Information processing of three-dimensional ~3-D!mages has been utilized in various fields such asndustrial design, medical treatment, telecommuni-ations, and computer simulations of physical phe-omena. In these applications the development of aractical stereoscopic 3-D display is desired. Three-imensional display systems based on binocular par-llax, which include polarized glasses, head-mountedisplays, and lenticular sheets, are used for thesepplications. However, eye strain occurs whenhese 3-D displays are viewed for a long time1 be-ause, except for binocular parallax, the physiologicalactors for stereoscopic vision, such as accommoda-ion and binocular convergence, are not satisfied.olography is another 3-D display technique that
atisfies all the criteria for stereoscopic vision. Sev-ral techniques for real-time holography have beeneveloped that use acousto-optic devices2 or liquid-
crystal displays.3 However, it is difficult to achievea rewritable high-resolution device that is capable ofdisplaying a hologram. In addition, a high-speedcomputer for synthesizing holograms is required forreal-time holography.
Another 3-D display technique that satisfies all the
D. Miyazaki [email protected]! and K. Matsus-hita are with the Department of Electrical Engineering, Faculty ofEngineering, Osaka City University, 3-3-138 Sugimoto,Sumiyoshi-ku, Osaka 558-8585, Japan.
Received 21 November 2000; revised manuscript received 28March 2001.
3354 APPLIED OPTICS y Vol. 40, No. 20 y 10 July 2001
criteria for stereoscopic vision is the volume-scanningmethod. In this technique a 3-D space is scanned bylight spots to form a 3-D image. One achieves 3-Dscanning by moving an image plane,4–6 a projectionscreen,7,8 or a two-dimensional ~2-D! display.9–11 In3-D display systems, in which a projection screen or a2-D display moves, the degree of movement increasesto enlarge the 3-D image. It is difficult for suchsystems to operate stably, because vibration and airresistance increase with the enlargement. More-over, it is not easy to project high-density images ontothe moving screen. In a moving-image-plane 3-Ddisplay it is necessary to use a varifocal lens, such asa vibrating mirror,4,5 and a liquid-crystal lens6 toenable the 2-D image to move in the direction of theoptical axis. However, formation of a high-resolution 3-D image is difficult, because such a vari-focal lens sacrifices imaging quality for dynamicchange in the focal length.
In this study we propose a new volume-scanning3-D display, which forms a natural autostereoscopic3-D image. The 3-D display proposed in this paperbelongs to the category of moving-image-plane dis-plays. In the proposed system the image of an in-clined 2-D display is moved in the lateral directionperpendicular to the optical axis. A lateral shift ofan image can be achieved with a mirror scanner moreeasily than can a longitudinal shift of an image alongthe optical axis. In Section 2 the principle of thistechnique is explained, and the distortion of a 3-Dimage owing to a change in magnification is de-scribed. In addition, the relation between a numer-ical aperture and the position of an observer isanalyzed. In Section 3, 3-D images obtained in anexperimental system are shown to verify the theory of
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this technique. In Section 4 the problems and theproposed improvements for our system are consid-ered.
2. Principles of a Volume-Scanning Three-DimensionalDisplay Using an Inclined Image Plane
Figure 1 is a schematic diagram of the proposed 3-Ddisplay system. A 2-D display is placed obliquelyin a telecentric imaging system into which a mirrorscanner is inserted. In Fig. 1 the 2-D display isplaced perpendicularly to the xz plane and inclined
ith respect to the yz plane. An inclined 2-D pla-ar image is formed in the image space of the opti-al system. When the mirror with a shaft parallelo the y axis is rotated, the inclined planar image inhe image space, whose coordinate system is x9, y9,9, is moved laterally in the direction of the x9 axis.
volume in the image space can be scanned byateral shifting of the inclined image plane. A lo-us of the moving image can be observed as a move-ent afterimage as a result of the high-speed
otation of the mirror. The 2-D display is modu-ated to generate the desired 3-D image. The in-lined cross-sectional images of the 3-D object areisplayed in accordance with the position of themage plane.
This 3-D display satisfies all the criteria for ste-eoscopic vision because an observer can see a 3-Deal image formed in the image space. This is andvantage when this technique is compared withther 3-D display techniques based on binoculararallax only. The proposed system does not needomplicated calculations as required for synthe-
Fig. 1. Schematic diagram of the volume-scanning 3-D displaysystem with an inclined 2-D display and a mirror scanner.
izing a hologram. In addition, a superhigh-esolution display device for displaying a holograms not required in this system. Therefore the pro-osed method has a better possibility of realizationhan real-time holography.
One of the keys in designing a practical volume-canning 3-D display is the development of an effec-ive scanning 3-D space. The mirror scanner used inhe proposed method has a simple rotation mecha-ism with a motor and a mirror. More-stable andigher-speed scanning for generating high-resolution-D images than with other volume-scanning meth-ds can be expected.It is important to consider the relationship be-
ween longitudinal positions of an image plane andagnification for preventing distortion of 3-D im-
ging. Figure 2~a! shows the simplest optical sys-em, which uses a mirror scanner without lenses.otating the mirror moves a virtual image laterally.
n this configuration, lenses do not restrict the an-le of observation; moreover, it has the advantagehat the image is not affected by optical aberrationsf lenses. The moving speed of the virtual image isroportional to the distance from the mirror to theight sources. Therefore the pixel interval in scan-ing directions of the 3-D image increases the far-her the image is from the mirror, when modulationrequencies of the light sources are equal. It isossible to equalize the pixel intervals by changinghe modulation frequencies of the light sources, de-ending on their depth. The optical system inhich a mirror is placed in the front focal plane of
he lens as shown in Fig. 2~b! is telecentric in imagepace. Therefore, pixel intervals in the scanningirection of the 3-D image are equal at each depth.owever, magnification depends on depth, because
he optical system is not telecentric in object space.hen a mirror scanner is placed in the back focal
lane as shown in Fig. 2~c!, the optical system iselecentric in object space. Both the pixel intervaln the scanning direction and the magnification ofmages change, depending on the depth. As shownn Fig. 2~d!, the 4-ƒ optical system that uses twoenses, in which a mirror scanner is placed in theocal plane of the both lenses, is telecentric in bothmage and object spaces. In this optical systemeither magnification nor pixel intervals in thecanning direction depend on depth.The region for seeing a 3-D real image is limited by
he effective numerical aperture of the optical sys-em. The observation region is within the positionst which one can observe the light from every point ofhe 3-D image. Figure 3 shows half of an opticalystem that contains a mirror, a lens, and an imagepace. If the sum of the width of a 3-D image li and
the effective aperture of a mirror scanner lm ismaller than the diameter of a lens D ~li 1 lm , D!,
the spread of the light from the 3-D image is limitedby the aperture lm of the mirror, as shown in Fig. 3~a!.
herefore the width lo, of an observation region, at
10 July 2001 y Vol. 40, No. 20 y APPLIED OPTICS 3355
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the distance from the image to an observer s, is ex-ressed by
lo 5slm
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However; if li 1 lm . D ~li , D!, the spread of light fromthe 3-D image is restricted by the aperture of the lens,D, as shown in Fig. 3~b!. Then lo is expressed by
lo 5s~D 2 li!
f2 li. (2)
To observe an image by using both eyes simulta-neously, one must have lo larger than the distancebetween the two eyes. It is necessary to increase theeffective numerical aperture of the optical system toextend the observation region.
3. Experimental Results
To confirm the principles of the 3-D display methodproposed in this study, we constructed an experimen-tal system. A block diagram of the experimentalsystem is shown in Fig. 4. A galvanometer mirrorwas used as a scanner, and an array of light-emittingdiodes ~LEDs! was used as a 2-D display. A com-
uter controlled the angle of the mirror. The size of
Fig. 2. Variations of scanning optical systems: ~a! lensless systepace, ~d! telecentric system in both image space and object space
356 APPLIED OPTICS y Vol. 40, No. 20 y 10 July 2001
the mirror was 25 mm 3 25 mm, and the maximumotation angle was 14°. The LED array consisted of3 8 green LEDs, and it was 56 mm wide and 40 mmigh. The direction of radiation from each LED was
Fig. 3. Observation region: ~a! li 1 lm , D and ~b! li 1 lm . D.
! telecentric system in image space, ~c! telecentric system in object
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adjusted to an angle of 45° with respect to the surfaceof the LED array. The LED panel inclined at 45° tothe optical axis was placed in the optical system.Each LED was connected to a personal computer andmodulated in synchronization with the angle of thegalvanometer mirror. The angle of the mirror waschanged in 15 steps to display a 3-D image in a cubicspace consisting of 8 3 8 3 8 pixels. We constructedtwo types of optical system, namely, system 1, shownin Fig. 2~b!, which is telecentric only in image space,nd system 2, shown in Fig. 2~d!, which is telecentric
in both object and image space. In system 1, a lensof 150-mm focal length and 80-mm diameter wasused. In system 2, a lens of 150-mm focal length and80-mm diameter was placed on the object side and alens of 100-mm focal length and 60-mm diameter wasplaced on the image side.
Three-dimensional images of a rectangular paral-lelepiped and stairs formed by system 1 are shown inFig. 5. We moved the 3-D image as shown in Figs.5~a! and 5~b! by changing the angle of the LED array.The image was a 40-mm cube. The 3-D images weredemagnified as the distance from the observer in-creased, because the magnification of the optical im-aging system changes depending on the object’slongitudinal position. Figure 6 shows the results forsystem 2. Inasmuch as the optical imaging systemwas telecentric, magnification did not change withlongitudinal position. The angle of divergence fromevery point of the 3-D image was ;10° in system 1and ;14° in system 2. In system 1 the 3-D imagecould be observed at a distance of more than 870 mm
Fig. 4. Block diagram of the experimental system; DyA, digital toanalog.
Fig. 5. Experimental results for 3-D images for system 1: ~a!, ~b!cube images as the angle of each LED array changes; ~c! a 3-Dimage of stairs.
from the image. In system 2 the image could beviewed from 400 mm. The frame frequency of the3-D image was ;12.7 Hz. Slight flickering was de-ected in the observed image.
It was possible to display a moving 3-D image byreparing a series of 3-D data and displaying them inrder. In Fig. 7, sequential 3-D images of a rotatingectangle obtained by system 2 are shown. Therame frequency of the moving image was 12.7 Hz.
4. Considerations
To develop a practical 3-D display, one should im-prove the proposed system in various areas such asthe frame rate, the pixel number, the observationregion, and coloring. The frame rate of the experi-mental system was restricted mainly by the responsetime of the galvanometer mirror, which was stoppedat every step. Scanning at a frequency of more than30 Hz can be achieved by continuous rotation of themirror synchronized with modulation of the lightsources. It is also possible to achieve more-rapidscanning by use of a polygonal mirror scanner insteadof the galvanometer mirror.
In the experimental system the number of pixels ofthe 3-D image in the scanning direction was re-stricted by the modulation frequency of the LEDs,which is determined by the output speed of the con-trol signals from the computer. Therefore a high-speed control circuit for LEDs is necessary forincreasing the pixel number. The pixel number of a3-D image in the direction perpendicular to the scan-ning depends on the number of LEDs. It is neces-sary to increase the elements of the LED array. Theuse of a cathode-ray tube in place of a LED array iseffective for getting high resolution. A vector-scancathode-ray tube display is more suitable than araster-scan cathode-ray tube display because a high-speed frame rate of much more than 30 Hz is requiredfor simultaneously observing many-section images ofa 3-D object as afterimages.
To extend the observation region, the numericalaperture of the optical system should be increased byuse of lenses that have large apertures and short focallengths. However, distortions and blurring of animage increase because of optical aberrations thatresult from the increased numerical aperture. Op-timum design of a 3-D imaging system requires thatthe characteristics of optical scanning be considered.
In the experiment the images generated weremonochromatic because we used only green LEDs.
Fig. 6. Experimental results for system 2: ~a!, ~b! 3-D rectangleimages as the angle of each LED array changes; ~c! 3-D image ofstairs.
10 July 2001 y Vol. 40, No. 20 y APPLIED OPTICS 3357
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To generate colored 3-D images, one can use a colored2-D display.
5. Conclusions
A new 3-D display system that uses an obliquelyplaced 2-D display and a mirror scanner has beenproposed. In an experimental system with a galva-nometer scanner and a 2-D LED array, 3-D real im-ages of 8 3 8 3 8 pixels, 40 mm 3 40 mm 3 40 mmn size, with a frame rate of 12.7 Hz were obtained.t was verified that 3-D images can be observed withatural perception of depth. For development of aractical system, further studies are required for in-reasing the frame rate with high-speed scanning,xpanding the observation region by increasing theumerical aperture of the optical system, and in-reasing the number of pixels through the modula-ion frequency and the number of components in theight sources.
This research was supported by a Grant-in-Aid forncouragement of Young Scientists from the Minis-
ry of Education, Science, Sports and Culture ~Ja-an!.
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Fig. 7. Moving 3-D im
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