Abstract

We discuss an optical system that encodes an input signal to a polarization state, using a spatial light modulator (SLM). Using two SLMs the optical system multiplexes two 2D signals in the polarization domain, and we demonstrate the multiplexing of two binary images. The encryption and decryption of two binary images using an xor operation is also presented.

© 2006 Optical Society of America

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  1. R. Simon and N. Mukunda, "Minimal three-component SU(2) gadget for polarization optics," Phys. Lett. A 143, 165-169 (1990).
    [CrossRef]
  2. V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. S. Spagnolo, "The Simon-Mukunda polarization gadget," Eur. J. Phys. 17, 279-284 (1996).
    [CrossRef]
  3. J. A. Davis, D. E. McNamara, D. M. Cottrell, and T. Sonehara, "Two-dimensional polarization encoding with a phase-only liquid-crystal spatial light modulator," Appl. Opt. 39, 1549-1554 (2000).
    [CrossRef]
  4. Z. Zhuang, S.-W. Suh, and J. S. Patel, "Polarization controller using nematic liquid crystals," Opt. Lett. 24, 694-696 (1999).
    [CrossRef]
  5. R. L. Eriksen, P. C. Mogenson, and J. Glückstad, "Elliptical polarization encoding in two dimensions using phase only spatial light modulator," Opt. Commun. 187, 325-336 (2001).
    [CrossRef]
  6. K. Kawano, T. Ishii, J. Minabe, T. Niitsu, Y. Nishikata, and K. Baba, "Holographic recording and retrieval of polarized light by use of polyester containing cyanoazobenzene units in the side chain," Opt. Lett. 24, 1269-1271 (1999).
    [CrossRef]
  7. G. Unnikrishnan, M. Pohit, and K. Singh, "A polarization encoded optical encryption system using ferroelectric spatial light modulator," Opt. Commun. 185, 25-31 (2000).
    [CrossRef]
  8. X. Tan, O. Matoba, Y. Okada-Shudo, M. Ide, T. Shimuda, and K. Kuroda, "Secure optical memory system with polarization encryption," Appl. Opt. 40, 2310-2315 (2001).
    [CrossRef]
  9. O. Matoba and B. Javidi, "Secure holographic memory by double-random polarization encryption," Appl. Opt. 43, 2915-2919 (2004).
    [CrossRef] [PubMed]
  10. B. Hennelly and J. T. Sheridan, "Optical image encryption by random shifting in fractional Fourier domains," Opt. Lett. 28, 269-271 (2003).
    [CrossRef] [PubMed]
  11. P. C. Mogenson and J. Glückstad, "A phase based optical encryption system with polarization encoding," Opt. Commun. 173, 177-183 (2000).
    [CrossRef]
  12. C.-J. Cheng and M.-L. Chen, "Polarization encoding for optical encryption using twisted nematic liquid crystal spatial light modulator," Opt. Commun. 237, 45-52 (2004).
    [CrossRef]
  13. F. T. S. Yu, S. Jutamulia, and D. A. Gregory, "Real-time liquid crystal TV XOR and XNOR gate binary image subtraction technique," Appl. Opt. 26, 2738-2742 (1987).
    [CrossRef] [PubMed]
  14. J. Nicolás, J. Campos, and M. J. Yzuel, "Phase and amplitude modulation of elliptic polarization states by nonabsorbing anisotropic elements: application to liquid-crystal devices," J. Opt. Soc. Am. A. 19, 1013-1020 (2002).
    [CrossRef]
  15. Information may be retrieved at http://www.holoeye.com.
  16. Information may be retrieved at http://www.imperx.com.
  17. W. A. Shurcliff, Polarized Light Production and Use (Harvard U. Press, 1962).
  18. D. J. Jackson and M. L. Juncosa, "Error analysis of high data rate, optical parallel processors," Appl. Opt. 40, 2253-2266 (2001).
    [CrossRef]
  19. R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification (Wiley, 2001).
  20. H. Demuth and M. Beale, Neural Network Toolbox, User's Guide Version 4; information may be retrieved at www.mathworks.com.
  21. G. Woods, Digital Image Processing (Prentice-Hall, 2003).

2004 (2)

O. Matoba and B. Javidi, "Secure holographic memory by double-random polarization encryption," Appl. Opt. 43, 2915-2919 (2004).
[CrossRef] [PubMed]

C.-J. Cheng and M.-L. Chen, "Polarization encoding for optical encryption using twisted nematic liquid crystal spatial light modulator," Opt. Commun. 237, 45-52 (2004).
[CrossRef]

2003 (1)

2002 (1)

J. Nicolás, J. Campos, and M. J. Yzuel, "Phase and amplitude modulation of elliptic polarization states by nonabsorbing anisotropic elements: application to liquid-crystal devices," J. Opt. Soc. Am. A. 19, 1013-1020 (2002).
[CrossRef]

2001 (3)

2000 (3)

G. Unnikrishnan, M. Pohit, and K. Singh, "A polarization encoded optical encryption system using ferroelectric spatial light modulator," Opt. Commun. 185, 25-31 (2000).
[CrossRef]

J. A. Davis, D. E. McNamara, D. M. Cottrell, and T. Sonehara, "Two-dimensional polarization encoding with a phase-only liquid-crystal spatial light modulator," Appl. Opt. 39, 1549-1554 (2000).
[CrossRef]

P. C. Mogenson and J. Glückstad, "A phase based optical encryption system with polarization encoding," Opt. Commun. 173, 177-183 (2000).
[CrossRef]

1999 (2)

1996 (1)

V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. S. Spagnolo, "The Simon-Mukunda polarization gadget," Eur. J. Phys. 17, 279-284 (1996).
[CrossRef]

1990 (1)

R. Simon and N. Mukunda, "Minimal three-component SU(2) gadget for polarization optics," Phys. Lett. A 143, 165-169 (1990).
[CrossRef]

1987 (1)

Baba, K.

Bagini, V.

V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. S. Spagnolo, "The Simon-Mukunda polarization gadget," Eur. J. Phys. 17, 279-284 (1996).
[CrossRef]

Beale, M.

H. Demuth and M. Beale, Neural Network Toolbox, User's Guide Version 4; information may be retrieved at www.mathworks.com.

Borghi, R.

V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. S. Spagnolo, "The Simon-Mukunda polarization gadget," Eur. J. Phys. 17, 279-284 (1996).
[CrossRef]

Campos, J.

J. Nicolás, J. Campos, and M. J. Yzuel, "Phase and amplitude modulation of elliptic polarization states by nonabsorbing anisotropic elements: application to liquid-crystal devices," J. Opt. Soc. Am. A. 19, 1013-1020 (2002).
[CrossRef]

Chen, M.-L.

C.-J. Cheng and M.-L. Chen, "Polarization encoding for optical encryption using twisted nematic liquid crystal spatial light modulator," Opt. Commun. 237, 45-52 (2004).
[CrossRef]

Cheng, C.-J.

C.-J. Cheng and M.-L. Chen, "Polarization encoding for optical encryption using twisted nematic liquid crystal spatial light modulator," Opt. Commun. 237, 45-52 (2004).
[CrossRef]

Cottrell, D. M.

Davis, J. A.

Demuth, H.

H. Demuth and M. Beale, Neural Network Toolbox, User's Guide Version 4; information may be retrieved at www.mathworks.com.

Duda, R. O.

R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification (Wiley, 2001).

Eriksen, R. L.

R. L. Eriksen, P. C. Mogenson, and J. Glückstad, "Elliptical polarization encoding in two dimensions using phase only spatial light modulator," Opt. Commun. 187, 325-336 (2001).
[CrossRef]

Frezza, F.

V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. S. Spagnolo, "The Simon-Mukunda polarization gadget," Eur. J. Phys. 17, 279-284 (1996).
[CrossRef]

Glückstad, J.

R. L. Eriksen, P. C. Mogenson, and J. Glückstad, "Elliptical polarization encoding in two dimensions using phase only spatial light modulator," Opt. Commun. 187, 325-336 (2001).
[CrossRef]

P. C. Mogenson and J. Glückstad, "A phase based optical encryption system with polarization encoding," Opt. Commun. 173, 177-183 (2000).
[CrossRef]

Gori, F.

V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. S. Spagnolo, "The Simon-Mukunda polarization gadget," Eur. J. Phys. 17, 279-284 (1996).
[CrossRef]

Gregory, D. A.

Hart, P. E.

R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification (Wiley, 2001).

Hennelly, B.

Ide, M.

Ishii, T.

Jackson, D. J.

Javidi, B.

Juncosa, M. L.

Jutamulia, S.

Kawano, K.

Kuroda, K.

Matoba, O.

McNamara, D. E.

Minabe, J.

Mogenson, P. C.

R. L. Eriksen, P. C. Mogenson, and J. Glückstad, "Elliptical polarization encoding in two dimensions using phase only spatial light modulator," Opt. Commun. 187, 325-336 (2001).
[CrossRef]

P. C. Mogenson and J. Glückstad, "A phase based optical encryption system with polarization encoding," Opt. Commun. 173, 177-183 (2000).
[CrossRef]

Mukunda, N.

R. Simon and N. Mukunda, "Minimal three-component SU(2) gadget for polarization optics," Phys. Lett. A 143, 165-169 (1990).
[CrossRef]

Nicolás, J.

J. Nicolás, J. Campos, and M. J. Yzuel, "Phase and amplitude modulation of elliptic polarization states by nonabsorbing anisotropic elements: application to liquid-crystal devices," J. Opt. Soc. Am. A. 19, 1013-1020 (2002).
[CrossRef]

Niitsu, T.

Nishikata, Y.

Okada-Shudo, Y.

Patel, J. S.

Pohit, M.

G. Unnikrishnan, M. Pohit, and K. Singh, "A polarization encoded optical encryption system using ferroelectric spatial light modulator," Opt. Commun. 185, 25-31 (2000).
[CrossRef]

Santarsiero, M.

V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. S. Spagnolo, "The Simon-Mukunda polarization gadget," Eur. J. Phys. 17, 279-284 (1996).
[CrossRef]

Schettini, G.

V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. S. Spagnolo, "The Simon-Mukunda polarization gadget," Eur. J. Phys. 17, 279-284 (1996).
[CrossRef]

Sheridan, J. T.

Shimuda, T.

Shurcliff, W. A.

W. A. Shurcliff, Polarized Light Production and Use (Harvard U. Press, 1962).

Simon, R.

R. Simon and N. Mukunda, "Minimal three-component SU(2) gadget for polarization optics," Phys. Lett. A 143, 165-169 (1990).
[CrossRef]

Singh, K.

G. Unnikrishnan, M. Pohit, and K. Singh, "A polarization encoded optical encryption system using ferroelectric spatial light modulator," Opt. Commun. 185, 25-31 (2000).
[CrossRef]

Sonehara, T.

Spagnolo, G. S.

V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. S. Spagnolo, "The Simon-Mukunda polarization gadget," Eur. J. Phys. 17, 279-284 (1996).
[CrossRef]

Stork, D. G.

R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification (Wiley, 2001).

Suh, S.-W.

Tan, X.

Unnikrishnan, G.

G. Unnikrishnan, M. Pohit, and K. Singh, "A polarization encoded optical encryption system using ferroelectric spatial light modulator," Opt. Commun. 185, 25-31 (2000).
[CrossRef]

Woods, G.

G. Woods, Digital Image Processing (Prentice-Hall, 2003).

Yu, F. T. S.

Yzuel, M. J.

J. Nicolás, J. Campos, and M. J. Yzuel, "Phase and amplitude modulation of elliptic polarization states by nonabsorbing anisotropic elements: application to liquid-crystal devices," J. Opt. Soc. Am. A. 19, 1013-1020 (2002).
[CrossRef]

Zhuang, Z.

Appl. Opt. (5)

Eur. J. Phys. (1)

V. Bagini, R. Borghi, F. Gori, M. Santarsiero, F. Frezza, G. Schettini, and G. S. Spagnolo, "The Simon-Mukunda polarization gadget," Eur. J. Phys. 17, 279-284 (1996).
[CrossRef]

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

J. Nicolás, J. Campos, and M. J. Yzuel, "Phase and amplitude modulation of elliptic polarization states by nonabsorbing anisotropic elements: application to liquid-crystal devices," J. Opt. Soc. Am. A. 19, 1013-1020 (2002).
[CrossRef]

Opt. Commun. (4)

R. L. Eriksen, P. C. Mogenson, and J. Glückstad, "Elliptical polarization encoding in two dimensions using phase only spatial light modulator," Opt. Commun. 187, 325-336 (2001).
[CrossRef]

P. C. Mogenson and J. Glückstad, "A phase based optical encryption system with polarization encoding," Opt. Commun. 173, 177-183 (2000).
[CrossRef]

C.-J. Cheng and M.-L. Chen, "Polarization encoding for optical encryption using twisted nematic liquid crystal spatial light modulator," Opt. Commun. 237, 45-52 (2004).
[CrossRef]

G. Unnikrishnan, M. Pohit, and K. Singh, "A polarization encoded optical encryption system using ferroelectric spatial light modulator," Opt. Commun. 185, 25-31 (2000).
[CrossRef]

Opt. Lett. (3)

Phys. Lett. A (1)

R. Simon and N. Mukunda, "Minimal three-component SU(2) gadget for polarization optics," Phys. Lett. A 143, 165-169 (1990).
[CrossRef]

Other (6)

Information may be retrieved at http://www.holoeye.com.

Information may be retrieved at http://www.imperx.com.

W. A. Shurcliff, Polarized Light Production and Use (Harvard U. Press, 1962).

R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification (Wiley, 2001).

H. Demuth and M. Beale, Neural Network Toolbox, User's Guide Version 4; information may be retrieved at www.mathworks.com.

G. Woods, Digital Image Processing (Prentice-Hall, 2003).

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Figures (12)

Fig. 1
Fig. 1

(a) Schematic of an optical system that encodes a signal in the polarization domain. (b) Transformations performed by the optical system. (c) Functional diagram of the optical system.

Fig. 2
Fig. 2

(a) Schematic of an optical system that multiplexes two signals in the polarization domain. (b) Transformations performed by the optical system. (c) Functional diagram of the optical system.

Fig. 3
Fig. 3

Transformations for (a) a multiplexing operation and (b) an xor operation when the two input signals are binary.

Fig. 4
Fig. 4

Optical system used for experiments. NDF, neutral density filter; BE, beam expander; CL, collimating lens; P1, polarizer; P2, analyzer; L1, L2, lens focal length 15 cm; SF, spatial filter; QWP, quarter-wave plate at 532 nm. The analyzer P2 and CCD are used to measure the polarization states.

Fig. 5
Fig. 5

(a) Representation of a polarization state with azimuth ψ and θ on a Poincaré sphere. (b) Relation between (ψ, θ) and the elliptical parameters α (azimuth) and ϵ (ellipticity angle).

Fig. 6
Fig. 6

(a) and (b) Two input signals and (c) the multiplexed output signal from the optical system. Each of the four gray levels in (c) represents a polarization state.

Fig. 7
Fig. 7

(Color online) Histogram of angle (θ) and azimuth (ψ) of the four polarization states for 250 × 250 measurements. The x axis of each subfigure denotes θ and ψ and is plotted in degrees and the y axis denotes the number of pixels.

Fig. 8
Fig. 8

(Color online) Two-dimensional histogram of 250 × 250 measurements of the four polarization states. Angle (θ) and azimuth (ψ) of the polarization states are plotted on the x and y axes. The mean values of θ and ψ for the four states are indicated.

Fig. 9
Fig. 9

(a) and (b) Two input signals. (c) Multiplexed output signal from the optical system. Each gray level in (c) represents a polarization state.

Fig. 10
Fig. 10

(a) and (b) Two input signals. (c) The multiplexed output signal from the optical system. Each gray level in (c) represents a polarization state.

Fig. 11
Fig. 11

(a) xor of the signals shown in Figs. 9(a) and 9(b). (b) Decoded signal in Fig. 9(a) with the knowledge of Fig. 9(b). (c) Decoded signal after applying a median filter of window size 7 × 7. (d) Pixels that are in error in (c).

Fig. 12
Fig. 12

(a) xor of the signals shown in Figs. 10(a) and 10(b). (b) Decoded signal in Fig. 10(a) with the knowledge of Fig. 10(b). (c) Decoded signal after applying a median filter of window size 7 × 7. (d) Pixels that are in error in (c).

Tables (1)

Tables Icon

Table 1 Mean and Variance for the Four Polarization States (in Degrees)

Equations (16)

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g = T g { s i } , s i S i , g G ,
p o = M SLM g M PE p , p P , p o P ,
p o = T p { s i } , s i S i , p o P .
g ^ = T ^ g { s ^ i } , s ^ i S i , g ^  ∈  G .
p ^ o = M ^ SLM g ̂ M ^ PE p ^ , p ^ P , p ^ o P .
p ^ o = T ^ p o { s ^ i } , s ^ i S i , p ^ o P .
p ^ o = T { s } , s S i × S i , p ^ o P .
s o = T o { p ^ o } , s o S o , p ^ o P ,
s o = s i s ^ i .
[ I cos ψ I sin ψ e i θ ]
I ϕ = I ( cos 2 ϕ cos 2 ψ + sin 2 ϕ sin 2 ψ + sin 2 ϕ sin 2 ψ cos θ 2 ) .
I 0 = I cos 2 ψ , I π / 2 = I sin 2 ψ ,
I π / 4 = 1 2 ( 1 + sin 2 ψ cos θ ) .
ψ = 1 2 cos 1 ( 2 I 0 I I ) , θ = cos 1 ( 2 I π / 4 I I sin 2 ψ ) .
I π / 4 = 1 2 ( 1 sin 2 ψ sin θ ) .
SNR = 1 L j = 1 i 1 i = 2 k d ( μ ψ , θ i , μ ψ , θ j ) i = 1 k v ψ , θ i .

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