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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 18 — Aug. 29, 2011
  • pp: 17621–17631
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Improving viewing region of 4f optical system for holographic displays

Takayuki Kurihara and Yasuhiro Takaki  »View Author Affiliations


Optics Express, Vol. 19, Issue 18, pp. 17621-17631 (2011)
http://dx.doi.org/10.1364/OE.19.017621


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Abstract

A 4f optical system with a single-sideband filter has been used for electronic holographic displays in order to obtain a reconstructed image without a conjugate image and zero-order diffraction light. However, the viewing region is inclined, and the viewing region in which an entire reconstructed image can be viewed is limited. In the present study, one of the Fourier transform lenses constituting the 4f optical system is shifted to correct the viewing region inclination. Moreover, a screen lens is added in the image plane of the 4f optical system to maximize the viewing region. The inclination of the viewing region can also be corrected by shifting the screen lens instead of shifting the Fourier transform lens. Experimental verifications of these corrections are described.

© 2011 OSA

1. Introduction

Holography [1

1. D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948). [CrossRef] [PubMed]

] is a three-dimensional (3D) display technique that reconstructs the wavefronts of light emitted from objects. Numerous researches have been conducted to develop electronic holographic displays.

The zone plate technique proposed by Waters [2

2. J. P. Waters, “Holographic image synthesis utilizing theoretical methods,” Appl. Phys. Lett. 9(11), 405–407 (1966). [CrossRef]

] synthesizes a computer generated hologram (CGH); a 3D image is represented by an aggregate of object points. Zone plates that generate the object points are summed to calculate a hologram distribution. This technique was inspired by the work of Rogers, who recognized that the Fresnel zone plate could be considered as a hologram [3

3. G. L. Rogers, “Gabor diffraction microscopy: the hologram as a generalized zone-plate,” Nature 166(4214), 237 (1950). [CrossRef] [PubMed]

]. Siemens-Wapniarski demonstrated that a hologram could be produced by summing the optically generated zone plates [4

4. W. J. Siemens-Wapniarski and M. P. Givens, “The experimental production of synthetic holograms,” Appl. Opt. 7(3), 535–538 (1968). [CrossRef] [PubMed]

]. The CGH produced by the zone plate technique faces the same problem as an optically produced hologram: a conjugate image and zero-order diffraction light are generated in addition to the reconstructed image.

These unwanted light components were eliminated by placing the single-sideband filter on the Fourier plane of the 4f optical system [5

5. O. Bryngdahl and A. Lohmann, “Single-sideband holography,” J. Opt. Soc. Am. 58(5), 620–624 (1968). [CrossRef]

]. A half-zone plate is used as a zone plate [6

6. T. Mishina, F. Okano, and I. Yuyama, “Time-alternating method based on single-sideband holography with half-zone-plate processing for the enlargement of viewing zones,” Appl. Opt. 38(17), 3703–3713 (1999). [CrossRef] [PubMed]

]; it generates a spherical wave and its complex-conjugate wave, which separate spatially on the Fourier plane. Because the zero-order diffraction light generated by the half-zone plate has a peak distribution at the origin of the Fourier plane, a single-sideband filter placed on the Fourier plane can eliminate the unwanted light components. The effectiveness of the half-zone plate to synthesize CGHs has been proved theoretically [6

6. T. Mishina, F. Okano, and I. Yuyama, “Time-alternating method based on single-sideband holography with half-zone-plate processing for the enlargement of viewing zones,” Appl. Opt. 38(17), 3703–3713 (1999). [CrossRef] [PubMed]

,7

7. Y. Takaki and Y. Tanemoto, “Band-limited zone plates for single-sideband holography,” Appl. Opt. 48(34), H64–H70 (2009). [CrossRef] [PubMed]

]; however, the use of the 4f optical system for electronic holographic displays has two drawbacks: the viewing region is inclined and the viewing region that the entire reconstructed image can be observed is restricted.

The separation of the reconstructed image from the unwanted light components can also be achieved by off-axis holography [8

8. E. N. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Am. 52(10), 1123–1128 (1962). [CrossRef]

]; it realizes this without using any imaging system, such as the 4f optical system. When an inclined reference wave is used to record a hologram and an inclined reconstruction wave is used to reconstruct the hologram, the viewing region is not inclined. However, the pixel pitch of the current spatial light modulators (SLMs) is not small enough to achieve sufficient angular separation between the reconstructed image and the unwanted light components; thus, the electronic implementation of the off-axis holography requires a considerably long distance for the separation.

In optical holography, because hologram films have ultra-high resolution, a large viewing zone angle is obtained. On the other hand, for electronic holographic displays, because the pixel pitch reduction of an SLM is limited, the viewing zone angle is restricted to several degrees, thus limiting the viewing region. Moreover, the existence of the region where an entire reconstructed image cannot be observed decreases the viewing region. Several techniques have been proposed to increase the viewing region such as using a field lens to shorten the viewing distance and increase the viewing zone angle [9

9. N. Fukaya, K. Maeno, K. Sato, and T. Honda, “Improved eletroholographic display using liquid crystal device to shorten the viewing distance with both-eye observation,” Opt. Eng. 35(6), 1545–1549 (1996). [CrossRef]

] and using a spherical wave to illuminate an SLM [10

10. Y. Yabe and Y. Sakamoto, “Enlargement of visual field with an LCD in computer generated holograms,” Proc. SPIE 6912, 69121A (2008). [CrossRef]

]. To increase the viewing region several times, several techniques have been proposed. For example, the spatial multiplexing techniques using multiple SLMs [11

11. K. Maeno, N. Fukaya, O. Nishikawa, K. Sato, and T. Honda, “Electro-holographic display using 15 mega pixels LCD,” Proc. SPIE 2652, 15–23 (1996). [CrossRef]

,12

12. J. Hahn, H. Kim, Y. Lim, G. Park, and B. Lee, “Wide viewing angle dynamic holographic stereogram with a curved array of spatial light modulators,” Opt. Express 16(16), 12372–12386 (2008). [CrossRef] [PubMed]

] and the time multiplexing techniques using high-speed SLMs [6

6. T. Mishina, F. Okano, and I. Yuyama, “Time-alternating method based on single-sideband holography with half-zone-plate processing for the enlargement of viewing zones,” Appl. Opt. 38(17), 3703–3713 (1999). [CrossRef] [PubMed]

,13

13. M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. G. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 247–258 (2003). [CrossRef]

], and the resolution redistribution technique [14

14. Y. Takaki and Y. Hayashi, “Increased horizontal viewing zone angle of a hologram by resolution redistribution of a spatial light modulator,” Appl. Opt. 47(19), D6–D11 (2008). [CrossRef] [PubMed]

,15

15. Y. Takaki and Y. Tanemoto, “Modified resolution redistribution system for frameless hologram display module,” Opt. Express 18(10), 10294–10300 (2010). [CrossRef] [PubMed]

] to increase the horizontal viewing zone angle without using multiple SLMs or time multiplexing.

In the present study, we propose a method to correct the inclination of the viewing region in the 4f optical system. We also propose a method to maximize the viewing region to view the entire reconstructed image. We experimentally verify the proposed methods.

2. Theory

2.1 Correction of viewing region inclination

First, we briefly explain the conventional single-sideband method for a 4f optical system. The original 4f optical system, shown in Fig. 1(a)
Fig. 1 Correction of viewing region inclination of 4f optical system: (a) original 4f optical system, which generates reconstructed image, conjugate image, and zero-order diffraction light, (b) elimination of conjugate image and zero-order diffraction light by single-sideband filter, and (c) correction of viewing region inclination by shifting screen-side Fourier transform lens.
, consists of two Fourier transform lenses aligned to have a common focal plane and generates a reconstructed image with unwanted light components, i.e., the conjugate image and the zero-order diffraction light. As shown in Fig. 1(b), a single-sideband filter is placed on the common focal plane in order to eliminate the unwanted light components. Because a half-zone plate has a real value distribution, a spherical wave and its complex conjugate are generated simultaneously, as shown in Fig. 2(a)
Fig. 2 Correction of inclined proceeding direction of spherical wave generated by half-zone plate: (a) inclined spherical wave generation by 4f optical system with single-sideband filter, and (b) correction of inclined proceeding direction of spherical wave by shifting screen-side Fourier transform lens.
. These two waves proceed in opposite vertical directions such that two spatially separated distributions on the Fourier plane are generated. The single-sideband filter blocks the complex-conjugate wave distribution on the Fourier plane [5

5. O. Bryngdahl and A. Lohmann, “Single-sideband holography,” J. Opt. Soc. Am. 58(5), 620–624 (1968). [CrossRef]

7

7. Y. Takaki and Y. Tanemoto, “Band-limited zone plates for single-sideband holography,” Appl. Opt. 48(34), H64–H70 (2009). [CrossRef] [PubMed]

]. In the present study, a horizontal edge is considered as the single-sideband filter because the horizontal viewing region is more important than the vertical viewing region for human 3D perception. The size of the Fourier transformed image is given by (λf/p) × (λf/p), where λ is the wavelength of light, f is the focal length of the Fourier transform lenses, and p is the pixel pitch of the SLM. Because the single-sideband filter blocks a vertical half of the Fourier transformed image, the height of the image decreases to λf/2p after passing through the single-sideband filter. The zero-order diffraction light, generated by the half-zone plate, produces a peak distribution at the center of the Fourier plane and can be easily eliminated by vertically shifting the single-sideband filter slightly.

Because the Fourier transformed image is vertically halved by the single-sideband filter, the center of the distribution after passing through the single-sideband filter and the center of the screen-side Fourier transform lens are shifted vertically by length λf/4p; therefore, the center line of the viewing region inclines in the vertical direction, as shown in Fig. 1(b). Because the horizontal edge of the single-sideband filter has to be located around the optical axis of the 4f optical system to eliminate the zero-order diffraction light, the viewing region inclines either upward or downward from the optical axis. Thus, viewers observe the reconstructed images from a vertically inclined direction. Without any instruction, viewers usually observe the image plane from the direction normal to the image plane. However, they cannot clearly observe the reconstructed images. When viewed from the vertically inclined direction, the reconstructed images reveal the upper or lower portions of the objects. The parts of the reconstructed objects farther from viewers appear to be located at higher or lower positions in the vertical direction. From Fig. 2(a), the inclination of the viewing region can be understood by considering the inclination of the proceeding direction of the spherical wave generated by the half-zone plate.

In this study, we modify the 4f optical system to correct the inclination of the viewing region. As illustrated in Fig. 1(c), the screen-side Fourier transform lens is shifted in the vertical direction by length λf/4p so that the center of the lens coincides with that of the Fourier transformed image after passing through the single-sideband filter. This vertical shift of the lens corrects the vertical inclination of the proceeding direction of the spherical wave generated by the half-zone plate, as shown in Fig. 2(b).

When the Fourier transform lens is shifted in the vertical direction, the reconstructed image rotates vertically; the vertical rotation angle is given by λ/4p. To correct the vertical image rotation, the hologram calculation method is modified. The position of a half-zone plate is shifted by distance λzo/4p in the vertical direction, where zo is the depth of an object point generated by the half-zone plate. The vertical shift of a half-zone plate depends on the depth of an object point.

2.2 Maximization of viewing region

Because the pixel pitch is constant across the entire display area of the SLM and on the image plane of the 4f optical system, light diffracts in the same manner on the entire image plane, as shown in Fig. 3
Fig. 3 Restricted viewing region in conventional 4f optical system.
. Therefore, the region where an entire reconstructed image can be viewed is restricted, as shown by the gray area in Fig. 3. When the magnification of the 4f optical system is unity, the diffraction angle on the image plane is given by φ = 2sin−1(λ/2p). The width of the viewing region, v, where an entire reconstructed image can be viewed, is given by
v=2ztan(φ/2)w,
(1)
where w is the image width of the SLM on the image plane and z is the observation distance from the image plane.

To enable the effective use of the diffraction capability of the SLM, we propose a method that maximizes the width of the viewing region where an entire reconstructed image can be observed at a fixed distance. A lens is placed on the image plane of the 4f optical system to bend the diffracted light inward, as shown in Fig. 4
Fig. 4 Maximization of viewing region by screen lens.
. Because parallel rays proceeding in the same direction are converged on the focal plane of the screen lens, an entire reconstructed image can be observed on the focal plane of the screen lens. A field lens was used to increase the viewing region in [9

9. N. Fukaya, K. Maeno, K. Sato, and T. Honda, “Improved eletroholographic display using liquid crystal device to shorten the viewing distance with both-eye observation,” Opt. Eng. 35(6), 1545–1549 (1996). [CrossRef]

]; it was introduced into a Fourier-transform holography system that employs one Fourier transform lens. The reconstructed image was generated on the focal plane of the Fourier transform lens, i.e., on the Fourier plane, where the field lens is placed. On the contrary, in this study, we consider the 4f optical system as a Fresnel type holography system.

With the proposed method, the width of the viewing region, where an entire reconstructed image can be observed, is given by
v={[2tan(φ/2)+w/fs]zw(zfs),[2tan(φ/2)w/fs]z+w(zfs),
(2)
where fs is the focal length of the screen lens.

The viewing region of the conventional 4f optical system is compared with that of the modified 4f optical system in Fig. 5
Fig. 5 Width of viewing region v at observation distance z (a) 2fstan(φ/2) ≥ w and (b) 2fstan(φ/2) ≤ w.
. Figure 5(a) shows the case when the width of the viewing region on the focal plane is larger than that of the SLM image, i.e., 2fstan(φ/2) ≥ w and Fig. 5(b) shows the opposite case: 2fstan(φ/2) ≤ w. In both cases, the viewing region, where an entire reconstructed image can be observed, is maximized in the vicinity of the focal plane of the screen lens.

The insertion of the screen lens on the image plane distorts the reconstructed image. To correct the image distortion, the hologram calculation method is modified. If an object point is generated at position (xo, yo, zo) without the screen lens, the position of the object point altered by the screen lens is denoted by (xo, yo, zo), i.e., position (xo, yo, zo) is imaged to position (xo, yo, zo) by the screen lens. From the lens imaging formula, the following relationships are obtained:
xo'=xo/(1+zo/f),
(3)
yo'=yo/(1+zo/f),
(4)
zo'=zo/(1+zo/f).
(5)
and

xo=xo'/(1zo'/f),
(6)
yo=yo'/(1zo'/f),
(7)
zo=zo'/(1zo'/f).
(8)

To correct the image distortion, the positions of the object points constituting a 3D image are substituted into (xo, yo, zo) to obtain position (xo, yo, zo) by using Eqs. (6)(8). Then, the half-zone plates that generate the object points at position (xo, yo, zo) are calculated. When the correction of the viewing region inclination, described in Sec. 2.1, is performed simultaneously, each half-zone plate is shifted by distance λzo/4p in the vertical direction before correcting the image distortion. Finally, the half-zone plates are summed to generate the image displayed on the SLM.

2.3 Correction of viewing region inclination by screen lens

In Sec. 2.1, the inclination of the viewing region was corrected by shifting the screen-side Fourier transform lens. Here, the inclination of the viewing region is corrected by shifting the screen lens in the vertical direction without shifting the screen-side Fourier transform lens, as shown in Fig. 6
Fig. 6 Correction of viewing region inclination of 4f optical system by shifting screen lens.
. The vertical rotation angle of the center line of the viewing region is θ = λ/4p (Sec. 2.1); to make the inclined center line parallel to the optical axis, the screen lens is vertically shifted by length λfs/4p. The vertical shift of the screen lens corrects the vertical inclination of the proceeding direction of the spherical wave generated by the half-zone plate, as shown in Fig. 7
Fig. 7 Correction of inclined proceeding direction of spherical wave generated by half-zone plate by shifting screen lens.
.

The modified hologram calculation method described in Sec. 2.2 can also be used for the modified 4f optical system described here.

3. Experiments

3.1 Correction of viewing region inclination

We experimentally verified the method to correct the inclination of the viewing region described in Sec. 2.1. We used custom Fourier transform lenses to construct the 4f optical system. The focal length of the two Fourier transform lenses was 150.0 mm. A reflection-type liquid-crystal SLM (LC-R 1080, HoloEye Corp.) was used. The resolution was 1,920 × 1,200 pixels and the pixel pitch was p = 8.1 μm. A He-Ne laser (λ = 632.8 nm) was used as a light source. As a single-sideband filter, a variable slit was used, whose aperture size could be continuously adjusted. The lower half of the Fourier transformed image of size 11.7 × 11.7 mm2 was cut by the variable slit. In order to eliminate the zero-order diffraction light, the edge of the slit was slightly shifted upward from the optical axis of the SLM-side Fourier transform lens.

In the conventional 4f optical system, the center line of the viewing region was inclined downward by 1.1°. The 4f optical system was modified by shifting the screen-side Fourier transform lens by 2.9 mm upward.

Two concentric circles of different diameters were displayed at 40 and 80 mm in front of the screen. Figure 8(a)
Fig. 8 Correction of viewing region inclination: reconstructed images produced by (a) conventional 4f optical system, and (b) modified 4f optical system by vertically shifting screen-side Fourier transform lens.
shows the reconstructed image obtained with the conventional 4f optical system. The centers of the two circles were separated in the vertical direction because the viewing region inclined downward; therefore, the image had to be captured from the lower position. The inner circle, displayed at 80 mm from the screen, appeared to be higher, while the outer circle, at 40 mm from the screen, appeared to be lower. Figure 8(b) shows the reconstructed image produced by the modified 4f optical system by using the modified hologram calculation method. The image was captured in front of the screen because the inclination of the viewing region was corrected. Concentric circles were obtained and the vertical inclination was corrected.

3.2 Maximization of viewing region

We experimentally verified the method to maximize the viewing region described in Sec. 2.2.

A plano-convex lens with a focal length of 400 mm was used as the screen lens. In the conventional 4f optical system without the screen lens, the width of the viewing region, where an entire reconstructed image can be observed, was 15.5 mm. The screen lens increased the width of the viewing region to 31.0 mm at a distance of 400 mm that is equal to the focal plane of the screen lens.

To verify the maximization of the viewing region by the screen lens, three rectangles were displayed at 10.0 mm from the screen. Figure 9
Fig. 9 Reconstructed images produced by conventional 4f optical system: images captured at (a) 15 mm left of center, (b) center, and (c) 15 mm right of center.
shows the reconstructed images produced by the conventional 4f optical system without the screen lens, which were captured at the distance of 400 mm from the screen. Figures 9(a), 9(b), and 9(c) were captured at 15 mm left from the center, at the center, and 15 mm right from the center of the viewing region, respectively. Partial images were observed at the left and right observation positions. Figure 10
Fig. 10 Reconstructed images produced by modified 4f optical system with screen lens: images captured at (a) 15 mm left of center, (b) center, and (c) 15 mm right of center.
shows the reconstructed images produced by the modified 4f optical system with the screen lens. The entire image was observed at all observation positions. The measured viewing width was 30 mm, which was slightly smaller than the designed value.

Next, we verify the correction of the image distortion by using the modified hologram calculation method. Two circles were displayed at 40 and 80 mm from the screen. The diameters of the two circles were chosen such that the diameter of one circle was apparently twice that of the other observed at 400 mm in front of the screen. Figure 11(a)
Fig. 11 Correction of image distortion caused by screen lens (a) conventional hologram calculation method, and (b) modified hologram calculation method.
shows the reconstructed image captured at 400 mm from the screen when the conventional hologram calculation method was used. The ratio of the diameters was incorrect. Figure 11(b) shows the reconstructed image when the modified hologram calculation method was used; the correct diameter ratio was obtained.

3.3 Correction of viewing region inclination by screen lens

We experimentally verified the correction of the inclination of the viewing region by vertically shifting the screen lens.

In this experiment, the screen-side Fourier transform lens was not shifted; however, the screen lens was vertically shifted by 7.8 mm.

The reconstructed image used in this experiment was the same as that used in Sec. 3.2. Figure 12(a)
Fig. 12 Correction of vertical viewing region inclination: reconstructed images produced (a) without shift of screen lens and (b) with vertical shift of screen lens.
shows the reconstructed image without shifting the screen lens, which was captured at 400 mm from the screen. The centers of the two circles were shifted in the vertical direction. Because of the vertical inclination of the viewing region, the reconstructed image was captured from the lower position. Figure 12(b) shows the reconstructed image when the screen lens was vertically shifted and the modified hologram calculation method was used. The reconstructed image was captured just in front of the screen and two concentric circles were obtained.

4. Discussion

To correct the inclination of the viewing region, two methods were proposed: (1) the Fourier transform lens was shifted, and (2) the screen lens was shifted. The two Fourier transform lenses were designed to reduce the lens aberration when the lenses were aligned on the same optical axis. Therefore, the reconstructed image quality is better when the screen lens is shifted. Figure 13
Fig. 13 Point spread functions (PSFs) of 4f optical system: (a)–(c) when screen-side Fourier transform lens is not shifted, (d)–(f) when it is vertically shifted. (a) and (d) are at the center of image, (b) and (e) are at the uppermost position, and (c) and (f) are at the rightmost position.
shows the calculated point spread functions of the 4f optical system with and without the vertical shift of the Fourier transform lens. Because the vertical shift was as small as 2.9 mm, the degradation of the imaging properties caused by the lens shift was quite small. The shift of the screen lens might affect the viewing region formation. When the screen lens is shifted, light passes through its outer area, so lens aberration degrades the viewing region formation. However, in the experiments described in this study, because the shift of the screen lens was also small, the difference in the viewing region formation was not clearly observed. The existence of the screen lens improves the intensity distribution of the reconstructed images. Figure 8(b) shows the reconstructed image when the viewing region was corrected by shifting the Fourier transform lens, and Fig. 12(b) shows the reconstructed image when the screen lens is shifted. The light intensity of the outer circle in Fig. 12(b) is higher than that in Fig. 8(b). Because the screen lens directs the diffracted light toward the viewing region, the decrease of the light intensity in the peripheral area of the reconstructed image can be reduced when viewed from the viewing region.

This study proposes the methods to correct the inclination of the viewing region and maximize the viewing region in the 4f optical systems for hologram reconstruction. For an off-axis holography display system, which does not employ the 4f optical system, the same effects can be achieved by changing light illumination of an SLM. By using an inclined plane wave as illumination light, the viewing region is generated without any inclination [8

8. E. N. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Am. 52(10), 1123–1128 (1962). [CrossRef]

]. By using a spherical wave, the viewing region is maximized at the distance where the spherical wave converges [10

10. Y. Yabe and Y. Sakamoto, “Enlargement of visual field with an LCD in computer generated holograms,” Proc. SPIE 6912, 69121A (2008). [CrossRef]

]. However, an SLM is usually designed to be illuminated by a normal incident plane wave. An SLM is illuminated by a normal incident plane wave in the methods proposed in this study.

In the present study, the viewing region of the Fresnel-type holography is maximized by introducing a screen lens. In [9

9. N. Fukaya, K. Maeno, K. Sato, and T. Honda, “Improved eletroholographic display using liquid crystal device to shorten the viewing distance with both-eye observation,” Opt. Eng. 35(6), 1545–1549 (1996). [CrossRef]

], the viewing region of the Fourier-transform holography is maximized by introducing a field lens on the Fourier plane. For Fresnel-type holography, the screen lens is placed on the image plane. In [9

9. N. Fukaya, K. Maeno, K. Sato, and T. Honda, “Improved eletroholographic display using liquid crystal device to shorten the viewing distance with both-eye observation,” Opt. Eng. 35(6), 1545–1549 (1996). [CrossRef]

], Fourier-transform holography was adopted because several SLMs with the pixel pitch of several tens of microns were used. Because the pixel pitch was relatively large, the diffraction angle of light produced by each SLM was small; therefore, the diffracted light waves were superimposed on the Fourier plane to increase the diffraction angle by several times. The pixel pitch of the SLM used in the present study is smaller than 10 μm; thus, a single SLM was used.

5. Conclusion

In a 4f optical system with a single-sideband filter, the conjugate image and zero-order diffraction light are eliminated in the reconstructed hologram. The vertical inclination of the viewing region was corrected by the vertical shift of the screen-side Fourier transform lens, and the image distortion caused by the lens shift was corrected. The viewing region was maximized by placing a screen lens on the image plane; the image distortion caused by the screen lens was also corrected. We showed that by vertically shifting the screen lens, the vertical inclination of the viewing region could be corrected without shifting the screen-side Fourier transform lens. The proposed methods were experimentally verified.

Acknowledgments

This research is partly supported by the National Institute of Information and Communications Technology (NICT), Japan.

References and links

1.

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948). [CrossRef] [PubMed]

2.

J. P. Waters, “Holographic image synthesis utilizing theoretical methods,” Appl. Phys. Lett. 9(11), 405–407 (1966). [CrossRef]

3.

G. L. Rogers, “Gabor diffraction microscopy: the hologram as a generalized zone-plate,” Nature 166(4214), 237 (1950). [CrossRef] [PubMed]

4.

W. J. Siemens-Wapniarski and M. P. Givens, “The experimental production of synthetic holograms,” Appl. Opt. 7(3), 535–538 (1968). [CrossRef] [PubMed]

5.

O. Bryngdahl and A. Lohmann, “Single-sideband holography,” J. Opt. Soc. Am. 58(5), 620–624 (1968). [CrossRef]

6.

T. Mishina, F. Okano, and I. Yuyama, “Time-alternating method based on single-sideband holography with half-zone-plate processing for the enlargement of viewing zones,” Appl. Opt. 38(17), 3703–3713 (1999). [CrossRef] [PubMed]

7.

Y. Takaki and Y. Tanemoto, “Band-limited zone plates for single-sideband holography,” Appl. Opt. 48(34), H64–H70 (2009). [CrossRef] [PubMed]

8.

E. N. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Am. 52(10), 1123–1128 (1962). [CrossRef]

9.

N. Fukaya, K. Maeno, K. Sato, and T. Honda, “Improved eletroholographic display using liquid crystal device to shorten the viewing distance with both-eye observation,” Opt. Eng. 35(6), 1545–1549 (1996). [CrossRef]

10.

Y. Yabe and Y. Sakamoto, “Enlargement of visual field with an LCD in computer generated holograms,” Proc. SPIE 6912, 69121A (2008). [CrossRef]

11.

K. Maeno, N. Fukaya, O. Nishikawa, K. Sato, and T. Honda, “Electro-holographic display using 15 mega pixels LCD,” Proc. SPIE 2652, 15–23 (1996). [CrossRef]

12.

J. Hahn, H. Kim, Y. Lim, G. Park, and B. Lee, “Wide viewing angle dynamic holographic stereogram with a curved array of spatial light modulators,” Opt. Express 16(16), 12372–12386 (2008). [CrossRef] [PubMed]

13.

M. Stanley, R. W. Bannister, C. D. Cameron, S. D. Coomber, I. G. Cresswell, J. R. Hughes, V. Hui, P. O. Jackson, K. A. Milham, R. J. Miller, D. A. Payne, J. Quarrel, D. C. Scattergood, A. P. Smith, M. A. G. Smith, D. L. Tipton, P. J. Watson, P. J. Webber, and C. W. Slinger, “100-megapixel computer-generated holographic images from Active Tiling: a dynamic and scalable electro-optic modulator system,” Proc. SPIE 5005, 247–258 (2003). [CrossRef]

14.

Y. Takaki and Y. Hayashi, “Increased horizontal viewing zone angle of a hologram by resolution redistribution of a spatial light modulator,” Appl. Opt. 47(19), D6–D11 (2008). [CrossRef] [PubMed]

15.

Y. Takaki and Y. Tanemoto, “Modified resolution redistribution system for frameless hologram display module,” Opt. Express 18(10), 10294–10300 (2010). [CrossRef] [PubMed]

OCIS Codes
(090.1760) Holography : Computer holography
(090.2870) Holography : Holographic display
(120.2040) Instrumentation, measurement, and metrology : Displays
(070.6120) Fourier optics and signal processing : Spatial light modulators

ToC Category:
Holography

History
Original Manuscript: June 22, 2011
Revised Manuscript: August 12, 2011
Manuscript Accepted: August 12, 2011
Published: August 23, 2011

Citation
Takayuki Kurihara and Yasuhiro Takaki, "Improving viewing region of 4f optical system for holographic displays," Opt. Express 19, 17621-17631 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-18-17621


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References

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