OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 11 — May. 24, 2010
  • pp: 11327–11334
« Show journal navigation

Reduction of image blurring of horizontally scanning holographic display

Yasuhiro Takaki and Naoya Okada  »View Author Affiliations


Optics Express, Vol. 18, Issue 11, pp. 11327-11334 (2010)
http://dx.doi.org/10.1364/OE.18.011327


View Full Text Article

Acrobat PDF (961 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A horizontally scanning holographic display offers a wide viewing angle and a large hologram size. To obtain this display, a series of images generated by a high-speed spatial light modulator are imaged to vertically long images (elementary holograms) by an anamorphic imaging system and are aligned horizontally by a horizontal scanner. However, scan error and focusing error cause blurring in the reconstructed images. In this study, the scan error is corrected by measuring the positions and pixel pitches of the elementary holograms in advance. The focusing error is corrected by experimentally determining the focusing parameter that is used to calculate the elementary holograms.

© 2010 OSA

1. Introduction

Holography is an ideal three-dimensional (3D) display technique. When a spatial light modulator (SLM) is used directly to display holograms, there are two major problems: limited viewing angle and small hologram size. A very fine pixel pitch is necessary for a wide viewing angle, and a huge pixel count is necessary for a large hologram size. Therefore, techniques have been explored to overcome these problems. In addition to several excellent techniques that have been proposed, we proposed horizontally scanning holography [1

1. Y. Takaki and N. Okada, “Hologram generation by horizontal scanning of a high-speed spatial light modulator,” Appl. Opt. 48(17), 3255–3260 (2009). [CrossRef] [PubMed]

]. In this technique, a series of elementary holograms generated by a high-speed SLM are aligned horizontally by a mechanical scanner.

Some of the techniques prior to our work are explained. MIT proposed the hologram display system [2

2. P. St. Hilaire, S. A. Benton, M. Lucente, M. L. Jepsen, J. Kollin, H. Yoshikawa, and J. Underkoffler, “Electronic display system for computational holography,” SPIE 1212, 174 (1990). [CrossRef]

,3

3. P. St. Hilaire, S. A. Benton, and M. Lucente, “Synthetic aperture hologram: a novel approach to three-dimensional display,” J. Opt. Soc. Am. 9(11), 1969–1977 (1992). [CrossRef]

], in which the high-resolution one-dimensional hologram distribution generated by an acousto-optic modulator is scanned two-dimensionally by a mechanical scanner to reduce the pixel pitch and to increase the pixel count. The technique to double the viewing angle using time-multiplexing was also proposed [4

4. 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]

,5

5. T. Mishina, M. Okui, and F. Okano, “Viewing-zone enlargement method for sampled hologram that uses high-order diffraction,” Appl. Opt. 41(8), 1489–1499 (2002). [CrossRef] [PubMed]

]. The active tilting technique [6

6. 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,” SPIE 5005, 247 (2003). [CrossRef]

] was proposed, with which de-magnified images generated by a high-speed SLM are tiled onto an optically addressed SLM in a time-sequential manner. Several authors have proposed techniques using multiple SLMs [7

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

,8

8. 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]

]. Our research group has also reported the use of the resolution redistribution optical system [9

9. 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]

,10

10. Y. Takaki and Y. Hayashi, “Elimination of conjugate image for holograms using a resolution redistribution optical system,” Appl. Opt. 47(24), 4302–4308 (2008). [CrossRef] [PubMed]

]. In this technique, the horizontal resolution is increased several times by sacrificing the vertical resolution.

In the present study, a technique to reduce blurring in reconstructed images produced by the horizontally scanning holographic display is presented.

2. Horizontally scanning holographic display

2.1 Operating principle

The horizontally scanning holographic display system is illustrated in Fig. 1
Fig. 1 Horizontally scanning holographic display.
. An image generated by a high-speed SLM is squeezed in the horizontal direction and enlarged in the vertical direction by an anamorphic imaging system. The anamorphic imaging system, consisting of two orthogonally aligned cylindrical lenses, has different magnifications in the horizontal and vertical directions. The generated vertically long image, which is an elementary hologram, is scanned horizontally by a mechanical scanner. The high-speed SLM displays a series of elementary images in synchronization with the horizontal scanning. The pixel pitch of the SLM is reduced in the horizontal direction in order to increase the horizontal viewing angle. Since the image is enlarged in the vertical direction and is scanned in the horizontal direction, the hologram size increases. Because the vertical pixel pitch increases, this system displays a horizontal parallax-only hologram. A screen lens redirects light to the observers, and a vertical diffuser is placed on the image plane to increase the vertical viewing zone.

2.2 Modification of the experimental system

3. Correction of scanning error

A nonlinear relationship exists between the scan position and the drive voltage in the galvano mirror scanning system. The magnification of the anamorphic imaging system slightly changes depending on the scan angle of the galvano mirror, and so the pixel pitches of the elementary holograms are not constant. The position error and the pixel pitch error of the elementary holograms degrade the sharpness of the reconstructed images. In the ideal condition, depicted in Fig. 3(a)
Fig. 3 Blurring of object point: (a) without scanning error and focusing error, (b) with scanning error, and (c) with focusing error.
, lights diffracted from several elementary holograms converge at one object point. The reconstructed image consists of numerous object points. When a scanning error exists, the lights do not converge at one point, as depicted in Fig. 3(b). The position error disturbs the position of the elementary hologram, and the pixel pitch error disturbs the light diffraction direction.

To reduce the image degradation caused by the scanning errors, the positions and the pixel pitches of the elementary holograms are measured in advance. Then, the hologram patterns of the elementary holograms are calculated, taking the measured data into account.

A triangular drive voltage for the galvano mirror was generated from the synchronization signal outputted from the DMD device. The scan angle changes 2.0° per one volt change. Because it is difficult to perform the measurements for all the elementary holograms, the measurements were done for 34 elementary holograms that corresponded to the drive voltages with an interval of one volt. In each measurement, only one elementary hologram was displayed to measure its position on the scan plane. The horizontal pixel pitch was calculated from the measured width of the elementary hologram. The measured positions are shown in Fig. 4(a)
Fig. 4 Measured results of elementary holograms: (a) positions, and (b) pixel pitches.
. There are two plots for each drive voltage. These plots correspond to the forward scan and the backward scan. A hysteresis behavior appears in the scanning position. The measured pixel pitches are shown in Fig. 4(b). The pixel pitch is larger when the position of the elementary hologram is farther from the center of the scan plane. The positions and the pixel pitches of non measured elementary holograms are interpolated from those of the measured elementary holograms.

Figure 5(a)
Fig. 5 Reconstructed images improved with correction of scanning error: (a) without correction, (b) with correction of pixel pitch error, and (c) with correction of position error and pixel pitch error.
shows the photograph of a reconstructed image without using the measured results. It is assumed that the position is proportional to the drive voltage and the pixel pitch is constant. Each object point was split into two blurred dots. Figure 5(b) shows the reconstructed image when the measured pixel pitches were used to calculate the elementary holograms. The dots are sharper. Figure 5(c) shows the result when both the measured positions and the pixel pitches were used for the calculation. Each object point is now one dot.

4. Correction of the focusing error

As illustrated in Fig. 6
Fig. 6 Generation of elementary holograms (horizontal sectional view).
, light converges horizontally on the focal plane of the cylindrical lens (1 in Fig. 1) or the focal plane of the spherical lens (Fig. 2). Therefore, the distribution of the elementary holograms on the scan plane is the multiplication of the magnified distribution displayed by the DMD, the phase distribution of the cylindrical wave diverged from the focal plane, and the phase distribution of the screen lens (linear Fresnel lens). Because the focal point of the screen lens coincides with the rotation center of the galvano mirror, the cylindrical wave after passing through the screen lens proceeds in the direction perpendicular to the scan plane and also proceeds as if it diverges from the diverging plane, as indicated by the dashed lines in Fig. 6. In the calculation of the elementary holograms, the phase distribution of the cylindrical wave must be canceled. Therefore, the optical length between the scan plane and the focal plane, denoted by t in Fig. 6, must be known. In this study, this optical length is assumed to be constant, although it actually changes slightly depending on the scan angle. It is not easy to measure this optical length directly in the experimental system because of the thickness of the optical components. If t is incorrect, light diffracted by the elementary holograms converges at a wrong distance so that a focusing error occurs; that is, the converging position does not coincide with the position where the lights from several elementary holograms intersect, as shown in Fig. 3(c).

Figure 9(a)
Fig. 9 Improvement of reconstruction image with correction of scanning and focusing errors when thin paper is placed around the front side of 3D image: (a) with correction of scanning error, and (b) with correction of scanning error and focusing error.
shows a photograph of the reconstructed image before correction of the focusing error (t = 45.7 mm). Figure 9(b) shows the result when t = 44 mm. A thin paper is placed around the front side of the 3D image to evaluate the spot sizes of the object points. The magnified images are shown in Figs. 9(c) and 9(d). The spot sizes became smaller after correction of the focusing error.

5. Discussion

In the modified experimental system described in Sec. 2.2, the linear Fresnel lens replaced the glass lens as the screen lens. We were concerned that speckles would appear on the reconstructed images, because the linear Fresnel lens has a saw-tooth surface structure. Fortunately, no speckles were observed, as shown in Fig. 5 and Fig. 8. However, the reconstructed images looked clearer when using the glass lens. Speckles were not observable because the reconstructed image consisted of a number of reconstructed images produced by the elementary holograms. Because the elementary holograms are displayed at different times, the intensity distributions of the reconstructed images generated by the elementary holograms are added to reduce the speckles by the time-averaging effect.

The horizontal width of the object points of the reconstructed image after correction of the scanning error and the focusing error was measured from the image projected on thin paper, shown in Fig. 9(d). The average width was approximately 0.5 mm. Because the DMD was illuminated by a pulse light to reduce the horizontal blurring caused by horizontal scanning as described in Ref [1

1. Y. Takaki and N. Okada, “Hologram generation by horizontal scanning of a high-speed spatial light modulator,” Appl. Opt. 48(17), 3255–3260 (2009). [CrossRef] [PubMed]

], the width of the object points stretched by 0.23 mm in the modified experimental system. The width also stretched due to the light diffraction caused by the limited width of the elementary holograms. The object points in Fig. 9(d) were located at approximately 50 mm in front of the scan plane, and so the diffraction increased the width by 12 μm. The evaluation of the width of the object points shows that there remains room for further improvement to reduce image blurring.

6. Conclusion

The horizontally scanning holographic display can solve the problems of a small viewing angle and a small screen size. In this paper, the image degradation caused by the scanning error and the focusing error was reduced. The scan error was corrected by calculating elementary holograms using measured parameters. The focusing error was corrected by experimentally determining the optical parameter used for the calculation of elementary holograms.

References and links

1.

Y. Takaki and N. Okada, “Hologram generation by horizontal scanning of a high-speed spatial light modulator,” Appl. Opt. 48(17), 3255–3260 (2009). [CrossRef] [PubMed]

2.

P. St. Hilaire, S. A. Benton, M. Lucente, M. L. Jepsen, J. Kollin, H. Yoshikawa, and J. Underkoffler, “Electronic display system for computational holography,” SPIE 1212, 174 (1990). [CrossRef]

3.

P. St. Hilaire, S. A. Benton, and M. Lucente, “Synthetic aperture hologram: a novel approach to three-dimensional display,” J. Opt. Soc. Am. 9(11), 1969–1977 (1992). [CrossRef]

4.

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]

5.

T. Mishina, M. Okui, and F. Okano, “Viewing-zone enlargement method for sampled hologram that uses high-order diffraction,” Appl. Opt. 41(8), 1489–1499 (2002). [CrossRef] [PubMed]

6.

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,” SPIE 5005, 247 (2003). [CrossRef]

7.

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

8.

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]

9.

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]

10.

Y. Takaki and Y. Hayashi, “Elimination of conjugate image for holograms using a resolution redistribution optical system,” Appl. Opt. 47(24), 4302–4308 (2008). [CrossRef] [PubMed]

OCIS Codes
(090.1760) Holography : Computer holography
(090.2870) Holography : Holographic display
(120.2040) Instrumentation, measurement, and metrology : Displays

ToC Category:
Holography

History
Original Manuscript: April 1, 2010
Revised Manuscript: April 30, 2010
Manuscript Accepted: May 6, 2010
Published: May 13, 2010

Citation
Yasuhiro Takaki and Naoya Okada, "Reduction of image blurring of
horizontally scanning holographic display," Opt. Express 18, 11327-11334 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-11-11327


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. Y. Takaki and N. Okada, “Hologram generation by horizontal scanning of a high-speed spatial light modulator,” Appl. Opt. 48(17), 3255–3260 (2009). [CrossRef] [PubMed]
  2. P. St. Hilaire, S. A. Benton, M. Lucente, M. L. Jepsen, J. Kollin, H. Yoshikawa, and J. Underkoffler, “Electronic display system for computational holography,” SPIE 1212, 174 (1990). [CrossRef]
  3. P. St. Hilaire, S. A. Benton, and M. Lucente, “Synthetic aperture hologram: a novel approach to three-dimensional display,” J. Opt. Soc. Am. 9(11), 1969–1977 (1992). [CrossRef]
  4. 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]
  5. T. Mishina, M. Okui, and F. Okano, “Viewing-zone enlargement method for sampled hologram that uses high-order diffraction,” Appl. Opt. 41(8), 1489–1499 (2002). [CrossRef] [PubMed]
  6. 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,” SPIE 5005, 247 (2003). [CrossRef]
  7. K. Maeno, N. Fukaya, O. Nishikawa, K. Sato, and T. Honda, “Electro-holographic display using 15 mega pixels LCD,” SPIE 2652, 15 (1996).
  8. 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]
  9. 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]
  10. Y. Takaki and Y. Hayashi, “Elimination of conjugate image for holograms using a resolution redistribution optical system,” Appl. Opt. 47(24), 4302–4308 (2008). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited