Abstract

Recently, we have experimentally demonstrated a new form of cross-sectional, coherence-gated fluorescence imaging referred to as SD-FCT (’spectral-domain fluorescence coherence tomography‘). Imaging in SD-FCT is accomplished by spectrally detecting self-interference of the spontaneous emission of fluorophores, thereby providing depth-resolved information on the axial positions of fluorescent probes. Here, we present a theoretical investigation of the factors affecting the detected SD-FCT signal through scattering media. An imaging equation for SD-FCT is derived that includes the effects of defocusing, numerical-aperture, and the optical properties of the medium. A comparison between the optical sectioning capabilities of SD-FCT and confocal microscopy is also presented. Our results suggest that coherence gating in fluorescence imaging may provide an improved approach for depth-resolved imaging of fluorescently labeled samples; high axial resolution (a few microns) can be achieved with low numerical apertures (NA<0.09) while maintaining a large depth of field (a few hundreds of microns) in a relatively low scattering medium (6 mean free paths), whereas moderate NA’s can be used to enhance depth selectivity in more highly scattering biological samples.

© 2007 Optical Society of America

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  1. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
    [CrossRef] [PubMed]
  2. J. M. Schmitt, A. Knuettel, A. Gandjbakhche, and R. F. Bonner, "Optical characterization of dense tissues using low-coherence interferometry," Proc. SPIE 1889, 197-211 (1993).
    [CrossRef]
  3. J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, and J. G. Fujimoto, "Optical coherence microscopy in scattering media," Opt. Lett. 19, 590-592 (1994).
    [CrossRef] [PubMed]
  4. M. Kempe and W. Rudolph, "Analysis of heterodyne and confocal microscopy for illumination with broad-bandwidth light," J. Mod. Opt. 43, 2189-2204 (1996).
    [CrossRef]
  5. E. Beaurepaire, A. C. Boccara, M. Lebec, L. Blanchot, and H. Saint-Jalmes, "Full-field optical coherence microscopy," Opt. Lett. 23, 244-246 (1998).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  9. S. Hell and E. H. K. Stelzer, "Properties of a 4Pi-confocal fluorescence microscope," J. Opt. Soc. Am. A 9, 2159-2166 (1992).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  12. M. Gu, Advanced optical imaging theory (Springer 1999).
  13. M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, "Full range complex spectral optical coherence tomography technique in eye imaging," Opt. Lett. 27, 1415-1417 (2002).
    [CrossRef]
  14. A. Bilenca, A. Desjardins, B. Bouma, and G. Tearney, "Multicanonical Monte-Carlo simulations of light propagation in biological media," Opt. Express 13, 9822-9833 (2005).
    [CrossRef] [PubMed]

2006 (1)

2005 (2)

2003 (3)

2002 (1)

1998 (1)

1996 (1)

M. Kempe and W. Rudolph, "Analysis of heterodyne and confocal microscopy for illumination with broad-bandwidth light," J. Mod. Opt. 43, 2189-2204 (1996).
[CrossRef]

1994 (1)

1993 (1)

J. M. Schmitt, A. Knuettel, A. Gandjbakhche, and R. F. Bonner, "Optical characterization of dense tissues using low-coherence interferometry," Proc. SPIE 1889, 197-211 (1993).
[CrossRef]

1992 (1)

1991 (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Aguirre, A. D.

Beaurepaire, E.

Bilenca, A.

Blanchot, L.

Boccara, A. C.

Bonner, R. F.

J. M. Schmitt, A. Knuettel, A. Gandjbakhche, and R. F. Bonner, "Optical characterization of dense tissues using low-coherence interferometry," Proc. SPIE 1889, 197-211 (1993).
[CrossRef]

Bouma, B.

Cantor, C. R.

A. K. Swan, L. A. Moiseev, C. R. Cantor, B. Davis, S. B. Ippolito, W. C. Karl, B. B. Goldberg, M. S. Unlu, "Toward nanometer-scale resolution in fluorescence microscopy using spectral self-interference," IEEE J. Sel. Top. Quantum Electron. 9, 294-300 (2003).
[CrossRef]

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Davis, B.

A. K. Swan, L. A. Moiseev, C. R. Cantor, B. Davis, S. B. Ippolito, W. C. Karl, B. B. Goldberg, M. S. Unlu, "Toward nanometer-scale resolution in fluorescence microscopy using spectral self-interference," IEEE J. Sel. Top. Quantum Electron. 9, 294-300 (2003).
[CrossRef]

Desjardins, A.

Fercher, A.

Fercher, A. F.

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Fujimoto, J. G.

Gandjbakhche, A.

J. M. Schmitt, A. Knuettel, A. Gandjbakhche, and R. F. Bonner, "Optical characterization of dense tissues using low-coherence interferometry," Proc. SPIE 1889, 197-211 (1993).
[CrossRef]

Goldberg, B. B.

A. K. Swan, L. A. Moiseev, C. R. Cantor, B. Davis, S. B. Ippolito, W. C. Karl, B. B. Goldberg, M. S. Unlu, "Toward nanometer-scale resolution in fluorescence microscopy using spectral self-interference," IEEE J. Sel. Top. Quantum Electron. 9, 294-300 (2003).
[CrossRef]

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Hartl, I.

Hee, M. R.

J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, and J. G. Fujimoto, "Optical coherence microscopy in scattering media," Opt. Lett. 19, 590-592 (1994).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Hell, S.

Hitzenberger, C.

Hsiung, P.

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Ippolito, S. B.

A. K. Swan, L. A. Moiseev, C. R. Cantor, B. Davis, S. B. Ippolito, W. C. Karl, B. B. Goldberg, M. S. Unlu, "Toward nanometer-scale resolution in fluorescence microscopy using spectral self-interference," IEEE J. Sel. Top. Quantum Electron. 9, 294-300 (2003).
[CrossRef]

Izatt, J. A.

Karl, W. C.

A. K. Swan, L. A. Moiseev, C. R. Cantor, B. Davis, S. B. Ippolito, W. C. Karl, B. B. Goldberg, M. S. Unlu, "Toward nanometer-scale resolution in fluorescence microscopy using spectral self-interference," IEEE J. Sel. Top. Quantum Electron. 9, 294-300 (2003).
[CrossRef]

Kempe, M.

M. Kempe and W. Rudolph, "Analysis of heterodyne and confocal microscopy for illumination with broad-bandwidth light," J. Mod. Opt. 43, 2189-2204 (1996).
[CrossRef]

Knuettel, A.

J. M. Schmitt, A. Knuettel, A. Gandjbakhche, and R. F. Bonner, "Optical characterization of dense tissues using low-coherence interferometry," Proc. SPIE 1889, 197-211 (1993).
[CrossRef]

Ko, T. H.

Kowalczyk, A.

Lebec, M.

Leitgeb, R.

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Moiseev, L. A.

A. K. Swan, L. A. Moiseev, C. R. Cantor, B. Davis, S. B. Ippolito, W. C. Karl, B. B. Goldberg, M. S. Unlu, "Toward nanometer-scale resolution in fluorescence microscopy using spectral self-interference," IEEE J. Sel. Top. Quantum Electron. 9, 294-300 (2003).
[CrossRef]

Owen, G. M.

Ozcan, A.

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Rudolph, W.

M. Kempe and W. Rudolph, "Analysis of heterodyne and confocal microscopy for illumination with broad-bandwidth light," J. Mod. Opt. 43, 2189-2204 (1996).
[CrossRef]

Saint-Jalmes, H.

Schmitt, J. M.

J. M. Schmitt, A. Knuettel, A. Gandjbakhche, and R. F. Bonner, "Optical characterization of dense tissues using low-coherence interferometry," Proc. SPIE 1889, 197-211 (1993).
[CrossRef]

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Stelzer, E. H. K.

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Swan, A. K.

A. K. Swan, L. A. Moiseev, C. R. Cantor, B. Davis, S. B. Ippolito, W. C. Karl, B. B. Goldberg, M. S. Unlu, "Toward nanometer-scale resolution in fluorescence microscopy using spectral self-interference," IEEE J. Sel. Top. Quantum Electron. 9, 294-300 (2003).
[CrossRef]

Swanson, E. A.

J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, and J. G. Fujimoto, "Optical coherence microscopy in scattering media," Opt. Lett. 19, 590-592 (1994).
[CrossRef] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Tearney, G.

Unlu, M. S.

A. K. Swan, L. A. Moiseev, C. R. Cantor, B. Davis, S. B. Ippolito, W. C. Karl, B. B. Goldberg, M. S. Unlu, "Toward nanometer-scale resolution in fluorescence microscopy using spectral self-interference," IEEE J. Sel. Top. Quantum Electron. 9, 294-300 (2003).
[CrossRef]

Wojtkowski, M.

Yang, C.

C. Yang, "Molecular contrast optical coherence tomography: A review," Photochemistry and Photobiology,  81, 215-237 (2005).

IEEE J. Sel. Top. Quantum Electron. (1)

A. K. Swan, L. A. Moiseev, C. R. Cantor, B. Davis, S. B. Ippolito, W. C. Karl, B. B. Goldberg, M. S. Unlu, "Toward nanometer-scale resolution in fluorescence microscopy using spectral self-interference," IEEE J. Sel. Top. Quantum Electron. 9, 294-300 (2003).
[CrossRef]

J. Mod. Opt. (1)

M. Kempe and W. Rudolph, "Analysis of heterodyne and confocal microscopy for illumination with broad-bandwidth light," J. Mod. Opt. 43, 2189-2204 (1996).
[CrossRef]

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

Opt. Express (3)

Opt. Lett. (4)

Photochemistry and Photobiology (1)

C. Yang, "Molecular contrast optical coherence tomography: A review," Photochemistry and Photobiology,  81, 215-237 (2005).

Proc. SPIE (1)

J. M. Schmitt, A. Knuettel, A. Gandjbakhche, and R. F. Bonner, "Optical characterization of dense tissues using low-coherence interferometry," Proc. SPIE 1889, 197-211 (1993).
[CrossRef]

Science (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Other (1)

M. Gu, Advanced optical imaging theory (Springer 1999).

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Figures (5)

Fig. 1.
Fig. 1.

SD-FCT system. Experimental arrangement (left). Object (right-top) and image (right-bottom) planes. The excitation optics (not shown) generates a point beam in the confocal configuration and a line beam in the non-confocal configuration. Correspondingly, confocal detection optics (not shown) followed by a non-imaging spectrometer is employed in the confocal setup, whereas an imaging spectrometer is used in the non-confocal arrangement.

Fig. 2.
Fig. 2.

Spectral fringe visibility of SD-FCT for a point object. Visibility values for three different objectives placed inside the interferometer are shown. NA=0.06 (left), NA=0.18 (middle), NA=0.54 (right).

Fig. 3.
Fig. 3.

Signal-to-noise ratio of SD-FCT for a point object located at geometric focal plane of the emission light. SNR values for three different objectives placed inside the interferometer are shown. NA=0.06 (left), NA=0.18 (middle), NA=0.54 (right).

Fig. 4.
Fig. 4.

Optical sectioning performance of SD-FCT and confocal microscopy. Depth response curves for NA=0.18 (left). The extent of the depth response against the NA value (right).

Fig. 5.
Fig. 5.

Theoretical limits to coherence gating in fluorescence imaging. The analyzed sample is shown on the right panel.

Equations (30)

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K L u L ( r i , ω ω 0 ) + K R u R ( r i , ω ω 0 ) ,
G ( Ω ) = ρ̃η ħ ω T [ K L 2 u L r i Ω 2 + K R 2 u R r i Ω 2
+ 2 K L K R Re { u L r i Ω u R * r i Ω } ] ,
h exc r o z o = 2 P πW 2 ( z o ) e ( r o 2 W 2 ( z o ) + μ t 2 ( n ( z f , em d ) + z o ) ) ,
W ( z o ) = W 0 ( 1 z f , em + z o n z f , exc ) 2 + ( z f , em + z o n k exc W 0 2 2 ) 2
z f , exc = d + n 1 ( 1 d f ) ( W 0 2 + f 2 ) n 2 W 0 2 , n 1 .
z f , em = d + n 1 ( 1 d f ) ( ( D 2 ) 2 + f 2 ) n 2 ( D 2 ) 2 , n 1 .
P f = K exc 2 A f h exc 2 r s z s δ ( r ̅ o r ̅ s , z o z s ) ,
NA 2 λ 0 2 M A f S f ( Ω ) K exc h exc r s z s e ik 0 ( nz s + Δz ) ( 1 + Ω ω 0 )
0 1 0 2 π dρdθρ J 0 ( ρ ( 1 + Ω ω 0 ) v i ) e iu i ρ 2 2 ( 1 + Ω ω 0 ) μ t 2 ( n ( z f , em d ) + z s ) 2 + r ̅ f , em r ̅ s 2 ,
v i = k 0 NA M r ̅ i M r ̅ s , u i = k 0 NA 2 M 2 z i , z i = M 2 z s .
NA 2 λ 0 2 M A f S f ( Ω ) K exc h exc ( r s , z s ) e ik 0 ( nz s + Δ z ) ( 1 + Ω ω 0 ) μ t 2 ( n ( z f , em d ) + z s ) 0 1 J 0 ( ρv i ) e iu i ρ 2 2 2 πρdρ .
G Ω ; r ̅ s , z s = ρ̃η ħ ω 0 TA f S f ( Ω ) K exc 2 h exc 2 r s z s 0 r d h i ( r ̅ i , Ω ; r ̅ s , z s ) 2 [ ( L 2 + R 2 )
+ 2 L R cos ( 2 h i ( r ̅ i , Ω ; r ̅ s , z s ) 2 k 0 ( nz s + Δ z ) ( 1 + Ω ω 0 ) ) ] 2 π ( d r ̅ i M r ̅ s ) ,
h i ( r ̅ i , Ω ; r ̅ s , z s ) = NA 2 λ 0 2 M 0 1 J 0 ( ρ ( 1 + Ω ω 0 ) v i ) e iu i ρ 2 2 ( 1 + Ω ω 0 ) 2 πρdρ
L = K L e μ t 2 ( n ( z f , em d ) + z s ) , R = K R e μ t 2 ( n ( z f , em d ) z s ) .
G ( Ω ; r ̅ s , z s ) = ρ̃η ħ ω 0 TA f S f ( Ω ) K exc 2 h exc 2 r s z s 0 r d h c r ̅ i ; r ̅ s , z s 2 [ ( L 2 + R 2 )
+ 2 L K ˜ R cos ( 2 h c ( r ̅ i ; r ̅ s , z s ) 2 k 0 ( nz s + Δ z ) ( 1 + Ω ω 0 ) ) ] 2 π ( d r ̅ i M r ̅ s ) ,
h c r ̅ i r ̅ s z s = NA 2 λ 0 2 M 0 1 J 0 ( ρv i ) e iu i ρ 2 2 2 πρd ρ .
ρ ˜ η ħ ω 0 TA f K exc 2 h exc 2 r s z s [ ( K ˜ L 2 + K ˜ R 2 ) I 1 r ̅ s z s R f ( z )
+ K ˜ L K ˜ R I 2 r ̅ s z s R f ( z 2 ( nz s + Δ z ) ) ] , z 0 ,
N max = max Ω n N ( Ω n ) ,
Fringe visibility = ( N max N min ) ( N max + N min ) .
2 K ˜ L K ˜ R K ˜ L 2 + K ˜ R 2 . 0 r d h c 2 ( r i ; 0 , z s ) dr i 0 r d h c ( r i ; 0 , z s ) 2 dr i .
[ 0 r d h i 2 ( r ̅ i , Ω ; r ̅ s , z s ) 2 π ( d r ̅ i M r ̅ s ) ] 2 k 0 ( nz s + Δ z ) ( 1 + Ω n ω 0 ) .
SNR = max n > 0 DFT 1 [ N AC ( Ω n ) ] ( n ) 2 σ Rec 2 + σ Shot 2 + σ RIN 2 ,
σ Rec 2 = σ read 2 + σ dark 2 N pixels ,
σ Shot 2 = 1 N pixes DEF 1 [ N DC ( Ω n ) ] ( 0 )
σ RIN 2 = 1 ω f [ DFT 1 [ N DC ( Ω n ) ] ( 0 ) ] 2 ,
1 N pixels ( ρη ħ ω 0 TR f ( 0 ) ) 2 h exc h c 4 L 2 R 2 σ read 2 + σ dark 2 + 1 N pixel ρη ħ ω 0 TR f ( 0 ) h exc h c 2 ( L 2 + R 2 ) ( 1 + ρη ħ ω 0 R f ( 0 ) Δ ω f h exc h c 2 ( L 2 + R 2 ) ) ,

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