Abstract

Laser projection based on phase modulation promises several advantages over amplitude modulation. We examine and compare the merits of two phase modulation techniques; phase-only computer generated holography and generalized phase contrast, for the application of dynamic laser image projection. We adopt information theory as a guiding framework and analyze information-relevant metrics such as space-bandwidth product, output display resolution, efficiency, speckle noise, computational load and device requirements. The analysis takes into account the perspective of potential end-users.

© 2008 Optical Society of America

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2007 (4)

2006 (1)

2005 (5)

2004 (2)

2003 (1)

M. P. MacDonald, G. C. Spalding, and K. Dholakia, "Microfluidic sorting in an optical lattice," Nature 426, 421-4 (2003).
[CrossRef] [PubMed]

2001 (3)

C. David, J. Wei, T. Lippert, and A. Wokaun, "Diffractive grey-tone phase masks for laser ablation lithography," Microelectron. Eng. 57-8, 453-460 (2001).
[CrossRef]

J. Glückstad and P. C. Mogensen, "Optimal Phase Contrast in Common-Path Interferometry," Appl. Opt. 40, 268-282 (2001).
[CrossRef]

R. W. Cohn, "Fundamental properties of spatial light modulators for the approximate optical computation of Fourier transforms: a review," Opt. Eng. 40, 2452-2463 (2001).
[CrossRef]

2000 (1)

1999 (3)

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

M. L. Hsieh, K. Y. Hsu, E. G. Paek, and C. L. Wilson, "Modulation transfer function of a liquid crystal spatial light modulator," Opt. Commun. 170, 221-227 (1999).
[CrossRef]

A. J. Waddie and M. R. Taghizadeh, "Interference Effects in Far-Field Diffractive Optical Elements," Appl. Opt. 38, 5915-5919 (1999).
[CrossRef]

1997 (2)

1996 (2)

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

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, and F. Wyrowski, "Theory of speckles in diffractive optics and its application to beam shaping," J. Mod. Opt. 43, 1409-1421 (1996).
[CrossRef]

1995 (1)

G. Moddel and L. Wang, "Resolution limits from charge transport in optically addressed spatial light modulators," J. Appl. Phys. 78, 6923-6935 (1995).
[CrossRef]

1991 (1)

1990 (1)

1986 (1)

1967 (1)

1966 (1)

1955 (2)

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

P. B. Fellgett and E. H. Linfoot, "On the assessment of optical images," Phil. Trans. R. Soc. London Ser. A 247, 369-407 (1955).
[CrossRef]

1948 (1)

D. Gabor, "A new microscopic principle," Nature 161, 777- 778 (1948).
[CrossRef] [PubMed]

Appl. Opt. (5)

Appl. Phys. Lett. (1)

M. Klosner and K. Jain, "Massively parallel, large-area maskless lithography," Appl. Phys. Lett. 84, 2880-2882 (2004).
[CrossRef]

J. Appl. Phys. (1)

G. Moddel and L. Wang, "Resolution limits from charge transport in optically addressed spatial light modulators," J. Appl. Phys. 78, 6923-6935 (1995).
[CrossRef]

J. Mod. Opt. (1)

H. Aagedal, M. Schmid, T. Beth, S. Teiwes, and F. Wyrowski, "Theory of speckles in diffractive optics and its application to beam shaping," J. Mod. Opt. 43, 1409-1421 (1996).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

Microelectron. Eng. (1)

C. David, J. Wei, T. Lippert, and A. Wokaun, "Diffractive grey-tone phase masks for laser ablation lithography," Microelectron. Eng. 57-8, 453-460 (2001).
[CrossRef]

Nature (2)

M. P. MacDonald, G. C. Spalding, and K. Dholakia, "Microfluidic sorting in an optical lattice," Nature 426, 421-4 (2003).
[CrossRef] [PubMed]

D. Gabor, "A new microscopic principle," Nature 161, 777- 778 (1948).
[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, "Phase contrast image synthesis," Opt. Commun. 130, 225-230 (1996).
[CrossRef]

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

M. L. Hsieh, K. Y. Hsu, E. G. Paek, and C. L. Wilson, "Modulation transfer function of a liquid crystal spatial light modulator," Opt. Commun. 170, 221-227 (1999).
[CrossRef]

Opt. Eng. (1)

R. W. Cohn, "Fundamental properties of spatial light modulators for the approximate optical computation of Fourier transforms: a review," Opt. Eng. 40, 2452-2463 (2001).
[CrossRef]

Opt. Express (3)

Opt. Laser Eng. (1)

P. Senthilkumaran, F. Wyrowski, and H. Schimmel, "Vortex Stagnation problem in iterative Fourier transform algorithms," Opt. Laser Eng. 43, 43-56 (2005).
[CrossRef]

Opt. Lett. (5)

P. Natl. Acad. Sci. USA (1)

M. G. L. Gustafsson, "Nonlinear structured-illumination microscopy: Wide-field fluorescence imaging with theoretically unlimited resolution," P. Natl. Acad. Sci. USA 102, 13081-13086 (2005).
[CrossRef]

Phil. Trans. R. Soc. London Ser. A (1)

P. B. Fellgett and E. H. Linfoot, "On the assessment of optical images," Phil. Trans. R. Soc. London Ser. A 247, 369-407 (1955).
[CrossRef]

Science (1)

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

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Figures (6)

Fig. 1.
Fig. 1.

Schematic representation of the system for rerouting of incident optical energy into multiple grey levels on a pre-defined output grid. Bottom left: optical system for a GPC-based projector; bottom right: optical system for a CGH-based laser projection system.

Fig. 2.
Fig. 2.

Simulated phase-only CGH-based grey-level projection showing dark spots due to optical vortices that are impervious to further iterations. The “bumpy” nature of the reconstruction is also evident (image adapted from ref. [25])

Fig. 3.
Fig. 3.

The optimum CGH efficiency for single beam rerouting as a function of target position.

Fig. 4.
Fig. 4.

(a). Radial SRW profiles for different PCF sizes (PCF size is expressed relative to the Airy disc generated by the circular input aperture); (b) GPC efficiency limit as a function of PCF size; indicated data points correspond to PCF sizes depicted in (a).

Fig. 5.
Fig. 5.

Optimum efficiency of holographic grey-level projection for different pixel fill factors (lower trace). The upper trace shows CGH efficiency relative to GPC efficiency.

Fig. 6.
Fig. 6.

Phase-only CGH and its reconstruction. The CGH shows sharp bright-to-dark transitions where the phase wraps from π to - π (grey levels correspond to phase values).

Equations (12)

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N C = log 2 M N F = N F log 2 M
N F = ( 1 + L x Δ f x ) ( 1 + L y Δ f y )
N F = ( 1 + L t Δ f t ) ( 1 + L x Δ f x ) ( 1 + L y Δ f y )
N C = N F log 2 M = ( 1 + L t Δ f t ) ( 1 + L x Δ f x ) ( 1 + L y Δ f y ) log 2 ( 1 + s n )
T ( f x , f y ) = A ( f x , f y ) { d 2 sinc ( f x d , f y d ) Q ( f x , f y ) } ,
σ R = f λ T 1.22 f λ D = D 1.22 T ,
N C = ( 1 + L t Δ f t ) ( 1 + L x Δ f x ) ( 1 + L y Δ f y ) log 2 ( 1 + η s 0 n )
η max = [ ( q , l ) Ω s η ql sinc 2 ( qd ) sinc 2 ( ld ) ] 1 ,
I ( x , y ) = p ( x , y ) + r s ( x , y ) 2 ,
r S ( r ) = 2 π Δ r 0 Δ f r J 1 ( 2 π Δ r f r ) J o ( 2 π r f r ) d f r .
η max = 1 2 ( Δ r ) 2 Δ r r S ( r ) 2 r dr
η = r 2 [ ( q , l ) Ω s η ql sinc 2 ( dq r ) sinc 2 ( ld r ) ] 1

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