Abstract

In this paper we propose a method to generate independent and simultaneous phase and amplitude modulation by a phase-only spatial light modulator and Fourier filtering. The incident light is modulated by a suitable phase pattern containing high spatial frequencies. The modulated light is transmitted through a 4f optical system having an appropriate spatial filter in the Fourier plane in order to synthesize the expected complex modulated wavefront on the output of the system. We propose a simple method to generate spatial filters applicable for the phase-only to complex modulated wavefront conversion. We analyze the quality of the output image related to the ideal wavefront using the proposed filters. We show that more efficient complex modulation can be realized by the proposed method than by the earlier solutions.

© 2013 Optical Society of America

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  1. C. Liu and M. K. Kim, “Digital holographic adaptive optics for ocular imaging: proof of principle,” Opt. Lett. 36, 2710–2712 (2011).
    [CrossRef]
  2. K. Jahn and N. Bokor, “Vector Slepian basis functions with optimal energy concentration in high numerical aperture focusing,” Opt. Commun. 285, 2028–2038 (2012).
    [CrossRef]
  3. T. Sarkadi and P. Koppa, “Quantitative security evaluation of optical encryption using hybrid phase- and amplitude-modulated keys,” Appl. Opt. 51, 745–750 (2012).
    [CrossRef]
  4. L. G. Neto, D. Roberge, and Y. Sheng, “Full-range, continuous, complex modulation by the use of two coupled-mode liquid-crystal televisions,” Appl. Opt. 35, 4567–4576 (1996).
    [CrossRef]
  5. D. A. Gregory, J. C. Kirsch, and E. C. Tam, “Full complex modulation using liquid-crystal televisions,” Appl. Opt. 31, 163–165 (1992).
    [CrossRef]
  6. S. Reichelt, R. Häussler, G. Fütterer, N. Leister, H. Kato, N. Usukura, and Y. Kanbayashi, “Full-range, complex spatial light modulator for real-time holography,” Opt. Lett. 37, 1955–1957 (2012).
    [CrossRef]
  7. R. W. Cohn and M. Liang, “Approximating fully complex spatial modulation with pseudorandom phase-only modulation,” Appl. Opt. 33, 4406–4415 (1994).
    [CrossRef]
  8. P. Birch, R. Young, D. Budgett, and C. Chatwin, “Dynamic complex wave-front modulation with an analog spatial light modulator,” Opt. Lett. 26, 920–922 (2001).
    [CrossRef]
  9. J. M. Florence and 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, and E. Lőrincz, “Hybrid multinary modulation using a phase modulating spatial light modulator and a low-pass spatial filter,” Opt. Lett. 32, 2336–2338 (2007).
    [CrossRef]
  11. B. Das, J. Joseph, and K. Singh, “Phase-image-based sparse-gray-level data pages for holographic data storage,” Appl. Opt. 48, 5240–5250 (2009).
    [CrossRef]
  12. B. Das, S. Vyas, J. Joseph, P. Senthilkumaran, and K. Singh, “Transmission type twisted nematic liquid crystal display for three gray-level phase-modulated holographic data storage systems,” Opt. Lasers Eng. 47, 1150–1159 (2009).
    [CrossRef]
  13. K. Curtis, L. Dhar, A. Hill, W. Wilson, and M. Ayres, Holographic Data Storage: From Theory to Practical Systems (Wiley, 2010).

2012

2011

2009

B. Das, J. Joseph, and K. Singh, “Phase-image-based sparse-gray-level data pages for holographic data storage,” Appl. Opt. 48, 5240–5250 (2009).
[CrossRef]

B. Das, S. Vyas, J. Joseph, P. Senthilkumaran, and K. Singh, “Transmission type twisted nematic liquid crystal display for three gray-level phase-modulated holographic data storage systems,” Opt. Lasers Eng. 47, 1150–1159 (2009).
[CrossRef]

2007

2001

1996

1994

1992

1991

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

Ayres, M.

K. Curtis, L. Dhar, A. Hill, W. Wilson, and M. Ayres, Holographic Data Storage: From Theory to Practical Systems (Wiley, 2010).

Birch, P.

Bokor, N.

K. Jahn and N. Bokor, “Vector Slepian basis functions with optimal energy concentration in high numerical aperture focusing,” Opt. Commun. 285, 2028–2038 (2012).
[CrossRef]

Budgett, D.

Chatwin, C.

Cohn, R. W.

Curtis, K.

K. Curtis, L. Dhar, A. Hill, W. Wilson, and M. Ayres, Holographic Data Storage: From Theory to Practical Systems (Wiley, 2010).

Das, B.

B. Das, S. Vyas, J. Joseph, P. Senthilkumaran, and K. Singh, “Transmission type twisted nematic liquid crystal display for three gray-level phase-modulated holographic data storage systems,” Opt. Lasers Eng. 47, 1150–1159 (2009).
[CrossRef]

B. Das, J. Joseph, and K. Singh, “Phase-image-based sparse-gray-level data pages for holographic data storage,” Appl. Opt. 48, 5240–5250 (2009).
[CrossRef]

Dhar, L.

K. Curtis, L. Dhar, A. Hill, W. Wilson, and M. Ayres, Holographic Data Storage: From Theory to Practical Systems (Wiley, 2010).

Erdei, G.

Florence, J. M.

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

Fütterer, G.

Göröcs, Z.

Gregory, D. A.

Häussler, R.

Hill, A.

K. Curtis, L. Dhar, A. Hill, W. Wilson, and M. Ayres, Holographic Data Storage: From Theory to Practical Systems (Wiley, 2010).

Jahn, K.

K. Jahn and N. Bokor, “Vector Slepian basis functions with optimal energy concentration in high numerical aperture focusing,” Opt. Commun. 285, 2028–2038 (2012).
[CrossRef]

Joseph, J.

B. Das, S. Vyas, J. Joseph, P. Senthilkumaran, and K. Singh, “Transmission type twisted nematic liquid crystal display for three gray-level phase-modulated holographic data storage systems,” Opt. Lasers Eng. 47, 1150–1159 (2009).
[CrossRef]

B. Das, J. Joseph, and K. Singh, “Phase-image-based sparse-gray-level data pages for holographic data storage,” Appl. Opt. 48, 5240–5250 (2009).
[CrossRef]

Juday, R. D.

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

Kanbayashi, Y.

Kato, H.

Kim, M. K.

Kirsch, J. C.

Koppa, P.

Leister, N.

Liang, M.

Liu, C.

Lorincz, E.

Neto, L. G.

Reichelt, S.

Reményi, J.

Roberge, D.

Sarkadi, T.

Senthilkumaran, P.

B. Das, S. Vyas, J. Joseph, P. Senthilkumaran, and K. Singh, “Transmission type twisted nematic liquid crystal display for three gray-level phase-modulated holographic data storage systems,” Opt. Lasers Eng. 47, 1150–1159 (2009).
[CrossRef]

Sheng, Y.

Singh, K.

B. Das, J. Joseph, and K. Singh, “Phase-image-based sparse-gray-level data pages for holographic data storage,” Appl. Opt. 48, 5240–5250 (2009).
[CrossRef]

B. Das, S. Vyas, J. Joseph, P. Senthilkumaran, and K. Singh, “Transmission type twisted nematic liquid crystal display for three gray-level phase-modulated holographic data storage systems,” Opt. Lasers Eng. 47, 1150–1159 (2009).
[CrossRef]

Tam, E. C.

Ujhelyi, F.

Usukura, N.

Vyas, S.

B. Das, S. Vyas, J. Joseph, P. Senthilkumaran, and K. Singh, “Transmission type twisted nematic liquid crystal display for three gray-level phase-modulated holographic data storage systems,” Opt. Lasers Eng. 47, 1150–1159 (2009).
[CrossRef]

Wilson, W.

K. Curtis, L. Dhar, A. Hill, W. Wilson, and M. Ayres, Holographic Data Storage: From Theory to Practical Systems (Wiley, 2010).

Young, R.

Appl. Opt.

Opt. Commun.

K. Jahn and N. Bokor, “Vector Slepian basis functions with optimal energy concentration in high numerical aperture focusing,” Opt. Commun. 285, 2028–2038 (2012).
[CrossRef]

Opt. Lasers Eng.

B. Das, S. Vyas, J. Joseph, P. Senthilkumaran, and K. Singh, “Transmission type twisted nematic liquid crystal display for three gray-level phase-modulated holographic data storage systems,” Opt. Lasers Eng. 47, 1150–1159 (2009).
[CrossRef]

Opt. Lett.

Proc. SPIE

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

Other

K. Curtis, L. Dhar, A. Hill, W. Wilson, and M. Ayres, Holographic Data Storage: From Theory to Practical Systems (Wiley, 2010).

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Figures (7)

Fig. 1.
Fig. 1.

Schematic of the 4f optical system. P(x,y), phase-only modulation pattern; F, Fourier lenses; SF(u,v), spatial filter; O(x,y), complex modulated output wavefront.

Fig. 2.
Fig. 2.

(a) Intensity distribution of the complex modulated data page, (b) phase distribution of the input phase modulator, (c) Fourier spectrum of the complex modulated data page, and (d) Fourier spectrum of the input phase distribution.

Fig. 3.
Fig. 3.

Transmittance distribution of the proposed spatial filter at different N subpixel array sizes: (a) N=2, (b) N=3, (c) N=4, and (d) N=5. The zero spatial frequency corresponds to the center of each image.

Fig. 4.
Fig. 4.

(a) Amplitude and (b) phase distribution of the complex modulated wavefront we would like to generate by the 4f system; (c) amplitude and (d) phase distribution of the output wavefront in the case where the proposed filter is not used (Nyquist aperture radius r=1); (e) amplitude and (f) phase distribution of the output wavefront in the case where the proposed filter is not used (Nyquist aperture radius r=4); (g) amplitude and (h) phase distribution of the output wavefront in the case where the proposed filter is applied (Nyquist aperture radius r=4).

Fig. 5.
Fig. 5.

Absolute error of the output wavefronts presented in Fig. 4 as a function of the position: error of the wavefront presented in Figs. 4(c) and 4(d) (solid gray curve), error of the wavefront presented in Figs. 4(e) and 4(f) (dotted gray curve), and error of the wavefront presented in Figs. 4(g) and 4(h) (black curve).

Fig. 6.
Fig. 6.

Correlation coefficient between the output wavefront and the expected data page as a function of the Nyquist aperture at N=2, 3, 4, and 5 subpixel array sizes. Dashed curves, circular low pass filters in the Fourier field; dotted curve, theoretical maximum of the correlation; solid curves, proposed filters in the Fourier field.

Fig. 7.
Fig. 7.

(a) Correlation coefficient κCO as a function of the lateral shift of the filter related to the ideal position at different subpixel array sizes N. The shift is measured in Nyquist aperture units. (b) The correlation coefficient as a function of the transmittance deviation of the filter. The transmittance deviation is characterized by the root mean square error related to the ideal transmittance distribution. The applied Nyquist aperture is r=4.

Equations (4)

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SF(u,v)=j|I(C(x,yj)|2j|I(P(x,yj)|2,
O(u,v)=I1(NA(u,v)·SF(u,v)I(P(x,y))),
NA(u,v)={1u2+v2r21u2+v2>r2,
κCO=|E((C(x,y)E(C(x,y)))(O(x,y)E(O(x,y))))σCσO|,

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