Abstract

We discuss a computer-generated hologram for encoding arbitrary complex modulation based on a commercial twisted-nematic liquid-crystal display. This hologram is implemented with the constrained complex modulation provided by the display in a phase-mostly configuration. The hologram structure and transmittance are determined to obtain on-axis signal reconstruction, maximum bandwidth, optimum efficiency, and high signal-to-noise ratio. We employed the proposed holographic code for the experimental synthesis of first-order Bessel beams.

© 2005 Optical Society of America

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References

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2004 (1)

M. A. Golub, “Laser beam splitting by diffractive optics,” Opt. Photon. News, February2004, pp. 36–41.

2003 (2)

2002 (2)

2001 (1)

2000 (1)

1998 (1)

1997 (2)

L. Legeard, P. Réfrégier, P. Ambs, “Multicriteria optimality for iterative encoding of computer-generated holograms,” Appl. Opt. 36, 7444–7449 (1997).
[CrossRef]

T. Haist, M. Schönleber, H. J. Tiziani, “Computer-generated holograms from 3D-objects written on twisted-nematic liquid crystal displays,” Opt. Commun. 140, 299–308 (1997).
[CrossRef]

1995 (1)

1994 (1)

1991 (1)

1979 (1)

1973 (1)

Ambs, P.

Arrizón, V.

Arrizón, V. M.

R. Ponce, A. Serrano-Heredia, V. M. Arrizón, “Simplified optimum phase-only configuration for a TNLCD,” in Photonic Devices and Algorithms for Computing VI, K. M. Iftekharuddin, A. A. S. Awwal, eds., Proc. SPIE5556, 206–213 (2004).
[CrossRef]

Birch, P. M.

Brauer, R.

Bryngdahl, O.

Bucklew, J.

Budgett, D.

Campos, J.

Chatwin, C.

Cohn, R. W.

Dallas, W. J.

Davis, J. A.

Escalera, J. C.

Gallagher, N. C.

Golub, M. A.

M. A. Golub, “Laser beam splitting by diffractive optics,” Opt. Photon. News, February2004, pp. 36–41.

Haist, T.

T. Haist, M. Schönleber, H. J. Tiziani, “Computer-generated holograms from 3D-objects written on twisted-nematic liquid crystal displays,” Opt. Commun. 140, 299–308 (1997).
[CrossRef]

Iemmi, C.

Ledesma, S.

Legeard, L.

Liang, M.

Mait, J. N.

Márquez, A.

Moreno, I.

Nicolás, J.

Ponce, R.

R. Ponce, A. Serrano-Heredia, V. M. Arrizón, “Simplified optimum phase-only configuration for a TNLCD,” in Photonic Devices and Algorithms for Computing VI, K. M. Iftekharuddin, A. A. S. Awwal, eds., Proc. SPIE5556, 206–213 (2004).
[CrossRef]

Réfrégier, P.

Schönleber, M.

T. Haist, M. Schönleber, H. J. Tiziani, “Computer-generated holograms from 3D-objects written on twisted-nematic liquid crystal displays,” Opt. Commun. 140, 299–308 (1997).
[CrossRef]

Serrano-Heredia, A.

R. Ponce, A. Serrano-Heredia, V. M. Arrizón, “Simplified optimum phase-only configuration for a TNLCD,” in Photonic Devices and Algorithms for Computing VI, K. M. Iftekharuddin, A. A. S. Awwal, eds., Proc. SPIE5556, 206–213 (2004).
[CrossRef]

Tiziani, H. J.

T. Haist, M. Schönleber, H. J. Tiziani, “Computer-generated holograms from 3D-objects written on twisted-nematic liquid crystal displays,” Opt. Commun. 140, 299–308 (1997).
[CrossRef]

Tsai, P.

Wyrowski, F.

Young, R.

Yzuel, M. J.

Appl. Opt. (7)

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

Opt. Commun. (1)

T. Haist, M. Schönleber, H. J. Tiziani, “Computer-generated holograms from 3D-objects written on twisted-nematic liquid crystal displays,” Opt. Commun. 140, 299–308 (1997).
[CrossRef]

Opt. Lett. (4)

Opt. Photon. News (1)

M. A. Golub, “Laser beam splitting by diffractive optics,” Opt. Photon. News, February2004, pp. 36–41.

Other (2)

Iterative methods for designing phase diffractive elements (or CGHs) whose purpose is to generate a signal field with a prespecified intensity distribution (while the phase is considered as a free parameter for design) have been widely discussed during the past two decades. Samples of such research can be found in Refs. 12–15.

R. Ponce, A. Serrano-Heredia, V. M. Arrizón, “Simplified optimum phase-only configuration for a TNLCD,” in Photonic Devices and Algorithms for Computing VI, K. M. Iftekharuddin, A. A. S. Awwal, eds., Proc. SPIE5556, 206–213 (2004).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Phase-mostly configuration based on a TNLCD employing (a) two retardation plates and (b) a single retardation plate.

Fig. 2
Fig. 2

Experimental phase-mostly configuration employing a single retardation plate with (a) normalized amplitude modulation and (b) phase modulation.

Fig. 3
Fig. 3

SLM modulation polar plot displaying the amplitude (radial coordinate) versus the phase (azimuthal coordinate).

Fig. 4
Fig. 4

Distribution of the main noise bands in the CGH Fourier domain.

Fig. 5
Fig. 5

Two possible definitions for vectors Mnm1 and Mnm2: (a) Mnm1 appears at the right position (and is redefined as MnmR) and (b) Mnm1 appears at the left position (and is redefined as MnmL). (c) Position of vectors MnmR and MnmL.

Fig. 6
Fig. 6

Distribution of vectors MnmR and MnmL for the top region Ω1 (with rnm ≥ 0) and the bottom region Ω2 (with rnm < 0) of a CGH.

Fig. 7
Fig. 7

Performance of the CGH designed for the synthesis of two central rings of a first-order Bessel field AJ1(2πρ0r)exp(iθ)circ(r/R) (numerical evaluation). Modulation of the encoded complex field appears at column 1; modulation of the CGH and the reconstructed field appear, respectively, at columns 2 and 3. Intensity modulation [(a)–(c)] appears at row 1 and phase modulation [(d)–(f)] at row 2.

Fig. 8
Fig. 8

Fourier spectrum of the CGH in Fig. 7.

Fig. 9
Fig. 9

Performance of the CGH designed for the synthesis of two central rings of the enhanced first-order Bessel field A r J 1 ( 2 π ρ 0 r ) exp ( i θ ) circ ( r / R ) (numerical evaluation). Modulation of the encoded complex field appears at column 1; modulation of the CGH and the reconstructed field appear, respectively, at columns 2 and 3. Intensity modulation [(a)–(c)] appears at row 1 and phase modulation [(d)–(f)] at row 2.

Fig. 10
Fig. 10

Experimental intensity distribution of the field generated with the CGH in Fig. 7 (a) at 5 cm and (b) at 90 cm from the second transforming lens of the 4-f spatial filtering setup.

Fig. 11
Fig. 11

Experimental intensity distribution of the field generated with the CGH in Fig. 9 (a) at 5 cm and (b) at 90 cm from the second transforming lens of the 4-f spatial filtering setup.

Equations (30)

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M g = M g exp ( i θ g ) ,
h ( x , y ) = n , m M n m w ( x - n p , y - m q ) ,
c ( x , y ) = n , m c n m w ( x - n p , y - m q ) ,
h ( x , y ) = A 0 c ( x , y ) + e ( x , y ) ,
e ( x , y ) = b ( x , y ) g ( x , y ) ,
b ( x , y ) = n , m b n m w ( x - n p , y - m q ) ,
g ( x , y ) = n , m g n m w ( x - n p , y - m q ) ,
b n m = ( - 1 ) n + m .
M n m = A 0 c n m + ( - 1 ) n + m g n m .
M n m = A 0 c n m + g n m .
M m m 1 = A 0 c n m + g n m ,
M n m 2 = A 0 c n m - g n m ,
A 0 c n m = ( M n m 1 + M n m 2 ) / 2.
g n m = ( M n m 1 - M n m 2 ) / 2.
A 0 c n m = ( M n m R + M n m L ) / 2 ,
g n m = d n m ( M n m R - M n m L ) / 2 ,
M n m = { M n m R if ( - 1 ) n + m d n m = 1 M n m L if ( - 1 ) n + m d n m = - 1 .
g n m = ( M n m R - M n m L ) / 2 ,
M nm = { M n m R ( n + m ) even M n m L ( n + m ) odd .
c n m = r n m exp ( i ϕ n m 0 ) ,
d n m = { 1 if r n m 0 - 1 if r n m < 0 .
η = A 0 2 s c ( x , y ) 2 d x d y s h ( x , y ) 2 d x d y ,
SNR = s c ( x , y ) 2 d x d y s c ( x , y ) - α 0 c t ( x , t ) 2 d x d y ,
α 0 = s c ( x , y ) 2 d x d y s c t ( x , y ) 2 d x d y .
B ( r , θ ) = A J 1 ( 2 π ρ 0 r ) exp ( i θ ) circ ( r / R ) ,
B e ( r , θ ) = A r J 1 ( 2 π ρ 0 r ) exp ( i θ ) circ ( r / R ) ,
ϕ n m R { ϕ n m 0 - arccos ( c n m ) r n m 0 ϕ n m 0 + π - arccos ( c n m ) r n m < 0 ,
ϕ n m L { ϕ n m 0 + arccos ( c n m ) r n m 0 ϕ n m 0 + π + arccos ( c n m ) r n m < 0 .
g i j = ( M i j R - M i j L ) / 2 ,
g q l d q l ( M i j L - M i j R ) / 2.

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