Abstract

Kant reported [J. Mod. Optics 47, 905 (2000) ] a formulation for solving the inverse problem of vector diffraction, which accurately models high-NA focusing. Here, Kant’s formulation is adapted to the method of generalized projections to obtain an algorithm for designing diffractive optical elements (DOEs) that reshape the axial point-spread function (PSF). The algorithm is applied to design a binary phase-only DOE that superresolves the axial PSF with controlled increase in axial sidelobes. An 11-zone DOE is identified that axially narrows the PSF central lobe by 29% while maintaining the sidelobe intensity at or below 52% of the peak intensity. This DOE could improve the resolution achievable in several applications without significantly complicating the optical system.

© 2007 Optical Society of America

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References

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2006 (1)

2005 (2)

C. Ibáñez-López, G. Saavedra, G. Boyer, and M. Martínez-Corral, Opt. Express 13, 6168 (2005).
[CrossRef] [PubMed]

C. Ibáñez-López, G. Saavedra, K. Plamann, G. Boyer, and M. Martínez-Corral, Microsc. Res. Tech. 67, 22 (2005).
[CrossRef] [PubMed]

2003 (1)

2002 (1)

2000 (1)

R. Kant, J. Mod. Opt. 47, 905 (2000).

1999 (1)

P. D. Higdon, P. Török, and T. Wilson, J. Microsc. 193, 127 (1999).
[CrossRef]

1998 (2)

1994 (3)

1993 (1)

H. Ando, T. Yokota, and K. Tanoue, Jpn. J. Appl. Phys., Part 1 32, 5269 (1993).
[CrossRef]

1990 (1)

1988 (1)

1984 (1)

1959 (1)

B. Richards and E. Wolf, Proc. R. Soc. London, Ser. A 253, 358 (1959).
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Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Wiley, 1972).

Ando, H.

H. Ando, T. Yokota, and K. Tanoue, Jpn. J. Appl. Phys., Part 1 32, 5269 (1993).
[CrossRef]

Blanca, C. M.

Boyer, G.

C. Ibáñez-López, G. Saavedra, G. Boyer, and M. Martínez-Corral, Opt. Express 13, 6168 (2005).
[CrossRef] [PubMed]

C. Ibáñez-López, G. Saavedra, K. Plamann, G. Boyer, and M. Martínez-Corral, Microsc. Res. Tech. 67, 22 (2005).
[CrossRef] [PubMed]

Catino, W. C.

Hegedus, Z. S.

Hell, S. W.

Higdon, P. D.

P. D. Higdon, P. Török, and T. Wilson, J. Microsc. 193, 127 (1999).
[CrossRef]

Ibáñez-López, C.

C. Ibáñez-López, G. Saavedra, K. Plamann, G. Boyer, and M. Martínez-Corral, Microsc. Res. Tech. 67, 22 (2005).
[CrossRef] [PubMed]

C. Ibáñez-López, G. Saavedra, G. Boyer, and M. Martínez-Corral, Opt. Express 13, 6168 (2005).
[CrossRef] [PubMed]

Jabbour, T. G.

Jin, G.

Kant, R.

R. Kant, J. Mod. Opt. 47, 905 (2000).

Kuebler, S. M.

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.

Levi, A.

Liu, H.

LoCicero, J. L.

Martínez-Corral, M.

C. Ibáñez-López, G. Saavedra, G. Boyer, and M. Martínez-Corral, Opt. Express 13, 6168 (2005).
[CrossRef] [PubMed]

C. Ibáñez-López, G. Saavedra, K. Plamann, G. Boyer, and M. Martínez-Corral, Microsc. Res. Tech. 67, 22 (2005).
[CrossRef] [PubMed]

Morris, G. M.

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

Piestun, R.

Plamann, K.

C. Ibáñez-López, G. Saavedra, K. Plamann, G. Boyer, and M. Martínez-Corral, Microsc. Res. Tech. 67, 22 (2005).
[CrossRef] [PubMed]

Richards, B.

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

Rosen, J.

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.

Saavedra, G.

C. Ibáñez-López, G. Saavedra, G. Boyer, and M. Martínez-Corral, Opt. Express 13, 6168 (2005).
[CrossRef] [PubMed]

C. Ibáñez-López, G. Saavedra, K. Plamann, G. Boyer, and M. Martínez-Corral, Microsc. Res. Tech. 67, 22 (2005).
[CrossRef] [PubMed]

Sales, T. R. M.

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

Shamir, J.

Sheppard, C. J. R.

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Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Wiley, 1972).

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H. Ando, T. Yokota, and K. Tanoue, Jpn. J. Appl. Phys., Part 1 32, 5269 (1993).
[CrossRef]

Török, P.

P. D. Higdon, P. Török, and T. Wilson, J. Microsc. 193, 127 (1999).
[CrossRef]

Wilson, T.

P. D. Higdon, P. Török, and T. Wilson, J. Microsc. 193, 127 (1999).
[CrossRef]

Wolf, E.

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

Wyrowski, F.

Yan, Y.

Yariv, A.

Yi, D.

Yokota, T.

H. Ando, T. Yokota, and K. Tanoue, Jpn. J. Appl. Phys., Part 1 32, 5269 (1993).
[CrossRef]

Appl. Opt. (1)

J. Microsc. (1)

P. D. Higdon, P. Török, and T. Wilson, J. Microsc. 193, 127 (1999).
[CrossRef]

J. Mod. Opt. (1)

R. Kant, J. Mod. Opt. 47, 905 (2000).

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

Jpn. J. Appl. Phys., Part 1 (1)

H. Ando, T. Yokota, and K. Tanoue, Jpn. J. Appl. Phys., Part 1 32, 5269 (1993).
[CrossRef]

Microsc. Res. Tech. (1)

C. Ibáñez-López, G. Saavedra, K. Plamann, G. Boyer, and M. Martínez-Corral, Microsc. Res. Tech. 67, 22 (2005).
[CrossRef] [PubMed]

Opt. Commun. (1)

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

Opt. Express (3)

Opt. Lett. (3)

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

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

Other (2)

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Wiley, 1972).

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.

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Figures (3)

Fig. 1
Fig. 1

Optical configuration for modifying the focused PSF using a DOE.

Fig. 2
Fig. 2

Calculated PSFs obtained (a) when the 11-zone DOE of Fig. 3a is placed before a 1.4 NA lens and (b) under diffraction-limited focusing (no DOE). These data are the normalized axial and transverse intensity distribution about the geometric focus within the plane of polarization ( x z plane). (c) Intensity along the optical axis.

Fig. 3
Fig. 3

(a) Profile of an axially superresolving 11-zone binary phase-only DOE obtained by using the MGP algorithm. (b) NMSE calculated during convergence to the solution DOE shown in (a) versus MGP iteration number.

Equations (5)

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F axial ( z ) = i A 0 α T ( θ ) ( cos θ ) 1 2 ( 1 + cos θ ) ( sin θ ) exp ( i k z cos θ ) d θ .
T ( cos θ ) ( cos θ ) 1 2 ( 1 + cos θ ) = s = 0 a s C s 1 2 ( cos θ ) .
E axial ( z ) = s = 0 a s i s j s ( k z ) ,
NMSE = z ( ρ I ξ I target ) 2 z I target 2 , ρ = z I target I ξ z I ξ 2 ,
P 2 [ E ξ ( z ) ] = { 1 2 [ 1 + cos ( z a ) ] exp [ i ϕ ξ ( z ) ] z Z PL primary - lobe region , 0 Z PL < z ( Z PL + Z ZR ) zero region , min [ E ξ ( z ) , A S L ] exp [ i ϕ ξ ( z ) ] z > ( Z PL + Z ZR ) sidelobe region . }

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