Abstract

We present a new family of pupil masks to control the axial component of the intensity distribution in the focal region of tightly focused light fields. The filters, which consist of a circular clear pupil with a single shaded ring, allow to control the width of the central lobe of the axial spot together with the residual sidelobes energy. The filters can be applied to improve the optical sectioning capacity of different scanning microscopes.

©2003 Optical Society of America

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References

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  1. J. Pawley (ed.), Handbook of Biological Confocal Microscopy (Plenun, New York, 1995).
    [Crossref]
  2. A. Diaspro (ed.) Confocal and Two-Photon Microscopy. Foundations, Applications and Advances (Wiley, New York, 2001).
  3. C. M. Blanca, J. Bewersdorf, and S. W. Hell, “Single sharp spot in fluorescence microscopy of two opposing lenses,” Appl. Phys. Lett. 79, 2321–2323 (2001)
    [Crossref]
  4. T. A. Klar, E. Engel, and S. W. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes”, Phys. Rev. E 64: 066613, 1–9 (2001).
    [Crossref]
  5. M. A. A. Neil, R. Juskaitis, T. Wilson, Z. J. Laczik, and V. Sarafis, “Optimized pupil-plane filters for confocal microscope point-spread function engineering,” Opt. Lett. 25, 245–247 (2000).
    [Crossref]
  6. Z. Ding, G. Wang, M. Gu, Z. Wang, and Z. Fan, “Superresolution with an apodization film in a confocal setup,” Appl. Opt. 36, 360–363 (1997).
    [Crossref] [PubMed]
  7. C. J. R. Sheppard, “Binary optics and confocal imaging,” Opt. Lett. 24, 505–506 (1999).
    [Crossref]
  8. M. Martínez-Corral, M. T. Caballero, E. Stelzer, and J. Swoger, “Tailoring the axial shape of the PSF using the Toraldo concept,” Opt. Express 10, 98–103 (2002). www.opticsexpress.org/abstract.cfm?URI=OPEX-10-1-98
    [Crossref] [PubMed]
  9. G. Boyer, “New class of axially apodizing filters for confocal scanning microscopy,” J. Opt. Soc. Am. A 19, 584–589 (2002).
    [Crossref]
  10. G. Boyer and V. Sarafis, “Two pinhole superresolution using spatial filters,” Optik 112, 177–179 (2001).
    [Crossref]
  11. C. M. Blanca and S. W. Hell, “Axial superresolution with ultrahigh aperture lenses,” Opt. Express 10, 893–898 (2002). www.opticsexpress.org/abstract.cfm?URI=OPEX-10-17-893
    [Crossref] [PubMed]
  12. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. (London) A 253, 358–379 (1959).
    [Crossref]
  13. P. D. Higdon, P. Török, and T. Wilson, “Imaging properties of high aperture multiphoton fluorescence scanning optical microscopes,” J. Microsc. 193, 127–141 (1998).
    [Crossref]
  14. C. J. R. Sheppard, “High apertured beams,” J. Opt. Soc. Am. A 18, 1579–1587 (2001).
    [Crossref]
  15. K. Bahlman and S. W. Hell, “Electric field depolarization in high aperture focusing with emphasis on annular apertures,” J. Microsc. 200, 59–67 (2000).
    [Crossref]
  16. M. A. A. Neil, F. Massoumian, R. Juskaitis, and T. Wilson, “A method for the generation of arbitrary complex vector wavefronts,” Opt. Lett. 27, 1929–1931 (2002).
    [Crossref]
  17. P. Török and F. J. Kao (eds.) Optical Imaging and Microscopy: Techniques and Advanced Systems, (Springer, Heidelberg, 2003).
  18. J. W. M. Chon, X. Gan, and M. Gu, “Splitting of the focal spot of a high-numerical objective in free space,” Appl. Phys. Lett. 81, 1576–1579 (2002).
    [Crossref]
  19. I. Akduman, U. Brand, J. Grochmalicki, G. Hester, R. Pike, and M. Bertero, “Superresolving masks for incoherent high-NA scanning microscopy in three dimensions,” J. Opt. Soc. Am. A 15, 2275–2287 (1998).
    [Crossref]
  20. D. M. de Juana, J. E. Oti, V. F. Canales, and M. P. Cagigal, “Design of superresolving continuous phase filters,” Opt. Lett. 28, 607–609 (2003).
    [Crossref] [PubMed]
  21. S. Mezouari and A. R. Harvey, “Phase pupil functions for reduction of defocus and spherical aberration,” Opt. Lett. 28, 771–773 (2003).
    [Crossref] [PubMed]
  22. H. Liu, Y. Yan, D. Yi, and G. Jin, “Design of three-dimensional superresolution filters and limits of axial optical superresolution,” Appl. Opt. 42, 1463–1476 (2003).
    [Crossref] [PubMed]
  23. G. Toraldo di Francia, “Nuovo pupille superresolventi,” Atti Fond. Giorgio Ronchi 7, 366–372 (1952).
  24. J. Campos, J. C. Escalera, C. J. R. Sheppard, and M. J. Yzuel, “Axially invariant pupil filters,” J. Mod. Opt. 47, 57–68 (2000).
  25. S. Grill and E. H. K. Stelzer, “Method to calculate lateral and axial gain factors of optical setups with a large solid angle,” J. Opt. Soc. Am. A 16, 2658–2665 (1999).
    [Crossref]
  26. C. J. R. Sheppard, “Leaky annular pupils for improved axial imaging,” Optik 99, 32–34 (1995).
  27. C. J. R. Sheppard and P. Török, “An electromagnetic theory of imaging in fluorescence microscopy, and imaging in polarization fluorescence microscopy,” Bioimaging 5, 205–218 (1997).
    [Crossref]
  28. D. Ganic, J. W. M. Chon, and M. Gu, “Effect of numerical aperture on the splitting feature near phase singularities of focused waves,” Appl. Phys. Lett. 82, 1527–1528 (2003).
    [Crossref]
  29. M. Martínez-Corral, L. Muñoz-Escrivá, M. Kowalczyk, and T. Cichocki, “One-dimensional iterative algorithm for three-dimensional point-spread function engineering,” Opt. Lett. 26, 1861–1863 (2001).
    [Crossref]

2003 (4)

2002 (5)

2001 (5)

C. M. Blanca, J. Bewersdorf, and S. W. Hell, “Single sharp spot in fluorescence microscopy of two opposing lenses,” Appl. Phys. Lett. 79, 2321–2323 (2001)
[Crossref]

T. A. Klar, E. Engel, and S. W. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes”, Phys. Rev. E 64: 066613, 1–9 (2001).
[Crossref]

G. Boyer and V. Sarafis, “Two pinhole superresolution using spatial filters,” Optik 112, 177–179 (2001).
[Crossref]

C. J. R. Sheppard, “High apertured beams,” J. Opt. Soc. Am. A 18, 1579–1587 (2001).
[Crossref]

M. Martínez-Corral, L. Muñoz-Escrivá, M. Kowalczyk, and T. Cichocki, “One-dimensional iterative algorithm for three-dimensional point-spread function engineering,” Opt. Lett. 26, 1861–1863 (2001).
[Crossref]

2000 (3)

K. Bahlman and S. W. Hell, “Electric field depolarization in high aperture focusing with emphasis on annular apertures,” J. Microsc. 200, 59–67 (2000).
[Crossref]

J. Campos, J. C. Escalera, C. J. R. Sheppard, and M. J. Yzuel, “Axially invariant pupil filters,” J. Mod. Opt. 47, 57–68 (2000).

M. A. A. Neil, R. Juskaitis, T. Wilson, Z. J. Laczik, and V. Sarafis, “Optimized pupil-plane filters for confocal microscope point-spread function engineering,” Opt. Lett. 25, 245–247 (2000).
[Crossref]

1999 (2)

1998 (2)

I. Akduman, U. Brand, J. Grochmalicki, G. Hester, R. Pike, and M. Bertero, “Superresolving masks for incoherent high-NA scanning microscopy in three dimensions,” J. Opt. Soc. Am. A 15, 2275–2287 (1998).
[Crossref]

P. D. Higdon, P. Török, and T. Wilson, “Imaging properties of high aperture multiphoton fluorescence scanning optical microscopes,” J. Microsc. 193, 127–141 (1998).
[Crossref]

1997 (2)

Z. Ding, G. Wang, M. Gu, Z. Wang, and Z. Fan, “Superresolution with an apodization film in a confocal setup,” Appl. Opt. 36, 360–363 (1997).
[Crossref] [PubMed]

C. J. R. Sheppard and P. Török, “An electromagnetic theory of imaging in fluorescence microscopy, and imaging in polarization fluorescence microscopy,” Bioimaging 5, 205–218 (1997).
[Crossref]

1995 (1)

C. J. R. Sheppard, “Leaky annular pupils for improved axial imaging,” Optik 99, 32–34 (1995).

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. (London) A 253, 358–379 (1959).
[Crossref]

1952 (1)

G. Toraldo di Francia, “Nuovo pupille superresolventi,” Atti Fond. Giorgio Ronchi 7, 366–372 (1952).

Akduman, I.

Bahlman, K.

K. Bahlman and S. W. Hell, “Electric field depolarization in high aperture focusing with emphasis on annular apertures,” J. Microsc. 200, 59–67 (2000).
[Crossref]

Bertero, M.

Bewersdorf, J.

C. M. Blanca, J. Bewersdorf, and S. W. Hell, “Single sharp spot in fluorescence microscopy of two opposing lenses,” Appl. Phys. Lett. 79, 2321–2323 (2001)
[Crossref]

Blanca, C. M.

C. M. Blanca and S. W. Hell, “Axial superresolution with ultrahigh aperture lenses,” Opt. Express 10, 893–898 (2002). www.opticsexpress.org/abstract.cfm?URI=OPEX-10-17-893
[Crossref] [PubMed]

C. M. Blanca, J. Bewersdorf, and S. W. Hell, “Single sharp spot in fluorescence microscopy of two opposing lenses,” Appl. Phys. Lett. 79, 2321–2323 (2001)
[Crossref]

Boyer, G.

G. Boyer, “New class of axially apodizing filters for confocal scanning microscopy,” J. Opt. Soc. Am. A 19, 584–589 (2002).
[Crossref]

G. Boyer and V. Sarafis, “Two pinhole superresolution using spatial filters,” Optik 112, 177–179 (2001).
[Crossref]

Brand, U.

Caballero, M. T.

Cagigal, M. P.

Campos, J.

J. Campos, J. C. Escalera, C. J. R. Sheppard, and M. J. Yzuel, “Axially invariant pupil filters,” J. Mod. Opt. 47, 57–68 (2000).

Canales, V. F.

Chon, J. W. M.

D. Ganic, J. W. M. Chon, and M. Gu, “Effect of numerical aperture on the splitting feature near phase singularities of focused waves,” Appl. Phys. Lett. 82, 1527–1528 (2003).
[Crossref]

J. W. M. Chon, X. Gan, and M. Gu, “Splitting of the focal spot of a high-numerical objective in free space,” Appl. Phys. Lett. 81, 1576–1579 (2002).
[Crossref]

Cichocki, T.

de Juana, D. M.

di Francia, G. Toraldo

G. Toraldo di Francia, “Nuovo pupille superresolventi,” Atti Fond. Giorgio Ronchi 7, 366–372 (1952).

Ding, Z.

Engel, E.

T. A. Klar, E. Engel, and S. W. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes”, Phys. Rev. E 64: 066613, 1–9 (2001).
[Crossref]

Escalera, J. C.

J. Campos, J. C. Escalera, C. J. R. Sheppard, and M. J. Yzuel, “Axially invariant pupil filters,” J. Mod. Opt. 47, 57–68 (2000).

Fan, Z.

Gan, X.

J. W. M. Chon, X. Gan, and M. Gu, “Splitting of the focal spot of a high-numerical objective in free space,” Appl. Phys. Lett. 81, 1576–1579 (2002).
[Crossref]

Ganic, D.

D. Ganic, J. W. M. Chon, and M. Gu, “Effect of numerical aperture on the splitting feature near phase singularities of focused waves,” Appl. Phys. Lett. 82, 1527–1528 (2003).
[Crossref]

Grill, S.

Grochmalicki, J.

Gu, M.

D. Ganic, J. W. M. Chon, and M. Gu, “Effect of numerical aperture on the splitting feature near phase singularities of focused waves,” Appl. Phys. Lett. 82, 1527–1528 (2003).
[Crossref]

J. W. M. Chon, X. Gan, and M. Gu, “Splitting of the focal spot of a high-numerical objective in free space,” Appl. Phys. Lett. 81, 1576–1579 (2002).
[Crossref]

Z. Ding, G. Wang, M. Gu, Z. Wang, and Z. Fan, “Superresolution with an apodization film in a confocal setup,” Appl. Opt. 36, 360–363 (1997).
[Crossref] [PubMed]

Harvey, A. R.

Hell, S. W.

C. M. Blanca and S. W. Hell, “Axial superresolution with ultrahigh aperture lenses,” Opt. Express 10, 893–898 (2002). www.opticsexpress.org/abstract.cfm?URI=OPEX-10-17-893
[Crossref] [PubMed]

T. A. Klar, E. Engel, and S. W. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes”, Phys. Rev. E 64: 066613, 1–9 (2001).
[Crossref]

C. M. Blanca, J. Bewersdorf, and S. W. Hell, “Single sharp spot in fluorescence microscopy of two opposing lenses,” Appl. Phys. Lett. 79, 2321–2323 (2001)
[Crossref]

K. Bahlman and S. W. Hell, “Electric field depolarization in high aperture focusing with emphasis on annular apertures,” J. Microsc. 200, 59–67 (2000).
[Crossref]

Hester, G.

Higdon, P. D.

P. D. Higdon, P. Török, and T. Wilson, “Imaging properties of high aperture multiphoton fluorescence scanning optical microscopes,” J. Microsc. 193, 127–141 (1998).
[Crossref]

Jin, G.

Juskaitis, R.

Klar, T. A.

T. A. Klar, E. Engel, and S. W. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes”, Phys. Rev. E 64: 066613, 1–9 (2001).
[Crossref]

Kowalczyk, M.

Laczik, Z. J.

Liu, H.

Martínez-Corral, M.

Massoumian, F.

Mezouari, S.

Muñoz-Escrivá, L.

Neil, M. A. A.

Oti, J. E.

Pike, R.

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. (London) A 253, 358–379 (1959).
[Crossref]

Sarafis, V.

Sheppard, C. J. R.

C. J. R. Sheppard, “High apertured beams,” J. Opt. Soc. Am. A 18, 1579–1587 (2001).
[Crossref]

J. Campos, J. C. Escalera, C. J. R. Sheppard, and M. J. Yzuel, “Axially invariant pupil filters,” J. Mod. Opt. 47, 57–68 (2000).

C. J. R. Sheppard, “Binary optics and confocal imaging,” Opt. Lett. 24, 505–506 (1999).
[Crossref]

C. J. R. Sheppard and P. Török, “An electromagnetic theory of imaging in fluorescence microscopy, and imaging in polarization fluorescence microscopy,” Bioimaging 5, 205–218 (1997).
[Crossref]

C. J. R. Sheppard, “Leaky annular pupils for improved axial imaging,” Optik 99, 32–34 (1995).

Stelzer, E.

Stelzer, E. H. K.

Swoger, J.

Török, P.

P. D. Higdon, P. Török, and T. Wilson, “Imaging properties of high aperture multiphoton fluorescence scanning optical microscopes,” J. Microsc. 193, 127–141 (1998).
[Crossref]

C. J. R. Sheppard and P. Török, “An electromagnetic theory of imaging in fluorescence microscopy, and imaging in polarization fluorescence microscopy,” Bioimaging 5, 205–218 (1997).
[Crossref]

Wang, G.

Wang, Z.

Wilson, T.

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. (London) A 253, 358–379 (1959).
[Crossref]

Yan, Y.

Yi, D.

Yzuel, M. J.

J. Campos, J. C. Escalera, C. J. R. Sheppard, and M. J. Yzuel, “Axially invariant pupil filters,” J. Mod. Opt. 47, 57–68 (2000).

Appl. Opt. (2)

Appl. Phys. Lett. (3)

C. M. Blanca, J. Bewersdorf, and S. W. Hell, “Single sharp spot in fluorescence microscopy of two opposing lenses,” Appl. Phys. Lett. 79, 2321–2323 (2001)
[Crossref]

D. Ganic, J. W. M. Chon, and M. Gu, “Effect of numerical aperture on the splitting feature near phase singularities of focused waves,” Appl. Phys. Lett. 82, 1527–1528 (2003).
[Crossref]

J. W. M. Chon, X. Gan, and M. Gu, “Splitting of the focal spot of a high-numerical objective in free space,” Appl. Phys. Lett. 81, 1576–1579 (2002).
[Crossref]

Atti Fond. Giorgio Ronchi (1)

G. Toraldo di Francia, “Nuovo pupille superresolventi,” Atti Fond. Giorgio Ronchi 7, 366–372 (1952).

Bioimaging (1)

C. J. R. Sheppard and P. Török, “An electromagnetic theory of imaging in fluorescence microscopy, and imaging in polarization fluorescence microscopy,” Bioimaging 5, 205–218 (1997).
[Crossref]

J. Microsc. (2)

P. D. Higdon, P. Török, and T. Wilson, “Imaging properties of high aperture multiphoton fluorescence scanning optical microscopes,” J. Microsc. 193, 127–141 (1998).
[Crossref]

K. Bahlman and S. W. Hell, “Electric field depolarization in high aperture focusing with emphasis on annular apertures,” J. Microsc. 200, 59–67 (2000).
[Crossref]

J. Mod. Opt. (1)

J. Campos, J. C. Escalera, C. J. R. Sheppard, and M. J. Yzuel, “Axially invariant pupil filters,” J. Mod. Opt. 47, 57–68 (2000).

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

Opt. Express (2)

Opt. Lett. (6)

Optik (2)

C. J. R. Sheppard, “Leaky annular pupils for improved axial imaging,” Optik 99, 32–34 (1995).

G. Boyer and V. Sarafis, “Two pinhole superresolution using spatial filters,” Optik 112, 177–179 (2001).
[Crossref]

Phys. Rev. E (1)

T. A. Klar, E. Engel, and S. W. Hell, “Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes”, Phys. Rev. E 64: 066613, 1–9 (2001).
[Crossref]

Proc. Roy. Soc. (London) A (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. Roy. Soc. (London) A 253, 358–379 (1959).
[Crossref]

Other (3)

P. Török and F. J. Kao (eds.) Optical Imaging and Microscopy: Techniques and Advanced Systems, (Springer, Heidelberg, 2003).

J. Pawley (ed.), Handbook of Biological Confocal Microscopy (Plenun, New York, 1995).
[Crossref]

A. Diaspro (ed.) Confocal and Two-Photon Microscopy. Foundations, Applications and Advances (Wiley, New York, 2001).

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Figures (3)

Fig. 1.
Fig. 1. (a) Mapped transmittance of a SR filter (black curve). The SR filter is composed by a DR filter (green curve) and a shaded ring (red curve); (b) Amplitude PSF of the SR filter (black curve) which is calculated as the sum of two amplitude PSF’s: the one of the DR filter and that of the shaded ring; (c) Intensity PSF of the SR filter, as compared with the PSF of the nonapodized objective. The parameters for the calculation were µ=0.75, η=0.68.

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Fig. 2.
Fig. 2. (a) SLPR values for families of SR filters with the same axial gain; (b) Numerically evaluated 3D PSF (pseudo-colored) of a confocal instrument with two circular pupils; (c) Same as (b) but with the selected SR filter in illumination. The parameters for the calculation where: φ=π/2, λill =350 nm, λdet =440 nm (Coumarin 400) and NA=1.2 (water).

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Fig. 3.
Fig. 3. (a) SLPR2p values for families of SR filters with the same axial gain; (b) Numerically evaluated 3D PSF (pseudo-colored) of a TPE scanning microscope with circular pupil (bottom) or with the selected SR filter (top); (c) Comparison of axial PSF’s corresponding to different kind of filters. The parameters for the calculation where: φ=π/2, λill =700 nm, and NA=1.2.

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Equations (10)

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E ( r , z , φ ; λ ) = [ I 0 ( r , z ; λ ) + I 2 ( r , z ; λ ) cos φ ] i + I 2 ( r , z ; λ ) sin 2 φ j − 2 I 1 ( r , z ; λ ) cos φ k ,
E ( r = 0 , z , φ ; λ ) = i I 0 ( r = 0 , z ; λ ) = i ∫ 0 α P ( θ ) ( 1 + cos θ ) exp ( i 2 π n cos θ λ z ) sin θ d θ ,
ζ = cos θ − cos α 1 − cos α − 0.5 ; Q ( ζ ) = ( 1 + cos θ ) P ( θ ) .
E ( r = 0 , z , φ ; λ ) = E o ( z N ) = ( 1 − cos α ) exp ( i π 1 + cos α 1 − cos α z N ) ∫ − 0.5 0.5 Q ( ζ ) exp ( i 2 π ζ z N ) d ζ ,
G A = ( 1 − η μ 3 ) ( 1 − η μ ) ,
PSF ( r , z , φ ; λ ill , λ det ) = PSF ill ( r , z , φ ; λ ill ) PSF det ( r , z ; λ ill ε ) =
= ∣ E ill ( r , z , φ ; λ ill ) ∣ 2 〈 ∣ E det ( r , z , φ ; λ ill ε ) ∣ 2 〉 φ ,
SLPR = ∫ z p + ∞ ∣ E ill ( r = 0 , z , φ ; λ ill ) ∣ 2 d z ∫ 0 z p ∣ E ill ( r = 0 , z , φ ; λ ill ) ∣ 2 d z ,
PSF 2 p ( r , z , φ ; λ ill ) = ∣ E ill ( r , z , φ ; λ ill ) ∣ 4 .
SLPR 2 p = ∫ z p + ∞ ∣ E ill ( r = 0 , z , φ ; λ ill ) ∣ 4 d z ∫ 0 z p ∣ E ill ( r = 0 , z , φ ; λ ill ) ∣ 4 d z .

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