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Description  |
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BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates generally to the field of holography. More particularly,
the present invention relates to a direct-to-digital hologram acquisition and replay
system (i.e., no film, no plates). In a preferred implementation of the present
invention, the hologram acquisition is based on a charge coupled device (CCD) camera.
The present invention thus relates to a holographic system.
2. Discussion of the Related Art
Traditional methods of holography have used film or holographic plates
(glass plates with a photographic emulsion optimized for holography) to record
the hologram.(1) Replay has only been possible using lasers (or in some
cases white light) and the original recorded hologram or a duplicate of it, in
an analog method. These analog methods are slow, cumbersome, and expensive.(4)
There is also no way to reduce them to electronic signals that can be transmitted
and replayed at another location. It is always necessary to send hard copy. Worse
still, the time delay involved in processing the film prevents the use of holography
and its variants in many situations. Even if the expense of the classical holographic
system itself was tolerable, the time delay and low throughput caused by the necessity
of processing the film, introduces expenses associated with the delay that are
absolutely intolerable (e.g., a tire manufacturer cannot wait 45 minutes, or even
two minutes, to know that a particular tire has a flaw in it).
Referring to FIG. 1, a classical side-band holography system recordation
geometry is shown.(2-3) Light from a laser 110 is expended by
a beam expander 120. After passing through a lens 130, the light
is split into two components by a beamsplitter 140. The beamsplitter 140
can be, for example, 90% reflective. The reflected beam constituting an object
beam 150 travels toward and is reflected by a mirror 160. The object
beam 150 then travels toward an object 170. The object beam 150
is then incident upon a holographic plate 190.
Meanwhile, that portion of the light from lens 130 that is transmitted
through the beamsplitter 140 constitutes a reference beam 180 that
travels toward and is reflected by a mirror 200. The reflected reference
beam is then incident upon the holographic plate 190.
More recently, holographic interferometry has been developed, albeit also as
an analog method.(5) This has included the development of focused holography.(6-7)
Within this application several publications are referenced by superscripts
composed of arabic numerals within parentheses. Full citations for these, and other,
publications may be found at the end of the specification immediately preceding
the claims. The disclosures of all these publications in their entireties are hereby
expressly incorporated by reference into the present application for the purposes
of indicating the background of the present invention and illustrating the state
of the art.
SUMMARY OF THE INVENTION
Therefore, there is a particular need for a method for 1) recording holograms
directly to a CCD (charged coupled device) camera or any other suitable video camera
with a digital computer interface and then 2) storing the holograms to a digital
storage medium (e.g., RAM, hard drive, tape, recordable CD, etc.). Significant
features of an apparatus for implementing this method include the use of a very
small angle between the reference beam and object beam and focusing the hologram
on the image plane to simplify the image. Additionally, the invention includes
1) a method of displaying the hologram phase or amplitude on a two-dimensional
display and 2) a method of replaying the holograms completely using an optically
active crystal and lasers. In contrast, the prior art does not include a description
of how to electronically (digitally) record an optical hologram, much less replay,
or broadcast an optical hologram.
The improvements disclosed herein allow for higher quality, lower-noise digital
hologram acquisition and replay. The improvements make use of variations in the
geometry and optical components to allow the acquisition and analysis of high resolution
holograms. In addition, improvements to the replay system have been made that allow
writing of a digital grating (hologram) to a photorefractive crystal, and then
the replay of that grating or hologram with a single laser beam.
One embodiment of the invention is based on an apparatus to record an off-axis
hologram, comprising: a laser; an illumination beamsplitter optically coupled to
said laser; an objective lens optically coupled to said illumination beamsplitter;
an object optically coupled to said objective lens; a reference beamsplitter coupled
to said laser; a reference mirror optically coupled to said reference beamsplitter;
a beam combiner optically coupled to both said reference beamsplitter and said
illumination beamsplitter; and a digital recorder optically coupled to said beam
combiner, wherein a reference beam and an object beam are combined at a focal plane
of said digital recorder to form an off-axis hologram, and said object beam and
said reference beam constitute a plurality of substantially simultaneous reference
and object waves. Another embodiment of the invention is based on a method of recording
an off-axis hologram, comprising: splitting a laser beam into an object beam and
a reference beam; reflecting said reference beam from a reference beam mirror;
reflecting said object beam from an illumination beamsplitter; passing said object
beam through an objective lens; reflecting said object beam from an object; focusing
said reference beam and said object beam at a focal plane of a digital recorder
to form an off-axis hologram; digitally recording said off-axis hologram; and transforming
said off-axis hologram in accordance with a Fourier transform to obtain a set of results.
Another embodiment of the invention is based on an apparatus to write an
off-axis hologram, comprising: a laser; a spatial light modulator optically coupled
to said laser; a lens optically coupled to said spatial light modulator; and a
photorefractive crystal optically coupled to said lens, wherein a write beam is
focused at a focal plane of said photorefractive crystal by said lens to impose
a holographic diffraction grating pattern on said photorefractive crystal. Another
embodiment of the invention is based on a method of writing an off-axis hologram,
comprising: passing a laser beam through a spatial light modulator; and focusing
said laser beam at a focal plane of a photorefractive crystal to impose a holographic
diffraction grating pattern on said photorefractive crystal.
Another embodiment of the invention is based on an apparatus to replay an
off-axis hologram, comprising: a laser; and a photorefractive crystal optically
coupled to said laser. Another embodiment of the invention method of replaying
an off-axis hologram, comprising: illuminating a photorefractive crystal having
a holographic diffraction grating with a replay beam.
These, and other, aspects of the present invention will be better appreciated
and understood when considered in conjunction with the following description and
the accompanying drawings. It should be understood, however, that the following
description, while indicating preferred embodiments of the present invention and
numerous specific details thereof, is given by way of illustration and not of limitation.
Many changes and modifications may be made within the scope of the present invention
without departing from the spirit thereof, and the invention includes all such modifications.
BRIEF DESCRIPTION OF THE DRAWINGS
A clear conception of the advantages and features constituting the present invention,
and of the components and operation of model systems provided with the present
invention, will become more readily apparent by referring to the exemplary, and
therefore nonlimiting, embodiments illustrated in the drawings accompanying and
forming a part of this specification, wherein like reference numerals designate
the same elements in the several views. It should be noted that the features illustrated
in the drawings are not necessarily drawn to scale.
FIG. 1 illustrates a schematic view of a classical (Leith & Upatnieks) sideband
holography system, appropriately labeled "PRIOR ART";
FIG. 2 illustrates a schematic view of a simple direct-to-digital holography
system, representing an embodiment of the present invention;
FIG. 3a illustrates a perspective view of a "Michelson" geometry direct-to-digital
holography setup, representing an embodiment of the present invention;
FIG. 3b illustrates another perspective view of the direct-to-digital
holography setup shown in FIG. 3A;
FIG. 4 illustrates a digitally acquired hologram of a scratch in a mirror, representing
an embodiment of the present invention;
FIG. 5 illustrates a plot of a 2-D Fourier transform of FIG. 4;
FIG. 6 illustrates a replay of hologram phase data from the hologram of FIG. 4;
FIG. 7 illustrates a schematic view of a holographic replay system, representing
an embodiment of the present invention;
FIG. 8 illustrates a selected area of a hologram of gold particles on an amorphous
carbon film, representing an embodiment of the present invention;
FIG. 9 illustrates a selected area of the modulus of the Fourier transform of
the hologram in FIG. 8 (center area: the autocorrelation; left and right area:
the sidebands), representing an embodiment of the present invention;
FIG. 10A illustrates a contrast transfer function at Scherzer focus;
FIG. 10B illustrates a holography special transfer function at Gabor focus,
representing an embodiment of the present invention;
FIG. 11 illustrates a modulus of discrete Fourier transform of cos-pattern sampled
with 32 points at sampling rate s=4.66 (number of display points in discrete Fourier
transform is 32), representing an embodiment of the present invention;
FIG. 12 illustrates a modulus of analytic Fourier transform of cos-pattern according
to Eq. (6) (cos-pattern is limited to same area (in real space) as data from FIG.
11 and none of the details in this figure can be found in FIG. 11), representing
an embodiment of the present invention;
FIG. 13 illustrates a modulus of extended Fourier transform of cos-pattern (original
set of display points was 32 as in FIG. 11; choosing parameter π to be 16,
number of display points in extended Fourier transform is 512 and shows same details
as visible in analytic Fourier transform), representing an embodiment of the present invention;
FIG. 14 illustrates the results of an extended Fourier algorithm which allows
display of conventional discrete Fourier transform but shifted by fraction of pixel
(again, same cos-pattern as for FIG. 11 is used; choosing true values for Δk
(and Δ1 in two dimensions), it is possible to display at least one peak in
Fourier space such that it falls directly on display point; in this case, sidelobes
disappear (see right peak)), representing an embodiment of the present invention;
FIG. 15 illustrates that reconstructing amplitude from a sideband that is not
truly centered causes artifacts in image (the worst situation is when center of
the sideband falls exactly in between display points in Fourier space), representing
an embodiment of the present invention;
FIG. 16 illustrates a Mach-Zender layout schematic of a hologram acquisition
system with through-the-lens illumination, representing an embodiment of the invention;
FIG. 17 illustrates a digital hologram acquisition system layout drawing illustrating
an object beam reflecting off from the face of an illumination beamsplitter and
beam combiner, thereby eliminating astigmatism, representing an embodiment of the invention;
FIG. 18 illustrates a photograph of a digital hologram acquisition system, representing
an embodiment of the invention;
FIG. 19 illustrates a schematic of a practical replay system, representing an
embodiment of the invention;
FIG. 20 illustrates a lithium niobate crystal and hologram write/replay optics,
representing an embodiment of the invention;
FIGS. 21A and 21B illustrate transmissive and reflective spatial light modulator
optical geometries suitable for a holographic replay system, respectively, representing
embodiments of the invention;
FIG. 22 illustrates an 800×600 computer driven spatial light modulator
followed by a polarizer as implemented in a hologram replay system, representing
an embodiment of the invention; and
FIG. 23 illustrates a photograph of a laser beam at a Fourier plane of a tube
lens showing spatial light modulator pixel edge diffracted orders (the center bright
spot is the zero order diffracted image), representing an embodiment of the invention.
FIGS. 24A-24D illustrate polarizing beamsplitters combined with ¼ wave
plates, representing embodiments of the invention.
DESCRIPTION OF PREFERRED EMBODIMENTS
The present invention and the various features and advantageous details thereof
are explained more fully with reference to the nonlimiting embodiments that are
illustrated in the accompanying drawings and detailed in the following description.
Descriptions of well known components and processing techniques are omitted so
as to not unnecessarily obscure the present invention in detail.
1. System Overview
The reason that digital holography has not been developed until now is that the
resolution of digital video cameras or cameras adaptable to digital media has,
heretofore, not been good enough to record the very high spatial frequencies inherent
in classical holograms. The invention combines several techniques that overcome
this difficulty, and allow recording of holograms and all of their spatial frequencies
up to the inherent holographic resolution of the recording camera for Fourier transform
hologram analysis.
It was necessary to realize how to digitally record an optical hologram (and
that
it is a hologram). It was also necessary to realize that the Fourier transform
techniques used in interferometry and electron holography could be used to analyze
the hologram. It was also necessary to realize that mathematical addition of a
plane wave to the digital hologram, and writing the resulting intensity function
to an optically sensitive crystal would allow actual replay of the hologram at
a different (and much larger) diffraction angle α, than the angle used to
create the original sideband hologram.
2. Detailed Description of Preferred Embodiments
Referring now to FIG. 2, a simple direct-to-digital holography system is
shown to illustrate the hardware concepts that have been combined to allow digital
recording and replay of holograms. Light from a laser 210 is expanded by
a beam expander/spatial filter 220. The expanded/filtered light then travels
through a lens 230. Then, the light travels to a beamsplitter 240.
Beamsplitter 240 can be, for example, 50% reflective. Light that is reflected
by the beamsplitter constitutes an object beam 250 which travels toward
and object 260. A portion of the light reflected from the object 260
then passes through the beamsplitter 240 and travels toward a focusing lens
270. This light then travels to a charged coupled device (CCD) camera (not shown).
Meanwhile, that portion of the light from lens 230 that passes
through beamsplitter 240 constitutes a reference beam 280. The reference
beam 280 is reflected from a mirror 290 at a small angle. The reflected
reference beam from mirror 290 then travels toward the beamsplitter 240.
That portion of the reflected reference beam that is reflected by the beamsplitter
240 then travels toward the focusing lens 270. The reference beam
from focusing lens 270 then travels toward the CCD camera. Together, the
object beam from the focusing lens 270 and the reference beam from the focusing
lens 270 constitute a plurality of simultaneous reference and object waves 300.
Comparing FIG. 2 to FIG. 1, it can be seen that at least the following
differences allow a CCD camera to record the hologram, rather than using film or
a photographic plate. 1) The invention uses a high resolution CCD (e.g., 1.4 million
pixels), (CCD's with over 60 million pixels are already available). 2) The invention
uses a "Michelson" geometry (the geometrical relationship of the beamsplitter,
reference beam and the object beam to be combined at a very small angle (the reference
beam mirror, and CCD resembles a Michelson interferometer geometry). This geometry
allows the reference beam mirror to be tilted to create the small angle that makes
the spatially heterodyne or sideband fringes for Fourier analysis of the hologram.
3) The invention uses a focusing lens to focus the object onto the focal plane
of the CCD. This lens also provides magnification or demagnification, as desired,
by using lenses of different focal length and adjusting the corresponding spatial
geometry (e.g., ratio of object distance to image distance). The foregoing three
factors allow direct to digital recording and replay of holograms when combined
with Fourier transform software analysis methods known in the literature.(10-12)
The system is suitable for recording and replaying holographic images in real
time or storing them for replay later. Since the holograms are digitally stored,
a series of holograms can be made to create a holographic motion picture or the
holograms can be broadcast electronically for replay at a remote site to provide
holographic television (HoloVision). Since a hologram stores amplitude and phase,
with phase being directly proportional to wavelength and optical path length, this
direct to digital holography can also serve as an extremely precise measurement
tool for verifying shapes and dimensions of precision components, assemblies, etc.
Similarly, the ability to store the holograms digitally immediately provides a
method for digital holographic interferometry. Holograms of the same object, after
some physical change (stress, temperature, micromachining, etc.), can be subtracted
from one another (direct subtraction of phase) to calculate a physical measurement
of the change (phase change being directly proportional to wavelength). Similarly
one object can be compared to a like object to measure the deviations of the second
object from the first or master object, by subtracting their respective holograms.
To unambiguously measure phase changes greater than 2π in the z-plane over
two pixels in the x-y plane, holograms must be recorded at more than one wavelength
(discussions of two-frequency interferometry are well-known in the literature and
will not be repeated here).
The invention combines the use of high resolution video cameras, very small angle
mixing of the holographic object and reference waves (mixing at an angle that results
in at least two pixels per fringe and at least two fringes per spatial feature
to be resolved), imaging of the object at the recording (camera) plane, and Fourier
transform analysis of the spatially low-frequency heterodyne (side-band) hologram
to make it possible to record holographic images (images with both the phase and
amplitude recorded for every pixel). Additionally, an aperture stop can be used
in the back focal plane of one or more lenses involved in focusing the object,
to prevent aliasing of any frequencies higher than can be resolved by the imaging
system (aliasing is thoroughly described in the literature and placing aperture
stops in the back focal plane of a lens to limit the spatial frequencies present
is also well described and well understood). No aperture is necessary if all spatial
frequencies in the object are resolvable by the imaging system. Once recorded,
it is possible to either replay the holographic images as 3-D phase or amplitude
plots on a two-dimensional display or to replay the complete original recorded
wave using a phase change crystal and white light or laser light to replay the
original image. The original image is replayed by writing it in the phase-change
medium with lasers, and either white light or another laser is used to replay it.
By recording an image with three different colors of laser and combining the replayed
images, it is possible to make a true-color hologram. By continuously writing and
relaying a series of images, it is possible to form holographic motion pictures.
Since these images are digitally recorded, they can also be broadcast with radio
frequency (RF) waves (e.g., microwave) or over a digital network of fibers or cables
using suitable digital encoding technology, and replayed at a remote site. This
effectively allows holographic television and motion pictures or "HoloVision."
With regard to the use of a lens to focus the object onto the focal plane of
the CCD, the diffraction pattern of a point can be described by a spherical function
which has increasingly close fringe as the distance from the center of the pattern
increases. As these fringes get closer and closer together, they are unresolvable
by a video camera. Worse yet, the interaction of these point diffraction patterns
from a complex object creates an impossibly dense and complicated pattern, which
cannot be anywhere resolved by a video camera. Focusing the object on the recording
plane eliminates these diffraction patterns, so that modern high-resolution video
cameras can record holograms with reasonable fidelity.
If the recording media resolves 100 lines/mm, the holographic resolution will
be approximately 16 lines/mm, or on the order of 50 microns, at unity magnification.
This limit can be increased by the use of a magnification lens. For a camera resolution
of 100 lines/mm, the hologram resolution will be approximately 160 lines/mm if
a magnification of 10 is used. Similarly, the spatial resolution will be decreased
by any de-magnification of the original image onto the recording camera.
The invention can also be embodied in a number of alternative approaches. For
instance, the invention can use phase shifting rather than heterodyne acquisition
of the hologram phase and amplitude for each pixel. Phase shifting interferometry
is well documented in the literature. As another example, the invention can use
numerous different methods of writing the intensity pattern to an optically sensitive
crystal. These include using a sharply focused scanning laser beam (rather than
using a spatial light modulator), writing with an spatial light modulator (SLM)
but without the biasing laser beam, and many possible geometric variations of the
writing scheme. As another example, the invention can use optically sensitive crystals
employing optical effects other than phase change to create the diffraction grating
to replay the hologram. As yet another example, the invention can actually use
a very fine-pixeled spatial light modulator to create the intensity pattern, thereby
obviating any need to write the intensity pattern to an optically active crystal
for replaying the hologram.
EXAMPLE
A specific embodiment of the present invention will now be further described
by
the following, nonlimiting example which will serve to illustrate in some detail
various features of significance. The example is intended merely to facilitate
an understanding of ways in which the present invention may be practiced and to
further enable those of skill in the art to practice the present invention. Accordingly,
the example should not be construed as limiting the scope of the present invention.
FIG. 3A is a perspective view of an exemplary "Michelson" geometry for direct-to-digital
holography is shown. Laser light is provided to a beamsplitter 310. An object
beam from the beamsplitter 310 travels to a semiconductor wafer mount 320
and then to a focusing lens 330. Meanwhile, a reference beam from the beamsplitter
310 travels to a reference beam mirror that is mounted on a piezoelectric
reference beam mirror mount 340.
FIG. 3B is another perspective view of the exemplary recording "Michelson" geometry
is shown. In this view, the position of a direct-to-digital CCD camera 350
with regard to the other subcomponents of the apparatus can be more readily appreciated.
In this view, the position of an object target mount 360 can also be more
readily appreciated.
FIG. 4 is a heterodyne (sideband) hologram of a scratch in a mirror (the object
in this case). The hologram was made with the direct to digital holography system
illustrated in FIGS. 3A-3B and described above. The fringes observable in the hologram
are due to the interference between the reference and object beams. The reference
beam mirror was tilted slightly to create these fringes. It is the presence of
these fringes which allows Fourier transform analysis of the hologram to calculate
the phase and amplitude for the pixels of the hologram. The Fourier transform analysis
will be discussed in more detail below.
FIG. 5 is a graphical plot of the two-dimensional Fourier transform of FIG.
4. The x axis is the spatial frequency axis along the x dimension and the y axis
is the spatial frequency axis along the y dimension. The actual data itself is
a matrix of numbers corresponding to the strength of a particular spatial frequency
in (fx, fy) frequency space. The number and brightness of
the white dots shows the strength and position in frequency space of the spatial
frequencies present in FIG. 4. It can be appreciated from FIG. 5 that the reference
beam fringes act as a heterodyne local oscillator shifting the real and virtual
hologram images off-axis and allowing their separation in frequency space. It is
known from Shannon's Theorem (or Nyquist's limit) that at least two pixels per
fringe are required to resolve a fringe, and from electron holography that at least
3 fringes per resolvable feature are required to resolve the object in the hologram
(nominally it would require three to four fringes per feature to allow resolution
of the carrier spatial frequency plus the object frequencies, but work on the extended
Fourier transform by Voelkl, et al.,(10-12) allows the use of 2 fringes
per feature). Thus, these two limits determine the required magnification of an
object and the tilt angle between the reference and object beams in order to resolve
a feature (spatial frequency) in a hologram.
The data shown in FIG. 5 is analyzed by transforming (shifting) the axes in Fourier
space to sit on top of the heterodyne carrier frequency (the spatial frequency
caused by the small angle tilt between the object and reference beams), then applying
a digital filter (e.g., a Hanning or Butterworth filter) to cut off the signals
around the original origin (these are actually the signals resulting from the reference
beam interacting with itself and the object beam interacting with itself, and are
just noise from the hologram point of view), and then performing the inverse Fourier
transform. All of this analysis can be carried out on a digital computer and can
be done in real time. Real time analysis may require as many as 30 to 100 high
performance parallel processors (e.g., Pentium Pro or DEC Alpha) to achieve a frame
rate of 30 frames per second. Computer systems of this size are presently commonly
used as large database servers and stock market calculational engines. They are
also suitable for short-term low resolution weather forecasting, and image manipulation
and creation for the film industry. It can be expected that such systems will be
desktop systems within 6 to 10 years.
FIG. 6 shows a replay of the phase data created by performing the described
analysis on the data (hologram) from FIG. 5. Replaying the data as an actual hologram
will require the creation of a diffraction grating in an optical crystal and illumination
of the diffraction grating with laser light (or appropriately treated white light)
at the correct angle. The data to be actually written to the optically sensitive
crystal is calculated from the hologram data by adding a function f(x,y,zo)
to each pixel h(x,y,zo) of the hologram data, where both functions are
complex and:
f(x,y)=eik cos(α)r
and r is the square root of x2+y2+z20.
The exponential function added above corresponds physically to adding a plane
wave intersecting at angle a with the original object wave of the hologram. The
function created by the sum is multiplied by its complex conjugate to form the
absolute value intensity function, which is written to the light-sensitive crystal
with the laser (it may also be possible to write only the intensity cross-term
of the reference beam with the object, and drop the autocorrelation terms). The
diffraction grating thus created in the light sensitive crystal can then be illuminated
with laser light at angle a to replay the original hologram. If a crystal is used
which has a temporary phase change or refractive index change when written with
laser light, then by continuously writing new images from either instantaneously
acquired or stored holograms, and illuminating each image with laser light from
another laser (or appropriately treated white light) at the angle α, a 3-D
motion picture or 3-D television image can be created. This is just one possible
method and not the only possible method for writing the holographic image to an
optically sensitive crystal and then replaying it.
FIG. 7 depicts a method for generating a motion picture or television using
the invention. It can be appreciated that the hologram is written to the phase
change or other optically active crystal by intersecting two laser beams in a phase
change crystal 710. Laser Beam 1 is passed through a spatial light
modulator 720 to modulate the hologram intensity pattern into it, created
mathematically from the original hologram as described above. SLM 720 is
controlled by a computer 740 via a data path 750. A focusing lens
730 focuses this pattern in the phase change crystal 710 at the intersection
of Laser Beam 1 with Laser Beam 3, where the combined intensity of
the two lasers is adequate to write the pattern to the crystal 710. After
the pattern is written, Laser Beam 2, incident on the crystal 710
at angle a replays the original hologram.
Introduction to Lightwave Holography
In order that the hologram processing steps described herein can be more easily
understood, it is useful briefly to review first the nature of off-axis holography.
In an electron microscope, equipped with a highly coherent electron source, e.g.
one using a field-emission electron gun, the electron beam that is incident on
the specimen is, ideally, a plane wave. In practice, this can be achieved to a
reasonable approximation if the illumination is spread over a large area. In this
ideal case, the object in the microscope modifies the incident plane wave exp (ik
{right arrow over (r)}) to the object wave o({right arrow over (r)}), which is
defined as:
o({right arrow over (r)})=a({right arrow over (r)})·eiφ({right
arrow over (r)}). (1)
Both a({right arrow ov | | |
