Acquisition and replay systems for direct-to-digital holography and holovision

What is claimed is:

1. 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.

2. The apparatus of claim 1, wherein said illumination beamsplitter, said objective lens, said object, said reference beamsplitter, said reference mirror, said beam combiner and said digital recorder define a Mach-Zender geometry.

3. The apparatus of claim 1, wherein an object beam from said object is reflected by a front face of said illumination beamsplitter and a reference beam from said reference mirror is reflected by a front face of said reference beamsplitter.

4. The apparatus of claim 1, wherein said illumination beamsplitter includes a polarizing illumination beamsplitter and said reference beamsplitter includes a polarizing reference beamsplitter, and,

further comprising, an illuminating quarter wave plate optically coupled between said polarizing illumination beamsplitter and said object; and a reference quarter wave plate optically coupled between said polarizing reference beamsplitter and said reference mirror.

5. The apparatus of claim 1, further comprising a first polarizer optically coupled between said illumination beamsplitter and said beam combiner; and a second polarizer optically coupled between said reference beamsplitter and said beam combiner.

6. The apparatus of claim 1, wherein an object beam path is substantially identical to a reference beam path.

7. The apparatus of claim 1, further comprising an acousto-optic modulator optically coupled between said laser and both said illumination beamsplitter and said reference beamsplitter.

8. The apparatus of claim 1, further comprising a first acousto-optic modulator optically coupled between said laser and said illumination beamsplitter; and a second acousto-optic modulator optically coupled between said laser and said reference beamsplitter.

9. The apparatus of claim 1, further comprising a first optic fiber optically coupled between said laser and said illumination beamsplitter; and a second optic fiber optically coupled between said laser and said reference beamsplitter.

10. The apparatus of claim 9, wherein said first optic fiber includes a first single mode polarization preserving optic fiber and said second optic fiber includes a second single mode polarization preserving optic fiber.

11. The apparatus of claim 1, further comprising a first tube lens optically coupled between said illumination beamsplitter and said beam combiner and a second tube lens optically coupled between said reference beamsplitter and said beam combiner.

12. The apparatus of claim 1, further comprising a first beam expander/spatial filter optically coupled between said laser and said illumination beamsplitter and a second beam expander/spatial filter optically coupled between said laser and said reference beamsplitter.

13. 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.

14. The method of claim 13, further comprising combining said object beam and said reference beam with a beam combiner, before digitally recording.

15. The method of claim 13, wherein i) reflecting said object beam from said illumination beamsplitter include reflecting said object beam from a front face of said illumination beamsplitter after reflecting said object beam from said object and ii) reflecting said reference beam from said reference beamsplitter includes reflecting said reference beam from a front face of said reference reflector after reflecting said reference beam from said reference mirror.

16. The method of claim 13, wherein i) reflecting said object beam from said illumination beamsplitter includes reflecting said object beam from a polarizing illumination beamsplitter and ii) reflecting said reference beam from said reference beamsplitter includes reflecting said reference beam from a polarizing reference beamsplitter, and,

further comprising, a) passing said object beam through an illuminating quarter wave plate both before and after reflecting said object beam from said object and b) passing said reference beam through a reference quarter wave plate both before and after reflecting said reference beam from said reference mirror.

17. The method of claim 14, further comprising:

passing said object beam through a first polarizer after reflecting said object beam from said illumination beamsplitter and before combining said object beam and said reference beam with said beam combiner; and

passing said reference beam through a second polarizer after reflecting said reference beam from said reference beamsplitter and before combining said object beam and said reference beam with said beam combiner.

18. The method of claim 13, wherein an object beam path traced by said object beam is substantially identical to a reference beam path traced by said reference beam.

19. The method of claim 13, further comprising passing said laser beam through an acousto-optic modulator before splitting said laser beam.

20. The method of claim 13, further comprising:

passing said object beam through a first acousto-optic modulator before reflecting said object beam with said illumination beamsplitter; and

passing said reference beam through a second acousto-optic modulator before reflecting said reference beam with said reference beamsplitter.

21. The method of claim 13, further comprising:

passing said object beam through a first optic fiber before reflecting said object beam with said illumination beamsplitter; and

passing said reference beam through a second optic fiber before reflecting said reference beam from said reference beamsplitter.

22. The method of claim 13, further comprising:

passing said object beam through a first tube lens after reflecting said object beam from said illumination beamsplitter; and

passing said object beam through a second tube lens after reflecting said reference beam from said reference beamsplitter.

23. The method of claim 13, further comprising:

passing said object beam through a first beam expander/spatial filter before reflecting said object beam with said illumination beamsplitter; and

passing said reference beam through second beam expander/spatial filter before reflecting said reference beam with said reference beamsplitter.

24. The method of claim 13, further comprising storing said off-axis hologram as digital data.

25. The method of claim 13, further comprising replaying said off-axis hologram.

26. The method of claim 13, further comprising transmitting said off-axis hologram.

27. An off-axis hologram prepared by the method of claim 13.

28. The off axis-hologram of claim 27, wherein said off-axis hologram is generated using an extended Fourier transform.

Description Submit all comments and votes

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..sup.(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..sup.(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..sup.(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..sup.(5) This has included the development of focused holography..sup.(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 .pi. 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 .DELTA.k (and, .DELTA.l 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.times.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 1/4 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 .alpha., 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..sup.(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 2.pi. 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 farther 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 (f.sub.x, f.sub.y) 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.,.sup.(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,z.sup.o) to each pixel h(x,y,z.sup.o) of the hologram data, where both functions are complex and:

f(x,y)=e.sup.ikcos(.alpha.)r

and r is the square root of x.sup.2 +y.sup.2 +z.sup.2.sup..sup.0

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 .alpha., 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 el