Abstract

A novel implementation of a real-time digital holographic system with a genetic feedback tuning loop is proposed. The proposed genetic feedback tuning loop is effective in encoding optimal phase holograms on a liquid-crystal spatial light modulator in the system. Optimal calibration of the liquid-crystal spatial light modulator can be achieved via the genetic feedback tuning loop, and the optimal phase hologram can then overcome the aberration of the internal optics of the system.

© 2006 Optical Society of America

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References

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  1. J. Tarunen and F. Wyrowski, Diffractive Optics for Industrial and Commercial Applications (Wiley, 1997).
  2. B. Kress and P. Meyrueis, Digital Diffractive Optics: An Introduction to Planar Diffractive Optics and Related Technology (Wiley, 2000).
  3. V. A. Soifer, V. V. Kotlyar, and L. Doskolovich, Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis, 1997).
  4. K. Choi and B. Lee, "A single-stage reconfigurable 2-D optical perfect-shuffle network system using multiplexed phase holograms," IEEE Photon. Technol. Lett. 17, 687-689 (2005).
    [CrossRef]
  5. K. Choi, H. Kim, and B. Lee, "Full-color autostereoscopic 3D display system using color-dispersion-compensated synthetic phase holograms," Opt. Express 12, 5229-5236 (2004).
    [CrossRef] [PubMed]
  6. K. Choi, H. Kim, and B. Lee, "Synthetic phase holograms for auto-stereoscopic image display using a modified IFTA," Opt. Express 12, 2454-2462 (2004).
    [CrossRef] [PubMed]
  7. H. Kim and B. Lee, "Optimal nonmonotonic convergence of the iterative Fourier-transform algorithm," Opt. Lett. 30, 296-298 (2005).
    [CrossRef] [PubMed]
  8. H. Kim, B. Yang, and B. Lee, "Iterative Fourier transform algorithm with regularization for the optimal design of diffractive optical elements," J. Opt. Soc. Am. A 12, 2353-2365 (2004).
    [CrossRef]
  9. L. Hu, L. Xuan, Y. Liu, Z. Cao, D. Li, and Q. Mu, "Phase-only liquid-crystal spatial light modulator for wave-front correction with high precision," Opt. Express 12, 6403-6409 (2004).
    [CrossRef] [PubMed]
  10. Z. Michalewicz, Genetic Algorithms + Data Structures =Evolution Programs (Springer-Verlag, 1999).
  11. H. Kim and B. Lee, "Calculation of the transmittance function of a multilevel diffractive optical element considering multiple internal reflections," Opt. Eng. 43, 2671-2682 (2004).
    [CrossRef]
  12. H. Kim and Y. H. Lee, "Unique measurement of the parameters of a twisted-nematic liquid-crystal display," Appl. Opt. 44, 1642-1648 (2005).
    [CrossRef] [PubMed]
  13. J. Reményi, P. Várhegyi, L. Domjan, P. Koppa, and E. Lorincz, "Amplitude, phase, and hybrid ternary modulation modes of a twisted-nematic liquid-crystal display at ∼400 nm," Appl. Opt. 42, 3428-3434 (2003).
    [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. M. C. Gardner, R. E. Kilpatrick, S. E. Day, R. E. Renton, and D. R. Selviah, "Experimental verification of a computer model for optimizing a liquid crystal display for spatial phase modulation," J. Opt. A 1, 299-303 (1999).
    [CrossRef]
  16. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

2005 (3)

2004 (5)

2003 (1)

2002 (1)

1999 (1)

M. C. Gardner, R. E. Kilpatrick, S. E. Day, R. E. Renton, and D. R. Selviah, "Experimental verification of a computer model for optimizing a liquid crystal display for spatial phase modulation," J. Opt. A 1, 299-303 (1999).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Campos, J.

Cao, Z.

Choi, K.

Day, S. E.

M. C. Gardner, R. E. Kilpatrick, S. E. Day, R. E. Renton, and D. R. Selviah, "Experimental verification of a computer model for optimizing a liquid crystal display for spatial phase modulation," J. Opt. A 1, 299-303 (1999).
[CrossRef]

Domjan, L.

Doskolovich, L.

V. A. Soifer, V. V. Kotlyar, and L. Doskolovich, Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis, 1997).

Gardner, M. C.

M. C. Gardner, R. E. Kilpatrick, S. E. Day, R. E. Renton, and D. R. Selviah, "Experimental verification of a computer model for optimizing a liquid crystal display for spatial phase modulation," J. Opt. A 1, 299-303 (1999).
[CrossRef]

Hu, L.

Kilpatrick, R. E.

M. C. Gardner, R. E. Kilpatrick, S. E. Day, R. E. Renton, and D. R. Selviah, "Experimental verification of a computer model for optimizing a liquid crystal display for spatial phase modulation," J. Opt. A 1, 299-303 (1999).
[CrossRef]

Kim, H.

Koppa, P.

Kotlyar, V. V.

V. A. Soifer, V. V. Kotlyar, and L. Doskolovich, Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis, 1997).

Kress, B.

B. Kress and P. Meyrueis, Digital Diffractive Optics: An Introduction to Planar Diffractive Optics and Related Technology (Wiley, 2000).

Lee, B.

K. Choi and B. Lee, "A single-stage reconfigurable 2-D optical perfect-shuffle network system using multiplexed phase holograms," IEEE Photon. Technol. Lett. 17, 687-689 (2005).
[CrossRef]

H. Kim and B. Lee, "Optimal nonmonotonic convergence of the iterative Fourier-transform algorithm," Opt. Lett. 30, 296-298 (2005).
[CrossRef] [PubMed]

K. Choi, H. Kim, and B. Lee, "Full-color autostereoscopic 3D display system using color-dispersion-compensated synthetic phase holograms," Opt. Express 12, 5229-5236 (2004).
[CrossRef] [PubMed]

K. Choi, H. Kim, and B. Lee, "Synthetic phase holograms for auto-stereoscopic image display using a modified IFTA," Opt. Express 12, 2454-2462 (2004).
[CrossRef] [PubMed]

H. Kim and B. Lee, "Calculation of the transmittance function of a multilevel diffractive optical element considering multiple internal reflections," Opt. Eng. 43, 2671-2682 (2004).
[CrossRef]

H. Kim, B. Yang, and B. Lee, "Iterative Fourier transform algorithm with regularization for the optimal design of diffractive optical elements," J. Opt. Soc. Am. A 12, 2353-2365 (2004).
[CrossRef]

Lee, Y. H.

Li, D.

Liu, Y.

Lorincz, E.

Meyrueis, P.

B. Kress and P. Meyrueis, Digital Diffractive Optics: An Introduction to Planar Diffractive Optics and Related Technology (Wiley, 2000).

Michalewicz, Z.

Z. Michalewicz, Genetic Algorithms + Data Structures =Evolution Programs (Springer-Verlag, 1999).

Mu, Q.

Nicolás, J.

Reményi, J.

Renton, R. E.

M. C. Gardner, R. E. Kilpatrick, S. E. Day, R. E. Renton, and D. R. Selviah, "Experimental verification of a computer model for optimizing a liquid crystal display for spatial phase modulation," J. Opt. A 1, 299-303 (1999).
[CrossRef]

Selviah, D. R.

M. C. Gardner, R. E. Kilpatrick, S. E. Day, R. E. Renton, and D. R. Selviah, "Experimental verification of a computer model for optimizing a liquid crystal display for spatial phase modulation," J. Opt. A 1, 299-303 (1999).
[CrossRef]

Soifer, V. A.

V. A. Soifer, V. V. Kotlyar, and L. Doskolovich, Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis, 1997).

Tarunen, J.

J. Tarunen and F. Wyrowski, Diffractive Optics for Industrial and Commercial Applications (Wiley, 1997).

Várhegyi, P.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Wyrowski, F.

J. Tarunen and F. Wyrowski, Diffractive Optics for Industrial and Commercial Applications (Wiley, 1997).

Xuan, L.

Yang, B.

H. Kim, B. Yang, and B. Lee, "Iterative Fourier transform algorithm with regularization for the optimal design of diffractive optical elements," J. Opt. Soc. Am. A 12, 2353-2365 (2004).
[CrossRef]

Yzuel, M. J.

Appl. Opt. (2)

IEEE Photon. Technol. Lett. (1)

K. Choi and B. Lee, "A single-stage reconfigurable 2-D optical perfect-shuffle network system using multiplexed phase holograms," IEEE Photon. Technol. Lett. 17, 687-689 (2005).
[CrossRef]

J. Opt. A (1)

M. C. Gardner, R. E. Kilpatrick, S. E. Day, R. E. Renton, and D. R. Selviah, "Experimental verification of a computer model for optimizing a liquid crystal display for spatial phase modulation," J. Opt. A 1, 299-303 (1999).
[CrossRef]

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

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]

H. Kim, B. Yang, and B. Lee, "Iterative Fourier transform algorithm with regularization for the optimal design of diffractive optical elements," J. Opt. Soc. Am. A 12, 2353-2365 (2004).
[CrossRef]

Opt. Eng. (1)

H. Kim and B. Lee, "Calculation of the transmittance function of a multilevel diffractive optical element considering multiple internal reflections," Opt. Eng. 43, 2671-2682 (2004).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Other (5)

Z. Michalewicz, Genetic Algorithms + Data Structures =Evolution Programs (Springer-Verlag, 1999).

J. Tarunen and F. Wyrowski, Diffractive Optics for Industrial and Commercial Applications (Wiley, 1997).

B. Kress and P. Meyrueis, Digital Diffractive Optics: An Introduction to Planar Diffractive Optics and Related Technology (Wiley, 2000).

V. A. Soifer, V. V. Kotlyar, and L. Doskolovich, Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis, 1997).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

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Figures (10)

Fig. 1
Fig. 1

Schematic of the digital holographic beam-shaping system.

Fig. 2
Fig. 2

Schematic of a real-time digital holographic beam-shaping system with a genetic feedback tuning loop.

Fig. 3
Fig. 3

Flow chart for the simplified genetic algorithm implemented in the genetic feedback tuning loop.

Fig. 4
Fig. 4

Schematic of the interferometer for measuring the phase modulation and amplitude transmission of the LCSLM

Fig. 5
Fig. 5

Characteristics of the LCSLM measured by interferometric methods: (a) phase modulation versus encoding index and (b) amplitude transmission versus encoding index.

Fig. 6
Fig. 6

Comparison of the phase-modulation tables obtained at three different stages of generation (1st, 43rd, and 299th) in SLM calibration.

Fig. 7
Fig. 7

Diffraction images observed during the calibration of the SLM with the genetic feedback tuning loop at (a) the 1st generation stage and (b) the 299th generation stage (the stagnated state).

Fig. 8
Fig. 8

Phase holograms and aberration compensation: (a) phase holograms without compensation at the 1st generation stage, (b) aberration compensation obtained by the genetic feedback tuning loop, and (c) phase holograms with compensation at the 553rd generation stage (stagnated state).

Fig. 9
Fig. 9

Diffraction images observed during compensating for aberration with the genetic feedback tuning loop: (a) at the 1st generation stage and (b) at the 553rd generation stage (the stagnated state).

Fig. 10
Fig. 10

Diffraction images in the tuned system from holograms (a) without and (b) with aberration compensation, which was previously obtained by the genetic feedback tuning loop.

Tables (4)

Tables Icon

Table 1 Evaluation Parameters of Diffraction Images in Spatial Light Modulator Calibration

Tables Icon

Table 2 Results of Aberration Compensation: Coefficients of the Zernike-Polynomials

Tables Icon

Table 3 Results of Aberration Compensation: Center Position of Zernike Polynomials

Tables Icon

Table 4 Evaluation Parameters of Diffraction Images in Aberration Compensation

Equations (23)

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max F [ p 1 , p 2 , p 3 , , p 254 ]
for  0   p 1 p 2 p 254 2 π ,
F ( x 2 , y 2 ) = F r [ G ( x 1 , y 1 ) ] = h ( x 2 , y 2 , x 1 , y 1 ) G ( x 1 , y 1 ) d x 1 d y 1 ,
h ( x 2 , y 2 , x 1 , y 1 ) = j | λ ( d 1 + d 2 ) λ d 1 d 2 f | × exp { j π λ ( d 1 + d 2 ) λ d 1 d 2 f × [ ( 1 d 1 f ) ( x 2     2 + y 2     2 ) 2 ( x 2 x 1 + y 2 y 1 ) + ( 1 d 2 f ) ( x 1     2 + y 1     2 ) ] }.
G ( x 1 , y 1 ) = A exp [ j Φ ( x 1 , y 1 ) ] ,
h real ( x 2 , y 2 , x 1 , y 1 ) = h ( x 2 , y 2 , x 1 , y 1 ) exp [ j Ω ( x 1 , y 1 ) ] .
G ( x 1 , y 1 ) = A exp [ j Φ ( x 1 , y 1 ) ] exp [ j Ω ( x 1 , y 1 ) ] .
Ω ( x 1 , y 1 ) = Ω ( ρ , θ )
= A 00 + 1 2 n = 2 A n 0 R n     0 ( ρ ) + n = 1 m = 1 n A n m R n     m ( ρ ) × cos m θ + n = 1 m = 1 n A n m R n     m ( ρ ) sin m θ ,
ρ = [ ( x x c ) 2 + ( y y c ) 2 ] 1 / 2 ,
θ = tan 1 ( y y c x x c ) ,
max F [ A n m , A n m , x c , y c ] .
Mean-square   error  =   S [ G L ( x 2 , y 2 ) 255 255 ] 2 S 1 ,
Normalized variation = N [ G L ( x 2 , y 2 ) G L N ¯ G L N ¯ ] 2 N 1 ,
G L N ¯ = N G L ( x 2 , y 2 ) / N 1,
Boundary length = S+N edge ( x 2 , y 2 ) ,
edge ( x 2 , y 2 ) = { 1           if G L ( x 2 , y 2 ) > threshhold and G L ( x 2 , y 2 ) < threshhold 0             otherwise ,
Phase   shift ( radiation ) = 2 π × Shift   of   fringe Period   of   fringe .
x i = { p i, n = n 255 × 2 π | n = 1 , 2 , 254 } .
x i = { p i, n + Δ ( t , 2 π p i, n )     for   r binary = 0 p i, n Δ ( t , p i, n 0 )         for   r binary = 1 ,
Δ ( t , y ) = y [ 1 - r ( 1 - t / T ) b ] ,
x i = { p l = 1 8 = A n m 2 π = 0 , p l = 9 13 = A n m 2 π = 0 , p 14 = x c = 0 , p 15 = y c = 0 | n = 0 , 1 , 2 , 3 , m = 0 , 1 , 2 , 3 , 4 } .
x i = { p i, l + Δ ( t , 0.25 p i, l )           for   r binary = 0 p i, l Δ ( t , p i, l + 0.25 )           for   r binary = 1 ,

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