Abstract

The superresolution technique is well known for its ability to compress the central diffractive spot that is smaller than the Airy diffractive spot. In this paper, we extend the superresolution technique for different laser beam shaping. A complete set of superresolution diffractive elements is developed for the flat-top beam shaping, the single-circle beam shaping, and the novel circular Dammann grating. Five phase plates, corresponding to each of its applications, have been made by use of micro-optics technology. Experiments that are presented are in good agreement with the theoretical results. The superresolution technique presented in this paper should be highly interesting for the wide applications of laser beam shaping.

© 2004 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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2003 (2)

J. Jia, C. Zhou, L. Liu, “Superresolution technology for reduction of the far-field diffraction spot size in the laser free-space communication system,” Opt. Commun. 228, 271–278 (2003).
[CrossRef]

C. Zhou, J. Jia, L. Liu, “Circular Dammann grating,” Opt. Lett. 28, 2174–2176 (2003).
[CrossRef] [PubMed]

2001 (1)

G. Zhou, X. Yuan, P. Dowd, Y. Lam, Y. Chan, “Design of diffractive phase elements for beam shaping: hybrid approach,” J. Opt. Soc. Am. A. 18, 971–800 (2001).
[CrossRef]

1999 (1)

1998 (1)

1997 (2)

1996 (1)

1995 (2)

1992 (1)

H. Ando, “Phase-shifting apodizer of three or more portions,” Jpn. J. Appl. Phys. 31, 557–567 (1992).
[CrossRef]

1991 (1)

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

1987 (2)

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1987).

M. A. Seldowitz, J. P. Allebach, D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt. 28, 2788–2798 (1987).
[CrossRef]

1983 (1)

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

1982 (1)

1980 (1)

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 197–305 (1980).
[CrossRef]

1977 (1)

H. Dammann, E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta. 24, 505–515 (1977).
[CrossRef]

1972 (1)

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

1952 (1)

G. T. di Francia, “Super-gain antennas and optical resolving power,” Nuovo Cimento Suppl., 9, 426–435 (1952).
[CrossRef]

Aleksoff, C. C.

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

Allebach, J. P.

M. A. Seldowitz, J. P. Allebach, D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt. 28, 2788–2798 (1987).
[CrossRef]

Ando, H.

H. Ando, “Phase-shifting apodizer of three or more portions,” Jpn. J. Appl. Phys. 31, 557–567 (1992).
[CrossRef]

Bertero, M.

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed., (University Press, Cambridge, UK, 1999), pp. 439–443.

Brady, D. J.

Chan, Y.

G. Zhou, X. Yuan, P. Dowd, Y. Lam, Y. Chan, “Design of diffractive phase elements for beam shaping: hybrid approach,” J. Opt. Soc. Am. A. 18, 971–800 (2001).
[CrossRef]

Dammann, H.

H. Dammann, E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta. 24, 505–515 (1977).
[CrossRef]

di Francia, G. T.

G. T. di Francia, “Super-gain antennas and optical resolving power,” Nuovo Cimento Suppl., 9, 426–435 (1952).
[CrossRef]

Dorsch, R. G.

Dowd, P.

G. Zhou, X. Yuan, P. Dowd, Y. Lam, Y. Chan, “Design of diffractive phase elements for beam shaping: hybrid approach,” J. Opt. Soc. Am. A. 18, 971–800 (2001).
[CrossRef]

Ellis, K. K.

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

Fienup, J. R.

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 197–305 (1980).
[CrossRef]

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Gerchberg, R. W.

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

Jia, J.

J. Jia, C. Zhou, L. Liu, “Superresolution technology for reduction of the far-field diffraction spot size in the laser free-space communication system,” Opt. Commun. 228, 271–278 (2003).
[CrossRef]

C. Zhou, J. Jia, L. Liu, “Circular Dammann grating,” Opt. Lett. 28, 2174–2176 (2003).
[CrossRef] [PubMed]

Kastner, C. J.

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Klotz, E.

H. Dammann, E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta. 24, 505–515 (1977).
[CrossRef]

Lam, Y.

G. Zhou, X. Yuan, P. Dowd, Y. Lam, Y. Chan, “Design of diffractive phase elements for beam shaping: hybrid approach,” J. Opt. Soc. Am. A. 18, 971–800 (2001).
[CrossRef]

Liu, L.

C. Zhou, J. Jia, L. Liu, “Circular Dammann grating,” Opt. Lett. 28, 2174–2176 (2003).
[CrossRef] [PubMed]

J. Jia, C. Zhou, L. Liu, “Superresolution technology for reduction of the far-field diffraction spot size in the laser free-space communication system,” Opt. Commun. 228, 271–278 (2003).
[CrossRef]

C. Zhou, L. Liu, “Numerical study of Dammann array illuminators,” Appl. Opt. 34, 5961–5969 (1995).
[CrossRef] [PubMed]

Mait, J. N.

Mendlovic, D.

Morris, G. M.

Neagle, B. D.

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

Sales, T. R. M.

Saxton, W. O.

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

Seldowitz, M. A.

M. A. Seldowitz, J. P. Allebach, D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt. 28, 2788–2798 (1987).
[CrossRef]

Sweeney, D. W.

M. A. Seldowitz, J. P. Allebach, D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt. 28, 2788–2798 (1987).
[CrossRef]

Turunen, J.

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1987).

Vasara, A.

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1987).

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Veldkamp, W. B.

Westerholm, J.

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1987).

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed., (University Press, Cambridge, UK, 1999), pp. 439–443.

Yuan, X.

G. Zhou, X. Yuan, P. Dowd, Y. Lam, Y. Chan, “Design of diffractive phase elements for beam shaping: hybrid approach,” J. Opt. Soc. Am. A. 18, 971–800 (2001).
[CrossRef]

Zalevsky, Z.

Zhou, C.

C. Zhou, J. Jia, L. Liu, “Circular Dammann grating,” Opt. Lett. 28, 2174–2176 (2003).
[CrossRef] [PubMed]

J. Jia, C. Zhou, L. Liu, “Superresolution technology for reduction of the far-field diffraction spot size in the laser free-space communication system,” Opt. Commun. 228, 271–278 (2003).
[CrossRef]

C. Zhou, L. Liu, “Numerical study of Dammann array illuminators,” Appl. Opt. 34, 5961–5969 (1995).
[CrossRef] [PubMed]

Zhou, G.

G. Zhou, X. Yuan, P. Dowd, Y. Lam, Y. Chan, “Design of diffractive phase elements for beam shaping: hybrid approach,” J. Opt. Soc. Am. A. 18, 971–800 (2001).
[CrossRef]

Appl. Opt. (3)

J. Opt. Soc. Am. A (3)

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

G. Zhou, X. Yuan, P. Dowd, Y. Lam, Y. Chan, “Design of diffractive phase elements for beam shaping: hybrid approach,” J. Opt. Soc. Am. A. 18, 971–800 (2001).
[CrossRef]

Jpn. J. Appl. Phys. (1)

H. Ando, “Phase-shifting apodizer of three or more portions,” Jpn. J. Appl. Phys. 31, 557–567 (1992).
[CrossRef]

Nuovo Cimento Suppl. (1)

G. T. di Francia, “Super-gain antennas and optical resolving power,” Nuovo Cimento Suppl., 9, 426–435 (1952).
[CrossRef]

Opt. Acta. (1)

H. Dammann, E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta. 24, 505–515 (1977).
[CrossRef]

Opt. Commun. (1)

J. Jia, C. Zhou, L. Liu, “Superresolution technology for reduction of the far-field diffraction spot size in the laser free-space communication system,” Opt. Commun. 228, 271–278 (2003).
[CrossRef]

Opt. Eng. (3)

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

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19, 197–305 (1980).
[CrossRef]

J. Turunen, A. Vasara, J. Westerholm, “Kinoform phase relief synthesis: a stochastic method,” Opt. Eng. 28, 1162–1167 (1987).

Opt. Lett. (4)

Optik (1)

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

Science (1)

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Other (1)

M. Born, E. Wolf, Principles of Optics, 7th ed., (University Press, Cambridge, UK, 1999), pp. 439–443.

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Figures (5)

Fig. 1
Fig. 1

Experimental system for superresolution beam shaping in the far field.

Fig. 2
Fig. 2

Structure of the N-zone binary pure-phase plate; r i is the radius of the ith zone. The radii are normalized.

Fig. 3
Fig. 3

Experimental images of (a) Airy pattern and (b) uniform pattern with a two-zone superresolution plate. We can see that the central spot of (b) is a flat-top beam with uniform intensity and the size of the central spot of (b) is wider than that of the well-known Airy pattern of (a). Experimental intensity comparison of Airy diffraction and uniform diffraction with a two-zone uniform phase plate is shown in (c), which are represented by the dotted curve (experimental) and the solid curve (theoretical), respectively. Experimental results verify that a high-quality uniform beam has been achieved.

Fig. 4
Fig. 4

(a) Experimental image of the single-circle pattern with a two-zone superresolution plate. We can see that the central spot of (a) has been decreased to zero and a single-circle beam has been achieved. (b) Experimental intensity comparison of Airy diffraction and the single-circle diffraction with a two-zone phase plate, which are represented by the dotted curves (experimental) and the solid curve (theoretical), respectively. Experimental results verify that a single-circle diffraction field has been achieved.

Fig. 5
Fig. 5

Experimental image of the diffraction pattern of (a) a first-order CDG with a two-zones plate. The first-order CDG pattern can generate a single-circle diffraction field with equal intensity to that of the central spot. (b) The theoretical normalized intensity in the far-field of the two-circular first-order CDG, where E is the efficiency of the energy within the first circle and r is the optimized radius of the binary-phase (0, π) first-order CDG.

Equations (3)

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Up=201ArexpiϕrJ0prrdr,
Up=2pj=1NexpiϕjrjJ1prj-rj-1J1prj-1,
Up=2pJ1p-1-expiϕ0-1N+1×j=1N-1-1jrjJ1prj.

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