Note: Descriptions are shown in the official language in which they were submitted.
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Improved 3D display
This invention relates to improvements to three-dimensional (3D) displays,
and their associated image generation means. More specifically, it relates to
a way of':improving the image quality of Diffraction Specific computer
generated holograms (CGH) by means of a novel way of representing and
calculating data relating to the image.
Introduction
Holographic displays can be seen as being potentially the best means of
generating a realistic 3D image, as they provide depth cues not available in
ordinary two dimensional displays or many other types of 3D display. The
accommodation depth cue, for example, is a cue that the brain receives when
a viewer's eye focuses at different distances and is important up to aboufi 3
meters in distance. This is, of course a cue that is used when looking at real
objects, but of the 3D display technOIOg~es currently available, only tr~!e
holograms provide 3D images upon which the eye can use its accommodation
ability. It is a desire to be able to produce reconfigurable holographic
displays
electronically, such that an image can be generated from computer held data.
This gives flexibility to produce holographic images of existing objects or
non-
existent objects without needing to go through the time consuming and
expensive steps normally associated with their production.
Unfortunately, producing such an image electronically is extremely
challenging. Methods exist, however, for just such generation, but they
currently require a large amount of computing time, and specialised display
hardware.
One such method of computing a CGH is to use what is known as the
Diffraction Specific (DS) algorithm. A DS CGH is a true CGH (as opposed to
a holographic stereogram variant) but has a lower computational load than
Interference Based true CGH algorithms. The reason for this is that the DS .
algorithm is currently the most effective in terms of controlling the
information
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content of CGH and avoiding unnecessary image resolution detail that cannot
be seen by the human eye.
A key concept of the DS algorithm is the quantisation of the CGH in both the
spatial and spectral domains. This allows control of the amount of data, or
the
information content of the CGH, that in turn reduces the computational load.
The CGH is divided up into a plurality of areas, known as hogels, and each
hogel has a plurality of pixels contained within it. The frequency spectrum of
each hogel is quantised such that a hogel has a plurality of frequency
elements known as hogef vector elements.
There are problems with this method however. The current method is subject
to a large number of constraints.
The system constraints that are present using the methods of the prior art
are:
a) Plane waves from more than 1 hogel must enter the eye pupil. This
prcvides a constraint on the hoge! aperture. Therefore, if the hogel is
smaller then fight from more of them can enter the eye.
b) The number of lateral image volume points (and therefore the number of
hogel vector components) must not exceed the number of pixels in a hogel
divided by 2. This means that a large number of pixels per hogel is needed
to give a good quality image.
c) The point-spread function (the fineness to which a point can be focussed)
of an image volume point is related to the distance the point is from the
focal plane and the size of the hogel aperture. A larger hogel will give a
sharper focussed point.
d) The achievable depth resolution is constrained by a large number of
interdependent parameters. Most severely this is constrained by the
number of hogel vector components which must be large.
e) The above constraints must be satisfied for the minimum eye viewing
distance. (The nearer the eye is to the image volume, the tougher the
constraints).
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Statement of invention
According to the present invention there is provided a computer generated
holographic display comprising at least a light diffraction plane notionally
divided into a plurality of hogels, an image volume space and image
calculation means, wherein image data is created by the steps of
* for each point in the image volume, a wavefront is mathematically
projected from the point to each hogel through any display optics that may be
present;
* the wavefront arriving at each hogel is sampled at a plurality of points
across the hogel;
* the wavefront is approximated into a set of frequency coefficients,
which are stored in memory;
*the coefficients are used to produce a diffraction pattern across the
hogel such that light diffracted by the hogel produces a curved wavefront,
this
wavefront going on to produce at least one point in the image volume.
The present invention allows each hogel in the system to generate curved
waveforms, as opposed to the plane waves as generated in the prior art. It
does this by sampling an imaginary wavefront coming from each point in the
3D volume at a plurality of points over the hogel, as opposed to the single
point of the prior art. These samples are used to produce a set of complex
Fourier coefficients that can be used to approximate the original waveform.
Each hogel has contained within it a plurality of pixels. The dimensions of
the
hogel, in terms of pixels, defines certain properties of the 3D image that is
produced by the system. A full parallax system allows a viewer of the
projected image to "see around" the image both horizontally and vertically.
This type of system would have hogels that have a plurality of pixels in two
dimensions. To cut down on the computation time involved with displaying
these images however, it is often acceptable from a system point of view to
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display images having horizontal parallax only (HPO). This restricts the
viewer of an image to being able to look around it in one 'plane only - the
horizontal one in this case. In this case, a hogel will be only one pixel
high,
but more than one pixel wide. The current invention is equally applicable to
both systems. The dimensions of the hogels will be different, and the HPO
system will save on computing power as the processing required for each
hogel is only one dimensional, and cylindrical as opposed to spherical
coordinates may be used. Anamorphic optics can also be used to replay such
a hologram.
~0
Assume that a given hogel has n pixels across its width. The number, m, of
Fourier components used to represent the wavefront is limited to 0 <_ m <_ n/2
to avoid undersampling of the wavefront and loss of information. These m
coefficients represent the magnitude of the first m possible grating
frequencies
in the hogel, and are the hogel vector components that are stored in the
diffraction table.
It will be understood by those skilled in the art that the present invention
can
be used in display systems that comprise either Fourier optics or Fresnel
optics.
As another aspect of the invention there is provided a method of producing a
computer generated hologram on a display comprising at least a light
diffracting panel notionally divided into a plurality of hogels, and image
calculation means, where the method comprises the steps of
* for each point in the image volume, mathematically projecting a
wavefront from the point to each hogel;
* sampling the wavefront at each hogel at a plurality of points across
the hogel;
~ * approximating the wavefront into a set of frequency coefficients,
which are stored;
* producing a diffraction pattern across the hogel using the coefficients
such that light difr=racted by the hogei produces a curved wavefront, this
wavefront going on to produce at least one point in the image volume.
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As a further aspect of the invention there is provided a method of correcting
for known aberrations present in the optical system of a computer generated
hologram display system comprising an image volume and a fight diffraction
panel notionally divided up into a plurality of hogels, wherein:
* a first wavefront is mathematically projected from a point in the image
volume through the optical system to a hogel, the wavefront being distorted by
any aberrations in the optical system;
* the distortions added to the first wavefront by the optical system are
used to generate a real, pre-distorted second wavefront emanating from the
hogel, such that as the second wavefront passes through the distorting optics
the pre-distortions on the second wavefront are removed.
It will be seen that providing a curved wavefront from each hogel enables
known defects or aberrations in the optical system to be corrected or reduced.
Should a spherical wave, as emanated from a point P in the image volume
arrive at a particular hcgel with distortions due to imperfections in the
optical
system, then the wavefront that is transmitted in a real system from the hogel
to the point P can be "pre distorted" such that when it arrives at the point
the
pre distortions and the actual distortions present in the system cancel each
other out.
The distortions present in a particular system need only be measured or
calculated once, and the data so obtained can be stored for later use with any
image to be displayed. The distortion information is used to compute a pre-
compensation in the diffraction table and is stored as more advanced form of
diffraction table. Patent application WO 00175733 provides a full description
of correcting aberrations by distorting the wavefront. The current invention ,
provides a particularly efficient means wifih which such an aberration
correction method may be implemented, as the information regarding the
required pre-distortions is stored in the diffraction table, and the
calculations
are hence done off line.
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Typically, the light diffraction plane, or CGH, will comprise of a.spatial
light
modulator, but any device capable of being addressed with a diffraction
pattern may be used.
The current invention may be implemented as a computer program running on
a computer system. The program may be stored on a carrier, such as a hard
disk system, floppy disk system, or other suitable carrier. The computer
system may be integrated into a single computer, or may contain distributed
elements that are connected together across a network.
Detailed Description and Drawings
The current invention will now be described in detail, by way of example only,
with reference to the following diagrams, in which
Figure 1 illustrates in diagrammatic form the geometry of the CGH replay
optics.
Figure 2 illustrates in diagrammatic form a CGH showing the division of the
area into hogels.
Figure 3 illustrates in diagrammatic form a typical hogel vector.
Figure 4 illustrates in diagrammatic form a series of planar wavefronts
emitted
from a hogel of the prior art.
Figure 5 illustrates in diagrammatic form the curved wavefronts that can be
emitted from a hogel of the present invention.
Figure 6 illustrates in diagrammatic form (a) a point in the image volume
being
formed using multiple hogels~from the prior art, and (b), a point being formed
by a single hogel using the curved wavefronts of the current invention.
Figure 7 illustrates in diagrammatic form the process of decoding a hogel
vector
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Figure 8 illustrates in diagrammatic form a system of the prior art using
multiple hogels to create an approximation to a curved wavefront.
Figure 9 illustrates in diagrammatic form the principle of the first stage of
calculation of the diffraction table.
Figure 10 shows a calculated point spread function for a hogel containing 500
pixels and subjected to certain constraints.
Figure 11 illustrates in diagrammatic form the distortions that can arise in a
practical system, and how, by pre-distorting a waveform from a hogel, these
distortions can be compensated for.
A person skilled in the art will realise that computer generated holograms are
displayed on a panel capable of being programmed to diffract light in a
controlled manner. This panel is usually a spatial light modulator, but for
the
purposes of this invention can be anything suitable. Note that the term
"diffraction panel" is used to describe this panel in this specification
before
diffraction information is written to it, although once the diffraction panel
is
written with diffraction information, it can be interchangeably termed a CGH.
The skilled person will also realise that the DS algorithm comprises the
following stages.
The 3D image is made up by the diffraction of light from the hogels. The
diffraction process sends light from one of the hogels in a number of discrete
directions, according to which basis fringes are selected, as described below.
A basis fringe represents part of the hogel vector spectrum, and when many
basis fringes are accumulated into a hogel a continuous spectrum is formed.
The basis fringes are calculated once for a given optical geometry, and are
independent of the actual 3D image to be displayed. They can therefore be
calculated offline, before the CGH is calculated and displayed.
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A given image must have the correct basis fringes selected in the appropriate
hogels in order to properly display the image components. A diffraction table
allows this selection to be done correctly. The diffraction table maps
locations
in the image volume to a given hogel, and to hogel vector components of that
hogel. These locations, or nodes, are selected according to the required
resolution of the 3D image. More nodes will give a better resolution, but will
require more computing power to generate the CGH. Having control of the
nodes therefore allows image quality to be traded for reduced processing
time. The hogel vector selects and weights which basis fringes are required
by a given hogel in order to construct the 3D-image information.
The hogel vectors themselves are generated from data based on the 3D
object or scene to be displayed. A geometric representation of the object is
stored in the computer system. The geometric information is rendered using
staridard computer graphics techniques in which the depth map is also stored.
The rendering frustum is calculated from the optical parameters of the CGH
replay system. The rendered image and the depth map are used to define, in
three dimensions, which parts of the 3D object geometry that the given hogel
must reconstruct. A hogel vector can then be calculated from a combination
of this information and the diffraction table to produce the hogel vector.
Finally, to produce the full CGH, the hogel vectors are used to select the
appropriate basis fringes needed to make up the image. The hogel vector is
decoded by accumulating the appropriate basis fringes into the hogel. This is
a linear process and is repeated for each hogel vector element. The result is
a complete hogel that is part of the final CGH.
Note that the wavelength of the light used to read the resultant hologram is a
parameter to be considered when calculating the hogel vector components
that are stored in the diffraction table. Although current embodiments are
based on only a single wavelength being. used, that wavelength may be
anything suitable for a given application. Off-line recalculation of the
diffraction table is all that is necessary if the wavelength needs to be
changed.
The diffraction table can be enlarged to include hogel vector components that
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are calculated for more than one wavelength simultaneously. In this way, the
system is able to quickly change between different readout wavelengths, or to
create holograms for multiple wavelength readout.
More details of this procedure can be found in refs. 1, 2, 3 and 4, which are
included in this specification by reference.
Figure 1 illustrates the replay optics of a general CGH system, including a
system capable of implementing the current invention. The diffraction panel 1
is shown transmitting a set of plane waves 7, encompassed by a diffraction
cone 5 through a Fourier lens 3, where the waves 7 get refracted towards an
image volume 2. It can be seen that the extent of diffraction of the plane
waves, given by the cone 5 defines the size of the image volume 2. As the
diffracted waves 7 radiate symmetrically from the diffraction panel 1, a
conjugate image volume 6 is also formed adjacent the image volume 2.
Figure 1 o.~ly shows plane waves ? radiating from one area of the panel 1, but
of course in practice, each hogel on the pane! 1 will be radiating such waves.
If the diffraction panel 1 is written correctly with appropriate basis fringe
data
for a given hologram, a viewer in the viewing zone 4 will see a true 3D image
in the image volume 2, and the image conjugate in the volume 6. In practice,
the conjugate image volume 6 is usually masked out.
The distance of separation between the Fourier lens 3 and the diffraction
panel 1 is kept as short as possible to simplify the processing. The steps
involved in calculating the hogei vector components as shown below assume
that this distance is zero.
Figure 2 shows the spatial quantisation of the diffraction panel 1 info a 2D
array of hogels. Each hogel (for example 8) is shown having a plurality of .
pixels in two dimensions. Therefore, a diffraction panel 1 so divided would be
suitable for implementing a full parallax system. The number of pixels shown
present in each of the hogels (for example 8) is shown figuratively only. In
practice there would be approximately 2000 to 4000 pixels in each hogel
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dimension. In a HPO system, each hogel would have only one pixel in the
vertical dimension, but approximately 2000 to 4000 in the horizontal
dimension. The current implementation is restricted to a HPO system, to ease
computing requirements.
Figure 3 shows the spectral elements 9 of a typical hogel vector that is
stored
for each hogel. Each component of the vector represents a spatial frequency
present in the image as viewed from the hogel in question.
Figure 4 shows light 11 being diffracted from a single hogel in a number of
discrete different directions, symmetrical about the normal 10. This is the
method of the prior art. The particular angle of diffraction, and hence
direction
of each of the plane waves 11 is chosen for the particular image that is
desired to be displayed in the image volume 2. It is the presence of a
particular basis fringe that decides the angle of diffraction of a particular
plane
wave.
In contrast to Figure 4, Figure 5 shows light emanating from a hogel that
produces curved wavefronts 12. This is the current invention, and results in
an image of better quality. The curved wavefronts 12 are produced by a
multiple sampling technique, as discussed later.
Figure 6 shows the different methods in which the optical systems of both the
prior art and the present invention display a point in the image volume.
Fourier optics are represented , but the idea is equally applicable to other
optical arrangements.
In Figure 6a, the light 11 diffracted from two different hogels 8a, 8b is seen
to
cross at a point 13, before it goes on to enter the eye of an observer. This
observer sees the light as if it emanated from the crossover point 13. In
practice, the light emanating from several different hogels, diffracted at
several different angles, is required to enter the eye of the observer to
build a
satisfactory representation of the point 13.
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In Figure 6b, the light pattern from just one hogel 8 is shown. This is a
curved
wavefront 12 of the current invention. It can be seen~that the representation
of a point in the image volume is done in a fundamentally different way, as
the
light from just a single hogel 8 is needed to give an observer the impression
of
seeing a point 14, as opposed to outputs from multiple hogels with the prior
art. Using Fourier optics, a wave 12 as it is emitted from a hogel 8 will,
after
passing through the Fourier lens 3, be converging on the point 14 before
diverging and passing on to the viewer. The viewer will thus see a point from
the wavefront emitted from a single hogel. The contribution from the other
hogels will also be present, and will add to the image quality.
The result of the invention is that many of the constraints and limitations
imposed upon the image by the prior art are, eliminated. Previously, the hogel
aperture size was constrained by the need to make it smaller so that as many
hogels as possible are used to make up the point, but also to make it larger
so
that the point can be sharply focussed by the eye. Other constraints exist as
described above, that are not present in a system of the current invention.
Figure 7 shows the process of decoding a hogel vector to produce a
continuous output spectrum. The vector, similar to that shown in Figure 3, is
multiplied with a- basis fringe 15 to produce a smooth output spectrum 16 as
shown in Figure 7b. A vector of the present invention will have more
coefficients 9 than one of the prior art, as a wavefront is sampled at
multiple
points across the hogel 8, allowing a hogel to produce curved wavefronts 12
as described below.
For clarity, the prior art method of generating an object point 13 is
illustrated in
Figure 8. This shows plane waves 11 emanating from four hogels that
converge at a point 13 that represents a point in the image volume. These
rays 11 go on to diverge, before entering the eye of an observer. This
observer will see the waves 11 as a point in space. It will be appreciated
that
the more plane waves 11 that go on to make the point 13, the more well
defined the point 13 will be. This, of course, means that more hogels are
required to define a point satisfactorily. It will be recalled from Figure 5
that
only one hogel is needed to define a point in space 14 with the current
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invention, due to the curved wavefront 12 that can be emanated from it. This
changes the constraints on hogel size etc such that a better quality image
may be produced.
The multiple point sampling of the wavefront across the hogel is illustrated
with the aid of Figure 9. The first action in the calculation of the hogel
vectors
of the current invention is to notionally transmit a wavefront from each point
in
the image volume 3. Consider a point P,14 coordinates (xp,zp) in the image
volume. As described above, P is at one of the nodes in the diffraction table
(the node spacings can be decided a priori and can be chosen to vary
nonlinearly and continuously over a wide range). To calculate the hogel
vector components 9 which are associated with the point P, the following
procedure can be used, where the optics of the system are assumed to be
well approximated by a thin, ideal Fourier lens:
Propagate a spherical wave 15 towards the Fourier transform lens, using P as
its source. The form of this (scalar) spherical wave can be described by:
A exp~ik3°~
where f-= ~x-xP~ +~z-zP~ and k is the wave vector magnitude,
A is the point amplitude.
This spherical wave 15 propagates towards the Fourier lens 3' of focal length
f. Assume the lens 3' is centred at (x=0, z=0). For the purposes of this
example, then lens 3' is approximated as an infinitely thin transparency,
having the transmission of:
expCik(f - x2 +yZ +f Z ~~
After propagating through the lens 3', the wavefront at the output of the lens
is
given by the product of the wavefront falling on the lens and the lens
transmission function. If the hogel is not in contact with the lens, a further
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propagation step needs to be made to calculate the wavefront across the
hogel.
The m hogel vector components associated with P can now be calculated.
This may be done using an FFT technique or numerical integration technique
to determine the first m complex coefficients of the Fourier series~of the
wavefront.
The theoretical number of frequency components required in each hogel
vector is estimated from the rate of change of the wavefront across the hogel.
A centrally positioned hogel will have a wavefront across it that has a lowei-
rate of change than a hogel on the extremities of the diffraction panel, where
the phase terms of the wavefront will vary much more quickly. As a general
rule of thumb, the largest value of m is proportional to Amax ~2~rr, where
Amax is
the maximum phase deviation of the waveform across the hogel.
The diffraction table may therefore be of varying dimensionality. Thus the
hogel vectors for the centrally positioned hogels will need fewer frequency
components to represent the vrravefront than those on the extremity of the
diffraction panel. The number of frequency components of the Fourier
transform can be reduced if this estimate derived from the paragraph above is
lower than half the number of pixels across the hogel, thus saving computing
time.
The choice of m also affects the desired object resolution. Figure 10 shows
the theoretical points spread function 16 for m=45, for a hogel containing 500
pixels, spacing 10 wavelengths, and hogel centred at {1.0 mm,0,0}. f--0.5 rm,
wavelength=500 nm. Also shown is the diffraction limited intensity for the
same hogel.assurning no wavefront approximations 17. Although the intensity
of the two peaks differ, the peak with a reduced number of Fourier
components still produces a good quality point localized in space. The
different intensities can be compensated for.
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Figure 11 shows, in a simplified form, (a) the effects on a wavefront being
emitted from a system that adds no compensation correction, and (b) the
current invention being used to pre-distort a wavefront to compensate for
aberrations present in the optical system. In the following description it is
assumed that the wavefronts from the hogel are intended to focus to as sharp
a point as possible in the image volume. Figure 11 a shows a wavefront 18
being emitted from a hogel and passing through an optical system comprising
two mirrors 19, 20. This system, like all optical systems, will not be
perfect,
and hence distortions will be introduced. After reflecting from the mirror 19
the wavefront will be distorted, shown as 18'. Further distortions 18" are
produced as the wavefront reflects from the mirror 20 These distortions
prevent the wavefront from focusing down to a sharp point in the image
volume 2. Instead, the "point" 21 has become spread, and less well defined,
as can be more clearly seen in the enlarged view 21'. of the point 21.
Figure 11 b shows how the present invention can correct for the aberrations
present in the mirror. As the present invention allows the waveforms emitted
from the hogel to be curved in a controlled manner, then the waveform can be
pre-distorted with the inverse distortions that are present in the optics.
This is
shown as the passage of waveform 17. The pre-compensation distortions
are present as the waveform is first emitted from the hogel, and these pre-
compensation distortions are gradually removed by the aberrations.in the
optical system. The waveform at 17' is less distorted, and the waveform at
17" less distorted still. This results in the wavefront coming to a much
sharper
point 22. The invention thus gives control over the desired image quality.
The current implementation of the invention is a HPO system, with the light
diffraction plane comprising 20 hogels in the horizontal dimension, where
each hogel has 1024 pixels. This is capable of providing 512 lateral
resolution
points across the image volume.
The current invention has been implemented on an Active-Tiling~ Computer
Generated Hologram display system. The computer system used to produce
the CGH can be a standalone unit, or could have remote elements connected
by a network.
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The Active Tiling system is a means of producing holographic moving images
by rapidly replaying different frames of a holographic animation. The Active
Tiling system essentially comprises a system for directing light from a light
source onto a first spatial light modulator (SLM) means and relaying a number
of SLM subframes of the modulated light from the first high speed SLM means
onto a second spatially complex SLM. The CGH is projected from this second
SLM.
The full CGH pattern is split up into subframes in which the number of pixels
is
equal to the complexity of the first SLM. These frames are displayed time-
sequentially on the first SLM and each frame is projected to a different part
of
the second SLM. The full image is thus built up on the second SLM over time.
The first SLM means comprises an array of the first SLMs that each tile
individual subframes on the second SLM over their respective areas.
Light f r om an SLM in the array must not stray onto parts of the second SLM
not intended for it. To prevent this a shutter can be placed between the first
SLM means and the second SLM, which masks off those areas of the second
SLM that are not currently being written to. Alternatively, electrodes on the
second SL.M that cover the area where it is not wished to write an image can
simply be not provided with a drive voltage. Thus any light that is falling
onto
the second SLM in these areas has no effect on the modulation layer. This
avoids the need for a shutter system. The first SLM of such a system is of a
type in which the modulation pattern can be changed quickly, compared to
that of the second SLM. Thus its updating frame rate is greater than the read-
out frame rate of the second SLM.
The Active Tiling system has the benefit that the image produced at the
second SLM, which is addressed at a rate much,slower than that of the first
SLM array, is effectively governed by the operation of the first SLM. This
permits a trade off between the temporal information available in the high
frame rate SLMs used in the SLM array and the high spatial resolution that
can be achieved using current optically addressed SLMs as the second SLM.
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In this way, a high spatial resolution image can be rapidly written to an SLM
using a sequence of lower resolution images.
See PCT/GB98/03097 for a full explanation of the active tiling system.
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References
1 "Diffraction specific fringe computation for electro-holography", M Lucente,
Doctoral thesis dissertation, MIT Department of Electrical Engineering and
Computer Science, September 1994.
2. "Computational holographic bandwidth compression", M Lucente, IBM
Systems Journal, October 1996.
3. Holographic bandwidth compression using spatial sub sampling, M
Lucente, Optical Engineering, June 1996.
4. M Lucente, Journal of electronic imaging 2(1 ), 28-34, Jan 1993
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