Abstract

We present what is to our knowledge a novel technique for efficient suppression of the zero-order beam inherent in light patterns projected via phase-only computer-generated holograms (CGHs). Encoding a CGH on a spatial light modulator (SLM) with a limited fill factor produces a disturbing zero-order beam at the optical axis. Here, we propose to derive a CGH, which includes holographic information to project a corrective beam that destructively interferes with the zero-order beam. The CGH for projecting arbitrary light patterns plus a corrective beam are derived using the Gerchberg–Saxton algorithm where the iterations impose both amplitude and phase constraints for the target field pattern at the Fourier plane. As proof of principle, we analyze the viability of the technique by simulating the performance when applied on a practical SLM with a limited fill factor, fixed number of phase-shifting pixels, and wavefront distortion associated with the surface roughness of the SLM.

© 2007 Optical Society of America

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  1. M. J. Thomson, J. Liu, and M. R. Taghizadeh, "Iterative algorithm for the design of free-space diffractive optical elements for fiber coupling," Appl. Opt. 43, 1996-1999 (2004).
    [CrossRef] [PubMed]
  2. V. R. Daria, P. J. Rodrigo, and J. Glückstad, "Programmable complex field coupling to higher order guided modes of microstructured fibers," Opt. Commun. 232, 229-237 (2004).
    [CrossRef]
  3. J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002).
    [CrossRef]
  4. K. L. Tan, S. T. Warr, I. G. Manolis, T. D. Wilkinson, M. M. Redmond, W. A. Crossland, R. J. Mears, and B. W. Robertson, "Dynamic holography for optical interconnections. II. Routing holograms with predictable location and intensity of each diffraction order," J. Opt. Soc. Am. A 18, 205-215 (2001).
    [CrossRef]
  5. J. W. Goodman and A. M. Silvestri, "Some effects of Fourier-domain phase quantization," IBM J. Res. Develop. 14, 478-484 (1970).
    [CrossRef]
  6. V. Arrizon and M. Testorf, "Efficiency limit of spatially quantized Fourier array illuminators," Opt. Lett. 22, 197-199 (1997).
    [CrossRef] [PubMed]
  7. V. Arrizon, E. Carreon, and M. Testorf, "Implementation of Fourier array illuminators using pixelated SLM: efficiency limitations," Opt. Commun 160, 207-213 (1999).
    [CrossRef]
  8. M. Gruber, "Phase quantization of a grating without altering the diffraction pattern," Opt. Lett. 26, 1122-1124 (2001).
    [CrossRef]
  9. A. Vargas, J. Campos, M. J. Yzuel, C. Iemmi, and S. Ledesma, "One-step multichannel pattern recognition based on the pixelated structure of a spatial light modulator," Appl. Opt. 37, 2063-2066 (1998).
    [CrossRef]
  10. I. Moreno, J. Campos, C. Gorecki, and M. J. Yzuel, "Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition," Jap. J. Appl. Phys. 34, 6423-6434 (1995).
    [CrossRef]
  11. M. Polin, K. Ladavac, S. Lee, Y. Roichman, and D. Grier, "Optimized holographic optical traps," Opt. Express 13, 5831-5845 (2005).
    [CrossRef] [PubMed]
  12. R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of the phase from image and diffraction plane pictures," Optik 35, 237-246 (1972).
  13. D. Palima and V. R. Daria, "Effect of spurious diffraction orders in arbitrary multi-foci patterns produced via phase-only holograms," Appl. Opt. 45, 6689-6693 (2006).
    [CrossRef] [PubMed]

2006

2005

2004

M. J. Thomson, J. Liu, and M. R. Taghizadeh, "Iterative algorithm for the design of free-space diffractive optical elements for fiber coupling," Appl. Opt. 43, 1996-1999 (2004).
[CrossRef] [PubMed]

V. R. Daria, P. J. Rodrigo, and J. Glückstad, "Programmable complex field coupling to higher order guided modes of microstructured fibers," Opt. Commun. 232, 229-237 (2004).
[CrossRef]

2002

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002).
[CrossRef]

2001

1999

V. Arrizon, E. Carreon, and M. Testorf, "Implementation of Fourier array illuminators using pixelated SLM: efficiency limitations," Opt. Commun 160, 207-213 (1999).
[CrossRef]

1998

1997

1995

I. Moreno, J. Campos, C. Gorecki, and M. J. Yzuel, "Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition," Jap. J. Appl. Phys. 34, 6423-6434 (1995).
[CrossRef]

1972

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of the phase from image and diffraction plane pictures," Optik 35, 237-246 (1972).

1970

J. W. Goodman and A. M. Silvestri, "Some effects of Fourier-domain phase quantization," IBM J. Res. Develop. 14, 478-484 (1970).
[CrossRef]

Arrizon, V.

V. Arrizon, E. Carreon, and M. Testorf, "Implementation of Fourier array illuminators using pixelated SLM: efficiency limitations," Opt. Commun 160, 207-213 (1999).
[CrossRef]

V. Arrizon and M. Testorf, "Efficiency limit of spatially quantized Fourier array illuminators," Opt. Lett. 22, 197-199 (1997).
[CrossRef] [PubMed]

Campos, J.

A. Vargas, J. Campos, M. J. Yzuel, C. Iemmi, and S. Ledesma, "One-step multichannel pattern recognition based on the pixelated structure of a spatial light modulator," Appl. Opt. 37, 2063-2066 (1998).
[CrossRef]

I. Moreno, J. Campos, C. Gorecki, and M. J. Yzuel, "Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition," Jap. J. Appl. Phys. 34, 6423-6434 (1995).
[CrossRef]

Carreon, E.

V. Arrizon, E. Carreon, and M. Testorf, "Implementation of Fourier array illuminators using pixelated SLM: efficiency limitations," Opt. Commun 160, 207-213 (1999).
[CrossRef]

Crossland, W. A.

Curtis, J. E.

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002).
[CrossRef]

Daria, V. R.

D. Palima and V. R. Daria, "Effect of spurious diffraction orders in arbitrary multi-foci patterns produced via phase-only holograms," Appl. Opt. 45, 6689-6693 (2006).
[CrossRef] [PubMed]

V. R. Daria, P. J. Rodrigo, and J. Glückstad, "Programmable complex field coupling to higher order guided modes of microstructured fibers," Opt. Commun. 232, 229-237 (2004).
[CrossRef]

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of the phase from image and diffraction plane pictures," Optik 35, 237-246 (1972).

Glückstad, J.

V. R. Daria, P. J. Rodrigo, and J. Glückstad, "Programmable complex field coupling to higher order guided modes of microstructured fibers," Opt. Commun. 232, 229-237 (2004).
[CrossRef]

Goodman, J. W.

J. W. Goodman and A. M. Silvestri, "Some effects of Fourier-domain phase quantization," IBM J. Res. Develop. 14, 478-484 (1970).
[CrossRef]

Gorecki, C.

I. Moreno, J. Campos, C. Gorecki, and M. J. Yzuel, "Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition," Jap. J. Appl. Phys. 34, 6423-6434 (1995).
[CrossRef]

Grier, D.

Grier, D. G.

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002).
[CrossRef]

Gruber, M.

Iemmi, C.

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002).
[CrossRef]

Ladavac, K.

Ledesma, S.

Lee, S.

Liu, J.

Manolis, I. G.

Mears, R. J.

Moreno, I.

I. Moreno, J. Campos, C. Gorecki, and M. J. Yzuel, "Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition," Jap. J. Appl. Phys. 34, 6423-6434 (1995).
[CrossRef]

Palima, D.

Polin, M.

Redmond, M. M.

Robertson, B. W.

Rodrigo, P. J.

V. R. Daria, P. J. Rodrigo, and J. Glückstad, "Programmable complex field coupling to higher order guided modes of microstructured fibers," Opt. Commun. 232, 229-237 (2004).
[CrossRef]

Roichman, Y.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of the phase from image and diffraction plane pictures," Optik 35, 237-246 (1972).

Silvestri, A. M.

J. W. Goodman and A. M. Silvestri, "Some effects of Fourier-domain phase quantization," IBM J. Res. Develop. 14, 478-484 (1970).
[CrossRef]

Taghizadeh, M. R.

Tan, K. L.

Testorf, M.

V. Arrizon, E. Carreon, and M. Testorf, "Implementation of Fourier array illuminators using pixelated SLM: efficiency limitations," Opt. Commun 160, 207-213 (1999).
[CrossRef]

V. Arrizon and M. Testorf, "Efficiency limit of spatially quantized Fourier array illuminators," Opt. Lett. 22, 197-199 (1997).
[CrossRef] [PubMed]

Thomson, M. J.

Vargas, A.

Warr, S. T.

Wilkinson, T. D.

Yzuel, M. J.

A. Vargas, J. Campos, M. J. Yzuel, C. Iemmi, and S. Ledesma, "One-step multichannel pattern recognition based on the pixelated structure of a spatial light modulator," Appl. Opt. 37, 2063-2066 (1998).
[CrossRef]

I. Moreno, J. Campos, C. Gorecki, and M. J. Yzuel, "Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition," Jap. J. Appl. Phys. 34, 6423-6434 (1995).
[CrossRef]

Appl. Opt.

IBM J. Res. Develop.

J. W. Goodman and A. M. Silvestri, "Some effects of Fourier-domain phase quantization," IBM J. Res. Develop. 14, 478-484 (1970).
[CrossRef]

J. Opt. Soc. Am. A

Jap. J. Appl. Phys.

I. Moreno, J. Campos, C. Gorecki, and M. J. Yzuel, "Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition," Jap. J. Appl. Phys. 34, 6423-6434 (1995).
[CrossRef]

Opt. Commun

V. Arrizon, E. Carreon, and M. Testorf, "Implementation of Fourier array illuminators using pixelated SLM: efficiency limitations," Opt. Commun 160, 207-213 (1999).
[CrossRef]

Opt. Commun.

V. R. Daria, P. J. Rodrigo, and J. Glückstad, "Programmable complex field coupling to higher order guided modes of microstructured fibers," Opt. Commun. 232, 229-237 (2004).
[CrossRef]

J. E. Curtis, B. A. Koss, and D. G. Grier, "Dynamic holographic optical tweezers," Opt. Commun. 207, 169-175 (2002).
[CrossRef]

Opt. Express

Opt. Lett.

Optik

R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of the phase from image and diffraction plane pictures," Optik 35, 237-246 (1972).

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Figures (4)

Fig. 1
Fig. 1

Light pattern at the Fourier plane obtained when using a spatial light modulator with a fill factor of F = 0.8 is encoded (a) without correction and (b) with a corrective phase component in the hologram. Line scans along the diagonal crossing the optical axis are shown below the patterns.

Fig. 2
Fig. 2

Plot of the diffraction efficiency as a function of fill factor for the corrected and uncorrected light pattern. The efficiency plot of the zero-order beam is also shown.

Fig. 3
Fig. 3

Plot of the amplitude and phase of the zero-order beam with respect to the strength of the wavefront distortion introduced by surface roughness of the SLM. The random phase shifts are blurred with a Gaussian profile with characteristic feature sizes of 4 %, 11%, 18%, 36%, and 54% with respect to the area of the SLM.

Fig. 4
Fig. 4

Histogram of phase pixels of a hologram for generating a tailored light pattern at the Fourier plane. The plots for fill factors of F = 0.6 , 0.7, 0.8, and 0.9 are shown.

Equations (8)

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t ( x , y ) = a ( x , y ) { rect ( x d , y d ) q ( x , y ) + [ rect ( x Δ d , y Δ d ) rect ( x d , y d ) ] p ( x , y ) } ,
q ( x , y ) = m , n = 0 M 1 δ ( x m Δ d , y n Δ d ) exp ( i ϕ m n ) ,
p ( x , y ) = m , n = 0 M 1 δ ( x m Δ d , y n Δ d ) exp ( i ϕ c ) .
T ( f x , f y ) = A ( f x , f y ) { d 2   sinc ( f x d , f y d ) Q ( f x , f y ) + [ Δ d 2   sinc ( f x Δ d , f y Δ d ) d 2   sinc ( f x d , f y d ) ] P ( f x , f y ) } ,
sinc ( ζ x , ζ y ) = sin ( π ζ x ) π ζ x sin ( π ζ y ) π ζ y .
P ( f x , f y ) = m , n = 0 M 1 δ ( f x m Δ d , f y n Δ d ) exp ( i ϕ c ) ,
T ( 0 , 0 ) = d 2 Q ( 0 , 0 ) + ( Δ d 2 d 2 ) exp ( i ϕ c ) = d 2 Q ( 0 , 0 ) + ( 1 F ) exp ( i ϕ c ) / Δ d 2 ,
η M f = | i = 1 N δ ( f x α i ) δ ( f y β i ) T ( f x , f y ) | 2 | t ( x , y ) | 2 d x d y ,

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