Abstract

Pupil filters for cylindrical (two-dimensional) focusing with extended depth of field are investigated. An important application is in generating light sheets with uniform intensity. Filters for spherical (three-dimensional) focusing with a flat axial intensity, coupled with weak side lobes are also discussed.

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  1. A. H. Voie, D. H. Burns, and F. A. Spelman, “Orthogonal-plane fluorescence optical sectioning: three-dimensional imaging of macroscopic biological specimens,” J. Microsc.170(3), 229–236 (1993).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. H.-U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods4(4), 331–336 (2007).
    [CrossRef] [PubMed]
  5. C. J. R. Sheppard and X. Mao, “Confocal microscopes with slit apertures,” J. Mod. Opt.35(7), 1169–1185 (1988).
    [CrossRef]
  6. R. Wolleschensky, B. Zimmermann, and M. Kempe, “High-speed confocal fluorescence imaging with a novel line scanning microscope,” J. Biomed. Opt.11(6), 064011 (2006).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  9. C. J. R. Sheppard, “Binary phase filters with a maximally-flat response,” Opt. Lett.36(8), 1386–1388 (2011).
    [CrossRef] [PubMed]
  10. C. J. R. Sheppard and S. Mehta, “Three-level filter for increased depth of focus and Bessel beam generation,” Opt. Express20(25), 27212–27221 (2012).
    [PubMed]
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    [CrossRef]
  12. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58(15), 1499–1501 (1987).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  19. C. J. R. Sheppard and K. G. Larkin, “Focal shift, optical transfer function, and phase-space representations,” J. Opt. Soc. Am. A17(4), 772–779 (2000).
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    [CrossRef]
  21. D. M. de Juana, J. E. Oti, V. F. Canales, and M. P. Cagigal, “Design of superresolving continuous phase filters,” Opt. Lett.28(8), 607–609 (2003).
    [CrossRef] [PubMed]
  22. M. P. Cagigal, J. E. Oti, V. F. Canales, and P. J. Valle, “Analytical design of superresolving phase filters,” Opt. Commun.241(4-6), 249–253 (2004).
    [CrossRef]
  23. C. J. R. Sheppard, S. Ledesma, J. Campos, and J. C. Escalera, “Improved expressions for performance parameters for complex filters,” Opt. Lett.32, 1713–1715 (2007).
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2013

2012

2011

2007

C. J. R. Sheppard, S. Ledesma, J. Campos, and J. C. Escalera, “Improved expressions for performance parameters for complex filters,” Opt. Lett.32, 1713–1715 (2007).
[CrossRef] [PubMed]

H.-U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods4(4), 331–336 (2007).
[CrossRef] [PubMed]

2006

R. Wolleschensky, B. Zimmermann, and M. Kempe, “High-speed confocal fluorescence imaging with a novel line scanning microscope,” J. Biomed. Opt.11(6), 064011 (2006).
[CrossRef] [PubMed]

2004

M. P. Cagigal, J. E. Oti, V. F. Canales, and P. J. Valle, “Analytical design of superresolving phase filters,” Opt. Commun.241(4-6), 249–253 (2004).
[CrossRef]

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. K. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science305(5686), 1007–1009 (2004).
[CrossRef] [PubMed]

2003

2002

2000

1997

1995

1993

A. H. Voie, D. H. Burns, and F. A. Spelman, “Orthogonal-plane fluorescence optical sectioning: three-dimensional imaging of macroscopic biological specimens,” J. Microsc.170(3), 229–236 (1993).
[CrossRef] [PubMed]

1988

C. J. R. Sheppard and X. Mao, “Confocal microscopes with slit apertures,” J. Mod. Opt.35(7), 1169–1185 (1988).
[CrossRef]

C. J. R. Sheppard and Z. S. Hegedus, “Axial behaviour of pupil plane filters,” J. Opt. Soc. Am. A5(5), 643–647 (1988).
[CrossRef]

1987

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun.64(6), 491–495 (1987).
[CrossRef]

Y. Li, “Three-dimensional intensity distribution in low Fresnel number focusing systems,” J. Opt. Soc. Am. A4(8), 1349–1353 (1987).
[CrossRef]

C. J. R. Sheppard and H. J. Matthews, “Imaging in high aperture optical systems,” J. Opt. Soc. Am. A4(8), 1354–1360 (1987).
[CrossRef]

1984

Y. Li and E. Wolf, “Three-dimensional intensity distribution near the focus in systems of different Fresnel numbers,” J. Opt. Soc. Am. A1(8), 801–808 (1984).
[CrossRef]

1978

C. J. R. Sheppard and T. Wilson, “Gaussian-beam theory of lenses with annular aperture,” IEE J. Microwaves, Opt. Acoust.2(4), 105–112 (1978).
[CrossRef]

Azam, F.

Becker, K.

H.-U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods4(4), 331–336 (2007).
[CrossRef] [PubMed]

Burns, D. H.

A. H. Voie, D. H. Burns, and F. A. Spelman, “Orthogonal-plane fluorescence optical sectioning: three-dimensional imaging of macroscopic biological specimens,” J. Microsc.170(3), 229–236 (1993).
[CrossRef] [PubMed]

Cagigal, M. P.

M. P. Cagigal, J. E. Oti, V. F. Canales, and P. J. Valle, “Analytical design of superresolving phase filters,” Opt. Commun.241(4-6), 249–253 (2004).
[CrossRef]

D. M. de Juana, J. E. Oti, V. F. Canales, and M. P. Cagigal, “Design of superresolving continuous phase filters,” Opt. Lett.28(8), 607–609 (2003).
[CrossRef] [PubMed]

Campos, J.

Canales, V. F.

M. P. Cagigal, J. E. Oti, V. F. Canales, and P. J. Valle, “Analytical design of superresolving phase filters,” Opt. Commun.241(4-6), 249–253 (2004).
[CrossRef]

D. M. de Juana, J. E. Oti, V. F. Canales, and M. P. Cagigal, “Design of superresolving continuous phase filters,” Opt. Lett.28(8), 607–609 (2003).
[CrossRef] [PubMed]

Casperson, L. W.

Cathey, W. T.

de Juana, D. M.

Deininger, K.

H.-U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods4(4), 331–336 (2007).
[CrossRef] [PubMed]

Del Bene, F.

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. K. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science305(5686), 1007–1009 (2004).
[CrossRef] [PubMed]

Deussing, J. M.

H.-U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods4(4), 331–336 (2007).
[CrossRef] [PubMed]

Dodt, H.-U.

H.-U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods4(4), 331–336 (2007).
[CrossRef] [PubMed]

Dowski, E. R.

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Eder, M.

H.-U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods4(4), 331–336 (2007).
[CrossRef] [PubMed]

Escalera, J. C.

Fuchs, E.

Gori, F.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun.64(6), 491–495 (1987).
[CrossRef]

Guattari, G.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun.64(6), 491–495 (1987).
[CrossRef]

Hall, D. G.

Hegedus, Z. S.

Huisken, J.

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. K. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science305(5686), 1007–1009 (2004).
[CrossRef] [PubMed]

Jaffe, J. S.

Jährling, N.

H.-U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods4(4), 331–336 (2007).
[CrossRef] [PubMed]

Kempe, M.

R. Wolleschensky, B. Zimmermann, and M. Kempe, “High-speed confocal fluorescence imaging with a novel line scanning microscope,” J. Biomed. Opt.11(6), 064011 (2006).
[CrossRef] [PubMed]

Larkin, K. G.

Ledesma, S.

Leischner, U.

H.-U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods4(4), 331–336 (2007).
[CrossRef] [PubMed]

Li, Y.

Y. Li, “Three-dimensional intensity distribution in low Fresnel number focusing systems,” J. Opt. Soc. Am. A4(8), 1349–1353 (1987).
[CrossRef]

Y. Li and E. Wolf, “Three-dimensional intensity distribution near the focus in systems of different Fresnel numbers,” J. Opt. Soc. Am. A1(8), 801–808 (1984).
[CrossRef]

Long, R. A.

Mao, X.

C. J. R. Sheppard and X. Mao, “Confocal microscopes with slit apertures,” J. Mod. Opt.35(7), 1169–1185 (1988).
[CrossRef]

Matthews, H. J.

Mauch, C. P.

H.-U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods4(4), 331–336 (2007).
[CrossRef] [PubMed]

Mehta, S.

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Oti, J. E.

M. P. Cagigal, J. E. Oti, V. F. Canales, and P. J. Valle, “Analytical design of superresolving phase filters,” Opt. Commun.241(4-6), 249–253 (2004).
[CrossRef]

D. M. de Juana, J. E. Oti, V. F. Canales, and M. P. Cagigal, “Design of superresolving continuous phase filters,” Opt. Lett.28(8), 607–609 (2003).
[CrossRef] [PubMed]

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun.64(6), 491–495 (1987).
[CrossRef]

Schierloh, A.

H.-U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods4(4), 331–336 (2007).
[CrossRef] [PubMed]

Sheppard, C. J. R.

Spelman, F. A.

A. H. Voie, D. H. Burns, and F. A. Spelman, “Orthogonal-plane fluorescence optical sectioning: three-dimensional imaging of macroscopic biological specimens,” J. Microsc.170(3), 229–236 (1993).
[CrossRef] [PubMed]

Stelzer, E. H. K.

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. K. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science305(5686), 1007–1009 (2004).
[CrossRef] [PubMed]

Swoger, J.

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. K. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science305(5686), 1007–1009 (2004).
[CrossRef] [PubMed]

Tovar, A. A.

Valle, P. J.

M. P. Cagigal, J. E. Oti, V. F. Canales, and P. J. Valle, “Analytical design of superresolving phase filters,” Opt. Commun.241(4-6), 249–253 (2004).
[CrossRef]

Voie, A. H.

A. H. Voie, D. H. Burns, and F. A. Spelman, “Orthogonal-plane fluorescence optical sectioning: three-dimensional imaging of macroscopic biological specimens,” J. Microsc.170(3), 229–236 (1993).
[CrossRef] [PubMed]

Wilson, T.

C. J. R. Sheppard and T. Wilson, “Gaussian-beam theory of lenses with annular aperture,” IEE J. Microwaves, Opt. Acoust.2(4), 105–112 (1978).
[CrossRef]

Wittbrodt, J.

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. K. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science305(5686), 1007–1009 (2004).
[CrossRef] [PubMed]

Wolf, E.

Y. Li and E. Wolf, “Three-dimensional intensity distribution near the focus in systems of different Fresnel numbers,” J. Opt. Soc. Am. A1(8), 801–808 (1984).
[CrossRef]

Wolleschensky, R.

R. Wolleschensky, B. Zimmermann, and M. Kempe, “High-speed confocal fluorescence imaging with a novel line scanning microscope,” J. Biomed. Opt.11(6), 064011 (2006).
[CrossRef] [PubMed]

Zieglgänsberger, W.

H.-U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods4(4), 331–336 (2007).
[CrossRef] [PubMed]

Zimmermann, B.

R. Wolleschensky, B. Zimmermann, and M. Kempe, “High-speed confocal fluorescence imaging with a novel line scanning microscope,” J. Biomed. Opt.11(6), 064011 (2006).
[CrossRef] [PubMed]

Appl. Opt.

IEE J. Microwaves, Opt. Acoust.

C. J. R. Sheppard and T. Wilson, “Gaussian-beam theory of lenses with annular aperture,” IEE J. Microwaves, Opt. Acoust.2(4), 105–112 (1978).
[CrossRef]

J. Biomed. Opt.

R. Wolleschensky, B. Zimmermann, and M. Kempe, “High-speed confocal fluorescence imaging with a novel line scanning microscope,” J. Biomed. Opt.11(6), 064011 (2006).
[CrossRef] [PubMed]

J. Microsc.

A. H. Voie, D. H. Burns, and F. A. Spelman, “Orthogonal-plane fluorescence optical sectioning: three-dimensional imaging of macroscopic biological specimens,” J. Microsc.170(3), 229–236 (1993).
[CrossRef] [PubMed]

J. Mod. Opt.

C. J. R. Sheppard and X. Mao, “Confocal microscopes with slit apertures,” J. Mod. Opt.35(7), 1169–1185 (1988).
[CrossRef]

J. Opt. Soc. Am. A

Y. Li and E. Wolf, “Three-dimensional intensity distribution near the focus in systems of different Fresnel numbers,” J. Opt. Soc. Am. A1(8), 801–808 (1984).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Methods

H.-U. Dodt, U. Leischner, A. Schierloh, N. Jährling, C. P. Mauch, K. Deininger, J. M. Deussing, M. Eder, W. Zieglgänsberger, and K. Becker, “Ultramicroscopy: three-dimensional visualization of neuronal networks in the whole mouse brain,” Nat. Methods4(4), 331–336 (2007).
[CrossRef] [PubMed]

Opt. Commun.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Opt. Commun.64(6), 491–495 (1987).
[CrossRef]

M. P. Cagigal, J. E. Oti, V. F. Canales, and P. J. Valle, “Analytical design of superresolving phase filters,” Opt. Commun.241(4-6), 249–253 (2004).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett.58(15), 1499–1501 (1987).
[CrossRef] [PubMed]

Science

J. Huisken, J. Swoger, F. Del Bene, J. Wittbrodt, and E. H. K. Stelzer, “Optical sectioning deep inside live embryos by selective plane illumination microscopy,” Science305(5686), 1007–1009 (2004).
[CrossRef] [PubMed]

Other

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1993).

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Figures (3)

Fig. 1
Fig. 1

The variation of the Strehl ratio S with transverse gain G T for different filters. The maximally flat filters 3a, 5a, 7a lie on the dashed line indicated. The maximally flat filters 3b, 5b, 7d lie on another dashed line. The behavior for general symmetrical 3 element binary phase filters is also shown as solid lines: there are two branches, shown in red for G T 1 and in green G T 1 .

Fig. 2
Fig. 2

The axial (a, c, e) and transverse (b, d, f) intensity variations of the different maximally flat filters. (a, b) show filters 3a, 5a, 7a. (c, d) show filters 7b, 7c. (e, f) show filters 3b, 5b, 7d. The curves for an unobstructed slit pupil are shown as dotted lines.

Fig. 3
Fig. 3

The transverse variation in normalized intensity if the focal plane of a spherical lens with MF filters of 1-5 elements, for the broad solution. 1 element (black dashed line) corresponds to an unobstructed circular pupil. The curves get wider as the number of elements increases. Red: 2 elements. Green: 3 elements. Blue: 4 elements. Orange: 5 elements.

Tables (2)

Tables Icon

Table 1 Values of Various Parameters for Filters with 1, 3 5 or 7 Elements

Tables Icon

Table 2 Values of Various Parameters for Circular Filters with 1-5 Elements

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

U ( v , u ) = e i k z 1 + i u b 2 cos ( v 1 + i u b 2 ) exp [ ( v 2 b 2 + i u ) 2 ( 1 + i u b 2 ) ] ,
U ( v , u ) = N ( z ) e i π / 4 e i k z exp [ i v 2 4 π N ( z ) ] 1 1 P ( ξ ) exp ( i u ξ 2 2 ) exp ( i v ξ ) d ξ ,
v = k f x z sin α = k x a z ,
u = k a 2 ( 1 f 1 z ) = ( f z ) k δ z sin 2 α ,
U ( v , u ) = 1 2 1 1 P ( ξ ) [ 1 ( v 2 + i u ) ξ 2 2 u 2 ξ 4 8 + ... ] d ξ                         = I 0 2 [ 1 ( v 2 + i u ) 2 I 2 I 0 u 2 8 I 4 I 0 + ... ] ,
I n = 1 1 P ( ξ ) ξ n d ξ
I ( v , u ) = I 0 2 4 { 1 v 2 ( I 2 I 0 ) 2 u 2 4 [ I 4 I 0 ( I 2 I 0 ) 2 ] } .
S = I 0 2 , G T = 3 I 2 I 0 , G A = 45 4 [ I 4 I 0 ( I 2 I 0 ) 2 ] ,
I ( v , u ) = S ( 1 G T v 2 3 G A u 2 45 ) .
E = 1 2 1 1 | P ( ξ ) | 2 d ξ / ( P max ) 2 ,
U ( v , u ) = i π N 2 u e i k z exp [ i v 2 ( u + 2 π N ) 4 π N u ] { Erf [ ( 1 + i ) ( b u v ) 2 u ] Erf [ ( 1 + i ) ( a u v ) 2 u ] } .

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