769
Photoacoustic
27. Photoacoustic Characterization of Materials
The basic principles of photoacoustic generation
of ultrasonic waves and applications to materials
characterization of solid structures are discussed in
this chapter. Photoacoustic techniques are a subset of ultrasonic methods wherein stress waves
are used to obtain information about structural
and material properties. In photoacoustic techniques, the ultrasound is typically generated using
lasers, thereby enabling noncontact nondestructive characterization of the material properties of
structures. Photoacoustic techniques have found
application over a wide range of length scales
ranging from macrostructures to nanometer-sized
thin films and coatings.
In this chapter, the basics of photoacoustics
primarily as they relate to nondestructive characterization of solid materials are discussed. In
Sect. 27.1, the basics of stress waves in solids is
outlined. In Sect. 27.2, the process of photoacoustic
generation is described. The major techniques of
optical detection of ultrasound are then described
in Sect. 27.3. The final section of this chapter is
then devoted to some representative recent applications of photoacoustic characterization of
materials. The objective here is to describe the
basic principles involved, and to provide illustrative applications which take specific advantage of
some of the unique features of the technique.
Photoacoustics (also known as optoacoustics, laser ultrasonics, etc.) deals with the optical generation and
detection of stress waves in a solid, liquid or gaseous
medium. Typically, the technique uses modulated laser
irradiation to generate high-frequency stress waves
(ultrasonic waves) by either ablating the medium or
through rapid thermal expansion. The resulting stress
27.1 Elastic Wave Propagation in Solids .........
27.1.1 Plane Waves in Unbounded Media .
27.1.2 Elastic Waves on Surfaces ..............
27.1.3 Guided Elastic Waves
in Layered Media .........................
27.1.4 Material Parameters
Characterizable Using Elastic Waves
770
771
772
774
776
27.2 Photoacoustic Generation .....................
27.2.1 Photoacoustic Generation:
Some Experimental Results............
27.2.2 Photoacoustic Generation: Models .
27.2.3 Practical Considerations: Lasers
for Photoacoustic Generation ........
777
27.3 Optical Detection of Ultrasound .............
27.3.1 Ultrasonic Modulation of Light .......
27.3.2 Optical Interferometry...................
27.3.3 Practical Considerations: Systems
for Optical Detection of Ultrasound .
783
783
785
777
780
783
789
27.4 Applications of Photoacoustics............... 789
27.4.1 Photoacoustic Methods
for Nondestructive Imaging
of Structures ................................ 789
27.4.2 Photoacoustic Methods
for Materials Characterization ........ 793
27.5 Closing Remarks ................................... 798
References .................................................. 798
wave packets are also typically measured using optical
probes. Photoacoustics therefore provides a noncontact way of carrying out ultrasonic interrogation of
a medium to provide information about its properties.
Photoacoustics can be used for nondestructive imaging
of structures in order to reveal flaws in the structure, as
well as to obtain the material properties of the structure.
Part C 27
Sridhar Krishnaswamy
770
Part C
Noncontact Methods
Photoacoustic measurement systems are particularly attractive for nondestructive structural and materials characterization of solids because:
•
•
Part C 27.1
•
•
•
•
they are noncontact;
they can be nondestructive if the optical power is
kept sufficiently small;
they can be used for in situ measurements in an
industrial setting;
they are couplant independent (unlike contact
acoustic techniques), providing absolute measurements of ultrasonic wave displacements;
they have a very small footprint and so can be operated on curved complex surfaces;
they are broadband systems providing information from the kHz to the GHz range, enabling
the probing of macrostructures to very thin
films.
Over the past two decades, photoacoustic methods
have evolved from being primarily laboratory research
tools, which worked best on highly polished optically
reflective specimens, to being incorporated in a wide
range of industries for process monitoring applications.
Photoacoustic methods are currently being used for
imaging of flaws in real composite aerospace structures.
They have been used for in situ process control in steel
mills to measure the thickness of rolled sheets on the fly.
Photoacoustic metrology tools are also widely used in
the semiconductor industry for making wafer thickness
measurements among other things.
For a more comprehensive discussion of the principles of photoacoustic metrology, the reader is referred
to the books by Scruby and Drain [27.1] and Gusev
and Karabutov [27.2], as well as to several excellent review articles on laser generation of ultrasound [27.3],
and optical detection of ultrasound [27.4–6].
27.1 Elastic Wave Propagation in Solids
There are many excellent books on stress waves in
solids [27.7–9]. Here, only a selective review of elastic
waves in solids is given.
The field equations of linear elastodynamics are
•
the equations of motion
∇ · σ = ρü
•
σij, j = ρü i ,
(27.1)
the constitutive relations
σ = C·ε
•
→
→
σij = Cijkl εkl ,
(27.2)
σ I = (σ11 σ22 σ33 σ23 =σ32 σ31 =σ13 σ12 =σ21 )T
and the strain–displacement relations
1
ε=
∇u + (∇u)T
2
→
view of these symmetries, there are at most 21 independent elastic stiffness constants for the most anisotropic
material. With increasing levels of material symmetry,
the number of independent elastic stiffness constants
decreases, with only three for cubic crystals, and only
two for isotropic materials.
For simplicity, a contracted notation is often preferred. The six independent components of the stress
and strain tensors are stacked up as six-dimensional
column vectors:
εI = (ε11 ε22 ε33 2ε23 =2ε32 2ε31 =2ε13 2ε12 =2ε21 )T .
1
εkl = (u k,l + u l,k ) ,
2
(27.3)
where σ is the stress tensor field, ε is the infinitesimal
strain tensor field, C is the elasticity tensor, u is the displacement vector field, and ρ is the material density.
Superposed dots imply time differentiation.
From angular momentum balance considerations of
nonpolar media, it can be shown that the stress tensor
σ is symmetric, i.e., σij = σ ji . From its definition, the
strain tensor ε is symmetric as well: εij = ε ji . It follows
therefore, that the elasticity tensor has the following
minor symmetries: Cijkl = C jikl and Cijkl = Cijlk . From
thermodynamic considerations, the elasticity tensor also
has the following major symmetry: Cijkl = Cklij . In
(27.4)
Thus, ij = 11 → I = 1; ij = 22 → I = 2; ij = 33 →
I = 3; ij = 23 or 32 → I = 4; ij = 31 or 13 → I = 5;
ij = 12 or 21 → I = 6. Capital subscripts will be used
whenever the contracted notation is used.
The constitutive relations in contracted notation
then become
⎞⎛ ⎞
⎛ ⎞ ⎛
σ1
c11 c12 c13 c14 c15 c16
ε1
⎟⎜ ⎟
⎜ ⎟ ⎜
⎜σ2 ⎟ ⎜c12 c22 c23 c24 c25 c26 ⎟ ⎜ε2 ⎟
⎟⎜ ⎟
⎜ ⎟ ⎜
⎜σ3 ⎟ ⎜c13 c23 c33 c34 c35 c36 ⎟ ⎜ε3 ⎟
⎟⎜ ⎟
⎜ ⎟=⎜
⎜σ ⎟ ⎜c c c c c c ⎟ ⎜ε ⎟
⎜ 4 ⎟ ⎜ 14 24 34 44 45 46 ⎟ ⎜ 4 ⎟
⎟⎜ ⎟
⎜ ⎟ ⎜
⎝σ5 ⎠ ⎝c15 c25 c35 c45 c55 c56 ⎠ ⎝ε5 ⎠
σ6
c16 c26 c36 c46 c56 c66
ε6
(27.5)
→ σ I = C I J εJ .
Photoacoustic Characterization of Materials
As will be seen later in this chapter, photoacoustic measurements can be useful in determining the
anisotropic elastic stiffness tensor.
27.1.1 Plane Waves in Unbounded Media
u(r, t) = U exp[ik( · r − vt)] ,
(27.6)
where U is the displacement amplitude vector, is a unit
vector along the propagation direction of the wave,
r = x1 ê1 + x2 ê2 + x3 ê3 is the position vector, k = 2π/λ
is the wavenumber, λ is the wavelength, and v is the
phase velocity of the wave. The angular frequency of
the harmonic wave is related to the wavenumber and
velocity through ω = kv = 2πv/λ. The êi are unit vectors√along the 1, 2, and 3 directions, and the symbol
i = −1.
Substituting the above into the field equations
(27.1)–(27.3), results in the so-called Christoffel equation
(27.7)
Γik − δik ρv2 Ui = 0 ,
where
Γik = Cijkl j l
(27.8)
is called the Christoffel matrix. The existence of plane
waves propagating along any direction in a general
anisotropic unbounded media follows directly from the
existence of real solutions to the eigenvalue problem
represented by (27.7). The eigenvalues are obtained by
solving the secular equation
det(Γik − δik ρv2 ) = 0 .
nondispersive (i. e., the phase velocity is independent of
the frequency).
Again from the spectral theorem, corresponding
to each of the real eigenvalues there is at least one
real eigenvector and, furthermore, one can always find
three orthogonal eigenvectors, say, U (i) . Therefore, in
any homogeneous anisotropic material, one can always
propagate three types of plane harmonic waves along
any chosen propagation direction . In general, these
three waves will have different phase velocities v(i) , and
the corresponding particle displacement vectors U (i)
will be mutually orthogonal. Each of these modes is
called a normal mode of propagation. The direction of
the displacement vector is called the polarization direction of the wave. Note, however, that the particle
displacement vector need not be parallel or perpendicular to the propagation direction in general. If the
polarization direction of a wave is parallel to the propagation direction, the wave is called a pure longitudinal
wave. Waves with polarization direction normal to the
propagation direction are pure shear waves. If the polarization directions are neither parallel nor perpendicular
to the propagation direction, the waves are neither
pure longitudinal nor pure shear. In such cases, the
mode whose polarization makes the smallest angle to
the propagation direction is called a quasi-longitudinal
wave, and the other two are called quasi-shear waves.
Plane Waves in Unbounded Isotropic Media
For an isotropic material, as all directions are equivalent, consider a convenient propagation direction such
as = ê1 so that the Christoffel matrix readily simplifies
to
⎞
⎛
c11 0 0
⎟
⎜
(27.10)
= ⎝ 0 c14 0 ⎠ .
0
(27.9)
It can be readily seen that the Christoffel matrix is symmetric, and under some nonrestrictive conditions on
the elastic stiffness tensor, one can show that it is also
positive definite. From the spectral theorem for positivedefinite symmetric matrices, it follows that there are
three positive, real eigenvalues for Γij . This implies that
the plane-wave phase velocities v (which are just the
square root of these eigenvalues divided by the density) are guaranteed to be real and so will represent
propagating modes. It should also be noted that, as
the eigenvalues are independent of the frequency (and
there are no boundary conditions to be satisfied here),
the plane waves in an unbounded anisotropic media are
0 c14
The secular or characteristic equation then becomes
c11 − ρv2 c44 − ρv2 c44 − ρv2 = 0 , (27.11)
whose roots are
v
(1)
≡ vL =
c11
ρ
(27.12)
with the corresponding polarization parallel to the propagation direction, which therefore represents a pure
longitudinal wave; and two degenerate roots
c44
(27.13)
v(2) = v(3) ≡ vT =
ρ
771
Part C 27.1
Consider a homogenous unbounded linear elastic
anisotropic medium. Seek plane harmonic waves in
such a medium given by the following displacement
field:
27.1 Elastic Wave Propagation in Solids
772
Part C
Noncontact Methods
with the corresponding polarization along any direction
on the plane perpendicular to the propagation direction,
which therefore represent pure shear waves.
Part C 27.1
Plane Waves in Unbounded Anisotropic Media
For a general anisotropic material, it is not easy to
simplify the secular equation analytically for arbitrary
propagation directions, even though it may be possible
to obtain analytically tractable expressions for special
cases of propagation along certain material symmetry
directions. In general, however, one seeks numerical solutions for the anisotropic problem. It is customary to
represent the inverse of the phase velocity along any
given propagation direction by means of slowness surfaces in so-called k-space with axes k
i /ω (which is
the reciprocal of velocity, hence slowness). Any direction in this space represents the propagation direction,
and the distance to the slowness surface gives the reciprocal of the phase velocity of the associated mode
in this direction. Figure 27.1 shows the slowness curves
for cubic Si material. Note that for an isotropic material the slowness surfaces are just spheres, the inner one
representing the longitudinal mode, and the two shear
slowness surfaces being degenerate.
Group Velocity
The group velocity (which is the velocity with which
a non-monochromatic wave packet of finite frequency
content propagates in a general dispersive medium) is
given by
(g)
Vj =
∂ω
,
∂k j
(27.14)
where k j = k
j and ω(k) in general. It can be shown that
the group velocity (which is also the direction of energy
flow) is always perpendicular to the slowness surface. It
should be noted that it is usually the group velocity that
is measured in experiments.
27.1.2 Elastic Waves on Surfaces
Surface waves are waves that propagate along the
surface of a body, and which typically decay in
amplitude very rapidly perpendicular to the surface.
Consider a half-space of an anisotropic but homogeneous medium (Fig. 27.2). In this case, in addition to the
field equations of motion (27.1)–(27.3), the top surface
(x3 = 0) is assumed to be traction free:
σi3 = Ci3kl εkl = Ci3kl u k,l = 0
on x3 = 0 for i = 1, 2, 3 .
(27.15)
Seek so-called inhomogeneous plane wave solutions of
the form
u(r, t) = U exp[ik
3 x3 ] exp[ik(
1 x1 + 2 x2 − vt)] ,
(27.16)
× 10– 4
2
kl2/ω
[001]
1.5
1
Pure shear [010]
ρ 1/2
Polarized: ⎛ ⎛
c
⎝ 44 ⎝
0.5
[100]
0
kl1/ω
–0.5
Quasi-longitudinal
–1
Quasi-shear
–1.5
–2
–2
–1.5
–1
– 0.5
0
Fig. 27.1 Slowness curves for silicon
0.5
1
1.5
2
× 10– 4
where it is required that the displacements decay with
depth (x3 -direction) and the propagation vector be restricted to the x1 –x2 plane, i. e., = 1 ê1 + 2 ê2 . Such
waves are called Rayleigh waves.
Note that the 3 term is not to be thought of as the x3
component of the propagation vector (which is confined
to be on the x1 –x2 plane), but rather a term that characterizes the decay of the wave amplitudes with depth.
In fact, both 3 and the wave velocity v are to be determined from the solution to the boundary-value problem.
If 3 = 0 or is pure real, then the wave does not decay
with depth, and is not a Rayleigh wave. If 3 is complex,
then in order to have finite displacements at x3 → ∞,
we note that the imaginary part of 3 must be positive.
This is the so-called radiation condition. Furthermore,
to have a propagating wave mode, the velocity v must
be positive and real.
Here again the equations of motion obviously
formally reduce to the same Christoffel equation
(27.7), where the Christoffel matrix is again given by
Γik = Cijkl j l . The solution to the eigenvalue problem
Photoacoustic Characterization of Materials
3 x
αn U (n) exp ik
(n)
3
3
u(r, t) =
n=1
× exp[ik(
1 x1 + 2 x2 − vt)] ,
(27.17)
where αn are weighting constants. Using the above displacement field in the traction-free boundary conditions
(27.15) results in a set of three homogenous equations
for the weighting constants αn :
σi3 =[ik]
3 x
C3 jkl αn Uk(n) l(n) exp ik
(n)
3
3
Swapping out the elastic stiffness in favor of the longitudinal and transverse velocities vL and vT one obtains
2 2 2
vT 3 + vT2 − v2 vL2 23 + vL2 − v2 = 0 ,
(27.22)
whose six roots are
⎧ 2 1/2
⎪
⎪
v
⎪
±i
1
−
,
⎪
vT
⎪
⎪
⎪
⎨
2 1/2
3 = ±i 1 − vv
,
T
⎪
⎪
⎪
1/2
⎪
⎪
2
⎪
⎪
.
⎩±i 1 − vvL
=0 ,
(27.18)
where (n)
1:2 = 1:2 is used for simplicity of notation. The
above can be cast as
dmn αn = 0 ,
(27.19)
where the elements of the 3 × 3 d matrix are:
dmn = C3mkl Uk(n) l(n) (no sum over (n) intended here).
Nontrivial solutions to the above are obtained if
det(dmn ) = 0 .
(27.20)
Rayleigh Waves on Isotropic Media
The isotropic surface wave problem is analytically
tractable. Since all directions are equivalent, pick = ê1
as the propagation direction. The corresponding secular
equation is
2
1
1
(C11 − C12 )
23 + (C11 − C12 ) − ρv2
2
2
× C11 23 + C11 − ρv2 = 0 .
(27.21)
(27.23)
Since it is required that the displacements decay with
depth, and since the velocities have to be real, the
three admissible roots for the Rayleigh wave velocity
v ≤ vT < vL are only those corresponding to the negative exponential. The corresponding eigenvectors are
⎛ ⎞
0
⎜ ⎟
U (1) = ⎝1⎠ ,
0
⎛
⎞
2 1/2
vT v
i
1
−
⎜ v
⎟
vT
⎜
⎟
U (2) = ⎜
⎟,
⎝
⎠
0
vT
v
vT
v
⎛
n=1
× exp[ik(
1 x1 + 2 x2 − vt)]
773
⎞
⎜
⎟
⎜
⎟
0
U (3) = ⎜
2 1/2 ⎟
⎝ v ⎠
−i vL 1 − vvL
(27.24)
and the boundary conditions (27.19) become
⎛
⎞
0
(U3(2)+U1(2) (2)
(U3(3)+U1(3) (3)
3 )
3 )
⎜ (1)
⎟
⎝
3
⎠
0
0
(2) (2)
(2)
(3) (3)
(3)
0 (c11 U3 3 +c12 U1 ) (c11 U3 3 +c12 U1 )
⎛ ⎞ ⎛
⎞
α1
0
⎜ ⎟ ⎜ ⎟
× ⎝α2 ⎠ = ⎝0⎠ .
(27.25)
α3
0
The determinant of the matrix above vanishes for two
cases. One case corresponds to a shear wave in the bulk
of the material with no decay with depth and this is not
a surface wave. The other case leads to the characteristic
Rayleigh wave equation
vT2
3
=0,
β − 8(β − 1) β − 2 1 − 2
vL
β=
v2
.
vT2
(27.26)
Part C 27.1
again formally yields the same secular equation (27.9),
except that in this case this leads to a sixth-order polynomial equation in both 3 and v, both of which are as yet
undetermined. It is best to think of this as a sixth-order
polynomial equation in 3 with velocity as a parameter. In general, there will be six roots for 3 (three pairs
of complex conjugates). Of these, only three are admissible so that the waves decay with depth according to
the radiation condition. Denote the admissible values by
(n)
3 , n = 1, 2, 3 and the corresponding eigenvectors as
U (n) . That is, there are three possible surface plane harmonic wave solutions, and the most general solution for
the displacement field is a linear combination of these
three
27.1 Elastic Wave Propagation in Solids
774
Part C
Noncontact Methods
This can be solved numerically for any given isotropic
material. Let the velocity corresponding to the solution
to (27.26) be called vR . The corresponding Rayleigh
wave displacement field is given by
Part C 27.1
u(r, t)
= U0 exp[ik(x 1 − vR t)]
⎡
⎤
⎤
⎛ ⎡
1
1 1
1 ⎞
2 2
2 4
2 4
2 2
vR
vR
vR
vR
⎣
⎣
⎦
⎜exp k 1− 2 x 3 − 1− 2
1− 2 exp k 1− 2 x 3⎦⎟
⎜
⎟
vL
vL
vL
vT
⎜
⎟
⎜
⎟
0
⎜
⎟
⎧
⎫
⎤
⎡
⎜
⎟
1
⎪
⎪
⎟
2 2
⎪
⎪
×⎜
v
⎥ ⎪ ⎟,
⎢
⎪
⎤
⎜
⎪ ⎡
x 3⎦ ⎪
exp⎣k 1− R
1⎪
1
⎪
⎜
⎟
2
⎨
⎬
vT
2
2
⎜
⎟
2
2
⎣k 1− vR x 3⎦ −
⎜ −i 1− vR
⎟
exp
2
2
⎜
1 1 ⎪ ⎟
vL
v
⎪
2 4
2 4 ⎪ ⎠
⎪
L
⎝
vR
vR
⎪
⎪
⎪
⎪
1−
1−
⎪
⎪
⎩
⎭
v2
v2
L
L
(27.27)
where U0 is the amplitude.
It should be noted that, for Rayleigh waves in
isotropic media, the vectorial displacement is entirely
in the plane contained by the propagation vector and the
normal to the surface (the so-called sagittal plane). The
x3 decay of the two nonzero components is not equal.
The u 3 component is phase delayed with respect to the
u 1 component by 90◦ , and they are not of equal magnitude. Therefore, the particle displacement is elliptical
in the sagittal plane. Also note that the velocity is independent of the frequency, and therefore the waves are
nondispersive.
may be larger than the slow (quasi-)transverse velocity
for the bulk material. Along neighboring directions
to these isolated directions, a pseudo-Rayleigh wave
solution exists which actually does not quite satisfy
the displacement decay condition at infinite depth.
(These pseudo-Rayleigh waves have energy vectors
with nonzero component perpendicular to the surface.)
In practice, these waves can actually be observed experimentally if the source-to-receiver distance is not too
great.
27.1.3 Guided Elastic Waves
in Layered Media
Elastic waves can also be guided in structures of finite
geometry. Guided waves in rods, beams, etc. are described in the literature. Of particular importance is the
case of guided waves in layered media such as composite materials and coatings [27.11]. The simplest case is
that of guided waves in plates. Consider an infinitely
wide plate of thickness h made of an anisotropic but
homogeneous medium (Fig. 27.3). Here, in addition to
the field equations of elastodynamics, there are two
traction-free boundary condition to be satisfied on the
two end planes x3 = 0, h. Once again seek solutions of
the form
u(r, t) = U exp[ik
3 x3 ] exp[ik(
1 x1 + 2 x2 − vt)] ,
(27.28)
Rayleigh Waves on Anisotropic Crystals
For a general anisotropic medium, the solution to
the Rayleigh wave problem is quite involved and
is typically only obtainable numerically. It has been
shown [27.10] that Rayleigh waves exist for every
direction in a general anisotropic medium, but their velocity depends on the propagation direction. In some
cases, the decay term 3 can be complex and not
just pure imaginary, which means that the decay with
x3 can be damped oscillatory. Along certain isolated
directions, the Rayleigh surface wave phase velocity
which represents an inhomogeneous plane wave propagating parallel to the plane of the plate with an
amplitude variation along the thickness direction given
by the 3 term. Again, as for the surface wave case, 3 is
at this point undetermined along with the wave velocity
v, but the depth decay condition is no longer valid. As
in the Rayleigh wave problem, solving the Christoffel
equation will lead to six roots for 3 (three pairs of complex conjugates), but now all of these are admissible.
Let the eigenvalues be denoted by (n)
3 , n = 1, 2, . . . , 6,
x1
x2
x1
x2
x3
l
x3
h
Fig. 27.2 Surface waves on a half-space
Fig. 27.3 Lamb waves in thin plates
Photoacoustic Characterization of Materials
and let U (n) be the corresponding eigenvectors. There
are therefore six plane-wave solutions to the Christoffel equation, each of which is called a partial wave. The
displacement field is therefore a linear combination of
the six partial wave solutions
Ωsym (ω,v,vL ,vT ) = (k2−β 2 )2 cos(αh/2) sin(βh/2)
+ 4k2 αβ sin(αh/2) cos(βh/2)
=0 ,
(27.29)
where
σi3 = (ik)
6 Ci3kl αn Uk(n) l(n) exp −ik
(n)
3 x3
n=1
× exp [ik (
1 x1 + 2 x2 − vt)] .
(27.30)
Using the above in the traction-free boundary conditions leads to a set of six homogenous equations:
dα = 0 ,
(27.31)
where the d matrix is now 6 × 6 and is given by
dmn
(1,2,3)
dmn
= (4,5,6)
dmn
(n)
= C3mkl Uk(n) l(n) eik
3 h
,
The first of the two dispersion relations corresponds to
symmetric modes, and the second gives rise to antisymmetric modes. These dispersion relations are quite
problematic because α, β can be real or complex depending on whether the phase velocity is less than or
greater than the bulk longitudinal or bulk shear wave
speeds in the material. Numerical solutions to the dispersion relations indicate that Lamb waves are highly
dispersive and multimodal. Figure 27.4 shows Lamb
wave dispersion for an isotropic aluminum plate.
12 000
10 000
(27.32)
8000
where for convenience of notation we define (n)
1:2
= 1:2 .
Nontrivial solutions for the weighting constants are obtained if
det(dmn ) = 0 .
1/2
v2
α = ik 1 − 2
,
vL
1/2
v2
β = ik 1 − 2
.
vT
Lamb wave phase velocity (m/s)
(1,2,3)
= C3mkl Uk(n) l(n)
dmn
(no sum over n intended here)
(4,5,6)
dmn
(27.33)
This provides the dispersion relation for the guided
waves. Note that, unlike for bulk waves and surface
waves, now the solution depends on the wavenumber k.
Therefore, we can now expect dispersive solutions
where the velocity will depend on frequency.
Guided Waves in Isotropic Plates
For an isotropic plate, one can show that the above leads
to so-called Lamb waves. Lamb wave dispersion parti-
6000
S0
4000
2000
0
A0
0
2
4
6
8
10
f h (MHz mm)
Fig. 27.4 Lamb-wave dispersion curve for an aluminum
plate. The horizontal axis is the frequency–thickness
product and the vertical axis is the phase velocity.
The fundamental antisymmetric mode A0 , the fundamental symmetric mode S0 , and higher-order modes are
shown
Part C 27.1
+ 4k2 αβ cos(αh/2) sin(βh/2)
(27.34)
=0 ,
n=1
where αn are weighting constants. The corresponding
stress components σi3 can then be readily expressed as
775
tions into two separate dispersion relations [27.7]
Ωasym (ω,v,vL ,vT ) = (k2−β 2 )2 sin(αh/2) cos(βh/2)
6 αn U (n) exp ik
(n)
u(r, t) =
3 x3
× exp [ik (
1 x1 + 2 x2 − vt)] ,
27.1 Elastic Wave Propagation in Solids
776
Part C
Noncontact Methods
Part C 27.1
Guided Waves in Multilayered Structures
Consider the N-layer structure on a substrate shown in
Figure 27.5. Acoustic waves may be coupled into the
structure either via air or a coupling liquid on the top
surface. We are interested in the guided plane acoustic waves that can be supported in such a system with
propagation in the plane of the structure. The six partial wave solutions obtained in Sect. 27.1.3 are valid for
a single layer, and these can be used to assemble the solution to the multilayer problem. The solution approach
is to determine the partial wave solutions for each layer,
and thereby the general solution in each layer as a linear combination of these partial wave solutions. We
then impose traction and displacement boundary and
continuity conditions at the interfaces. This is most
effectively done by means of the transfer matrix formulation [27.12, 13]. For this purpose, a state vector is
created consisting of the three displacements and the
three tractions that are necessary to ensure continuity
conditions:
S = (u 1 u 2 u 3 σ33 σ32 σ31 )T .
(27.35)
This vector must be continuous across each interface.
For any single layer, following (27.29, 30), we have the
state vector in terms of the weighting constants as follows:
S = D(x3 ) (α1 α2 α3 α4 α5 α6 ) ,
T
(27.36)
where the common term exp[ik(
1 x1 + 2 x2 − vt)] is
omitted for simplicity, and the matrix D(x3 ) is determined either analytically or numerically given the
material properties and frequency and wavenumber.
Note that the above state vector can be used for a substrate (treated as a half-space) by recognizing that in the
R (θ)
θ
Coupling water/air
Top
Layer 1
h1
h2
Layer 2
..
.
Plane wave
hn
Layer N
Substrate: half-space
x3
Fig. 27.5 Waves in layered structures
T (θ)
x1
Phase velocity (m/s)
8000
6000
Longitudinal velocity of Ti
4000
Shear velocity of Ti
2000
0
2
4
6
8
10
f h (MHz mm)
Fig. 27.6 Guided wave dispersion curves for an aluminum
layer on a titanium half-space (Al/Ti)
substrate layer the radiation condition is valid, which
means that for this last layer only three partial waves
are admissible. For a single layer of finite thickness, the
state vector at the two sides are related through direct
elimination of the weighting constants vector:
[S(−) (x3 = 0)]
= [D(x3 = 0)][D(x3 = h)]−1 [S(+) (x3 = h)]
≡ [T1 ][S(+) (x3 = h)] ,
(27.37)
where T1 is called the transfer matrix of the layer. For
an N-layer system, it readily follows from continuity
conditions that the state vector at the top and bottom
surfaces are related through
[S(−) ] = [T1 ][T2 ][T3 ] . . . [T N ][S(+) ] ≡ [T][S(+) ] ,
(27.38)
where T is called the global transfer matrix of the
N-layer system. Given the boundary conditions for the
top and bottom surfaces, or the radiation condition if the
bottom layer is a substrate (half-space), the above provides the appropriate dispersion relations for the various
guided-wave modes possible. This can be solved numerically for a given system. For illustrative purposes,
Fig. 27.6 shows the guided-wave dispersion curves for
an aluminum layer on a titanium substrate.
27.1.4 Material Parameters Characterizable
Using Elastic Waves
Since elastic wave propagation in a solid depends on
the material properties and the geometry of the struc-
Photoacoustic Characterization of Materials
measurements can often be made independent of the
support conditions of the structure. An example of this
will be seen in section Sect. 27.4.2 on photoacoustic
characterization of ultrathin films.
It should be noted that techniques based on interrogation using linear elastic waves can only access stiffness properties and cannot in general reveal information
about the strength of a material. If large-amplitude
stress waves can be generated, material nonlinearity can
be probed. However, we will not address this issue here
since photoacoustic generation is generally kept in the
so-called thermoelastic regime where the stress waves
are typically of small amplitude.
27.2 Photoacoustic Generation
Photoacoustics arguably traces its history back to
Alexander Graham Bell, but the field really got its
impetus in the early 1960s starting with the demonstration of laser generation of ultrasound by White [27.14].
Since then, lasers have been used to generate ultrasound
in solids, liquids, and gases for a number of applications. A comprehensive review of laser generation of
ultrasound is given in Hutchins [27.3] and Scruby and
Drain [27.1]. Here we will restrict attention to the generation of ultrasound in solids using pulsed lasers.
The basic mechanisms involved in laser generation
of ultrasound in a solid are easy to outline. A pulsed
laser beam impinges on a material and is partially or
entirely absorbed by it. The optical power that is absorbed by the material is converted to heat, leading
to rapid localized temperature increase. This results in
rapid thermal expansion of a local region, which in turn
leads to generation of ultrasound into the medium. If
the optical power is kept low enough that the material does not melt and ablate, the generation regime is
called thermoelastic (Fig. 27.7a). If the optical power
is high enough to lead to melting of the material and
plasma formation, once again ultrasound is generated,
but in this case via momentum transfer due to material
ejection (Fig. 27.7b). The ablative regime of generation
is typically not acceptable for nondestructive characterization of materials, but is useful in some process
monitoring applications especially since it produces
strong bulk wave generation normal to the surface. In
some cases where a strong ultrasonic signal is needed
but ablation is unacceptable, a sacrificial layer (typically
a coating or a fluid) is used either unconstrained on the
surface of the test medium or constrained between the
medium and an optically transparent plate. The sacrificial layer is then ablated by the laser, again leading
to strong ultrasound generation in the medium due to
momentum transfer.
27.2.1 Photoacoustic Generation:
Some Experimental Results
Before delving into the theory of photoacoustic generation, it is illustrative to look at some of the kinds of
ultrasonic signals that can be generated using photoacoustic generation.
Photoacoustic Longitudinal and Shear Wave
Generation Using a Point-Focused Laser Source
Figure 27.8 shows the surface normal displacement at
the epicentral location generated by a point-focused
thermoelastic source and measured using a homodyne
interferometer (described in Sect. 27.3.2). The arrival
a)
b)
Thermoelastic
expansion
Thermoelastic expansion
and momentum transfer
due to material ejection
x3
x1
Ablation
Generating
laser
Generating
laser
Fig. 27.7a,b Laser generation of ultrasound in (a) the thermoelastic
regime and (b) the ablative regime
777
Part C 27.2
ture, elastic waves can be used to measure some of these
parameters. For instance, by measuring the bulk wave
speeds of an anisotropic medium in different directions,
it is possible to obtain the elasticity tensor knowing the
density of the material. Using guided acoustic waves
in multilayered structures, it may be possible to infer
both material stiffnesses as well as layer thicknesses.
The primary advantage of using elastic waves over performing standard load–deflection type of measurements
arises from the fact that these measurements can be
made locally. That is, while load–deflection measurements require accurate knowledge of the boundary or
support conditions of the entire structure, elastic wave
27.2 Photoacoustic Generation
778
Part C
Noncontact Methods
0
Epicentral
displacement
–8
–10
Part C 27.2
–12
–14
Thermoelastic
generation
Longitudinal wave
arrival
–16
0.8
1
1.2
1.4
1.6
1.8
2
2.2
Time (μs)
Fig. 27.8 Experimentally measured epicentral surface normal displacement
of a longitudinal wave is seen distinctly, followed by
a slowly increasing wash, until the shear wave arrives.
a)
The directivity (i. e., the wave amplitude at different angles to the surface normal) of the longitudinal
and shear waves generated by a thermoelastic source
have been calculated theoretically and measured experimentally by a number of researchers [27.1]. The
longitudinal and shear wave directivity using a shear
dipole model (described later) for the thermoelastic
laser source have been obtained using a mass–spring
lattice elastodynamic calculation [27.15] and are shown
in Fig. 27.9. It is seen that, for thermoelastic generation, longitudinal waves are most efficiently generated
in directions that are at an angle to the surface normal.
Epicentral longitudinal waves are much weaker. This is
consistent with the results of other models as well as
with those from experiments [27.16].
Photoacoustic Rayleigh Wave Generation
Using a Point- and Line-Focused Laser Source
Thermoelastic generation of Rayleigh waves has been
extensively studied (see Scruby and Drain [27.1]).
a) Displacement (arb. units)
90
120
60
150
30
180
0
b) Displacement (arb. units)
Laser source
b)
Rayleigh wave
90
120
60
150
30
180
0
Laser source
Fig. 27.9a,b Calculated directivity pattern of thermoelastic laser generated ultrasound: (a) longitudinal waves and
(b) shear waves
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Time (μs)
Fig. 27.10a,b Rayleigh wave generation using a pointfocused laser source. (a) Experimental results for surface
normal displacements. (b) Theoretical calculations of the
surface normal (solid) and horizontal (dotted) displacements
Photoacoustic Characterization of Materials
27.2 Photoacoustic Generation
779
Displacement (arb. units)
a) Displacement (arb. units)
5
0
0
5
10
15
20
25
–5
–15
Rayleigh wave
0
2
4
6
8
Time (μs)
Photoacoustic Guided-Wave Generation
in Multilayered Structures
Thermoelastic generation of ultrasound on multilayered
structures has also been demonstrated, motivated by potential applications to the characterization of coatings.
In these cases, again the various guided modes are gen-
b) Displacement (arb. units)
0.1
0
–0.1
Rayleigh wave
–0.2
–0.3
0
2
a thin aluminum plate. The surface normal displacements
at some distance from the generating source shows the
dispersive nature of Lamb waves
4
a) Displacement (arb. units)
6
8
Time (μs)
Fig. 27.11a,b Surface normal displacement showing a monopolar Rayleigh wave from a thermoelastic line source:
(a) theoretical and (b) experimental
Shown in Fig. 27.10a are measurements of the far-field
surface normal displacement made using a homodyne interferometer (discussed in Sect. 27.3.2). Figure 27.10b shows the theoretically calculated surface
displacements in the far field of a thermoelastic
point source, using a shear-dipole model [27.15].
A strong bipolar Rayleigh wave is seen to be generated by the thermoelastic source. If the laser source
is a line source rather than a point-focused source,
the Rayleigh wave becomes a monopolar pulse,
as shown both theoretically and experimentally in
Fig. 27.11 [27.15].
Photoacoustic Lamb Wave Generation
Thermoelastic Lamb wave generation in thin plates has
been experimentally studied by Dewhurst et al. [27.17],
and has been modeled by Spicer et al. [27.18]. Figure 27.12 shows the Lamb waves that are generated by
a single thermoelastic line source on a thin aluminum
plate. The detection system used was a broadband twowave mixing interferometer (Sect. 27.3.2). The figure
shows the dispersive nature of Lamb wave propagation.
0
200
400
600
800
Time (ns)
600
800
Time (ns)
b) Displacement (arb. units)
0
200
400
Fig. 27.13a,b Thermoelastic generation on a 2.2 μm Ti
thin-film coating on an aluminum substrate. Surface normal displacement at a distance of 1.5 mm (a) measured
experimentally and (b) predicted by the theoretical model
Part C 27.2
Fig. 27.12 Thermoelastically generated Lamb waves in
–10
–20
30
Time (μs)
780
Part C
Noncontact Methods
Part C 27.2
erally dispersive. Murray et al. [27.19] have performed
comparisons of theoretical and experimental signals in
layered structures on a substrate. High-frequency ultrasonic guided waves were generated with a miniature
Nd:YAG laser with a 1 ns pulse width and 3 μJ per
pulse, focused down to a point source of about 40 μm
diameter. Figure 27.13a shows the ultrasonic surface
displacements measured using a broadband stabilized
Michelson interferometer (described in Sect. 27.3.2) at
a distance of 1.5 mm from the laser source. The specimen was a 2.2 μm Ti coating on aluminum. Also shown
in Fig. 27.13b are the theoretically expected signals using a thermoelastic model for the two-layer case. It is
seen that the thermoelastic model adequately captures
the experimental behavior.
From these examples, it is clear that photoacoustic
generation of bulk and guided waves is technically feasible using pulsed laser sources, and theoretical models
for the process are well established. In the next section,
the basic theoretical models for photoacoustic generation are outlined.
27.2.2 Photoacoustic Generation: Models
It is important to characterize the ultrasound generated
by laser heating of a material in order to determine
the amplitude, frequency content, and directivity of the
ultrasound generated. In general, models are also useful in extracting material property information from the
measured data.
There are two modes of photoacoustic generation
in solids: ablative and thermoelastic. If the material
ablates, the ultrasound that results from momentum
transfer can be modeled as arising from a normal impulsive force applied to the surface. Analytical solutions to
this problem can be obtained by appropriate temporal
and spatial convolution of the elastodynamic solution
for a point impulsive force on a half-space [27.7].
Recently, a complete model of ultrasound generation
in the ablative regime has been given by Murray
et al. [27.20]. As ablative generation is typically not
used in nondestructive evaluation, we will not explore
this further here. We will only consider thermoelastic
generation.
The basic problem of thermoelastic generation of
ultrasound can be decomposed into three subproblems:
(i) electromagnetic energy absorption by the medium
(ii) the consequent thermal diffusion problem with heat
sources (due to the electromagnetic energy absorbed)
(iii) the resulting elastodynamic problem with volumetric sources (due to thermal expansion)
There are two important cases that are relevant to materials characterization:
(i) bulk-wave photoacoustics where typically onedimensional bulk waves of GHz frequency range
are launched using femtosecond pulsed laser
sources to characterize thin films and coatings
(ii) guided-wave photoacoustics where nanosecond focused laser sources are used to launch kHz to MHz
ultrasonic waves
Guided-Wave Photoacoustic Generation
For simplicity a fully decoupled linear analysis for
homogeneous, isotropic materials is considered. The
optical energy that is absorbed depends on the wavelength of the laser light and the properties of the
absorbing material. The optical intensity variation with
depth inside an absorbing medium that is illuminated
by a light beam at normal incidence is given by an
exponential decay relation
I (x1 , x2 , x3 , t) = I0 (x1 , x2 , t) exp(−γ x3 ) ,
(27.39)
where I0 (x1 , x2 , t)is the incident intensity distribution
at the surface (which is a function of the laser parameters) and γ is an absorption coefficient characteristic
of the material for the given wavelength of light. The
optical energy absorbed by the material leads to a distributed heat source in the material given by
q(x1 , x2 , x3 , t) = q0 (x1 , x2 , t)γ exp(−γ x3 ) ,
(27.40)
where q0 is proportional to I0 and has the same spatial
and temporal characteristics as the incident laser source.
The corresponding thermal problem is then solved for
the given thermal source distribution using the equations of heat conduction
∂T
(27.41)
= κ∇ 2 T + q ,
ρC
∂t
where T is the temperature, ρ is the material density,
C is the heat capacity at constant volume, and κ is
the thermal diffusivity. The necessary thermal boundary conditions arise from the fact that there is no heat
flux across the surface, and initially the medium is at
uniform temperature.
The temperature distribution can be calculated for
a given laser source and material by solving the heat
conduction equation (27.41). For most metals, heat diffusion can be significant and needs to be taken into
Photoacoustic Characterization of Materials
u = ∇φ + ∇ × ψ ,
(27.42)
where φ and ψ are the scalar and vector potentials,
respectively. The equations of motion including the volumetric expansion source then become
1
φ̈ = φT ,
vL2
1
∇ 2 ψ − 2 ψ̈ = 0 ,
vT
∇2φ −
(27.43)
where vL and vT are the longitudinal and shear wave
speeds of the material, respectively, and a superposed
dot indicates time differentiation. The temperature rise
from the laser energy absorbed leads to a volumetric
expansion source given by
φT =
3λ + 2μ
αT T ,
λ + 2μ
(27.44)
where αT is the coefficient of linear thermal expansion,
and λ and μ are the Lamé elastic constants of the material. The above wave equations need to be solved along
with the boundary conditions that the surface tractions
vanish.
Given the laser source parameters, the resulting
temperature and elastodynamic fields are obtained
from the above system of equations using transform
techniques [27.21, 22]. The heat conduction and the
elastodynamic equations are transformed using onesided Laplace transform in time, and either a Fourier
(for a line source) or Hankel (for a point source) transform in space. Closed-form solutions can be obtained
analytically in the transformed domain, and numerically
inverted back into the physical domain [27.21–23].
For most metallic materials, the absorption coefficient is high enough that the optical energy does
not penetrate very much into the material. The optical penetration depth defined as 1/γ is on the order
of a few nanometers for most metals over the optical
wavelengths typically used for laser generation of ultrasound. If, in addition, the time scale of interest is
such that significant thermal diffusion does not occur,
and therefore the volumetric thermoelastic expansion
source is confined to the surface region, it has been
shown that the volumetric sources can be replaced by
an equivalent traction boundary condition on the surface. Scruby et al. [27.24] have argued that the relevant
elastodynamic problem is that of shear dipoles acting
on the surface of the body. Their argument was based
on the consideration that a point expansion source in
the interior of a solid can be modeled as three mutually orthogonal dipoles [27.7], and this degenerates into
a pair of orthogonal dipoles as the expansion source
moves to a free surface (Fig. 27.7a). This approach was
given a rigorous basis in the form of the surface center
of expansion (SCOE) model proposed by Rose [27.25],
which predicts all the major features that have been
observed in thermoelastic generation.
Specifically, if the optical penetration depth is very
small (i. e., γ → ∞), and the laser beam is assumed
to be focused into an infinitely long line along the
x1 -direction, and with a delta-function temporal dependence, the resulting heat source simplifies to
q(x1 , x2 , x3 , t) = Q 0 δ(x1 )δ(x3 )δ(t) ,
(27.45)
where Q 0 is the strength of the heat source proportional
to the laser energy input. If thermal diffusion is also
neglected, the resulting simplified problem can be explicitly solved [27.21, 23]. The corresponding in-plane
stresses are given by [27.23]
σ31 = Dδ (x1 )H(t) ,
(27.46)
where a prime indicates differentiation with respect to
the argument, and H(t) is the Heaviside step function. The above indicates that the shear dipole model
of Scruby et al. [27.24] is indeed valid in this limit of no
thermal diffusion and no optical penetration. The dipole
magnitude D is given by [27.23]
D=
αT Q 0
2μ
(3λ + 2μ)
.
λ + 2μ
ρC
(27.47)
Solutions to the more general case where the temporal
and spatial characteristics are more typical of real laser
pulses can be readily obtained from the above solution using a convolution over space and time. If optical
penetration depth is significant or if thermal diffusion
is important, solutions to the complete system of equations will have to be obtained numerically [27.22, 23].
The shear-dipole model can also be extended to
multilayered structures by using the transfer matrix formulation described in Sect. 27.1.3. Murray et al. [27.19]
have shown results for guided-wave photoacoustic generation in a two-layer system consisting of a 2.2 μm Ti
781
Part C 27.2
account by solving the full heat conduction equation.
For insulators, heat conduction may be neglected and
the resulting adiabatic temperature rise is readily obtained by setting κ → 0 in (27.41).
Next the elastodynamic problem is considered. For
isotropic materials, the equations of elastodynamics can
be cast in terms of the scalar and vector displacement
potentials [27.7]. The elastic displacement field u can
be decomposed into
27.2 Photoacoustic Generation
782
Part C
Noncontact Methods
coating on an aluminum substrate. Typical results are
shown in Fig. 27.13b.
Part C 27.2
Bulk-Wave Photoacoustic Generation
For photoacoustic characterization of very thin films
and coatings, an alternate approach is to use very highfrequency (very short-wavelength) bulk longitudinal
waves that are launched into the depth of the specimen.
This technique has come to be known as picosecond ultrasonics [27.26]. This necessitates the use of unfocused
femtosecond laser sources that impinge on the specimen
surface. If the diameter of the heating region (typically
tens of μm) is much larger than the film thickness (typically nanometers), and the optical skin depth is much
less than the film thickness, a one-dimensional thermoelastic model can be used [27.27, 28]. The temperature
field T therefore only varies with the depth direction
x, and the only nonzero displacement component is
the one along the x-direction, denoted by u. To solve
the complete thermoelastic problem in multilayer structures, a photothermoelastic transfer matrix approach
is adopted, as shown in Fig. 27.14. Following Miklos
et al. [27.29] we apply the classical partially coupled
thermoelastic differential equations for the heat transfer and wave propagation in homogeneous isotropic or
cubic media as follows:
κ
∂T
∂2 T
− ρC
= −q
2
∂t
∂x
∂2u
∂2u
∂T
c 2 −ρ 2 = λ
,
∂x
∂x
∂t
be expressed as λ = cαT , where αT is the thermal expansion coefficient, and q is the absorbed energy due
to laser irradiation (27.40). The linear coupled thermoelastic equations (27.48) hold for every thin layer in the
multilayer structure, with total thickness h, as shown in
Fig. 27.14. The boundary conditions are assumed to be
no heat transfer or tractions across the surfaces at x = 0
and x = h. It is also assumed that all thin layers are in
perfect contact, which ensures continuity of displacement, temperature, heat flux J = −κ∂T /∂x, and elastic
stress σ = c∂u/∂x − λT at every interface.
The coupled problem given by (27.48) can be
readily solved using the transfer-matrix formulation
a) Reflection coefficient change (arb. units)
1.2
1
0.6
where ρ is the density, κ is the thermal conductivity, C is
the specific heat per unit volume, c is the effective elastic stiffness, λ is the thermal stress tensor, which can
Supported film
0.4
Unsupported film
0.2
0
(27.48)
Acoustic echoes
0.8
0
100
200
300
400
Delay time (ps)
b) Elastic strain (10– 4)
Al
2
10 ps
30 ps
50 ps
70 ps
1
y
Pump laser
Layer 1
Layer 2
···
Layer n-1
Layer n
0
Si3N4
–1
Heat flux and elastic wave
d1
0
d2
x1
0
dn–1
x2
dn
xn–1
xn (h) x
Fig. 27.14 Geometry of the photothermoelastic model for multilayer structures
100
200
300
400
500
600
Depth (nm)
Fig. 27.15 (a) Simulated transient optical reflectivity
change due to femtosecond laser heating for both supported and unsupported 300 nm aluminum and 300 nm
silicon nitride double-layer thin films; (b) corresponding
thermoelastic strain pulse shape and propagation in the
unsupported double-layer thin film
Photoacoustic Characterization of Materials
properties of the materials determine the thermoreflectivity signal.
27.2.3 Practical Considerations: Lasers
for Photoacoustic Generation
Several different types of lasers are commercially available. The material in which the ultrasound is to be
generated, and the desired frequency content of the
ultrasound, dictate the type of laser to use. The generating laser wavelength, its energy, its pulse duration,
and its repetition rate are all parameters that can be
selected based on applications. The repetition rate is
important primarily for speed of testing. The pulse
duration along with other parameters such as the spatial extent of the generating volume/area dictate the
frequency content of the ultrasound generated. A modulated continuous-wave laser is possibly adequate for
low-frequency (order of tens of kHz) generation. Typically, laser pulses on the order of 10 ns are used for
the generation of ultrasound in the 100 kHz–10 Mhz frequency range. For even higher frequencies, pulse widths
on the order of 100 ps (resulting in ultrasound in the order of 100 MHz frequency range) or even femtosecond
(for GHz range) laser systems may be necessary.
The optical power required depends on the material
to be tested and whether laser damage is acceptable or
not. Lasers with optical power ranging from nanojoules
to microjoules to several hundred millijoules have all
been used to produce ultrasound in structures.
Finally, the choice of laser wavelength primarily depends on the material absorption. Laser wavelengths
ranging from the ultraviolet to the infrared and higher
have been used for laser generation of ultrasound.
27.3 Optical Detection of Ultrasound
Optical detection of ultrasound is attractive because it
is noncontact, with high detection bandwidth (unlike
resonant piezoelectric transducers), and it can provide
absolute measurement of the ultrasonic signal. In this
section, the ways in which ultrasonic signal information
can be encoded onto a light beam are first described, followed by a discussion of two methods of demodulating
the encoded information using optical interferometry.
For a more complete review of optical detection of ultrasound, the reader is referred to a number of excellent
review articles on the subject [27.4–6].
783
27.3.1 Ultrasonic Modulation of Light
To monitor ultrasound optically, a light beam should
be made to interact with the object undergoing such
motion. Interaction of acoustic waves and light waves
in transparent media has a long history (see, for
instance, [27.32]), and will not be reviewed here. Attention will be confined here to opaque solids that either
reflect or scatter light. In this case, the light beam can
only be used to monitor the surface motion associated
with the ultrasound.
Part C 27.3
as described in Sect. 27.1.3 but now in the Laplacetransformed (over time) domain. As an illustrative example, bulk-wave photoacoustic generation in a 300 nm
aluminum and 300 nm silicon nitride double-layer
film with and without silicon substrate are shown in
Fig. 27.15. Figure 27.15a shows the simulation of the
transient thermoelastic strain that propagates in the unsupported film. The laser pulse duration used in the
calculation is a 100 fs Hanning function [27.29]. The
elastic strain generated on the near surface propagates
toward the interface with the velocity of longitudinal
waves in aluminum and arrives at the Al and Si3 N4
interface at about 50 ps. Part of the energy is transmitted into the silicon nitride layer and the rest is
reflected back toward the front surface, as shown in
Fig. 27.15a.
Also shown in Fig. 27.15b is the transient change
in the surface reflectivity due to temperature and strain
changes induced by the laser. It should be pointed out
that, in picosecond ultrasonics, the transient reflectivity is typically monitored in a snapshot manner using
a femtosecond laser pulse that is progressively time delayed with respect to the photoacoustic generation pulse
(see [27.30, 31], for instance). This is necessitated by
the very high temporal resolutions needed to monitor
the transient photothermoacoustic phenomena that arise
from femtosecond laser irradiation. The initial transient
rise and subsequently exponential-like decay process
are due to the thermoreflectivity changes. The superimposed multiple spikes are due to the acoustic waves
that are reflected from the Al/Si3 N4 interface and the
Si3 N4 /silicon or air interface. The elastic properties and
density of each layer affect the acoustic wave arrival
time as well as the signal amplitude, while the thermal
27.3 Optical Detection of Ultrasound
784
Part C
Noncontact Methods
Typically laser beams are used as the optical source,
and these can provide monochromatic, linearly polarized, plane light beams. The electric field of such beams
can be expressed as
E = a exp[i(ωopt t − φ)] ,
(27.49)
Part C 27.3
where E is the electric field of amplitude a, frequency
ωopt , and phase φ. It is important to note that extant photodetectors cannot directly track the optical phase (the
optical frequency ωopt is just too high), and as such only
the optical intensity (proportional to P = E E ∗ = a2 ,
where ∗ represents the complex conjugate) can be directly measured.
There are a number of ways in which ultrasound can affect the light beam. These can be
broadly classified into intensity-modulated techniques
and phase/frequency-modulated techniques.
Intensity Modulation Induced by Ultrasound
The intensity of the reflected light beam can change due
to ultrasound-induced changes in the refractive index
of the medium, and this can be monitored directly using a photodetector. Though these changes are typically
very small for most materials, this method has been
used successfully in picosecond ultrasonics [27.30] to
measure the properties of thin films [27.31] and nanostructures [27.33]. Another intensity-based technique
utilizes the surface tilt associated with ultrasonic motion [27.34]. The probe light beam is tightly focused
onto an optically reflective object surface. A partial
aperture (usually called a knife edge in this context)
is placed behind a recollimating lens located in the
path of the reflected beam prior to being focused onto
a photodetector. The reflected light beam will undergo
a slight tilt due to the ultrasonic displacement. This in
turn will cause varying portions of light to be blocked
by the knife edge, resulting in an intensity change at
the photodetector. A third class of intensity-based techniques is applicable to continuous or tone-burst surface
acoustic wave (SAW) packets of known frequency and
velocity. In this case, the ultrasonic surface displacement acts like a surface diffraction grating, and an
incident plane light beam will undergo diffraction in
the presence of the SAW wave packet. A photodetector placed in the direction of either of the two expected
diffracted first-order beams can be used to monitor
the SAW wave packet [27.35]. Recently, diffraction
detection has been used to measure the mechanical
properties of thin films [27.36]. In general, intensitymodulated techniques are typically less sensitive than
phase/frequency-modulated techniques. As such, their
use in nondestructive characterization has been limited.
The reader is referred to the review papers [27.4, 5] for
further information on intensity-modulation techniques.
Phase or Frequency Modulation
Induced by Ultrasound
Ultrasonic motion on the surface of a body also affects the phase or frequency of the reflected or scattered
light. For simplicity, consider an object surface illuminated at normal incidence by a light beam, as shown in
Fig. 27.16. Let the surface normal displacement at the
point of measurement be u(t) due to ultrasonic motion,
where t is time. We shall assume that the surface tilt
is not so large that the reflected optical beam is tilted
significantly away. Therefore the object surface displacement just changes the phase of the light by causing
a change in the path length (equal to twice the ultrasonic normal displacement) that the light has to travel.
In the presence of ultrasonic displacement, the electric
field can therefore be expressed as
E s = as exp[i(ωopt t − 2kopt u(t) − ϕs )] ,
(27.50)
where kopt = 2π/λopt is the optical wavenumber, λopt
is the optical wavelength, and ϕs is the optical phase
(from some common reference point) in the absence of
ultrasound.
For time-varying phase modulation such as that
caused by an ultrasonic wave packet, it is also possible
to view the optical interaction with the surface motion
as an instantaneous Doppler shift in optical frequency.
To see this, note that (27.50) can be equivalently written in terms of the surface velocity V (t) = du/ dt as
follows:
E s = as exp[i(ω̃opt t − ϕs )] ,
(27.51)
u (x1, x2, t)
Incident
light
Reflected
light
Fig. 27.16 Phase modulation of light due to ultrasonic dis-
placement
Photoacoustic Characterization of Materials
where the instantaneous optical frequency is now given
by
't
ω̃opt t =
2V
ωopt 1 −
dt ,
c
(27.52)
0
27.3.2 Optical Interferometry
The phase of a single optical beam cannot be measured
directly since the optical frequency is too high to be
monitored directly by any extant photodetector. Therefore, a demodulation scheme has to be used to retrieve
phase-encoded information. There are a number of optical interferometers that perform this demodulation
(see [27.37] for a general discussion on optical interferometry). Here we will only consider two systems
that have found wide extensive application in photoacoustic metrology. Another common device that has
found extensive applications in photoacoustic metrology is the confocal Fabry–Pérot interferometer. Due to
space limitations, this will not be discussed here, and
the reader is referred to the review paper by Dewhurst
and Shan [27.6].
Reference-Beam Interferometers
The simplest optical interferometer is the two-beam
Michelson setup shown in Fig. 27.17. The output from
a laser is split into two at a beam splitter and one of
the beams is sent to the test object, and the other is sent
to a reference mirror. Upon reflection, the two beams
are recombined parallel to each other and made to interfere at the photodetector. The electric fields at the
photodetector plane can be written as
E r = ar exp[i(ωopt t − kopt L r )] ,
E s = as exp[i(ωopt t − kopt (L s + 2u(t)))] ,
(27.53)
(27.54)
where (i = r, s) refer to the reference and signal beams,
respectively. Here E i are the electric fields of the two
beams of amplitudes ai and optical frequency ωopt . The
phases φi = kopt L i are due to the different path lengths
L i that the two beams travel from a point of common
phase (say at the point just prior to the two beams
splitting at the beam splitter). Here, it is convenient to
consider the phase term for the signal beam as being
comprised of a static part kopt L s due to the static path
length, and a time-varying part due to the time-varying
ultrasonic displacement u(t). The total electric field at
the photodetector plane is then the sum of the fields of
the two beams, and the resulting intensity is therefore
obtained as
PD = Ptot {1 + M cos[kopt (L r − L s ) − 2kopt u(t)]} ,
(27.55)
Pi = ai2
where
are the optical intensities (directly proportional to the power in Watts) of the two beams
individually. In the last expression above, we have defined the total optical power Ptot = Pr + Ps . The factor
√
2 Pr Ps
M=
Ptot
is known as the modulation depth of the interference
and ranges between 0 (when one of the beams is not
present) to 1 (when the two beams are of equal intensity).
If the phase change due to the signal of interest
2kopt u(t) 1 – as is the case for typical ultrasonic displacements – the best sensitivity is obtained by ensuring
I
Photodetector
Laser
Signal beam
Reference beam
Fig. 27.17 Two-beam homodyne (Michelson) interferome-
ter
785
Δφ
Fig. 27.18 Two-beam interferometer output intensity as
a function of phase change. The largest variation in output
intensity for small phase changes occurs at quadrature
Part C 27.3
where c is the speed of light. The surface velocity associated with the ultrasonic motion therefore leads to
a frequency shift of the optical beam.
27.3 Optical Detection of Ultrasound
786
Part C
Noncontact Methods
Part C 27.3
that the static phase difference is maintained at quadrature, i. e., at kopt (L r − L s ) = π2 (Fig. 27.18). This can
be achieved by choosing the reference and signal beam
path lengths appropriately. The two-beam Michelson interferometer that is maintained at quadrature therefore
provides an output optical power at the photodetector
given by
PD = Ptot [1 + M(2kopt u(t))] ,
kopt u 1 . (27.56)
This shows that the output of a Michelson interferometer that is operated at quadrature is proportional to the
ultrasonic displacement. In reality, even the static optical path is not quite static because of low-frequency
ambient vibration that can move the various optical
components or the object around. If the signal of interest is high frequency (say several kHz or higher) –
which is the case for ultrasonic signals – it is possible to
use an active stabilization system using a moving mirror
(typically mounted on a piezoelectric stack) on the reference leg such that the static (or, more appropriately,
low-frequency) phase difference is always actively kept
constant by means of a feedback controller. The piezoelectric mirror can also be used to calibrate the full
fringe interferometric output by intentionally inducing
an optical phase change in the reference leg that is larger
than 2π. This will provide both the total power Ptot and
the modulation depth M. Therefore, an absolute measurement of the ultrasonic displacement can be obtained
from (27.56).
It is important to characterize the signal-to-noise
ratio (SNR), or equivalently the minimum detectable
displacement of the optical interferometer. There are
several possible noise sources in an optical detection
system. These include noise from the laser source, in
the photodetector, in the electronics, and noise in the
a)
Speckled object
Photodetector
Planar reference
b)
Speckled object
Photodetector
Wavefront-matched reference
Fig. 27.19a,b Ultrasound detection on rough surfaces. (a) Interference of speckled signal and planar reference beams is nonoptimal.
(b) Wavefront-matched interference
optical path due to ambient vibrations and thermal currents. Most of these noise sources can be stabilized
against or minimized by careful design and isolation,
leaving only quantum or shot noise arising from random
fluctuations in the photocurrent. Shot noise increases
with increasing optical power, and it therefore basically
sets the absolute limit of detection for optical measurement systems. It can be shown that the SNR of
a shot-noise-limited Michelson interferometer operating at quadrature is given by [27.5]
(
ηPtot
(27.57)
,
SNR = kopt MU
hνopt B
where η is the detector quantum efficiency, νopt is
the optical (circular) frequency in Hertz, h is Planck’s
constant, B is the detection bandwidth, and U is the
ultrasonic displacement. The minimum detectable ultrasonic signal can then be readily determined from
(27.57) based on the somewhat arbitrary criterion that
a signal is detectable if it is equal to the noise magnitude, i. e., if SNR = 1. For a detection bandwidth of
1 Hz, detector efficiency of 0.5, modulation depth M
of 0.8, and total collected optical power of 1 W from
a green laser (514 nm), the minimum detectable sensitivity is on the order of 10−17 m.
Of all possible configurations, the two-beam homodyne interferometer provides the best shot-noise
detection sensitivity as long as the object beam is specularly reflective. If the object surface is rough, the
scattered object beam will in general be a speckled
beam. In this case, the performance of the Michelson interferometer will be several orders of magnitude
poorer due to two factors. First, the total optical power
Ptot collected will be lower than from a mirror surface. Secondly, the mixing of a nonplanar object beam
(one where the optical phase varies randomly across
the beam) with a planar reference beam is not efficient
(Fig. 27.19a), and indeed could be counterproductive
with the worst-case situation leading to complete signal cancellation occurring. Therefore, interferometers
such as the Michelson, which use a planar reference
beam, are best used in the laboratory on optically
mirror-like surfaces. For optically scattering surfaces,
self-referential interferometers such as the adaptive
interferometers based on two-wave mixing in photorefractive crystals are preferred.
Dynamic Holographic Interferometers
This class of interferometers is based on dynamic holographic recording typically in photorefractive media.
Photoacoustic Characterization of Materials
(a) creation of optical intensity gratings due to coherent interference of the interacting beams, leading
to
(b) nonuniform photoexcitation of electric charges in
the PRC, which then diffuse/drift to create
(c) a space-charge field within the PRC, which in turn
creates
(d) a refractive index grating via the electro-optical effect, and which causes
(e) diffraction of the interacting beams
A net consequence of this is that at the output of the
PRC we have not only a portion of the transmitted
probe beam, but also a part of the pump beam which
is diffracted into the direction of the probe beam. The
pump beam diffracted into the signal beam direction
has the same wavefront structure as the transmitted signal beam. Since the PRC process has a certain response
time (depending on the material, the applied electric
field, and the total incident optical intensity), it turns out
that it is unable to adapt to sufficiently high-frequency
modulations in the signal beam. The PRC can only
adapt to changes in the incident beams that are slower
than the response time. This makes two-wave mixing in-
λ/2
PRC
BC
λ/2
terferometers especially useful for ultrasound detection.
High-frequency ultrasound-induced phase modulations
are essentially not seen by the PRC, and therefore the
diffracted pump beam will have the same wavefront
structure as the unmodulated signal beam. The transmitted signal beam, however, obviously will contain
the ultrasound-induced phase modulation. By interfering the diffracted (but unmodulated) pump beam with
the transmitted (modulated) signal beam (both otherwise with the same wavefront structure) one obtains
a highly efficient interferometer. Furthermore, any lowfrequency modulation in the interfering beams (such
as those caused by noise from ambient vibration, or
slow motion of the object) will be compensated for
by the PRC as it adapts and creates a new hologram. Two-wave mixing interferometers therefore do
not need any additional active stabilization against ambient noise.
Several different types of photorefractive two-wave
mixing interferometers have been described in the literature [27.40–42]. Here we will describe the isotropic
diffraction configuration [27.44] shown in Fig. 27.20.
For simplicity, optical activity and birefringence effects
in the PRC will be neglected.
Let the signal beam obtained from the scatter from
the test object be s-polarized. As shown in Fig. 27.20,
a half-wave plate (HWP) is used to rotate the incident
signal beam polarization by 45◦ leading to both s- and
p-polarized phase-modulated components of equal intensity given by
a
(27.58)
E s0 = √ exp{i[ωopt t − φ(t)]} .
2
A photorefractive grating is created by the interference
of the s-polarized component of the signal beam with
the s-polarized pump beam. The diffracted pump beam
(also s-polarized for this configuration of the PRC) upon
exiting the crystal is then given by [27.44]
a
E r = √ exp(iωopt t) exp(−αL/2)
2
× {[exp(γ L) − 1] + exp[−iφ(t)]} ,
(27.59)
BS
Signal beam
PD 2
Pump beam
PD 1
Fig. 27.20 Configuration of isotropic
diffraction setup (λ/2: half-wave
plate, PRC: photorefractive crystal,
BC: Berek compensator, BS: beam
splitter; PD: photodetector)
787
Part C 27.3
One approach is to planarize the speckled object beam
by using optical phase conjugation [27.38, 39]. The planarized object beam can then be effectively interfered
with a planar reference beam in a two-beam homodyne
or heterodyne interferometer. Alternatively, a reference
beam with the same speckle structure as the static object
beam can be holographically reconstructed for interference with the object beam containing the ultrasonic
information (Fig. 27.19b) [27.40–42]. This is most readily achieved by using the process of two-wave mixing in
photorefractive media [27.43].
Two-wave mixing is essentially a dynamic holographic process in which two coherent optical beams
(pump/reference and probe/signal beams) interact
within a photorefractive crystal (PRC). The process of
TWM can be briefly summarized as
27.3 Optical Detection of Ultrasound
788
Part C
Noncontact Methods
a)
Detection
beam splitter (PBS) oriented at 45◦ to the s- and pdirections, giving rise to two sets of optical beams
that interfere at the two photodetectors. The intensities
recorded at the two photodetectors are then given by (for
φ(t) π/2)
Ptot −αL 2γr L
+ 2 e2γr L {cos(γi L − φL )
e
e
PD1 =
4
+φ(t) sin(γi L − φL ) + sin(γi L)}
+ 2φ(t) sin φL + 1
Ptot −αL 2γr L
PD2 =
− 2 e2γr L {cos(γi L − φL )
e
e
4
+φ(t) sin(γi L − φL ) − sin(γi L)}
− 2φ(t) sin φL + 1 ,
(27.61)
Source
25 m
3
1
Part C 27.3
R
R
30 mm
70 mm
b)
0.32
R
0.24
0.16
S1
0.08
P1
P3
0
–0.08
–0.16
RR
–0.24
10
20
30
40
50
60
Time (μm)
Fig. 27.21a,b Photoacoustically generated waves detected on an un-
polished aluminum block using a two-wave mixing interferometer.
(a) Specimen configuration. (b) Optically detected ultrasonic signal.
The vertical axis is displacement in nanometers (R: direct Rayleigh
wave; RR: once reflected Rayleigh wave; P1: once reflected longitudinal wave; P3: three-times reflected longitudinal wave; S1: once
reflected shear wave)
where γ = γr + iγi is the complex photorefractive gain,
α is the intensity absorption coefficient of the crystal,
and L is the length of the crystal. The p-polarized component of the signal beam is transmitted by the PRC
undisturbed (except for absorption) and may be written
as
a
E s = √ exp(−αL/2) exp{i[ωopt t − φ(t)]} .
2
(27.60)
Upon exiting the PRC, the diffracted pump and the
transmitted signal beams are now orthogonally polarized. A Berek’s wave plate is interposed so as to
introduce an additional phase shift of φL in the transmitted signal beam to put the interference at quadrature.
The two beams are then passed through a polarizing
where Ptot = a2 is proportional to the optical power
collected in the scattered object beam. In the case of
a pure real photorefractive gain, quadrature is obtained
by setting φL = π/2. In this case, upon electronically
subtracting the two photodetector signals using a differential amplifier, the output signal is
(27.62)
S = Ptot e−αL eγ L − 1 ϕ(t) .
Since the phase modulation
φ(t) = 2kopt u(t) ,
the output signal is directly proportional to the ultrasonic displacement. The signal-to-noise ratio of the
two-wave mixing interferometer in the isotropic configuration for real photorefractive gain can be shown to
be [27.44]
(
ηPtot − αL
eγ L − 1
e 2 SNR = 2kopt U
1/2 .
hvopt
e2γ L + 1
(27.63)
It is clear that, the lower the absorption and the higher
the photorefractive gain, the better the SNR. Minimum
detectable sensitivities on the order of 10−15 m have
been reported on optically scattering surfaces using dynamic holographic interferometers [27.42].
As an illustration, Fig. 27.21 shows the ultrasonic
surface displacements monitored using a two-wave
mixing interferometer on an unpolished aluminum
block using a 500 mW laser source. The generation
was using a photoacoustic point source using a 15 mJ
Nd:YAG pulsed laser.
Photoacoustic Characterization of Materials
27.3.3 Practical Considerations: Systems
for Optical Detection of Ultrasound
put together by an experienced engineer. Of greater
interest are confocal Fabry–Pérot systems and the dynamic holographic interferometers, which work well
on unpolished surfaces not only in the laboratory
but also in industrial settings. These detection systems are commercially available from a number of
sources.
27.4 Applications of Photoacoustics
Photoacoustic methods have found wide-ranging applications in both industry and academic research.
Here we will consider some illustrative applications in
nondestructive flaw identification and materials characterization.
27.4.1 Photoacoustic Methods
for Nondestructive Imaging
of Structures
Photoacoustic techniques have been used for nondestructive flaw detection in metallic and composite
structures. Here we review a few representative example
applications in flaw imaging using bulk waves, surface
acoustic waves, and Lamb waves.
Flaw Imaging Using Bulk Waves
As discussed earlier, thermoelastic generation of bulk
waves in the epicentral direction is generally weak in
materials for which the optical penetration depth and
thermal diffusion effects are small. Therefore, laser ultrasonic techniques using bulk waves have been used
primarily for imaging of defects in composite structures
(where the penetration depth is large), or on structures
that are coated with a sacrificial film that enhances
epicentral generation. Recently, Zhou et al. [27.45]
have developed efficient photoacoustic generation layers which they have used in conjunction with an
ultrasonic imaging camera to image the interior of aluminum and composite structures (Fig. 27.22).
Lockheed Martin has recently installed a large-scale
laser ultrasonic facility for inspecting polymer-matrix
composite structures in aircraft such as the joint strike
fighter [27.46]. In this system, a pulsed CO2 laser was
used to thermoelastically generate bulk waves into the
composite part. A coaxial long-pulse Nd:YAG detection
laser demodulated by a confocal Fabry–Pérot was used
to monitor the back reflections of the bulk waves. The
system has been demonstrated on prototype F-22 inlet
ducts. Yawn et al. [27.46] estimate that the inspection
time using the noncontact laser system is about 70 min
as opposed to about 24 h for a conventional ultrasonic
squirter system.
Flaw Imaging Using Surface Acoustic Waves
Photoacoustic systems can also be used to generate and
detect surface acoustic waves on specimens such as the
aircraft wheel shown in Fig. 27.23a,b. Here the high de-
Fig. 27.22 Imaging of subsurface features in aluminum structures using photoacoustically generated bulk waves. The
subsurface features were 12.7 mm inside an aluminum block, and the feature size is on the order of 6.35 mm
789
Part C 27.4
Reference-beam
interferometers,
discussed
in
Sect. 27.3.2, are primarily laboratory tools which
work well typically only on highly polished reflective specimens. These systems can be very easily
27.4 Applications of Photoacoustics
790
Part C
Noncontact Methods
a)
b)
EDM notch
15 mm
11 mm
Part C 27.4
Laser generation
Fiber-optic
interferometer
probe
c) Surface displacement (nm)
d) Surface displacement (nm)
0.15
0.15
Direct rayleigh
0.1
0.11
0.07
Reflection
from crack
0.05
0.03
0
–0.05
–0.01
0
2
4
6
8
–0.05
10
Time (μs)
0
2
4
6
8
10
Time (μs)
e) Reflection coefficient
0.5
0.4
0.3
0.2
0.1
0
–0.1
–5
Actual crack position
0
5
10
15
20
25
Position (mm)
Fig. 27.23a–e Photoacoustic surface acoustic wave imaging. (a) Aircraft wheel part containing cracks. (b) Schematic of
the scanning setup. Signal from locations (c) without a crack and (d) with a crack indicated by presence of reflections.
(e) Reflection coefficient measured at different scanning locations of the wheel
gree of double curvature of the wheel makes the use of
contact transducers difficult. Huang et al. [27.47] used
laser generation along with dual-probe heterodyne interferometer detection. The presence of cracks along
Photoacoustic Characterization of Materials
Tomographic Imaging Using Lamb Waves
Tomographic imaging of plate structures using Lamb
waves is often desired when the test area is not directly
accessible and so must be probed from outside the area.
Computer algorithms are used to reconstruct variations
of a physical quantity (such as ultrasound attenuation)
within a cross-sectional area from its integrated projection in all directions across that area. Photoacoustic
tomographic systems using attenuation of ultrasound
for tomographic reconstruction need to take into account the high degree of variability in the generated
ultrasound arising from variation in the thermal absorption at different locations on the plate. A schematic
of the setup is shown in Fig. 27.24a. Narrow-band
Lamb waves were generated using an array of ther-
moelastic sources. Figure 27.24b shows a cross-section
of the simulated corrosion defect produced in epoxybonded aluminum plates. The specimen is composed
of two aluminum plates of thickness 0.65 mm and an
approximately 13 μm-thick epoxy film. Corrosion was
simulated by partially removing the surface of the bottom plate and inserting a fine nickel powder in the
cavity prior to bonding. Figure 27.24c,d show typical
narrow-band Lamb waves detected using the dual-probe
interferometer in the presence and absence of the inc) Amplitude (mV)
0.2
0.15
0.1
0.05
0
–0.05
–0.1
–0.15
–0.2
0
5
10
15
Time (μs)
5
10
15
Time (μs)
d) Amplitude (mV)
0.2
0.15
a)
0.1
YAG Laser
0.05
Photodiode
0
Dual-probe fiber-optic
interferometer
–0.05
–0.1
Defects
Specimen
Oscilloscope
b)
Computer
display
–0.15
GPIB
Line
source
Rotation and
translation stages
5.5 mm
0.65 mm
0.65 mm
Aluminum
plates
0.22 mm
Ni powder
Bonded together
by epoxy film
Fig. 27.24a–e Photoacoustic Lamb-wave tomography.
(a) Setup. (b) Cross-section of bonded thin plates con-
taining an inclusion. Typical Lamb-wave signals after
band-pass filtering (c) without defect, (d) with the defect
between the two detecting points. (e) Superposed image
of the tomographic image (solid line) and a conventional
ultrasonic C-scan image
–0.2
e)
0
791
Part C 27.4
the doubly curved location is indicated by the presence of reflected ultrasound signals in some locations
but not in others (Fig. 27.23c,d). A reflection coefficient,
calculated as the ratio of the reflected signal to the original signal power, is plotted in Fig. 27.23e and provides
a measure of the length of the crack. Such pitch-catch
approaches to detecting cracks using laser ultrasonics
are feasible on cracks that are large enough to provide
a sufficiently strong reflected signal.
27.4 Applications of Photoacoustics
792
Part C
Noncontact Methods
Part C 27.4
clusion. By tomographically scanning the plate, Nagata
et al. [27.48] were able to create a tomographic image
of the specimen, as shown in Fig. 27.24e. Also shown
superposed in Fig. 27.24e is an ultrasonic C-scan image
of the same sample obtained using a commercial scanning acoustic microscope. The size and the shape of the
tomographically reconstructed image is consistent with
that of the C-scan.
Scanning Laser Source Imaging
of Surface-Breaking Flaws
In the applications described thus far, photoacoustic
methods have been used in a conventional pitch-catch
ultrasonic inspection mode, except that lasers were used
to generate and detect the ultrasound. For detecting
very small cracks, the pitch-catch technique requires
that the crack reflect a significant fraction of the in-
Laser
Receiver source
a)
x2
Scanning
Crack
x1
x3
b) Interferometer signal (mV)
4
4
4
3
3
3
2
2
2
1
1
1
0
0
0
–1
–1
–1
–2
0
0.5
1
1.5
2
–2
2.5 3
Time (μs)
0.5
0
1
1.5
2
2.5 3
Time (μs)
–2
0
0.5
1
1.5
2
2.5 3
Time (μs)
c) Ultrasonic amplitude (mV)
6
II
5
Crack
4
I
3
III
2
1
0
0
1
2
3
4
5
6
SLS position (mm)
Fig. 27.25a–c The scanning laser source (SLS) technique. (a) Schematic of the SLS technique. (b) Ultrasonic surface
normal displacement as a function of time (in μs) at three locations of the scanning laser source – left: far from the defect;
center: close to the defect; and right: behind the defect. (c) Typical characteristic signature of ultrasonic peak-to-peak
amplitude versus SLS location as the source is scanned over a surface-breaking defect
Photoacoustic Characterization of Materials
793
tering of the generated signal by the defect (zone III in
Fig. 27.25c).
The variation in signal amplitude is due to two
mechanisms:
(a) near-field scattering by the defect
(b) changes in the conditions of generation of ultrasound when the SLS is in the vicinity of the defect
As such, the SLS technique is not very sensitive to
flaw orientation [27.50]. In addition to the amplitude signature shown above, spectral variations in the
detected ultrasonic signal also show characteristic features [27.50]. Both amplitude and spectral variations
can form the basis for an inspection procedure using
the SLS technique. The SLS technique has been applied
to detect small electric discharge machined notches in
titanium engine disk blade attachment slots [27.49].
27.4.2 Photoacoustic Methods
for Materials Characterization
Photoacoustic metrology has been used to characterize the properties of materials ranging from the macroto the microscale. Here we describe applications to
thin-film and coating characterization and to the determination of material anisotropy.
Characterization of Material Anisotropy
Photoacoustic methods have been used by a number
of researchers to investigate the anisotropy of materials [27.51–55]. Both point- and line-focused laser
Specimen
y
Circular array
receiver
r
θ
Point source
x
Fig. 27.26 Point source generation and multiplexed array
detection of surface acoustic waves in anisotropic materials
Part C 27.4
cident wave, and furthermore that the generating and
receiving locations be in line and normal to the crack.
Recently, Kromine et al. [27.49, 50] have developed
a scanning laser source (SLS) technique for detecting
very small surface-breaking cracks that are arbitrarily
oriented with respect to the generating and detecting
directions. The SLS technique has no counterpart in
conventional ultrasonic inspection methodologies as it
relies on near-field scattering and variations in thermoelastic generation of ultrasound in the presence and
absence of defects.
In the SLS technique, the ultrasound generation
source, which is a point- or line-focused high-power
laser beam, is swept across the test specimen surface
and passes over surface-breaking flaws (Fig. 27.25a).
The generated ultrasonic wave packet is detected using an optical interferometer or a conventional contact
piezoelectric transducer either at a fixed location on
the specimen or at a fixed distance between the source
and receiver. The ultrasonic signal that arrives at the
Rayleigh wave speed is monitored as the SLS is
scanned. Kromine et al. [27.50] and Sohn et al. [27.15]
have shown that the amplitude and frequency of the
measured ultrasonic signal have specific variations
when the laser source approaches, passes over, and
moves behind the defect.
Kromine et al. [27.50] have experimentally verified the SLS technique on an aluminum specimen with
a surface-breaking fatigue crack of 4 mm length and
50 μm width. A broadband heterodyne interferometer
with 1–15 MHz bandwidth was used as the ultrasonic
detector. The SLS was formed by focusing a pulsed
Nd:YAG laser beam (pulse duration 10 ns, energy 3 mJ).
The detected ultrasonic signal at three locations of the
SLS position is presented in Fig. 27.25b. The Rayleigh
wave amplitude as a function of the SLS position is
shown in Fig. 27.25c. Several revealing aspects of the
Rayleigh wave amplitude signature should be noted.
In the absence of a defect or when the source is far
ahead of the defect, the amplitude of the generated ultrasonic direct signal is constant (zone I in Fig. 27.25c).
The Rayleigh wave signal is of sufficient amplitude
above the noise floor to be easily measured by the
laser detector (Fig. 27.25b), but the reflection is within
the noise floor. As the source approaches the defect,
the amplitude of the detected signal significantly increases (zone II in Fig. 27.25c). This increase is readily
detectable even with a low sensitivity laser interferometer as compared to weak echoes from the flaw
(Fig. 27.25b). As the source moves behind the defect,
the amplitude drops lower than in zone I due to scat-
27.4 Applications of Photoacoustics
794
Part C
Noncontact Methods
Part C 27.4
sources have been used to generate the ultrasound. The
ultrasound generated by a point laser source is typically detected by a point receiver and group velocity
information is obtained at different angles. Doyle and
Scala [27.56] have used a line-focused laser to determine the elastic constants of composite materials
using the measured phase velocities of surface acoustic
waves. Huang and Achenbach [27.57] used a line source
and a dual-probe Michelson interferometer to provide
accurate measurements of time of flight of SAWs on
silicon.
Zhou et al. [27.58] have recently used a multiplexed
two-wave mixing interferometer with eight detection
channels to provide group velocity slowness images.
Figure 27.26 shows the configuration of the optical
beams for anisotropic material characterization using
a)
θ = 90°
θ = 80°
θ = 70°
θ = 60°
θ = 50°
θ = 40°
θ = 30°
θ = 20°
θ = 10°
θ = 0°
0.8
1
1.2
b) × 10–4
1.4
1.6
1.8
Time (μs)
120
Slowness (ms/mm)
0.3
90
2.1
SAWs. In this setup, a pulsed Nd:YAG laser (pulse energy of approximately 1 mJ) is focused by a lens system
onto the sample surface to generate the SAWs. The
eight optical probe beams are obtained using a circular
diffraction grating and focused onto the sample surface
by a lens system to fall on a circle of radius r centered about the generation spot. The whole array of
eight points was rotated every 2◦ to obtain the material anisotropy over the entire 360◦ range. Since a point
source and point receiver configuration is used, the surface wave group velocity is obtained in this case.
Figure 27.27a shows the time-domain SAW signals
on (001) silicon from 0◦ to 90◦ . The group velocity
slowness in each direction is obtained from the timedomain data through a cross-correlation technique and
is shown in Fig. 27.27b where the filled circles are
the experimental values. Also shown in Fig. 27.27b is
the theoretical group velocity slowness calculated using
nominal material values. The discontinuities that appear in both the experimental and the theoretical curves
are due to the presence of pseudo-surface waves. Zhou
et al. [27.58] have also obtained group velocity slowness curves on the (0001) surface of a block of quartz.
The time-domain traces and the corresponding group
velocity slowness curves are shown in Fig. 27.28. The
multiple pulses observed are due to a combination of
the presence of SAWs and pseudo-SAWs as well as the
energy folding that occurs in anisotropic materials such
as (0001) quartz. The group velocity slowness curves
obtained experimentally can be further processed to ob-
60
Experiment
Theory
0.2
2
150
30
0.1
1.9
0
1.8 180
0
–0.1
1.9
210
330
–0.2
2
–0.3
2.1
240
300
270
Fig. 27.27 (a) SAW signals detected in different directions
on z-cut silicon. (b) Slowness curve for z-cut silicon
–0.3 –0.2 –0.1
0
0.1 0.2 0.3
Slowness (ms/mm)
Fig. 27.28 Group velocity slowness of z-cut quartz
Photoacoustic Characterization of Materials
tain the anisotropic material constants as described by
Castagnede et al. [27.59].
PZT driver
Attenuator
780 nm
femtosecond laser
λ/2
532 nm CW
laser
Aperture
PBS
λ/4
Stabilizer
PZT
BS
Sample
Optical
fibers
Oscilloscope
BPD
Fig. 27.29 Guided-wave photoacoustic setup (BS: beam splitter, PBS: polarized beam splitter, BPD: balanced photodetector,
λ/4: quarter-wave plate, λ/2: half-wave plate, PZT: piezoelectric
mounted mirror)
of hundreds of nanometers, followed by a Cr adhesion metallic layer with thickness about 100 nm right
on the steel substrate. The properties of the interpolated
layer are taken to be the average of those of the DLC
and the metallic layers. The transfer matrix method
described in Sect. 27.1.3, was used to obtain the theoretical guided-wave dispersion curves. To derive the
mechanical properties, an inverse problem has to be
solved to calculate the parameters from the measured
velocity dispersion curve v( f ). A nonlinear regression
method is used to minimize the least-square error function
y=
N
2
1 theo
v
− vmeas ,
N
795
(27.64)
i=1
where vmeas are the measured velocities, and vtheo
are the theoretically calculated velocities, which are
functions of the mechanical properties of each layer.
A simplex method of least-square curve fitting is useful
for fitting a function of more than one variable [27.64].
The thicknesses of the coatings were separately measured and used in the calculation. The reliability of the
results mainly depends on the accuracy of the experiments, the choice of initial parameters, and the number
of fitted variables. The Young’s modulus, Poisson’s ratio, and density of the DLC coating layer were set as
variables to be determined in the iteration. Repetitive fitting showed a variation of up to 5% for the fitted values
of Young’s moduli and densities.
Part C 27.4
Characterization
of the Mechanical Properties of Coatings
The small footprint and noncontact nature of photoacoustic methods make them especially useful for
characterizing coatings. Several optical techniques have
been devised and implemented. A pump-probe technique has been used in which very high-frequency
(GHz) acoustic waves are generated that propagate perpendicular to the film and reflect off of the film/substrate
interface [27.26, 31]. This bulk wave technique requires an ultrafast laser source, and material attenuation
of high-frequency ultrasound limits the useful measurement range to reasonably thin films. For thicker
films, guided-wave ultrasonic techniques are more
practical. The impulsive stimulated thermal scattering (ISTS) [27.60] technique and the phase velocity
scanning (PVS) [27.61] technique both use a spatially
periodic irradiance pattern to generate single-frequency
surface acoustic wave (SAW) tone bursts which are detected through probe-beam diffraction, interferometry,
or contact transducers. Broadband techniques [27.19,
62] can also be used where SAWs are generated with
a simple pulsed laser point or line source which are then
detected with an interferometer after some propagation
distance along the film.
Ultrahard coatings such as diamond, diamond-like
carbon (DLC), cubic BN, etc., are of great interest
due to their unique mechanical, thermal, and electrical
properties. In particular, the high hardness and stiffness of diamond-like thin films make them excellent
coating materials for tribological applications. Unfortunately, the coating properties are highly sensitive to the
processing parameters, and photoacoustic methods provide a way to measure the properties of these coatings
nondestructively. Figure 27.29 shows the guided-wave
photoacoustic setup used for characterizing multilayer
Cr-DLC specimens. A pulsed laser was line-focused
to a line width of 10 μm on the surface of the specimen to generate broadband guided acoustic waves.
The acoustic waves were monitored by a stabilized
balanced Michelson interferometer. By monitoring the
guided waves at multiple source to receiver locations
(Fig. 27.30a), the dispersion curves for these waves
were obtained, as shown in Fig. 27.30b.
To interpret the measurements, the multilayer DLC
specimen was modeled as a three-layer system [27.63].
Below the top layer of DLC, there is an interpolated
transition layer of Cr and DLC with various thickness
27.4 Applications of Photoacoustics
796
Part C
Noncontact Methods
Part C 27.4
The experimentally measured dispersion curves for
several Cr-DLC coatings are shown in Fig. 27.30b as
dots. The solid lines in Fig. 27.30b are the theoretically fitted dispersion curves as described above for the
inverse problem. The good agreement indicates that material properties can be extracted with a high degree
of confidence. Note that significant variations in DLC
a) Signal amplitude (arb. units)
0.2
0.1
0
–0.1
–0.2
–0.3
3
3.2
3.4
3.6
3.8
0.1
0
–0.1
–0.2
5
5.2
5.4
5.6
5.8
6
Time (μs)
b) Phase velocity (m/s)
3060
(A) Cr-DLC specimens
#1
#2
#3
#4
#5
#6
3040
3020
properties can be obtained, arising from fabrication process variations [27.63]. Photoacoustic characterization
of such coatings is therefore very useful in process control applications to assure quality.
Characterization
of the Mechanical Properties of Thin Films
Photoacoustic techniques can also be used to characterize the properties of free-standing nanometer-sized
thin films [27.36, 65]. Such thin films are widely used
in micro-electromechanical systems (MEMS) devices
such as radiofrequency (RF) switches, pressure sensors,
and micromirrors. Described below are guided-wave
and bulk-wave photoacoustic methods for characterizing free-standing thin films.
Two-layer thin films of Al/Si3 N4 were fabricated
on a standard Si wafer using standard microfabrication processes [27.65]. The film thicknesses were in
the range of hundreds of nanometers. Several windows
were etched in the wafer to provide unsupported membranes of Al/Si3 N4 which were only edge supported
(Fig. 27.31). In a first set of experiments, bulk-wave
photoacoustic measurements were made. A standard
pump-probe optical setup operated at 780 nm using
a Ti:sapphire femtosecond laser (100 fs pulse duration,
80 MHz repetition rate) was used in this work. Both the
substrate-supported and unsupported region were measured as, indicated in Fig. 27.31. Figure 27.32 shows
the normalized measured pump-probe signals for the
thin films on the silicon substrate supported region.
As shown in Fig. 27.32, the time of flight of the first
ultrasonic echo reflected from the first Al/Si3 N4 interface is marked as τ1 and that of the echo from
the Si3 N4 /Si interface is marked as τ2 . To deduce
Pump pulses
Probe pulses
3000
Al
Si3N4
2980
GW
0
d1
d2
BW
Si
2960
0
50
100
x
150
Frequency (MHz)
Fig. 27.30a,b Guided-wave photoacoustic measurement
of Cr-DLC coatings. (a) Broadband SAW signals detected
at two source–receiver locations. (b) SAW dispersion
curves
Michelson interferometer
Fig. 27.31 Bulk-wave and guided-wave photoacoustic
characterization of free-standing thin films: schematic diagram of the compact optical setup for both bulk-wave and
guided-wave detection
Photoacoustic Characterization of Materials
0.2
2
Short source –receiver distance
0.1
τ1
τ2
0
5
4
1
3
0.5
2
1
0
50
100
150
200
250 300 350
Delay time (ps)
Fig. 27.32 The experimental transient thermoreflectivity
Part C 27.4
Sample 6
0
797
a) Relative amplitude (arb. units)
Reflection coefficient change (arb. units)
1.5
27.4 Applications of Photoacoustics
– 0.1
– 0.2
– 0.3
Long source – receiver distance
– 0.4
0.2
0.8
1
1.2
1.4
Time (μs)
1.6
Specimen #1
Specimen #2
Specimen #3
Specimen #4
1.4
where h is the thickness, ρ is the density of the film, and
σ is the in-plane stress in the film (typically caused by
residual stress). The flexural rigidity D is related to the
Young’s modulus E, Poisson’s ratio ν, and the geometry
of the film.
0.6
b) (phase velocity υa0)2 (km2/s2)
signals for double-layer thin films
the elastic moduli E accurately, the theoretical simulated transient thermoelastic signals (Sect. 27.2.2) with
various moduli were calculated and compared with
the experimental signals, and the moduli that give
the smallest error for the time of flight of acoustic echoes were determined iteratively. In general, the
measured Young’s modulus of the aluminum layer falls
in the range 47–65 GPa. The experimentally determined Young’s moduli of silicon nitride films range
from about 220 to 280 GPa and are in good agreement
with the Young’s modulus of low-pressure chemical
vapor deposition (LPCVD)-fabricated silicon nitride reported in the literature.
The same set of specimens was also tested using
guided-wave photoacoustics. Only the lowest-order antisymmetric Lamb-wave mode was efficiently generated
and detected in such ultrathin films. For ultrathin films
such as these, for small wavenumbers, a simple expression for the acoustic phase velocity of A0 mode in terms
of the wavenumber k can be derived [27.65]:
(
D 2 σ
ω
(27.65)
k + ,
v A0 = =
k
ρh
ρ
0.4
1.2
1
0.8
0.6
0.4
0.2
0
0
0.1
0.2
0.3
0.4
(k h)2
Fig. 27.33a,b Guided-wave photoacoustic characterization of two-layer ultrathin films. (a) Measured signals at
two source-to-receiver locations for thin-film sample #1,
and (b) measured dispersion curves (dots) and linear fitted
curves (lines) for samples #1–#4. The average measured
flexural rigidities are 4.82, 5.82, 3.64, 1.76 × 10−9 Nm;
and the residual stresses are 235, 299, 334, 242 MPa, respectively
Figure 27.33a shows typical measured time traces of
the A0 mode at two source-to-receiver positions. Figure 27.33b shows the experimentally determined A0
mode dispersion curves for four specimens. From the
figure, it is clear that (27.65) represents the measurements well, thereby enabling direct determination of the
residual stresses in the film [27.65].
798
Part C
Noncontact Methods
27.5 Closing Remarks
Part C 27
In this chapter, only a selective review of photoacoustic metrology as applied to mechanical characterization
of solids has been provided. Applications of photoacoustic methods of course extend well beyond the ones
discussed here. Photoacoustic spectroscopy is a wellestablished set of methods for the characterization
of the composition of condensed and gaseous matter [27.66]. Recent developments in biomedical photoacoustics promise new methods of characterization
and imaging of tumors and blood vessels [27.67, 68].
Photoacoustic methods are also being used to characterize nanostructures such as superlattices [27.69] and
nanoparticles [27.70]. The photoacoustic phenomenon,
which Alexander Graham Bell originally investigated,
possibly with applications to telephony in mind, has
since yielded several powerful metrology tools for both
the laboratory researcher and for industrial applications.
References
27.1
27.2
27.3
27.4
27.5
27.6
27.7
27.8
27.9
27.10
27.11
27.12
27.13
27.14
27.15
C.B. Scruby, L.E. Drain: Laser Ultrasonics: Techniques and Application (Adam Hilder, New York
1990)
V.E. Gusev, A.A. Karabutov: Laser Optoacoustics
(American Institute of Physics, New York 1993)
D.A. Hutchins: Ultrasonic Generation by Pulsed
Lasers. In: Physical Acoustics, Vol. XVIII, ed. by
W.P. Mason, R.N. Thurston (Academic, New York
1988) pp. 21–123
J.P. Monchalin: Optical detection of ultrasound,
IEEE Trans. Ultrason. Ferroelectr. Frequ. Control,
33(5), 485–499 (1986)
J.W. Wagner: Optical Detection of Ultrasound. In:
Physical Acoustics, Vol. XIX, ed. by R.N. Thurston,
A.D. Pierce (Academic, New York 1990)
R.J. Dewhurst, Q. Shan: Optical remote measurement of ultrasound, Meas. Sci. Technol. 10,
R139–R168 (1999)
J.D. Achenbach: Wave Propagation in Elastic Solids
(North-Holland/Elsevier, Amsterdam 1973)
B.A. Auld: Acoustic Fields and Waves in Solids
(Krieger, Malabar 1990)
D. Royer, E. Dieulesaint: Elastic Waves in Solids
(Springer, New York 1996)
G.W. Farnell: Properties of Elastic Surface Waves.
In: Physical Acoustics, Vol. VI, ed. by W.P. Mason,
R.N. Thurston (Academic, New York 1970)
G.W. Farnell, E.L. Adler: Elastic Wave Propagation
in Thin Layers. In: Physical Acoustics, Vol. IX, ed.
by W.P. Mason, R.N. Thurston (Academic, New York
1974)
W.T. Thomson: Transmission of Elastic Waves
through a Stratified Solid Medium, J. Appl. Phys.
21, 89–93 (1950)
N.A. Haskell: The dispersion of surface waves on
multilayered media, Bull. Seism. Soc. Am. 43(1),
17–34 (1953)
R.M. White: Generation of elastic waves by
transient surface heating, J. Appl. Phys. 24(12),
3559–3567 (1963)
Y. Sohn, S. Krishnaswamy: Interaction of a scanning laser-generated ultrasonic line source with
27.16
27.17
27.18
27.19
27.20
27.21
27.22
27.23
27.24
27.25
27.26
27.27
a surface-breaking flaw, J. Acoust. Soc. Am. 115(1),
172–181 (2004)
A.M. Aindow, D.A. Hutchins, R.J. Dewhurst,
S.B. Palmer: Laser-generated ultrasonic pulses at
free metal-surfaces, J. Acoust. Soc. Am. 70, 449–
455 (1981)
R.J. Dewhurst, C. Edwards, A.D.W. McKie,
S.B. Palmer: Estimation of the thickness of thin
metal sheet using laser generated ultrasound,
Appl. Phys. Lett. 51, 1066–1068 (1987)
J. Spicer, A.D.W. McKie, J.W. Wagner: Quantitative
theory for laser ultrasonic waves in a thin plate,
Appl. Phys. Lett. 57(18), 1882–1884 (1990)
T.W. Murray, S. Krishnaswamy, J.D. Achenbach:
Laser generation of ultrasound in films and coatings, Appl. Phys. Lett. 74(23), 3561–3563 (1999)
T.W. Murray, J.W. Wagner: Laser generation of
acoustic waves in the ablative regime, J. Appl.
Phys. 85(4), 2031–2040 (1999)
F.A. McDonald: Practical quantitative theory of
photoacoustic pulse generation, Appl. Phys. Lett.
54(16), 1504–1506 (1989)
J. Spicer: Laser Ultrasonics in Finite Structures:
Comprehensive Modeling with Supporting Experiments. Ph.D. Thesis (The Johns Hopkins University,
Baltimore 1991)
I. Arias: Modeling of the Detection of Surface
Breaking Cracks by Laser Ultrasonics. Ph.D. Thesis
(Northwestern University, Evanston 2003)
C.B. Scruby, R.J. Dewhurst, D. Hutchins, S. Palmer:
Quantitative studies of thermally-generated elastic
wave in laser irradiated solids, J. Appl. Phys. 51,
6210–6216 (1980)
L. Rose: Point-source representation for laser
generated ultrasound, J. Acoust. Soc. Am. 75(3),
723–732 (1984)
C. Thomsen, H.T. Grahn, H.J. Maris, J. Tauc:
Surface generation detection of phonons by picosecond light-pulses, Phys. Rev. B 34, 4129–4138
(1986)
C.J.K. Richardson, M.J. Ehrlich, J.W. Wagner: Interferometric detection of ultrafast thermo-elastic
Photoacoustic Characterization of Materials
27.28
27.29
27.31
27.32
27.33
27.34
27.35
27.36
27.37
27.38
27.39
27.40
27.41
27.42
27.43
27.44
27.45
27.46
27.47
27.48
27.49
27.50
27.51
27.52
27.53
27.54
27.55
P. Delaye, A. Blouin, D. Drolet, L.A. Montmorillon,
G. Roosen, J.P. Monchalin: Detection of ultrasonic
motion of a scattering surface by photorefractive
InP:Fe under an applied dc field, J. Opt. Soc. Am. B
14(7), 1723–1734 (1997)
Y. Zhou, G. Petculescu, I.M. Komsky, S. Krishnaswamy: A high-resolution, real-time ultrasonic
imaging system for NDI applications, SPIE, Vol. 6177
(2006)
K.R. Yawn, T.E. Drake, M.A. Osterkamp, S.Y. Chuang,
D. Kaiser, C. Marquardt, B. Filkins, P. Lorraine, K. Martin, J. Miller: Large-Scale Laser
Ultrasonic Facility for Aerospace Applications. In:
Review of Progress in Quantitative Nondestructive
Evaluation, Vol. 18, ed. by D.O. Thompson, D.E. Chimenti (Kluwer Academic/Plenum, New York 1999)
pp. 387–393
J. Huang, Y. Nagata, S. Krishnaswamy, J.D. Achenbach: Laser based ultrasonics for flaw detection,
IEEE Ultrasonic Symposium, ed. by M. Levy,
S.C. Schneider (IEEE, New York 1994) pp. 1205–
1209
Y. Nagata, J. Huang, J.D. Achenbach, S. Krishnaswamy: Computed Tomography Using LaserBased Ultrasonics. In: Review of Progress in
Quantitative Nondestructive Evaluation, Vol. 14, ed.
by D.O. Thompson, D.E. Chimenti (Plenum, New
York 1995)
A. Kromine, P. Fomitchov, S. Krishnaswamy,
J.D. Achenbach: Scanning Laser Source Technique
and its Applications to Turbine Disk Inspection.
In: Review of Progress in Quantitative Nondestructive Evaluation, Vol. 18A, ed. by D.O. Thompson,
D.E. Chimenti (Plenum, New York 1998) pp. 381–
386
A.K. Kromine, P.A. Fomitchov, S. Krishnaswamy,
J.D. Achenbach: Laser ultrasonic detection of
surface breaking discontinuities: Scanning laser
source technique, Mater. Eval. 58(2), 173–177 (2000)
A.A. Maznev, A. Akthakul, K.A. Nelson: Surface
acoustic modes in thin films on anisotropic substrates, J. Appl. Phys. 86(5), 2818–2824 (1999)
D.C. Hurley, V.K. Tewary, A.J. Richards: Surface acoustic wave methods to determine the
anisotropic elastic properties of thin films, Meas.
Sci. Technol. 12(9), 1486–1494 (2001)
B. Audoin, C. Bescond, M. Deschamps: Measurement of stiffness coefficients of anistropic materials from pointlike generation and detection
of acoustic waves, J. Appl. Phys. 80(7), 3760–3771
(1996)
A. Neubrand, P. Hess: Laser generation and detection of surface acoustic waves: elastic properties of
surface layers, J. Appl. Phys. 71(1), 227–238 (1992)
A.G. Every, W. Sachse: Determination of the elastic
constants of anisotropic solids from acoustic-wave
group-velocity measurements, Phys. Rev. B 42,
8196–8205 (1990)
799
Part C 27
27.30
transients in thin films: theory with supporting
experiment, J. Opt. Soc. Am. B 16, 1007–1015 (1999)
Z. Bozoki, A. Miklos, D. Bicanic: Photothermoelastic transfer matrix, Appl. Phys. Lett. 64, 1362–1364
(1994)
A. Miklos, Z. Bozoki, A. Lorincz: Picosecond transient reflectance of thin metal films, J. Appl. Phys.
66, 2968–2972 (1989)
H.T. Grahn, H.J. Maris, J. Tauc: Picosecond ultrasonics, IEEE J. Quantum Electron. 25(12), 2562–2569
(1989)
C. Thomsen, H.T. Grahn, H.J. Maris, J. Tauc:
Ultrasonic experiments with picosecond time resolution, J. Phys. Colloques. C10 46, 765–772 (1985)
P.A. Fleury: Light scattering as a probe of phonons
and other excitations. In: Physical Acoustics,
Vol. VI, ed. by W.P. Mason, R.N. Thurston (Academic, New York 1970)
G.A. Antonelli, H.J. Maris, S.G. Malhotra, M.E. Harper: Picosecond ultrasonics study of the vibrational
modes of a nanostructure, J. Appl. Phys. 91(5),
3261–3267 (2002)
R. Adler, A. Korpel, P. Desmares: An instrument for
making surface waves visible, IEEE Trans. Sonics.
Ulrason. SU-15, 157–160 (1967)
E.G.H. Lean, C.C. Tseng, C.G. Powell: Optical probing of acoustic surface-wave harmonic generation,
Appl. Phys. Lett. 16(1), 32–35 (1970)
J.A. Rogers, G.R. Bogart, R.E. Miller: Noncontact
quantitative spatial mapping of stress and flexural
rigidity in thin membranes using a picosecond transient grating photoacoustic technique,
J. Acoust. Soc. Am. 109, 547–553 (2001)
D. Malacara: Optical Shop Testing (Wiley, New York
1992)
M. Paul, B. Betz, W. Arnold: Interferometric detection of ultrasound from rough surfaces using
optical phase conjugation, Appl. Phys. Lett. 50,
1569–1571 (1987)
P. Delaye, A. Blouin, D. Drolet, J.P. Monchalin:
Heterodyne-detection of ultrasound from rough
surfaces using a double-phase conjugate mirror,
Appl. Phys. Lett. 67, 3251–3253 (1995)
R.K. Ing, J.P. Monchalin: Broadband optical detection of ultrasound by two-wave mixing in
a photorefractive crystal, Appl. Phys. Lett. 59,
3233–3235 (1991)
P. Delaye, L.A. de Montmorillon, G. Roosen: Transmission of time modulated optical signals through
an absorbing photorefractive crystal, Opt. Commun. 118, 154–164 (1995)
B.F. Pouet, R.K. Ing, S. Krishnaswamy, D. Royer:
Heterodyne interferometer with two-wave mixing
in photorefractive crystals for ultrasound detection
on rough srufaces, Appl. Phys. Lett. 69, 3782–2784
(1996)
P. Yeh: Introduction to Photorefractive Nonlinear
Optics (Wiley, New York 1993)
References
800
Part C
Noncontact Methods
27.56
27.57
Part C 27
27.58
27.59
27.60
27.61
27.62
27.63
P.A. Doyle, C.M. Scala: Toward laser-ultrasonic
characterization of an orthotropic isotropic interface, J. Acoust. Soc. Am. 93(3), 1385–1392
(1993)
J. Huang, J.D. Achenbach: Measurement of material anisotropy by dual-probe laser interferometer,
Res. Nondestr. Eval. 5, 225–235 (1994)
Y. Zhou, T.W. Murray, S. Krishnaswamy: Photoacoustic imaging of surface wave slowness using
multiplexed two-wave mixing interferometry, IEEE
UFFC 49(8), 1118–1123 (2002)
B. Castagnede, K.Y. Kim, W. Sachse, M.O. Thompson: Determination of the elastic constants of
anistropic materials using laser-generated ultrasonic signals, J. Appl. Phys. 70(1), 150–157 (1991)
A.R. Duggal, J.A. Rogers, K.A. Nelson: Real-time
optical characterization of surface acoustic modes
of polyimide thin-film coatings, J. Appl. Phys.
72(7), 2823–2839 (1992)
A. Harata, H. Nishimura, T. Sawada: Laser-induced
surface acoustic-waves and photothermal surface
gratings generated by crossing two pulsed laserbeams, Appl. Phys. Lett. 57(2), 132–134 (1990)
D. Schneider, T. Schwartz, A.S. Bradfordm, Q. Shan,
R.J. Dewhurst: Controlling the quality of thin films
by surface acoustic waves, Ultrasonics 35, 345–356
(1997)
F. Zhang, S. Krishnaswamy, D. Fei, D.A. Rebinsky,
B. Feng: Ultrasonic characterization of mechanical
27.64
27.65
27.66
27.67
27.68
27.69
27.70
properties of diamond-like carbon hard coatings,
Thin Solid Films 503, 250–258 (2006)
J.D. Achenbach, J.O. Kim, Y.C. Lee: Acoustic microscopy measurement of elastic-constants and
mass density. In: Advances in Acoustic Microscopy,
ed. by A. Briggs (Plenum, New York 1995)
C.M. Hernandez, T.W. Murray, S. Krishnaswamy:
Photoacoustic characterization of the mechanical
properties of thin films, Appl. Phys. Lett. 80(4),
691–693 (2002)
A. Rosencwaig: Photoacoustics and photoacoustic
spectroscopy (Wiley, New York 1980)
R.G.M. Kolkman, E. Hondebrink, W. Steenburgen,
F.F.M. de Mul: In vivo photoacoustic imaging of
blood vessels using an extreme-narrow aperture
sensor, IEEE J. Sel. Top. Quantum Electron. 9(2),
343–346 (2003)
V.G. Andreev, A.A. Karabutov, A.A. Oraevsky: Detection of ultrawide-band ultrasound pulses in
optoacoustic tomography, IEEE Trans. Ultrason,
Ferroelectr. Frequ. Control 50(10), 1183–1390 (2003)
N.W. Pu: Ultrafast excitation and detection of
acoustic phonon modes in superlattices, Phys. Rev.
B 72, 115428 (2005)
M. Nisoli, S. de Silvestri, A. Cavalleri, A.M. Malvezzi,
A. Stella, G. Lanzani, P. Cheyssac, R. Kofman:
Coherent acoustic oscillation in metallic nanoparticles generated with femtosecond optical pulses,
Phys. Rev. B 55, R13424 (1997 )