaussian beam 65

5.6.. Result from pulse generation on mirror surface . 67

6.1. Two beam system for detection of bulk waves in water . 71

6.2. Water tank 72

6.3. Data for the scan of a standing bulk wave in the water tank . . . . . . . . . . 74

6.4. Sensitivity of system to position of beams on bulk waves in water . . 75

6.5. Data for the detection of pulse using two beam system 77

6.6. Path of ultrasonic pulse in the water tank 78

6.7. Four beam system for detection of direction of bulk waves in water . . . . . . . . 81

6.8. Diffraction patterns due to a single and crossed gratings . . . . . . 82

6.9. Modified four beam system . 85

6.10. Data from four beam system 86

7.1. Diffraction pattern due to grating and square aperture . 92

A.1. Path of ray of light through a step index optical fiber . . . . . . . . . . . . . 99

A.2. Transmission modes in an optical fiber 102

C.l. Detection of ultrasonic pulse using two beam system 118

C.2. Comparison of RF noise to signal from the two beam system . . . . . . . 119

D.l. Detection of the pulsed bulk wave in water (vertical pair of beams) 122

vii

D.2. Detection of pulsed bulk wave in water (horizontal pairs of beams) .

D.3. RF noise due to Metrotek pulser and laser noise

D.4. Detection of direction of pulsed wave in water using one set of beams

D.S. Detection of direction of pulsed wave in water using the remaining pair of beams .

viii

123

124

125

126

Chapter I

INTRODUCTION

Practical measurements of surface acoustic waves (SAW)

and bulk waves in materials evaluation applications require

the use of sensing systems with a linear response and good

sensitivity over a wide dynamic range. More importantly,

these devices should be insensitive to low frequency speci-

men translations, such as those typically caused by back-

ground vibrational noises in on-site measurement situations,

and must be adaptable to specimen surface orientation.

Several types of transducers may be used for these mea-

surements, all having their respective advantages and disad-

vantages. Piezoelectric transducers are perhaps the most

easily used but they tend to mechanically load the surface,

thereby distorting the surface particle displacement fields

to be measured. Like the non-contacting electromagnetic and

capacitive transducers, they also effectively integrate par-

ticle motion across their active surface areas, producing

output signals for which the transfer functions are not very

well characterized.

Optical techniques are thus pref erred over these trans-

ducers because they off er a wide dynamic range and because

1

2

output signals from these techniques are directly propor-

tional to surface acoustic wave amplitude. Optical techni-

ques offer sensitivity and frequency response similar to or

better than the surface contacting and non-contacting trans-

ducers, and at the same time also allow point surface prob-

ing without surface loading. Although many optical techni-

ques due to their design are sensitive to surface acoustic

wave signals and low frequency vibrational noises, differen-

tial methods having variable acoustic bandwiths which can be

tuned to eliminate the noise component from the ouput signal

are preferred. In addition to these advantages, optical

techniques are available which can be made insensitive to

surface irregularities.

Here we descibe the construction and theory of opera-

tion of one such optical technique. This system has all the

above mentioned advantages of the various optical techniques

and in addition is convenient for the inspection of surfaces

oriented in any direction. This has been achieved by the use

of optical fibers for transmitting light from input optics

to output optics, thus providing separate input and detec-

tion units which may be easily positioned.

3

The application of the same type of optical probing to

bulk waves in liquids is also described. Specifically, dif-

ferential interferometric techniques have been used for the

detection of pulsed bulk waves in water. Herein we describe

a pulsed two laser beam system and a four beam system for

determining the propagation direction of the bulk wave.

The discussion follows with Chapter 2 which introduces

elastic waves and their properties which have made them

popular in field of nondestructive testing. We then consider

in Chapter 3 the various surface contacting and non-contact-

ing devices for the detection of SAW on specimen surfaces.

Chapter 4 briefly introduces various optical techniques

including the theory behind the Michelson and differential

interferometers. With the theory behind us we now discuss

the development, construction and results of the fiber dif-

ferential system. Chapter 6 deals with the detection of com-

pressional waves in water using two and four beam diff eren-

tial interferometric techniques.

Chapter II

SURFACE ELASTIC WAVES

2.1 PROPERTIES OF SURFACE ELASTIC WAVES

Interest in elastic waves in electronics and signal

processing applications can be attributed to their various

properties, the most important one being their very low vel-

ocities as compared to those of electromagnetic waves. These

velocities range from 1.Sxl0 3 m/s to approximately 12xl0 3

m/s, with surface elastic wave velocities lying in the lower

third of this range; this is about 10 5 times smaller than

electromagnetic wave velocities [1]. The major advantage of

this low velocity is that the physical size of elastic wave

resonators is 105 · times smaller than their electromagnetic

counterparts. Thus, attractively small elastic wave tran-

smission components such as resonators, filters, and delay

lines can be made for use in electronics.

Interactions between elastic waves and other waves and

beams can also be used for modulation and detection. El as-

tic waves can be amplified by allowing them to propagate in

a medium which also contains charge carriers drifting under

the influence of an applied voltage. Nonreciprocal propaga-

tion of elastic waves occurs in certain magnetic materials

located in a steady magnetic field. Also, in some magnetic

4

5

materials there is a strong interaction between elastic

waves and magnetic waves and this property can be used for

the transduction of bulk elastic waves. Interaction of sound

and elastic waves has been used in devices like ultrasonic

beam deflectors.

Elastic waves can also propagate along the external

boundaries of solids and these surface waves can be used for

flaw detection in manufactured objects. Since the velocity

and direction of propagation of the surface acoustic wave

can be altered by surface and substrate treatment, these

observables can be used to determine surface characteris-

tics. These properties and various others have made surface

elastic waves useful in the field of nondestructive testing

and evaluation.

2.2 TYPES OF ELASTIC WAVES

Elastic waves can be categorized depending upon their

properties and modes. The two major groups are bulk waves

and surface elastic waves.

Bulk waves can propagate in any direction in a solid

irrespective of the isotropic or anisotropic elastic nature

of the solid. The phase velocities of the bulk waves are

6

independent of frequency (at least from below 20 kHz up to

the microwave frequency range) and are numerically equal to

the square root of a linear combination of the elastic

stiffness constants divided by the mass density of the sol-

ids. Three independent bulk waves can propagate in a given

direction. One of these is along the direction of propaga-

tion (longitudinal bulk waves). The other two are transverse

bulk waves having particle displacements entirely tran-

sverse to the direction of propagation.

On the other hand, as a surf ace wave propagates along

the free surface of a solid, the particles on the surf ace

move in elliptical paths. This motion of a surface wave can

be decomposed into two components, one in the direction of

propagation and one normal to the free surface. Both longi-

tudinal and transverse strain are associated with the

motion. The phase velocity is similar to that of bulk waves,

but since the particles at a free surface are subjected to

less strain than particles deep inside the bulk of the

solid, the surface wave velocity is lower than the bulk wave

velocities. Because of the low velocities the surface wave

energy thus cannot propagate into the interior and hence

tends to remain on the surface. The surface wave amplitude

decreases from its value at the surface to small values at a

7

depth of about a wavelength. As an example of the distances

involved, ~ surface wave in glass has a velocity of 3180

m/s, so that a wavelength at 2. 25 MHz is approximately 1. 4

mm.

Other important distinguishing charactersitics of sur-

face waves are the accompanying electromagnetic field in

piezoelectric and magnetic materials, and their dispersive

propagation in layered media. At high frequencies surface

waves are also quite sensitive to surface irregularities and

to contamination on the surfaces. This can be used to advan-

tage in the nondestructive testing of various materials, as

this characteristic permits easy damping of unwanted surface

waves and also accounts for loss and scattering.

Surface elastic waves can be further subclassified

according to their various modes of propagation. Elastic

waves traveling on a .free

on the surface of water)

Lord Rayleigh in 1885 and

solid surface (analogous to waves

were mathematically predicted by

hence are called Rayleigh waves

[4]. These waves are frequently used in nondestructive test-

ing and evaluation. In addition to these types of surface

waves, there are waves with characteristics similar to Ray-

leigh waves although they are not free surface phenomena;

8

these are interface waves. In 1924 Stoneley analyzed the

more generalized case of elastic waves propagating along the

surface of separation of two solids [4]. His results con-

firm that elastic waves similar to Rayleigh waves may exist

along the boundary between two solids under the more strin-

gent conditions that the shear wave velocities of the two

media be nearly equal. Hence these interface waves have been

called Stoneley waves. Other waves like Love waves in seis-

mology, consisting of transverse guided waves in bound solid

layers, and Lamb waves in thin plates or laminations, have

been classified as surface waves although their basic nature

is very much different from the Rayleigh and Stoneley waves.

Besides these, there also exist refraction arrivals. This

type of wave can be readily excited in the ultrasonic range

at the contact interface between two different media. This

type of elastic wave, although a body wave, is guided by the

interface and is usually termed an interface wave. This is

actually the refracted wave commonly used in geophysical

exploration and subsurface geological mapping [4].

2.3 RAYLEIGH WAVES

The characteristics of Rayleigh waves (waves traveling

on the surface of a homogeneous solid medium in a vacuum or

9

air) are that their amplitude decreases rapidly with dis-

tance from the surface, their propagation velocities are

less than that of bulk waves in an unbounded medium, and,

except in the plane wave case, their intensity diminishes

with propagation distance at a rate proportional to the

inverse first power of the distance rather than the usual

inverse square law relationship. This diminishing amplitude

of the Rayleigh wave exemplifies the inhomogeneous nature of

these waves and is analagous to the skin effect of electro-

magnetic waves.

A plane inhomogeneous wave can be expressed by the gen-

eralized wave expression

¢'=Aexp[-(k" x+k" y+k" z)]x x y z

exp[-i(wt-k' x-k' y-k' z)], x y z (2.3.1)

where the wave now propagates in the (k'x,k'y,k'z) direction

and its amplitude decreases in the perpendicular direction

given by (k"x,k"y,k"z). This is the inhomogeneous wave con-

dition.

Assume an inhomogeneous plane wave in rectangular coor-

dinates with the direction of propagation parallel to the

x-y plane. Let 80 be the angle of incidence with respect to

10

the x-axis; 80 is a complex quantity 80 =a+ie. Thus under

proper substituion the wave equation now becomes:

~'=Aexp{-ksinhe[ysina-xcosa]}x

exp{-i[wt-kcoshe(xsina+ycosa)]}. (2.3.2)

This function again shows the exponential decrease in ampli-

tude at right angles to the direction of propagation and

also shows the effective wave propagation vector to be

kcoshe. Using this effective wave number , the wave velocity

is noted to be

c'=w/(kcoshe)=c/(coshe),

where c is the plane wave velocity.

(2.3.3)

The velocity of the

inhomogeneous wave is thus less than the plane wave veloc-

ity. Moreover, for large values of e, low propagation veloc-

ity occurs in the x direction as well as a rapid decrease in

amplitude in the y direction.

2.4 STONELEY WAVES

Waves traveling along the bounding interface between

two solids are kn~wn as Stoneley waves. If a layer of a dif-

ferent material is attached to a surface of a semi-infinte

solid, a Stoneley wave may propagate with a phase velocity

which is frequency dependent such that the wavelength is

11

comparable with the layer thickness. This effect in layered

solids permits one to fabricate wave guiding structures with

which the wave energy can be directed about in the surface

plane; it also permits construction of delay lines in which

the delay depends on the frequency [11]. The velocity of

the Stoneley waves has been shown to be less than that of

the slowest shear waves in either medium. Also the veloci-

ties of Stoneley waves have been found to be higher than

highest value of free surface Rayleigh waves in either med-

ium. This constraint strongly limits the existence of

Stoneley waves.

Chapter III

DETECTION OF SURFACE WAVES USING SURFACE DEVICES

3.1 TRANSDUCTION

Interaction of the detection system and an acoustic

wave on a surface is termed transduction. This interaction,

however, should take place so as to create a negligible

effect on the surface wave being detected. Various types of

contacting and noncontacting transducers have been used for

the detection of elastic waves (mainly surface elastic

waves). Each of these have their inherent advantages and

disadvantages which determine their particular uses. Piezoe-

lectric transducers are very highly sensitive devices and

have a wide dynamic range but they tend to load the surf ace

under test. Noncontacting transducers like electromagnetic

and electrostatic transducers solve this loading problem to

some extent, but due to their finite size they tend to inte-

grate over the area of their surface giving transforms of

signals which cannot be easily characterized. Their finite

size also makes point probing of a surface impossible.

Optical detection techniques have

made transduction possible with

been developed which have

negligible loading on the

surface and which at the same time permit point probing of

the surface. These techniques are highly sensitive anti have

12

13

a very wide dynamic range. They also eliminate the depen-

dence of the system on the type of material surface being

tested.

3.2 PIEZOELECETRIC TRANSDUCERS

3.2.1 Piezoelectricity

Certain crystals, when mechanically strained by the

application of an external stress, generate electric charges

on certain of their crystal surfaces. The polarity of these

charges reverses when the direction of strain is reversed.

This effect is called the piezoelectric effect. Conversely,

when charges are applied by external means to faces of the

crystal, the crystal exihibits strain, i.e. dimensions of

the crystal change. Reversing the direction of the applied

field reverses the sign (direction) of this strain.

Piezoelectric axes of the crystal are defined as direc-

tions in which tension or compression develop polarization

parallel to the strain. A crystal is said to be an "X-cut"

when its plate is cut with its face perpendicular to the

X-axis of the crystal; while one cut with its faces parallel

to the lateral faces of the crystal is termed as a "Y-cut". :1

Other often used crystal cuts include the "Z-cut" and the

"AC-cut" crystals. The various cuts dictate "the various uses

of the transducers and are shown in Figure 3.1 (11]. Their

14

z z

y

Left Hand Right Hand

z

x I. R. E. Axes and angles.

FIGURE 3.la. Quartz crystal structure [ll].

15

z

X-CUT

Z-CUT

AT +35.15° BT- 49° CT+ 3 8° OT- '52° ET+ 66° FT - 57°

z

Y-CUT

y

CUT e ¢ l/J x 0 90 90 y 90 90 90 z 0 0 0

AC 90 59 90

FIGURE 3.lb. Principal crystal cuts used in piezoelectric transduction [ 1 1 ].

16

advantages and disadvantages have been discussed in the

following section.

The piezoelectric crystal, due to its piezoelectric

properties, can be used for converting mechanical signals

into electrical signals and vice-versa. This property has

been utilized to manufacture piezoelectric transducers. Dif-

ferent piezoelectric crystals used for the manufacture of

transducers are listed in Table 3.1. The strain and stress,

related by elastic constants of the crystals, can be related

to the electrical parameters like electrical charge, vol-

tage, and polarization by constants of proportionality.

These constants are the piezoelectric constants for the par-

ticular crystal. Since the crystals are not isotropic,

these constants and elastic constants are different for dif-

ferent directions in the crystal [11].

Depending on the direction of the applied field and the

orientation of the crystal, various stresses and strains in

the crystal can be produced. An electric field applied per-

pendicular to the faces of an X-cut quartz plate will pro-

duce elongation along the X-axis,

Y-axis and shear in the Y plane.

compression along the

If an alternating field

with this orientation is applied to the crystal, the crystal

17

TABLE 3.1.

MATERIAL FORMULA PIEZOELECTRIC CONSTANTS DIELECTRIC CONSTANT coulombs/newtons with respect

or to air meters/volt

x 10-12

Quartz Si02 dll -2.3 4.5

dl4 +0.7 4.5

Tourmaline Silicate of dl5 -3.7 6.3

B and Al with d22 -0.3 6.3 one or more

other metals. d31 -0.3 7.1 Variable comp-

d33 -1.9 7.1 osition.

Rochelle KNaC4H4o6 .4H20 dl4 = approx. 550 350 Salt 30° at

ADP NH4H2Po4 dl4 -1.5 56

d36 +48 16

KDP KH2Po4 dl4 +l. 3 42

d36 +21 21

Barium BaTi03 dlS +390 2900 Titanate

d31 -37 170 Crystal d33 +84 170

Barium BaTi03 dl5 +280 1450 Titanate Ceramic d31 -78 1700

d33 +190 1700

18

can be made to oscillate with a frequency dependent upon the

thickness of the crystal.

Crystal quartz is the most widely used piezoelectric

material for the construction of stable oscillators. This

can be attributed to two of its major properties: (1)

quartz can be used for its piezoelectric properties up to

573° c, and 2) the piezoelectric constants of quartz are

less temperature dependent than those of other materials.

3.2.2 Piezoelectric Transducers

Piezoelectric transduction can be accomplished by pro-

ducing an RF (radio frequency) electric field between the

end faces of a massive piezoelectric crystal or a thin pie-

zoelectric crystal mounted on a massive substrate.

The design of the mounting for the crystals is impor-

tant in many applications. Crystal mounting can affect its

freedom to oscillate, its damping, and its sensitivity as a

detector of mechanical motion. The design is also critical

because mapy times it is desired to have the crystal serve

as an interface between one fluid medium and other. Here

the seal has to be liquid tight and gas tight.

19

A much utilized piezoelectric element is a plate cut

from a piezoelectric crystal such that a voltage applied to

the two parallel surfaces of the plate produce a strain in

the direction perpendicular to these surfaces. This is some-

times called a compression plate. A widely used plate of

this type is an X-cut quartz plate; the parallel surfaces

are cut perpendicular to the X-axis of the crystal. The

applicable piezoelectric constant for this X-cut quartz is

d 22 in Table 3.1. X-cut quartz crystal is especially useful

in transducer design to generate ultrasonic longitudinal

vibrations in liquids, gases, and solids [11]. A basic

design for a pizoelectric transducer is shown in Figure 3.2

[ 23 l .

The compression plate described has the interesting

property that the displacement of one of the surfaces with

respect to the other, i.e., the change in thickness ot, is

directly proportional to the voltage difference V between

the surfaces, and is independent of the thickness t of the

plate. This can be shown as follows. The strain is directly

proportional to charge Q per unit surface area, as

ot/t = d 22 Q4TI/K. (3.3.l)

Considering the crystal plate as a parallel plate capacia-

tor,

PIEZOELECTRIC -----t-+-t-~--D IS K

WEAR PLATE

20

---CASE

BNC

CONNECTOR

FIGURE 3.2. Schematic of a typical piezoelectric transducer [30].

21

Q = KV I ( 41Tt) I ( 3 . 3 . 2 )

where K is the appropriate dielectric constant of the X-cut

quartz. Therefore,

6t/t = d2 2 ( v /t) t (3.3.3)

or ct is directly proportional to voltage V, independent of

t [ 11] .

X-cut quartz transducers are primarily used for the

generation of longitudinal or compressional waves; AC-cut or

Y-cut quartz finds uses in the generation and detection of

shear or transverse waves. The Y-cut is one of the most

coupled of the series of different cut transducers for it is

not completely free from parasitic vibrations caused by

cross coupling between modes. It also has a frequency change

in its thickness vibration as the temperature is changed.

The AC-cut vibrates in a very pure shear mode with a low

temperature coeffiecent of frequency change. The AC-cut is

also less fragile than the Y-cut for a given thickness and

may be driven at higher voltages [11].

Finally, because of the symmetrical elastic properties

of tourmaline about the Z-axis, a Z-cut tourmaline trans-,,

ducer gives a pure compressional wave in the Z-direction.

22

3.3 ELECTROMAGNETIC TRANSDUCERS

The progress of ultrasonics was hampered by the lack of

development of transducer materials. Lorentz force transduc-

tion solved this problem to a great extent. In the process

of Lorentz force transduction, an electric current flowing

through a conductor such as a coil induces eddy currents on

a separate electrically conducting substrate subjected to an

external magnetic field.

In electromagnetic transducers, a field is electromag-

netically induced across the gap between the coil and the

conducting substrate and the field decays exponentially with

distance from the surface according to the classical skin

depth effect.

Electromagnetic acoustic transducers (EMATs, EMTs, or

EATs) are devices consisting of a flat coil placed near the

surf ace of a conducting nonmagnetic specimen placed in an

external magnetic field. The energized coils induce an eddy

current in the skin depth region of the conductor which,

because of the static magnetic field, exerts a Lorentz force

per unit volume resulting in a mechanical wave. The direc-

tion of the magnetic field parallel to the specimen surface

governs the type of wave, longitudinal or shear, to ~e gen-

erated in the specimen [19].

Figure 3.3.

23

Some basic EMATs are shown in

The major advantage of these transducers over previous

transducers is the absence of a coupling layer which permits

unique measurement possibilities in severe environments,

under dynamic conditions, and on unprepared specimen sur-

faces. In addition, absolute measurements of sound fields,

in principle, are possible. This feature indicates the

reproducibility of ultrasonic measurements so such transduc-

ers can also be used for the calibration of other transduc-

ers.

3.4 ELECTROSTATIC TRANSDUCERS

Like electromagnetic transducers, electrostatic trans-

ducers (ESATs) can be used as noncontacting transmitters and

receivers of ultrasound in materials. An ESAT is essentially

a capaciator whose two electrodes are the specimen itself

and one external electrode with a gap between them. Figure

3.4 shows a typical ESAT. The electrodes are parallel to

each other and their surfaces should be resonably smooth.

Polarization charges appear on both electrodes in the pres-

ence of an applied field. This electric field may result

either from an alternating potential difference or a static

ELECT RI CAL COIL

ELECTRIC AL COIL

24

SAMARIUM COBALT --- MAGNET

s I } MEANDER

"' COIL EMAT

/ , ,

/ /

/ / / /

I / / I

/ / I /

~sv' {a)

SAMARIUM COBALT .. ,..__ MAGNET

[I ~ I ~ I ~ I : II]}~;~~~~ c

a ~

~ ) ., s Q ~

Q 8 ( ~ a> I ® ~

0 ~ l Q l3J I

~

f) ~SH ( b)

FORCES F= JxB

J t-+ F . B

WAVE

FORCES F=JxB

WAVE

FIGURE 3.3. Electromagnetic transducers with (a) meander coil to excite vertically polarized shear wave, and (b) periodic magnet to excite horizontally polarized shear wave[36].

25

ELECTRODE

OPTICAL FLAT

•

FIGURE 3.4. Schematic of an electrostatic transducer [27,35).

26

bias voltage applied across the gap (19]. The first method

limits the use of an ESAT as a source only whereas the sec-

ond method permits ESATs to be used as either a receiver or

a source of ultrasound on a surface.

The basis of an electrostatic transducer as an ultra-

sound source is the coulomb force excited on the polariza-

tion charges. For a polarization charge density o, the cou-

lomb force exerted is (19]

(3.5.l)

where Ea is the permittivity of the dielectric between the

two electrodes. The surface charge is [19]

where C = Ea/h is the capacitance per unit area across the m

gap hand Vt= Va+V(w). Va is the static de bias voltage and

V(w) is the signal voltage (19].

The system traction F2 which acts normal to the speci-

men is (28]

F (w) = (C 2 Va/Ea)V(w}. z m (3.5.3)

In the alternate excitation method, no de bias field is

used, but rather a high amplitude, time varying signal, e.g.

27

V0 sinwt, is applied [19]. As shown by Cantrell and Breazeale

[27], the surface tractions F, z acting on the specimen sur-

face in this case, are

F (w) = (SV 0 2 /(2h 2 ))(1-cos2wt), z (3.5.4)

which is twice the frequency of the applied voltage. In most

applications of the ESAT as a detector of ultrasound, a~vol-

tage proportional to capacitance charge is produced, pro-

vided that the de polarizing voltage is connected to the

ESAT with a large (~20 Megohm) resistor [19].

Chapter IV

OPTICAL DETECTION TECHNIQUES

4.1 INTERACTION OF SURFACE WAVES WITH OPTICAL WAVES

In the study of nondestructive testing and evaluation

using acoustic systems, one is frequently concerned with the

geometric distribution of acoustic fields on a free surface.

Surface acoustic waves which produce surface disturbances

can be directly measured using phase measurement techniques.

Hence, we require instruments which probe both the amplitude

and phase of the local field. Direct measurement instru-

ments include piezoelectric and electromagnetic transducers,

both of which require contact with the sample and are lim-

ited in frequency response. In addition, use of such a sur-

face probe tends to perturb the acoustic field distribution

and the extent of this perturbation is not easily assessed.

In contrast, optical probes certainly interact with the

surface but have a little effect on the acoustic field pro-

pagation. This "low coupling" implies a correspondingly low

optical power and hence loading effects are negligible. Use

of optical probes allows the easy probing at different

points on the surface. Other advantages include no compli-

cated mechanical or electrical connections (as in the case

of electromagnetic and electrostatic transducers) or p~epa-

28

29

ration of the surface other than polishing. Additionally,

optical techniques are applicable, unlike piezoelectric and

electromagnetic transducers,

which are at least partially

to virtually all materials

reflecting and over a wide

range of surface acoustic wave frequencies. Even with their

loose coupling, optical techniques have a very high sensi-

tivity. Typically, optical interferometers have been devel-

oped with capabilites of measuring vibrations of the order

of 3x10- 10 cm [2].

Different types of optical interactions have been used

to detect surface acoustic waves and bulk waves. Perhaps the

most common one is the detection of surface displacements by

the phase modulation of a laser beam by the acoustic wave.

Because photodetectors are insensitive to phase changes in

the optical beam, the output beam must be amplitude modu-

lated with a signal retaining the acoustic phase informa-

tion. This can be done by interferometric techniques which

involve some type of a phase bridge. A Michelson interferom-

eter, for example, is set up using a fixed or a moving mir-

ror to supply the reference beam and a partially reflecting

surface under test to supply the signal beam. Provided that

the laser beam diameter is smaller than the SAW wavelength,

the acoustic wave modulates the phase of the beam reflected

30

from the surface relative to the reference beam. This

modulation is detected and by using techniques described by

various authors can be converted to amplitude modulation for

detection by the photodetector [29].

Laser interferometry is capable of very high sensitiv-

ity in the detection of vibrational amplitudes. This techni-

que is ideal for detecting small piezoelectrically induced

vibrations. In the past many authors have employed two beam

interferometers such as Michelson, Fizeau, or Tyman-Green

types. The best of the Michelson interferometers has a sen-

sitivity of io-g cm. Laser interferometers of the Fizeau

type are capable of measuring vibrations of the order of

3x10- 10 cm. Unfortunately, these interferomters must be cal-

ibrated at vibrational amplitudes of the order of io- 5 cm or

larger [ 2] .

A significant improvement in the performance of a

Michelson interferometer was acheived by Sizogric and Gund-

j ian, who were able to measure vibrational amplitudes of

io- 10 cm by use of lock-in detection techniques [21]. Another

advantage of their method was the elimination of the need of

calibration at large amplitudes. However, any Michelson

interferometer design involves two serious disadvantages: it

31

is only a two beam interference device, and it is quite sus-

ceptible to environmental acoustic noises.

Another type of interferometer is the flat plate

Fabry-Perot interferometer which is a multiple beam device,

but its resulting high sensitivity requires that a high

degree of parallelism be maintained between the plates.

Hunsinger used the flat plate Fabry-Perot interferometr sys-

tern for real time analysis of signals generated due to sur-

face acoustic waves travelling on one of the two mirrors of

Fabry-Perot system [7]. A simplified version of the experi-

mental set up used by him is shown in Figure 4.1. One of

the two mirrors of the Fabry-Perot system has a surface wave

coupled to it using a transducer for its generation. The

propagation of SAW on one of the mirrors modulates the width

of the cavity between the two reflecting surfaces of the

Fabry-Perot system giving fringes whose spacings are depen-

dent on the cavity modulation. This modulation is detected

and analyzed. However, two major defects are present in a

system like this: ( 1 ) the system ~equires mirrors with . reflectivity of 95% to 98% which means that the intensity of

the output pattern is very low, and (2) as mentioned before,

the Fabry-Perot system requires a high degree of parallelism

between its two flat plate mirrors, which makes it a very

SURFACE WAVES

INCIDENT BEAM~ __ __._.....,..

INTERDIGITAL CONNECTORS 1--;.."~·

INFORMATION INPUT

FIGURE 4 .1.

32

ACOUSTICAL ABS ORR ER

FLUID COUPLING REGION

: SECOND ORDER L..--=-~-;?: FIRST ORDER

~~~==~::::~! ZERO ORDER ~""""""-~-::::::::::,,......1 FIRST ORDER

: SECOND ORDER

FQURIER PLANE

PIEZOELECTRIC SUBSTRATE

Detection of SAW using flat plate Fabry-Perot interferometer [7].

33

inconvenient device for practical applications. Bruins,

Garland and Greytak developed a spherical Fabry-Perot inter-

ferometric system which, when compared to the flat plate

Fabry-Perot system, has high sensitivity; its transmission

characteristics are changed much less by small angular dis-

placements of the mirrors and therefore it is less suscepti-

ble to acoustic noises. They have measured oscillatory dis-

placements of 4x10- 12 cm [2,6].

A Fabry-Perot interferometer is inherently more sen-

si tve to small changes in optical path than a Michelson

interferometer or other two beam interferometers. This is

due to the sharpness of the multiple beam interference

fringes as compared to those of two beam systems. With phase

sensitive detection of the interferometer output, fringe

sharpness implies a much larger relative change in the out-

put intensity for a given change in the optical path.

Surface acoustic waves have also been studied using

reflected light [20]. In this method acoustic surface waves

with straight parallel wavefronts are launched on a reflect-

ing surface which is illuminated by a laser beam incident

normally on this surface. The reflected wave is a plane wave

as is the incident light wave. Due to the acoustic surface

34

wave, the surface becomes corrugated and the reflected wave-

front parallel to the surface will exhibit a phase corruga-

tion. Amplitude corrugation of the optical wavefront as it

travels away from the surface occurs and this may be

detected and analyzed.

Bulk waves can be detected using the acoustooptical

interaction of light with bulk waves. This involves the dif-r

fraction of light from ultrasonic waves which can occur due

to several reasons. Bulk waves, like sound waves, are long-

itudinal waves. They travel by the displacement of material

along the direction of propagation (longitudinal). As an

analogous case, consider a long tube of water with a piston

transducer mounted at one end as shown in Figures 4.2. When

the transducer surface moves forward, the liquid in front of

the transducer is compressed, and the fluid pressure and

density rise above their unperturbed values, as shown in

Figure 4.2a. This compressed fluid travels forward, com-

pressing the fluid layers next to it, and a compressional

pulse travels down the tube as shown in Figure 4.2b. When

the transducer face moves back, the fluid in front of the

transducer expands, its pressure and density falling below "

the unperturbed values, and a pulse of rarefaction travels

down the tube as in Figure 4.2c. Now if we apply an ~C sig-

35

TRANSDUCER WAT JR PIPE

l~lllll I I I II I I l I I l I I I ITIU \I\ 1111111 / c0 1

I~ I 111111111111111111111111111111111 c b 1

I ~Ill I I 11111111111111111111111111111 cc 1

~ · I I 1~1111 I I 111~1111111111111111111 c d 1

-~ ~ ( e )

I COMPRESSIO N

RAREFACTION

FIGURE 4.2. Passage of ultrasonic compressional waves in water.

36

nal to the tranducer, alternating pulses of rarefaction and

compression will travel down the tube as shown in Figure

4.2d and Figure 4.2e. The refractive index of a transparent

medium is directly dependent on the density of the medium.

Thus, a bulk wave travelling through a semi-transparent med-

ium makes the medium appear like a phase grating to a beam

of light incident on it. By diffraction theory, when a beam

of light encounters a phase grating the output of the grat-

ing is a series of diffraction orders as shown in Figure

4.3. The spacing and intensity of the orders is directly

dependent on the frequency of the phase grating, which in

this case is in one-to-one correspondence with the bulk wave

frequency. Thus, interaction of the bulk wave and light wave

by this technique gives both magnitude and phase information

about the bulk wave.

4.2 MICHELSON INTERFEROMETER

Perhaps the most common and simple interferometer is

the Michelson interferometer. This device consists of a

coherent collimated beam of light which is split into a

reference beam and a signal beam at the surface of a par-

tially reflecting mirror or beam splitter as shown in Figure

4.4. These two beams are reflected from the surf aces of two

TANK

INPUT

BEAM

COM PR ESSlON

RAREFACTION

37

WATER

LENS

TRANSDUCER

FIGURE 4.3. Diffraction due to bulk waves in liquids.

SCREEN

+I

0

-1

38

INPUT BEAM

OUTPUT FRINGE i• PATTERN

REFERENCE

ARM

- -- -SAMPLE

ARM

FIGURE 4.4. Michelson interferometer. The system is very sensitive to changes in either of its arms.

39

mirrors, recollimated and superimposed to create an

interference pattern. The position of this pattern is highly

sensitive to any relative optical phase (path length)

changes between the two beams. These phase differences can

occur due to either relative movement between the mirrors or

a local change in the index of refraction of the material in

the path of one of the beams. These two potential causes of

phase modulation permit accurate measurement of both small

displacements by reflection and small changes in index of

refraction by transmission. The absolute magnitude of the

effective pathlength changes in both the cases are small

with respect to the wavelength of the light source.

Since the input beam undergoes amplitude division at

the beam splitter to produce the signal and reference beams,

these beams are of equal amplitude and the same frequency

under ideal conditions but they differ in phase depending on

the distances they travel independently. Assuming an arbi-

trary relative phase difference,

represented mathematically as:

these two beams can be

E E 0 sin(wt+k(x+6x)), and (4.2.1) s

E = E 0 sin(wt+kx), (4.2.2) r

where ox is the difference in optical path between the two

beams and k is the propagation constant.

40

If these two beams are collimated and superimposed, the

total field E at the output may be written as:

E = E +E . s r (4.2.3)

Using trignometric identities and subsequent simplification,

Equation 4.2.3 then becomes

where

E E sin[wt+kx+(kox)/2], m

Em= E 0 cos[(kox)/2].

(4.2.4)

Equation 4.2.4 clearly shows the dominance of the ox

term in the amplitude Em of the final output field E. If ox

<< \ the resultant output field E has an amplitude almost

equal to 2E 0 ; while if ox= A/2 it is zero. This gives rise

to a series of bright and dark lines due to constructive and

destructive interference.

Thus, for

kox/2 = (2n+l)TI/2, (4.2.5)

cos[(kox)/2] = 0,

where

k = 2TI/L

Equation 4.2.5 becomes

41

ox = (2n+l)A/2, (4.2.6)

where n 0,1,2,3, ... giving rise to destructive interfer-

ence.

Similarly,

cos[k6x/2] 1

when

kox/2 = nTI. (4.2.7)

Using the previous substitutions this becomes

ox = nA., (4.2.8)

where n = 0,1,2,3,

ence.

giving rise to constructive interfer-

Although the Michelson interferometer is highly sensi-

tive it has some very serious disadvantages. These include:

l. High susceptibility to low frequency vibrations

and DC movements of the signal or reference mir-

rors

2. Critical alignment of the entire interferometric

system

42

3. Inability to be tuned to any one particular

£regency for the detection of surface acoustic

waves

In addition, due to its construction and severe limitations

it has to be mounted on a relatively heavy and vibration

free optical table, making it extremely inconvenient for

pratical use in the nondestructive testing of large struc-

tures.

4.3 STABILIZED PATH INTERFEROMETER

Palmer and Green developed an interferometric technique

which uses a closed loop feedback system to stabilize a

Michelson interferometer with respect to low frequency vib-

rations and DC movements of the signal mirror [30]. Here,

the low frequency and DC signals are detected by the photo-

detector as shown in Figure 4.5 and fedback to a piezoelec-

tric crystal which has the reference mirror mounted on it.

The reference mirror moves in accordance with the signal

mirror for "noise" frequencies, resulting in the effective

neutralization of relative path changes due to DC or low

frequency movements of either of the two mirrors. Although

this system does eliminate the problem of low frequency

noise vibrations, it retains other disadvantages including

Specimen

Photodetector

43

Control Circuit

RF Amplifier AE Signal Output

FIGURE 4.5. Stabilized optical path interferometer. The stabilizing circuitry eliminates the low frequency noise vibrations (less than 1 .kHz) and also makes the system relatively insensitive to DC movements of the specimen [30].

44

critical alignment, inconvenience, and the potential for

nonlinear closed loop feedback instability.

4.4 DIFFERENTIAL INTERFEROMETER

The interferometric technique developed by Palmer,

Claus and Fick solved most of the problems encountered by

the Michelson interferometer. See Figure 4.6. The differen-

tial interferometer is insensitive to low frequency vibra-

tions and eliminates the need for critical alignment of the

specimen surface. It can also be tuned to detect surface

acoustic waves with frequencies ranging from 20 kHz to above

200 MHz. Other advantages of this technique include [23],

1. The output

optical path

signal is directly proportional to

changes so that both amplitude and

phase of an acoustic wave can be measured.

2. For the same reason, surface, dilatational, and

shear waves can be measured.

3. Absolute calibration is easily accomplished.

4. Waves can be measured on a point-to-point basis in

any plane of interest in or on a specimen.

MASK BEAM EXPANDER AND COLLIMAOTR --------...

I LASER]~' 480 Hz Ll L2 H L3

CHOPPER :J·~ REF. I

L4

M

VARIFOCAL LENS ~

R F SIGNAL OUTPUT

SPECIMEN

,,,,-: --

~ /

t MECHANICAL

DRIVE

FIGURE 4.6. Experimental setup for a two beam differential interferometer. The expanded laser beam illuminates the holographic divider H and mask M transmits the two desired beams for the interferometer. The output fringe pattern is spatially filtered by grid G [23].

+:> U1

46

5. In some cases where both dilatational and shear

waves are present,

isolated.

the two types can be easily

Using their notation, two collimated beams, incident on

a varif ocal lens system, are focused at points P and Q on

the surface of an unperturbed specimen as illustrated in

Figure 4.7 (10). The two beams make a small angle 8 with

respect to the z axis.

cally as,

These can be represented mathemati-

E 0 expi[w 0 t-k(xsin8+zcos8)+¢], and

E2 = E 0 expi[w 0 t-k(-xsin8+zcos8)+¢],

(4.4.1)

(4.4.2)

where ¢ is half the phase difference between the two beams,

w0 the optical radian frequency, k the propagation constant,

and E 0 the wave amplitude.

The two beams, reflected from the specimen surface, are

collimated by the lens and superimposed to give a total

field E, in the region of overlap, where

E = E1 +E 2 • (4.4.3)

Use of trignometric identities and additional simplification

yields,

47

z -8 +8

x VARI FOCAL LENS

F

J_ --........ ......--....... p -- ,,.- Q __ , __ _ ..--- ___ SPECIMEN

r--.A12--..: PLANE I

FIGURE 4.7. Basic two beam differential interferometer geometry with beams focussed at points P and Q which are half an acoustic wavelength apart. The reflected wavefronts emerge at an angle to the normal and superimpose to form an interference pattern [10].

48

E = 2E 0 [expi(w 0 t-kzcos8)]cos(kxsin8+¢). (4.4.4)

The total optical irradiance is given by the product of the

complex conjugates of the total ouput field:

H EE* I

H = 4E 0 2 cos 2 (kxsin8+¢). (4.4.5)

Since 8 is very small, sin s~s and

(4.4.6)

This equation represents the straight line interference pat-

tern. From this equation it can be deduced that H is a maxi-

mum when cos 2 (kx8+¢) is a maximum. The cosine term is maxi-

mum for

kx8+¢ = m1T, m O, l,2,3, • • • /

x = (m1T-¢)/k8. (4.4.7)

The values of x give the positions of intensity maxima, or

constructive interference.

Similarly, H is a minimum when the cosine term is a

minimum. This occurs when

kx8+¢ = (2n+l)1T/2, n O, l,2,3, • • • • /

49

x = (n(2n+l)/2 - ¢)/k8, (4.4.8)

giving the positions of intensity minima, or destructive

interference.

The fringe spacing ox (distance between two maxima or

two minima) is given by

ox = x -x m m-1

= (mn-¢)/k8 - ((m-l)n-¢)/k8

= 1T/k8 I (4.4.9)

or, since k = 2n/A.,

x = A./28. (4.4.10)

As seen from Figure 4.8, and derived later in this sec-

tion, maximum signal sensitivity is obtained when points P

and Q are separated by half the acoustic wavelength A/2.

For small angles 8,

tans ,,,9 (4.4.11)

Thus,

(A/2)F = 28, and (4.4.12)

F = A/48 = oxA/2A.. (4.4.13)

50

BEAM I BEAM 2

NARROWBAND DIFFERENTIAL INTERFEROMETRY

W(x,t) = 2A sin ( w0 t - Kx)

~x = (2n +I )A/2

n = {0,1,2,3, ... }

A = 27T/K

FIGURE 4.8. Positions of the beams on the specimen surface for a narrowband differential interfer9meter {24].

51

Equation 4.4.9 shows that F, the focal length of the

lens system, is proportional to the surface acoustic wavel-

ength. Thus, to have the system tunable to any desired fre-

quency we need a varifocal lens system. Letting d = 6x and

substituing the above derived values in Equation 4.4.5, we

obtain

H 4E 0 2 cos 2 [(nx/d)+¢]. (4.4.14)

Referring to Figure 4.4.4, assume a surf ace wave of

frequency f velocity v, wavelength A and amplitude E 0

traveling on a specimen surface. Two optical beams 61 and 62

separated by a distance d, probe at points P and Q on the

specimen surface. Let the surface displacements at P and Q

be denoted as,

61 = E 0 cos(2nft), and

62 = E 0 cos(2nft-2nd/A).

The total phase difference is given by 6

6 = E 0 [cos(2nft) - cos(2nft - 2nd/A)].

Differentiating the above equation results in,

d6/dt = E 0 [-sin(2nft) +

sin(2nft - 2nd/A)]2nf.

(4.4.15)

(4.4.16)

52

Equating this to zero and solving for t we get,

t = (l/2nf)arctan[(sin2nd/A)/(cos(2nft)-l)]. (4.4.17)

The above derived value for t can either be a maximum

or a minimum. To resolve this situation we differentiate

Equation 4.4.16 again

d 2 o/dt 2 = E 0 [-cos(2nft) + cos(2nft - 2nd/A)]4n 2 f 2 .

(4.4.18)

To find the maximum value of function o, Equation

4.4.14 should be less than zero. Thus,

cos(2nft) < cos(2nft - 2nd/A}, (4.4.19)

cos(2nft) < cos(2nft)cos(2nd/A) + sin(2nft)sin(2nd/A),

(4.4.20)

cos(2nft)[l - cos(2nd/A)] < sin(2nft)sin(2nd/A}, and

(4.4.21)

tan(2nft) > [l - cos(2nd/A)]/sin(2nd/A). (4.4.22)

Equation 4.4.22 is the condition on t for which o can

be a maximum. This is satisfied by Equation 4.4.17. Thus,

Equation 4.4.17 gives the value fort= t . Using this value m

oft in Equation 4.4.15 we get, m

53

6 = E 0 [cos(2nft ) - cos(2nft - 2nd/A)]. m m m (4.4.23)

Assuming, for simplicity, a value of t such that

cos(2nft) = 1, a graph of 6 as a function of d/A is plotted

as shown in Figure 4.9 [24]. From the graph it is apparent

that the maximum for 6 is obtained when d/A = 0.5 or an odd

multiple of this, i.e. ford/A= (2n+l)/2, for n=0,1,2, ..

Figure 4.10 shows the graph with 6 plotted as a func-

tion of frequncy with d/A chosen for a maximum sensitivity

for a surface acoustic wave of 1 MHz on glass. It can be

seen from plots a, b, and c that the bandwith dro~s off as

d/A increases from 1/2 to 5/2. Ideally, infinitely small

bandwith is possible and is limited only by the equipment

used [24].

-CD 'O ->-~

> ~ Cf)

z w Cf)

er w

0

- 5

~ -10 ~ 0 er w u.. a::: w -15 ~ z

54

BANDWIDTH at -3 dB

POINTS

di.A = O· 5 ()..

-3 dB -3 dB

-20!.._~~___....~~~-+--~~~~~~~-­

FIGURE 4.9.

n n+Q·25 n+0·50 nf().75 n-+1·00

d/A.Q.

Interferometer sensitivity as a function of beam spacings d and acoustic wavelength, plotted using Equation 4.4.23 [24J.

dB

55

0 BW = f

d = A/2

-10

-20 f

0 BW = f/3

d = 3A/2

-10

-20 f

0 BW = f/5

d = 5A/2

-10

FIGURE 4.10. Sensitivity of a differentiai interferoweter is directly related to the spot separation d between the two beams on the specimen surface [24].

Chapter V

FIBER DIFFERENTIAL INTERFEROMETER

5.1 DIFFERENTIAL FIBER SYSTEM

Although highly sensitive, the differential interferom-

eter and other optical detection systems are not useful for

the practical nondestructive evaluation of large specimen

surfaces because the alignment and relative positioning of

the optical components is critical and requires the use of a

massive and vibration-free support table. To eliminate this

disadvantage a similar system has been developed which

effectively separates the fixed input optics from a portable

remote detection head using single mode fiber waveguide. In

this system a 2.0 mW helium-neon laser and beam shaping

optics are rigidly mounted in one enclosure as shown in Fig-

ure 5.1. The coherent light beam is amplitude divided into

two beams which are focused using lOX microscope objectives

onto the ends of two ITT-110 single mode fibers having nomi-

nal 4.5 micron diameter cores. To simplify the procedure of

focusing the beams on such small areas, the cut and modes-

tripped ends of the fibers were mounted in six-axis posi-

tioners. The two fibers, each two meters long, transmitted

the light to the remote detection head through a flexible

cable assembly.

56

LASER BE.AM +V REMOTE DETECTION

HEAD

I '•<c aV P

10 x FOCUSING EYEPIECE

~

FIBER 1 HOLDER

FlBER

AMPLIFIER

SIX AXIS POSITIONERS

SPECIMEN/ SURFACE

DIGITAL STORAGE

OSCILLOSCOPE

FIGURE 5.1. Fiber Differential interferometer. The input laser beam is split into two beams of equal amplitude and focussed onto two ends of optical fibers poitioned using six axes positioners. These fibers transmit the beams to a remote detection head.

I _/

Ul '--1

58

Inside the remote detection head, the fibers are

mounted parallel with their adjacent ends spaced 1.0 mm

apart as shown in Figure 5.2. The beams emitted from the

ends of the two optical fibers are then focused, using a

varifocal lens system constructed of four lenses, to points

P and Q on the specimen surface. Here, the lenses Ll and L4

are fixed lenses with the position of lens L4 adjusted so

the specimen surface is always in its back focal plane.

Lenses L2 and L3 are movable lenses which can be translated

by microprocessor-controlled stepping motors to change the

focal length of the entire varifocal length assembly, thus

changing the separation between spots P and Q. Spot separa-

ti on, as explained in Chapter 4, tunes the interferometer

to be highly sensitive to one particular SAW frequency. A

computer program for calculating the positions of lenses L2

and L3 which are required for various spot separations and

corresponding surface wave frequencies is given in Appendix

B.

The focused beams are reflected from the specimen sur-

face and superimpose to give an optical interference pattern

as shown. This interference pattern is spatially filtered

using a Ronchi ruling with a grid spacing equal to the spa-

tial periodicity of the pattern. The output of this filter

CABLE

FIGURE 5.2.

SPATIAL FILTER

BEAMSPLI TTER

~=r=====_J~p

L4

DETECTOR

SPECIMEN SURFACE

Remote detection head. Lenses L1 L2 , L3, and L4 form a varifocal lens system for focussing the two beams onto the specimen. Lenses L and L3 are movable lenses for tuning the interferometer. Lenses L. ana L4 are fixed lenses with specimen lying in the back focal plane of lens L4 . The reflected interference pattern is spatially filtered by the spatial filter and detected by the photodetector.

\JI \()

60

is then focused onto the optical detector which demodulates

the intensity variations and generates an electronic signal

proportional to instantaneous surface displacement. This

signal is electronically filtered and acquired by a digital

storing oscilloscope where it can be processed.

5.2 MAXIMUM PERMISSIBLE DC MOVEMENT OF THE SURFACE

The beam emmitted from a laser has a Gaussian profile

wavefront [33]. At large distances z from the waist as shown

in the Figure 5.3, this wavefront is essentially, a spheri-

cal wave radiated fromn a quasi-point source located at the

waist position. The far field angle 8 of the beam may be

defined as [ 33],

8 = w(z)/z ::: \/(nw 0 ), Z >> Zo (5.2.1)

where w0 is the half power radius of the waist of the beam

at position z 0 , w(z) is the waist at some position z,

is the wavelength of the light beam.

and \

Gaussian beams can be focused to extremely small spots

making them useful for point, probing, local heating, for

drilling holes and generally in carrying out operations in

area only a wavelength or two in diameter [33]. The waist

radius w0 of the focused spot shown in Figure 5.4 ~an be

shown to be,

Xo1'jo

..; Wo

WAIST (z =0)

61

x,y

-\ e 1~

z

FIGURE 5.3. Gaussian wavefront in the far field propagating from a waist located at z=O. The angle at which a gaussian beam diverges or converges from the waist is inversly proportional to the spot size w at the waist [33).

0

62

w'

d

1 _, ___ _

FIGURE 5.4. Gaussian beam of diameter d focussed to a spot of diameter d [33].

0

63

w0 = 2F\, (5.2.2)

where F is the f number of the lens system given by,

F = f/d, (5.2.3)

where f is the focal length of the lens system and d is the

aperture diameter or the waist of the input beam (which ever

is smaller).

Thus for a collimated beam of spot size w, again shown

in Figure 5.4, incident on the lens, the two spot sizes, w0

(waist radius of focused spot) and w can be related by (33],

wo = fA/(Tiw). (5.2.4)

Using the criterion that the focusing lens must have a diam-

eter d=3w to pass the incident light, and since 86% of

energy will be focused into the area of diameter 2w 0 , the

focused spot can be defined to have a full diameter of only

d 0 = 2w 0 (33). This focused spot diameter then gives,

d 0 "' 2£\/d, (5.2.5)

where F = f/d "' f/3w, thus,

d"' 2FL (5.2.6)

A collimated beam of waist radius w0 diverges bet'ore

and after collimation. The waist size of the diverged beam

can be written as [33],

w(z) = Wo

64

~ [l+(Az/(1TW02))2] 2, (5.2.7)

where w(z) is the waist at some point z as shown in Figure

5. 5.

Assuming w0 = A/10, where A is the SAW wavelength, we

can calculate the maximum distance the mirror can move for

change in spot radius by 10%. Thus, using Equation 5.2.7,

for a change in spot radius by 10%, i.e. w(z) = 1.1 x w0 ,

l.lw 0

0.21

~ w D [ 1 + ( ( AZ ) I ( 'ITW D 2 ) ) 2 l 2 I

Z = 0 . 461TW o 2 /A.

Using Equation 5.2.4 Equation 5.2.10 becomes,

(5.2.8)

(5.2.9)

(5.2.10)

(5.2.11)

where w1 is the diameter of the input beam. This z is the

movement of surface in one direction only. Thus the surface

can move 2z before it spot radius increases more than 10% of

its minimum value w0 •

Using actual values for f which is 50 mm, A. is 6328 x

10- 10 m and w is 20 mm in Equation 5.2.11, we get the maxi-

mum permissible distance to be,

z - 11.6 x 10-4 mm.

65

l --·- .-.---·--·1-·-

I 2z = 2 7T'W! If

RAYLEIGH RANGE

FIGURE S.S. Collimated gaussian laser beam. This is actually a long slender beam waist of length 2ZR, where ZR is defined as the distance from the waist to the point where the beam area has doubled (33].

66

5.3 MEASUREMENTS

The fiber differential interferometric system was

applied to the detection of pulsed broadband ultrasonic sur-

face waves similar to those generated by acoustic emission

events in stressed solids. To simulate these events, 0.5mm

diameter graphite pencil lead was broken against the surface

of a front surfaced mirror. Several authors have investi-

gated the acoustic signals produced by such a source and

have shown that the resulting particle displacements approx-

imate those which in principle would be generated by a step

function load applied to the surface (31,32]. In these

experiments, the normal component of the particle displace-

ment was detected at several positions near the location of

the acoustic source. Typical output from the digital oscil-

loscope is shown in Figure 5.5 and compared to theoretical

predictions.

5.4 RESULTS

The fiber differential interferometer allows the prac-

tical detection of surface displacements on large material

structures using sensitive optical techniques. All of the

optical components which require either stable alignment or

critical adjustments are housed in a rigid enclosure. This

10

rnV/div.

"' u '1 1 J.-'- 6.2 '.). 3

,.., ••J

x 10 sec.

17- .11 1.5. 5 18.6

FIGURE 5.6. Data got by generating SAW on specimen surface by breaking 0.5 mm. pencil leads against the surface.

"' '-J

68

enclosure is connected to a small detection head using

cabled optical fiber waveguide. The head then may be scanned

conveniently over the surface of the specimen without moving

the entire optical system. Potential applications in a var-

iety of nondestructive evaluation environments are sug-

gested.

Chapter VI

BULK WAVE DETECTION USING DIFFERENTIAL INTERFEROMETRIC TECHNIQUES

6.1 TECHNIQUE FOR THE DETECTION OF BULK WAVES

The detection of bulk waves in transparent solid and

liquid media usually involves the acoustooptic interaction

between the waves and a beam of light. One such technique

has been briefly descibed in Chapter 4. Our goal in this

research was to develop an optical system for the detection

of compressional waves in transparent, specifically liquid,

media, which

1. Was insensitive to low frequency vibrations,

2. Could be used to determine the direction of propa-

gation of standing or traveling compressional

waves,

3. Had sensitivity which was tunable over a range of

ultrasonic frequencies, and which

4. Was sensitive to a pulsed acoustic wideband bulk

wave traveling through liquids.

These requirements suggested modification to the type

of differential interferometric system developed by Palmer,

69

70

Claus and Fick [23]. Since their two beam system could not

accurately determine the direction vector of the bulk wave,

modifications were needed to develop a four beam differen-

tial interferometer.

6.2 TWO BEAM DIFFERENTIAL SYSTEM FOR BULK WAVE DETECTION

Referring to Figure 6.1, a 2.0 mW helium-neon laser

beam is expanded and collimated to give a beam 1.0 cm in

diameter. This beam is incident on a Ronchi ruling with a

grid period of 200 lines/inch. The resulting output diffrac-

tion spectrum is then focused using lens Ll with a 200 mm

focal length onto an aluminium mask. The mask allows only

the +l and -1 spectral orders to be transmitted. Lenses L2,

L3, and L4 form a varifocal lens system which collimates the

two beams and individually focuses the beams inside the tank

so the diameter of each focused beam is less than one tenth

the wavelength of the ultrasonic bulk wave. The tank itself

is constructed using 4 cm x 4 cm glass slides with a 1.5 cm

diameter X-cut quartz crystal transducer mounted at the bot-

tom of the tank as shown in Figure 6.2. The beams emerging

from the tank are superimposed using a long focal length a

lens and the resulting interference pattern is spatially

filtered by a Ronchi ruling with a grid spacing 0~ 133

LASER

BE AM COLLIMATOR

L2

~ RONCHI GRID G1

TRANSDUCER

TANK WATER

MIRROR

10 x EYEPIECE

L5------

RO NC HI GRID I I ·zg G2 . I

L6

PHOTO DETECTOR -------. DIGITAL

STORAGL OSCILLOSCOPE

~~·-\ I

FIGURE 6.1. Two beam differential interferometric system for detection of compressional waves in water. Ronchi grid G1 illuminated by an expanded laser beam is imaged onto a mask wnich permits only the +l and -1 orders of diffrction pattern to pass through to form the interferometer. Lenses L3 and L4 form the varifocal lens system. Lens L5 collimates and superimposes the two beams to give an interference pattern which is spatially filtered by G2 .

---1 I-'

GLASS SLIDES

~ , ,

I

I I

I

I I I ' I I

72

~-- -- - - - - - -I I ,. . ' '

I !-·· • - ·-- - - - - - -

I I

I

I ,.

LEADS

I

----_.,..__._1

TRANSDUCER

FIGURE 6.2. Water Tank used for detection of compressional waves in water.

73

lines/inch. The spatially filtered pattern is focused onto a

photodetector receiver which demodulates the optical signal

and generates an rf electronic signal. This . 1 . s1gna~ is fil-

tered and stored using a digital storing oscilloscope.

The experiment was performed in two parts. The two

beams in the tank were separated by 0.275 cm which is 8.65 x

A/2 where, A is the wavelength of the bulk wave which in

this case had a frequency of 2.25 MHz. First, a sinusoidal

signal with a 300 volt peak-to-peak amplitude was applied to

the transducer to produce a sinusoidal bulk wave of fre-

quency 2.25 MHz. The output as seen by the detector was a

sinusoidal wave with an amplitude dependent on the relative

position of the beams in the tank. Due to the size of the

tank, a standing wave was set up and, as the beams were ver-

tically scanned, the amplitude of the signal varied as shown

in Figure 6.3. This variation agrees with the theory that

describes the dependence of the sensitivity of the system on

the relative focus positions of the two beams on the sta-

tionary waves. This is shown in Figure 6.~.

The second part of the experiment consisted of the

detection of a pulsed ultrasonic bulk wave traveling in the

water. The pulsed broadband bulk wave was generated by

->O mV/<li'l.

<J ;:J p, J,J ;:l 0

)1 0 jJ (.) Q) .:J CJ ~

0 J L I I I I I

2.5 5.0 7.5 10.0 12.5 15.0 17.5 -3 x 10 m.

Vertical Displacement of the tank.

FIGURE 6.3. Data got by scanning the two beams of the two beam differential interferometer across the standing wave generated by a 2.25 MHz sinusoidal wave. The beams scanned the water tank vertically, for a distance of 20 mm.

'-l ~

75

L, WATER TANK /

l .-----·---

p

p

A;---.1 ~f;-1-?Zi?A-m -+-rl--111'

TRAN SO UCER

Q

(a)

LASER BEAMS

z

~A-I

p Q

z

FIGURE 6.4. Positions of the laser beams on the compressional waves travelling in water (a) maximum sensitivity of the system occurs when P and Q are half the acoustic wavelength apart, and (b) the system is least sensitive when the beams are separated by a multiple of the acousttc wavelength.

76

applying a 300 volt 10 nanosecond pulse to the transducer

using a Metrotek MP215 pulser u~it. Typical recorded results

from this experiment are shown in Figure 5.5; other results

are included in the Appendix C. Theoretical calculations for

a bulk wave traveling with a velocity of 1430 meters

second predict that such a pulse would take 1.8 microseconds

to travel the distance of 0.275 cm between the two beams.

Refering to Figure 6.5, points A and B are 1.8 microseconds

apart and are also 180 degrees out of phase, which is also

predicted by theory. The pulse continues to reflect in the

tank and crosses the two beams several times before it is

significantly attenuated. The timings for the pulse cross-

ing the beams, which appear in the output as points C, D, E,

and F, were noted as shown in Figure 6.6 and were within

3.6% of the calculated theoretical values. The calculated

and the observed values are listed in Table 6.1. From this

table one notices discrepancy in the results towards the

later part of the table. This is probably due to the trans-

ducer not being perfectly horizontal and the pulsed bulk

wave not traveling perpendicular to the beams as was assumed

for the theoretical calculation. To rectify this problem,

the four beam system descibed below was developed.

c B

so ~nv I div.

0 31.0 62.0 93.0 -6 x 10 sec.

124.0 155.0 186.0

FIGURE 6.5. Data for detection of a traveling ultrasonic pulse packet in the tank using the two beam differential interferometer.

.~

'-.] '-.]

LASER BEAMS

PATH

78

..__ ___ .... '9F.\--· -__ ._,,,_,, -

~ t ~ ' ' I • ' . : ' I I

t~ i I '

I • I t ' ' . •.

TRANSDUCER

(a)

n . \ • • I

OF

TANK

WATER

PATH OF THE PULSE

TANK

~ LASER BEAMS

THE PULSE TRANSDUCER

( b)

FIGURE 6.6. Path of ultrasonic pulse in water tank. (a) Water level is parallel to the transducer. (b) Water level is at any arbritrary angle to the

transducer.

79

PATH OF ULTRASONIC r PULSE

__ ----:-~- ___ I WATE~ I , ! l 23· 75 mm

36-75 mm 2 ·75 mm

l _i r 2Z5 mm

t 2·5mm TRANSDUCER

POSITION

A B c D E F H G

LASER BEAMS

TABLE G .1.

DISTANCE TRAVELED BY PULSE

mm

7.75 10.50 58.00 60.75 76.25 79.00

126.50 127.25

TIME TAKEN TIME TAKEN CALCULATED EXPERIMENTAL

VALUE VALUE -6 x 10 sec -6 x 10 sec

5.419 5.4 7.343 7.2

40.559 38.7 42.482 40.8 53.320 55.240 88.460 84.9 90.380 88.2

Data for the detection of ultrasonic pulse in water using two beam sytem.

80

6. 3 FOUR BEAM DIFFEP.ENTIAL SYSTEM FOR DETECTION OF BULK ---WAVES

The four beam differential system is a modification of

the basic two beam system. Effectively, it is a dual two

beam differential interferometer of the type discussed by

Turner and Claus [15]. Their system, however, is too bulky

and rather difficult to set up. Due to fewer critically

aligned optical components, the four beam system described

here is relatively insensitive to small misalignments.

Referring to Figure 6.7, a 2.0 mW helium-neon laser

beam is expanded and collimated to give a beam 1.0 cm in

diameter. This beam is incident on a pair of Ronchi rul-

ings, with grid periods of 200 lines/inch, placed such that

the ruling lines are at 90° to each other and the ruled

sides are facing each other, preferably against each other

as shown in Figure 6.8a. The resulting output diffraction

spectrum, similar to the diffraction pattern from a square

hole as shown in Figure 6.8b, is then focused using lens Ll

with a 200 mm focal length onto an aluminium mask. The mask

allows only the the +l and -1 spectral orders, i.e. beams

8 3 and 64 , to be transmitted such that they lie at

the four corners of a square just above the transducers in

the water tank. Lenses L2, L3, and L4 form a varifoc~: lens

CROSSED

LASER ~ •

BEAM EXPANDER ! AND CO LUMA "TOR

-- HORIZONT Al PAIR OF BEAMS

---- - - VERTICAL PAIR OF BEAMS

DIGITAL STORAGE

OSCILLOSCOPE

L2

TRANSDUCER

TANK

.:.~·.· ..

WATER MASK

-·-/=11.-~2 ... LI •r- ..,.,..,. __

MIRROR

I Ox EYEPIECE

RONCHI GRID 62 --

L6 PHO TODETECTOR

----------. l AMPLIFIER ·~

['JGlJRI!: 6, 7. ~·our beaio differential J.nterferometer for detection of ultrasonic com1>ress1onal waves in water. 'fhe crossed paJ r of Ranchi grids illuminated by an expanded laser beam is imaged onto a mask M1 which p~rmits the +i and -1 orders to pass through, Mask M selects Che desired pair of beams to be transmltteJ to detection optics. ~he interference pattern is spatially filtered hy Rond1i grid G7 and detected by Lhc photodetector.

co I-·-'

PLANE WAVE

82

RONCHI RULING

• • • •

(a) Diffraction pattern due to a single Ranchi ruling.

PLANE WAVE CROSSED RONCHI RULING

LENS

• • • • • • • • • •

(o). Diffraction pattern due. to a pair of crossed Ranchi rulings-.

FIGURE 6,8.

83 . system which collimates the four beams and individually

focuses the beams inside the tank so the diameter of each

focused beam is less than one tenth the wavelength of the

ultrasonic bulk wave. The tank itself is constructed using 4

cm x 4 cm glass slides with a 1.5 cm diameter X-cut quartz

crystal transducer mounted at the bottom of the tank as

shown in Figure 6.2. The beams emerging from the tank are

are then filtered using a mask M2 such that only two diago-

nally opposite beams are transmitted to detection optics.

The detection of the pulsed compressional waves in

water was performed in two parts. First, the mask M2 tran-

smitted only the vertical pairs of beams to the detection

system. For the next part the mask was rotated to transmit

the horizonatal pairs of beams. The transmitted beams in

both cases are then superimpos-ed using a long focal length

lens and the resulting interference pattern is spatially

filtered by a Ronchi ruling with grid spacing of 200

lines/inch. The spatially filtered pattern is focused onto a

photodetector receiver which demodulates the optical signal

and generates an rf electronic signal. This signal is fil-

tered and stored using a digital storage oscilloscope. The

two sets cf signals, one produced by the horizontal pair of

pair of beams and one by the vertical pair, is then analyzed

84

to give the required data on the direction and magnitude of

the pulsed wave.

The inconvenience of rotating the output optics for

detection of the second pair of beams can be avoided by sim-

ultaneous detection of both the horizontal and vertical

pairs of beams as shown in Figure 6.9. The beam pairs can

be isolated by using pair of thin mirrors to reflect the

horizontal pairs of beams and transmit the vertical pairs of

beams. However, this cannot be done by etching a transparent

line in the mirror because the glass from the etched part

still reflects. Though weak, this reflection tends to inter-

fere with the inteference caused by the horizontal beams,

hence an arrangement consisting of two mirrors, with a small

gap between them for transmission of the vertical pairs of

beams, has to be used for reflection of the horizonatal

pair.

To detect a pulsed ultrasonic bulk wave traveling in

water, a pulsed broadband bulk wave was generated by apply-

ing a 300 volt 10 nanosecond pulse tb the transducer using a

Metrotek MP215 pulser unit. Typical recorded results from

this experiment are shown in Figure 6.10; other results are

included in the Appendix D. Theoretical calculati0n~ for a

CROSSED RONCHI GR ID MASK TANK G1 \.,. ~

WATER SPLIT

\--~J~ .. ·-=-=--_-~4-+=. -.;;=~-~~~,:.,/~ LASEll__j-~. - . -- I

----------BEAM EXPANDER I • L 2 L3 L4 f=" 0 t MIRROR!:

; . A ND COLLIMATOR

__ llORIZONT AL PAIR OF BEAMS

VERTICAL PAIR OF BEAMS

DUAL CHANNEL DIGIT AL STORAGE

OSCILLOSCOPE

TRANSDUCER L~......---

. . . I

~~ ·., ..

~ E yEPIECES * . : \ i I RONcH1 GRm · mnmlrmmumnnrm G2'

62 l l : I

Le--_ ---

I A.MPLIFIE8=1------

~ ~MPLIFIER l----

!.!~ 6'--,~

9 FIGURE 6.9. Hodified four beam differential interferometric syotem for detection

of the direction of the compreosional waves in water by simultaneous evaluation of data from the horizontal nn<l vertical pairs of beams.

0:) U1

-·A llB

30

mV/div.

0 7.75 15.50

C1 D

23. 25 x 10-6 sec.

31.00

F

E

38.75 46.50

FIGURE 6.10. Detection of an ultrasonic pulse packet traveling in a water tank using the four beam differential system. (A) This is data got by analyzing the interference pattern caused by

the vertical pair of beams.

00

°'

87

bulk wave traveling with a velocity of 1430 meters per sec-

ond predict that such a pulse would take 4.2 x 10- 5 seconds

to travel the distance of 0.6 cm between the two beams.

Referring to Figure 6.10, points A and Bare 3.9 x 10- 5 sec-

onds apart and are also 180 degrees out of phase, which is

also predicted by theory. The pulse continues to reflect in

the tank and crosses the two beams several times before it

is significantly attenuated. This explains the generation

of other pulses. The calculated and the observed values are

listed in Table 6.2. As can be seen from table 6.2 the

experimental and theoretically calculated results differ are

within 3.5% of the calculated values. This difference can be

attributed to various reasons. However, the major reason

could be the level of water not being perfectly parallel to

the transducer as discussed before.

Measurements to detect the direction of propagation of

the pulse packet were made. A pair of diagonally opposite

beams were allowed to interfere. The data obtained from this

is shown in Figure D.4. Next the remaining diagonally oppo-

site pairs of beams were used. The data obained from this

is shown in Figure D.S. Both of these results were stored

on a floppy disk in the digital storage oscilloscope. For

reasons discussed in Appendix D accurate direction of the

88

propagation of a pulse packet could not be determined. The

simultaneous detection technique discussed above will give

accurate results.

6.4 RESULTS

The two beam and four beam differential interferometric

systems for the detection of direction of the propagation of

the ultrasonic pulse packet in water were developed and

used.

rnent.

7.

These are basic systems and require further develope-

Some suggested improvements are discussed in Chapter

POSITION

A A' B c ()'

D E E'

0.53crn

~, 1~ WATER

f t ----···----:-····-;;-,---. I PATii OF ULTRASONIC PULSE I I· ···---;-) • 65cm I +: ..

3 05 _u_ --------1~!.~-~l~·-'·~-------. cm I 1 O. 5cm _____ ..,..11 . .. ~l--~o' • .L ___ tf..... .... ~ o oc;cni -rL .... --~~-e\ ..... /o··· :·"-------··· .ta5 ci! . ...

... , _j__

t THANSDUCER d 1,<l2 ,d 3 , and d4 are

focussed laser beams.

VEHTICAL PAlR OF BEAMS llOIHZONTAL PAIR OF BEAMS DISTANCE TRAVELED TIME TAKEN TIME TAKEN TIME TAKEN TIME TAKEN

UY TllE PULSE CALCULATED EXPERIMENTAL CALCULATED EXPERIMENTAL VALUE VALUE VALUE VALUE

-6 -6 -6 -6 cm x 10 sec. x 10 sec. x 10 sec. x 10 sec.

0 0 0 0 0 0.05 - - 0.35 0.3 0.55 3.85 3.825 3.85 26.93 26.935 4.35 - - 30.42 4.40 30. 77 29.950 30. 77 6.10 42.26 41.50 6.15 - - 43.01 Lil. 75

TABLE 6.2

Data for detection of pulsed ultaso11ic wave in water using four beam differential interfernmetric system.

00 \()

Chapter VII

CONCLUSIONS AND FURTHER REFINEMENTS

The fiber differential system developed was sensitive

to pulses generated by step impulse functions. However, the

system barely detected the continuous SAW generated on the

mirror surface by a wedge transducer.j.This lack in sensitiv-"\

ity can be attributed to various practical difficulties

involved in the system.\ Considering the system itself, due

to the use of single mode fiber the intensity of the output

pattern is low. This is further reduced considerably by use

of two beamsplitters; more than 50% of the intensity of the

output pattern is lost at each beamsplitter. This low inten-

sity coupled with a shot noise limited wideband detector

made it difficult to see SAW signals of very low magnitude.

Laser power could not be increased as laser noise increases

with power of the laser. Recommended improvements in the

system would be (1) an electronic detector which has a

higher signal-to-noise ratio and which can be tuned to

reject the laser noise, (2) custom made biconvex or plane-

co~vex lenses be used because aspheric lenses have tc be

used within the paraxial region 6nly or the output pattern

is distorted, ( ( 3) input laser power be increased,) ( 4) fiber

system be improved to avoid the use of two beamspl~tters,

90

and if possible,

be used.

( 5 )

9l

single mode fibers of larger diameter

The two beam system for detection of bulk waves was

more sensitive to pulsed and countinous compressional waves

in water than the four beam system. This again was due to a

great reduction of intensity of the output pattern when

crossed gratings were used; the crossed gratings reduce the

intensity of the individual beams by more than 50%. The

major intensity of the laser beam is now divided between

nine spots as compared to three spots due to diffraction by

a single grating as shown in Figure 7.1. The experiment as

performed by us also had the system spread over a large

area, larger than necessary for this system. This was a

practical difficulty because we were limited by the focal

lengths and sizes of lenses available to us when this exper-

iment was performed. Reducing the size of the system will

not only increase intensity of the light at the output of

the system due to less spreading of light but will also

reduce the number of lenses involved, thereby reducing the

sensitivity of the system to low frequency vibrations.

Another major improvement in the four beam system would be

the simul~aneous detection of both the horizcntal and verti-

cal pairs of beams, as explained in Chapter 6, using a pre-

92

(a) Diffraction pattern due to a pair of crossed Ronchi rulings.

(b) Diffraction pattern due to a square aperture.

FIGURE 7.1.

93

calibrated detection system. A computer aided data recording

system could easily be developed to per~it simultaneous

acquisition and analysis of such four beam data to give

immediate results which, in cases such as the alignment of

the system and the detection of propagation direction of the

wave are useful.

REFERENCES

[l] R. M. White, "Surface elastic waves," Proc. IEEE, Vol. 58, pp. 1238-1276, No. 8, August 1970.

[2] D. E. Bruins and C. W. Garland, "New interferometric methods for piezoelectric measurements," Rev. Sci. Instrum., Vol. 46, pp. 1167-1170, No. 9 September 1975.

[3] R. M. De La Rue, R. F. Humphreys, I. M. Mason and E. A. Ash, "Acoustic surface-wave amplitude and phase measurements using laser probe, " Proc. IEE, Vol. 119, pp. 117-126, February 1972.

[4] T. E. Owen, "Surface wave phenomenon in ultrasonics," Prog. Appl. Mat. Res. (GB), 6, 69 (1964).

[5] A. Alippi, A. Palma, L. Palmieri and G. Socino, "Incidence angle and polarization dependence of light diffracted acoustic surface waves," Journal of Applied Physics, Vol. 45, pp. 1492-1497, No. 4, April 1974.

[6] M. Hercher, "The spherical mirror Fabry-Perot interferometer," Applied Optics, Vol. 7, pp. 951-966, No. 5, May 1968.

[7] B. J. Hunsinger, "Analysis of interferometers with acoustic surface waves on one mirror," Applied Optics, Vol. 10, pp. 390-395, No. 2, February 1971.

[8] R. 0. Claus and J. H. Cantrell, "Detection of ultrasonic waves in solids by an optical fiber interferometer," 1980 IEEE Ultrasonics Symposium (Boston, MA), Nov. 1980.

[9] R. L. Whitman and A. Karpel, "Probing of acoustic surface pertubations by coherent light," Applied Optics, Vol. 8, pp. 1567-1576, No. 8, August 1969

[10] C. H. Palmer, "Ultrasonic surface wave detection by optical interferometry," J. Acoustical Soc. of America, Vol. 53, pp. 948, March 1973.

[ 11] "An introduction to piezoelectric transducers," supplement by Valpey-Fisher Corporation, July 1972.

94

95

(12] M. Imai, T. Ohashi and Y. Ohtsuka, "Fiber-optic Michelson interferometer using optical power divider," Optical Society of America, preprint submitted Ju~e 1980.

[ 13] J. C. Wade, P .· S. Zerwekh, and R. 0. Claus, "Detection of acoustic emission in composites by optical fiber interferometry," Proc. 1981 IEEE Ultrasonics Symposium (Chicago, IL), October 1981.

[14] R. 0. Claus and J. H. Cantr-ell, "Rayleigh wave detection by Wideband differential interferometry," Acoustical Society of America Annual Meeting (Los Angeles, CA), Nov. 1980; J. Acoust. Soc. Am., 68, 5108 (1980).

[15] T. M. Turner and R. 0. Claus, "Dual differential interferometer for measurements of broadband surface acoustic waves," Proc. 198l IEEE Ultrasonics Symposium (Chicago, IL), October 1981.

(16] R. 0. Claus and J. H. Cantrell, "DC calibration of the strain sensitivity of a single mode optical fiber interferometer," Proc. 1981 IEEE Region 3 Conf. (Huntsville, AL), April 1981.

[17] T. M. Turner, R. 0. Claus and S. L. Ocheltree, "Pulse-echo interface wave characterization of bolted plates," Proc. 1981 IEEE Region 3 Conf. (Huntsville, AL), April 1981.

(18] R. 0. Claus and R. T. Rogers, !!Waves guided by a thin viscoelastic layer between elastic solids," Proc. 1981 IEEE Ultrasonics Symposium (Chicago, IL), April 1981.

(19] H. M. Frost, "Electromagnetic-ultrasound transducers: principles, practice, and applications," in Physical Acoustics, Vol. 14, W. P. Mason and R. N. Thurston eds., Academic Press (New York) 1979.

(20] A. Karpel, L. J. Laub, and H. L. Sievering, 11 Measurement of acoustic waves propagation characterization by reflected light," Applied Physics Letters, Vol. 10, pp. 295-297, No. 10, May 15, 1967.

(21] S. Sizgoric and A. A. Gundjan, Proc. IEEE 57, 1313 (1969).

96

[22] Stress waves in solids, H. Kolsky, Dover publications: New York, 1963.

(23] C. H. Palmer, R. 0. Claus, and S. E. Fick, "Ultrasonic wave measurement· by differential interferometry," Applied Optics, Vol. 16, pp. 1849-1856, No. 7, July 1977.

(24] D. P. Jabalonowski, "Simple interferometer for monitoring Rayleigh waves," Applied Optics, Vol. 17, pp. 2064-2070, No. 13, July 1978.

[25] A. 0. Garg and R. 0. Claus, "Optical fiber path differential wideband interferometer," .~coustical Soc. of America (Chicago, IL), April 1982.

(26] R. 0. Claus and A. 0. Garg, "Measurement of pulsed ultrasonic waves in liquids by wideband differential interferometry," Acoustical Soc. of America (Orlando, FL), November 1982.

(27] J. H. Cantrell and M. A. Breazeale, "Elimination of transducer band corrections in accurate ultrasonic-wave velocity measuremenL.s by use of capacitive transducers", J. Acoutic Soc. of America, Vol. 61, pp. 403-406, No. 2, February 1977.

[28] H. Shimiz~ and A. J. Bahr, IEEE Ultrasonics Symp. Proc. Cat. No. 76 CH 1120-SSU p.17, 1976.

[29] G. I. Stegeman, "Optical probing of surface waves and surface wave devices," IEEE trans. on Sonics and Ultrasonics, Vol. SU-23, pp 33-63, No. 1, January 1976.

[30] C. H. Palmer, R. A. Klien, and R. E. Green, "A comparison of optically , and piezoelectrically sensed acoustic emission signals," Journal of Acoustical Society of America, Vol. 64, pp. 1633-1639, No. 6, December 1978.

[31] L. Knopof=:, "Surface Motion of a thick plate," Journal of Applied Physics, Vol. 29, pp. 661-670, No. 4, April 1958.

[32] C. L. Pekeris, "The seismic surface pulse," Proc. National Academy of Science Vcl. 41, pp. 649, (1955).

(33) An Introduction to Lasers and Masers, A. E. Siegrnan, McGraw Hill: New York, 1971.

97

[34] M. I. Cohen and R. B. Snyder, "Lightwave systems: an overview," The Western Electric Engineer, special issue on Lightwaves, Winter 1980.

[35) W. Sachse and.H. M. Hsu, "Ultrasonic transducers for mechanical testing and characterization," in Physical Acoustic, Vol. 14, W. P. Mason and R. N. Thurston eds., Academic Press (New York) 1979.

[36] J. F. Martin and R. B. Thompson, "The twin magnet EMAT configuration for exciting horizontaly polarized shear waves," 1981 IEEE Ultrasonics Sympossium Preprint.

Appendix A

PREPARATION OF SINGLE MODE FIBERS FOR EXPERIMENTS

Optical glass fibers have been used for communication

purposes due to their ability to transmit a larger bandwith

of information per unit area than conventional copper

cables. The strength of a smooth glass fiber can far exceed

that of a comparable metal wire, but small surface cracks

quickly degrade their strength (34).

A simple circular lightguide is one in which a glass

cladding ~aterial with a refractive index n 2 surrounds a

core with refractive index n 1 which is higher than n 2 by a

small amount 6.. A typical value for the refractive index of

the cladding is 1.46 and that for the core is 1.48. A ray of

light traveling in the core is partially refracted into the

cladding and partially reflected within the core unless the

ray angle e is less than a ''critical" value as shown in Fig-

ure A.l. This critical value for total internal reflection,

or complete guiding of the ray, is defined from Snell's law,

cose = n 2 /n 1 , r (A. 1)

where 8 is the critical angle for total internal reflec-r

ti on.

98

eo

/ /

r------ ---- ------• COATING

i ------. . ........ ...____,

CORE n1 1--~-"''--~~~-"'L-~~~~~~~~~~~~~~~~~---1-------·...-------'

FICURE A. l.

CLADDING n2 _____ ....

. . ----------- -- _ ... - . -·

Path of light through a step index optical fiber. A is the critical angle below which the light r~y refracts into the cladding [34].

INDEX PROFILE

n1 = I ·48

n2=1·46 <..O \.0

100

If Equation A.l is applied to the glass air boundary at

the input end of the fiber and the refractive index of air,

n 0 is assumed to unity, a basic parameter known as the num-

erical aperture (NA) may be defined by

NA = sin8 0 (A. 2)

This parameter defines the maximum

allowable angle for a ray of incident light to be totally

internally reflected.

The propagation of light in an optical fiber is

governed by Maxwell's electromagnetic field equations, which

predict the number of "modes" that will propagate through a

certain glass fiber of a given core diameter and refractive

index. The solutions of Maxwell's equations also predict

propagation of light in the cladding. The number of modes

that a given lightguide can support is related to a dimen-

sionless quantity usually referred to as the V number,

V = 2Tia(NA)/A, (A. 3)

(A.4)

where A is the wavelength of the light being transmitted and

a is the core radius of the fiber. It can be shown tha~ the

101

number of propagating modes is approximately equal to M

where,

(A.5)

This is valid for step index fibers only. Thus, it can be

seen from the Figure A.2 and above equations that single

mode propagation in a step index fiber takes place when the

value of Vis below 2.405 [34]. Below this value all other

modes are forced into cutoff. To obtain very low V number

for operating wavelength of 0.82 x io-s m and 1.6 x io-s m,

the product of core radius and NA must be small [34],i.e.,

k a(a) 2 < 0.24 for 1.3 x io-s m, and

k a(a) 2 < 0.15 for 0.82 x io-s m.

This shows that single mode fibers must have core diam-

eters of less than 10 x io-s m and must also be made with a

small index difference ~.

The optical fibers are highly sensitive to microbending

and microfractures which can occur when fibers are placed in

structures that impose random bends in their axes, resulting

in a loss of optical power. These microbends make the

selection of materials used in cable jacketing extremly cri-

tical. Optical fibers used for underground cabeling purposes

102

900 FOR

800 A= O· 82 µm STEP INDEX NA= 0·23 PROFILE 700

a = V/ 1 ·76 (J) 600 w 0 0 50'0 :?

lJ... 400 0

a: 300 GRADED INDEX w Ill PROFILE ~ 200 :::> z

100

10 20 30 40

v NUMBER

1-4 6 11 17 23

CORE RADIUS, 10- 6 m

FIGVRE A.2. Number of transmmission modes in a light guide increases with core radius a and v· number. Single mode fiber have V number less than 2.405 [34].

103

have a PVC coating extruded over the coated lightguide

fiber. This is then imbedded between strands of Kevlar and

further protection is supplied by enclosing the fibers in

PVC and metal tubings.

However, optical fibers used for laboratory purpose are

not subjected to strains experienced by underground fiber

cables. The laboratory optical fiber supplied to us by ITT

had a RTV sleeving and a plastic jacketing over the glass

lightguide. Both of these coatings could be easily scraped

off using a razor blade and Acetone. The RTV sleeving and

plastic coating were removed from t~e first 10 cm of both

ends of the fiber. These ends were then cut by scribing the

fiber at approximately 2 cm from the tip. By applying slight

lengthwise pressure, the fiber snapped giving "good" ends. A

"good" end is defined as a flat end with no pits or jaged-

ness on its surface. The exposed cylindrical ends of the

fibers were then coated with a index matching mode stripping

fluid to eliminate the interferenc~ of light traveling in

the cladding with that traveling in the core.

The prepared ends of the fibers were placed in brass

fiber holders which were positoned using six axis position-

ers as shown in Figure l of Chapter 2.

Appendix B

COMPUTER PROGRAM FOR CALCULATING THE POSITIONS OF LENSES FOR VARIOUS SAW FREQUENCIES

The following pages contain two computer programs which

were used with the fiber differential interferometer. The

first program calculates all the different positions possi-

ble for a given lens sytem. These positions correspond to

the different frequencies the system can be tuned to. The

second program plots out the sensitivity curve for various

spot separations. A set of plots for two spot separations of

2 mm and 18 mm have been included for comparison. Also plots

as a function of d/A = n + d/\ , where d is the spot separa-

tion and \ is the acoustic wavelength, have been included

for comparison. In the plots LA = A.

104

l REM 2 REM 3 REM 4 REM 5 REM

20 REM 30 REM 40 REM 50 REM ~~ REM

. 70 REM 80 REM

IJE:::;. ·~~~:1 F.·E=·t·I ... -· . -

100 F::EM 110 PEM

****************~******************************************** AUCL6.BAS NOV-10-81 A.O.GARG ~~~·ti~~1-~~~~~~~~~~~~~~~~~~~·t~~~~·t·~~~~~~~~~~~~~~~~~~·~~~~~~~~~·**~ ·1 · ·1 · ·1'· · · ·1 · · ··•'I" ·T· ·1'· ·T··1 • ·1'··1 · ·1'· ·T· ·T· ·1 · ·t· ·1 · ·1 · ·'f· ·1'· ·t· ·1 · ·1"· · ··T· ·T· ·T·· • -1 · ·1 · ·1'·•1'• ·t· "T··"f·.,-. 1"··1"··,.· If'· ·'f··l"··T· .,._,, .. T·-1"··T·'1'· ...---?·"1"· 'f· ·f'.1"· -t'·1"· ........

TH IS I:::; ~i ::WEC I t:il PROGF.:?if·l FOP THE U:3E IN FI BEF.: . OIFFERENTiru_ INTERFEROMETER DESIGNED BY MR.A.0.GARG ANO [·,c::. F·' f'I r·L ·:· 11·::· _ r'. . · .. _ . _. -~ i _ ·-·· . THI::; F'F.'.OGP{if·l ::rrnTE:::; THE HUME~'.IC~iL APEF~:TUF.:E OF. THE FIBER AND .-:···L r:t IL"""TE'.=: i"HE" '.:;f·r:::·E·"·[1 It·' E:Er-t"'"l ·"·T 1.1···~·1n11::: (IJ'.:;T·"·t··r·E~ .. H _ .. .. H _ . ... 1~. -t1 . . . 1 r 1· H , 1-ir~.. -· - - - 1-i 1..- _ •

THIS PROGRAM ALSO CALCULATES THE REQUIRED POSTION OF THE LEN::; ~iND THE FOC~~L LENGTH OF THE LEt-r::ES FOR • . ..'fiRIOUS :::At·J FREOIJENC

l 20 PR I HT I I MPUT t·fUMEF.: I CAL ~iF'EF.:TUF;:E OF THE FI BE~: I .i

130 INPUT Nt'.:t 140 FRINT ·INPUT THE FOCAL LENGTH oF THE FIF.:::::r LENS IN MM ONLY • _. l ::;o I HPUT F 1 i i:.o PF: r NT • r NPUT THE DI :::r ~iNCE OF Fr E:ER FORM THE LENS r M MM ONL..... • .i 17'0 INPUT Ul 180 Vl=FllUl/(Ul-Fl) 190 F'F.'.Hff I INPUT THE :::EPEF.'.fiTION E:ETMEEN THE FIBERS IN MM I.:

·::·i:::1n I t··IF'll1- :=;[: .: ... -· .. -· ·-2 l 0 Pt'.iGE 220 REM SIN(ANGLE OF ACCEPTANCE)=NUMER!CAL APERTURE 230 REM FOR SMALL ANGLE SINE OF THE ANGLE = THE ANGLE ?4t1 D==~i nv NA ) 250 SP=(0/2)*(Ul) 260 H1=2l(2tSP+SE) 270 PRINT 'THE MINIMUM HEIGHT OF THE FIRST LENS= ';Hl 2:::0 pf;,: I MT I THE I f'l•iGE I::;; ( I .• I.) 1 .• I > MM FOF~M THE FI ~:ST LEHS' 290 PF.'.INT 'THE SPOTS ARE ( ';Ul/Ul; I) ~U1 APART'

I-' 0 U1

:-:•:~:1n F:·t~· J .. t· 11···· ... -· ... - . . 1

PF:IMT .. ··.

F'l?lHT"·· ..

F'PlNT"··. PP It-ff"·· .. PklMT

~ 1 :, F·r:· l. · 11· • · E~·. nE:· 1r:r·Y [1 I ·=··1· ··· t·•r·E ? • ; ·-· t f". . t 1 t ~ -~ ! ... ..... - ... I . · •• • H 1 ... • .

320 I HPUT O:t: ~J~ ~;:i:1 c. ··· r·r:: _ -· -· r· H .l ·-

340 IF 0$='Y' THEN GOTO 120 350 PF.:Hff • Mm·J ME HILL CALCUL.t1TE THE SPF.:EAD IM BEAM :::POT OH SIF.:FACE' :-:~.:::·f1 F·c· I ·'T • llt·1[·1E·c:·rT11· t·1I· TE-::-1· 1 • .... • -·· o•• ... o t 1 H• 1 . _r .. O~ - • 1 _, 0 ·-·

:·.p·~~1 l·'H··· Ii· 1 c1ru-:1 ·-· -· .f ----... -. - F· .·. ,-E . . : .. :.~.:.1 HJ -:::s~o PF::nff • M~ii<IMUM DIST~iNCE BETl·~EEN THE FIRST ~iMO LAST LENS • _; 400 lNPUT DM 410 P~: I NT I FOC~il LEt·~GTH OF THE SECOND LEMS I .i

4~~0 H~PUT F2 430 PRINT 1 FOCAL LENGTH OF THE THIRD LENS '; 440 INPUT F3 4~~0 PP INT I FOC~iL LENGTH OF THE FOUF.:TH LEHS I ,i

460 JMF'UT F4 4?0 PAGE 4:::0 pp I NT I FOC~iL LENGTH OF FI F.:ST LEHS = ' i F 1 4 90 pp I MT ' FOC~il LEJ~GTH OF TH I RD LEHS ::: I .: F2 ~:;(10 PP I HT • FOC~il.. LENGTH OF THI~::[I LEM::: ::.-: I .i F3 ~~ 10 PF: I MT ' FOCt~L LEMGTH OF FOUPTH LEHS :: 1 .• F 4 ~;20 PPIHT • roT~iL DH:;r~1MCE BETHEEN FIF~::::r {iMD LAST LENS == • .i Df'I c.-~ -· F··F·· l. t •r·· ..... .::.t.1 . : .. ·1 •·•

PPIHT"··. PF.:It~r·· .. PF.:IHT'"··. PF.:IHT'"·· Pf~: I Mr· ..

f-"' 0

°'

l'·· w

=I _

I ...... .... -.. -· w

-. -· .-. ,_, m

.;J: .. u... .-. ,_. •. -·--:r-::;: "•.I.

w

! ., -· - ..:.... ..... .... :c C

: .-. ·-· . --, .-. ,_. -. -·-

::::: 1

·t; r,= i i=

I :-.-. ·-· ~~ ·-· ..... ...:.... ... u

.i ....-..... ;-

107

...... .. ·-·.

w

c:.:; a... 1:0 .. 1!.J ..J

:-(J)

-0 .. .. ..... ..J !-u) -0 •.

('J iJ

) . __, ·:l: ( .. ) •=t u. •.

.-! 1)) 1T

-. -·· ..-.. C

l :-

;=; i::: :S) ;!::; 1::;:, i::; i::i i=

i ;::; ;~& •=I ;~i ;::: 1Z1 1::1 '=' 1::; i=l 1:::1 1::1 -1:) •=• 1=1 1~; 1::1 1~; •=i •=1 i~f 1::i 1S:: •=i •=;

~ iJ~i !.£; r·--

i:(i i:r·, ,~, .-; (\J r~:i 7 u-:; i.D r··-o:i iJ·, ,=, .,... (1.J r.o:~j

.... tr lf) ~ . .er r··-;:o ;::··, 1::• ~ (a.J f-:) '1'"' t;~i i.£1

l.i"'.• 1.r' :.n u'°'.' it:• Lr: >..o !.£! !.£! 1 . .::r 1.J:i '·D ! . .(i '·D ;_.i:: i.J:i r-._ r··-r··-r --r··-r··-r··-r-·-r---r··-1:;:: o:i ;:e; ;)) i:i:: i:ei ;))

0 ·:I

::::-;:~~:.1

:::::::a.J

t·~ >

890 900 910 920 930 940 950 960 970 980 ~0

]··F~ tf)til- 111 ){~ ·1-•JE;t•I ~t1·1·n 1A4A • •• - • .. • • I • I ... .... .. .... ... . ..

F·r:1·t 11·· F·c- F-.··· '" ··c··r1 L1 •• ·1· .. ·· 11·-tL1·-· ·' 1·-:~ . . ·1 ._:. .• · t:. .• .=·· •. • '·· ..I • ~- .,. ..' .• .• t:. .• ··· ~=· · r1 1:•

CT::::CT 1- J. ·1·F~ ~l-=~ 7 ·1-uE~t· 1 1 • 1 ~Il" ~AA . . ..• • ... t1 I 1... 1 Htl , .•...•. . ,. F" •.. ,. -·-: , .. l JE"t I F' ... ""E"" . . t. :::::.;'.•U n .: ., · Hl.i :~

)·r: ~l·=~A l"uE=t·' ~1-=A . _ _ ... r1 .. 1 ... ...

t··E· ... ·1·· .... • 1 ·-·"·, •··•

pp I MT I DO YOU HI '.::;H TO ~:EF.:EUM TH Is ~d~D CALCULATE THE ABOl.JE FOF.: MEH I

F·.c:-· It a·y· 1 I 1 ··· L I IE'-. •· F' F" J f-.-.. F-' f"4 .-;. ·· '·" "t 1 •• . · r~. ·1 ..• ..... • ..• • •. :. IJ .. • · .:::. .• -.:!• .• • ! •.. I ·" ·1 ) ·'

l MPUT t·U·U: F'~tGE IF HM$=. y I THEM GOTO lt1 F'PIMT 1 DO '/OU l·JISH TO F.'.EREUN THIS USIMG USIMG SAME OLD l.JAUJES '? ( Y/

J.1.)0f1 J NPUT OL:f l.010 P~iGE 1020 IF OL$= 1 Y1 THEN GOTO 580 1 c-1~~:~-:-1 ·=·rnF· ·--- ._. -1 040 PF.: I NT 1050 PF.: I MT"··,

PF.'.INT"·· .. f'F.:IMT"·· .. PF.:I t-tr· ... F'F.'.IMT

l f.1·~~1 P0 It·'T ·~*~*~***~*~**~Wl'**·~·t.'*'*****~~~***W*'**~•~*~**~****~~*·~~*~***•' _I:·~ r;, 1 ·t'· ·T· ·T· •T··1"·f·-T··T··1 ··T· ·T··T•·T··T·•1 ·· ··T· • ·T· · ·· · ·1'··~·T•·t'•-T··1···1"••T- ·1'·•1'·t"··~ · ~·T· ·f'·f\ 'T··1'·1 ··T·.,....·1'·1'·-T• .. T··'f'o·T··1'-.lfl.·T··f'io•T•1"·'t··'t··1'-·t"·-1'·

1070 P~: I MT I THE FOLLOl·J I NG • ... l~iLUESOF [I I STANCE L 1 ~iRE GF.:EA TER THAN L2 I l AOA p•DJt··T '*~***~*~W~***********~***~~~**~*********W~~*·~-**~~*'****W~~·· -- •-• - rr.. 1 ·T· ·T· ·T· If· •1'• ·1 · 'f· 'I'· ·1--~ ·'f· ·T· •T· ·'f· ·T· ·T· 1'··T· •'I'· ·T·"1'• •1 · ·T· ·T· ·1'· •T••1'••T· •1°" ·T· -T- ·'f··'f• ~· •1'··T· -1' ·1' "'1\-•T· ·1 ... T. •'I'• ·1' .,... ..... ·1'-•1'-• .,_..'t'.. •1'•'f'o.•T•1'- ·1"··1'--1'-""'

1091?.1 F'F.: I MT 1 1 00 PF.: I MT 1110 PF.'.Il···IT I DO YOU MISH TO COHTIHUE '? ( Y/N) I l l. ~~~; I HPUT DO~:: 113Ct F'f:tGE 1140 IF 00$='Y' THEN GOTO 880

I-' 0 00

109

* *

* *

a~a :..;.

. :.+-* r··-;.f · .. ·~· .. ·

~~~

*<I:* ~ rt1 :;..;.

:+.:. .:::· ~

*ZI~

~ ~

a w

0) <I: w

(_I) 1--1

(1) -, i11 1 ......

w

-, -· .. ~ -((t l-.-. ·-· _J a... :::: <! U:: ' " ·-· ,-, Ii a_

((1 ~

..,.. --i-

a·~

w

-.. ,-, ~I,:: - .:... W

>-

l-' LiJ "' :r:: W

>-

-. WI~

--=" "9

-- .-... ,_._....... ::i: r··J

i-1

ll.L.l

-. _..,.

_. ...... •• ,.. 1

-1

:Cr-

llO

.. -..

... II

.. -.. .. -..

,~,.

..... ··-·· li.. - ...... ··-·· ;::; LI..

111

...

l-ll..

- :r ((I

( . ..) CJ

w

==·

... -,

·~·

CCO 01 IFFR t·f Ol·U:~pf-1 670 08(1)=20~LOG<OE(I )/MA) 6f:(1 ()t~EPF:: MOL·~~iPN t::~~O t·IE:>::T l ?OC1 DI ==M l t-10:: Db > 7 ln F-n~ ~=~ i·n t·•f:(~) ~TE:F~ 1 I •. .• I', I , '\., •. 1 , •• • •• .• -, -· - 1· F' [" E . .. -· l"l E" I [' E . • . . (" I ( :::'.~J . . .I .K t::, _)::;~.::I d :h ..I.::•:. :: .. )::: _I ?30 NE::O::T K 740 PRINT TA8(30); 1 08 PLOT OF SENSITIUITY 1

7~;.::1 ':-:"· ·'F'l ri1· Ff'• . [·1f:: I ... •.. • •I - -· ..... • • .. -:~,::::~::! 1•1H"· ]. l . . -· - .... . . 77'0 F'~iGE 780 PRINT 'RERUN THIS PROGRAM ? I

7'90 IMPUT F.:E:f 800 IF RE$= 1 N1 THEN GOTO 850 810 PRltlT 'SAME UALUES OF FREQ ANO VELOCITY ? S FOR SAME~O FOR OIFFERNT'

:::::::::o I MPUT ::~•.,.t:f 830 IF SU$= 1 0 1 THEN GOTO 100 840 IF SUt= 1 S 1 T~EN GOTO 350 850 PRINT 1 REORAW SENSITIUITY CURUE ? Y/N 1

::::i::o I HF'UT PD:;: 870 IF ROf= 1 Y1 THEN GOTO 500 :=:::::a:1 ~=;-r f ·1 F' ...... - - ...

F.'.E~iD\' l

..... ..... N

113

...-..:... ::::: (•.j

.. ii

c ....... • . ...;_ w

~

.• . .... • -·. i

114

..... ~~I 1.• . ... ·' 1\j '-~) ;,.(!

w

...-;

':t

(•.;

::--.. -· LL .-. ·-· :-. -. ,_, . ~ u...

E

E

:c '"""

.... :.;...' i.i") i

ll5

'i~1 lf) .-t

I (t.j I -

! . .(!

... i.,;.; .-i

;_"•.J

116

-

::::::: ~

-• . .(;

•):i

-. -. .. , .

~

..... . ..

-~

...... .....

--

"!t ~

z ;~:.j

~·~· i)~I

-.-. '-I ·- ..... ~ . ' u

..i Ct:: .•. u.. .·.·. ,_,_.

C:::•

,-. : ' .,

i:! ......

1::1 1".'"1

1:;1 1

:; .~ .

..... l=i

..... u-::

l.O U~i

i::l U~:

I -

-C•.j

(•.J I

I I

I I

Appendix C

DATA FOR THE DETECTION OF PULSED WAVE IN WATER USING TWO BEAM DIFFERENTIAL SYSTEM

The following plots are data for the detection of

ultrasonic compressional waves in water using the two beam

differential interferometric system. Figure C.2 is a compar-

ison of the rf noise generated by the Metrotek pulser to the

signal due to the pulsed compressional wave traveling

through the water tank. Laser noise was not seen during this

experiment. This is probably due to the long

the laser had before it was used.

117

warm up ~· ~ime

20 mV/div.

0

A

B

31 62 93

~

124 155 186 x 10-6 sec.

FIGURE C.l. Data for detection of an ultrasonic pulse packet traveling in water tank 11sing the two beam system. The notations used are identical to those used in Chapter 6. TI1e above data is within 5% of the calculated theoritical value.

,-

f-' f-' 00

so mV/div.

0

R.F. noise

31 62 93 124 155 x 10-6 sec.

FIGURE C.2. Comparison of the rf noise (due to Metrotek pulser) to the signal (due to ultrasonic pulse traveling in water tank).

186

I-' I-' l.O

Appendix D

DATA FOR DETECTION OF THE DIRECTION OF PULSED WAVE IN WATER USING FOUR BE~~~ SYSTEM

The following plots are data from the detection of

ultrasonic pulses in the water tank using the four beam sys-

tern. Figure D.3 is the rf noise due to the Metrotek pulser

unit and laser noise due to the laser. Both are rf signals

and are unaffected by the presence of the optical signal at

the photodiode. Figures D.4 and D.5 were obtained for beams

positioned to form a square and diagonally opposite pairs of

beams were used for interference. However, since the system

had to be reset for every measurement, these results do not

give an accurate indication of the direction of propagation

of the pulse packet. A much better result can be obtained if

both pairs of beams are simultaneously evaluated using pre-

calibrated detectors.

However, if data from Figures D.4 and D.5 is considered

correct the vertical amplitude for the pulse packet A in

Figure D.4 is 240 mV while amplitude of pulse packet A in

Figure D.5 is 90 mV. Using the formula

tans = amplitude of A in Figure D.5/amplitude of A

in Figure D.4

we get

120

121

a= tan- 1 (90/240)

a = 20.55° to the left of the diagonal formed by two

spots used for interference for Figure D.S. Thus e gives the

direction of propagation of pulse packet in water.

result seems reasonable.

This

Cl ID

E IF

30

m\'/c~iv.

,-- ' 0 15.5 31.0 46.5 62.0 77 .5 93.0

-6 x 10 sec.

FIGURE D.l. Data for detection of ultrasonic pulse packet traveling in water. This detection was done by using the vertical pair of beams of the four beam system. The notations are identical to ones used in Chapter 6. Pulse packets of laser noise are also clearly seen in this plot.

I-' N N

30

mV/div.

A D

E

+-~~~~~~~...&.~~~~~~~-'~~~~~~~~-L-~~~~~~~-L~~~~~~~_j___~~~~~~·...&.~~~~

0 15.5 31.0 46.5 -6 x 10 sec.

62.0 77 .5 93.0

FIGURE D.2. Data for detection of an ultrasonic pulse packet in water using the horizontal pairs of beams of the four beam differential system. The data is within 10% of the calculated value. The notations are identical to those used in Chapter 6. The pulse packets not named are due to laser noise. This laser noise makes identification of ultrasonic pulse very difficult.

~ .... ~..)

(.,)

30

mV/div. ~ --

0 31 62 93 124 155 186

x 10-6 sec.

FIGURE D.3. This data is obtained when the laser beam is blocked . The large initial pulse is the rf pulse generated by the Metrotek pulser. ~he following pulse packets are rf noises generated by the laser itself.

...... N +:--

A

B c D F

E H

30

mV/div.

G

1 I I I

0 15.5 31.0 46.5 62.0 77.5 93.0

x 10-6 sec..

FIGURE D.4. Data for the detection of ultrasonic pulse packet traveling in a water tank using the four beam differential interferometric system. The four beams of the interferometer were positioned such that they lay at the four corners of of a square. The experiment was conducted in two parts. First, a set of diagonally opposite pairs of beams were superimposed and the interference pattern detected. This is shown above. The next part was . .same using the remaining diagonally opposite pairs, results of which are shown in Figure D.5. Unfortunately as the system had to be realigned everytime it could not be calibrated and hence accurate results could not be obtained.

I-' N lJ1

'° N ......

15

mV/div.

[ _ _,______~____,_______.__ _ __.___ _ __,___

0 15.5 31.0 46.5 62.0 77. 5 93.0

x 10-6 sec.

FIGURE D.S. Data for the direction of ultrasonic pulse traveling in a water tank. As explained in Figure D.4. accurate results were impossible. However, one does notice a change in amplitude of the ultrasonic pulse when compared to those in Figure D.4. This can help us to conclude that the direction of the pulse was oriented more along the diagonal formed by the two beams used for Figure D.4.

The vita has been removed from the scanned document

APPLICATION OF OPTICAL FIBERS TO WIDEBAND DIFFERENTIAL

INTERFEROMETRY AND MEASUREMENTS OF PULSED WAVES IN LIQUIDS

by

Avinash 0. Garg

(ABSTRACT)

Wideband differential interferometry has been applied

to the detection of SAW on specimen surfaces and ultrasonic

compressional waves in liquids. Herein is described the

performance of a wideband differential system which uses

single mode optical fibers to transmit coherent light from

input optics to a surface which supports which supports

ultrasonic waves. Polarized light from a 2.0 mW helium-neon

laser source is divided and coupled to two flexible bundled

single mode optical fibers which transmit the light to a

small remote detection head. The light at the output end of

the fibers is collimated and focused by a varifocal lens

system to points on the surface of a specimen to be

inspected. Elastic waves on the specimen differentially

modulate the relative phases of the two optical beams due to

periodic changes in particle displacement at the surface.

Upon reflection, the two beams are superimposed, filtered,

and detected to produce an optical signal directly propor-

tional to instantaneous displacements.

Also described is the development of two beam and four

beam differential systems for the detection of ultrasonic

compressional waves in water. Two laser beams are transmit-

ted through a water tank and combined to produce an inter-

ference pattern. The detected motion of the pattern yields a

differential measure of the acoustic field amplitude at the

location of the two probe beams. If a pulsed ultrasonic wave

is generated in the tank in a direction perpendicular to and

coplanar with the probe beams, each beam is modulated inde-

pendently and output signals of opposite phase are produced.

The acoustic sensitivity of both the above systems may

be adjusted by changing the separation between the two spots

on the surface or the two beams in the tank. The system

effectively discriminates against low frequency noise vibra-

tions, while the upper acoustic frequency response exceeds

100 MHz. Applications requiring flexibility allowed by a

remote detection head can use the fiber system to their

advantage while potential applications of the four beam sys-

tem to three dimensional mapping and ultrasonic field scat-

tering is suggested.