Abstract

The three-dimensional optical transfer function is derived for analyzing the imaging performance in fiber-optical two-photon fluorescence microscopy. Two types of fiber-optical geometry are considered: The first involves a single-mode fiber for delivering a laser beam for illumination, and the second is based on the use of a single-mode fiber coupler for both illumination delivery and signal collection. It is found that in the former case the transverse and axial cutoff spatial frequencies of the three-dimensional optical transfer function are the same as those in conventional two-photon fluorescence microscopy without the use of a pinhole. However, the transverse and axial cutoff spatial frequencies in the latter case are 1.7 times as large as those in the former case. Accordingly, this feature leads to an enhanced optical sectioning effect when a fiber coupler is used, which is consistent with our recent experimental observation.

© 2003 Optical Society of America

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References

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2002

1998

M. Gu, D. K. Bird, “Fiber-optical double-pass confocal microscopy,” Opt. Laser Technol. 30, 91–93 (1998).
[CrossRef]

1996

H. Zhou, C. J. R. Sheppard, M. Gu, “A compact confocal interference microscope based on a four-port single-mode fiber coupler,” Optik (Stuttgart) 103, 45–48 (1996).

1995

A. Lago, A. T. Obeidat, A. E. Kaplan, J. B. Khurigan, P. L. Shkolnikov, “Two-photon-induced fluorescence of biological markers based on optical fibers,” Opt. Lett. 20, 2054–2056 (1995).
[CrossRef] [PubMed]

M. Gu, T. Tannous, C. J. R. Sheppard, “Three-dimensional confocal fluorescence imaging under ultrashort pulse illumination,” Opt. Commun. 117, 406–412 (1995).
[CrossRef]

1994

1993

A. F. Gmitro, D. Aziz, “Confocal microscopy through a fiber optic imaging bundle,” Opt. Lett. 18, 565–567 (1993).
[CrossRef]

T. Wilson, “Image formation in two-mode fiber-based confocal microscopes,” J. Opt. Soc. Am. A 10, 1535–1543 (1993).
[CrossRef]

M. Gu, C. J. R. Sheppard, “Fiber-optical confocal scanning interference microscopy,” Opt. Commun. 100, 79–86 (1993).
[CrossRef]

M. Gu, C. J. R. Sheppard, “Effect of a finite-sized pinhole on 3D image formation in confocal two-photon fluorescence microscopy,” J. Mod. Opt. 40, 2009–2024 (1993).
[CrossRef]

1992

1991

1990

W. Denk, J. H. Strickler, W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–75 (1990).
[CrossRef] [PubMed]

1989

1967

Arimoto, R.

Aziz, D.

Benschop, J.

Bird, D.

Bird, D. K.

M. Gu, D. K. Bird, “Fiber-optical double-pass confocal microscopy,” Opt. Laser Technol. 30, 91–93 (1998).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Delaney, P. M.

Denk, W.

W. Denk, J. H. Strickler, W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–75 (1990).
[CrossRef] [PubMed]

Frieden, B. R.

Gan, X.

Gmitro, A. F.

Gradstein, I. S.

I. S. Gradstein, I. M. Ryshik, Tables of Series, Products and Integrals (Deutscher, Verlag, Frankfurt, 1981).

Gu, M.

D. Bird, M. Gu, “Compact two-photon fluorescence mi-croscope using a single-mode optical fiber coupler,” Opt. Lett. 27, 1031–1033 (2002).
[CrossRef]

D. Bird, M. Gu, “Resolution improvement in two-photon fluorescence microscopy using a single-mode fiber,” Appl. Opt. 41, 1852–1857 (2002).
[CrossRef] [PubMed]

M. Gu, D. K. Bird, “Fiber-optical double-pass confocal microscopy,” Opt. Laser Technol. 30, 91–93 (1998).
[CrossRef]

H. Zhou, C. J. R. Sheppard, M. Gu, “A compact confocal interference microscope based on a four-port single-mode fiber coupler,” Optik (Stuttgart) 103, 45–48 (1996).

M. Gu, T. Tannous, C. J. R. Sheppard, “Three-dimensional confocal fluorescence imaging under ultrashort pulse illumination,” Opt. Commun. 117, 406–412 (1995).
[CrossRef]

M. Gu, C. J. R. Sheppard, “Effect of a finite-sized pinhole on 3D image formation in confocal two-photon fluorescence microscopy,” J. Mod. Opt. 40, 2009–2024 (1993).
[CrossRef]

M. Gu, C. J. R. Sheppard, “Fiber-optical confocal scanning interference microscopy,” Opt. Commun. 100, 79–86 (1993).
[CrossRef]

M. Gu, C. J. R. Sheppard, “Confocal fluorescent microscopy with a finite-sized circular detector,” J. Opt. Soc. Am. A 9, 151–153 (1992).
[CrossRef]

M. Gu, C. J. R. Sheppard, “Three-dimensional optical transfer function in a fiber-optical confocal fluorescent microscope using annular lenses,” J. Opt. Soc. Am. A 9, 1991–1999 (1992).
[CrossRef]

M. Gu, X. Gan, C. J. R. Sheppard, “Three-dimensional coherent transfer functions in fiber-optical confocal scanning microscopes,” J. Opt. Soc. Am. A 8, 1019–1025 (1991).
[CrossRef]

M. Gu, C. J. R. Sheppard, X. Gan, “Image formation in a fiber-optical confocal scanning microscope,” J. Opt. Soc. Am. A 8, 1755–1761 (1991).
[CrossRef]

M. Gu, Principles of Three-Dimensional Imaging in Confocal Microscopes (World Scientific, Singapore, 1996).

Harris, M. R.

Kaplan, A. E.

Kawata, S.

Khurigan, J. B.

Kimura, S.

King, R. G.

Lago, A.

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

Munakata, C.

Nakamura, O.

Obeidat, A. T.

Ryshik, I. M.

I. S. Gradstein, I. M. Ryshik, Tables of Series, Products and Integrals (Deutscher, Verlag, Frankfurt, 1981).

Sheppard, C. J. R.

H. Zhou, C. J. R. Sheppard, M. Gu, “A compact confocal interference microscope based on a four-port single-mode fiber coupler,” Optik (Stuttgart) 103, 45–48 (1996).

M. Gu, T. Tannous, C. J. R. Sheppard, “Three-dimensional confocal fluorescence imaging under ultrashort pulse illumination,” Opt. Commun. 117, 406–412 (1995).
[CrossRef]

M. Gu, C. J. R. Sheppard, “Effect of a finite-sized pinhole on 3D image formation in confocal two-photon fluorescence microscopy,” J. Mod. Opt. 40, 2009–2024 (1993).
[CrossRef]

M. Gu, C. J. R. Sheppard, “Fiber-optical confocal scanning interference microscopy,” Opt. Commun. 100, 79–86 (1993).
[CrossRef]

M. Gu, C. J. R. Sheppard, “Confocal fluorescent microscopy with a finite-sized circular detector,” J. Opt. Soc. Am. A 9, 151–153 (1992).
[CrossRef]

M. Gu, C. J. R. Sheppard, “Three-dimensional optical transfer function in a fiber-optical confocal fluorescent microscope using annular lenses,” J. Opt. Soc. Am. A 9, 1991–1999 (1992).
[CrossRef]

M. Gu, X. Gan, C. J. R. Sheppard, “Three-dimensional coherent transfer functions in fiber-optical confocal scanning microscopes,” J. Opt. Soc. Am. A 8, 1019–1025 (1991).
[CrossRef]

M. Gu, C. J. R. Sheppard, X. Gan, “Image formation in a fiber-optical confocal scanning microscope,” J. Opt. Soc. Am. A 8, 1755–1761 (1991).
[CrossRef]

Shkolnikov, P. L.

Snyder, A. W.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

Strickler, J. H.

W. Denk, J. H. Strickler, W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–75 (1990).
[CrossRef] [PubMed]

Tannous, T.

M. Gu, T. Tannous, C. J. R. Sheppard, “Three-dimensional confocal fluorescence imaging under ultrashort pulse illumination,” Opt. Commun. 117, 406–412 (1995).
[CrossRef]

Von Rosmalen, G.

Webb, W. W.

W. Denk, J. H. Strickler, W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–75 (1990).
[CrossRef] [PubMed]

Wilson, T.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Zhou, H.

H. Zhou, C. J. R. Sheppard, M. Gu, “A compact confocal interference microscope based on a four-port single-mode fiber coupler,” Optik (Stuttgart) 103, 45–48 (1996).

Appl. Opt.

J. Mod. Opt.

M. Gu, C. J. R. Sheppard, “Effect of a finite-sized pinhole on 3D image formation in confocal two-photon fluorescence microscopy,” J. Mod. Opt. 40, 2009–2024 (1993).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

M. Gu, T. Tannous, C. J. R. Sheppard, “Three-dimensional confocal fluorescence imaging under ultrashort pulse illumination,” Opt. Commun. 117, 406–412 (1995).
[CrossRef]

M. Gu, C. J. R. Sheppard, “Fiber-optical confocal scanning interference microscopy,” Opt. Commun. 100, 79–86 (1993).
[CrossRef]

Opt. Laser Technol.

M. Gu, D. K. Bird, “Fiber-optical double-pass confocal microscopy,” Opt. Laser Technol. 30, 91–93 (1998).
[CrossRef]

Opt. Lett.

Optik (Stuttgart)

H. Zhou, C. J. R. Sheppard, M. Gu, “A compact confocal interference microscope based on a four-port single-mode fiber coupler,” Optik (Stuttgart) 103, 45–48 (1996).

Science

W. Denk, J. H. Strickler, W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–75 (1990).
[CrossRef] [PubMed]

Other

M. Gu, Principles of Three-Dimensional Imaging in Confocal Microscopes (World Scientific, Singapore, 1996).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

I. S. Gradstein, I. M. Ryshik, Tables of Series, Products and Integrals (Deutscher, Verlag, Frankfurt, 1981).

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Figures (9)

Fig. 1
Fig. 1

3-D OTF for fiber-optical two-photon fluorescence microscopy with a large-area detector: (a) A 1 = 1 and A 2 , (b) A 1 = 10 and A 2 .

Fig. 2
Fig. 2

(a) Transverse and (b) axial cross sections of the 3-D OTF for fiber-optical two-photon fluorescence microscopy with a large-area detector for different values of the normalized optical spot size parameter A 1 ( A 2 ) .

Fig. 3
Fig. 3

(a) 2-D in-focus and (b) 1-D on-axis OTFs for fiber-optical two-photon fluorescence microscopy with a large-area detector for different values of the normalized optical spot size parameter A 1 ( A 2 ) .

Fig. 4
Fig. 4

3-D OTF for fiber-optical two-photon fluorescence microscopy with an optical coupler ( A 2 = 4 A 1 ) : (a) A 1 = 2 , (b) A 1 = 10 .

Fig. 5
Fig. 5

(a) Transverse and (b) axial cross sections of the 3-D OTF for fiber-optical two-photon fluorescence microscopy with an optical coupler for different values of the normalized optical spot size parameter A 1 ( A 2 = 4 A 1 ) .

Fig. 6
Fig. 6

(a) 2-D in-focus and (b) 1-D on-axis OTFs for fiber-optical two-photon fluorescence microscopy with an optical coupler for different values of the normalized optical spot size parameter A 1 ( A 2 = 4 A 1 ) .

Fig. 7
Fig. 7

Calculated axial response of a thin fluorescent sheet for fiber-optical two-photon fluorescence microscopy with a large-area detector for different values of the normalized optical spot size parameter A 1 ( A 2 ) . u = 8 π z   sin 2 ( α / 2 ) / λ 2 , where z is the scanning distance of the fluorescent sheet.

Fig. 8
Fig. 8

Calculated axial response of a thin fluorescent sheet in fiber-optical two-photon fluorescence microscopy with an optical coupler for different values of the normalized fiber spot size parameter A 1 ( A 2 = 4 A 1 ) . u = 8 π z   sin 2 ( α / 2 ) / λ 2 where z is the scanning distance of the fluorescent sheet.

Fig. 9
Fig. 9

Half-width at half-maximum of the axial response, Δ u 1 / 2 , as a function of the normalized fiber spot size parameter A 1 . The solid curve is the case for fiber-optical two-photon fluorescence microscopy with a large-area detector ( A 2 ) , and the dotted curve is the case with a fiber coupler implementation ( A 2 = 4 A 1 ) .

Equations (15)

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I ( r s ) = - - f 1 ( x 0 ,   y 0 ) δ ( z 0 ) exp [ ik ( z 0 - z 1 ) ] × h 1 ( r 0 + M 1 r 1 ) d r 0 4 o f ( r s - r 1 ) - f 2 * ( x 2 ,   y 2 ) × δ ( z 2 ) exp [ ik ( ± z 1 - z 2 ) ] h 2 ( r 1 + M 2 r 2 ) d r 2 2 d r 1 ,
h j ( x ,   y ,   z ) = - P j ( ξ ,   η ,   z ) × exp i 2 π d j λ j   ( ξ x + η y ) d ξ d η ,
h i ( r ) = | f 1 ( M 1 x ,   M 1 y )   2   h 1 ( M 1 r ) | 4 × | f 2 * ( M 1 x ,   M 1 y )   2   h 2 ( r ) | 2 ,
C ( m ) = C 1 ( m )   3   C 2 ( m ) ,
C 1 ( m ) = F 3 { | f 1 ( M 1 x ,   M 1 y )   2   h 1 ( M 1 r ) | 4 } ,
C 2 ( m ) = F 3 { | f 2 * ( M 1 x ,   M 1 y )   2   h 2 ( r ) | 2 } .
C 1 ( m ) = C 1 ( m )   3   C 1 ( m ) ,
C 1 ( m ) = F 3 { | f 1 ( M 1 x ,   M 1 y )   2   h 1 ( M 1 r ) | 2 } .
C ( l ,   s ) = [ C 1 ( l ,   s )   3   C 1 ( l ,   s ) ]   3   C 2 ( l ,   s ) ,
C 1 ( l ,   s ) = π exp { - A 1 [ ( β 2 l 2 ) / 4 + ( s / l ) 2 ] } A 1 β l × erf A 1 Re 1 - | s | l + β l 2 2 1 / 2 ,
C 2 ( l ,   s ) = π exp { - A 2 [ l 2 / 4 + ( s / l ) 2 ] } A 2 l × erf A 2 Re 1 - | s | l + l 2 2 1 / 2 ,
A j = 2 π aa j λ j d 1 2 , j = 1 ,   2 ,
erf ( x ) = 2 π 0 x exp ( - r 2 ) d t ,
C ( l ,   s ) = C 2 ( l ,   s )
C ( l ,   s ) = C 1 ( l ,   s )   3   C 1 ( l ,   s )

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