Implementation of a spatially multiplexed pixelated ... - OSA Publishing

Implementation of a spatially multiplexed pixelated three-dimensional display by use of a holographic optical element array Shih-Tun Chen and Monish R. Chatterjee

A pixelated holographic stereogram is proposed and experimentally studied for the emulation of a spatially multiplexed composite three-dimensional ~3-D! pixel display. With this approach, pixelated holograms are utilized to compose spatially multiplexed images. Each composite pixel in the holographic optical element array has a diffraction pattern that scatters light into predefined spatial directions. Under reconstruction, each pixel generates different intensities along a range of viewing angles. When the composite holographic pixel array is assembled, it has the capability to deliver 3-D effects. The technique, together with a novel recording scheme that is designed to synthesize a computerized 3-D display system based on this concept, is described in some detail. © 1998 Optical Society of America OCIS codes: 090.2870, 090.2890, 090.1760, 090.4220, 120.2040, 160.2900.

1. Introduction

In traditional display systems a pixel represents light of a certain intensity emitted over a small area defined by the pixel size. The emitted light, in general, is projected in the forward direction with a broad angular spread. In such systems viewers cannot intercept or perceive any change in the image when their viewing angle is changed. A spatially multiplexed recording is sometimes called a stereogram when two or more images from a single picture are viewed ~or projected! at the same time.1 These images can be spatially multiplexed to construct a three-dimensional ~3-D! view for human eyes. Several tools are available for obtaining a 3-D effect; these include a computer-controlled virtualreality simulator2 and a mazelike optical-illusion stereogram.3 The spatial-multiplexing technique developed in this study allows direct viewing of a 3-D image and does not require the viewer to stare at an illusion stereogram or use gadgets such as virtualreality goggles. Such direct viewing of 3-D images

The authors are with the Department of Electrical Engineering, Binghamton University, State University of New York, Binghamton, New York 13902-6000. M. R. Chatterjee’s e-mail address is [email protected]. Received 9 February 1998; revised manuscript received 29 April 1998. 0003-6935y98y327504-10$15.00y0 © 1998 Optical Society of America 7504

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that are based on autostereoscopic screens and displays has been explored by several investigators within the past decade.4,5 Conventional display technologies, including liquid-crystal displays, electric-plasma displays, and cathode-ray tubes, have improved considerably in the past decade. The next generation of 3-D displays will also take advantage of the current technological advances in integrated electronics and electronic computing. The effort to develop an electronically controllable holographic grating encompasses several optical and materials research areas, including the nonlinear optical properties of photorefractive materials, nematic liquid crystals, and photopolymers. Khoo6 recently reported the formation of a holographic grating in fullerene-C60doped liquid crystals. Meerholz7 has recorded high-efficiency holographic gratings in photorefractive polymers. Considerable work is also underway for the development of dynamic 3-D display systems; some of the techniques include holographic movies, synthetic aperture 3-D displays, partial-pixel stereoscopic displays, LCD stereoscopic displays with diffractive optical elements, polarized stereoscopic displays, virtual-reality systems, and scanning holography-based 3-D displays that use spatial light modulators.8 –14 In this paper a composite, pixelated hologram consisting of an array of holographic optical elements ~HOE’s! is proposed for use as a holographic stereogram.14 The HOE array is used to produce an effect

similar to that of a stereogram. The concept of using a HOE array as a holographic stereogram is different from that of the traditional holographic stereograms investigated by King,16 King et al.,17 and Benton18 or from the so-called multiple photogenerated holograms reported recently by Spierings and van Nuland.19 A conventional stereogram technique exposes different segmented slits on a photographic film to prerecorded scenes from different perspectives, i.e., each slit is responsible for a single perspective. This approach has proven successful in recording computer-generated images.17,19 However, in our approach, a partial-object-pixel ~hereafter referred to as POP! recording technique is applied to record the HOE array. Our intention is to use a HOE array to display a set of digitized and spatially multiplexed images. Each pixel in the array contains information from the same pixel position in every perspective; in other words, the images of a given object from different perspectives are not used directly in the recording. Thus, instead of recording with total pictures, each time we use partial– pixelated picture samples from corresponding address locations on all the images ~obtained with a LCD gate array as a spatial light modulator! to record each HOE pixel. We must emphasize here, however, that, in principle, the technique described in this paper does not represent a new methodology for recording 3-D stereograms. It is instead an experimental demonstration of the emulation of a pixelated 3-D display architecture with a HOE array generated optically by means of a microprocessor interface. The standard procedure for obtaining partial-pixel architectures11 consists of multiplexing smaller segments of the pixels in an image, which results in a partial 3-D pixel and a ~relatively! limited number of viewing angles. The POP architecture proposed here, although it requires a large number of exposures, nevertheless emulates a whole instead of a partial pixel, which is displayed in a specific direction. In Section 2 we discuss conventional computergenerated Fourier transform holograms and holographic stereograms. The POP technique proposed in this study is described in Section 3. Section 4 describes some of the common problems encountered in recording holograms with the POP technique and suggests ideas for minimizing these problems. Some experimental HOE arrays obtained with the technique are presented in Section 5, with some discussion of the results. Section 6 concludes this paper.

Fig. 1. A spatially multiplexed display ~stereogram! projects two patterns in different directions.

ten used to generate two-dimensional ~2-D! instead of 3-D object patterns. Three-dimensional objects with complicated wave fronts require more complex computations for recording the corresponding computergenerated holograms. A. Conventional Holograms Versus Holographic Stereograms

A holographic stereogram6,7 is composed of a series of pictures from different aspects of an object scene by use of either a camera or a computerized imagesynthesizing program. These pictures are first recorded on the narrow vertical slits of a film by means of conventional two-beam recording, thus forming a master hologram from which the viewable hologram is recorded subsequently in a second recording stage. As a result, a viewer is able to see a different picture by varying the viewing angle with respect to the hologram. To a certain degree, a conventional hologram can be regarded as a linear or a continuous version of a holographic stereogram, which continually reconstructs different images along linearly varying viewing angles. Conversely, a holographic stereogram can be considered a digitized or a segmented conventional hologram, which reconstructs different images over a range of discrete or segmented viewing angles. A simple two-image stereogram projects two images along spatially multiplexed directions, as depicted schematically in Fig. 1.

2. Holographic Stereograms

As is well known, holograms have the ability to record and reconstruct the light waves from an object as a whole, i.e., they preserve both the amplitude and the phase information of the light waves emanating from the object. One can make a computergenerated Fourier transform hologram by calculation of the Fourier transform of an object wave front and embedding it as a transmittance function on a film.19 For simplicity, computer-generated holograms are of-

Fig. 2. Recording of a holographic stereogram ~top view! in which the film is recorded slit by slit ~after Iizuka1!. 10 November 1998 y Vol. 37, No. 32 y APPLIED OPTICS

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Fig. 5. Recording scheme for a horizontally multiplexed POP. The object beam consists of nine object segments. Fig. 3. POP technique used to make a hologram with properties similar to those seen when one looks into a small opening in front of a large object at close range.

B.

Recording a Conventional Holographic Stereogram

The holographic multiplexing technique for stereograms was developed by King et al.17 in 1968. The technique was originally designed to multiplex different scenes of a particular object spatially to cover perspectives from 0°–360°. In this technique the holographic stereogram is recorded in a slit-by-slit fashion, as depicted in Fig. 2. The vertical slits on the hologram are exposed to different scenes so that the composite hologram can display a different scene, depending on the viewing angle used by the viewer. 3. Partial-Object-Pixel-Based Three-Dimensional Display Architecture

The POP hologram is recorded with relatively large object scenes ~compared with the size of the hologram! so that the reconstructed scene from the recorded hologram does not cover the whole object. When the hologram is viewed, only a small portion of the object is observed. One analogy to this technique is for one to observe scenes by looking into a small opening with a large object ~relative to the opening! placed close behind, as in Fig. 3. Similar to the case for partial-object recording, only a small part of the object can be seen from any given viewing angle. To record a POP, we expose the film with the object scene projected onto a screen, as depicted in Fig. 4. In this figure a recording for a horizontally multiplexed pixel with nine viewing windows is de-

Fig. 4. Images on the projection screen and views in the observation plane seen through a small opening in the mask. 7506


picted. The information embedded in the pixel is determined by the arrangement of the intensity distribution on the screen. Therefore the diffraction pattern of a resulting pixel over the viewing space is determined by the intensity distribution on the projection screen during recording. After the pixel is recorded with the partial object scene, its diffraction profile over the viewing angular range is defined by the content of the screen. The object beam, which consists of the divided segments on the projection screen, is added with a reference beam for recording a HOE. The two beams are applied to expose the film in a holographic recording setup, as shown in Fig. 5. In this figure the film is placed behind the mask, which defines the pixel size and shape. The opening on the mask allows the light beams to expose an area for the pixel hologram that is identical to the size and the shape of the opening. After the recording is complete and the film is developed, the recorded information can be reconstructed by use of the same reference beam. The pixel diffracts the reference beam along the original object-beam direction. As the object beam is reconstructed, information that is on the projection screen during recording is retrieved but in reverse order, as shown in Fig. 6. The segments that are numbered from left to right on the

Fig. 6. Reconstruction of information recorded on a holographic pixel.

Fig. 7. HOE array used for diffracting the reference light beam along different directions.

projection screen during recording are reconstructed in reverse order ~right to left!. During reconstruction, the viewing windows at the observation plane are multiplexed according to the scene recorded on the projection screen. Each window can show a different light intensity on the POP. The pixel area has a higher intensity when one is looking toward a brighter recorded object segment and a lower intensity when one is looking toward a darker one. A.

Diffraction from a Holographic Optical Element Array

Our approach is to use the POP HOE’s as the pixels in a display array. The pixels render individually recorded intensity distributions over the range of viewing angles. When the viewing angle is varied, the composite reconstructed image changes accordingly. Therefore, by arrangement of the multiplexed images, a 3-D scene can be observed. In Fig. 7 a transmission-type HOE-array display is shown. As described, each element ~a 3-D pixel! in the display is assumed to diffract light into a predefined angular intensity distribution and shares the same reference beam for reconstruction with the other elements. This HOE array can construct different images along the multiplexing directions with these 3-D pixels.

Fig. 8. Two images projected by the HOE array along two directions. The individual diffraction patterns of each element are shown on the right-hand side.

As an illustration, suppose that two different images are to be viewed from two different directions, e.g., a vertical bar to the left-hand side and a horizontal bar to the right-hand side. The light diffracted by the required HOE array consists of two images, as depicted by views A and B in Fig. 8. A 2 3 2 HOE array is used as a display for the images. The elements of the 2 3 2 array are numbered counterclockwise from 1 to 4. Unlike conventional holographic stereogram techniques in which the images are recorded by use of the whole prerecorded scenes, each of the elements in this example is obtained by our recording information from the same pixel location in every scene. Each element has its own diffraction pattern, as shown on the right-hand side of Fig. 8. A viewer looking into the resulting hologram from the left-hand side will see pixels 1 and 2 turned on and pixels 3 and 4 turned off. Similarly, a viewer looking from the right-hand side would see pixels 2 and 3 turned on and pixels 1 and 4 turned off. The recording of the array is performed in a pixel-by-pixel manner. For a pixel at a given position, recording consists of collecting all the information from the same position on all sampled images. In the 2 3 2 array example, there are two horizontal viewing angles at the observation plane; hence there are two segments at the projection screen for recording. To record element 1, which has a single diffraction toward the left-hand direction, one must turn on the area to the right-hand side of the two segments on the projection screen in accordance with the scheme shown in Fig. 5. Similarly, for element 2, both segments on the projection screen have to be turned on to generate diffraction patterns along both the right and the left directions. The projection-screen configuration for recording individual pixels is shown in Fig. 9. B.

Superposed Versus Divided-Area Gratings

It needs to be mentioned that superposed gratings are more difficult to implement and require a significantly greater number of exposures than is required in the recording of divided-area ~or partial-pixel! gratings. However, a recent report by Khoo6 on a class of fullerene-doped nematic liquid crystals indicates that such grating superpositions can be accomplished more readily, whereby spatial multiplexing

Fig. 9. Individual diffraction patterns and projection-screen configurations for recording. The ~common! reference beam is not shown. 10 November 1998 y Vol. 37, No. 32 y APPLIED OPTICS

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of images by means of the POP architecture described here would become a feasible technique. In this paper we introduce the concept behind the proposed technique and present a few simple experimental results intended to illustrate the spatial- ~angular-! multiplexing capability of the technique as well as verify its ability to produce a 3-D stereoscopic effect. 4. Factors to Consider for Optimal Recording A. Problem of Uniform Angular Multiplexing for All Pixels in the Holographic Optical Element Array

The individual pixel in a HOE-array stereogram diffracts light along predefined angular divisions. An entire HOE array similarly projects images toward the same predefined angular divisions. The angular relations between the diffraction patterns from the pixels in the array have to be carefully designed. If the mask and the projection screen are held fixed during recording and the film is moved in the x direction, we obtain diffracted outputs that do not completely overlap the corresponding partitions on the observation plane; hence the reconstructed pixels from the same scene are angularly distributed so that adjacent scenes suffer spatial misalignment. The spatial misalignment of two pixels at different locations is shown in Fig. 10. We note from Fig. 10 that the diffraction patterns of the two pixels do not overlap each other entirely. Each pixel has its own angularly multiplexed range. As a result, in the observation plane one can see the diffracted light from both pixels within only the common, overlapped divisions shown in the figure. The angular range of the common or overlapping divisions is determined by the recording parameters, such as the projectionscreen size in the direction of multiplexing ~the x axis!, the distance between the most distant pair of pixels along the x axis in the array, and the distance from the projection screen to the film.

Fig. 11. Perfectly aligned diffraction of pixels at the observation plane, where d is the ~maximum! distance of the leftmost and the rightmost pixels.

plane is not abrupt but gradual. Thus the image of the neighboring scene persists even when the observer has moved to the next viewing window. The running effect arises from the fact that the angularmultiplexing divisions of each individual pixel are separated slightly from those of the neighboring pixels. When the observation point is moved in the direction of multiplexing ~the x axis in Fig. 10!, the switching of the multiplexed scenes can be seen only gradually. One way to demonstrate such an effect is to record an array with two fixed divisions of dark and bright ~pixel 1 in the previous example!. On reconstruction, the dark and bright interface or transition boundary is found to change as the viewing angle is varied.

There is also a running effect associated with the uniform angular multiplexing of all pixels for which the transition from one scene to the next at the observation

1. Elimination of the Running Effect A set of well-multiplexed scenes must possess abrupt switching characteristics, i.e., the multiplexed angular divisions of individual pixels have to be spatially synchronized. The divisions of pixel 1 must overlap the divisions of pixel n, as shown in Fig. 11. If spatial synchronization is achieved, the running effect is expected to disappear. From Fig. 11 we note that the angular ranges of any two pixels are not identical to each other. Therefore, for generating perfect alignment of the diffraction patterns, the configura-

Fig. 10. Spatial-division misalignments from two pixels with uniform angular multiplexing during reconstruction.

Fig. 12. Schematic setup for recording the HOE array. The electronic shutter, the LCD, and the 2-D dynamic carriage are controlled by a computer. The attenuators A1 and A2 are used to control the beam-intensity ratio for recording.

B.

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Running Effect


tion of the projection screen has to be modified to eliminate the misalignment between the angular ranges of the pixels. The configuration of the projection screen for each pixel can be adjusted according to the desired angular-multiplexing range under reconstruction. If we consider the recording setup shown in Fig. 12, the film is moved first along the x axis and then one step along the y axis. The film is placed on an x–y carriage, which allows the film to move in both directions, controlled by a computer. The HOE array is recorded in a pixel-by-pixel manner. The light source is a 10-mW He–Ne laser. The light beam is split into reference and object beams. The object beam is expanded and projected onto a LCD, used as a computer-controlled spatial light modulator, to configure the object beam. The configured object beam is dispersed by a diffuser thereafter to generate a broader angular range. The broader angular range allows the light emerging from any point on the LCD to reach the opening on the mask. 2. Geometric Analysis The recording geometry is analyzed here on the basis of one-dimensional multiplexing and can be extended to 2-D multiplexing to include both the x and the y axes. Assuming x-axis multiplexing, the recording geometry can be depicted as in Fig. 13 for the rightmost ~nth! pixel in the HOE array being recorded. From the figure we can note that the available display area of the LCD is not 100% utilized, since compromises have been made to accommodate the common multiplexing window available. In the figure, lIF is the distance from the image plane on the LCD to the film, lFO is the distance from the film to the observation plane, wd is the width of the viewing window, and lLCD is the total width of the LCD. The width of the common multiplexing window ~or, equivalently, the width of the viewing window!, wd, is determined by lFO wd 5 lLCD 2 d. lIF

(1)

Fig. 14. Recording geometry for the ith pixel located at x. Within the range R–L, the LCD displays the pattern to be reconstructed later during replay.

The common multiplexing window in the observation plane is mapped through the individual pixel to a portion of the available area on the LCD, i.e., the window of that particular pixel. The LCD is programmed to present a specific pattern within this window during recording. The boundaries of the window on the available display area have to be found and mapped to the numerical numbers of pixels out of the N pixels on the LCD along the multiplexing axis ~640 for the LCD used in the experiment!. In Fig. 14, the two boundary points nR~x! and nL~x! ~measured as the number of dots on the LCD! can be found for the ith pixel located at x. uR~x! and uL~x! are the angles from the pixel to the right and left pattern edges, respectively, on the projection screen, which are defined ~counterclockwise! as uR~x! 5 p 2 tan21 uL~x! 5 tan21

Fig. 13. Recording geometry for the rightmost pixel n.

S

S

D

wd 2 xylFO , 2

D

wd 1 xylFO , 2

(2)

(3)

Fig. 15. Replay setup for holographic stereograms. The film is placed on a film holder. The stereographic images are observed from a finite viewing distance over the predefined angular range. 10 November 1998 y Vol. 37, No. 32 y APPLIED OPTICS

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Fig. 16. Four of 20 horizontally multiplexed images viewed from different perspectives.

where x is measured from the z axis ~which bisects the multiplexing window!. When we translate the coordinate positions to the pixel numbers on the LCD, the pixel numbers of the right and left boundaries are obtained as

nR~x! 5

N lIF cot uR~x! , 1N 2 lLCD

nL~x! 5

H

(4a)

J

lIF@cot uR~x! 1 cot uL~x!# N 1 nR~x!, (4b) lLCD

where nR~x! and nL~x! are the dot positions on the LCD to the right and left, respectively, of the recording window on the projection screen and N is the total number of pixels along the multiplexing axis ~the x axis, in this case!. The range nR–nL is divided into m divisions for multiplexing m images. An extension to 2-D multiplexing would involve applying the above technique to a similar set of geometrical calculations, thus dividing the area in that case into ~mx 3 my! chessboardlike divisions. The recording may be done with binary, i.e., dark and bright, or varying gray levels. 7510


5. Experiments

An experimental setup similar to the one shown in Fig. 12 was implemented. The monochrome LCD used has 640 ~H! 3 480 ~V! pixels with 16 gray levels. The recording film–plate ~Kodak high-speed holographic film SO-253 was used for most of the experiments! is placed on a 2-D controllable carriage. The overall exposed area of the film is approximately 2 in. 3 3 in. ~5.08 cm 3 7.62 cm!. A personal computer is used to control the carriage movement, pattern presentation, and exposure time. The LCD used in recording is Model 1600 GS by In Focus, Inc. ~Wilsonville, Oregon 97070-9215!. The exposure time per pixel is approximately 0.5 s, and the total time expended to complete the HOE-array recording is approximately 50 min. Several recordings were made to demonstrate the multiplexing capability of the POP holographic stereogram technique, including those of images multiplexed horizontally, images multiplexed horizontally and vertically, and images with multiple gray scales ~to illustrate the 3-D stereoscopic effect!. The results were satisfactory in many cases; in a few cases, however, further refinements might be necessary. The recorded film is replayed with a reconstruction beam that covers the entire HOE array, as shown in Fig. 15.

Fig. 17. Multiplexed scenes from a horizontally and vertically multiplexed holographic stereogram.

A.

Horizontally Multiplexed Images

A series of images multiplexed along the horizontal axis was recorded. In the final setup, 20 images consisting of the numbers 1–20 were encoded in the recording patterns. The resulting stereogram is expected to project the numbers from right to left. In the actual experiment, of the 20 images intended to be multiplexed, three ~the numbers 1, 2, and 3! replayed particularly well. The rest were also clearly visible and were of sufficient intensity to be picked up by a CCD camera. Shown in Fig. 16 are several captured images from the reconstruction. It is clear that the number 20 @Fig. 16~d!# was not reconstructed as well as, say, the number 9 @Fig. 16~b!#. Several factors influenced the fidelity of the recorded images. These included the smoothness of the carriage motion, the alignment of the holographic film, and the specific pixel location. The exposure time was also a critical factor, and the optimal exposure time was arrived at after several empirical–iterative trial recordings. Improper exposure times easily lead to washout or saturation.

horizontal directions. The resulting multiplexed scenes from such a stereogram are shown in Fig. 17. C.

Gray-Level Differences between Images Recorded

The monochrome LCD used in these experiments is capable of displaying 16 gray levels. In this experiment we applied two different gray levels to two images being recorded ~to illustrate stereoscopic image formation! and compared the results with those from a single-level recording. The results are shown in Fig. 18. The recessed nature of the two overlapping triangles is clearly discernible when the different gray levels are incorporated ~right-hand figures!, while the distinction vanishes when a single gray level is used ~left-hand figures!. A point to be noted regarding the experimental results is that, even though the presence of some minor cross talk was observed near the boundaries between viewing angles, there was little or no speckle in the images during readout. It is conjectured that the speckle effect is minimal owing to the relatively wide separation between the fringes in adjacent viewing windows ~of the order of a few degrees!. 6. Concluding Remarks

B.

Horizontally and Vertically Multiplexed Images

An experiment for testing the multiplexing capability is to multiplex the images in both the vertical and the

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Fig. 18. Recording with a variable gray level ~right-hand side! and without ~left-hand side!.

sized with a microprocessor interface. A 3-D picture can be constructed by means of the multiplexing capabilities of the POP holographic stereogram. In this paper we have introduced the concepts and demonstrated these capabilities by means of simple experiments. Although the recording technique reported in this paper applies to a static holographic pixel-array display, and in principle requires a large number of exposures, its feasibility might improve considerably with the emergence of novel recording media such as doped nematic liquid crystals. The extension of traditional displays to displays with static ~and perhaps dynamic! 3-D features is expected to be an area of emerging interest in the foreseeable future. References 1. K. Iizuka, Engineering Optics ~Springer-Verlag, Heidelberg, 1985!. 2. T. Takeda, Y. Fukui, K. Hashimoto, and N. Hiruma, “Threedimensional visual stimulator,” Appl. Opt. 34, 732–738 ~1995!. 3. K. R. Boff, L. Kaufman, and J. P. Thomas, Handbook of Perception and Human Performance ~Wiley, New York, 1986!. 4. A. R. Travis, “Autostereoscopic 3-D display,” Appl. Opt. 29, 4341– 4343 ~1990!. 5. N. A. Dodgson, “Analysis of the viewing zone of the Cambridge autostereoscopic display,” Appl. Opt. 35, 1705–1710 ~1996!. 7512


6. I. Khoo, “Holographic grating formation in dye- or fullereneC60-doped liquid crystal film,” Opt. Photon. News 6~12!, 29 ~1995!. 7. K. Meerholz, “A photorefractive polymer with high gain and diffraction near 100%,” Nature 371, 497 ~1994!. 8. J. C. Palais and M. E. Miller, “Holographic movies,” Opt. Eng. 35, 2578 –2582 ~1996!. 9. K. E. Jachimowicz and R. S. Gold, “Stereoscopic 3D projection display using polarized color multiplexing,” Opt. Eng. 29, 838 – 842 ~1990!. 10. P. St. Hilaire, S. A. Benton, and M. Lucente, “Synthetic aperture holography: a novel approach to three-dimensional displays,” J. Opt. Soc. Am. A 9, 1969 –1977, ~1992!. 11. J. H. Kulick, G. P. Nordin, A. Parker, S. T. Kowel, R. G. Lindquist, M. Jones, and P. Nasiatka, “Partial pixels: a three-dimensional diffractive display architecture,” J. Opt. Soc. Am. A 12, 73– 83 ~1995!. 12. D. L. MacFarlane, “Volumetric three-dimensional display,” Appl. Opt. 33, 7453–7457 ~1994!. 13. T. Takeda, Y. Fukui, K. Hashimoto, and N. Hiruma, “Threedimensional visual stimulator,” Appl. Opt. 34, 732–738 ~1995!. 14. T.-C. Poon, K. B. Doh, B. Schilling, Y. Suzuki, and M. H. Wu, “Holographic three-dimensional display using an electronbeam-addressed spatial light modulator,” Opt. Rev. 4, 567–571 ~1997!. 15. S.-T. Chen and M. R. Chatterjee, “Computer generated, spatially multiplexed message display using a holographic optical element array,” paper presented at the OSA Annual Meeting,

Portland, Oregon, 10 –15 September 1995 ~Optical Society of America, Washington, D.C.!, p. 150. 16. M. C. King, “Multiple exposure hologram recording of a 3-D image with a 360° view ~L!,” Appl. Opt. 7, 1641–1642 ~1968!. 17. M. C. King, A. M. Noll, and D. H. Berry, “A new approach to computer generated holography,” Appl. Opt. 9, 471– 475, 1969.

18. S. A. Benton, “Holgraphic displays: 1975–1980,” Opt. Eng. 19, 686 – 690 ~1980!. 19. W. Spierings and E. van Nuland, “Development of an office holoprinter II,” in Practical Holography VI, S. A. Benton, ed., Proc. SPIE 1667, 52– 62 ~1992!. 20. L. P. Yaroslavski and N. S. Merzlyakov, Methods of Digital Holography ~Consultants Bureau, New York, 1980!.

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