Holographic particle image velocimetry

INSTITUTE OF PHYSICS PUBLISHING
MEASUREMENT SCIENCE AND TECHNOLOGY
Meas. Sci. Technol. 13 (2002) R61–R72
PII: S0957-0233(02)31362-6
REVIEW ARTICLE
Holographic particle image velocimetry
K D Hinsch
Applied Optics, FB8, Department of Physics, Carl von Ossietzky University Oldenburg, D-26111 Oldenburg,
Germany
Received 10 December 2001, accepted for publication 30 April 2002
Published 20 June 2002
Online at stacks.iop.org/MST/13/R61
Abstract
Holography is truly the key to three dimensions in particle image velocimetry, i.e. the
measurement of all spatial components of the velocity vector—and this over a deep
measuring field. Sophisticated instruments have been designed that successfully tackle
practical problems such as the low scattering efficiency of particles, the inferior depth
resolution or the aberrations and distortions in the reconstruction. Furthermore, efficient
strategies are introduced to interrogate the holographic storage and process the huge amount
of data towards a final flow field representation. Recently, phase-sensitive metrology,
familiar in many fields of experimental mechanics, has been examined for use in particle
velocimetry. Suitable methods are holographic and speckle interferometry or the optical
processing of data for three-dimensional correlation. While in these techniques the power of
optics is unrivalled, the practical advantage of video and digital techniques over
photographic recording is obvious. The electronic version of speckle interferometry
(ESPI/DSPI) is a well-established method used in laser metrology and has received further
exploitation for applications in flow analysis recently. Finally, the state-of-the-art of digital
particle holography is reviewed to allow estimates of its future in experimental flow analysis.
Keywords: fluid flow velocity, holography, holographic interferometry,
speckle interferometry, flow diagnostics, particle image velocimetry (PIV)
1. Introduction
Today’s challenging problems in fluid dynamics concern complex three-dimensional non-stationary flows. It is generally
agreed that there is a considerable developmental need for
diagnostic tools that cope with these demands. Thus, extensions of well-established particle imaging techniques towards
higher dimensionality are topics of increasing interest. While
the supplementation of classical PIV towards a stereoscopic
metrology has become standard to obtain three-component
(3C) velocity data, the coverage of all of space (3D) requires the
specific adaptation of holography to the registration of critical
objects such as micron-sized tracer particles. It is interesting
to note that some of the very early objects in quantitative holographic metrology were small particles—some 35 years ago (cf
the review by Vikram (1990)). However, finding the economic
means to extract and process the immense amount of data
available in a single hologram of a flow scene has required researchers to wait for the development of sophisticated electrooptic instrumentation and fast digital hard- and software.
Holography for particle velocimetry has revived the role
of optics in flow diagnostics. Traditional PIV, originally a
0957-0233/02/070061+12$30.00
© 2002 IOP Publishing Ltd
predominantly optical method not only in the photographic
recording of particle images, but also in large parts of
the interrogation procedures, has matured into a robust and
efficient method by using CCD-cameras and digital image
processing. Pioneers in the field still recall that twodimensional Fourier transformations were performed optically
by creating Young’s fringes. A museum of PIV would have
to put on display the many ingenious inventions to speed up
the production and processing of these fringes. Examples are
the purely optical correlation using an optically addressable
spatial light modulator (OASLM) (Vogt et al 1994), high-speed
automatic processing employing a network of modulators,
deflectors and detectors (Mao et al 1993) or the parallel
optical processing of a photographic PIV-record introducing
a synthetic holographic array of micro-lenses to avoid the
time needed to scan the photo sequentially (Arnold and
Hinsch 1989). When the pioneers met, there were nostalgic
reminiscences of those days.
The successful implementation of stereoscopic viewing
provides a good example showing that, even today, optics
should be exploited to their very best before digital
improvements are applied. Good depth resolution requires
Printed in the UK
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K D Hinsch
large viewing angles and sets problems regarding the depth of
field in the angular viewing set-up. Here, an old principle,
the Scheimflug condition with tilted camera back-plane,
performed in a superior fashion to all other a posteriori image
processing (Hinsch et al 1993, Prasad and Jensen 1995).
Recent progress in holographic velocimetry has been
truly powered by technological advancements. Sophisticated
HPIV apparatus has been set up in different parts of the
world to yield impressive results. We will briefly recall
features of such successful systems. However, there are
still domains for novel optical contributions to the basic
challenge and our main concern will be to outline the
prospects and status of several optical methods that—like
three-dimensional imaging by holography—make use of the
phase of light waves. While such techniques are familiar
in other disciplines they have found their way into particle
velocimetry rather recently. We will recall that the application
of short-coherence tomography improves the signal-to-noise
ratio in deep measuring volumes. Furthermore, we will
show that holographic interferometry (HI) and digital speckle
pattern interferometry (DSPI) also provide the metrology for
displacement mapping in flow diagnostics, exceeding the
performance of ordinary PIV by two orders of magnitude
in sensitivity. Similarly, optical interrogation of holographic
particle records by so-called object conjugate reconstruction
yields much improved accuracy and offers operating
parameters suitable for combination with simultaneous rigid
body deformation analysis.
Even in situations where optical solutions dominate, there
is also a trend towards applying more digitization. Obviously,
the introduction of any flow-analytical method for industrial
use must comply with economy considerations. A hologram,
we learned a long time ago, is worth a thousand pictures,
as a picture is equivalent to a thousand words—concerning
the information content held by each. Yet, design engineers
are reserved when results are not available on the spot
and when complex procedures such as dark-room work are
involved in obtaining them. As an example from standard
optical metrology, HI has been available for decades, yet
only through its digital version DSPI did it find a way into
everyday diagnostics. Full-scale digital holography on CCDsensors, however, still has shortcomings compared to full-field
holography of particles on photographic film. Yet, we will also
treat current trends in digital holography, where recording of
a hologram as well as the reconstruction of object fields are
entirely performed by computer.
2. The development of holographic particle image
velocimetry
Generally, holography is a method used to store the amplitude
and phase of a light wave by recording the interference pattern
that occurs when a second wave, the so-called reference
wave, is superimposed. The processed interference pattern—
a hologram—is used to reconstruct the original wave field
by illuminating it with a replica of the reference wave
(Collier et al 1971). There are several methods used to
perform such a recording of particles (Royer 2000). Let
us illustrate the situation for the so-called off-axis set-up
that has become the predominant version used in HPIV. In
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(a)
(b)
Object wave
(scattered
particle light)
Particles
Off-axis
reference wave
Hologram
Virtual
particle images
Original
reference wave
Photographic
plate
(c)
Hologram
Real
particle images
Conjugate
reference wave
Figure 1. Schematic of optical off-axis set-ups in particle
holography. (a) Recording of a hologram of a particle field;
(b) reconstruction of a virtual image; (c) reconstruction of a real
image.
figure 1 we meet the familiar arrangement where the hologram
is recorded by superimposing the scattered particle light—
the object wave—with a reference wave on a photographic
plate. Later, the developed photo (the hologram) is illuminated
with the reference wave and diffraction from the pattern of
microscopic interference structures reproduces a wave that
seems to originate from a particle field—the virtual image.
A startling feature of holography is that by reversing
the direction of the reconstructing wave—this is called the
conjugate reference wave (for a plane wave this is achieved by
rotating the plate through 180◦ )—a real image of the particle
field can be produced in space. This lens-less imaging has
become the standard configuration in reconstructing particle
fields from holograms. Here, the aperture responsible for the
accuracy in the particle position is limited only by the area on
the hologram that intercepts scattered light from the particles.
All efforts connected to large-aperture optics in traditional
imaging can be avoided. Real-image reconstruction may also
be employed for the successful compensation of aberrations
from difficult environments or low-cost relay imaging which
is often applied to improve the geometry of the set-up. For
this purpose, the aberrating media (like the transparent wall of
a circular pipe or an engine head) must be reinserted into the
reconstructed object wave (Barnhart et al 1994).
In classical light-sheet PIV, lasers are preferred because
they provide short pulses of high energy. For holography lasers
are definitely needed because interference requires coherence.
Any light source is characterized by its coherence length,
which is the maximum detour path length of two beams that
still provides a good interference pattern, i.e. a satisfactory
hologram. This value depends on the number of activated
axial resonator modes and is related to the spectral width of the
fluorescence line of the laser emission and the resonator length.
Intra-cavity etalons reduce this number and thus increase the
coherence length. In Nd:YAG lasers the coherence length is
increased by injection seeding where a high-energy laser is
Holographic particle image velocimetry
driven by a low-output laser of high coherence. Usually a long
coherence length is required in holography to relax restrictions
on the depth of the object and the matching of optical paths.
Both ruby and Nd:YAG lasers provide coherence of at least
a metre. The ultimate limit, of course, is set by the length
equivalent to the pulse duration. For special applications such
as light-in-flight holography, coherence can be reduced to a
few millimetres either by removing etalons or by switching off
the seeder. The shortest coherence length is given when all
possible modes radiate—the wider the fluorescence line the
smaller this value.
This all looks simple. However, there are several basic
issues that have influenced all practical realizations and can
be encountered throughout the history of HPIV; for earlier
overviews see, for example, Rood (1993) and Hinsch (1995).
Some of these are tackled by novel methods such as HI,
electronic speckle pattern interferometry or optical processing
and even digital holography—as will be shown in subsequent
sections.
2.1. Light scattering and resolution
The useful light in PIV arises from scattering by seeding
particles. Here, the essential features are the light scattering
efficiency and angular scattering characteristic of the particles.
These data are governed by Mie scattering and follow a
complicated angular pattern depending on the indices of
refraction involved and the ratio of particle size to wavelength
λ. Often, much light goes into the forward direction,
less backwards and even less at 90◦ viewing. Due to the
low photographic speed of holographic recording media and
limited laser energy available the forward direction is favoured.
Due to basic optics, the accuracy in the determination
of the position coordinate of a particle increases with the
angular range over which light contributes to the imaging.
Resolution in the transverse direction xt and in the longitudinal
direction xl are calculated according to
xt ≈
λ
(1)
λ
.
(2)
2
When = 0.2, we find values of 5λ and 25λ, respectively.
Obviously, the longitudinal resolution length is poorer than
the transversal resolution length. Thus, should be made
as large as possible. Here, the narrow cone of forward
scattering in conjunction with the limited dynamic range of
the photographic material are disadvantagous. Around 90◦
viewing there is a much larger angular range of almost constant
average value—albeit some pronounced lobes in the scattering
pattern.
In view of these conflicting requirements, many
researchers have chosen to maintain the advantage of the
superior light efficiency in forward scattering (two to three
orders of magnitude more than for perpendicular viewing)
in the so-called in-line holography where the spare light of
a collimated beam passing the particle field unaffected is
used for the reference light (Thompson 1989). This set-up
benefits additionally from the simplicity and low requirements
with respect to the coherence and film resolution. The small
xl ≈
angular range of forward scattering, however, restricts .
Furthermore, there is no way for optimum adjustment of
the ratio of reference-to-signal light, and the particle number
density must not get too high which could result in data holes.
Sophisticated set-ups have been designed to cope with this
problem (Hussain et al 1993). Simultaneous illumination or
observation is made from several directions in multi-beam
holographic particle velocimetry or from two perpendicular
directions (Bernal and Scherer 1993, Zhang et al 1997) which
were recently combined into a robust set-up by introducing a
45◦ -mirror (Sheng et al 2001). To cope with the poor signalto-noise ratio due to speckle formation by the virtual-image
light (Meng et al 1993) in-line recording is combined with offaxis viewing (Meng and Hussain 1995), an off-axis reference
beam is added to in-line illumination (forward scattering!) and
a high-pass spatial filter in this illumination additionally blocks
noise (Hussain et al 1993, Zhang et al 1997).
All these features have to be carefully balanced in the
optical design of the holographic set-up and are responsible
for the basically different performance of in-line and offaxis particle holography. Off-axis configurations benefit from
a larger effective angular scattering range and thus better
resolution, flexibility in the ratio of reference-to-object light
and—above all—the possibility to use angular multiplexing
of the reference beam to separate a sequence of holographic
recordings upon reconstruction.
This is important for
ambiguity removal (for which purpose holography has already
been used long ago in ordinary PIV (Coupland et al 1987))
and for cross-correlation evaluation. When viewing at 90◦ to
the illumination light, however, a largely reduced scattering
efficiency has to be accepted which may be compensated by
large particles as in liquid flows but can become a limiting
aspect in air flows. A good way to increase the effective
recording aperture and still have sufficient scattering is to
record light in two symmetric directions close to forward
(Barnhart et al 1994) or on both sides of the light-sheet (Fabry
and Sieverding 2000) and use stereoscopic evaluation of the
particle positions.
Another question concerns spatial resolution, i.e. the
smallest flow structures resolvable. The transverse resolution
is the same as in two-dimensional PIV. Here, the magnification
and size of the interrogation window determine resolution—
provided the particle density is sufficient. These parameters
must be chosen in accordance with the fluid-dynamical
problem. In HPIV the interrogation volume is equivalent
to the interrogation area in the two-dimensional case. Most
practical work places resolution dimensions of similar size
in the transverse and axial directions (typically 1–2 mm).
However, we have seen that the imaging resolution in depth
(z-direction) is much poorer than in the transverse direction.
Thus the particle image is smeared over several times as long a
distance and therefore the z-direction pitch in the interrogation
is generally set some ten times larger than the pixel size that is
usually <10 µm. When all data used in the calculation of the
correlation peak originate from inside the interrogation volume
its size sets the spatial resolution cell—in all three dimensions.
The z-component of the velocity vector, of course, retains its
lower accuracy.
Another issue related to the poor scattering and small
amount of object light available is the diffraction efficiency
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K D Hinsch
of holograms. For each photographic emulsion there is an
optimum ratio of object-to-reference light to stay within the
linear recording range and to assure high diffraction, i.e.
a bright reconstructed image. Usually this value is about
1:5. Even when using today’s high-energy lasers this rule
restricts the cross-sectional dimensions of the measuring field
to a few centimetres for air flows (µm-particles required).
However, when the registration of the reconstructed particle
images is performed by using a light-sensitive sensor that
has the capability of time-integration it is possible to operate
at object-to-reference ratios several orders of magnitudes
smaller than what is usually recommended and compensate for
the low diffraction efficiency by long-exposure interrogation.
Background reconstruction noise mainly originating from the
photographic plate is the basic limit to this strategy (Herrmann
and Hinsch 2001). As a consequence, the maximum size of
measuring volumes can be increased. Another possibility is
the repeated use of the illuminating light in a folded lightsheet configuration which has been applied in conjunction with
coherence considerations (Hinrichs and Hinsch 1996) or in a
specially designed multi-beamsplitter (Arroyo et al 2001).
2.2. Aberrations
A reliable holographic image of the object requires an
undistorted registration of the hologram and a faithful replica
of the reference wave. Problems occur when the hologram
is misaligned in the reference beam, when the reconstruction
wavelength is different from the recording wavelength or when
the photographic emulsion shrinks during the processing. The
first large-scale demonstration of HPIV in a flow analysis
was largely possible because such problems were mastered
(Barnhart et al 1994). Real-image reconstruction compensated
optical distortions in the imaging path and careful control
of the development procedure reduced shrinkage. Relay
optics concentrated particle light to a finite area on the
hologram, small enough to avoid effects by large-scale
emulsion distortions, yet sufficiently large for resolution
requirements—which were further relaxed by stereoscopic
registration. In other work the alignment accuracy has been
improved by a control grid (Lozano et al 1999). Basic
investigations are still dedicated to this field (Chan et al 2000,
Sholes and Farrell 2000).
2.3. Noise
It has been mentioned that the small-size tracer particles scatter
only little light so precautions must be taken to eliminate all
background radiation for a good signal-to-noise ratio. While
thoughtful prevention of all non-essential scattering sources
is a must, the simultaneous illumination of a large volume of
particles provides much unavoidable light when concentrating
on a certain interrogation region in space. Generally speaking,
one tries to gain data on a flow region that is deeply embedded
in a surrounding fog. Solutions to this problem make use of
the requirement that, for a holographic recording, reference
and object light should not differ in optical path by more
than the coherence length. A multiple-pass folded lightsheet configuration in combination with several matching
reference beams has provided simultaneous recording but
separate reconstruction of single light sheets (Hinrichs and
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Hinsch 1996). Light-in-flight holography in backscattering
geometry allows one to interrogate a shell of a few millimetres
width in depth from a continuous measuring field (Hinrichs
et al 1997, 2000). Here, due to the short coherence length
of the laser source it is possible to register all of the object
field simultaneously, but reconstruct the particle-image field
slice by slice in depth without disturbance from the rest of the
volume. The optical set-up is such that any finite sub-aperture
on the hologram is only responsible for a certain region in
depth. Restrictions as to particle-number density and limits of
the field depth are thus relaxed. The true power of this approach
will be obvious in very deep fields as predicted by numerical
and experimental simulation considerations (Hinrichs et al
1998). A nice experiment still pending will be to turn on or
off the Nd:YAG seeder in a light-in-flight set-up and change
the coherence length from more than a metre to less than a
centimetre.
2.4. Photographic recording
Traditionally, holograms are recorded on photographic film.
Special fine-grain emulsions have been developed to resolve
the microscopic details in the interference patterns of two
superimposing waves—typically of the order of a wavelength.
A 12×9 cm2 photographic plate of 5000 lines mm−1 resolution
is a powerful storage device for the holographically encoded
information about thousands of particles in the flow. Still,
trends to avoid the delay due to cumbersome darkroom work
which led to the replacement of traditional photographic PIV
by digital PIV are also observed in HPIV. Several other
holographic recording media such as photo-thermoplastics,
photo-refractive crystals, photo-polymers or biorhodopsin
have been considered or even tried out. Yet, presently there is
no equivalent substitute that allows comparable set-ups and
competes with film in terms of resolution and sensitivity.
However, we will show later that even CCD-recording is
possible when severe restrictions are accepted.
2.5. Interrogation and visualization
The effort to evaluate a particle field from a deep-volume
hologram increases over efforts in ordinary PIV with the new
spatial dimension. Real-image fields must be scanned in
three dimensions and particles identified in the presence of
noise from many out-of-focus particle images from other depth
regions. Next, the large amount of data has to be extracted,
processed and visualized, which requires large-array CCDs
and powerful computer capacity. HPIV benefits greatly from
the ever increasing power of digital processing. Since many
of the techniques used in data processing are similar to those
in planar PIV we will not go into details here. Later, however,
we will point out a way to utilize optical processing for these
purposes. It should also be mentioned that new visualization
methods are needed to handle the multi-dimensional data.
3. State-of-the-art in HPIV
We have seen that particle holography can be operated in
various schemes for velocimetry. The most advanced is
to superimpose holographic recordings from two subsequent
Holographic particle image velocimetry
states of the flow field but record them with off-axis
reference waves at different angles. Typically, a difference in
polarization of the two laser pulses can be employed to assign
each wave a different path. Upon reconstruction either wave
produces the corresponding particle-field image that can be
interrogated separately—yielding unambiguous velocity data
and allowing superior cross-correlation processing.
Once the particle-field image (either real or virtual)
has been reconstructed faithfully the challenge is to extract
the information on particle positions required to calculate a
velocity map. Different philosophies are applied—similar to
those from two-dimensional particle velocimetry which largely
depend on the number density of particles (correlation versus
particle tracking). The particle field is either interrogated
plane-wise and the two-dimensional cuts through the flow field
are subjected to established PIV interrogation by correlation.
Alternatively, single particles are identified, paired and the
displacement is determined. Finally, the interrogation could
aim directly at a three-dimensional correlation (Barnhart et al
1999) for which an optical solution is presented in a later
paragraph.
Let us briefly look at the features of several experimental
presentations of recently applied HPIV-instrumentation that
are good examples to demonstrate the utilization of earliermentioned features and illustrate the state-of-the-art. Later
sections will be devoted to additional approaches that utilize
novel techniques.
• In a version called hybrid HPIV advantages of forward
scattering, as in in-line holography, are combined with the
flexibility of an off-axis reference wave to study a waterduct flow with 15 µm particles (Zhang et al 1997). An optical high-pass filter (an on-axis stop) is introduced in combination with a relay lens to eliminate a large portion of
the annoying background light. The use of a plain doublepulse ruby laser allows only auto-correlation processing.
Two such set-ups are combined that observe the measuring
volume from perpendicular directions to obtain equally accurate data for all spatial dimensions. A 10% difference
between the recording and reconstruction wavelengths
(ruby laser to He–Ne laser) can be compensated by correct
change in the reconstruction angle of a collimated reference wave; the relay lenses are properly reintroduced into
the reconstructed wave to cancel aberrations.
• In a recent development this set-up has been modified for
a simpler layout by placing a mirror at 45◦ to the illuminating light directly behind the particles. This produces
the second observation direction at 90◦ without the need
for another illumination branch (Sheng et al 2001).
• Lozano et al (1999) study a swirling water flow with a
double Nd:YAG-laser set-up that comprised a 90◦ lensless viewing of 16 µm particles and virtual image interrogation. Since the exposures were recorded with different
reference wave directions the images could be separated
for cross-correlation interrogation.
• In another version (Pu and Meng 2000, Pu et al 2000)
5 µm droplets were introduced to study a vortex ring in
air. Once more, a dual injection-seeded YAG laser allowed
two reference beams to obtain a separate frame for each
of the exposures. A sophisticated system of shutters and
polarization-sensitive beamsplitters allowed pulse tailoring and adjustment of light intensities.
• The challenging task of HPIV measurements within the
cylinder of an IC engine is treated in a recent study (Konrath et al 2001). Again, a dual reference beam off-axis
configuration is realized with a ruby laser, the illuminating light traverses the cylinder through windows in two
directions at 90◦ to each other and is collected via mirrors and relay lenses on a single holographic plate. Realimage reconstruction by conjugate reference beams from
a laser diode of the same wavelength eliminates all distortion effects including those of windows and lenses.
• In a principally different set-up of backscattering geometry a study is conducted of the onset of turbulence in
an air-jet flow with light-in-flight holography (Herrmann
et al 2000a, 2000b, Hinsch et al 2000). Light from
a ruby laser several millimetres in coherence length allows one to extract sheet-wise information from the deepvolume reconstructed virtual particle-image field—to be
interrogated by traditional PIV software. To allow crosscorrelation with this type of light source an electro-optical
switching device had to be inserted to change the direction
of the reference beam between exposures. The complete
volume is assembled from many such sample planes. The
quality of results is indeed comparable to light-sheet PIV.
• In a reflection-type holographic set-up (Barnhart et al
2000) the reconstructed real-image wave field is used
for optical interrogation employing processing towards
optical correlation—a system that will be covered in more
detail in the final section of this paper.
A real challenge is the economic extraction of data from
the holograms. In the water-tunnel investigation (Zhang et al
1997) the real-image space was subdivided into depth-wise
slices which were sampled in frames by a CCD-target for
auto-correlation processing. The whole flow field was then
patched together from these data. The enormous amount
of data is illustrated by some 800 000 final velocity vectors
each for both the observation directions, the accumulation of
which took more than 200 h of time. A different approach
was taken in the air-jet study (Pu and Meng 2000) where a
special processing algorithm was developed that relies initially
on particle identification and position determination, and
performs the correlation not with images but on the set of
position coordinates, termed concise cross-correlation (Sheng
and Meng 1998). The aquisition could be achieved in the
10 Hz sequence of the Nd:YAG laser automatically switching
between reference beams and traversing the CCD-camera
through the real image. Again, hundreds of thousands of
vectors were produced in an effort of many hours. It remains
a problem to develop improved effective means to display
these results in a way that is appropriate for the derivation
of conclusions.
In either case, impressive data have been presented that
fully demonstrate the capability of holographic velocimetry in
flows that otherwise could not be analysed quantitatively. So
far, the applications have been restricted to sample situations
and wait for routine investigations in fluid mechanics. As an
example, new mathematical strategies for the classification of
turbulence can be extended to spatial data (Geiger et al 2000).
Up to now such studies had to rely on time records of the
velocity taken at a single location.
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K D Hinsch
where the so-called sensitivity vector K is defined by
Particle P(t)
∆ rK
ki
∆r
P(t+ ∆t)
P(t+∆
ko
K
To observer
From laser
Figure 2. The sensitivity vector K in HI depends on the
illumination and observation directions.
4. Holographic interferometry
We have seen that holography obtains its unique properties
from storing phase information about a light wave. When
the object wave field is reconstructed it is a direct copy of
the original version including the phase of the light field.
This provides the possibility to reproduce three-dimensional
images of objects—a feature that we have exploited so far.
However, there is more to the utilization of phase information
and that is interferometry. Retardation of a light wave by an
optical path of just half a wavelength produces a profound
effect when superimposed with the original wave, i.e. the
waves cancel and darkness is observed. Bear in mind that
it takes less than half a micron of change to impose this effect!
Different from classical interferometry where both interfering
object states had to be represented by their wave-equivalent
at the same time, in HI object states from different instants of
time can be compared by superimposing their reconstructed
versions. A vast collection of metrological tools to measure
object changes with sub-lambda sensitivity has grown and finds
application in different fields (Vest 1979).
In fluid-mechanical applications HI has been mainly
applied in the analysis of transparent fluids to visualize phase
changes invoked by temperature, concentration or pressure
gradients. For a direct comparison of recordings in particle
velocimetry, however, there are only a few early examples
restricted to liquid flows at low velocities of some 1 mm s−1
(Ueda et al 1982). The present status of HPIV suggests
one should revisit HI since it opens a sub-micron range of
sensitivities that is a factor of ten or a hundred better than
in particle imaging (Arroyo et al 2000). There are typical
situations in 3C flow analysis where one of the velocity
components is much smaller than the other (often the outof-plane component), yet all are to be measured with similar
relative accuracy.
Let us introduce the essential features of a HI measurement
of a particle displacement (figure 2). Assume a particle to move
within a time interval t from its original position P (t) by a
displacement vector r to a new position P (t + t). The
displacement produces a phase change ϕ in the scattered
light which is measured by interference when superimposing
the wave fields from both the particle positions.
We characterize the optical situation by wavevectors ki
of the illuminating light and ko of the observation light. The
resulting phase shift due to the altered path of the light is then
given as
(3)
ϕ = K r
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K = ko − ki =
2π
(uo − ui )
λ
(4)
with unit vectors uo and ui pointing in the propagation
directions of the respective light waves.
Obviously, the method responds to the component of the
displacement vector r parallel to the bisector between ko
and −ki . Take, for example, the common configuration of 90◦
viewing of a light sheet, then the sensitivity vector points at
45◦ backwards to the direction of the illuminating light.
Now, there is one important requirement to succeed in
this type of interferometry. Necessarily, light from both
the particle positions must superimpose during reconstruction
which requires that the particle images be smeared by
diffraction to such an extent that they overlap. Consequently,
a sufficiently small hologram aperture should be used for the
reconstruction. We see this requirement counteracts the PIV
postulate to make particle images as small as possible by using
a large aperture. However, in interferometry we no longer
rely on the subtraction of accurate particle positions but rather
derive the displacement from an interference of the according
waves. It may even happen that, for high particle-number
density, particle images are no longer resolved and a speckle
pattern occurs—nevertheless, the technique still works. Bear
in mind that besides the actual displacement, the illumination
direction as well as observation direction enter into the result!
We can show this nicely by a basic performance test where
the displacement of a block of 10 µm particles embedded in
plastic is studied by HI (figure 3). The familiar light-sheet
illumination is incident from the left. Between exposures the
block as a whole has been displaced horizontally to the right.
Figure 4 shows the resulting pattern of vertical interference
fringes. The existence of these fringes, of course, does not
indicate that the amount of motion has changed along the
block. Rather, it demonstrates the changing viewing direction
and its influence on the sensitivity vector as is obvious from
figure 3 where we have introduced the K -vectors for three
different positions. If all particles in a flow had experienced
the same displacement, say its average value, we would find
a parallel fringe system that represents the sensitivity-vector
dependence. In reality, the local displacement fluctuates
around the average value and the fringe contours will deviate
from straight lines accordingly. A larger displacement will
shift the fringe to one side, a smaller to the other. This is
indicated schematically by the irregular white line in figure 4.
The situation is analogous to the introduction of reference
fringes in ordinary HI. At each point this fringe deformation
must be evaluated taking into account the geometry of the
optical set-up. When the observation distance is much larger
than the size of the object the situation is simplified by
almost parallel K -vectors such that the absolute fringe order
is proportional to the particle displacement.
Two important features should be noted. First of
all, a given combination of illumination and observation
directions renders a single displacement component. For
three-dimensional displacement mapping, three such images
are required that can be obtained by switching between three
illumination set-ups. Secondly, there is ambiguity since the
result does not distinguish between increasing and decreasing
Holographic particle image velocimetry
Particles in
plastic block
Light sheet
Light sheet
ki
ki
K2
K1
K3
ko
ko
K
y
x
Flow
z
Cylinder
Hologram
Observer
position
Figure 3. Optical set-up and sensitivity vectors for the study of
particle displacements in a transparent block by HI. Rigid-body
motion is in-plane and to the right.
Figure 5. Set-up for a study of the axial velocity component of the
vortex-street flow behind a cylinder. The sensitivity vector K is
placed parallel to the cylinder axis by proper directions of
illumination ki and observation ko (towards the hologram).
The irregular fringes shown in figure 6 are evidence of a distinct
flow component parallel to the cylinder axis. In this case the
underlying parallel fringe pattern can be clearly seen at the
upper and lower boundaries of the field of view which are
outside the vortex region—the fringes are inclined at about
45◦ and have been extended by white lines. To illustrate the
evaluation, take the location indicated by the black ring in
the upper left where the dark fringe has been displaced by
almost one fringe spacing. This indicates an axial velocity of
50 mm s−1 —which is less than 10% of the mean flow.
Fringe deformation by
non-uniform displacement
Figure 4. Interferometric fringes for constant in-plane displacement
of a particle block due to the change of sensitivity vector K for
different positions in the block. A similar pattern would occur in a
constant-velocity flow. A non-uniform flow field distorts the fringe
pattern as schematically shown by the curve; the direction and
magnitude of its shift from the original fringe position are used to
evaluate the local velocity.
phase values. There are, however, techniques to eliminate this
dilemma where known external phase shifts are applied on
purpose. For details we refer to the basic literature (Jones and
Wykes 1983).
Generally in any PIV application, classical or holographic,
the time separation between exposures is set to produce
displacements that are appropriate for the method. Since HI
and HPIV may differ in sensitivity by a factor of about 100,
the flexibility of particle velocimetry is extended. Moreover,
by a combination of techniques and correct geometric layout,
flows can be tackled where velocities in the different spatial
directions differ considerably in magnitude.
HI has been used to supplement PIV results in convective
flows and in vortex-street analysis (Andr´es et al 1997, 2001a).
We present an example to study the irregular axial component
of a vortex-street flow behind a cylindrical rod (diameter 6 mm)
in a wind tunnel at 0.63 m s−1 mean flow velocity. Ideally
this is a two-dimensional problem in the plane perpendicular
to the axis of the rod. Usually, however, there are various
reasons that this situation is disturbed; for example, by effects
from the finite length of the cylinder. Figure 5 shows how the
sensitivity vector was aligned parallel to the rod by placing
the light sheet at 45◦ to the rod axis. While HPIV required
a time interval of 500 µs, a double exposure of 10 µs pulse
separation from the ruby laser produced the hologram for HI.
5. Electronic speckle pattern interferometry
Today, particle holography is still a technique that requires
the handling of a photographic emulsion in a dark-room
environment, associated with wet processing and timeconsuming laboratory work. We have mentioned earlier
that there are some competing registration media for fairly
instantaneous on-the-spot recording which have already been
checked for the purpose. The favourite solution, however,
would be to take holograms like ordinary images by video
sensors and transfer them digitally to computer for further
handling. This situation is similar to a certain phase in
traditional PIV when researchers looked for electro-optic and
computer-based alternatives to the photographic film and the
optical processing of PIV records. We will come back to
developments for computerized particle holography in the next
section. Presently, let us explore the suitability of a technique
that has found widespread use in optical metrology called
video holography or electronic (or digital) speckle pattern
interferometry (ESPI or DSPI) (Jones and Wykes 1983).
What are the problems in recording a hologram using a
CCD-camera? Primarily, the element size of such a target,
some 5–10 µm, is greatly inferior to the resolution properties
of the holographic film that allows one to record patterns
containing small details corresponding to spatial frequencies
of several thousand lines per millimetre. Usually we need
this high resolution due to the large angle between the object
and reference wave that is the result of the off-axis set-up.
The fringe period d generated by two superimposing waves
of wavelength λ is determined by the angle θ between their
propagation directions
d=
λ
.
2 sin θ
(5)
R67
K D Hinsch
Figure 6. HI of a vortex-street flow behind a cylinder in a wind-tunnel experiment; the flow is from left to right at 0.63 m s−1 . Regular
parallel fringes are extrapolated from the pattern along the top and bottom and are due to changing viewing direction. The irregular fringe
pattern in the vortex-street region represents the velocity component parallel to the cylinder axis (from Andr´es et al 2001a). At the sample
point marked by the black ring the fringe is displaced by almost one fringe spacing, which yields a velocity of 50 mm s−1 .
For a typical pixel size of 8 µm this restricts angles to
values of <2◦ which makes it impossible to take off-axis
holograms. Even for an in-line set-up the field width is limited
considerably. Furthermore, a hologram existing merely as
an array of intensity values in the computer cannot be used
to physically reconstruct an object wave. Thus, the unique
inversion to object-related coordinates is not directly possible
any more. Before computers became sufficiently powerful
to tackle such a task digitally, people thought of ESPI as a
different solution. When applied to particle holography we
obtain a 2D3C-method.
Figure 7 presents the basic scheme for this concept. The
particles in the light sheet are imaged onto a CCD-chip just
as in ordinary video-based PIV. To make the arrangement
sensitive to phase, however, a reference wave is introduced
via a beam combiner, thus creating an interference pattern on
the CCD. The reference wave is introduced in such a way
that it is collinear with the object light to avoid large-angle
interference which would not be resolved by the coarse pixel
structure of the CCD. Furthermore, the aperture of the imaging
lens must be stopped down (f -numbers usually are larger
than 5.6) to produce structures (speckles) on the CCD that
are also large enough to be resolved. The signal on the CCD is
called an image-plane hologram since the ordinary image has
been superimposed with reference light. As a consequence
this image becomes sensitive to small displacements in the
object, once more governed by the sensitivity vector K . Any
displacement component parallel to K will change the phase
of the light in the image plane. In the general case the signal
wave is not an image of particles but rather a speckle field.
The technique got its name from the interference of this speckle
pattern with the reference wave on an electronic detector. Since
the data are processed on a computer the method is sometimes
termed ‘digital’.
We start the measurement by storing an initial image in
the computer memory. In the following images, captured at
either video rate or laser-firing rate, the scattering particles
in the light sheet have moved. The optical situation of the
initial image is restored wherever and whenever this motion has
caused a phase change of an integer multiple of 2π . The video
hologram in this area will resume its original pattern. When
R68
Light-sheet
≈45°
K
Beam combiner
CCD-chip
ko
ki
Reference beam
Figure 7. The optical set-up of ESPI for the study of particle
displacements in a light-sheet. Interferometric sensitivity is
achieved by adding the reference beam. The instrument responds to
displacements parallel to the sensitivity vector K .
the incoming images are continuously subtracted from the start
image, dark contour lines in image space will be created, each
of which connects locations where ϕ = Nπ for a given evenvalued N—from which equation (1) yields the displacement.
At odd multiples of π two uncorrelated speckle patterns are
subtracted, rendering some average grey level. Thus, a fringe
system is produced that represents iso-lines of the velocity
component parallel to K .
ESPI has revolutionized many fields of laser metrology
because it provides measuring conditions of interferometric
sensitivity that can easily be applied even under adverse
everyday conditions.
Its application for fluid-dynamic
purposes promises similar advances. In a test a vortex-street
flow in air at 0.5 m s−1 has been studied (Andr´es et al 1999,
2001b) utilizing paired pulses from a twin-oscillator Nd:YAG
laser separated by 6 µs and repeated at 5 Hz. In the same
set-up, digital PIV recordings were obtained—blocking the
reference wave and setting the pulse separation to 400 µs.
Here, the light-sheet came from above and normal to the axis
of the cylinder, and viewing was at 90◦ parallel to the cylinder
axis. Therefore, the sensitivity vector pointed at 45◦ to the
cylinder axis upwards and towards the observer. Assuming a
negligible out-of-plane component we get a set-up that yields
mainly the vertical velocity component. Since ESPI is an
interferometric method it requires sufficient coherence of the
Holographic particle image velocimetry
(a)
(b)
-31.5
-31.5
-31.5
-31.5
-31.5
20
-31.5
20
0
0
-63.0
Z (mm)
15
-
.5
31
63.0
10
63.0
94.5
.5
-94
-126
31.5
0
-94.5
31.5
.0
63
15
Z (mm)
25
10
5
5
0 0
0
0
5
10
15
20
25
5
10
X (mm)
15
20
X (mm)
Figure 8. Light-sheet ESPI study of a vortex-street flow behind a cylinder in a wind-tunnel experiment. The optics is set to yield contour
lines of the vertical in-plane velocity component vy . (a) Iso-velocity contours for vy obtained from a traditional PIV record. (b) ESPI fringes
for a similar situation in the same flow.
laser light. In perpendicular light-sheet viewing, the size
of the sheet along the propagation direction of the light is
therefore limited by the coherence length. In the present case
this dimension was little more than a centimetre. However,
there are ways to expand this limit by intra-cavity etalons,
injection seeding or special optical devices partly delaying the
reference wave. Figure 8 demonstrates good agreement of
the vy -component as determined from a traditional PIV record
with the ESPI contour lines corresponding to a similar situation
in the same flow.
In summary, an ESPI set-up is a very convenient
instrument to improve the performance of a PIV system. In its
basic configuration any digital PIV CCD-camera set-up could
be modified by adding a reference wave. By turning this on and
off one could choose between ordinary and interferometric PIV.
Additional equipment can provide for phase-shifted recording
to eliminate ambiguity and to provide for automatic evaluation
by phase unwrapping (Jones and Wykes). A variety of
sophisticated algorithms are available for this purpose.
6. Digital particle holography
As mentioned above, ESPI is sometimes called video
holography, but as its name implies it is rather a kind of
interferometry, in which the interference pattern is recorded
electronically. The computer provides useful storage and
processing means, but it is not essential to the technique. As
a matter of fact, there is a version of ESPI used for studying
vibrating objects which has been in operation since long before
computer power was available for image processing.
In true computer holography, recording of the hologram
and reconstruction of the object wave are completely left
to the machine (Schnars et al 1994). A beautiful feature
of holography, of course, is lost, i.e. the production of a
fascinatingly faithful image of the object. The reconstructed
object will exist only as a set of sampled intensity data in
the computer’s memory. However, there is no need for
photographic film—a problem of increasing importance as
the number of commercially offered products shrinks—and
cumbersome darkroom work can be avoided. Furthermore,
in digital particle holography (Murata and Yasuda 2000)
the object image is readily available for further processing,
and hours and hours of interrogation time can be saved.
As an alternative, a traditional hologram could be taken
on photographic film to be scanned subsequently for digital
reconstruction.
At this point it is useful to estimate the amount of
information stored in a standard holographic plate. At a
resolution of, say, some 3000 line-pairs per millimetre each
square millimetre contains roughly 5 Mbyte of data; a 100 ×
100 mm2 plate thus contains a total of 50 Gbyte of information.
It is no wonder that it may take many hours to extract the
data from this powerful storage facility. Furthermore, it is
obvious that present electro-optic recording will fall short of
such performance.
There are three technological limits set in the electrooptic recording of a digital hologram: the size and spacing
of the individual pixels as well as the number of pixels in the
two-dimensional array, i.e. the CCD-chip. Presently, pixel
size is between 5 and 10 µm and—depending on the fill
factor—the spacing is similar. Array sizes range typically
from squares of 500 to 4000 pixels. In the latter case, the
overall dimension of 40 mm becomes comparable to the
holographic film size. As already stated in equation (3),
present pixel data allow only angles of a few degrees between
the object and reference light. This favours in-line set-ups
where the reference light is provided by the background
light propagating undisturbed through the large empty region
between particles. Under such conditions the maximum spatial
frequencies that have to be recorded on the hologram can be
made to fall within the frequency limit of the CCD-array.
Even here, restrictions are put on the distance between the
R69
K D Hinsch
Hologram
Aperture stop
CCD
Reference
wave
Hologram
Particle
Reconstructing
wave
Real particle
image
Figure 9. Optical set-up for Bragg-type reflection holography of a
particle field. The object and reference waves are incident on the
photographic plate from opposite sides. The reconstructing
conjugate reference wave is reflected by the interference pattern in
the emulsion to form a real particle image.
object and holographic plate as well as on transverse object
size. The pixel characteristics also impose image resolution
as set by the speckle noise produced by the low numerical
aperture configurations. Recent developments in solid-state
sensor devices such as CMOS active-pixel sensors—where
each detector element has an electronic amplifier circuit
attached to it—promise novel features in favour of holographic
applications (Jaquot et al 2001).
The second important component in digital holography is
the implementation of algorithms to perform the reconstruction
procedure on the hologram data, in our case, to reconstruct
digital images of the point-like particles. Here, the propagation
of light is modelled by Fresnel diffraction and the according
integrals have to be solved for the region of interest in
image space. Several approaches have been tried out, some
employing Fourier transformations (Kreis and J¨uptner 1997,
Pan and Meng 2001), others turning to wavelet transforms
(Onural 1993, Buraga-Lefebvre et al 2000, Co¨etmellec et al
2001).
Simulation experiments have been carried out to explore
the feasibility of the method on simple model objects consisting
of a few ideal particles. An interesting version that improved
depth resolution by repeated traversing of the object in different
directions has been demonstrated by Adams et al (1997). Here,
the various aspect angles of the object region could be extracted
from a single hologram as they were found at different
distances from the plate. The spatial object distribution was
assembled by application of tomographic principles. The basic
disadvantage of today’s digital particle holography—noise and
the extremely poor resolution due to the small aperture—has
been tackled in a promising novel approach by Pan and Meng
(2001). It could be shown that the utilization of the complex
light amplitude to determine particle positions in the calculated
image field relaxes these constraints considerably and also
reduces the adverse effects of speckle noise.
Generally, the future of digital particle holography
will benefit greatly from present technological progress in
electronic imaging and digital image processing that is also
fuelled by other powerful requirements in addition to those
in flow diagnostics. Just as PIV changed with the advent of
CCD-sensors and high-performance small computers, so will
the prospects grow for a widely applicable digital version of
particle holography.
R70
fiber
Fourier
transform lens
Optical
or digital
processor
Figure 10. Optical correlation for evaluation of a three-dimensional
real-image particle field. The image space is scanned with a
fibre-end light source. The hologram generates a converging wave
for each particle which superimpose for a three-dimensional fringe
system that is processed further.
7. Optical three-dimensional correlation
interrogation
For quite some time it has been considered a challenge
to present a three-dimensional optical correlation technique
equivalent to the two-dimensional Young’s fringe correlation
of the early PIV age. A method proposed a decade ago by
Coupland and Halliwell (1992) has been refined to offer a true
alternative to computer-based interrogation of particle images
reconstructed from holograms (Coupland and Halliwell 1997,
Barnhart et al 1999). It has the advantage that it produces
sub-micron accuracy in the position data which is comparable
to interferometric results. The present state of the method has
been communicated in details (Barnhart et al 2000, 2001), thus
it suffices to give a brief idea of the strategy. It is appropriate
to use a heuristic model that relates the performance of this
correlation to holographic principles (Hinsch 1993).
Recall the basic configuration to record a hologram of a
single particle (figure 1). Two spherical waves are incident
on the photographic plate from the same side: one of them
is the light scattered by the particle, the other comes from
the reference-source point. In a variation of this arrangement
called Bragg-reflection holography (figure 9), the reference
wave is incident from the reverse side. This also has the
practical advantage that the holographic plate can be placed
close to the object. In this geometry, the contour surfaces of
equal interference intensity are mainly parallel to the plate and
form a stack of reflecting planes in the emulsion which interact
with the reconstructing light according to the rules of Bragg
reflection. Upon illumination with the complex conjugate of
this reference wave, we thus obtain a reflected converging wave
focusing into a real particle image.
Now, assume that the roles of the waves for reconstruction
are interchanged: the reconstruction is done with a wave
identical to the original spherical wave from the particle which
then produces a conjugate reference wave, i.e. a wave focusing
into the former reference-wave focus. When the illuminating
light does not come exactly from the particle position but from
a location close by, the reconstructed wave will change slightly
in direction (if the focus has been displaced transversely) and
curvature (if it has moved axially)—but still remain a spherical
wave. Since we are performing double-exposure particle
velocimetry our hologram has registered particles always in
pairs and there will be two such waves for each particle pair, i.e.
we will find a pair of focus points in the vicinity of the original
reference-source point. When we place a point source at an
Holographic particle image velocimetry
arbitrary location in the real image region, we thus get a replica
of the arrangement of particle pairs in its neighbourhood—
located around the reference-source point.
Let us now assume that we illuminate such a double
exposure particle hologram from the end of a fibre placed
at some object position of interest (figure 10). Around the
reference-source point we find an ensemble of point foci
(crosses) that resemble the particles in the neighbourhood of
the fibre probe (dots). By scanning the fibre end through space
we can sample the particle field. A small-size aperture defines
the interrogation cross-section. A lens is now employed to
create the spatial-frequency power spectrum of these point
sources which is a system of fringes—usually curved lines
determined by the three-dimensional displacement in the
double particle field. Here, we have the three-dimensional
equivalent to Young’s fringes. Their analysis by Fourier
transformation—which in the practical set-up can be done
optically or by computer—renders the three-dimensional
correlation function.
There are more details to this technique that go beyond
the scope of this paper. It combines rapid field sampling
(by traversing the fibre probe) with fast dedicated analogue
processing to provide interferometric accuracy that is beyond
the sub-pixel accuracy of time-consuming digital evaluations.
Furthermore, it provides for simultaneous displacement
analysis of an adjacent rigid body surface. This example shows
that there are still areas where optics is very competitive with
digital techniques.
8. Conclusions
The past years have seen particle holography develop to such
a state that it has become a tool to be considered when the
fluid-dynamical problem under study requires an extended
measuring region to be investigated at a single instant of
time. Several impressive applications in flow facilities also
illustrate the size of the data set obtained from a single
holographic record and the need for economic extraction,
processing and visualization of the material. There are
constant novel developments improving the performance such
as noise suppression by short-coherence recording, to name
but one. In view of the unpopular photographic processing
involved in present-day high-resolution holography serious
efforts are undertaken to turn particle holography into a purely
electronic and digital technique. Such work has good chances
in the future because it is supported by the constant boom in
powerful electro-optic devices and computers. The presently
preferred type of holography is still a three-dimensional
extension of particle imaging. However, there are approaches
to apply otherwise established interferometric methods such
as HI and electronic speckle pattern interferometry to the task
of measuring particle displacements. At least an order of
magnitude in sensitivity can be obtained in this way. Finally,
even some schemes for optical processing of the holographic
particle data are applied successfully that save time and provide
sub-micron sensitivity during interrogation.
Acknowledgments
The work presented in this paper has benefited from a long
period of cooperative contacts with colleagues throughout the
world to whom I am very grateful. The mutual exchange with
J Kompenhans (DLR G¨ottingen) deserves special mention.
The European dialogue has been promoted considerably by
the EU-projects EUROPIV and PIVNET. A working group
on Holographic PIV has been established recently to promote
and stimulate work in this field. Members can participate
in its web-page http://photon.physik.uni-oldenburg.de/hpiv.
Sincere thanks are due to Heiko Hinrichs, Christof Surmann
and Sven Herrmann for the wealth of ideas that have fertilized
the Oldenburg activities in PIV.
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