Abstract

We propose a spatial cross modulation method using a random diffuser and a phase-only spatial light modulator (SLM), by which arbitrary complex-amplitude fields can be generated with higher spatial resolution and diffraction efficiency than off-axis and double-phase computer-generated holograms. Our method encodes the original complex object as a phase-only diffusion image by scattering the complex object using a random diffuser. In addition, all incoming light to the SLM is consumed for a single diffraction order, making a diffraction efficiency of more than 90% possible. This method can be applied for holographic data storage, three-dimensional displays, and other such applications.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. W. Lohmann, D. P. Paris, “Binary Fraunhofer holograms, generated by computer,” Appl. Opt. 6(10), 1739–1748 (1967).
    [CrossRef] [PubMed]
  2. A. W. Lohmann, D. P. Paris, “Computer generated spatial filters for coherent optical data processiing,” Appl. Opt. 7(4), 651–655 (1968).
    [CrossRef] [PubMed]
  3. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11(5), 288–290 (1986).
    [CrossRef] [PubMed]
  4. V. Bagnoud, J. D. Zuegel, “Independent phase and amplitude control of a laser beam by use of a single-phase-only spatial light modulator,” Opt. Lett. 29(3), 295–297 (2004).
    [CrossRef] [PubMed]
  5. Y. Sando, M. Itoh, T. Yatagai, “Holographic three-dimensional display synthesized from three-dimensional Fourier spectra of real existing objects,” Opt. Lett. 28(24), 2518–2520 (2003).
    [CrossRef] [PubMed]
  6. A. J. MacGovern, J. C. Wyant, “Computer generated holograms for testing optical elements,” Appl. Opt. 10(3), 619–624 (1971).
    [CrossRef] [PubMed]
  7. V. Arrizón, G. Méndez, D. Sánchez-de-La-Llave, “Accurate encoding of arbitrary complex fields with amplitude-only liquid crystal spatial light modulators,” Opt. Express 13(20), 7913–7927 (2005).
    [CrossRef] [PubMed]
  8. C. K. Hsueh, A. A. Sawchuk, “Computer-generated double-phase holograms,” Appl. Opt. 17(24), 3874–3883 (1978).
    [CrossRef] [PubMed]
  9. J. M. Florence, R. D. Juday, “Full complex spatial filtering with a phase mostly DMD,” Proc. SPIE 1558, 487–498 (1991).
    [CrossRef]
  10. Z. Göröcs, G. Erdei, T. Sarkadi, F. Ujhelyi, J. Reményi, P. Koppa, E. Lorincz, “Hybrid multinary modulation using a phase modulating spatial light modulator and a low-pass spatial filter,” Opt. Lett. 32(16), 2336–2338 (2007).
    [CrossRef] [PubMed]
  11. L. B. Lesem, P. M. Hirch, J. A. Jordan., “The kinoform: A new wavefront reconstruction device,” IBM J. Res. Develop. 13(2), 150–155 (1969).
    [CrossRef]
  12. A. V. Oppenheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69(5), 529–541 (1981).
    [CrossRef]
  13. J. L. Horner, P. D. Gianino, “Phase-only matched filtering,” Appl. Opt. 23(6), 812–816 (1984).
    [CrossRef] [PubMed]
  14. M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, C. W. Slinger, A. Wood, “3D electronic holography display system using a 100Mega-pixel spatial light modulator,” Proc. SPIE 5249, 297–308 (2004).
    [CrossRef]
  15. E. N. Leith, A. Kozma, J. Upatnieks, J. Marks, N. Massey, “Holographic data storage in three-dimensional media,” Appl. Opt. 5(8), 1303–1311 (1966).
    [CrossRef] [PubMed]
  16. K. Anderson, K. Curtis, “Polytopic multiplexing,” Opt. Lett. 29(12), 1402–1404 (2004).
    [CrossRef] [PubMed]
  17. M. Takabayashi, A. Okamoto, “Self-referential holography and its applications to data storage and phase-to-intensity conversion,” Opt. Express 21(3), 3669–3681 (2013).
    [CrossRef] [PubMed]
  18. K. Zukeran, A. Okamoto, M. Takabayashi, A. Shibukawa, K. Sato, A. Tomita, “Double-referential holography and spatial quadrature amplitude modulation,” Jpn. J. Appl. Phys. 52(9S2), 09LD13 (2013).
    [CrossRef]
  19. L. G. Shirley, N. George, “Wide-angle diffuser transmission functions and far-zone speckle,” J. Opt. Soc. Am. A 4(4), 734–745 (1987).
    [CrossRef]
  20. A. Okamoto, K. Kunori, M. Takabayashi, A. Tomita, K. Sato, “Holographic diversity interferometry for optical storage,” Opt. Express 19(14), 13436–13444 (2011).
    [CrossRef] [PubMed]

2013 (2)

M. Takabayashi, A. Okamoto, “Self-referential holography and its applications to data storage and phase-to-intensity conversion,” Opt. Express 21(3), 3669–3681 (2013).
[CrossRef] [PubMed]

K. Zukeran, A. Okamoto, M. Takabayashi, A. Shibukawa, K. Sato, A. Tomita, “Double-referential holography and spatial quadrature amplitude modulation,” Jpn. J. Appl. Phys. 52(9S2), 09LD13 (2013).
[CrossRef]

2011 (1)

2007 (1)

2005 (1)

2004 (3)

V. Bagnoud, J. D. Zuegel, “Independent phase and amplitude control of a laser beam by use of a single-phase-only spatial light modulator,” Opt. Lett. 29(3), 295–297 (2004).
[CrossRef] [PubMed]

M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, C. W. Slinger, A. Wood, “3D electronic holography display system using a 100Mega-pixel spatial light modulator,” Proc. SPIE 5249, 297–308 (2004).
[CrossRef]

K. Anderson, K. Curtis, “Polytopic multiplexing,” Opt. Lett. 29(12), 1402–1404 (2004).
[CrossRef] [PubMed]

2003 (1)

1991 (1)

J. M. Florence, R. D. Juday, “Full complex spatial filtering with a phase mostly DMD,” Proc. SPIE 1558, 487–498 (1991).
[CrossRef]

1987 (1)

1986 (1)

1984 (1)

1981 (1)

A. V. Oppenheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69(5), 529–541 (1981).
[CrossRef]

1978 (1)

1971 (1)

1969 (1)

L. B. Lesem, P. M. Hirch, J. A. Jordan., “The kinoform: A new wavefront reconstruction device,” IBM J. Res. Develop. 13(2), 150–155 (1969).
[CrossRef]

1968 (1)

1967 (1)

1966 (1)

Anderson, K.

Arrizón, V.

Ashkin, A.

Bagnoud, V.

Bjorkholm, J. E.

Cameron, C. D.

M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, C. W. Slinger, A. Wood, “3D electronic holography display system using a 100Mega-pixel spatial light modulator,” Proc. SPIE 5249, 297–308 (2004).
[CrossRef]

Chu, S.

Coomber, S. D.

M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, C. W. Slinger, A. Wood, “3D electronic holography display system using a 100Mega-pixel spatial light modulator,” Proc. SPIE 5249, 297–308 (2004).
[CrossRef]

Curtis, K.

Dziedzic, J. M.

Erdei, G.

Florence, J. M.

J. M. Florence, R. D. Juday, “Full complex spatial filtering with a phase mostly DMD,” Proc. SPIE 1558, 487–498 (1991).
[CrossRef]

George, N.

Gianino, P. D.

Göröcs, Z.

Hirch, P. M.

L. B. Lesem, P. M. Hirch, J. A. Jordan., “The kinoform: A new wavefront reconstruction device,” IBM J. Res. Develop. 13(2), 150–155 (1969).
[CrossRef]

Horner, J. L.

Hsueh, C. K.

Itoh, M.

Jordan, J. A.

L. B. Lesem, P. M. Hirch, J. A. Jordan., “The kinoform: A new wavefront reconstruction device,” IBM J. Res. Develop. 13(2), 150–155 (1969).
[CrossRef]

Juday, R. D.

J. M. Florence, R. D. Juday, “Full complex spatial filtering with a phase mostly DMD,” Proc. SPIE 1558, 487–498 (1991).
[CrossRef]

Koppa, P.

Kozma, A.

Kunori, K.

Leith, E. N.

Lesem, L. B.

L. B. Lesem, P. M. Hirch, J. A. Jordan., “The kinoform: A new wavefront reconstruction device,” IBM J. Res. Develop. 13(2), 150–155 (1969).
[CrossRef]

Lim, J. S.

A. V. Oppenheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69(5), 529–541 (1981).
[CrossRef]

Lohmann, A. W.

Lorincz, E.

MacGovern, A. J.

Marks, J.

Massey, N.

Méndez, G.

Okamoto, A.

Oppenheim, A. V.

A. V. Oppenheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69(5), 529–541 (1981).
[CrossRef]

Paris, D. P.

Reményi, J.

Sánchez-de-La-Llave, D.

Sando, Y.

Sarkadi, T.

Sato, K.

K. Zukeran, A. Okamoto, M. Takabayashi, A. Shibukawa, K. Sato, A. Tomita, “Double-referential holography and spatial quadrature amplitude modulation,” Jpn. J. Appl. Phys. 52(9S2), 09LD13 (2013).
[CrossRef]

A. Okamoto, K. Kunori, M. Takabayashi, A. Tomita, K. Sato, “Holographic diversity interferometry for optical storage,” Opt. Express 19(14), 13436–13444 (2011).
[CrossRef] [PubMed]

Sawchuk, A. A.

Shibukawa, A.

K. Zukeran, A. Okamoto, M. Takabayashi, A. Shibukawa, K. Sato, A. Tomita, “Double-referential holography and spatial quadrature amplitude modulation,” Jpn. J. Appl. Phys. 52(9S2), 09LD13 (2013).
[CrossRef]

Shirley, L. G.

Slinger, C. W.

M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, C. W. Slinger, A. Wood, “3D electronic holography display system using a 100Mega-pixel spatial light modulator,” Proc. SPIE 5249, 297–308 (2004).
[CrossRef]

Smith, A. P.

M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, C. W. Slinger, A. Wood, “3D electronic holography display system using a 100Mega-pixel spatial light modulator,” Proc. SPIE 5249, 297–308 (2004).
[CrossRef]

Smith, M. A.

M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, C. W. Slinger, A. Wood, “3D electronic holography display system using a 100Mega-pixel spatial light modulator,” Proc. SPIE 5249, 297–308 (2004).
[CrossRef]

Stanley, M.

M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, C. W. Slinger, A. Wood, “3D electronic holography display system using a 100Mega-pixel spatial light modulator,” Proc. SPIE 5249, 297–308 (2004).
[CrossRef]

Takabayashi, M.

Tomita, A.

K. Zukeran, A. Okamoto, M. Takabayashi, A. Shibukawa, K. Sato, A. Tomita, “Double-referential holography and spatial quadrature amplitude modulation,” Jpn. J. Appl. Phys. 52(9S2), 09LD13 (2013).
[CrossRef]

A. Okamoto, K. Kunori, M. Takabayashi, A. Tomita, K. Sato, “Holographic diversity interferometry for optical storage,” Opt. Express 19(14), 13436–13444 (2011).
[CrossRef] [PubMed]

Ujhelyi, F.

Upatnieks, J.

Watson, P. J.

M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, C. W. Slinger, A. Wood, “3D electronic holography display system using a 100Mega-pixel spatial light modulator,” Proc. SPIE 5249, 297–308 (2004).
[CrossRef]

Wood, A.

M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, C. W. Slinger, A. Wood, “3D electronic holography display system using a 100Mega-pixel spatial light modulator,” Proc. SPIE 5249, 297–308 (2004).
[CrossRef]

Wyant, J. C.

Yatagai, T.

Zuegel, J. D.

Zukeran, K.

K. Zukeran, A. Okamoto, M. Takabayashi, A. Shibukawa, K. Sato, A. Tomita, “Double-referential holography and spatial quadrature amplitude modulation,” Jpn. J. Appl. Phys. 52(9S2), 09LD13 (2013).
[CrossRef]

Appl. Opt. (6)

IBM J. Res. Develop. (1)

L. B. Lesem, P. M. Hirch, J. A. Jordan., “The kinoform: A new wavefront reconstruction device,” IBM J. Res. Develop. 13(2), 150–155 (1969).
[CrossRef]

J. Opt. Soc. Am. A (1)

Jpn. J. Appl. Phys. (1)

K. Zukeran, A. Okamoto, M. Takabayashi, A. Shibukawa, K. Sato, A. Tomita, “Double-referential holography and spatial quadrature amplitude modulation,” Jpn. J. Appl. Phys. 52(9S2), 09LD13 (2013).
[CrossRef]

Opt. Express (3)

Opt. Lett. (5)

Proc. IEEE (1)

A. V. Oppenheim, J. S. Lim, “The importance of phase in signals,” Proc. IEEE 69(5), 529–541 (1981).
[CrossRef]

Proc. SPIE (2)

M. Stanley, M. A. Smith, A. P. Smith, P. J. Watson, S. D. Coomber, C. D. Cameron, C. W. Slinger, A. Wood, “3D electronic holography display system using a 100Mega-pixel spatial light modulator,” Proc. SPIE 5249, 297–308 (2004).
[CrossRef]

J. M. Florence, R. D. Juday, “Full complex spatial filtering with a phase mostly DMD,” Proc. SPIE 1558, 487–498 (1991).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (15)

Fig. 1
Fig. 1

Conceptual diagrams of spatial cross modulation. (a) Digital encode step in a computer. (b) Optical decode step.

Fig. 2
Fig. 2

Simulation models.

Fig. 3
Fig. 3

Simulation flows.

Fig. 4
Fig. 4

Pixel layouts on SLM plane for each complex modulation. (a) Zero padding rate N0 provides extra area to diffuse the original image. (b) One data pixel consists of Nux × Nuy subpixels (SLM pixels). (c) One data pixel consists of NsNg × NsNg SLM pixels.

Fig. 5
Fig. 5

Example of encoded images displayed on the SLM. These are used for reconstructing the original complex object.

Fig. 6
Fig. 6

Full complex amplitude modulation by spatial cross modulation method. Number of data pixel in used image is 256 × 256 and diffusion ratio by diffuser is 4.0. Note that the number of data pixel is different from that shown in Table 1 just in this case. (a) Original amplitude image; (b) Original phase image; (c) Spatial profile of random diffuser; (d) Diffused amplitude image; (e) Diffused phase image (Cross-modulated image); (f) Reproduced amplitude image; (g) Reproduced phase image.

Fig. 7
Fig. 7

Reconstruction quality vs. diffusion ratio of the random diffuser, Ndiff.

Fig. 8
Fig. 8

Comparison of the achievable spatial resolutions for SCMM and conventional methods. The code rate, on the horizontal axis, is defined as the ratio of the size of original image to the encoded image on the SLM, and is used for evaluating the achievable spatial resolution. For example, in the SCMM, if the phase-only diffusion image is displayed on the SLM in the region being 4 × 4 times larger than the original image, the code rate is 4. As well, in the case of the double-phase hologram, if the number of subpixels Nux × Nuy within one data pixel is 4 × 4, the code rate is 4. In the case of the off-axis amplitude hologram, if the number of SLM pixels NsNg × NsNg within one data pixel is 4 × 4, the code rate is regarded as 4. The size of the square aperture used in the off-axis amplitude hologram and double-phase hologram is optimized to obtain the highest SNR in order for a fair comparison.

Fig. 9
Fig. 9

Comparison of achievable diffraction efficiency of SCMM and conventional methods. The size of the square aperture used in the off-axis amplitude hologram and double-phase hologram is the same as used in Fig. 8.

Fig. 10
Fig. 10

Spatial Fourier spectrum for each complex modulation method. (a) No unwanted diffraction order appears. (b) The zeroth diffraction order corresponds to the desired complex signal. (c) The first diffraction order corresponds to the desired complex signal.

Fig. 11
Fig. 11

Conceptual diagrams of our system with spatial cross modulation introduced in holographic data storage.

Fig. 12
Fig. 12

Experimental setup. Reference 1 is for optical hologram recording/reading. Reference 2 is for the phase detection method. In this experiment, holographic recording/reading is not conducted for simplicity, so the reference 1 is not used in actuality. The SLM used in our experiment is a phase-only LCoS-SLM (Hamamatsu, x10468). The recording medium arranged in the focal plane of L2 is a nanogel photopolymer with thickness of 400µm, provided by Kyoeisha Chemical Co. The phase of the diffusion image propagated from the SLM is detected by a holographic diversity interferometer (HDI) composed of two CCDs.

Fig. 13
Fig. 13

Original SQAM signal used in our experiment. Each pixel in the intensity image randomly takes either of two values, 1 and 0.25. Each pixel in the phase image has either of four values: π/2, π, 3π/2, and 2π. Therefore, a 8-level SQAM is to be used. Each data pixel consists of 16 × 16 SLM pixels.

Fig. 14
Fig. 14

(a) Cross-modulated image displayed on SLM. LCoS-SLM used in our experiment can modulate phase delay of 2π when the gray level is 85. This image was displayed on a region of 512 × 512 SLM pixels. (b) Cross-modulated image measured with holographic diversity interferometer using two CCDs. This image is also detected on a region of 512 × 512 CCD pixels.

Fig. 15
Fig. 15

SQAM signals recovered through digital phase conjugate reconstruction in Fig. 11(c).

Tables (3)

Tables Icon

Table 1 Summarized simulation parameters.

Tables Icon

Table 2 Example of reproduced complex images for each complex modulation methods when code rate is 8.

Tables Icon

Table 3 Experimental results for reconstruction quality vs. diffusion ratio Ndiff.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

θ 1 ( x , y ) = φ ( x , y ) + cos 1 [ A ( x , y ) 2 ] ,
θ 2 ( x , y ) = φ ( x , y ) cos 1 [ A ( x , y ) 2 ] .
I ( x , y ) = I 0 + A ( x , y ) cos [ k x sin θ i n φ ( x , y ) ] ,
N d i f f = θ d i f f + cos 1 ( N d x L d x / 2 L f ) cos 1 ( N d x L d x / 2 L f ) .
t(x,y)=exp[ i 2π λ ( n diff 1 )h( x,y ) ],
S N R ( d B ) = 10 log 1 0 m = 0 N d x 1 n = 0 N d y 1 O ( m L d x , n L d y ) 2 m = 0 N d x 1 n = 0 N d y 1 { O ( m L d x , n L d y ) 2 R ( m L d x , n L d y ) 2 } ,

Metrics