Abstract

A holographic 3D printer produces a high-quality 3D image reproduced by a full-color, full-parallax holographic stereogram with high-density light-ray recording. In order to produce a high-resolution holographic stereogram, we have to solve the problem of speckle noise in this system. For equalizing an intensity distribution inside the elementary hologram, the object beam is modulated by a diffuser. However the diffuser typically generates speckles, which is recorded in the holographic stereogram. It is localized behind the reconstructed image as a granularity noise. First we show the problems of some conventional ways for suppressing the granularity noise using a band-limited diffuser, and then we analyze an approach using a moving diffuser for the reduction of this noise. In the result, it is found that recording with a moving diffuser is effective for reducing the granularity noise at infinity of reconstructed image, although an alternative noise occurs. Moreover we propose a new method introducing multiple exposures to suppress the noise effectively.

© 2013 OSA

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2012 (3)

2011 (1)

2008 (1)

S. Maruyama, Y. Ono, and M. Yamaguchi, “High-density recording of full-color full-parallax holographic stereogram,” Proc. SPIE6912, 69120N, 69120N-10 (2008).
[CrossRef]

2001 (1)

L. E. Helseth and I. Singstad, “Diffusers for holographic stereography,” Opt. Commun.193(1-6), 81–86 (2001).
[CrossRef]

1999 (2)

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, and T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev.6(4), 339–344 (1999).
[CrossRef]

J. Yang, L. M. Bernardo, and Y. S. Bae, “Improving holographic data storage by use of an optimized phase mask,” Appl. Opt.38(26), 5641–5645 (1999).
[CrossRef] [PubMed]

1995 (1)

P. St.-Hilaire, “Phase profiles for holographic stereograms,” Opt. Eng.34(1), 83–89 (1995).
[CrossRef]

1994 (1)

1993 (1)

M. A. Klug, M. W. Halle, M. E. Lucente, and W. J. Plesniak, “Compact prototype one-step Ultragram printer,” Proc. SPIE1914, 15–24 (1993).
[CrossRef]

1992 (1)

1991 (1)

1988 (1)

1980 (1)

1979 (1)

1978 (1)

Y. Torii, “Synthesis of deterministic phase codes for phase shifter in holography,” Opt. Commun.24(2), 175–180 (1978).
[CrossRef]

1976 (1)

S. Yonezawa, “A deterministic phase shifter for holographic memory devices,” Opt. Commun.19(3), 370–373 (1976).
[CrossRef]

1973 (2)

1972 (1)

1970 (2)

Bae, Y. S.

Beauchamp, H. L.

Bernardo, L. M.

Bräuer, R.

Bryngdahl, O.

Burckhardt, C. B.

Craggs, G.

Dallas, W. J.

DePalma, J. J.

Endoh, H.

Engström, D.

Goksör, M.

Halle, M. W.

M. A. Klug, M. W. Halle, M. E. Lucente, and W. J. Plesniak, “Compact prototype one-step Ultragram printer,” Proc. SPIE1914, 15–24 (1993).
[CrossRef]

Hara, T.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, and T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev.6(4), 339–344 (1999).
[CrossRef]

Helseth, L. E.

L. E. Helseth and I. Singstad, “Diffusers for holographic stereography,” Opt. Commun.193(1-6), 81–86 (2001).
[CrossRef]

Hoadley, H. O.

Honda, T.

Hsu, W. F.

Igasaki, Y.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, and T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev.6(4), 339–344 (1999).
[CrossRef]

Inoue, T.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, and T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev.6(4), 339–344 (1999).
[CrossRef]

Iwamoto, A.

Janssens, P.

Kato, M.

Klug, M. A.

M. A. Klug, M. W. Halle, M. E. Lucente, and W. J. Plesniak, “Compact prototype one-step Ultragram printer,” Proc. SPIE1914, 15–24 (1993).
[CrossRef]

Kobayashi, Y.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, and T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev.6(4), 339–344 (1999).
[CrossRef]

Kurtz, C. N.

Li, F.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, and T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev.6(4), 339–344 (1999).
[CrossRef]

Liang, X.

D. C. Ong, S. Solanki, X. Liang, and X. Xu, “Analysis of laser speckle severity, granularity, and anisotropy using the power spectral density in polarcoordinate representation,” Opt. Eng.51(5), 054301 (2012).
[CrossRef]

Lin, L. H.

Lucente, M. E.

M. A. Klug, M. W. Halle, M. E. Lucente, and W. J. Plesniak, “Compact prototype one-step Ultragram printer,” Proc. SPIE1914, 15–24 (1993).
[CrossRef]

Maruyama, S.

S. Maruyama, Y. Ono, and M. Yamaguchi, “High-density recording of full-color full-parallax holographic stereogram,” Proc. SPIE6912, 69120N, 69120N-10 (2008).
[CrossRef]

Meuret, Y.

Miyamura, Y.

Mukohzaka, N.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, and T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev.6(4), 339–344 (1999).
[CrossRef]

Nakayama, Y.

Ohyama, N.

Ong, D. C.

D. C. Ong, S. Solanki, X. Liang, and X. Xu, “Analysis of laser speckle severity, granularity, and anisotropy using the power spectral density in polarcoordinate representation,” Opt. Eng.51(5), 054301 (2012).
[CrossRef]

Ono, Y.

S. Maruyama, Y. Ono, and M. Yamaguchi, “High-density recording of full-color full-parallax holographic stereogram,” Proc. SPIE6912, 69120N, 69120N-10 (2008).
[CrossRef]

Oshida, Y.

Persson, M.

Plesniak, W. J.

M. A. Klug, M. W. Halle, M. E. Lucente, and W. J. Plesniak, “Compact prototype one-step Ultragram printer,” Proc. SPIE1914, 15–24 (1993).
[CrossRef]

Roelandt, S.

Singstad, I.

L. E. Helseth and I. Singstad, “Diffusers for holographic stereography,” Opt. Commun.193(1-6), 81–86 (2001).
[CrossRef]

Solanki, S.

D. C. Ong, S. Solanki, X. Liang, and X. Xu, “Analysis of laser speckle severity, granularity, and anisotropy using the power spectral density in polarcoordinate representation,” Opt. Eng.51(5), 054301 (2012).
[CrossRef]

St.-Hilaire, P.

P. St.-Hilaire, “Phase profiles for holographic stereograms,” Opt. Eng.34(1), 83–89 (1995).
[CrossRef]

Takeda, Y.

Thienpont, H.

Torii, Y.

Y. Torii, “Synthesis of deterministic phase codes for phase shifter in holography,” Opt. Commun.24(2), 175–180 (1978).
[CrossRef]

Toyoda, H.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, and T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev.6(4), 339–344 (1999).
[CrossRef]

Verschaffelt, G.

Wyrowski, F.

Xu, X.

D. C. Ong, S. Solanki, X. Liang, and X. Xu, “Analysis of laser speckle severity, granularity, and anisotropy using the power spectral density in polarcoordinate representation,” Opt. Eng.51(5), 054301 (2012).
[CrossRef]

Yamaguchi, M.

Yang, J.

Yeh, C. F.

Yonezawa, S.

S. Yonezawa, “A deterministic phase shifter for holographic memory devices,” Opt. Commun.19(3), 370–373 (1976).
[CrossRef]

Yoshida, N.

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, and T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev.6(4), 339–344 (1999).
[CrossRef]

Appl. Opt. (8)

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

Opt. Commun. (3)

S. Yonezawa, “A deterministic phase shifter for holographic memory devices,” Opt. Commun.19(3), 370–373 (1976).
[CrossRef]

Y. Torii, “Synthesis of deterministic phase codes for phase shifter in holography,” Opt. Commun.24(2), 175–180 (1978).
[CrossRef]

L. E. Helseth and I. Singstad, “Diffusers for holographic stereography,” Opt. Commun.193(1-6), 81–86 (2001).
[CrossRef]

Opt. Eng. (2)

D. C. Ong, S. Solanki, X. Liang, and X. Xu, “Analysis of laser speckle severity, granularity, and anisotropy using the power spectral density in polarcoordinate representation,” Opt. Eng.51(5), 054301 (2012).
[CrossRef]

P. St.-Hilaire, “Phase profiles for holographic stereograms,” Opt. Eng.34(1), 83–89 (1995).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Opt. Rev. (1)

Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, and T. Hara, “High efficiency electrically-addressable phase-only spatial light modulator,” Opt. Rev.6(4), 339–344 (1999).
[CrossRef]

Proc. SPIE (2)

M. A. Klug, M. W. Halle, M. E. Lucente, and W. J. Plesniak, “Compact prototype one-step Ultragram printer,” Proc. SPIE1914, 15–24 (1993).
[CrossRef]

S. Maruyama, Y. Ono, and M. Yamaguchi, “High-density recording of full-color full-parallax holographic stereogram,” Proc. SPIE6912, 69120N, 69120N-10 (2008).
[CrossRef]

Other (2)

N. Kihara, A. Shirakura, and S. Baba, “Method and apparatus for creating holographic stereogram,” U.S. Patent 5,949,559 (1999).

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Company, Englewood, 2007).

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Figures (15)

Fig. 1
Fig. 1

Optical setup for an elementary hologram recording. A phase modulation means placing a diffuser or a digital diffuser and Pphase is a pitch of phase cell of the digital diffuser. D is a pitch of the elementary hologram.

Fig. 2
Fig. 2

Simulation results of PRPS: Reconstructed light distribution of HS with (a) 2level-random phase, (b) 4level-PRPS and (c) 6level-complex-PRPS. Fourier spectrum with (d) 2level-random phases, (e) 4level-PRPS, (f) 6level-complex-PRPS and red-rectangle is the aperture size. The Fourier spectrums (d)~(f) are almost equalized although the reconstructed angular distributions (a)~(c) become characteristic patterns.

Fig. 3
Fig. 3

Simulation results of IFTA: A speckle contrast “C” vs. smoothness “S” of digital diffusers designed by IFTA. Mark (a)~(d) are corresponding to Fig. 4. There is a trade-off between C and S. S can be controlled by changing the clipping level of the Fourier domain constraint in IFTA.

Fig. 4
Fig. 4

Simulation results of IFTA: (a)~(d) Reconstructed light distribution of HS corresponding to the mark of Fig. 3(a)~(d). (e)~(h) Fourier spectrum corresponding to (a)~(d) each other. Red-rectangle is the aperture size. IFTA method and the choice of initial phase are same as [14]. This simulation is calculated with 128 × 128 phase cells and the results are made by 50 iterations.

Fig. 5
Fig. 5

Principle of reducing the granularity noise perceived at infinity by a moving diffuser. Each elementary hologram reconstructs the LCD image with the uncorrelated speckle pattern as the angular distribution. When the observer focuses on infinity of the reconstructed image, these patterns superposed at the retina incoherently, and then granularity noise contrast can be reduced.

Fig. 6
Fig. 6

Reconstructed image with a static diffuser (M = 1) focus on (a) the hologram plane and (b) infinity, and with a moving diffuser (M = 250) focus on (c) the hologram plane and (d) infinity.

Fig. 7
Fig. 7

(a) Optical setup for the granularity noise evaluation of HS at infinity, f1 = 80mm, f2 = 150mm and D = 200μm. (b) Granularity noise contrast at infinity with a moving diffuser (the cases of single exposure ”Csingle” is described in section 3.2 and multiple exposures ”Cmulti” is described in section 4.1). Dot-line is the theoretical value, where Csyst = 0.085. Granularity noise contrast is evaluated by averaging the divided 3 × 3 segments to reduce the effect of unevenness of the object beam distribution.

Fig. 8
Fig. 8

Granularity noise in the reconstructed image at infinity captured by the experiment shown in Fig. 7. (a) M = 1, (b) M = 2, (c) M = 4, (d) M = 8, (e) M = 16, (f) M = 32.

Fig. 9
Fig. 9

(a) Optical setup for the noise evaluation of the hologram plane. (b) High-frequency noise at the hologram plane with the moving diffuser. (“Single exposure” is described in section 3.3 and “Multiple exposures” is described in section 4.1).

Fig. 10
Fig. 10

Principle of appearing the high-frequency noise at the hologram plane. Each elementary hologram reconstructs the uncorrelated speckle pattern, and the observer perceives a luminance variation at the elementary hologram as high-frequency noise.

Fig. 11
Fig. 11

Concept of the proposed method: Speckle reduction by multiple exposures with 4level-PRPS. Multiple exposing an elementary hologram four times with shifting the diffuser half-length of the phase cell pitch, the dot-like pattern reconstructed from the elementary hologram is multiplexed incoherently.

Fig. 12
Fig. 12

Simulation and experimental results of the granularity noise reduction (red channel). Reconstructed light distribution by (a) single exposure and by (d) 4 times shifted and multiple exposures (proposed method) with 4level-PRPS generated by numerical simulation. The granularity noise contrast of (d) is 0.105. (b) and (e) are experimental results of (a) and (d), respectively. (c) Is a granularity noise by single exposure with static diffuser and (f) is granularity noise by multiple exposures with moving diffuser (uncorrelated phase pattern).

Fig. 13
Fig. 13

The image focused on hologram plane (red channel). (a) The case of “single exposure with moving diffuser (M=4)”, (b) “proposed method”, and (c) “single exposure with static diffuser”. The proposed method (b) can suppress the high frequency noise in contrast to the moving diffuser method (a).

Fig. 14
Fig. 14

Comparison between the proposed method and the moving diffuser method. (a) Granularity noise contrast at infinity and (b) high frequency noise at hologram plane. Since the DOE used here is designed for wavelength of 633nm, these results are measured using HS's recorded with a He-Ne laser (633nm) different from Fig. 7(b) and Fig. 9(b) that are recorded with a “green” laser (532nm).

Fig. 15
Fig. 15

Example of a pixel crosstalk of a phase only SLM: The reconstructed light distribution of HS with 4level-PRPS, (a) the simulation result and (b) the experimental result. A boundary between 3π/2 and 0 phase modulation have high frequency due to the pixel crosstalk. The crosstalk is calculated by convoluting a gauss function to the original phase pattern in this simulation [23]. (b) is the result of PAL-SLM [22].

Tables (1)

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Table 1 Experimental Results of the Proposed Method

Equations (2)

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S= I F I Fmax ,C= σ LCD I LCD ,
C theo = ( C init M ) 2 + C syst 2 ,

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