Abstract

We analyze the effect of spurious diffraction orders when generating functional multifoci patterns produced by illuminating a phase-only hologram with a single Gaussian beam. Using a practical device for encoding a hologram generates an undesirable zero order and high-diffraction orders at the Fourier plane. This translates to the fact that a significant fraction of the incident light does not necessarily convert to functional multifoci patterns. In most applications, the zero order can be avoided by generating foci patterns shifted off the optical axis, which further increases the amount of light distributed to spurious high-diffraction orders owing to the reduction of light directed to the desired foci pattern. We analyze the amount of light dispersed to spurious orders and show that these unwanted orders can be a major limiting factor for most applications based on arbitrary multifoci patterns.

© 2006 Optical Society of America

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References

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    [CrossRef]

2005 (1)

2004 (3)

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]

O. Ripoll, V. Kettunen, and H. P. Herzig, "Review of iterative Fourier transform algorithms for beam shaping applications," Opt. Eng. 43, 2549-2556 (2004).
[CrossRef]

2002 (2)

R. L. Eriksen, V. R. Daria, and J. Glückstad, "Fully dynamic multiple-beam optical tweezers," Opt. Express 10, 597-602 (2002).
[PubMed]

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

2001 (1)

2000 (1)

J. Glückstad, "Phase contrast imaging," U.S. patent 6,011,874 (4 January 2000).

1999 (1)

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

1997 (1)

1992 (1)

1972 (1)

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 (1)

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

1967 (1)

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]

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.

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.

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]

R. L. Eriksen, V. R. Daria, and J. Glückstad, "Fully dynamic multiple-beam optical tweezers," Opt. Express 10, 597-602 (2002).
[PubMed]

Eriksen, R. L.

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]

R. L. Eriksen, V. R. Daria, and J. Glückstad, "Fully dynamic multiple-beam optical tweezers," Opt. Express 10, 597-602 (2002).
[PubMed]

J. Glückstad, "Phase contrast imaging," U.S. patent 6,011,874 (4 January 2000).

Goodman, J. W.

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

Grier, D. G.

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

Herzig, H. P.

O. Ripoll, V. Kettunen, and H. P. Herzig, "Review of iterative Fourier transform algorithms for beam shaping applications," Opt. Eng. 43, 2549-2556 (2004).
[CrossRef]

Kettunen, V.

O. Ripoll, V. Kettunen, and H. P. Herzig, "Review of iterative Fourier transform algorithms for beam shaping applications," Opt. Eng. 43, 2549-2556 (2004).
[CrossRef]

Koss, B. A.

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

Krackhardt, U.

Liu, J.

Lohmann, A. W.

Mait, J. N.

Manolis, I. G.

Mears, R. J.

Paris, D. P.

Redmond, M. M.

Ripoll, O.

O. Ripoll, V. Kettunen, and H. P. Herzig, "Review of iterative Fourier transform algorithms for beam shaping applications," Opt. Eng. 43, 2549-2556 (2004).
[CrossRef]

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]

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).

Schmitz, C.

Silvestri, A. M.

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

Spatz, J.

Streibl, N.

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.

Warr, S. T.

Wilkinson, T. D.

Appl. Opt. (3)

IBM J. Res. Dev. (1)

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

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

Opt. Commun. (3)

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]

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. Eng. (1)

O. Ripoll, V. Kettunen, and H. P. Herzig, "Review of iterative Fourier transform algorithms for beam shaping applications," Opt. Eng. 43, 2549-2556 (2004).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Optik (1)

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).

Other (1)

J. Glückstad, "Phase contrast imaging," U.S. patent 6,011,874 (4 January 2000).

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Figures (3)

Fig. 1
Fig. 1

Geometry of the M × M phase-only spatial light modulator with a square pixel length d while Δ d is the period length. The active phase-encoding area of a pixel is shaded gray.

Fig. 2
Fig. 2

Plot of the diffraction efficiency of the spurious diffraction orders (solid curves) and N-foci spots (dashed curves) as a function of fill factor (a) when the center of mass of the foci pattern is located at the optical axis or ( c f x , c f y ) = ( 0 , 0 ) and (b) when the foci pattern is shifted ( c f x , c f y ) = ( 0.2 λ f / Δ d , 0.2 λ f / Δ d ) . Plots for PL = 2, 4, and 16 are shown.

Fig. 3
Fig. 3

Plot of the diffraction efficiency of the spurious diffraction orders (solid curves) and N-foci spots (dashed curves) as a function of distance, ( c f x 2 + c f y 2 ) 1 / 2 λ f Δ d 1 m , from the optical axis. Plot for fill factors of F = 1.0 , 0.9, and 0.8 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 sin c ( f x d , f y d ) Q ( f x , f y ) + [ Δ d 2 sin c ( f x Δ d , f y Δ d ) d 2 sin c ( f x d , f y d ) ] P ( f x , f y ) } ,
sin c ( 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 )
η SO = 1 ( | T ( 0 , 0 ) | 2 | t ( x , y ) | 2 d x d y + η N f ) ,
η N 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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