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Phil. Trans. R. Soc. A (2010) 368, 1705–1737
doi:10.1098/rsta.2009.0285
REVIEW
High-performance holographic technologies
for fluid-dynamics experiments
B Y S ERGEI S. O RLOV1, *, S NEZHANA I. A BARZHI2 , S E B AEK O H3 ,
G EORGE B ARBASTATHIS3,4 AND K ATEPALLI R. S REENIVASAN5,6
1 Department
of Electric Engineering, Stanford University, Stanford, CA, USA
of Physical Sciences and Department of Astronomy and
Astrophysics, University of Chicago, Chicago, IL, USA
3 Department of Mechanical Engineering, Massachusetts Institute of Technology
(MIT ), Cambridge, MA, USA
4 Singapore–MIT Alliance for Research and Technology
(SMART ) Centre, Singapore
5 International Center for Theoretical Physics, Trieste, Italy
6 Department of Physics and Courant Institute of Mathematical Sciences,
New York University, New York, NY, USA
2 Division
Modern technologies offer new opportunities for experimentalists in a variety of research
areas of fluid dynamics. Improvements are now possible in the state-of-the-art in
precision, dynamic range, reproducibility, motion-control accuracy, data-acquisition rate
and information capacity. These improvements are required for understanding complex
turbulent flows under realistic conditions, and for allowing unambiguous comparisons to
be made with new theoretical approaches and large-scale numerical simulations.
One of the new technologies is high-performance digital holography. State-of-the-art
motion control, electronics and optical imaging allow for the realization of turbulent flows
with very high Reynolds number (more than 107 ) on a relatively small laboratory scale,
and quantification of their properties with high space–time resolutions and bandwidth.
In-line digital holographic technology can provide complete three-dimensional mapping
of the flow velocity and density fields at high data rates (over 1000 frames per second)
over a relatively large spatial area with high spatial (1–10 mm) and temporal (better
than a few nanoseconds) resolution, and can give accurate quantitative description of
the fluid flows, including those of multi-phase and unsteady conditions. This technology
can be applied in a variety of problems to study fundamental properties of flow–particle
interactions, rotating flows, non-canonical boundary layers and Rayleigh–Taylor mixing.
Some of these examples are discussed briefly.
Keywords: fluid-dynamics experiments; optical diagnostics; holographic technology;
rotating flows; turbulent mixing; Rayleigh–Taylor instability
*Author for correspondence ([email protected]).
One contribution of 13 to a Theme Issue ‘Turbulent mixing and beyond’.
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This journal is © 2010 The Royal Society
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1. Preamble
In 1893, John Williams Strutt, later Lord Rayleigh, performed a series of
experiments on the determination of the absolute densities of atmospheric gases
with an unprecedented accuracy of one hundredth of a per cent. For direct
measurements of pressure that extended over very small ranges, he designed
and constructed a manometric gauge, an apparatus offering several points of
novelty, mechanical precision and advanced optical diagnostics. Rayleigh noticed
that the density of nitrogen extracted from air disagreed with that of nitrogen
released from chemical reactions, particularly prepared from ammonia (Rayleigh
1893). This discrepancy amounted to one-half of a per cent and might not have
been noticed by a less scrupulous scientist. However, the result was beyond
measurement error and definitive. These observations attracted the attention
of William Ramsay, who suggested that atmospheric nitrogen may contain an
admixture of another heavier gas. The idea was audacious, as the composition
of air had been studied extensively during those times. Support for this idea
came unexpectedly from another highly accurate experiment. As early as 1785,
when applying electric sparks to atmospheric nitrogen and oxygen in the presence
of alkali, Henry Cavendish reported that about 1/120 of the bulk of air did
not participate in chemical reactions (Cavendish 1785). Repeating Cavendish’s
experiments, applying various techniques for extracting atmospheric nitrogen
and systematically studying its physical and chemical properties, Rayleigh and
Ramsay reported the discovery of a new, chemically neutral, monatomic gas
that was named argon (‘inactive’ in ancient Greek). In the following years, there
followed the discoveries of helium, xenon, neon and krypton; in 1899, in studies
of radioactive decay of thorium, radon was found, completing the eighth group
of chemical elements in Mendeleev’s periodic table. A release of 300 ml of xenon
required processing of 77.5 million litres of air. The delicacy and precision of
Rayleigh’s investigations were extraordinary (Rayleigh & Ramsay 1895).
We recount this bit of history here as a classic example of how highprecision quantitative measurements may lead to scientific discoveries and reveal
qualitative secrets of nature that go far beyond a large collection of perceptible
facts. This lesson also has implications for turbulent mixing.
2. Introduction
Turbulent motion of fluids is often characterized by non-equilibrium heat and
mass transport and sharp gradients of density and pressure, and may be a subject
to spatially varying and time-dependent acceleration or rotation (e.g. Reynolds
1894; Tennekes & Lumley 1972; Frisch 1995; Sreenivasan 1999; Abarzhi 2008). Its
theoretical description is challenging, and its complexity encourages large-scale
numerical simulations. On the experimental side, such turbulent flows are hard to
study systematically in a well-controlled laboratory environment (e.g. Bradshaw
1971; Meshkov 2006). Their sensitivity to details and the transient character of
the dynamics impose constraints on the accuracy and spatio-temporal resolution
of the measurements of the flow quantities, as well as on the data-acquisition
rate. Despite several state-of-the-art experiments in the past, the question ‘how
to quantify these flows reliably’ remains still open.
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Even for the simplest canonical turbulent flows, whose dynamics is statistically
steady, existing experimental capabilities do not provide sufficient information
for a precise and quantitative verification of predictions of theories and models
(Kolmogorov 1941a,b; Batchelor 1953; Monin & Yaglom 1975; Barenblatt 1979;
Pope 2000). The theories and models, in contrast, frequently become either
too mathematical or needlessly empirical, involve a multiplicity of adjustable
parameters and do not always identify a set of robust parameters that need to be
diagnosed precisely (e.g. Reynolds 1883; Barenblatt & Goldenfeld 1995; Abarzhi
2008; Procaccia & Sreenivasan 2008). Massive information is usually available
in numerical simulations, which can track all predetermined flow quantities (e.g.
Kaneda et al. 2003; Dimonte et al. 2004; Donzis et al. 2005; Arneodo 2008).
However, compared with experiments, simulations are less informative about the
physical phenomena, as they sample a mathematical model and do not always
quantify the amount of error, which may be substantial, especially when the
turbulent processes depart from familiar scenarios. To identify the universality
and randomness of realistic turbulent processes and to extend our knowledge
of turbulence beyond idealized considerations, one requires new experimental
methodologies that are capable of providing adequate statistics and that augment
existing approaches in non-canonical circumstances with tight control over the
experimental parameters (Orlov & Abarzhi 2007).
The methods of experimental diagnostics of fluid turbulence have improved
steadily over time. Until the late 1920s, the flow measurements were limited to
time-averaged properties such as the average velocity and pressure differences
(e.g. Reynolds 1883; Schlichting 1956; Bradshaw 1971). Valuable insights into
turbulence characteristics were provided by Prandtl (1925), who perfected
qualitative flow visualization techniques (Prandtl & Tietjens 1934). Schlieren and
shadowgraph techniques became widespread in flows with density differences (e.g.
Settles 2001). In the 1950s, thermal anemometry became a basic metrological tool
as it allowed for the quantification of the rapid velocity fluctuations, by measuring
the change in resistance of a small probe, when slightly heated and placed in the
flow (e.g. Bruun 1995). A little later, laser Doppler velocimetry became available
(e.g. Durst 1981). These traditional turbulence measurements are made at one
(or, a few) point(s) in the flow and yield the temporal dependencies of the
velocity, temperature or other fields. Spatial properties of turbulent dynamics
along the direction of the mean velocity are often derived from the temporal
linear traces via Taylor’s hypothesis (Taylor 1935), whose limitations are not
completely understood, even in the case of simple canonical flows (Lumley 1965;
Badri Narayanan et al. 1977; Douady et al. 1991; Sreenivasan 1991). Indeed, the
assumptions involved in the hypothesis make it hardly applicable under transient
conditions (Abarzhi 2008). A broad introduction to the traditional methods of
flow visualization and measurement techniques is given in Goldstein (1996) and
Tavoularis (2009).
In the past 20 years, two major accomplishments in experimental diagnostics
of turbulent flows are particle image velocimetry (PIV; e.g. Dudderar & Simpkins
1977; Meynart 1980; Adrian 1991; Willert & Gharib 1991; Raffel et al. 2007) and
planar laser-induced fluorescence (e.g. PLIF; Sreenivasan et al. 1989; Seitzman &
Hanson 1993), applied to measure velocity and passive scalars, respectively.
Volumetric measurement of the scalar volume has also been attempted (e.g.
Prasad & Sreenivasan 1990; Buch & Dahm 1996, 1998). In high Reynolds number
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flows, characteristic velocities and accelerations are high and orient themselves
increasingly more rapidly, and, to follow the flow, the seed particles tracking
the motion should be relatively small. The small scattering cross section and
low light-collection efficiency, combined with the short-time exposures needed to
capture images without blur, led to the use of high-intensity lasers. For better
resolution of small-scale dynamics, the flow is seeded with multiple particles,
and the auto-correlation of double exposure is applied for processing images of
the particle fields (e.g. Adrian 2005). Conventional particle techniques analyse
data taken from a single plane within the volume of fluid flow and provide twodimensional velocity distributions. More advanced stereoscopic PIV allows for a
derivation of a third out-of-plane velocity component in a single or in a few planes
(Lecerf et al. 1999). These tools have played an important role in studies of a
variety of practical problems including atmosphere pollution, combustion in diesel
engines, particle segregation and clustering (Bec et al. 2006). They need further
development for studies of fundamental aspects of canonical turbulent flows, such
as small-scale intermittency or the connection between Lagrangian and Eulerian
descriptions, in part due to resolution limitations of the measurement technology
(Crawford et al. 2005; Donzis et al. 2005; Schumacher 2007). Grasping essentials
of the turbulent dynamics in non-canonical circumstances will certainly require
novel approaches for flow visualization and for the measurement of turbulent
flow quantities.
As in all natural processes, turbulent transport obeys laws of conservation
of mass, momentum (angular momentum, if applicable) and energy (Landau &
Lifshitz 1987a,b). In the description of canonical Kolmogorov-type turbulence,
mass and momentum are conserved owing to conditions of homogeneity, isotropy
and locality. In the asymptotic regime of statistically steady flows, when the
influence of initial and boundary conditions is regarded as negligible, the flow
is driven solely by the transport of kinetic energy (Kolmogorov 1941a,b).
Energy is conjugated with time, and space–time properties are related by the
Taylor hypothesis, thus allowing for the interpretation of experimental data,
such as linear tracers in thermal anemometry or instantaneous snapshots of
particle fields in PIV, as markers of turbulent dynamics. Substantial dynamic
range, extending over several decades, is required for accurate quantification of
power laws describing turbulent dynamics, whereas large values of macroscopic
hydrodynamic numbers, such as the Reynolds number, ensure that the flow is
truly turbulent (e.g. Sreenivasan & Meneveau 1988; Jayesh & Warhaft 1992).
In contrast to the classical Kolmogorov scenario, realistic turbulent processes
are often statistically unsteady and are governed by (in general, independent)
transport laws for mass, momentum and potential and kinetic energies.
Momentum is conjugated with space, and to capture momentum transport, one
has to diagnose spatial distributions of the velocity and density fields, along
with their temporal dependencies (Landau & Lifshitz 1987a,b; Abarzhi 2008).
Furthermore, for accurate experimental quantification of space–time properties
of non-equilibrium dynamics, these measurements would require relatively high
spatial accuracy and temporal resolution, sufficient for the evaluation of spatial
and temporal derivatives of the flow quantities, whereas dynamic range and dataacquisition rate should be adequate for providing ample statistics from a single
experimental run (Abarzhi 2008). Compared with canonical cases, repeatable
implementation of non-equilibrium turbulent flows in the laboratory environment
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requires tighter control of the macroscopic parameters, as well as of the initial
and boundary conditions owing to sensitivity and the transient character of
their dynamics.
Reliable quantification of such turbulent processes appears to be a formidable
experimental task. Current flow-diagnostics technologies restrict application to
nearly canonical flows, whereas there is a substantial need, in both practical
applications and validation of new theoretical approaches and large-scale
numerical simulations, to understand complex turbulent flows under realistic
conditions, including multi-phase, buoyancy-driven and high Reynolds number
flows, and to provide adequate experimental description for their scaling,
structure and statistics (e.g. Kaneda et al. 2003; Dimonte et al. 2004; Meshkov
2006; Abarzhi et al. 2007; Arneodo 2008; Benzi et al. 2008). Application of
modern technologies developed in several optical engineering and industrial
fields can potentially offer significant leverage in this direction (Orlov 2008).
Enhancement by orders of magnitude in accuracy, precision, reproducibility,
control, data-acquisition rate and information capacity can be envisaged using
these new technologies, so that the quality of experimental data can be brought
to higher standards.
This review is structured as follows. In §3, the basics of digital holographic
storage technology are discussed with emphasize on the aspects that are most
relevant to the design and actual implementation of the high-performance
hydrodynamic experiments, including advanced optical imaging, high-precision
motion control and digital signal processing. In §4, we describe digital holography
and several three-dimensional imaging techniques with a particular focus on their
application for holographic PIV (HPIV). Section 5 outlines two laboratory-scale
integrated experimental platforms for studies of hydrodynamic instabilities and
turbulence in rotating flows at high Reynolds numbers that may incorporate these
technologies, both for precise realization of the complex flows and for advanced
three-dimensional holographic diagnostics. We conclude the review with a brief
summary in §6.
3. Digital holographic technology
In hydrodynamics experimental systems, the quality of flow diagnostics (e.g.
optics and imaging) needs to be adequate to characterize the complex fluid
flows realized by sophisticated mechanical and motion-control technologies (e.g.
wind tunnels, laboratory-scale mechanical setups, etc.). This situation is similar
to digital holographic storage, which relies on several enabling technologies
including precision mechanics, motion control, lasers, high-resolution optics and
digital signal processing. The performance of each of these components has to
be closely matched in order to maximize the holographic system capabilities,
while emphasizing only one or few of the aspects of the system is not sufficient
to obtain the ultimate system-performance characteristics. We will provide an
overview of how the capabilities of advanced holographic technology have evolved
in the last 10–15 years and how techniques developed in digital holography
may be applied to improve the quality and precision of the hydrodynamics
experiments.
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detector
array (CCD)
storage
medium
lens
laser
lens
al
n
sig
mirror
arm
rm
ea
SLM
c
ren
addressing
device
(e.g. galvo scanner)
e
ref
beam splitter
mirror
Figure 1. Basic holographic data-storage system comprising a coherent laser source, a spatial light
modulator (SLM), imaging optics, charge-coupled device (CCD) or complementary metal-oxide
semiconductor (CMOS) detector array, addressing unit and storage medium.
(a) Principles of information recording, storage and retrieval via holography
Holography provides the physical ability to reconstruct an object’s wavefront
from the imprinted fringes, created by the interference of two optical beams in a
photosensitive material (Gabor 1948; Leith & Upatnieks 1962; Denisyuk 1963). In
digital holographic data storage, information is presented in the form of pixelated
pages, which can be rather large (of the order of 1 million pixels), stored in the
form of volumetric gratings. The data-page storage is performed by intersecting
two coherent laser beams within the photosensitive storage material (figure 1).
The object beam contains the information to be stored, and the reference beam is
designed to be simple to reproduce, for example, a collimated beam with a planar
wavefront, or a spherical wave. The resulting optical interference pattern causes
chemical and/or physical changes in the photosensitive medium: a replica of the
interference pattern is stored as a change in the refractive index, absorption or
thickness of the photosensitive medium. When the stored interference grating is
illuminated with a reference beam, some fraction of the incident light is diffracted
by the grating, thus reconstructing the original signal pattern that contains the
stored data.
Owing to the Bragg selectivity of volume holograms, a large number of
data pages can be superimposed in the same location of the medium and
accessed independently by probing with an appropriate reference beam, as
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long as the gratings belonging to the different pages are distinguishable. The
process of superimposing multiple holograms is referred to as multiplexing. Basic
multiplexing techniques include the angular method (Leith et al. 1966; d’Auria
et al. 1973), in which the reference beams differ by the angle of their incidence,
the wavelength method (Leith et al. 1966; Yu et al. 1991; Rakuljic et al. 1992),
in which the references differ in their optical wavelengths, and the shift method
(Psaltis et al. 1995), in which the same reference beam of a curved wavefront
(e.g. spherical) is used, but the recording and readout are performed at different
lateral positions of the medium.
Theoretically, holography offers high-volumetric storage density with an upper
limit of approximately V /l3 (van Heerden 1963), where V is the material volume
and l is the light wavelength, which translates into several terabits per cubic
centimetre of the storage medium. Data pages can contain large numbers of
data pixels and, practically, up to several millions of bits per page have been
demonstrated. Since a page is stored and recalled as a whole, data-transfer rates
can be extremely high, exceeding 10 Gb s−1 . Among other unique properties of
holographic data storage is the possibility of realizing an extremely fast dataaccess time, as short as 50 ms or less, because the optical reference beam can be
moved very rapidly without any inertia.
(b) High-resolution imaging and digital signal processing
in holographic data storage
The holographic pages usually include modulation-channel coding and error
correction in order to make the data more robust, but it is very important that
the image of the data page is as close to the original object as possible. During
the readout of the stored holographic data, the pixels in the image captured
by the camera have to match the pixels of the charge-coupled device (CCD) or
complementary metal-oxide semiconductor (CMOS) detector with approximately
±1 mm accuracy. Any optical aberrations and distortion in the imaging system
or defocus of the detector array would spread energy from one pixel to its
neighbours and introduce errors in the retrieved data. To provide high-quality
imaging, several architectures employing different optical arrangements have been
employed (figure 2).
Double Fourier transform imaging (figure 2b) usually outperforms other
architectures and provides the best-quality images with lowest distortions for
the same level of optical complexity compared with other solutions. The imaging
optics used in the real high-performance holographic storage platforms is rather
sophisticated and is designed with multiple lens elements in order to realize the
required low-distortion crisp imaging (figure 3).
A distinctive feature of the digital holography is that each pixel in a data page
(figure 4) is treated as a unique data channel, and its spatial position is controlled
with nearly submicron accuracy throughout the image, whereas the digitized pixel
values are measured with high precision (8 bits or higher), resulting in high spatial
resolution and signal-to-noise ratio (SNR) over the entire image.
In digital holographic storage, the concepts of image data fidelity and the
information capacity of the imaging data are treated rather rigorously and
quantitatively and are characterized by the bit-error-rate (BER) and, more
generally, by the SNR. The BER is the fraction of bits that are detected
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(a) SLM
lens
f
di
(b)
SLM
lens
SLM
telecentric
2FT lens
optics
f
image plane
telecentric
2FT lens
optics
f1
CCD
f1
Fourier plane
holographic
medium
CCD
f
holographic
f2 medium f2
SLM
lens ( f1)
lens
Fourier plane
f
f1
(d )
holographic
do medium
holographic
partial Fourier
medium location of medium
f
(c)
CCD
Fourier plane
CCD
lens ( f2)
I
Figure 2. Optical imaging architectures used for holographic data storage: (a) conventional Fresnel
imaging, (b) double Fourier transform, (c) image plane re-imaging using telecentric double Fourier
transform optics (the object is de-magnified by f2 /f1 , arrangement of the optical relay optics
is similar to (b)) and (d) van der Lugt’s system (the imaging condition is 1/f1 +1/l=1/f2 , the
magnification is f1 /l) (van der Lugt 1973). 2FT is double Fourier transform.
incorrectly after passing through the data channel when the bitstream size
approaches infinity. In practice, the BER can be evaluated statistically by
using the histogram of the received signal amplitudes constructed from a
sufficiently large dataset: the CCD pixels are divided into two populations: those
corresponding to 0s (OFF pixel) and 1s (ON pixel) of the original image (figure 5).
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(a) l /4
photopolymer media
CCD
REF
FLC
SLM
REF
(b)
SLM
CCD
Figure 3. (a) Optical schematic and (b) a photograph of a compact custom-built 12-element double
Fourier transform lens implemented in a holographic disc system developed at Stanford (Orlov et al.
2004). The lens provided imaging of 1024 × 1024 pixels array onto the high-speed CCD camera with
optical distortions of less than 1 mm over the entire field of view (figure 4). (a) REF is the reference
beam and FLC is the ferroelectric liquid crystal. (b) Scale bar, 1 cm.
(a)
(b)
(c)
Figure 4. (a) A digitized high-resolution (1024 × 1024 pixels; 13.1 × 13.1 mm) holographic image
captured at 1000 frames per second (fps) (Orlov et al. 2004), the octagonal shape, ‘voids’ and a
complicated ‘maze’ of bright pixels were imprinted during the signal encoding, (b) same image after
digital thresholding and (c) enlarged fragment of the digitized image. Each pixel is a 12.8 × 12.8 mm
square. The image was captured from a rotating disc (at linear velocity of approx. 1 m s−1 ) using
a single, 15 ns, 500 mJ pulse of a frequency-doubled Nd:YAG laser.
The measured pixel intensities can be used to compute the normalized probability
density functions W0 (x) and W1 (x) of the received signal strength for 0s and 1s,
respectively, and to compute the BER as the integral over the overlapping regions
of the distributions.
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W0(x)
probability density
W1(x)
w0(x)
w1(x)
xthr
x
Figure 5. The distribution functions of received ON and OFF pixels can be estimated from the
histogram of a sufficiently large experimental dataset. The area of the shaded region on the graph is
equal to the BER. Shoulders of the distributions can be approximated by analytical functions w0 (x)
and w1 (x), (for example, by Gaussian distributions), allowing us to evaluate BER quantitatively,
even when it is extremely low and there were no or few actual errors detected in a given experimental
dataset (Hoffnagle & Jefferson 2000).
In holographic storage, the SNR is defined and evaluated numerically as
m1 − m 0
,
SNR = 2
2
s1 + s 0
(3.1)
where m1 and m0 are the average values of detected 1s and 0s of an initially binary
image, respectively, and s1 and s0 are the corresponding statistical variances. The
SNR is the parameter that determines the BER in communications and data
storage. In a more general sense, the SNR governs the information capacity of
any experimental datasets, irrespective of their physical representation—whether
the data are instantaneous snapshots, such as images obtained in PLIF or PIV,
or one-dimensional temporal traces such as in thermal anemometry.
(c) The Stanford digital holographic storage system
The development of data storage systems based on holography started in the
early 1960s, stimulated by the invention of the laser as well as by the pioneering
work of van Heerden (1963), which postulated that storing an interference
pattern in a three-dimensional medium can be used to store and retrieve digital
information. The first systems built at Bell Labs, International Business Machines
(IBM) and Radio Corporation of America (Anderson 1968; Lipp & Reynolds
1970; Steward et al. 1973) employed photographic films or plates, in which the
recording layer was rather thin, making the massive multiplexing in the same
volume difficult.
In the 1990s, a new wave of research and development activity in the field of
holographic memories was triggered by the overall need in high-capacity archival
data storage and by the rapid progress in the development of enabling technologies
such as the compact integrated SLMs and CCD cameras and the all-solid-state
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high-precision
translation stage
computer
control
high-speed
High-speed
air-bearing
spindle
optical shaft
encoder
Displaytech
650 fps SLM
driver
pulsed Nd:YAG
laser (532 nm)
data out
Polaroid/Aprilis
photopolymer
medium
Siros
Siros
1Gbit/sec
1Gbit s–1
HDSchannel
HDS channel
electronics
electronics
9696
parallel
parallel
bitbit
streams
streams
each
each
10Mbit/s
Mbit s–1
atat10
compensating
plate
FT
lens
FT
lens
FLC
SLM
Synchronization
synchronization
electronics
electronics
Kodak
1000 fps
1000fps
digital
CCD
Control
control
computer
computer
address
address
memory
memory
Figure 6. Architecture of the Stanford holographic storage system. HDS is holographic data storage,
FT is Fourier transform.
lasers. These enabled the design and construction (at relatively low cost) of
holographic storage systems with as many as 1 million pixels per page, in which
the data pages could be read at video or higher rates (Hong et al. 1995). Further
advancements in optics, materials and digital signal processing ultimately allowed
a density as high as 388 bits mm−2 to be attained (Burr et al. 2001), proving the
potential of the holographic technology for ultra-high-density storage. In parallel
with systems development, a significant progress has been made in developing
high-sensitivity photopolymer media (Waldman et al. 1997; Dhar et al. 1998) for
high-density holographic recording. Novel approaches have been introduced in
both holographic multiplexing methods and imaging optics. New techniques, such
as correlation (Darskii & Markov 1988), fractal (Psaltis et al. 1990), peristrophic
(Curtis et al. 1994) and shift (Psaltis et al. 1995) multiplexing, were introduced
and developed, while the introduction of high numerical aperture (NA) optics in
holographic recording (Orlov et al. 2004) allowed for high individual data-page
densities (more than 0.5 bit mm−2 per page).
The 1 Gb s−1 digital holographic system was developed at Stanford in the late
1990s and demonstrates the state-of-the-art holographic technology capabilities.
It incorporates unique state-of the-art custom imaging optics, holographic imageprocessing electronics, high-precision electro-mechanical and motion control
technology, a dedicated high-speed CCD camera and synchronization electronics
and sophisticated control software (figures 6 and 7).
The complete design of a digital holographic storage system is complex
since multiple performance trade-offs have to be balanced simultaneously and
accounted for (see Mikaelian et al. 1970; Bernal et al. 1996; Coufal et al. 2000;
Orlov et al. 2004). Simultaneous requirements of high storage density and high
data rate represent particular challenges since the optical signal strength of the
images (which needs to be rather high for high readout speed) drops with the
number of superimposed holograms, which, in turn, directly affects the storage
density. Another important aspect is the implementation of precise and accurate
motion control of the system, which becomes a substantial challenge since the
holograms have to be transported under the holographic head at approximately
1 m s−1 linear velocity of the medium with a few tens of nanometres mechanical
accuracy and with timing precision of a few tens of nanoseconds.
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Double Fourier
transform lens
pulsed Nd:YAG
laser (not shown)
Kodak C7
1000 fps CCD
IBM FLC
640 fps SLM
laser shaft
encoder
air-bearing
spindle
Polaroid / Aprilis
photopolymer disk
MEMS accelerometers (2)
Figure 7. Photograph of the digital holographic system (for scale, the disc diameter is 165 mm).
MEMS is micro-electro-mechanical systems.
Holographic recording and readout are performed with a pulsed frequencydoubled Nd:YAG laser (532 nm, 500 mJ per pulse and 20 ns pulse length). A
1024 × 1024 IBM ferroelectric liquid crystal SLM was pixel-matched to a 1000
frames per second (fps) digital Kodak C7 CCD camera. The holographic disc,
comprising the 200 mm thick photopolymer medium, sandwiched between the
two optically flat glass substrates, is mounted on a precision air-bearing spindle
capable of up to 10 000 r.p.m. The rotation rate, stabilized through the active
feedback digital electronic control, is typically better than 0.01 per cent, while the
air-bearing mechanical stiffness provides the reproducible frictionless motion with
a radial accuracy of 10 nm or better. The stability of the radial positioning during
the disc rotation is actively monitored using a pair of high-sensitivity microelectro-mechanical accelerometers (figure 7) employed in the differential mode
to improve the detection capability of any mechanical imbalances. Addressing
of different angular positions on the disc is performed using a precision laser
shaft encoder, which provided up to 16 384 locations along the disc with a
few nanoseconds (typically ±5 ns) timing accuracy. The shaft encoder and
synchronization electronics allowed addressing any angular location on the disc
with an accuracy and repeatability of better than ±20 nm. In order to access the
different radial positions of the disc, the spindle was mounted on a high-precision
mechanical stage with positioning repeatability of ±25 nm.
Real-time digital signal processing and holographic channel decoding were
performed by custom high-speed reprogrammable electronics. The megapixel
images from the camera are processed on-the-fly by the electronics at 1000 fps,
providing the real-time channel decoding, data de-interleaving and error
correction.
The SLM is optically imaged onto the CCD array using a short-focal-length
low-distortion (less than ±1.0 mm over the entire CCD field) custom-built optical
double Fourier transform lens pair (figures 3 and 4). The total NA of 0.75 is
divided between the central, high-resolution, low distortion portion (NA = 0.36),
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(b)
Figure 8. (a) A sample digital hologram read at 1000 fps and (b) a retrieved decoded JPEG colour
image; the diffraction efficiency of the hologram was approximately 0.5 per cent.
used by the SLM, and the outer area, used by the reference light.1 The signal and
reference beams pass through the same set of optics, minimizing the physical size
of the optical system and eliminating mechanical constraints typical for high NA
optical systems. In order to minimize the imaging distortion, the optical design
is made fully symmetrical using an optical compensator plate, whose thickness
equals that of the disc; the plate is incorporated into the second objective lens
(figure 3).
A series of performance demonstrations were carried out using this system. In
the first demonstration, the source user data were encoded into digital holographic
pages, stored in the holographic disc, retrieved at 1 Gb s−1 from a disc rotating
at 300 r.p.m. (i.e. approx. 1 m s−1 linear velocity with respect to the optical head)
and decoded on-the-fly by the electronics (Orlov et al. 2004). The decoded data
were captured and converted back into original file format (JPEG colour images).
A sample hologram readout and decoded at 1 Gb s−1 is shown in figure 8. In a
later demonstration, 12 parallel uncompressed digital video streams were encoded
and stored in the holographic disc, and subsequently retrieved, at 0.65 Gb s−1 ,
electronically decoded on-the-fly and simultaneously displayed on three computer
monitors (four video streams per computer).
The hologram’s signal strength and the timing precision of the components
and control hardware allowed for much higher optical data rates, given that
the holograms could be physically transported and moved under the optical
readout head and addressed with sufficient speed and accuracy. In high datarate experiments (Orlov et al. 2004), sustained optical readout data rates as high
as 10 Gb s−1 were demonstrated (figure 9).
As of today, the demonstrated 10 Gb s−1 optical transfer rate represents the
highest data rate ever produced by any optical storage device. This, along
with other unique attributes of the system, such as fully hardware-implemented
1 In a PIV system, the effective NA can be estimated as D/2L, where D is the diameter of the lens
entrance pupil and L is the distance from the light sheet to the camera. For the parameters of
a typical PIV setup employed in, for example, a wind tunnel: D ∼ 5 cm and L ∼ 100 cm, the NA
would be approximately 0.025.
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Figure 9. A sample 1 Mpixel holographic image captured at 10 Gb s−1 (i.e. 10 000 fps). The insets
on the right show the details of the holographic channel block coding. At high readout rates, the
image is somewhat more ‘blurry’ owing to higher levels of electronic noise and lower optical signals.
1 Gb s−1 holographic channel electronics and a high-resolution optical-imaging
system, makes the Stanford holographic system an important and yet
unsurpassed milestone in the development of digital holographic data-storage
technology.
4. In-line digital holography and three-dimensional imaging
This section presents several specific implementations of holographic imaging
methods, including one of the most common holographic measurement techniques
that has been employed in experimental fluid mechanics: HPIV. While the
traditional HPIV involved recording holograms from the flow-marking particles
on holographic medium or plates (Barnhart et al. 1994; Meng & Hussain
1995a,b; Zhang et al. 1997; Sheng et al. 2003), as new digital sensors and
computation methods have been developed, it became apparent that recording
the interferogram on a digital camera rather than film was advantageous,
provided that the interferogram was being sampled sufficiently. Owing to its
relative simplicity compared with the traditional HPIV, digital HPIV evolved
to become more attractive and popular. As in conventional HPIV, complete
three-component three-dimensional (3C-3D) velocity vector fields of the flow
can be characterized by the digital HPIV with high spatial and temporal
resolution, and accurate quantitative description of the fluid flow can be obtained.
There are many different types of HPIV and other holographic techniques
in fluid velocimetry, such as digital speckle pattern interferometry (Bhaduri
et al. 2006) and optical diffraction tomography (Lobera & Coupland 2008).
In this section, we focus the attention of the reader on some aspects of inline digital HPIV. The in-line digital HPIV requires a relatively simple setup
and, at the same time, has a unique capability to perform a three-dimensional
measurement. Besides, upon some modifications enabling three-dimensional
diagnostics, numerous particle-tracking techniques traditionally applied in PIV
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can still be employed in HPIV. For a more detailed state-of-the-art and history
on various HPIV methodologies, as well as for an outline of technical issues and
comparison of performance, the reader is referred to Hinsch (2002, 2004) and
references therein.
Multiplexed volume holographic imaging (VHI) is another digital threedimensional imaging method. Multiplexed VHI captures longitudinally
distributed multiple focus planes and rearranges them laterally onto the image
plane. This mapping is implemented in optics by using volume holographic
diffractive optical elements. Multiplexed VHI has the potential to extend
the capabilities of the traditional two-dimensional PIV systems to true
three-dimensional imaging.
(a) In-line digital holography
Digital holography revolutionized holography in many ways since it was
first implemented (Goodman 1967; Goodman & Lawrence 1967; Schnars &
Jüptner 1994). Digital holograms are recorded by digital detectors instead of
holographic media and are reconstructed numerically. Although holograms are
recorded with the same optical setup as in traditional holography, the digital
reconstruction process is significantly more convenient, and eliminates the need
of a physical holographic medium. In addition, digital holography is capable
of capturing holograms over an extended period of time, allowing to capture
‘holographic movies’, i.e. record and store a succession of digital holograms.
Thus, dynamic events can be observed with fine temporal and three-dimensional
spatial resolution. As various numerical/statistical analyses, digital processing,
as well as digital compensation of optical aberrations can be easily incorporated
with reconstructed images or holograms, digital holography provides a versatile
analysis tool. Digital holography has been studied extensively and implemented in
a variety of applications such as topology measurement of micro-optics (Charrière
et al. 2006), morphology analysis of cells (Marquet et al. 2005), refractive
index measurements (Rappaz et al. 2005) and imaging colloidal particles
(McGorty et al. 2008).
As in traditional holography, both in-line (Gabor 1948) and off-axis
(Leith & Upatnieks 1962; Denisyuk 1963) configurations are employed in digital
holography. For particle imaging, in-line geometry is usually preferred for the
following reasons: (i) forward scattering from particles is captured, which is
significantly stronger than side scattering (Thompson 1989), (ii) since particles
are sparsely distributed in the volume of interest, the reference wave is unaffected,
and the uniform background and halo signals do not severely deteriorate the
reconstructed images, and (iii) better lateral resolution is achieved than in the
off-axis configuration because higher spatial frequency components are better
preserved in reconstruction. However, controlling the intensity ratio of objectto-reference waves is easier in the off-axis geometry. Hence, interference fringes
of high contrast and higher SNR can be achieved. The reconstructed images of
particles appear differently in the in-line and off-axis geometries, and the off-axis
geometry may allow using smaller particles and at higher densities than the in-line
geometry. To date, many different optical configurations have been implemented
to balance SNR in HPIV (Bernal & Scherer 1993; Hussain et al. 1993; Zhang
et al. 1997; Sheng et al. 2003).
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reference wave
R(x, y)
object waves
O(x, y)
Δ
N pixels
x
particles
z
propagation
distance, z0
detector
Figure 10. Typical configuration of in-line digital holography. A plane reference wave propagating
parallel to the optical axis illuminates the particles. Each particle produces scattering, and
interference is created by the scattered light and the reference wave. A digital detector records
the intensity of the interference pattern.
A typical optical setup of in-line digital holography is shown in figure 10. A
reference wave R(x, y), typically a plane or spherical wave of uniform amplitude,
illuminates particles in the volume of interest. As the reference wave propagates,
scattering from the particles (denoted by an object wave O(x, y)) produces
spherical wavefronts. In particle imaging, particles are small and sparsely
distributed, and the largest fraction of the reference wave is not affected by the
particles; instead, it keeps propagating to the detector. Interference is created by
the object wave and the reference wave, and is captured by the digital detector.
In order to control lateral magnification, imaging optics may be placed in front
of the detector.
The captured holograms contain phase information of the object waves, and
digital reconstruction decodes the phase information. The hologram signal is
multiplied by the reference wave to obtain the reconstructed wave, and this
process is equivalent to illuminating the hologram with the reference wave in
optical reconstruction. Light propagation from the reconstructed wave is then
computed in the reverse fashion (Goodman 1996).
Since the typical size of the detector (N D in figure 10) is much smaller
than the propagation distance from the particle, the paraxial approximation
can be applied and the light propagation can be computed using the Fresnel
diffraction formula (Goodman 1996). In most cases, the Fresnel diffraction
formula is implemented in the spatial frequency domain via fast Fourier transform
because of simple and faster computation, and the Fresnel kernel for various
propagation distances can be pre-computed and stored in memory. We emphasize
that the Fresnel approximation is applicable only in low NA systems. If
the NA is greater than approximately 0.5, then more rigorous reconstruction
methods are required, such as direct evaluation of the Rayleigh–Sommerfeld
diffraction integral (Zhang et al. 2006) and the Kirchhoff–Helmholtz transform
(Kreuzer et al. 1992).
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Computing the Fresnel diffraction for sequential values of the propagation
distance z provides the entire three-dimensional field distribution sampled at
the respective planes. If the distance z coincides with the actual propagation
distance of a scattering source, a crisp image of a particle appears in the
reconstructed image, similar to an in-focus image in traditional photography.
Digital holography can be performed in real time or off-line and achieves
digital refocusing in reconstruction without any form of opto-mechanical
scanning. This is a unique property of digital holography that allows for
determination of particle locations in three-dimensional space, even from a single
hologram.
The lateral resolution is determined by the maximum spatial frequency that
can be measured. The axial resolution is relatively poor compared with the lateral
resolution, and identification of the axial position requires careful estimation. As
a rule of thumb, the lateral resolution is proportional to the optical wavelength
and is inversely proportional to the NA of the system, whereas the axial
resolution is inversely proportional to (NA)2 , similar to many of the free-space
optical imaging systems. The actual resolution depends on the specifics of the
optical system such as aberrations and noise. The resolution is dependent on
the space–bandwidth product and the distance to the reconstruction plane,
and, furthermore, it is non-uniform across the reconstructed volume. This
phenomenon is common in many cases of axial imaging and, usually, is not
severe enough to merit concern, provided that the axial reconstruction range
is smaller than the mean distance to the camera. The sample volume or depth
of field also depends on the resolution and SNR. More detailed dicussion on
the resolution and the sample volume can be found elsewhere (Hinsch 2002;
Meng et al. 2004).
(b) In-line digital holographic particle image velocimetry
In order to obtain the 3C-3D velocity fields from holograms, different methods
have been developed: particle tracking, intensity correlation (Barnhart et al.
1994), complex field correlation (or object conjugate reconstruction) (Coupland &
Halliwell 1992; Barnhart et al. 2002) and tomographic reconstruction (Soria &
Atkinson 2008). Particle tracking is the simplest method: from the reconstructed
field or intensity, all particles are detected and tracked over different time frames
so that the 3C-3D velocity fields can be measured. The overall system performance
is determined by the accuracy in identifying particles and finding their locations.
In correlation methods, such as intensity or complex field cross-correlation,
the 3C-3D fluid velocity fields are directly recovered from the cross- or
auto-correlation of the reconstructed intensity or complex field, respectively,
without detecting individual particles. In tomographic reconstruction, multiple
holograms captured in different directions reconstruct three-dimensional intensity
tomographically and find particles. Each of these methods has its own advantages
and disadvantages and also technical issues that depend on resolution, accuracy,
sample volume, scale of experiments, size and number of particles, etc. More
detailed discussion on these competing techniques can be found in Hinsch (2004).
In this section, we focus on the particle-tracking method because it is intuitive
and does not depend on a particular imaging implementation (e.g. holographic,
tomographic, etc.).
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Y
Z
X
6000
4000
2000
54 000
52 000
50 000
48 000
46 000
44 000
42 000
40 000
0
0
2000
4000
6000
8000
Figure 11. A snapshot of the reconstructed instantaneous three-dimensional particle distribution
in isotropic turbulence from digital holographic measurement (Meng et al. 2004). Measurement
volume is 8.09 × 6.47 × 12 mm3 .
In order to obtain the 3C-3D fluid velocity fields, after multiple holograms
were captured over time (the time period between holograms should be known
for the velocity computation), all holograms are reconstructed numerically. Then,
particles are identified and their three-dimensional positions are estimated using
signal and image processing, as shown in figure 11. In identifying and locating
particles, it is a significant advantage that rotationally symmetric particles are
traced and their size variation is minimal. Simple pattern matching techniques
(e.g. the centroid of a circular intensity image as in concise cross-correlation,
Pu & Meng 2000) can rigorously identify the particles and provide a good
estimate of their lateral positions. The reconstructed three-dimensional optical
field distributions are employed in estimating the axial position. To estimate
accurately the axial distance z, various focus metrics have been proposed,
including spectral l1 norms (Li et al. 2007), integration of the amplitude modulus
(Dubois et al. 2006), decomposition of the object image with the Fresnelet
bases and sharpness metric (Liebling & Unser 2004), iterative techniques (Yu &
Cai 2001; Thelen et al. 2005) and particle extraction using complex amplitude
(Pan & Meng 2003).
After all the particles are identified, particles in two neighbouring time
frames should be matched to find their correspondence. At this stage, one
can employ numerous techniques applied in traditional PIV. Computing crosscorrelation of images (reconstructed images in digital HPIV) is often used, in
which three-dimensional cross-correlation of a subimage finds the displacement
of particles. This image-based methodology is simple and intuitive and can
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use either amplitude or intensity of the signal (Wormald & Coupland 2009),
but its accuracy is limited, as subimages should be properly chosen for
optimal system performance. Alternatively, the coordinates of the particles
can be employed to find correct particle correspondence. There are two
types of coordinate-based matching methods (Meng et al. 2004): (i) the
synthesized particle-image method that computes correlation of synthesized
particles (Pereira & Gharib 2002) and (ii) direct coordinate-based methods
pairing particles with genetic algorithms (Sheng & Meng 1997), concise crosscorrelation (Pu & Meng 2000) or expectation minimization (Stellmacher &
Obermayer 2000). Each method has different requirements and performance in
terms of computation speed, memory and reliability. Prior knowledge of the flow
properties, e.g. flow direction, speed and geometry of the flow channels, can
improve the accuracy and speed of the particle-matching process significantly. In
experiments, a choice of a proper particle-matching method depends on the flow
characteristics.
In order to obtain the velocities of the particles and, hence, the threedimensional flow-velocity map, the displacement of each particle is divided by
the time difference of two adjacent time frames (figures 12 and 13). Figure 12
represents the historically first HPIV measurement of the volumetric threedimensional velocity distribution performed by Barnhart et al. (1994). The
holograms of particles in a 25.4 × 25.4 × 60 mm3 volume in a pipe channel flow
(with the mean velocity of 0.8 m s−1 ) were recorded using two consecutive pulses
of a Nd:YAG laser and reconstructed using the phase-conjugate approach. More
than 400 000 three-dimensional velocity vectors have been extracted from the
measurement volume. Figure 13 presents a three-dimensional velocity map in the
vicinity of a laminar jet measured with HPIV (Meng et al. 2004).
In-line digital holography is advantageous in particle imaging since, with a
relatively simple setup, complete four-dimensional information can be obtained
with high spatial and temporal resolution. Unlike conventional PIV (Adrian
2005), which relies on the weak scattered signal from the particle, in HPIV, the
entire illumination beam is captured by the camera. This allows for the use of
low-power lasers and thus results in both less intrusive diagnostics and significant
cost reduction of the experiments. In the next section, we introduce a new multiexposure technique that enables a further increase in the data-acquisition rate
for particle imaging.
(c) Multi-exposure digital holography
In digital holography, the measurement speed is limited mainly by three
parameters, specifically, camera frame rate, numerical reconstruction speed and
computation time for identifying and matching particles. Reconstruction and
computation speed can be significantly improved by using multiple processors
or a specialized graphics processing unit (Shimobaba et al. 2008). In order to
acquire data at speeds beyond the camera frame rate limit, multi-exposure digital
holographic imaging (MEDHI) was developed (Dominguez-Caballero et al. 2007).
In MEDHI, the reference wave is modulated as short laser pulses, where the
modulating speed is faster than the frame rate of a camera. MEDHI takes multiple
snapshots and encodes them into a single hologram. During the integration
time, multiple laser pulses illuminate particles in the volume of interest, and
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Figure 12. Three-dimensional velocity map measured in a pipe channel flow in a 25.4 × 25.4 ×
60 mm3 volume using the first implementation of HPIV (Barnhart et al. 1994).
Y
jet direction
Z
X
jet
Figure 13. Three-dimensional velocity map in the vicinity of a laminar jet measured with HPIV
with a measurement volume of 1.4 × 4.3 × 8 mm3 (Meng et al. 2004).
multiple holograms are incoherently added and recorded in a single frame. In
reconstruction, the trajectory of a particle during the integration time is obtained
from a single hologram (figure 14). MEDHI is particularly useful in high-speed
HPIV, although the allowable particle density in the flow is somewhat limited,
and sophisticated particle matching algorithms are required.
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in focus
out of focus
z position (μm)
(b)
(a)
9300
9250
9200
9150
9100
9050
9000
8950
200
220
240
x position 260
280
(μm)
300
400
380
320
360 340
m)
(μ
n
o
ti
si
y po
300
Figure 14. (a) Reconstruction of a moving object in static water with MEDHI. Seven laser pulses
were used, whose duration was 100 ms, with 250 ms separation. (b) Trajectory of a target in threedimensional space. The average speed of the target was 233 mm s−1 , and the measurement volume
was 100 × 100 × 300 mm3 (Dominguez-Caballero et al. 2007).
As a concluding remark, we note that digital holography is still an
interferometric measurement method. This means that phase variation of the
wavefront, e.g. refractive-index change of flow, can, in principle, be measured
directly and visualized by digital holography without using any particles by
employing optical tomographic techniques (Wolf 1969, 1970; Berry & Gibbs 1970)
to reconstruct the three-dimensional structure of the flow with sufficient contrast.
This interferometric measurement approach can be potentially useful for studies
of interfacial dynamics or capillary turbulence (surface water waves).
(d) Multiplexed volume holographic imaging
Volume holograms exhibit Bragg selectivity that forms the basis of operation of
holographic memories. Recently, a scheme of VHI was proposed, in which Bragg
selectivity is instead used for imaging (Sinha et al. 2004). In VHI, the pointspread function of the imaging system is engineered such that multi-dimensional
information can be extracted efficiently. VHI has been demonstrated in different
imaging modes and platforms such as a telescope (Sinha & Barbastathis
2004), microscope (Barbastathis et al. 1999; Luo et al. 2008), profilometer
(Sinha & Barbastathis 2003), a hyperspectral imager (Liu et al. 2004; Sun
et al. 2005) and a passive monochromatic binary depth-discrimination system
(Oh & Barbastathis 2008).
Figure 15 shows the principle of VHI in a depth-selective imaging mode for a
point source; for example, a PIV particle. In the recording process (figure 15a),
a volume hologram is recorded by two mutually coherent plane waves. Then, the
hologram is inserted at the Fourier plane of a traditional 4-f (telescopic) imaging
system and behaves as a wavefront-selective device. If a point source is located
at the focal plane of the objective lens (figure 15b), a spherical wave emitted
from the point source becomes identical to the wavefront that had been used
during the recording process. Strong Bragg diffraction then appears because the
phase of an incident wavefront, as it propagates, perfectly matches the phase
of the stored wavefront. If a point source is defocused (figure 15c), then the
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(a)
X″
X
point
source
volume
hologram
f1
signal wave
X′
(b)
X′
(c)
Z
strong
diffraction
weak
diffraction
Z
X
X
f2
f2
f1
volume
hologram
δz
f1
volume
hologram
Figure 15. Principle of depth-selective imaging of VHI systems: (a) recording geometry, (b) focused
object and (c) defocused object.
light incident on the volume hologram is not a plane wave; Bragg diffraction
is dramatically attenuated. This particular configuration of VHI converts the
defocus of a point source into intensity contrast (Sinha et al. 2004).
Owing to the Bragg selectivity properties of the volumetric holograms, multiple
holograms can be recorded in the same location of the holographic material
and be retrieved independently. Figure 16 shows the procedure of multiplexing
two holograms in a VHI process. At the first exposure, a volumetric hologram
is recorded in a standard geometry, as shown in figure 15a. At the second
exposure, the point source is shifted longitudinally, and the signal wave is rotated
to avoid overlap of images at the detector. In the imaging mode, the two
fields of view located at two distinct depth planes are Bragg-matched with the
multiplexed volume holograms, and two strong diffraction signals are produced
and are laterally arranged on the image plane. Since all multiplexed holograms
are optically reconstructed, the multiplexed VHI provides longitudinally spaced
multiple fields of view at different depths. Since the diffraction efficiency is
inversely proportional to the square of the number of multiplexed holograms
(e.g. Coufal et al. 2000), careful tuning of the recording parameters is required to
ensure that all the multiplexed holograms have sufficient diffraction efficiencies.
Figure 17 shows images of fluorescent particles in a water tank captured
by multiplexed VHI presented in figure 16, and three depth slices are imaged
simultaneously (Liu et al. 2004). Recently, up to five multiplexed volume
holograms have been used in a microscopy system (Luo et al. 2008).
Image stacking of multiple images reconstructs three-dimensional information
on particle positions, while no numerical reconstruction is required. Once the
three-dimensional data from multiple slices are recovered, the particle
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y
#2
#1
x
y
#2
#1
image
plane
z
x
Dz
f2
multiplexed
volume
hologram
f1
Figure 16. Principle of multiplexed VHI. Two longitudinally distinct volumes are sampled and
appear separated laterally at the image plane.
(b)
0.10
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
y′ (yP)
diffraction efficiency
(a)
50
100 150 200
depth, ZP (mm)
250
300
z′ (XP, lP)
Figure 17. (a) Diffraction efficiencies of three depths and (b) simultaneous images of the three
slices. Simultaneous optical sectioning by multiplexed volume holograms (Liu et al. 2004). Three
holograms were recorded at 488 nm with a 40×, 0.65 NA objective lens in phenanthrequinone
(PQ)-doped polymethylmethacrylate (PMMA). Three recording point sources were on-axis and
separated by 50 mm longitudinally. The lateral field of view is 300 mm. With PQ–PMMA volume
holograms, a diffraction efficiency of approximately 30 per cent has been achieved (Luo et al. 2009).
identification and matching can be implemented. Optical systems of a traditional
two-dimensional PIV system can be used in conjunction with the multiplexed
volume hologram. Using the VHI, a quasi-three-dimensional PIV, i.e. PIV
with a multitude of conventional two-dimensional measurement planes, can be
implemented.
5. Fluid-dynamics experiments employing new technologies and diagnostics
Quantification of realistic turbulent processes requires non-intrusive diagnostics
of fast events with ultra-high performance in space–time resolution, bandwidth
and data-acquisition rate, and calls for elaboration of integrated experimental
systems that incorporate the state-of-the-art in optical imaging, digital signal
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processing, image processing, precision mechanics, motion control and material
science. Employing experimental and metrological capabilities of the holographic
technology, one can potentially implement and accurately measure highReynolds-number turbulent flows in a relatively small laboratory form-factor
and provide data suitable for a direct comparison with large-scale numerical
simulations. Appreciating that the future is subject to change, we briefly
discuss here some opportunities for improvement of precision, accuracy, dynamic
range, reproducibility and information capacity of the experimental dataset for
turbulence in rotating fluids and for Rayleigh–Taylor (RT) turbulent mixing.
(a) Turbulence in rotating flows
The understanding of turbulence in rotating systems is of fundamental
importance in many instances in engineering (e.g. turbo-machinery), geophysics
(e.g. ocean circulation and hurricanes) and astrophysics (e.g. star formation)
(Lathrop et al. 1992; Frisch 1995; Baroud et al. 2002). The problems are often
unsteady and anisotropic, and, in relation to what we know about homogeneous
and isotropic turbulence, call for new techniques of data analysis. While many
studies of rotating flows exist, there are relatively few that examine fundamental
issues. For instance, the conventional wisdom is that the only effect of rotation
on decaying grid turbulence is to slow down its decay rate while preserving selfsimilarity. In reality, in any confined system that is created in a laboratory,
there exist inertial wave modes of the container, in addition to the turbulent
motion. These modes are relatively well defined and discrete. The extent to
which the modes interact with turbulence is presently unclear. Understanding
this interaction is a basic problem in any laboratory study, and characterizing its
spatial structure is an arduous but interesting task.
The two dimensionless parameters characterizing rotating flows are the
Reynolds number and the Rossby number. The Reynolds number is Re = UR2 /n,
where U is the rotation rate, R is the radius of the chamber and n is the fluid
kinematic viscosity, and it is about 107 –108 in realistic turbulent flows. The
Rossby number U /UL is inversely proportional to the rate of rotation, and it
appears to be between 0.01 and 0.1 for typical large-scale geophysical flows
(Pedloski 1987). Most experiments do not achieve such small Rossby numbers
(with the exception of the liquid helium experiments of Bewley et al. (2007))
because high rotation rates are hard to implement owing to limitations of the
technology employed currently. Furthermore, the nature of data obtained is
relatively primitive.
Utilizing the experimental capabilities of holographic technology, digital
motion control and precision mechanics, one can achieve conditions of high
Reynolds numbers (up to 107 for water), high rotation rate (up to 10 000 r.p.m.
i.e. approx. 103 rad s−1 ), low Rossby number and prescribed time-varying
accelerations in a laboratory-scale platform for an apparatus with a chamber
radius of only 20 cm (Orlov & Abarzhi 2007). Even higher Reynolds numbers can
be envisaged if fluids of low kinematic viscosity are employed. The experimental
and flow-diagnostics parameters derived from the parameters of the holographic
platform described in §3 (Orlov et al. 2004) are summarized in table 1.
The HPIV based on the in-line digital holography or volume HPIV based on
VHI can be employed for complete three-dimensional flow visualization. Smallsize (diameter from 0.1 to a few microns) neutrally buoyant particles can be
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Table 1. Summary of experimental capabilities and the flow diagnostics for rotating turbulence.
rotation rate
angular acceleration
maximum g
radial
tangential
rotation accuracy
positioning accuracy
radial
tangential
laser pulse rate
chamber size
height
diameter
camera speed
optical spatial resolution
temporal resolution
30–10 000 r.p.m.
(0.5–167 Hz)
up to 1000 r.p.m. s−1
stability: ±0.01%
1.2 × 105 m s−2 (12 000 g)
21 m s−2 (2 g)
<10 nm radial run-out
R = 20 cm at 7500 r.p.m.
R = 20 cm at 1000 r.p.m. s−1
at 30–10 000 r.p.m.
16.7 s−2
25 nm
100 nm
0–30 kHz
up to 30 cm
up to 40 cm
1000 fps at 2 Mpixels;
6000 fps at 512 × 512 size
∼1 mm
∼10 mm
5 ns
1 cm field of view
10 cm field of view
added to the flow, and the chamber can be illuminated with laser pulses at
specific times and imaged onto the high-speed digital camera using a highresolution high-NA optical system. High spatial (approx. 10 mm over 10 cm area)
and temporal (less than 5 ns) resolution of the system may allow for mapping the
flow-velocity fields with extreme accuracy and high data rate (more than 1000
flow images per second), thus providing statistical evaluation of the turbulent-flow
quantities.
(b) Rayleigh–Taylor instability and turbulent mixing
Turbulent mixing induced by the RT instability plays a key role in a wide
variety of natural phenomena, ranging from astrophysical to micro-scales, and
including inertial confinement fusion, flows in atmosphere and ocean, explosion
of supernovae, Universe formation and in industrial applications in aeronautics
and optical telecommunications (Rayleigh 1882; Davies & Taylor 1950; Abarzhi
2008). RT mixing can be considered a sample case of a non-equilibrium turbulent
process, whose fundamental scaling and spectral and statistical properties depart
substantially from the classical scenario. For instance, it is unclear whether the
concepts of non-dissipative energy cascade, the existence of inertial interval and
k −5/3 velocity spectrum (that are compatible with the time and scale invariance of
the rate of energy dissipation in isotropic homogeneous turbulence, Kolmogorov
1941a,b) are applicable to an accelerating RT flow (where the rate of energy
dissipation is statistically unsteady; e.g. Abarzhi et al. 2005, 2007). A trustworthy
guidance is required from the experiments to quantify the transports of mass,
momentum and energy in the non-equilibrium turbulent process and to extend
our knowledge of turbulence flows well beyond idealized isotropic consideration.
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S. S. Orlov et al.
Table 2. Summary of the experimental parameters for RT instability and turbulent-mixing studies
and the optical-diagnostics capabilities.
experimental and diagnostics parameters
linear acceleration
maximum linear velocity
sizes of the mixing chambers
time of sustained acceleration
data-acquisition rate
spatial resolution
HPIV particle size
hydrodynamic parameters
Atwood number
expected turbulent-mixing zone size
observation area size
0 g to ±10 g, full digital control
±10 m s−1
300 (L) × 300 (W) × 300 (H) mm
150 (L) × 150 (W) × 300 (H) mm
cylindrical 300 (dia) × 300 (H) mm
up to 1000 ms
1000–2000 fps
∼10 mm (over 10 cm field of view)
1–10 mm
0.15 to near 1.0
up to 100 mm
∼100 × 100 × 100 mm
(centre of the chamber)
RT flows are rather difficult to implement and study in a laboratory
environment, and progress achieved over recent decades in the experimental
studies of RT instability was significant (e.g. Read 1984; Dalziel et al. 1999;
Dimonte & Schneider 2000; Waddell et al. 2001; Kucherenko et al. 2003;
Ramaprabhu & Andrews 2003; Dimonte et al. 2004; Meshkov 2006). To quantify
scaling, structure and statistics of RT flows, one requires a diagnostics ability to
measure with high accuracy and precision, both in space and in time, the multiple
and time-dependent scales in a single experimental run and to augment it with
high reproducibility of the acceleration history and accurate control of the initial
and boundary conditions and other macroscopic parameters (Abarzhi 2008).
The experimental capabilities in precision mechanics, motion control, highresolution imaging, digital holography and data-analysis techniques can be
integrated into a new experimental platform for studying RT instabilities
and turbulent mixing (table 2). HPIV based on digital in-line holography,
combined with PLIF, can allow for direct observations and mapping of the
three-dimensional velocity and density fields with a high data-acquisition rate
(more than 1000 fps) over a large spatial area with high spatial (approx. 10 mm)
and temporal (better than 5 ns) resolution. High NA imaging optics may yield
high light-collection efficiency and, hence, SNR at moderate power lasers (approx.
1 W at 1 kHz), thus providing non-invasive and accurate diagnostics of the flow
parameters.
6. Summary and conclusions
The state-of-the-art techniques in motion control, electronics, digital signal
processing and optical imaging may allow for realization of turbulent flows with
very high Reynolds number (107 and higher) in relatively small laboratory-scale
experiments, and the quantification of their properties with high spatio-temporal
resolution and bandwidth. These experimental and metrological capabilities
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could be used for simultaneous, three-dimensional, diagnostics of spatial and
temporal properties concerning the transport of momentum, angular momentum
and energy, as well as the identification of scaling, invariants and statistical
properties of the complex unsteady turbulent flows. The new technologies can be
used to investigate a large variety of hydrodynamic problems of non-Kolmogorov
turbulence, accelerating and rotating flows, turbulent boundary layers, RT
instability and turbulent mixing.
The development of the holographic storage system at Stanford was supported by the Defense
Advanced Research Projects Agency (Dr L. N. Durvasula) and the International Storage
Industry Consortium (INSIC) within the Holographic Data Storage Systems (HDSS) and
Photorefractive Information Storage Materials (PRISM) university–industry consortia. S.S.O.
gratefully acknowledges technical contributions of and valuable discussion with members of the
HDSS and PRISM consortia, including R. T. Ingwall and D. A. Waldman of Aprilis, Inc., B. V.
K. V. Kumar and V. Vadde of Carnegie-Mellon University, M. O’Callaghan of Displaytech, Inc.
(Boulder, CO, USA), G. W. Burr, H. J. Coufal, C. M. Jefferson, B. Marcus, R. M. Shelby and
G. T. Sincerbox of IBM Almaden (San Jose, CA, USA), J. Sanford of IBM Yorktown, B. H.
Schechtman of INSIC, D. G. Koch and K. P. Thompson of Optical Research Associates (Pasadena,
CA, USA), J. Hong and J. Ma of Rockwell International (Thousand Oaks, CA, USA), A. Daiber,
M. McDonald and R. Okas of Siros Technologies (San Jose, CA, USA), W. Phillips, E. Bjornson, F.
I. Dimov and X. Li (formerly of Stanford University), R. K. Kostuk and M. Neifeld of University
of Arizona and, in particular, L. Hesselink of Stanford University who served as a coprincipal
investigator of both DARPA/INSIC consortia. At MIT, the work on the digital holography and on
the three-dimensional imaging was supported by the Defense Advanced Research Projects Agency
(USA), the National Institutes of Health (USA) and the National Research Foundation (NRF)
through the Center for Environmental Sensing and Modeling (CENSAM) of the Singapore–MIT
Alliance for Research and Technology (SMART) Centre. S.B.O. and G.B. gratefully acknowledge
José A. Domínguez-Caballero, Nick Loomis, Laura A. Waller, Lei Tian, Jerome H. Milgram, Cabell
S. Davis, Jason Dahl and Michael S. Triantafyllou for valuable discussions and suggestions. At the
University of Chicago, this work has been partially supported by the US Department of Energy
and the US Department of Defense. S.I.A. expresses her gratitude to L. P. Kadanoff and R. Rosner
for discussions.
References
Abarzhi, S. I. 2008 Review of nonlinear coherent dynamics of unstable fluid interface: conservation
laws and group theory. Phys. Scr. T132, 014 012. (doi:10.1088/0031-8949/2008/T132/014012)
Abarzhi, S. I., Gorobets, A. & Sreenivasan, K. R. 2005 Turbulent mixing in immiscible, miscible
and stratified media. Phys. Fluids 17, 081 705. (doi:10.1063/1.2009027)
Abarzhi, S. I., Cadjun, M. & Fedotov, S. 2007 Stochastic model of Rayleigh–Taylor turbulent
mixing. Phys. Lett. A 371, 457–461. (doi:10.1016/j.physleta.2007.06.048)
Adrian, R. J. 1991 Particle imaging techniques for experimental fluid mechanics. Annu. Rev. Fluid
Mech. 23, 261–304. (doi:10.1146/annurev.fl.23.010191.001401)
Adrian, R. J. 2005 Twenty years of particle image velocimetry. Exp. Fluids 39, 159–169.
(doi:10.1007/s00348-005-0991-7)
Anderson, L. K. 1968 Holographic optical memory for bulk data storage. Bell Labs. Rec. 45,
319–326.
Arneodo, A. 2008 Universal intermittent properties of particle trajectories in highly turbulent flows.
Phys. Rev. Lett. 100, 254 504. (doi:10.1103/PhysRevLett.100.254504)
Badri Narayanan, M. A., Rajagopalan, S. & Narasimha, R. 1977 Experiments on fine structure of
turbulence. J. Fluid Mech. 80, 237–255. (doi:10.1017/S0022112077001657)
Barbastathis, G., Balberg, M. & Brady, D. J. 1999 Confocal microscopy with a volume holographic
filter. Opt. Lett. 24, 811–813. (doi:10.1364/OL.24.000811)
Phil. Trans. R. Soc. A (2010)
Downloaded from http://rsta.royalsocietypublishing.org/ on August 11, 2017
1732
S. S. Orlov et al.
Barenblatt, G. I. 1979 Similarity, self-similarity and intermediate asymptotics. New York, NY:
Consultants Bureau.
Barenblatt, G. I. & Goldenfeld, N. 1995 Does fully developed turbulence exist? Reynolds
number independence versus asymptotic covariance. Phys. Fluids 7, 3078–3082. (doi:10.1063/
1.868685)
Barnhart, D. H., Adrian, R. J. & Papen, G. C. 1994 Phase-conjugate holographic system for highresolution particle-image velocimetry. Appl. Opt. 33, 7159–7170. (doi:10.1364/AO.33.007159)
Barnhart, D. H., Hallwell, N. A. & Coupland, J. M. 2002 Object conjugate reconstruction
(OCR): a step forward in holographic metrology. Proc. R. Soc. Lond. A 458, 2038–2097.
(doi:10.1098/rspa.2001.0956)
Baroud, C. N., Plapp, B. B., She, Z.-S. & Swinney, H. L. 2002 Anomalous selfsimilarity in a turbulent rapidly rotating fluid. Phys. Rev. Lett. 88, 114 501. (doi:10.1103/
PhysRevLett.88.114501)
Batchelor, G. K. 1953 The theory of homogeneous turbulence. Cambridge, UK: Cambridge
University Press.
Bec, J., Biferale, L., Boffetta, G., Celani, A., Cenciini, M., Lanotte, A., Masacchio, S. & Toschi, F.
2006 Acceleration statistics of heavy particles in turbulence. J. Fluid Mech. 550, 349–358.
(doi:10.1017/S002211200500844X)
Benzi, R., Biferale, L., Fisher, R. T., Kadanoff, L. P., Lamb, D. Q. & Toschi, F. 2008 Intermittency
and universality in fully developed inviscid and weakly compressible turbulent flows. Phys. Rev.
Lett. 100, 234 503. (doi:10.1103/PhysRevLett.100.234503)
Bernal, L. P. & Scherer, J. 1993 HPIV measurements in vortical flows: lessons learned and future
prospects. Prof. Fluids Eng. Div. ASME 148, 43–50.
Bernal, M.-P. et al. 1996 A precision tester for studies of holographic optical storage materials and
recording physics. Appl. Opt. 35, 2360–2374. (doi:10.1364/AO.35.002360)
Berry, M. V. & Gibbs, D. F. 1970 The interpretation of optical projections. Proc. R. Soc. Lond. A
314, 143–152. (doi:10.1098/rspa.1970.0001)
Bewley, G. P., Lathrop, D. P., Maas, L. R. M. & Sreenivasan, K. R. 2007 Inertial waves in rotating
grid turbulence. Phys. Fluids 19, 071 701. (doi:10.1063/1.2747679)
Bhaduri, B., Mohan, N. K., Kothiyal, M. P. & Sirohi, R. S. 2006 Use of spatial phase shifting
technique in digital speckle pattern interferometry (DSPI) and digital shearography (DS). Opt.
Express 14, 11 598–11 607. (doi:10.1364/OE.14.011598)
Bradshaw, P. 1971 An introduction to turbulence and its measurement. New York, NY: Pergamon
Press.
Bruun, H. H. 1995 Hot-wire anemometry: principles and signal analysis. Oxford, UK: Oxford
Science Publications.
Buch Jr, K. A. & Dahm, W. J. A. 1996 Experimental study of the fine-scale structure
of conserved scalar mixing in turbulent shear flows. Part 1. J. Fluid Mech. 317, 21–71.
(doi:10.1017/S0022112096000651)
Buch Jr, K. A. & Dahm, W. J. A. 1998 Experimental study of the fine-scale structure of
conserved scalar mixing in turbulent shear flows. Part 2. J. Fluid Mech. 364, 1–29. (doi:10.1017/
S0022112098008726)
Burr, G. W., Jefferson, C. M., Coufal, H., Jurich, M., Hoffnagle, J., Macfarlane, R. M. & Shelby,
R. M. 2001 Volume holographic data storage at an areal density of 250 gigapixels/in2 . Opt. Lett.
26, 444–446. (doi:10.1364/OL.26.000444)
Cavendish, H. 1785 Experiments on air. Phil. Trans. R. Soc. Lond. 75, 372–384. (doi:10.1098/
rstl.1785.0023)
Charrière, F., Kühn, J., Colomb, T., Montfort, F., Cuche, E., Emery, Y., Weible, K., Marquet, P. &
Depeursinge, C. 2006 Characterization of microlenses by digital holographic microscopy. Appl.
Opt. 45, 829–835. (doi:10.1364/AO.45.000829)
Coufal, H. J., Psaltis, D. & Sincerbox, G. T. (eds) 2000 Holographic data storage. Springer Series
in Optical Sciences, vol. 76. New York, NY: Springer-Verlag.
Coupland, J. M. & Halliwell, N. A. 1992 Particle image velocimetry: three dimensional fluid
velocimetry measurements using holographic recording and optical correlation. Appl. Opt. 131,
1005–1007. (doi:10.1364/AO.31.001005)
Phil. Trans. R. Soc. A (2010)
Downloaded from http://rsta.royalsocietypublishing.org/ on August 11, 2017
Review. High-performance holography
1733
Crawford, A. M., Mordant, N. & Bodenschatz, E. 2005 Joint statistics of the Lagrangian
acceleration and velocity in fully developed turbulence. Phys. Rev. Lett. 94, 024 501.
(doi:10.1103/PhysRevLett.94.024501)
Curtis, K., Pu, A. & Psaltis, D. 1994 Method for holographic storage using peristrophic
multiplexing. Opt. Lett. 19, 993–995. (doi:10.1364/OL.19.000993)
Dalziel, S. B., Linden, P. F. & Youngs, D. L. 1999 Self-similarity and internal structure of
turbulence induced by Rayleigh–Taylor instability. J. Fluid Mech. 399, 1–48. (doi:10.1017/
S002211209900614X)
Darskii, A. M. & Markov, V. B. 1988 Shift selectivity of holograms with a reference speckle wave.
Opt. Spectrosc. 65, 392–395.
d’Auria, L., Huignard, J. P. & Spitz, E. 1973 Holographic read–write memory and capacity
enhancement by 3-D storage. IEEE Trans. Mag. 9, 83–94. (doi:10.1109/TMAG.1973.1067578)
Davies, R. M. & Taylor, G. I. 1950 The mechanics of large bubbles rising through extended liquids
and through liquids in tubes. Proc. R. Soc. Lond. A 200, 375–390. (doi:10.1098/rspa.1950.0023)
Denisyuk, Yu. N. 1963 On the reproduction of the optical properties of an object by the wave field
of its scattered radiation. Opt. Spectrosc. 15, 279–283.
Dhar, L. et al. 1998 Holographic storage of multiple high-capacity digital pages in thick
photopolymer systems. Opt. Lett. 23, 1710–1712. (doi:10.1364/OL.23.001710)
Dimonte, G. & Schneider, M. 2000 Density ratio dependence of Rayleigh–Taylor mixing for
sustained and impulsive acceleration histories. Phys. Fluids 12, 304–321. (doi:10.1063/1.870309)
Dimonte, G. et al. 2004 A comparative study of the turbulent Rayleigh–Taylor instability using
high-resolution three-dimensional numerical simulations: the Alpha-Group collaboration. Phys.
Fluids 16, 1668–1693. (doi:10.1063/1.1688328)
Dominguez-Caballero, J. A., Loomis, N. C., Barbastathis, G. & Milgram, J. 2007 Techniques based
on digital multiplexing holography for three-dimensional object tracking. In IEEE Conf. on
Lasers and Electro-Optics (CLEO ), Baltimore, MD, 10 May 2007, paper JThD84.
Donzis, D. A., Sreenivasan, K. R. & Yeung, P. K. 2005 Scalar dissipation rate and dissipative
anomaly in isotropic turbulence. J. Fluid Mech. 532, 199–216. (doi:10.1017/S0022112005004039)
Douady, S., Couder, Y. & Brachet, M. E. 1991 Direct observation of the intermittency
of intense vorticity filaments in turbulence. Phys. Rev. Lett. 67, 983–986. (doi:10.1103/
PhysRevLett.67.983)
Dubois, F., Schockaert, C., Callens, N. & Yourassowsky, C. 2006 Focus plane detection
criteria in digital holography microscopy by amplitude analysis. Opt. Express 14, 5895–5908.
(doi:10.1364/OE.14.005895)
Dudderar, T. D. & Simpkins, P. G. 1977 Laser speckle photography in a fluid medium. Nature 270,
45–47. (doi:10.1038/270045a0)
Durst, F. 1981 Principles and practice of laser-Doppler velocimetry. Amsterdam, The Netherlands:
Elsevier.
Frisch, U. 1995 Turbulence, the legacy of A. N. Kolmogorov. Cambridge, UK: Cambridge University
Press.
Gabor, D. 1948 A new microscopic principle. Nature 161, 777–778. (doi:10.1038/161777a0)
Goldstein, R. J. (ed.) 1996 Fluid mechanics measurements. London, UK: Taylor & Francis.
Goodman, J. W. 1967 Digital image formation from electronically detected holograms. In Proc.
SPIE, Seminar on Computerized Imaging Techniques, Bellingham, WA, January 1967, pp. xv11–xv1-6.
Goodman, J. W. 1996 Introduction to Fourier optics. New York, NY: McGraw-Hill.
Goodman, J. W. & Lawrence, R. W. 1967 Digital image formation from electronically detected
holograms. Appl. Phys. Lett. 11, 77–79. (doi:10.1063/1.1755043)
Hinsch, K. D. 2002 Holographic particle image velocimetry. Meas. Sci. Technol. 13, R61–R72.
(doi:10.1088/0957-0233/13/7/201)
Hinsch, K. D. 2004 Holographic particle image velocimetry. Meas. Sci. Technol. 15, 601–769.
(doi:10.1088/0957-0233/15/4/E01)
Hoffnagle, J. A. & Jefferson, C. M. 2000 Bit error rate for holographic data storage. In Holographic
data storage (eds H. J. Coufal, D. Psaltis & G. T. Sincerbox). Springer Series in Optical Sciences,
vol. 76, pp. 91–100. New York, NY: Springer-Verlag.
Phil. Trans. R. Soc. A (2010)
Downloaded from http://rsta.royalsocietypublishing.org/ on August 11, 2017
1734
S. S. Orlov et al.
Hong, J. H., McMichael, I., Chang, T. Y., Christian, W. & Paek, E. G. 1995 Volume holographic
memory systems—techniques and architectures. Opt. Eng. 34, 2193–2203. (doi:10.1117/
12.213214)
Hussain, F., Liu, D. D., Simmons, S. & Meng, H. 1993 Holographic particle velocimetry: prospects
and limitations. Proc. Fluids Eng. Div. ASME 148, 1–11.
Jayesh & Warhaft, Z. 1992 Probability distribution, conditional dissipation and transport of
passive temperature fluctuations in grid-generated turbulence. Phys. Fluids A 4, 2292–2307.
(doi:10.1063/1.858469)
Kaneda, Y., Ishihara, T., Yokokawa, M., Itakura, K. & Uno, A. 2003 Energy dissipation rate and
the energy spectrum in high resolution direct numerical simulations of turbulence in a periodic
box. Phys. Fluids 15, L21–L24. (doi:10.1063/1.1539855)
Kolmogorov, A. N. 1941a Local structure of turbulence in an incompressible fluid for very large
Reynolds numbers. Dokl. Akad. Nauk. SSSR 30, 299–303.
Kolmogorov, A. N. 1941b Energy dissipation in locally isotropic turbulence. Dokl. Akad. Nauk.
SSSR 32, 19–21.
Kreuzer, H. J., Nakamura, K., Wierzbicki, A., Fink, H.-W. & Schmid, H. 1992 Theory of the point
source electron microscope. Ultramicroscopy 45, 381–403. (doi:10.1016/0304-3991(92)90150-I)
Kucherenko, Y. A., Shestachenko, O. E., Balabin, S. I. & Pylaev, A. P. 2003 RFNC-VNIITF
multi-functional shock tube for investigating the evolution of instabilities in non-stationary gas
dynamic flows. Laser Part. Beams 21, 381–384. (doi:10.1017/S0263034603213148)
Landau, L. D. & Lifshitz, E. M. 1987a Course of theoretical physics VI, fluid mechanics. New York,
NY: Pergamon Press.
Landau, L. D. & Lifshitz, E. M. 1987b Course of theoretical physics I, mechanics. New York, NY:
Pergamon Press.
Lathrop, D. P., Fineberg, J. & Swinney, H. L. 1992 Turbulent flow between concentric
rotating cylinders at large Reynolds number. Phys. Rev. Lett. 68, 1515–1518. (doi:10.1103/
PhysRevLett.68.1515)
Lecerf, A., Renou, B., Allano, D., Boukhalfa, A. & Trinite, M. 1999 Stereoscopic PIV: validation
and application to an isotropic turbulent flow. Exp. Fluids 26, 107–115. (doi:10.1007/
s003480050269)
Leith, E. & Upatnieks, J. 1962 Reconstructed wavefront and communication theory. J. Opt. Soc.
Am. 52, 1123–1130. (doi:10.1364/JOSA.52.001123)
Leith, E. N., Kozma, A., Upatnieks, J., Marks, J. & Massey, N. 1966 Holographic data storage in
three-dimensional media. Appl. Opt. 5, 1303–1311. (doi:10.1364/AO.5.001303)
Li, W., Loomis, N. C., Hu, Q. & Davis, C. S. 2007 Focus detection from digital in-line holograms
based on spectral l1 norms. J. Opt. Soc. Am. A 24, 3054–3062. (doi:10.1364/JOSAA.24.003054)
Liebling, M. & Unser, M. 2004 Autofocus for digital Fresnel holograms by use of a Fresnelet-sparsity
criterion. J. Opt. Soc. Am. A 21, 2424–2430. (doi:10.1364/JOSAA.21.002424)
Lipp, J. & Reynolds, J. 1970 A high capacity holographic storage system. In Applications of
holography (eds E. S. Barrakette, W. E. Kock, T. Ose, J. Tsujiuchi & G. W. Stroke), pp. 377–388.
New York, NY: Plenum Press.
Liu, W., Psaltis, D. & Barbastathis, G. 2004 Volume holographic hyperspectral imaging. Appl.
Opt. 43, 3581–3599. (doi:10.1364/AO.43.003581)
Lobera, J. & Coupland, J. M. 2008 Optical diffraction tomography in fluid velocimetry: the
use of a priori information. Meas. Sci. Technol. 19, 094 013. (doi:10.1088/0957-0233/19/
7/074013)
Lumley, J. L. 1965 Interpretation of time spectra measured in high-intensity shear flows. Phys.
Fluids 8, 1056–1062. (doi:10.1063/1.1761355)
Luo, Y., Gelsinger-Austin, P. J., Watson, J. M., Barbastathis, G., Barton, J. K. & Kostuk,
R. K. 2008 Laser induced fluorescence imaging of sub-surface tissue structures with a
volume holographic spatial-spectral imaging system. Opt. Lett. 33, 2098–2100. (doi:10.1364/
OL.33.002098)
Luo, Y., Gelsinger, P. J., Barton, J. K., Barbastathis, G. & Kostuk, R. K. 2009 Spectral-spatial
depth sectioning of samples using silicon oxide nano-particles doped PQ-PMMA. In OSA Topical
Meeting on Digital Holography and Three-Dimensional Imaging (DH ), paper DTuB5.
Phil. Trans. R. Soc. A (2010)
Downloaded from http://rsta.royalsocietypublishing.org/ on August 11, 2017
Review. High-performance holography
1735
Marquet, P., Rappaz, B., Magistretti, P. J., Cuche, E., Emery, Y., Colomb, T. & Depeursinge, C.
2005 Digital holographic microscopy: a noninvasive contrast imaging technique allowing
quantitative visualization of living cells with subwavelength axial accuracy. Opt. Lett. 30,
468–470. (doi:10.1364/OL.30.000468)
McGorty, R., Fung, J., Kaz, D., Ahn, S. & Manoharan, V. 2008 Measuring dynamics and
interactions of colloidal particles with digital holographic microscopy. In Digital holography and
three-dimensional imaging, OSA Technical Digest, St. Petersburg, FL, 18 March 2008, paper
DTuB1.
Meng, H. & Hussain, F. 1995a In-line recording and off-axis viewing (IROV) technique for
holographic particle velocimetry. Appl. Opt. 34, 1827–1840. (doi:10.1364/AO.34.001827)
Meng, H. & Hussain, F. 1995b Instantaneous flow field in an unstable vortex ring measured by
holographic particle velocimetry. Phys. Fluids 7, 9–11. (doi:10.1063/1.868741)
Meng, H., Pan, G., Pu, Y. & Woodward, S. H. 2004 Holographic particle image velocimetry: from
film to digital recording. Meas. Sci. Technol. 15, 673–685. (doi:10.1088/0957-0233/15/4/009)
Meshkov, E. E. 2006 Studies of hydrodynamic instabilities in laboratory experiments (in Russian).
Sarov, Russia: FGYC-VNIIEF.
Meynart, R. 1980 Equal velocity fringes in a Rayleigh–Benard flow by a speckle method. Appl.
Opt. 19, 1385–1386. (doi:10.1364/AO.19.001385)
Mikaelian, A. L., Bobrinev, V. L., Naumova, S. M. & Sokolova, L. Z. 1970 Design principles
of holographic memory devices. IEEE J. Quant. Electron. 6, 193–198. (doi:10.1109/
JQE.1970.1076437)
Monin, A. S. & Yaglom, A. M. 1975 Statistical fluid mechanics, vol. 2. Cambridge, MA: MIT Press.
Oh, S. B. & Barbastathis, G. 2008 Passive quasi-monochromatic depth discrimination using a
coherence imager with volume holographic pupil. Appl. Opt. 47, 6881–6888. (doi:10.1364/AO.
47.006881)
Orlov, S. S. 2008 New technologies for fluid dynamics experiments and optical diagnostics. Phys.
Scr. T132, 014 056. (doi:10.1088/0031-8949/2008/T132/014056)
Orlov, S. S. & Abarzhi, S. I. 2007 New experimental platform for studies of turbulence and turbulent
mixing in accelerating and rotating fluids at high Reynolds numbers. Astrophys. Space Sci. 307,
241–244. (doi:10.1007/s10509-006-9289-3)
Orlov, S. S., Phillips, W., Bjornson, E., Takashima, Y., Sundaram, P., Hesselink, L., Okas, R.,
Snyder, R. & Kwan, D. 2004 High-transfer-rate high-capacity holographic disk data-storage
system. Appl. Opt. 43, 4902–4914. (doi:10.1364/AO.43.004902)
Pan, G. & Meng, H. 2003 Digital holography of particle field: reconstruction by use of complex
amplitude. Appl. Opt. 42, 827–833. (doi:10.1364/AO.42.000827)
Pedloski, J. 1987 Geophysical fluid dynamics, 2nd edn. Berlin, Germany: Springer.
Pereira, F. & Gharib, M. 2002 Defocusing digital particle image velocimetry and the threedimensional characterization of two-phase flows. Meas. Sci. Technol. 13, 683–694. (doi:10.1088/
0957-0233/13/5/305)
Pope, S. B. 2000 Turbulent flow. Cambridge, UK: Cambridge University Press.
Prandtl, L. 1925 A report on testing for built-up turbulence. Zeitschrift fur Angewandte Mathematik
und Mechanik 5, 136–139.
Prandtl, L. & Tietjens, O. G. 1934 Applied hydro- and aeromechanics. New York, NY: Dover.
Prasad, R. R. & Sreenivasan, K. R. 1990 Quantitative three-dimensional imaging and the
structure of passive scalar fields in fully turbulent flows. J. Fluid Mech. 216, 1–34.
(doi:10.1017/S0022112090000325)
Procaccia, I. & Sreenivasan, K. R. 2008 The state of the art in hydrodynamic turbulence: past
successes and future challenges. Physica D 237, 2176–2183. (doi:10.1016/j.physd.2008.01.025)
Psaltis, D., Brady, D., Gu, X.-G. & Lin, S. 1990 Holography in artificial neural networks. Nature
343, 325–330. (doi:10.1038/343325a0)
Psaltis, D., Levene, M., Pu, A., Barbastathis, G. & Curtis, K. 1995 Holographic storage using shift
multiplexing. Opt. Lett. 20, 782–784. (doi:10.1364/OL.20.000782)
Pu, Y. & Meng, H. 2000 An advanced off-axis holographic particle image velocimetry (HPIV)
system. Exp. Fluids 29, 184–197. (doi:10.1007/s003489900088)
Phil. Trans. R. Soc. A (2010)
Downloaded from http://rsta.royalsocietypublishing.org/ on August 11, 2017
1736
S. S. Orlov et al.
Raffel, M., Willert, C., Wereley, S. & Kompenhans, J. 2007 Particle image velocimetry: a practical
guide. Berlin, Germany: Springer.
Rakuljic, G. A., Leyva, V. & Yariv, A. 1992 Optical data storage by using orthogonal wavelengthmultiplexed volume holograms. Opt. Lett. 17, 1471–1473. (doi:10.1364/OL.17.001471)
Ramaprabhu, P. & Andrews, M. J. 2003 Experimental investigation of Rayleigh–Taylor mixing at
small Atwood numbers. J. Fluid Mech. 503, 233–271.
Rappaz, B., Marquet, P., Cuche, E., Emery, Y., Depeursinge, C. & Magistretti, P. J. 2005
Measurement of the integral refractive index and dynamic cell morphometry of living cells with
digital holographic microscopy. Opt. Express 13, 9361–9373. (doi:10.1364/OPEX.13.009361)
Rayleigh. 1882 Investigations of the character of the equilibrium of an incompressible heavy fluid
of variable density. Proc. Lond. Math. Soc. 14, 170–177. (doi:10.1112/plms/s1-14.1.170)
Rayleigh. 1893 On the densities of principal gases. Proc. R. Soc. 53, 134–149. (doi:10.1098/
rspl.1893.0017)
Rayleigh & Ramsay, W. 1895 Argon, a new constituent of atmosphere. Phil. Trans. R. Soc. Lond.
A 186, 187–241. (doi:10.1098/rsta.1895.0006)
Read, K. I. 1984 Experimental investigation of turbulent mixing by Rayleigh–Taylor instability.
Physica D 12, 45–58. (doi:10.1016/0167-2789(84)90513-X)
Reynolds, O. 1883 An experimental investigation of the circumstances which determine where the
motion of water shall be direct or sinuous and of the law of resistance in parallel channels. Phil.
Trans. R. Soc. 174, 84–99. (doi:10.1098/rstl.1883.0029)
Reynolds, O. 1894 On the two manners of motion of waves. Phil. Trans. R. Soc. Lond. A 186,
123–164. (doi:10.1098/rsta.1895.0004)
Schlichting, H. 1956 Boundary-layer theory. New York, NY: McGraw-Hill.
Schnars, U. & Jüptner, W. 1994 Direct recording of holograms by a CCD target and numerical
reconstruction. Appl. Opt. 33, 179–181. (doi:10.1364/AO.33.000179)
Schumacher, J. 2007 Sub-Kolmogorov-scale fluctuations in fluid turbulence. Europhys. Lett. 80,
54001. (doi:10.1209/0295-5075/80/54001)
Seitzman, J. M. & Hanson, R. K. 1993 Planar fluorescence imaging in gases. In Instrumentation
for flows with combustion (ed. A. M. K. P. Taylor), pp. 405–466. New York, NY: Academic
Press.
Settles, G. S. 2001 Schlieren and shadowgraph techniques: visualizing phenomena in transparent
media. Berlin, Germany: Springer-Verlag.
Sheng, J. & Meng, H. 1997 A genetic algorithm approach for 3D velocity field extraction in
holographic particle image velocimetry. Exp. Fluids 25, 461–473. (doi:10.1007/s003480050252)
Sheng, J., Malkiel, E. & Katz, J. 2003 Singlebeam two-views holographic particle image velocimetry.
Appl. Opt. 42, 235–250. (doi:10.1364/AO.42.000235)
Shimobaba, T., Sato, Y., Miura, J., Takenouschi, M. & Ito, T. 2008 Real-time digital
holographic microscopy using the graphic processing unit. Opt. Express 16, 11 776–11 781.
(doi:10.1364/OE.16.011776)
Sinha, A. & Barbastathis, G. 2003 Volume holographic imaging for surface metrology at long
working distances. Opt. Express 11, 3202–3209.
Sinha, A. & Barbastathis, G. 2004 Broadband volume holographic imaging. Appl. Opt. 43,
5214–5221. (doi:10.1364/AO.43.005214)
Sinha, A., Sun, W., Shih, T. & Barbastathis, G. 2004 Volume holographic imaging in transmission
geometry. Appl. Opt. 43, 1533–1551. (doi:10.1364/AO.43.001533)
Soria, J. & Atkinson, C. 2008 Towards 3C-3D digital holographic fluid velocity vector field
measurement—tomographic digital holographic PIV (Tomo-HPIV). Meas. Sci. Technol. 19,
074 002. (doi:10.1088/0957-0233/19/7/074002)
Sreenivasan, K. R. 1991 On local isotropy of passive scalars in turbulent shear flows. Proc. R. Soc.
Lond. A 434, 165–182. (doi:10.1098/rspa.1991.0087)
Sreenivasan, K. R. 1999 Fluid turbulence. Rev. Mod. Phys. 71, S383–S395. (doi:10.1103/
RevModPhys.71.S383)
Sreenivasan, K. R. & Meneveau, C. 1988 Singularities of the equations of fluid motion. Phys. Rev. A
38, 6287–6295. (doi:10.1103/PhysRevA.38.6287)
Phil. Trans. R. Soc. A (2010)
Downloaded from http://rsta.royalsocietypublishing.org/ on August 11, 2017
Review. High-performance holography
1737
Sreenivasan, K. R., Ramshankar, R. & Meneveau, C. 1989 Mixing, entrainment and fractal
dimensions of surfaces in turbulent flows. Proc. R. Soc. Lond. A 421, 79–107. (doi:10.1098/
rspa.1989.0004)
Stellmacher, M. & Obermayer, K. 2000 A new particle tracking algorithm based on deterministic
annealing and alternative distance measures. Exp. Fluids 28, 506–518. (doi:10.1007/
s003480050412)
Steward, W. C., Mezrich, R. S., Cosentino, L. S., Nagle, E. M., Wendt, F. S. & Lohman, R. D.
1973 An experimental read–write holographic memory. RCA Rev. 34, 3–44.
Sun, W., Tian, K. & Barbastathis, G. 2005 Hyper-spectral imaging with volume holographic lenses.
In IEEE Conf. on Lasers and Electro-Optics (CLEO ), Baltimore, MD, 27 May 2005, paper
CFP2.
Tavoularis, S. 2009 Measurement in fluid mechanics. Cambridge, UK: Cambridge University Press.
Taylor, G. I. 1935 Statistical theory of turbulence. Proc. R. Soc. Lond. A 151, 421–444. (doi:10.1098/
rspa.1935.0158)
Tennekes, H. & Lumley, J. L. 1972 A first course in turbulence. Cambridge, MA: MIT Press.
Thelen, A., Bongartz, J., Dominik, G., Frey, S. & Hering, P. 2005 Iterative focus detection in
hologram tomography. J. Opt. Soc. Am. A 22, 1176–1180. (doi:10.1364/JOSAA.22.001176)
Thompson, B. J. 1989 Holographic methods for particle size and velocity measurement—recent
advances. Proc. SPIE 1136, 308–326.
van der Lugt, A. 1973 Design relationships for holographic memories. Appl. Opt. 12, 1675–1685.
(doi:10.1364/AO.12.001675)
van Heerden, P. 1963 Theory of optical information storage in solids. Appl. Opt. 2, 393–400.
(doi:10.1364/AO.2.000393)
Waddell, J. T., Niederhaus, C. E. & Jacobs, J. W. 2001 Experimental study of Rayleigh–Taylor
instability: low Atwood number liquid systems with single-mode initial perturbations. Phys.
Fluids 13, 1263–1273. (doi:10.1063/1.1359762)
Waldman, D. A., Li, H.-Y. S. & Horner, M. G. 1997 Volume shrinkage in slant fringe
gratings of a cationic ring-opening volume hologram material. J. Imaging Sci. Technol. 41,
497–514.
Willert, C. E. & Gharib, M. 1991 Digital particle image velocimetry. Exp. Fluids 10, 181–193.
(doi:10.1007/BF00190388)
Wolf, E. 1969 Three dimensional structure determination of semi-transparent objects from
holographic data. Opt. Commun. 1, 153–156. (doi:10.1016/0030-4018(69)90052-2)
Wolf, E. 1970 Determination of the amplitude and the phase of scattered fields by holography.
J. Opt. Soc. Am. 60, 18–20. (doi:10.1364/JOSA.60.000018)
Wormald, S. A. & Coupland, J. 2009 Particle image identification and correlation analysis in
microscopic holographic particle image velocimetry. Appl. Opt. 48, 6400–6407. (doi:10.1364/
AO.48.006400)
Yu, L. & Cai, L. 2001 Iterative algorithm with a constraint condition for numerical reconstruction of
a three-dimensional object from its hologram. J. Opt. Soc. Am. A 18, 1033–1045. (doi:10.1364/
JOSAA.18.001033)
Yu, F. T. S., Wu, S., Mayers, A. & Rajan, S. 1991 Wavelength multiplexed reflection matched
spatial filters using LiNbO3 . Opt. Commun. 81, 343–347. (doi:10.1016/0030-4018(91)90595-5)
Zhang, J., Tao, B. & Katz, J. 1997 Turbulent flow measurement in a square duct with hybrid
holographic PIV. Exp. Fluids 23, 373–381. (doi:10.1007/s003480050124)
Zhang, F., Pedrini, G. & Osten, W. 2006 Reconstruction algorithm for high-numericalaperture holograms with diffraction-limited resolution. Opt. Lett. 31, 1633–1635. (doi:10.1364/
OL.31.001633)
Phil. Trans. R. Soc. A (2010)