Abstract

We show that the volumetric field distribution in the focal region of a high numerical aperture focusing system can be efficiently calculated with a three-dimensional Fourier transform. In addition to focusing in a single medium, the method is able to calculate the more complex case of focusing through a planar interface between two media of mismatched refractive indices. The use of the chirp z-transform in our numerical implementation of the method allows us to perform fast calculations of the three-dimensional focused field distribution with good accuracy.

© 2012 OSA

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  1. J. J. Stamnes, Waves in Focal Regions (Hilger, 1986).
  2. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  3. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999).
  4. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
    [CrossRef]
  5. M. Leutenegger, R. Rao, R. A. Leitgeb, and T. Lasser, “Fast focus field calculations,” Opt. Express 14(23), 11277–11291 (2006).
    [CrossRef] [PubMed]
  6. A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-time signal processing, 2nd ed. (Prentice Hall, 1999).
  7. C. W. McCutchen, “Generalized aperture and the three-dimensional diffraction image,” J. Opt. Soc. Am. 54(2), 240–244 (1964).
    [CrossRef]
  8. C. W. McCutchen, “Generalized aperture and the three-dimensional diffraction image: erratum,” J. Opt. Soc. Am. A 19(8), 1721–1721 (2002).
    [CrossRef]
  9. I. Iglesias and B. Vohnsen, “Polarization structuring for focal volume shaping in high-resolution microscopy,” Opt. Commun. 271(1), 40–47 (2007).
    [CrossRef]
  10. J. Lin, X.-C. Yuan, S. S. Kou, C. J. R. Sheppard, O. G. Rodríguez-Herrera, and J. C. Dainty, “Direct calculation of a three-dimensional diffracted field,” Opt. Lett. 36(8), 1341–1343 (2011).
    [CrossRef] [PubMed]
  11. P. Török, P. R. T. Munro, and E. E. Kriezis, “Rigorous near- to far-field transformation for vectorial diffraction calculations and its numerical implementation,” J. Opt. Soc. Am. A 23(3), 713–722 (2006).
    [CrossRef] [PubMed]
  12. D. Ganic, X. Gan, and M. Gu, “Focusing of doughnut laser beams by a high numerical-aperture objective in free space,” Opt. Express 11(21), 2747–2752 (2003).
    [CrossRef] [PubMed]
  13. J. Lin, X.-C. Yuan, S. H. Tao, and R. E. Burge, “Variable-radius focused optical vortex with suppressed sidelobes,” Opt. Lett. 31(11), 1600–1602 (2006).
    [CrossRef] [PubMed]
  14. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1(1), 1–57 (2009).
    [CrossRef]
  15. C. J. R. Sheppard and M. Gu, “Axial imaging through an aberration layer of water in confocal microscopy,” Opt. Commun. 88(2-3), 180–190 (1992).
    [CrossRef]
  16. P. Török, P. Varga, Z. Laczik, and G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: an integral representation,” J. Opt. Soc. Am. A 12(2), 325–332 (1995).
    [CrossRef]
  17. S. H. Wiersma, P. Török, T. D. Visser, and P. Varga, “Comparison of different theories for focusing through a plane interface,” J. Opt. Soc. Am. A 14(7), 1482–1490 (1997).
    [CrossRef]
  18. P. Török and P. Varga, “Electromagnetic diffraction of light focused through a stratified medium,” Appl. Opt. 36(11), 2305–2312 (1997).
    [CrossRef] [PubMed]

2011 (1)

2009 (1)

2007 (1)

I. Iglesias and B. Vohnsen, “Polarization structuring for focal volume shaping in high-resolution microscopy,” Opt. Commun. 271(1), 40–47 (2007).
[CrossRef]

2006 (3)

2003 (1)

2002 (1)

1997 (2)

1995 (1)

1992 (1)

C. J. R. Sheppard and M. Gu, “Axial imaging through an aberration layer of water in confocal microscopy,” Opt. Commun. 88(2-3), 180–190 (1992).
[CrossRef]

1964 (1)

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[CrossRef]

Booker, G. R.

Burge, R. E.

Dainty, J. C.

Gan, X.

Ganic, D.

Gu, M.

D. Ganic, X. Gan, and M. Gu, “Focusing of doughnut laser beams by a high numerical-aperture objective in free space,” Opt. Express 11(21), 2747–2752 (2003).
[CrossRef] [PubMed]

C. J. R. Sheppard and M. Gu, “Axial imaging through an aberration layer of water in confocal microscopy,” Opt. Commun. 88(2-3), 180–190 (1992).
[CrossRef]

Iglesias, I.

I. Iglesias and B. Vohnsen, “Polarization structuring for focal volume shaping in high-resolution microscopy,” Opt. Commun. 271(1), 40–47 (2007).
[CrossRef]

Kou, S. S.

Kriezis, E. E.

Laczik, Z.

Lasser, T.

Leitgeb, R. A.

Leutenegger, M.

Lin, J.

McCutchen, C. W.

Munro, P. R. T.

Rao, R.

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[CrossRef]

Rodríguez-Herrera, O. G.

Sheppard, C. J. R.

J. Lin, X.-C. Yuan, S. S. Kou, C. J. R. Sheppard, O. G. Rodríguez-Herrera, and J. C. Dainty, “Direct calculation of a three-dimensional diffracted field,” Opt. Lett. 36(8), 1341–1343 (2011).
[CrossRef] [PubMed]

C. J. R. Sheppard and M. Gu, “Axial imaging through an aberration layer of water in confocal microscopy,” Opt. Commun. 88(2-3), 180–190 (1992).
[CrossRef]

Tao, S. H.

Török, P.

Varga, P.

Visser, T. D.

Vohnsen, B.

I. Iglesias and B. Vohnsen, “Polarization structuring for focal volume shaping in high-resolution microscopy,” Opt. Commun. 271(1), 40–47 (2007).
[CrossRef]

Wiersma, S. H.

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[CrossRef]

Yuan, X.-C.

Zhan, Q.

Adv. Opt. Photon. (1)

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

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

Opt. Commun. (2)

I. Iglesias and B. Vohnsen, “Polarization structuring for focal volume shaping in high-resolution microscopy,” Opt. Commun. 271(1), 40–47 (2007).
[CrossRef]

C. J. R. Sheppard and M. Gu, “Axial imaging through an aberration layer of water in confocal microscopy,” Opt. Commun. 88(2-3), 180–190 (1992).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Proc. R. Soc. Lond. A Math. Phys. Sci. (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[CrossRef]

Other (4)

A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-time signal processing, 2nd ed. (Prentice Hall, 1999).

J. J. Stamnes, Waves in Focal Regions (Hilger, 1986).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999).

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