Abstract

We show that the generalized phase contrast method (GPC) can be used as a versatile tool for shaping an incident Gaussian illumination into arbitrary lateral beam profiles. For illustration, we use GPC in an energy-efficient phase-only implementation of various apertures that do not block light but instead effectively redirect the available photons from a bell-shaped light distribution. GPC-based generation of lateral beam profiles can thus be achieved using a simplified optical implementation as it eliminates the need for a potentially lossy initial beam shaping. The required binary phase input is simple to fabricate for static applications and can be easily reconfigured up to device frame refresh rates for dynamic applications.

© 2007 Optical Society of America

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2007 (6)

2006 (3)

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

I. R. Perch-Nielsen, P. J. Rodrigo, C. A. Alonzo, and J. Glückstad, "Autonomous and 3D real-time multi-beam manipulation in a microfluidic environment," Opt. Express 14, 12199-12205 (2006).
[CrossRef] [PubMed]

S. Maruo and H. Inoue, "Optically driven micropump produced by three-dimensional two-photon microfabrication," Appl. Phys. Lett. 89, 144101 (2006).
[CrossRef]

2005 (4)

Y. Liu, S. Sun, S. Singha, M. R. Cho, and R. J. Gordon, "3D femtosecond laser patterning of collagen for directed cell attachment," Biomaterials 26, 4597-4605 (2005).
[CrossRef] [PubMed]

P. Rodrigo, L. Gammelgaard, P. Bøggild, I. Perch-Nielsen, and J. Glückstad, "Actuation of microfabricated tools using multiple GPC-based counterpropagating beam traps," Opt. Express 13, 6899-6904 (2005).
[CrossRef] [PubMed]

N. Arneborg, H. Siegumfeldt, G. H. Andersen, P. Nissen, V. R. Daria, P. J. Rodrigo, and J. Glückstad, "Interactive optical trapping shows that confinement is a determinant of growth in a mixed yeast culture," FEMS Microbiol. Lett. 245, 155-159 (2005).
[CrossRef] [PubMed]

P. J. Rodrigo, V. R. Daria, and J. Glückstad, "Four-dimensional optical manipulation of colloidal particles," Appl. Phys. Lett. 86, 074103 (2005).
[CrossRef]

2004 (2)

P.J. Rodrigo, V.R. Daria, and J. Glückstad, "Real-time three-dimensional optical micromanipulation of multiple particles and living cells," Opt. Lett.  29 2270-2272 (2004).
[CrossRef] [PubMed]

V. R. Daria, P. J. Rodrigo, S. Sinzinger, and J. Glückstad, "Phase-only optical decryption in a planar-integrated micro-optics system," Opt. Eng.  43 2223-2227 (2004).
[CrossRef]

2002 (5)

2001 (2)

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

J. Glückstad and P.C. Mogensen, "Optimal phase contrast in common-path interferometry," Appl. Opt. 40, 268-282 (2001).
[CrossRef]

2000 (2)

1997 (2)

1996 (1)

J. Glückstad, "Phase contrast image synthesis," Opt. Commun. 130, 225-230 (1996).
[CrossRef]

1995 (1)

J. Glückstad, "Adaptive array illumination and structured light generated by spatial zero-order self-phase modulation in a Kerr medium," Opt. Commun. 120,194-203 (1995).
[CrossRef]

1989 (1)

1965 (1)

1955 (1)

F. Zernike, "How I discovered phase contrast," Science 121, 345-349 (1955).
[CrossRef] [PubMed]

Appl. Opt. (7)

Appl. Phys. Lett. (2)

S. Maruo and H. Inoue, "Optically driven micropump produced by three-dimensional two-photon microfabrication," Appl. Phys. Lett. 89, 144101 (2006).
[CrossRef]

P. J. Rodrigo, V. R. Daria, and J. Glückstad, "Four-dimensional optical manipulation of colloidal particles," Appl. Phys. Lett. 86, 074103 (2005).
[CrossRef]

Biomaterials (1)

Y. Liu, S. Sun, S. Singha, M. R. Cho, and R. J. Gordon, "3D femtosecond laser patterning of collagen for directed cell attachment," Biomaterials 26, 4597-4605 (2005).
[CrossRef] [PubMed]

FEMS Microbiol. Lett. (1)

N. Arneborg, H. Siegumfeldt, G. H. Andersen, P. Nissen, V. R. Daria, P. J. Rodrigo, and J. Glückstad, "Interactive optical trapping shows that confinement is a determinant of growth in a mixed yeast culture," FEMS Microbiol. Lett. 245, 155-159 (2005).
[CrossRef] [PubMed]

New J. Phys. (1)

C. A. Alonzo, P. J. Rodrigo, and J. Glückstad, "Photon-efficient grey-level image projection by the generalized phase contrast method," New J. Phys. 9, 132 (2007).
[CrossRef]

Opt. Commun. (3)

J. Glückstad, "Adaptive array illumination and structured light generated by spatial zero-order self-phase modulation in a Kerr medium," Opt. Commun. 120,194-203 (1995).
[CrossRef]

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

J. Glückstad, "Phase contrast image synthesis," Opt. Commun. 130, 225-230 (1996).
[CrossRef]

Opt. Eng. (1)

V. R. Daria, P. J. Rodrigo, S. Sinzinger, and J. Glückstad, "Phase-only optical decryption in a planar-integrated micro-optics system," Opt. Eng.  43 2223-2227 (2004).
[CrossRef]

Opt. Express (6)

Opt. Lett. (5)

Phys. Rev. Lett (1)

S. A. Tatarkova, A. E. Carruthers, and K. Dholakia, "One-dimensional optically bound arrays of microscopic particles," Phys. Rev. Lett 89, 283901 (2002).
[CrossRef]

Rep. Prog. Phys. (1)

C. O. Weiss and Y. Larionova, "Pattern formation in optical resonators," Rep. Prog. Phys. 70,255-335 (2007).
[CrossRef]

Science (2)

D. Psaltis, "Coherent optical information systems," Science 298, 1359-1363 (2002).
[CrossRef] [PubMed]

F. Zernike, "How I discovered phase contrast," Science 121, 345-349 (1955).
[CrossRef] [PubMed]

Other (3)

V. A. Soifer, Methods for Computer Design of Diffractive Optical Elements (John Wiley & Sons, New York, 2002).

F. M. Dickey and S. C. Holswade, Laser Beam Shaping: Theory and Techniques (Marcel Dekker, New York, 2000).
[CrossRef]

F. M. Dickey, S. C. Holswade, & D. L. Shealy, eds., Laser. Beam Shaping Applications (CRC Press, 2005).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Optical setup for projecting arbitrary beam patterns by the generalized phase contrast method.

Fig. 2.
Fig. 2.

Radial variation of the SRW profile, g(r′), for different PCF sizes (a) Gaussian illumination: PCF sizes 0.5, 1.0, 1.5, 2.0, 2.5 times the Gaussian zero-order beam waist (b) Top-hat illumination: PCF sizes 0.627, 1.44, 2.26, 3.08, 3.9 times that of the Airy central lobe. The red traces indicate the profile of the incident field.

Fig. 3.
Fig. 3.

(a) Effect of aperture size on efficiency for Gaussian beam truncation. 1 GPC aperture; 2 hard aperture; 3 GPC gain. (b) Outputs for an aperture with radius=0.255w 0. black: line-scan across the GPC output; red: line-scan across the hard aperture output. Insets: Gaussian input (left), GPC output (center), and aperture output (right).

Fig. 4.
Fig. 4.

Output of numerical experiments implementing various GPC-based phase-only apertures. The efficiencies of the patterns are shown below each pattern, followed by the efficiencies of corresponding amplitude masks (in parenthesis). The scale bar indicates the 1/e2 width of the Gaussian beam relative to the patterns.

Equations (9)

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H ( f x , f y ) = 1 + [ exp ( i θ ) 1 ] S ( f x , f y ) ,
I ( x , y ) a ( x , y ) exp [ i ϕ ( x , y ) ] + α ̅ [ exp ( i θ ) 1 ] g ( x , y ) 2 .
α ̅ = α ̅ exp ( i ϕ α ̅ ) = a ( x , y ) exp [ i ϕ ( x , y ) ] d x d y a ( x , y ) d x d y .
g ( x ' , y ' ) = 1 { S ( f x , f y ) { a ( x , y ) } } .
2 K α ̅ sin ( θ 2 ) = 1 ,
a ( x , y ) = a r ( r ) = exp [ r 2 w 0 2 ] .
{ a r ( r ) } = π w 0 2 exp [ π 2 w 0 2 f r 2 ]
g ( x , y ) = g r ( r ) = 4 π 2 0 Δ f r 0 exp ( r 2 w 0 2 ) J 0 ( 2 π f r r ) r J 0 ( 2 π f r r ) f r dr d f r .
I ( x , y ) exp ( 2 r 2 w 0 2 ) exp [ i ϕ ( x , y ) ] + exp [ i ( ϕ α ̅ + θ 2 + π 2 ) ] 2 .

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