Hologram generation by horizontal scanning of ahigh-speed spatial light modulator

Yasuhiro Takaki* and Naoya OkadaInstitute of Symbiotic Science and Technology, Tokyo University of Agriculture and Technology,

2–24–16, Naka-cho, Koganei, Tokyo 184–8588, Japan

*Corresponding author: ytakaki@cc.tuat.ac.jp

Received 3 April 2009; accepted 8 May 2009;posted 27 May 2009 (Doc. ID 109281); published 8 June 2009

In order to increase the image size and the viewing zone angle of a hologram, a high-speed spatial lightmodulator (SLM) is imaged as a vertically long image by an anamorphic imaging system, and this imageis scanned horizontally by a galvano scanner. The reduction in horizontal pixel pitch of the SLM providesa wide viewing zone angle. The increased image height and horizontal scanning increased the image size.We demonstrated the generation of a hologram having a 15° horizontal viewing zone angle and an imagesize of 3.4 inches with a frame rate of 60Hz using a digital micromirror device with a frame rate of13:333kHz as a high-speed SLM. © 2009 Optical Society of America

OCIS codes: 090.2870, 090.1760, 070.6120, 090.1970, 100.2000.

1. Introduction

Recently, the development of three-dimensional dis-plays has accelerated. In many of these displays, raysemitted from an object are reconstructed. In contrast,holography reconstructs the wavefront emitted froman object and so is considered to be an ideal three-dimensional display technique. However, an ex-tremely high-resolution spatial light modulator(SLM) is required to display practical three-dimensional images. When a SLM has a pixel pitchof p and a resolution of Nx ×Ny and the wavelengthof light is denoted by λ, 2 sin−1ðλ=2pÞ gives the diffrac-tion angle, which determines the viewing zone angle,and Nxp ×Nyp gives the display screen size. A veryfine pixel pitch is required for a wide viewing zoneangle, and a large pixel count is required for a largescreen size. For example, in order to obtain a three-dimensional image with a screen size of 20 in. and aviewing angle of 30°, the pixel pitch should be0:97 μm and the resolution should be approximately420; 000 × 316; 000, when the wavelength of lightis 0:5 μm.

One of the most effective techniques for reducingthe resolution required for an SLM is horizontal-parallax-only (HPO) holography. The HPO hologra-phy technique limits the parallax of a three-dimensional image only in the horizontal directionbecause horizontal parallax is dominant in humanthree-dimensional perception. The HPO hologramconsists of horizontal scan lines, which are one-dimensional holograms. Thus, the vertical pixel pitchand the vertical pixel count are comparable to thoseof conventional two-dimensional televisions. How-ever, a very fine pixel pitch and a large pixel countin the horizontal direction are still required in orderto generate one-dimensional holograms.

Several techniques by which to increase both theviewing zone angle and the screen size have beenproposed. In the HPO hologram display systemdeveloped at MIT [1], a high-resolution one-dimensional hologram distribution generated by anacousto-optic modulator (AOM) is scanned two-dimensionally by a mechanical scanner. A hologramhaving an image size of 150mm × 75mm (6.6 in.) anda viewing zone angle of 30° was generated using 18AOMs and six mechanical scanners. Slinger et al. [2]proposed the active tiling technique whereby demag-nified images generated by a high-speed SLM are

0003-6935/09/173255-06$15.00/0© 2009 Optical Society of America

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tiled onto an optically addressed SLM. A hologramhaving an image size of 136mm×34mm (5.5 in.)and a pixel pitch of 6:6 μm with a frame rate of30Hz was demonstrated using four tiling systems.Several techniques by which to increase the viewingzone angle have also been proposed. Maeno et al. [3]proposed the use of multiple SLMs. Mishina et al.[4,5] proposed a time-multiplexing technique, andTakaki et al. [6] proposed the use of a resolution re-distribution system.In the present study, we propose a new technique

by which to increase both the viewing zone angle andthe screen size of a hologram that incorporates ahigh-speed SLM, an anamorphic imaging system,and a horizontal scanner.

2. Proposed Technique

A. Quasi-Coherent Holography

The technique proposed in the present study usesspatial scanning of a small elementary hologram.As shown in Fig. 1, light diffracted from an elemen-

tary hologram converges to generate points that con-stitute a three-dimensional image and then entersthe viewer’s pupil. Thus, the coherence of lightshould be maintained only in the elementary holo-gram and not in the complete hologram. Ignoringthe diffraction effect, the width of an elementaryhologram should be larger than approximatelyjdz=ðl − zÞj, where d is the pupil diameter, z is the dis-tance between the display screen and a three-dimensional point, and l is the distance betweenthe screen and the viewer. For example, the widthof the elementary hologram should be at least2:5mm when d ¼ 5mm (average pupil diameter),z ¼ 200mm, and l ¼ 600mm.The reconstructed image is generated by spatially

scanning the elementary hologram. However, thelight diffracted from an elementary hologram doesnot always cover the entire pupil of the eye whenan elementary hologrammoves spatially. The diffrac-tion light partially covers the pupil, when the diffrac-tion light enters the pupil and leaves the pupil.Therefore, the spatially scanning holography de-scribed herein generates a quasi-coherent hologram.The image quality of the quasi-coherent holographyis worse than that of fully coherent holography anddepends on the width of the elementary hologram.However, the condition given in the previous para-

graph describes the critical width for the elementaryhologram.

The concept of scanning a small hologram was pre-viously proposed by Haussler et al. [7].

B. Horizontally Scanning Holography System

The holographic display system proposed in the pres-ent study is illustrated in Fig. 2. The proposed sys-tem incorporates a high-speed SLM, an anamorphicimaging system, and a horizontally scanning system.

The high-speed SLM modulates light two-dimensionally with a high frame rate. The frame rateis denoted by f slm. The pixel pitch of the high-speedSLM is denoted by p, and the resolution is denotedby Nx ×Ny.

A two-dimensional light distribution generated bythe high-speed SLM is squeezed in the horizontal di-rection and expanded in the vertical direction by ananamorphic imaging system. The vertically long im-age generated by this process is an elementary holo-gram. The anamorphic imaging system consists oftwo orthogonal cylindrical lenses, and has differentmagnifications in the horizontal and the vertical di-rections. Horizontal magnification is performed bycylindrical lens 1, the centerline of which is alignedvertically, and the vertical magnification is per-formed by the other cylindrical lens 2, the centerlineof which is aligned horizontally. The absolute magni-fication in the horizontal direction is denoted byMxð< 1Þ, and that in the vertical directions is de-noted by Myð> 1Þ. The horizontal pixel pitch is re-duced to Mxp so that the diffraction angle isincreased to 2 sin−1ðλ=2MxpÞ. The width and heightof an elementary hologram are given by MxNxp andMyNyp, respectively.

The elementary hologram generated by the ana-morphic imaging system is scanned horizontally bya horizontal scanner. The high-speed SLM displaysa series of elementary images in synchronizationwith the horizontal scanner. The horizontal scanpitch is denoted by q, and the scan frequency is de-noted by f scan. A complete hologram consists off slm=f scan elementary holograms. The horizontal scanpitch should be equal to or less than the horizontalwidth of the elemental hologram, i.e., q ≤ MxNxp.

Fig. 1. Hologram generation by scanning an elementaryhologram.

Fig. 2. Hologram generation by horizontal scanning of an ele-mentary hologram generated by a high-speed SLM.

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The width of a complete hologram is given byqf slm=f scan þMxNxp.Cylindrical lens 3 is placed on the display screen to

redirect the light proceeding direction toward theviewers. A vertical diffuser is also placed over the dis-play screen to increase the vertical viewing zone.The vertical image enlargement by the ana-

morphic imaging system and the horizontal scanningincrease the size of the complete hologram. Thewidth and height of the complete hologram are qf slm=f scan þMxNxp and MyNyp, respectively.The proposed holography display system gener-

ates all of the horizontal scan lines of a HPOhologram simultaneously. The horizontal scan fre-quency f scan should be higher than 60Hz in orderto achieve flicker-free image generation.

3. Experimental System

Figure 3 shows the experimental system used todemonstrate the hologram display system proposedin the present study.A digital micromirror device (DMD) was used as a

high-speed SLM. An ALP-3 (ViALUX GmbH) wascombined with a Discovery 3000 (Texas Instruments,Inc.) to enable high-frame-rate operation. The resolu-tion was 1; 024 × 768, and the pixel pitch was p ¼13:68 μm. The frame rate depends on the numberof gray levels, because the ratio on time of the mirrordevice determines the gray level (binary pulse-widthmodulation). The maximum frame rate is 13:333kHzwhen the number of gray levels is two (binary graylevel). In the experimental system, the DMD wasdriven with the maximum frame rate, i.e.,f slm ¼ 13:333kHz.A laser diode with a wavelength of 635nm was

used as an illumination light source. The laser lightwas collimated and set to illuminate the DMD at theangle specified by the tilt angle of the micromirror.For the sake of simplicity, the illumination opticsis not shown in Fig. 3. The use of the laser diode en-ables not only the compact system size, but also thepulse modulation of an illumination light to reduceimage blurring, as described below.

The anamorphic imaging system consisted of onespherical lens and three cylindrical lenses with theiraxes aligned horizontally, instead of two orthogonallyaligned cylindrical lenses. The cylindrical lens 1 inFig. 2 must be large in order to reduce the horizontalpixel size several times to obtain a small pixel pitch.Unfortunately, such a large cylindrical lens was notavailable. Therefore, instead of a cylindrical lens, alarge spherical lens was used for the horizontal mag-nification. The horizontal magnification was Mx ¼0:183. In the vertical direction, two 4f imagingsystems were constructed by adding three cylindricallenses to the spherical lens to obtain the verticalmagnification. The vertical magnifications of thetwo 4f imaging systems were 1.67 and 3.00 so thatthe total vertical image magnification was My ¼5:00. The horizontal pixel pitch was reduced to2:50 μm to increase the horizontal viewing zone angleto 14:5°. The size of the elementary hologram was2:56mm×52:5mm. The quasi-coherent holographycondition requires that a three-dimensional imagebe displayed within a distance of 0:339l from thescreen.

A galvano mirror was used for the horizontal scan.In order to obtain a flicker-free reconstructed image,a complete hologram was constructed from 222 ele-mentary holograms, and the horizontal scan fre-quency f scan of the galvano mirror was set to60:045Hz. The hologram was displayed with bothclockwise and counterclockwise rotating directions,and so the vibration frequency of the mirror wasset to 30:023Hz. The rotation angle of the mirrorwas �5°, so that the horizontal scan angle of the ele-mentary hologram was �10°. The distance betweenthe rotating mirror and the display screen was200mm. Therefore, the horizontal scan width was70:6mm, and the elementary holograms were dis-played with a horizontal pitch of 0:32mm on the dis-play screen. There were substantial overlaps amongthe elementary holograms. The size of the completehologram was 73:1 mm×52:5mm. The size of the gal-vanomirror was determined to reflect the whole lightbundle in the anamorphic imaging system.

Instead of a cylindrical lens 3 placed on the displayscreen shown in Fig. 2, a spherical lens was used, be-cause a cylindrical lens whose size is larger than thecomplete hologram was not available. The focallength of the spherical lens was 200mm, whichwas equal to the distance between the rotating mir-ror and the display screen. A lenticular sheet wasused as a vertical diffuser.

Fig. 3. Experimental system: (a) horizontal cross section and(b) vertical cross section.

Table 1. Specifications of the Proposed Holographic DisplaySystema

Screen size 73:1 mm×52:5mm (3.5 in.)Horizontal viewing zone angle 14:6°Frame rate 60:045HzDimensions of E.H. 2:56mm×52:5mmNumber of E.H. 222Horizontal pitch of E.H. 0:32mm

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The laser was driven by a pulse signal that wassynthesized from an image update signal from aDMD driver. The pulse width was 37:5 μs, which ishalf of the pulse period, in order to reduce the hori-zontal image blurring caused by the horizontal scan.The horizontal image blurring occurs because the im-age of the SLM does not change during a single frametime, whereas the image is scanned continuously.The horizontal image blurring width of the experi-mental system was 0:16mm.The conjugate image and the zeroth order diffrac-

tion light were removed using the single-sidebandtechnique [8]. A horizontal edge was placed on theFourier plane of one of the two vertical 4f imagingsystems. Therefore, the vertical resolution of elemen-tary holograms became half that of the SLM so that areconstructed image consisted of 384 horizontalscan lines.The specifications of the constructed hologram dis-

play system are listed in Table 1.

4. Experimental Results

The elementary hologram patterns were calculatedas Fresnel holograms. The phase distribution ofthe lens on the screen was included in the hologramcalculations. Some of elementary holograms withbinary gray level are shown in Fig. 4.Photographs of the reconstructed image captured

from different horizontal viewpoints are shown inFig. 5. The circle and the cross, respectively, ap-peared at 100mm and 150mm in front of the screen.The measured viewing zone angle was 15°, andthe measured screen size was 70mm×52mm (3.4

in.). The reconstructed image was visible to both eyesbecause the viewing zone angle was increased. Themotion parallax was very smooth, and flicker wasnot observed. Additional examples of reconstructedimages are shown in Fig. 6.

5. Discussion

The proposed system enabled the viewing zone angleto be increased to 15°. In addition, the viewing zoneangle could be increased by further reducing thepixel pitch. In this case, a larger numerical aperture(N:A:) is required for the horizontal imaging system.A larger N:A: requires a larger galvano mirror. Thediameter of the spherical lens 1 in the current ex-perimental system is 145mm in order to obtainN:A: ≥ 0:26.

There are substantial overlaps among the elemen-tary holograms in the experimental system, and it ispossible to increase the screen size. Increasing thescreen size can be achieved by increasing the scanwidth and the vertical magnification of the ana-morphic imaging system. The screen size of theexperimental systemwas determined while consider-ing the mirror size of the galvano mirror and the sizeof the screen lens. The scan angle can easily be in-creased to over �10°. In order to increase the screensize, increasing the size of the galvano mirror and in-creasing the size of the screen lens are also required.

In this experimental system, all spherical lensesand cylindrical lens are plano–convex lenses. There-fore, the lens aberrations might have deterioratedthe reconstructed images, and distortion of theelementary images was observed. Since precise

Fig. 4. Examples of elementary holograms: (a) 66th hologram, (b) 111th hologram, and (c) 156th hologram.

Fig. 5. Reconstructed three-dimensional image captured from (a) the left, (b) the center, and (c) the right.

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alignment of the scanning system was difficult, thedistance between the mirror and the screen lenswas not clearly determined. This distance is requiredin order to calculate the elementary holograms. Thereconstructed image might be improved by improv-ing the optical system.The proposed technique is compared to the HPO

hologram technique developed at MIT [1]. TheMIT system generates each scan line by horizontalscanning, and the scan lines are aligned verticallyby the vertical scanner. Therefore, the horizontalscanner must have a very high-speed scanning fre-quency. In contrast, the technique proposed in thepresent study generates all scan lines simulta-neously. Therefore, the vertical scanner is not re-quired, and the horizontal scan frequency can bedecreased to as low as the video frame rate (∼60Hz).Since the size of the scanning mirror should be largein order to achieve sufficient demagnification of thepixel pitch in the horizontal direction, a low horizon-tal scanning frequency is preferable for rotating alarge mirror. The high-speed SLM used in the pro-posed technique can modulate only binary ampli-tude. The AOM used in the MIT display canmodulate a continuous amplitude. The image qualityof the reconstructed image of the binary amplitudehologram is generally lower than that of the contin-uous amplitude hologram. A number of studies haveinvestigated the design of binary-amplitude holo-grams, and the results of these studies will be usedfor the hologram calculation in our system. As de-scribed in Section 3, horizontal image blurring occursin the proposed system because the modulation pat-tern of the DMD does not change during a singleframe time, whereas the image is moved continu-

ously in the horizontal direction by the horizontalscanner. The horizontal image blurring might be de-creased by reducing the pulse width of the illumina-tion light. The pulse width of the laser diode caneasily be reduced to<μs while maintaining sufficientoptical energy. The characteristics of the MIT systemand the proposed system are given in Table 2.

6. Conclusions

We proposed a new technique that enables both thescreen size and the viewing zone angle of a hologramto be increased. The proposed technique uses a high-speed SLM, an anamorphic imaging system, and ahorizontal scanner. The image generated by the high-speed SLM is converted to an elementary hologramby the anamorphic imaging system, and the elemen-tary hologram is scanned horizontally by the hori-zontal scanner.

We demonstrated the proposed holographic dis-play system using a DMD and a galvano mirror.The horizontal pixel pitch was reduced to 2:5 μm toachieve a horizontal viewing zone angle of 15°. Thescreen size was increased to 70mm×50mm (3.4inches). The frame rate was 60:045Hz.

The experimental system shown in this paper is apreliminary demonstration system. The screen sizeand viewing zone angle can be increased by using lar-ger lenses and a larger galvano mirror. The recon-structed image can be improved through the use ofaberration-corrected lenses. Precise alignment ofthe optical system would also improve the recon-structed image.

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H. Yoshikawa, and J. Underkoffler, “Electronic display systemfor computational holography,” Proc. SPIE 1212, 174–182 (1990).

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Table 2. Characteristics of the MIT System and the Proposed System

MIT System Proposed System

Spatial scan Horizontal andvertical

Horizontal

Light modulationdevice

AOM DMD

Horizontal scan High speed Low speed (60Hz)Vertical scan Low speed (30Hz) NoneGray level of hologram Continuous BinaryIllumination laser Continuous wave Pulse wave

Fig. 6. Reconstructed three-dimensional images: (a) apple, (b) teapot, and (c) wine glass.

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4. T. Mishina, F. Okano, and I. Yuyama, “Time-alternatingmethod based on single-sideband holography with half-zone-plate processing for the enlargement of viewing zones,”Appl. Opt. 38, 3703–3713 (1999).

5. T. Mishina, M. Okui, and F. Okano, “Viewing-zoneenlargement method for sampled hologram that useshigh-order diffraction,” Appl. Opt. 41, 1489–1499(2002).

6. Y. Takaki and Y. Hayashi, “Increased horizontal viewing zoneangle of a hologram by resolution redistribution of a spatiallight modulator,” Appl. Opt. 47, D6–D11 (2008).

7. R. Haussler, A. Schwerdtner, and N. Leister, “Large holo-graphic displays as an alternative to stereoscopic displays,”Proc. SPIE 6803, 68030M (2008).

8. O. Bryngdahl and A. Lohmann, “Single-sideband holography,”J. Opt. Soc. Am. 58, 620–624 (1968).

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