Abstract

We demonstrate a digital micromirror device (DMD)-based optical system that converts a spatially noisy quasi-Gaussian to an eighth-order super-Lorentzian flat-top beam. We use an error-diffusion algorithm to design the binary pattern for the Texas Instruments DLP device. Following the DMD, a telescope with a pinhole low-pass filters the beam and scales it to the desired sized image. Experimental measurements show a 1% root-mean-square (RMS) flatness over a diameter of 0.28mm in the center of the flat-top beam and better than 1.5% RMS flatness over its entire 1.43mm diameter. The power conversion efficiency is 37%. We develop an alignment technique to ensure that the DMD pattern is correctly positioned on the incident beam. An interferometric measurement of the DMD surface flatness shows that phase uniformity is maintained in the output beam. Our approach is highly flexible and is able to produce not only flat-top beams with different parameters, but also any slowly varying target beam shape. It can be used to generate the homogeneous optical lattice required for Bose–Einstein condensate cold atom experiments.

© 2009 Optical Society of America

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2008

2007

2006

2005

2004

2003

E. Jane, G. Vidal, W. Dur, P. Zoller, and J. I. Cirac, “Simulation of quantum dynamics with quantum optical systems,” Quantum Inf. Comput. 3, 15-37 (2003).

2000

1997

R. Bourouis, K. A. Ameur, and H. Ladjouze, “Optimization of the Gaussian beam flattening using a phase-plate,” J. Mod. Opt. 44, 1417-1427 (1997).
[CrossRef]

1996

L. A. Romero and F. M. Dickey, “Lossless laser beam shaping,” J. Opt. Soc. Am. A 13, 751-760 (1996).
[CrossRef]

F. M. Dickey and S. C. Holswade, “Gaussian laser beam profile shaping,” Opt. Eng. 35, 3285-3295 (1996).
[CrossRef]

1994

1993

1991

C. C. Aleksoff, K. K. Ellis, and B. D. Neagle, “Holographic conversion of a Gaussian-beam to a near-field uniform beam,” Opt. Eng. 30, 537-543 (1991).
[CrossRef]

1982

1981

J. C. Stoffel and J. F. Moreland, “A survey of electronic techniques for pictorial image reproduction,” IEEE Trans. Commun. 29, 1898-1925 (1981).
[CrossRef]

Agresti, J.

Ait-Ameur, K.

Aleksoff, C. C.

C. C. Aleksoff, K. K. Ellis, and B. D. Neagle, “Holographic conversion of a Gaussian-beam to a near-field uniform beam,” Opt. Eng. 30, 537-543 (1991).
[CrossRef]

Ameur, K. A.

R. Bourouis, K. A. Ameur, and H. Ladjouze, “Optimization of the Gaussian beam flattening using a phase-plate,” J. Mod. Opt. 44, 1417-1427 (1997).
[CrossRef]

Audouard, E.

Auerbach, J. M.

Bourouis, R.

R. Bourouis, K. A. Ameur, and H. Ladjouze, “Optimization of the Gaussian beam flattening using a phase-plate,” J. Mod. Opt. 44, 1417-1427 (1997).
[CrossRef]

Cirac, J. I.

E. Jane, G. Vidal, W. Dur, P. Zoller, and J. I. Cirac, “Simulation of quantum dynamics with quantum optical systems,” Quantum Inf. Comput. 3, 15-37 (2003).

Cordingley, J.

D'Ambrosio, E.

de Saint Denis, R.

DeMarco, B.

DeSalvo, R.

Dickey, F. M.

L. A. Romero and F. M. Dickey, “Lossless laser beam shaping,” J. Opt. Soc. Am. A 13, 751-760 (1996).
[CrossRef]

F. M. Dickey and S. C. Holswade, “Gaussian laser beam profile shaping,” Opt. Eng. 35, 3285-3295 (1996).
[CrossRef]

Dorrer, C.

Dur, W.

E. Jane, G. Vidal, W. Dur, P. Zoller, and J. I. Cirac, “Simulation of quantum dynamics with quantum optical systems,” Quantum Inf. Comput. 3, 15-37 (2003).

Ellis, K. K.

C. C. Aleksoff, K. K. Ellis, and B. D. Neagle, “Holographic conversion of a Gaussian-beam to a near-field uniform beam,” Opt. Eng. 30, 537-543 (1991).
[CrossRef]

Forest, D.

Higashi, R.

M. Takamoto, F. L. Hong, R. Higashi, and H. Katori, “An optical lattice clock,” Nature 435, 321-324 (2005).
[CrossRef] [PubMed]

Hoffnagle, J. A.

Holswade, S. C.

F. M. Dickey and S. C. Holswade, “Gaussian laser beam profile shaping,” Opt. Eng. 35, 3285-3295 (1996).
[CrossRef]

Hong, F. L.

M. Takamoto, F. L. Hong, R. Higashi, and H. Katori, “An optical lattice clock,” Nature 435, 321-324 (2005).
[CrossRef] [PubMed]

Huignard, J. P.

Huot, N.

Jane, E.

E. Jane, G. Vidal, W. Dur, P. Zoller, and J. I. Cirac, “Simulation of quantum dynamics with quantum optical systems,” Quantum Inf. Comput. 3, 15-37 (2003).

Jefferson, C. M.

Jia, J.

Karpenko, V. P.

Kastner, C. J.

Katori, H.

M. Takamoto, F. L. Hong, R. Higashi, and H. Katori, “An optical lattice clock,” Nature 435, 321-324 (2005).
[CrossRef] [PubMed]

Ladjouze, H.

R. Bourouis, K. A. Ameur, and H. Ladjouze, “Optimization of the Gaussian beam flattening using a phase-plate,” J. Mod. Opt. 44, 1417-1427 (1997).
[CrossRef]

Lagrange, B.

Larat, C.

Laroche, M.

Liu, L.

Loiseaux, B.

Mackowsky, J. M.

Michel, C.

Miller, J.

Mohammed-Brahim, T.

Montorio, J. L.

Moreland, J. F.

J. C. Stoffel and J. F. Moreland, “A survey of electronic techniques for pictorial image reproduction,” IEEE Trans. Commun. 29, 1898-1925 (1981).
[CrossRef]

Morgado, N.

Neagle, B. D.

C. C. Aleksoff, K. K. Ellis, and B. D. Neagle, “Holographic conversion of a Gaussian-beam to a near-field uniform beam,” Opt. Eng. 30, 537-543 (1991).
[CrossRef]

Pasienski, M.

Passilly, N.

Pinard, L.

Remilleux, A.

Romero, L. A.

Sanner, N.

Simoni, B.

Stoffel, J. C.

J. C. Stoffel and J. F. Moreland, “A survey of electronic techniques for pictorial image reproduction,” IEEE Trans. Commun. 29, 1898-1925 (1981).
[CrossRef]

Sun, X.

Takamoto, M.

M. Takamoto, F. L. Hong, R. Higashi, and H. Katori, “An optical lattice clock,” Nature 435, 321-324 (2005).
[CrossRef] [PubMed]

Tarallo, M. G.

Veldkamp, W. B.

Vidal, G.

E. Jane, G. Vidal, W. Dur, P. Zoller, and J. I. Cirac, “Simulation of quantum dynamics with quantum optical systems,” Quantum Inf. Comput. 3, 15-37 (2003).

Willems, P.

Zhou, C.

Zoller, P.

E. Jane, G. Vidal, W. Dur, P. Zoller, and J. I. Cirac, “Simulation of quantum dynamics with quantum optical systems,” Quantum Inf. Comput. 3, 15-37 (2003).

Zuegel, J. D.

Appl. Opt.

IEEE Trans. Commun.

J. C. Stoffel and J. F. Moreland, “A survey of electronic techniques for pictorial image reproduction,” IEEE Trans. Commun. 29, 1898-1925 (1981).
[CrossRef]

J. Mod. Opt.

R. Bourouis, K. A. Ameur, and H. Ladjouze, “Optimization of the Gaussian beam flattening using a phase-plate,” J. Mod. Opt. 44, 1417-1427 (1997).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Nature

M. Takamoto, F. L. Hong, R. Higashi, and H. Katori, “An optical lattice clock,” Nature 435, 321-324 (2005).
[CrossRef] [PubMed]

Opt. Eng.

F. M. Dickey and S. C. Holswade, “Gaussian laser beam profile shaping,” Opt. Eng. 35, 3285-3295 (1996).
[CrossRef]

C. C. Aleksoff, K. K. Ellis, and B. D. Neagle, “Holographic conversion of a Gaussian-beam to a near-field uniform beam,” Opt. Eng. 30, 537-543 (1991).
[CrossRef]

Opt. Express

Opt. Lett.

Quantum Inf. Comput.

E. Jane, G. Vidal, W. Dur, P. Zoller, and J. I. Cirac, “Simulation of quantum dynamics with quantum optical systems,” Quantum Inf. Comput. 3, 15-37 (2003).

Other

“A641f camera specification, measurement protocol using the EMVA Standard 1288” (Basler Vision Solutions AG, 2007).

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Figures (6)

Fig. 1
Fig. 1

Cross sections of a simulated Gaussian input beam ( r G = 256 pixels), an eighth-order super-Lorentzian (SL) beam ( r SL = r G / 1.5 = 171 pixels), and the desired reflectance function, R, to transform one into the other. The beam profiles and R are defined in Eqs. (3, 4).

Fig. 2
Fig. 2

Flat-top laser beam optical test bench configuration.

Fig. 3
Fig. 3

DMD pattern design algorithm flowchart.

Fig. 4
Fig. 4

Plot of the uniform amplitude reflectance sent to the error-diffusion algorithm (fraction of DMD mirrors to be turned ON) versus the power delivered to the desired diffraction order (▪) and the calculated square root of the delivered power (▴).

Fig. 5
Fig. 5

Vertical cross section of the measured quasi-Gaussian input beam and its gray-scale image (inset). The horizontal axis is scaled by 5 / 6 to match the scale of the output plane images in Fig. 6. Each camera pixel is 4.4 μm , and the 1 / e 2 beam waist at the output is r G 420 pixels = 1.85 mm .

Fig. 6
Fig. 6

(a) Cross section of the experimental flat-top laser beam with a 500 μm pinhole. (b) Experimental cross section with a 5.5 mm pinhole compared to the ideal super-Lorentzian profile. (c) Spatial frequency spectra of the target super-Lorentzian, the experimental flat-top beam with a 500 μm pinhole, and the experimental beam with a 5.5 mm pinhole. In (a) and (b), each camera pixel is 4.4 μm , while in (c) the pixel number represents spatial frequency from a 1200-point Fourier transform of the flat-top image (200 pixels = 38 lp / mm and zero frequency is at pixel number 600).

Tables (1)

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Table 1 Measured RMS Flatness of the Output Flat-Top Beam

Equations (7)

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g 2 ( x , y ) = g 1 ( x , y ) × DMD ( x , y ) .
g 3 ( f x , f y ) = F { g 2 ( x , y ) } × h ( f x , f y ) ,
G 1 ( x , y ) = G o exp [ 2 r 2 r G 2 ] , SL ( x , y ) = SL o [ 1 + | r r SL | 8 ] 1 ,
R 1 ( x , y ) = SL ( x , y ) / G 1 ( x , y ) .
e ( x , y ) = r 1 ( x , y ) DMD ( x , y ) ,
r 1 ( x + a , y + b ) = r 1 ( x + a , y + b ) + c ( a , b ) × e ( x , y ) ,
c ( 1 , 1 ) = 3 / 16 , c ( 1 , 0 ) = 5 / 16 , c ( 1 , 1 ) = 1 / 16 ,   and c ( 0 , 1 ) = 7 / 16.

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