Introduction to Acoustics

Optical Methods for Acoustics and Vibration Measurements 27.2 Measurement Principles and Some Applications 1109
the fine structure of the object surface. One technically
important property of the speckles is that the speckles
seem to move as if glued to the object surface when
the object is moved or deformed. A change in illumination
or observation directions of the object will however
also change the speckle pattern. Two different observers
both see speckles but with different distributions. The
speckles were earlier looked upon as unwanted noise
but as they also carry information; they also form the basis
for techniques such as speckle photography (SP)and
speckle interferometry (SI). They both belong to a group
of methods named speckle metrology [27.32–34]. In SP
the in-plane motion of the speckles themselves is measured,
and in SI the change in intensity of the speckles
(i. e. the phase change of interfering beams) are used.
Hologram interferometry is also based on recording the
information of the same speckles.
The optical arrangement of a speckle interferometer
setup called TV holography or electro-optic holography
[27.25] (alsonamedDSPI or ESPI) isshown
in Fig. 27.4. A special computer board is developed
that allows real-time presentations of phase-stepped
interferograms.
Laser light is divided by a beam splitter (BS) into
an object illumination part and a reference wave part.
The object space, situated to the right, is illuminated
and imaged almost along the z-axis of the object. The
measuring sensitivity of this configuration therefore also
becomes highest along the same direction and consequently
zero along the x–y-axes. The object light
amplitude field, Eobj, is imaged by a video lens and
some transferring optics onto the photosensitive surface
of the CCD chip, where the smooth reference beam, Eref,
also emanating from the end of an optical reference fiber
is added. Each pixel of the CCD camera pictures a small
area in the object space, i. e. this can be described as
an in-line, image-plane holographic setup. Via a special
personal computer (PC) image-processor board, results
are presented at the rate allowed by the digital camera
(25 or 30 Hz) on a monitor, which is a highly valuable
feature in many experimental situations. In the setup
there are mirrors mounted on piezoelectric crystals, allowing
phase modulation (PM) and phase stepping (PS).
These options are used to determine the relative phase
of vibration fields and to extract quantitative data from
the interferograms.
The optical detectors are so-called quadratic detectors.
They measure intensity or irradiance which in turn
is proportional to the square of the sum of the two
interfering electromagnetic amplitude fields. The instantaneous
intensity I(x, y) atapixeloftheCCD detector
can therefore be written:
I(x, y) =|(Eobj + Eref)| 2 = I0 + IA cos(∆Φ) ,
(27.5)
where I0 is the background intensity and IA the modulating
intensity. The desired information however, is found
in ∆Φ, the relative optical phase difference between the
(constant) reference and the object field in each pixel.
A difficulty exists since there are three unknowns in
(27.5); ∆Φ, I0 and IA but only one equation. This can
be solved by Fourier-filtering methods or phase-stepping
(shifting) techniques [27.22–24]. In the phase-stepping
technique, PS in Fig. 27.3 is used to shift the phase with,
for instance, π/2 in steps between consecutive recorded
frames to obtain four equations. With four equations and
three unknowns, ∆Φ can be calculated with good accuracy.
In double-exposure and pulsed TV holography two
series of recordings are made, one before and one after
some deformation or change is introduced to the object.
The corresponding phase changes ∆Φ(x, y) for each of
the two states are determined as above and then subtracted.
Since the same reference beam is used in the
recording of both states, ideally only the difference in
object phase will remain after subtraction. The change
in object phase, Ω = ∆Φ1 − ∆Φ2, between the two objects
fields are thus obtained. This quantity, Ω in turn is
defined as the change (∆) of the product of refractive index
n, the geometrical path length l and the laser wave
number k. That is, the measured change in optical phase
between two object states can be written as:
Ω = ∆(knl) = k(n∆l +l∆n) . (27.6)
The wave number, k = 2π/λ, is (most often) a constant
since λ, the laser wavelength, is the same in all recordings.
Equation (27.6) illustrates two main application
areas: one where the optical phase change is proportional
to the change in path length (i. e. vibration amplitudes,
deformation fields etc.) and one where it is proportional
to the change in refractive index (caused by, for instance,
wave propagation in fluids, flames etc.).
The TV holography system, shown in Fig. 27.4, illuminating
and observing the object along its normal, is
highly sensitive to out-of-plane vibrations or object motions
and insensitive to in-plane motions. A frequency
doubled, continuous-wave Nd:YAG laser with a wavelength
of 532 nm, is often used. Such lasers often have
a higher output power and a longer coherence length
than most comparable He–Ne lasers, say 50 mW and
a few meters in coherence length. The object size can
now vary from a few mm up to meter-sized objects both
Part H 27.2