Abstract

A particle-swarm optimization (PSO) algorithm was developed for designing binary-phase-only diffractive optical elements (DOEs) that superresolve the axially focused point-spread function. The method is based on vector diffraction theory to ensure solutions are valid under high-NA conditions. A DOE is identified that superresolves the focal spot by 34% and maintains the sidelobes below 50% of the peak intensity. The algorithm was used to obtain the Pareto front of the fitness-value space, which describes the achievable superresolution versus an allowed upper bound in sidelobe intensity. The results suggest that the algorithm yields solutions that are global in terms of the co-optimized fitness values G and M.

© 2008 Optical Society of America

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References

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2008 (1)

T. G. Jabbour, M. Petrovich, and S. M. Kuebler, Opt. Commun. 281, 2002 (2008).
[CrossRef]

2007 (1)

S. Lee, H. Park, and M. Jeon, IEICE Trans. Fundamentals E90-A, 2253 (2007).
[CrossRef]

2006 (1)

2005 (1)

V. F. Canales, J. E. Oti, and M. P. Cagigal, Opt. Commun. 247, 11 (2005).
[CrossRef]

2004 (1)

S. F. Pereira and A. S. van de Nes, Opt. Commun. 234, 119 (2004).
[CrossRef]

2003 (2)

L. Lin, X. Wang, Z. Wang, and G. Mu, Optik (Stuttgart) 114, 329 (2003).
[CrossRef]

H. Liu, Y. Yan, D. Yi, and G. Jin, Appl. Opt. 42, 1463 (2003).
[CrossRef] [PubMed]

2002 (1)

1998 (1)

T. R. M. Sales and G. M. Morris, Opt. Commun. 156, 227 (1998).
[CrossRef]

1995 (1)

H. Y. Chen, N. Mayhew, E. G. S. Paige, and G. G. Yang, Opt. Commun. 119, 381 (1995).
[CrossRef]

1994 (1)

1959 (1)

B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
[CrossRef]

Caballero, M. T.

Cagigal, M. P.

V. F. Canales, J. E. Oti, and M. P. Cagigal, Opt. Commun. 247, 11 (2005).
[CrossRef]

Canales, V. F.

V. F. Canales, J. E. Oti, and M. P. Cagigal, Opt. Commun. 247, 11 (2005).
[CrossRef]

Chen, H. Y.

H. Y. Chen, N. Mayhew, E. G. S. Paige, and G. G. Yang, Opt. Commun. 119, 381 (1995).
[CrossRef]

Diaspro, A.

A. Diaspro, Confocal and Two-Photon Microscopy: Foundations, Applications, and Advances (Wiley-Liss, 2002).

Eberhart, R. C.

J. Kennedy and R. C. Eberhart, in Proceedings of IEEE International Conference on Neural Networks (IEEE, 1995).

X. Hu and R. C. Eberhart, in Proceedings of the Congress on Evolutionary Computation, CEC '02 (IEEE, 2002).

J. Kennedy and R. C. Eberhart, IEEE Intl. Conf. Systems, Man, and Cybernetics, Piscataway, NJ (1997).

Y. Shi and R. C. Eberhart, in Evolutionary Programming VII: Proceedings of the Seventh Annual Conference on Evolutionary Programming (Springer-Verlag, 1998).
[PubMed]

Grann, E. B.

Hu, X.

X. Hu and R. C. Eberhart, in Proceedings of the Congress on Evolutionary Computation, CEC '02 (IEEE, 2002).

Jabbour, T. G.

T. G. Jabbour, M. Petrovich, and S. M. Kuebler, Opt. Commun. 281, 2002 (2008).
[CrossRef]

T. G. Jabbour and S. M. Kuebler, Opt. Express 14, 1033 (2006).
[CrossRef] [PubMed]

Jeon, M.

S. Lee, H. Park, and M. Jeon, IEICE Trans. Fundamentals E90-A, 2253 (2007).
[CrossRef]

Jin, G.

Kennedy, J.

J. Kennedy and R. C. Eberhart, IEEE Intl. Conf. Systems, Man, and Cybernetics, Piscataway, NJ (1997).

J. Kennedy and R. C. Eberhart, in Proceedings of IEEE International Conference on Neural Networks (IEEE, 1995).

Kuebler, S. M.

T. G. Jabbour, M. Petrovich, and S. M. Kuebler, Opt. Commun. 281, 2002 (2008).
[CrossRef]

T. G. Jabbour and S. M. Kuebler, Opt. Express 14, 1033 (2006).
[CrossRef] [PubMed]

S. M. Kuebler and M. Rumi, in Encyclopedia of Modern Optics, R.D.Guenther, D.G.Steel, and L.Bayvel, eds. (Elsevier, 2004), p. 189.

Lee, S.

S. Lee, H. Park, and M. Jeon, IEICE Trans. Fundamentals E90-A, 2253 (2007).
[CrossRef]

Lin, L.

L. Lin, X. Wang, Z. Wang, and G. Mu, Optik (Stuttgart) 114, 329 (2003).
[CrossRef]

Liu, H.

Martinez-Corral, M.

Mayhew, N.

H. Y. Chen, N. Mayhew, E. G. S. Paige, and G. G. Yang, Opt. Commun. 119, 381 (1995).
[CrossRef]

Moharam, M. G.

Morris, G. M.

T. R. M. Sales and G. M. Morris, Opt. Commun. 156, 227 (1998).
[CrossRef]

Mu, G.

L. Lin, X. Wang, Z. Wang, and G. Mu, Optik (Stuttgart) 114, 329 (2003).
[CrossRef]

Oti, J. E.

V. F. Canales, J. E. Oti, and M. P. Cagigal, Opt. Commun. 247, 11 (2005).
[CrossRef]

Paige, E. G. S.

H. Y. Chen, N. Mayhew, E. G. S. Paige, and G. G. Yang, Opt. Commun. 119, 381 (1995).
[CrossRef]

Park, H.

S. Lee, H. Park, and M. Jeon, IEICE Trans. Fundamentals E90-A, 2253 (2007).
[CrossRef]

Pereira, S. F.

S. F. Pereira and A. S. van de Nes, Opt. Commun. 234, 119 (2004).
[CrossRef]

Petrovich, M.

T. G. Jabbour, M. Petrovich, and S. M. Kuebler, Opt. Commun. 281, 2002 (2008).
[CrossRef]

Pommet, D. A.

Richards, B.

B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
[CrossRef]

Rumi, M.

S. M. Kuebler and M. Rumi, in Encyclopedia of Modern Optics, R.D.Guenther, D.G.Steel, and L.Bayvel, eds. (Elsevier, 2004), p. 189.

Sales, T. R. M.

T. R. M. Sales and G. M. Morris, Opt. Commun. 156, 227 (1998).
[CrossRef]

Shi, Y.

Y. Shi and R. C. Eberhart, in Evolutionary Programming VII: Proceedings of the Seventh Annual Conference on Evolutionary Programming (Springer-Verlag, 1998).
[PubMed]

Stelzer, E. H. K.

Swoger, J.

van de Nes, A. S.

S. F. Pereira and A. S. van de Nes, Opt. Commun. 234, 119 (2004).
[CrossRef]

Wang, X.

L. Lin, X. Wang, Z. Wang, and G. Mu, Optik (Stuttgart) 114, 329 (2003).
[CrossRef]

Wang, Z.

L. Lin, X. Wang, Z. Wang, and G. Mu, Optik (Stuttgart) 114, 329 (2003).
[CrossRef]

Wolf, E.

B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
[CrossRef]

Yan, Y.

Yang, G. G.

H. Y. Chen, N. Mayhew, E. G. S. Paige, and G. G. Yang, Opt. Commun. 119, 381 (1995).
[CrossRef]

Yi, D.

Yuan, L.

L. Yuan and Z.-D. Zhao, in Proceedings of the IEEE International Conference on Machine Learning and Cybernetics (IEEE, 2007).

Zhao, Z.-D.

L. Yuan and Z.-D. Zhao, in Proceedings of the IEEE International Conference on Machine Learning and Cybernetics (IEEE, 2007).

Appl. Opt. (1)

IEICE Trans. Fundamentals (1)

S. Lee, H. Park, and M. Jeon, IEICE Trans. Fundamentals E90-A, 2253 (2007).
[CrossRef]

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

Opt. Commun. (5)

T. G. Jabbour, M. Petrovich, and S. M. Kuebler, Opt. Commun. 281, 2002 (2008).
[CrossRef]

S. F. Pereira and A. S. van de Nes, Opt. Commun. 234, 119 (2004).
[CrossRef]

T. R. M. Sales and G. M. Morris, Opt. Commun. 156, 227 (1998).
[CrossRef]

V. F. Canales, J. E. Oti, and M. P. Cagigal, Opt. Commun. 247, 11 (2005).
[CrossRef]

H. Y. Chen, N. Mayhew, E. G. S. Paige, and G. G. Yang, Opt. Commun. 119, 381 (1995).
[CrossRef]

Opt. Express (2)

Optik (Stuttgart) (1)

L. Lin, X. Wang, Z. Wang, and G. Mu, Optik (Stuttgart) 114, 329 (2003).
[CrossRef]

Proc. R. Soc. London, Ser. A (1)

B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
[CrossRef]

Other (7)

J. Kennedy and R. C. Eberhart, IEEE Intl. Conf. Systems, Man, and Cybernetics, Piscataway, NJ (1997).

L. Yuan and Z.-D. Zhao, in Proceedings of the IEEE International Conference on Machine Learning and Cybernetics (IEEE, 2007).

Y. Shi and R. C. Eberhart, in Evolutionary Programming VII: Proceedings of the Seventh Annual Conference on Evolutionary Programming (Springer-Verlag, 1998).
[PubMed]

J. Kennedy and R. C. Eberhart, in Proceedings of IEEE International Conference on Neural Networks (IEEE, 1995).

X. Hu and R. C. Eberhart, in Proceedings of the Congress on Evolutionary Computation, CEC '02 (IEEE, 2002).

S. M. Kuebler and M. Rumi, in Encyclopedia of Modern Optics, R.D.Guenther, D.G.Steel, and L.Bayvel, eds. (Elsevier, 2004), p. 189.

A. Diaspro, Confocal and Two-Photon Microscopy: Foundations, Applications, and Advances (Wiley-Liss, 2002).

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Figures (2)

Fig. 1
Fig. 1

PSF within the plane of incident polarization resulting (a) with a BSO-designed superresolving DOE ( G = 0.66 , M = 0.50 ) and (b) for diffraction-limited focusing (no DOE).

Fig. 2
Fig. 2

Pareto front of the G - M fitness space for axially superresolving binary phase DOEs.

Equations (4)

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E axial ( z ) = i A q ( 0 ) q ( α ) T ( q ) q ( 1 + q ) e i k z q d q ,
E axial ( z ) = i A [ ± q 0 q 1 q ( 1 + q ) e i k z q d q ± q 1 q 2 q ( 1 + q ) e i k z q d q ± q N 1 q N q ( 1 + q ) e i k z q d q ] .
v i j m + 1 = w v i j m + C 1 r 1 ( b i j x i j m ) + C 2 r 2 ( b G j x i j m ) ,
if [ r 3 < S ( v i j m ) ] then x i j m + 1 = x ¯ i j m else x i j m + 1 = x i j m .

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