Abstract

Optical transfer functions are presented for the confocal theta fluorescence microscope, which uses an orthogonally placed objective lens to detect the fluorescence emission. Therefore the transfer functions do not exhibit cylindrical symmetry about the illumination axis. We show that in an ideal noise-free system, confocal theta microscopy increases the cutoff spatial frequency along the illumination axis by a factor of 3.5 to 3.7 for a numerical aperture of 0.75. In a system with 10% noise the improvement by confocal theta microscopy is even greater, between a factor of 4.1 and 4.4. This explains the improved three-dimensional imaging properties of theta microscopy.

© 1996 Optical Society of America

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References

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  1. S. Lindek, E. H. K. Stelzer, “Confocal theta microscopy and 4Pi-confocal theta microscopy,” in Three-Dimensional Microscopy: Image Acquisition and Processing, C. J. Cogswell, K. Carlsson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2184, 188–194 (1994).
    [CrossRef]
  2. E. H. K. Stelzer, S. Lindek, “Fundamental reduction of the observation volume in far-field light microscopy by detection orthogonal to the illumination axis: confocal theta microscopy,” Opt. Commun. 111, 536–547 (1994).
    [CrossRef]
  3. S. Lindek, R. Pick, E. H. K. Stelzer, “Confocal theta microscope with three objective lenses,” Rev. Sci. Instrum. 65, 3367–3372 (1994).
    [CrossRef]
  4. E. H. K. Stelzer, S. Lindek, S. Albrecht, R. Pick, G. Ritter, N. Salmon, R. Stricker, “A new tool for the observation of embryos and other large specimens: confocal theta fluorescence microscopy,” J. Microsc. 179, 1–10 (1995).
    [CrossRef]
  5. C. J. R. Sheppard, M. Gu, “3-D transfer functions in confocal scanning microscopy,” in Visualization in Biomedical Microscopies, A. Kriete, ed. (Verlag Chemie, Weinheim, Germany, 1992), pp. 251–282.
  6. C. J. R. Sheppard, H. J. Matthews, “Imaging in high-aperture optical systems,” J. Opt. Soc. Am. A 4, 1354–1360 (1987).
    [CrossRef]
  7. B. R. Frieden, “Optical transfer of the three-dimensional object,” J. Opt. Soc. Am. 57, 56–66 (1967).
    [CrossRef]
  8. C. J. R. Sheppard, M. Gu, “The significance of 3-D transfer functions in confocal scanning microscopy,” J. Microsc. 165, 377–390 (1992).
    [CrossRef]
  9. M. Gu, T. Tannous, C. J. R. Sheppard, “Improved axial resolution in confocal fluorescence microscopy using annular pupils,” Opt. Commun. 110, 533–539 (1994).
    [CrossRef]
  10. M. Gu, C. J. R. Sheppard, “Comparison of three-dimensional imaging properties between two-photon and single-photon confocal fluorescence microscopy,” J. Microsc. 177, 128–137 (1995).
    [CrossRef]
  11. S. Wolfram, mathematica—A System for Doing Mathematics by Computer(Addison-Wesley, Redwood City, Calif., 1991).

1995 (2)

E. H. K. Stelzer, S. Lindek, S. Albrecht, R. Pick, G. Ritter, N. Salmon, R. Stricker, “A new tool for the observation of embryos and other large specimens: confocal theta fluorescence microscopy,” J. Microsc. 179, 1–10 (1995).
[CrossRef]

M. Gu, C. J. R. Sheppard, “Comparison of three-dimensional imaging properties between two-photon and single-photon confocal fluorescence microscopy,” J. Microsc. 177, 128–137 (1995).
[CrossRef]

1994 (3)

M. Gu, T. Tannous, C. J. R. Sheppard, “Improved axial resolution in confocal fluorescence microscopy using annular pupils,” Opt. Commun. 110, 533–539 (1994).
[CrossRef]

E. H. K. Stelzer, S. Lindek, “Fundamental reduction of the observation volume in far-field light microscopy by detection orthogonal to the illumination axis: confocal theta microscopy,” Opt. Commun. 111, 536–547 (1994).
[CrossRef]

S. Lindek, R. Pick, E. H. K. Stelzer, “Confocal theta microscope with three objective lenses,” Rev. Sci. Instrum. 65, 3367–3372 (1994).
[CrossRef]

1992 (1)

C. J. R. Sheppard, M. Gu, “The significance of 3-D transfer functions in confocal scanning microscopy,” J. Microsc. 165, 377–390 (1992).
[CrossRef]

1987 (1)

1967 (1)

Albrecht, S.

E. H. K. Stelzer, S. Lindek, S. Albrecht, R. Pick, G. Ritter, N. Salmon, R. Stricker, “A new tool for the observation of embryos and other large specimens: confocal theta fluorescence microscopy,” J. Microsc. 179, 1–10 (1995).
[CrossRef]

Frieden, B. R.

Gu, M.

M. Gu, C. J. R. Sheppard, “Comparison of three-dimensional imaging properties between two-photon and single-photon confocal fluorescence microscopy,” J. Microsc. 177, 128–137 (1995).
[CrossRef]

M. Gu, T. Tannous, C. J. R. Sheppard, “Improved axial resolution in confocal fluorescence microscopy using annular pupils,” Opt. Commun. 110, 533–539 (1994).
[CrossRef]

C. J. R. Sheppard, M. Gu, “The significance of 3-D transfer functions in confocal scanning microscopy,” J. Microsc. 165, 377–390 (1992).
[CrossRef]

C. J. R. Sheppard, M. Gu, “3-D transfer functions in confocal scanning microscopy,” in Visualization in Biomedical Microscopies, A. Kriete, ed. (Verlag Chemie, Weinheim, Germany, 1992), pp. 251–282.

Lindek, S.

E. H. K. Stelzer, S. Lindek, S. Albrecht, R. Pick, G. Ritter, N. Salmon, R. Stricker, “A new tool for the observation of embryos and other large specimens: confocal theta fluorescence microscopy,” J. Microsc. 179, 1–10 (1995).
[CrossRef]

E. H. K. Stelzer, S. Lindek, “Fundamental reduction of the observation volume in far-field light microscopy by detection orthogonal to the illumination axis: confocal theta microscopy,” Opt. Commun. 111, 536–547 (1994).
[CrossRef]

S. Lindek, R. Pick, E. H. K. Stelzer, “Confocal theta microscope with three objective lenses,” Rev. Sci. Instrum. 65, 3367–3372 (1994).
[CrossRef]

S. Lindek, E. H. K. Stelzer, “Confocal theta microscopy and 4Pi-confocal theta microscopy,” in Three-Dimensional Microscopy: Image Acquisition and Processing, C. J. Cogswell, K. Carlsson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2184, 188–194 (1994).
[CrossRef]

Matthews, H. J.

Pick, R.

E. H. K. Stelzer, S. Lindek, S. Albrecht, R. Pick, G. Ritter, N. Salmon, R. Stricker, “A new tool for the observation of embryos and other large specimens: confocal theta fluorescence microscopy,” J. Microsc. 179, 1–10 (1995).
[CrossRef]

S. Lindek, R. Pick, E. H. K. Stelzer, “Confocal theta microscope with three objective lenses,” Rev. Sci. Instrum. 65, 3367–3372 (1994).
[CrossRef]

Ritter, G.

E. H. K. Stelzer, S. Lindek, S. Albrecht, R. Pick, G. Ritter, N. Salmon, R. Stricker, “A new tool for the observation of embryos and other large specimens: confocal theta fluorescence microscopy,” J. Microsc. 179, 1–10 (1995).
[CrossRef]

Salmon, N.

E. H. K. Stelzer, S. Lindek, S. Albrecht, R. Pick, G. Ritter, N. Salmon, R. Stricker, “A new tool for the observation of embryos and other large specimens: confocal theta fluorescence microscopy,” J. Microsc. 179, 1–10 (1995).
[CrossRef]

Sheppard, C. J. R.

M. Gu, C. J. R. Sheppard, “Comparison of three-dimensional imaging properties between two-photon and single-photon confocal fluorescence microscopy,” J. Microsc. 177, 128–137 (1995).
[CrossRef]

M. Gu, T. Tannous, C. J. R. Sheppard, “Improved axial resolution in confocal fluorescence microscopy using annular pupils,” Opt. Commun. 110, 533–539 (1994).
[CrossRef]

C. J. R. Sheppard, M. Gu, “The significance of 3-D transfer functions in confocal scanning microscopy,” J. Microsc. 165, 377–390 (1992).
[CrossRef]

C. J. R. Sheppard, H. J. Matthews, “Imaging in high-aperture optical systems,” J. Opt. Soc. Am. A 4, 1354–1360 (1987).
[CrossRef]

C. J. R. Sheppard, M. Gu, “3-D transfer functions in confocal scanning microscopy,” in Visualization in Biomedical Microscopies, A. Kriete, ed. (Verlag Chemie, Weinheim, Germany, 1992), pp. 251–282.

Stelzer, E. H. K.

E. H. K. Stelzer, S. Lindek, S. Albrecht, R. Pick, G. Ritter, N. Salmon, R. Stricker, “A new tool for the observation of embryos and other large specimens: confocal theta fluorescence microscopy,” J. Microsc. 179, 1–10 (1995).
[CrossRef]

E. H. K. Stelzer, S. Lindek, “Fundamental reduction of the observation volume in far-field light microscopy by detection orthogonal to the illumination axis: confocal theta microscopy,” Opt. Commun. 111, 536–547 (1994).
[CrossRef]

S. Lindek, R. Pick, E. H. K. Stelzer, “Confocal theta microscope with three objective lenses,” Rev. Sci. Instrum. 65, 3367–3372 (1994).
[CrossRef]

S. Lindek, E. H. K. Stelzer, “Confocal theta microscopy and 4Pi-confocal theta microscopy,” in Three-Dimensional Microscopy: Image Acquisition and Processing, C. J. Cogswell, K. Carlsson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2184, 188–194 (1994).
[CrossRef]

Stricker, R.

E. H. K. Stelzer, S. Lindek, S. Albrecht, R. Pick, G. Ritter, N. Salmon, R. Stricker, “A new tool for the observation of embryos and other large specimens: confocal theta fluorescence microscopy,” J. Microsc. 179, 1–10 (1995).
[CrossRef]

Tannous, T.

M. Gu, T. Tannous, C. J. R. Sheppard, “Improved axial resolution in confocal fluorescence microscopy using annular pupils,” Opt. Commun. 110, 533–539 (1994).
[CrossRef]

Wolfram, S.

S. Wolfram, mathematica—A System for Doing Mathematics by Computer(Addison-Wesley, Redwood City, Calif., 1991).

J. Microsc. (3)

E. H. K. Stelzer, S. Lindek, S. Albrecht, R. Pick, G. Ritter, N. Salmon, R. Stricker, “A new tool for the observation of embryos and other large specimens: confocal theta fluorescence microscopy,” J. Microsc. 179, 1–10 (1995).
[CrossRef]

C. J. R. Sheppard, M. Gu, “The significance of 3-D transfer functions in confocal scanning microscopy,” J. Microsc. 165, 377–390 (1992).
[CrossRef]

M. Gu, C. J. R. Sheppard, “Comparison of three-dimensional imaging properties between two-photon and single-photon confocal fluorescence microscopy,” J. Microsc. 177, 128–137 (1995).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Commun. (2)

M. Gu, T. Tannous, C. J. R. Sheppard, “Improved axial resolution in confocal fluorescence microscopy using annular pupils,” Opt. Commun. 110, 533–539 (1994).
[CrossRef]

E. H. K. Stelzer, S. Lindek, “Fundamental reduction of the observation volume in far-field light microscopy by detection orthogonal to the illumination axis: confocal theta microscopy,” Opt. Commun. 111, 536–547 (1994).
[CrossRef]

Rev. Sci. Instrum. (1)

S. Lindek, R. Pick, E. H. K. Stelzer, “Confocal theta microscope with three objective lenses,” Rev. Sci. Instrum. 65, 3367–3372 (1994).
[CrossRef]

Other (3)

C. J. R. Sheppard, M. Gu, “3-D transfer functions in confocal scanning microscopy,” in Visualization in Biomedical Microscopies, A. Kriete, ed. (Verlag Chemie, Weinheim, Germany, 1992), pp. 251–282.

S. Lindek, E. H. K. Stelzer, “Confocal theta microscopy and 4Pi-confocal theta microscopy,” in Three-Dimensional Microscopy: Image Acquisition and Processing, C. J. Cogswell, K. Carlsson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2184, 188–194 (1994).
[CrossRef]

S. Wolfram, mathematica—A System for Doing Mathematics by Computer(Addison-Wesley, Redwood City, Calif., 1991).

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Figures (4)

Fig. 1
Fig. 1

Normalized 1-D OTF’s for confocal fluorescence microscopy with a NA = 0.75: axial refers to the on-axis OTF, and lateral refers to the in-focus OTF. These functions describe the contrast transfer of spatial frequencies for line objects.

Fig. 2
Fig. 2

Normalized 1-D OTF’s for confocal theta fluorescence microscopy with NA = 0.75: the OTF for line objects along the illumination or the detection axis (x/z) and the OTF for line objects along the orthogonal axis (y). These functions describe the contrast transfer of spatial frequencies for line objects.

Fig. 3
Fig. 3

Cross sections through the normalized 3-D OTF for confocal fluorescence microscopy with NA = 0.75: axial refers to the cross section along the optical axis, and lateral refers to the cross section in the lateral direction. These functions describe the contrast transfer of spatial frequencies for thick objects.

Fig. 4
Fig. 4

Cross sections through the normalized 3-D OTF for confocal theta fluorescence microscopy with NA = 0.75: the cross section along the illumination or the detection axis (x/z) and the cross section along the orthogonal axis (y). These functions describe the contrast transfer of spatial frequencies for thick objects.

Tables (2)

Tables Icon

Table 1 Cutoff Spatial Frequencies, Value at 10%, and Area under the Graph for 1-D OTF’s for 1-D Line Objects (Figs. 1 and 2)

Tables Icon

Table 2 Cutoff Spatial Frequencies, Value at 10%, and Area under the Graph for Cross Sections through the 3-D OTF’s for Thick Objects (Figs. 3 and 4)

Equations (8)

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h cf ( v , u ) 2 = h ill ( v , u ) 2 h det ( v , u ) 2 ,
h cf ( v , w , u ) 2 = h ill ( v , w , u ) 2 h det ( v , w , u ) 2 ,
h cf , theta ( v , w , u ) 2 = h ill ( v , w , u ) 2 h det , theta ( v , w , u ) 2 = h ill ( v , w , u ) 2 h det ( u , w , v ) 2 .
C ( m , n , s ) = F { h cf , theta ( v , w , u ) 2 } = F { h ill ( v , w , u ) 2 } F { h det ( u , w , v ) 2 } ,
c ( l , s ) = 1 l 1 - ( s l - l 2 ) 2 ,
c 1 ( s ) = c ( m , n , s ) d m d n = 2 π l c ( l , s ) d l , c 1 ( m ) = c ( m , n , s ) d n d s .
C 1 ( s ) = c 1 ( s ) c 1 ( s ) ,             C 1 ( m ) = c 1 ( m ) c 1 ( m ) .
C 1 , theta ( r ) = c 1 ( s ) c 1 ( m ) ;

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