Abstract

We present a diffraction analysis for image formation in fluorescence confocal microscopy with divided apertures. The three-dimensional optical transform function is given, and axial resolution and transverse resolution are investigated. The results show that the employment of a divided-aperture technique in fluorescence confocal microscopy can enhance the rejection of background scattering. In addition, the axial resolution and transverse resolution can be improved by adjusting the width of the divider strip. For a given detector size, an optimum value of the divider strip width is given to obtain the best axial resolution or transverse resolution. The integrated intensity and signal-to-background ratio are also discussed.

© 2010 Optical Society of America

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  1. H. Siedentopf and R. Zsigmondy, “Uber Sichtbarmachung und Grössenbestimmung ultramikroskopischer Teilchen, mit besonderer Anwendung auf Goldrubingläser,” Ann. Phys. 10, 1-39 (1903).
  2. H. Goldman, “Spaltlampenphotographie und -photometrie,” Ophthalmologica 98, 257-270 (1940).
    [CrossRef]
  3. D. M. Maurice, “Cellular membrane activity in the corneal endothelium of the intact eye,” Experientia 24, 1094-1095(1968).
    [CrossRef] [PubMed]
  4. C. J. Koester, “A scanning mirror microscope with optical sectioning characteristics: applications in ophthalmology,” Appl. Opt. 19, 1749-1757 (1980).
    [CrossRef] [PubMed]
  5. C. J. Koester, “Comparison of optical sectioning methods: the scanning slit confocal microscope,” in Handbook of Confocal Microscopy, J. Pawley, ed. (Plenum, 1990).
  6. P. J. Dwyer and C. A. DiMarzio, “Confocal reflectance theta line scanning microscope for imaging human skin in vivo,” Opt. Lett. 31, 942-944 (2006).
    [CrossRef] [PubMed]
  7. P. J. Dwyer, C. A. DiMarzio, and M. Rajadhyaksha, “Confocal theta line-scanning microscope for imaging human tissues,” Appl. Opt. 46, 1843-1851 (2007).
    [CrossRef] [PubMed]
  8. C. J. R. Sheppard, W. Gong, and K. Si, “The divided aperture technique for microscopy through scattering media,” Opt. Express 16, 17031-17038 (2008).
    [CrossRef] [PubMed]
  9. K. Si, W. Gong, and C. J. R. Sheppard, “Three-dimensional coherent transfer function for a confocal microscope with two D-shaped pupils,” Appl. Opt. 48, 810-817 (2009).
    [CrossRef] [PubMed]
  10. W. Gong, K. Si, and C. J. R. Sheppard, “Optimization of axial resolution in confocal microscope with D-shaped apertures,” Appl. Opt. 48, 3998-4002 (2009).
    [CrossRef] [PubMed]
  11. W. Gong, K. Si, and C. J. R. Sheppard, “Improvements in confocal microscopy imaging using serrated divided apertures,” Opt. Commun. 282, 3846-3849 (2009).
    [CrossRef]
  12. P. M. Delaney, M. R. Harris, and R. G. King, “Fiber-optic laser scanning confocal microscope suitable for fluorescence imaging,” Appl. Opt. 33, 573-577 (1994).
    [CrossRef] [PubMed]
  13. R. Kiesslich, J. Burg, M. Vieth, J. Gnaendiger, M. Enders, P. Delaney, A. Polglase, W. McLaren, D. Janell, S. Thomas, B. Nafe, P. R. Galle, and M. F. Neurath, “Confocal laser endoscopy for diagnosing intraepithelial neoplasias and colorectal cancer in vivo,” Gastroenterology 127, 706-713 (2004).
    [CrossRef] [PubMed]
  14. M. Gu and C. J. R. Sheppard, “Three-dimensional imaging in confocal fluorescent microscopy with annular lenses,” J. Mod. Opt. 38, 2247-2263 (1991).
    [CrossRef]
  15. T. Wilson, “Optical sectioning in confocal fluorescent microscopes,” J. Microsc. 154, 143-156 (1989).
    [CrossRef]
  16. M. Gu, T. Tannous, and C. J. R. Sheppard, “Improved axial resolution in confocal fluorescence microscopy using annular pupils,” Opt. Commun. 110, 533-539 (1994).
    [CrossRef]
  17. M. Gu and C. J. R. Sheppard, “Comparison of three-dimensional imaging properties between two-photon and single-photon fluorescence microscopy,” J. Microsc. 177, 128-137 (1995).
    [CrossRef]
  18. C. J. R. Sheppard and T. Wilson, “Depth of field in the scanning microscope,” Opt. Lett. 3, 115-117 (1978).
    [CrossRef] [PubMed]
  19. C. J. R. Sheppard and M. D. Sharma, “Integrated intensity, and imaging through scattering media,” J. Mod. Opt. 48, 1517-1525 (2001).

2009

2008

2007

2006

2004

R. Kiesslich, J. Burg, M. Vieth, J. Gnaendiger, M. Enders, P. Delaney, A. Polglase, W. McLaren, D. Janell, S. Thomas, B. Nafe, P. R. Galle, and M. F. Neurath, “Confocal laser endoscopy for diagnosing intraepithelial neoplasias and colorectal cancer in vivo,” Gastroenterology 127, 706-713 (2004).
[CrossRef] [PubMed]

2001

C. J. R. Sheppard and M. D. Sharma, “Integrated intensity, and imaging through scattering media,” J. Mod. Opt. 48, 1517-1525 (2001).

1995

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

1994

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

P. M. Delaney, M. R. Harris, and R. G. King, “Fiber-optic laser scanning confocal microscope suitable for fluorescence imaging,” Appl. Opt. 33, 573-577 (1994).
[CrossRef] [PubMed]

1991

M. Gu and C. J. R. Sheppard, “Three-dimensional imaging in confocal fluorescent microscopy with annular lenses,” J. Mod. Opt. 38, 2247-2263 (1991).
[CrossRef]

1989

T. Wilson, “Optical sectioning in confocal fluorescent microscopes,” J. Microsc. 154, 143-156 (1989).
[CrossRef]

1980

1978

1968

D. M. Maurice, “Cellular membrane activity in the corneal endothelium of the intact eye,” Experientia 24, 1094-1095(1968).
[CrossRef] [PubMed]

1940

H. Goldman, “Spaltlampenphotographie und -photometrie,” Ophthalmologica 98, 257-270 (1940).
[CrossRef]

1903

H. Siedentopf and R. Zsigmondy, “Uber Sichtbarmachung und Grössenbestimmung ultramikroskopischer Teilchen, mit besonderer Anwendung auf Goldrubingläser,” Ann. Phys. 10, 1-39 (1903).

Burg, J.

R. Kiesslich, J. Burg, M. Vieth, J. Gnaendiger, M. Enders, P. Delaney, A. Polglase, W. McLaren, D. Janell, S. Thomas, B. Nafe, P. R. Galle, and M. F. Neurath, “Confocal laser endoscopy for diagnosing intraepithelial neoplasias and colorectal cancer in vivo,” Gastroenterology 127, 706-713 (2004).
[CrossRef] [PubMed]

Delaney, P.

R. Kiesslich, J. Burg, M. Vieth, J. Gnaendiger, M. Enders, P. Delaney, A. Polglase, W. McLaren, D. Janell, S. Thomas, B. Nafe, P. R. Galle, and M. F. Neurath, “Confocal laser endoscopy for diagnosing intraepithelial neoplasias and colorectal cancer in vivo,” Gastroenterology 127, 706-713 (2004).
[CrossRef] [PubMed]

Delaney, P. M.

DiMarzio, C. A.

Dwyer, P. J.

Enders, M.

R. Kiesslich, J. Burg, M. Vieth, J. Gnaendiger, M. Enders, P. Delaney, A. Polglase, W. McLaren, D. Janell, S. Thomas, B. Nafe, P. R. Galle, and M. F. Neurath, “Confocal laser endoscopy for diagnosing intraepithelial neoplasias and colorectal cancer in vivo,” Gastroenterology 127, 706-713 (2004).
[CrossRef] [PubMed]

Galle, P. R.

R. Kiesslich, J. Burg, M. Vieth, J. Gnaendiger, M. Enders, P. Delaney, A. Polglase, W. McLaren, D. Janell, S. Thomas, B. Nafe, P. R. Galle, and M. F. Neurath, “Confocal laser endoscopy for diagnosing intraepithelial neoplasias and colorectal cancer in vivo,” Gastroenterology 127, 706-713 (2004).
[CrossRef] [PubMed]

Gnaendiger, J.

R. Kiesslich, J. Burg, M. Vieth, J. Gnaendiger, M. Enders, P. Delaney, A. Polglase, W. McLaren, D. Janell, S. Thomas, B. Nafe, P. R. Galle, and M. F. Neurath, “Confocal laser endoscopy for diagnosing intraepithelial neoplasias and colorectal cancer in vivo,” Gastroenterology 127, 706-713 (2004).
[CrossRef] [PubMed]

Goldman, H.

H. Goldman, “Spaltlampenphotographie und -photometrie,” Ophthalmologica 98, 257-270 (1940).
[CrossRef]

Gong, W.

Gu, M.

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

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

M. Gu and C. J. R. Sheppard, “Three-dimensional imaging in confocal fluorescent microscopy with annular lenses,” J. Mod. Opt. 38, 2247-2263 (1991).
[CrossRef]

Harris, M. R.

Janell, D.

R. Kiesslich, J. Burg, M. Vieth, J. Gnaendiger, M. Enders, P. Delaney, A. Polglase, W. McLaren, D. Janell, S. Thomas, B. Nafe, P. R. Galle, and M. F. Neurath, “Confocal laser endoscopy for diagnosing intraepithelial neoplasias and colorectal cancer in vivo,” Gastroenterology 127, 706-713 (2004).
[CrossRef] [PubMed]

Kiesslich, R.

R. Kiesslich, J. Burg, M. Vieth, J. Gnaendiger, M. Enders, P. Delaney, A. Polglase, W. McLaren, D. Janell, S. Thomas, B. Nafe, P. R. Galle, and M. F. Neurath, “Confocal laser endoscopy for diagnosing intraepithelial neoplasias and colorectal cancer in vivo,” Gastroenterology 127, 706-713 (2004).
[CrossRef] [PubMed]

King, R. G.

Koester, C. J.

C. J. Koester, “A scanning mirror microscope with optical sectioning characteristics: applications in ophthalmology,” Appl. Opt. 19, 1749-1757 (1980).
[CrossRef] [PubMed]

C. J. Koester, “Comparison of optical sectioning methods: the scanning slit confocal microscope,” in Handbook of Confocal Microscopy, J. Pawley, ed. (Plenum, 1990).

Maurice, D. M.

D. M. Maurice, “Cellular membrane activity in the corneal endothelium of the intact eye,” Experientia 24, 1094-1095(1968).
[CrossRef] [PubMed]

McLaren, W.

R. Kiesslich, J. Burg, M. Vieth, J. Gnaendiger, M. Enders, P. Delaney, A. Polglase, W. McLaren, D. Janell, S. Thomas, B. Nafe, P. R. Galle, and M. F. Neurath, “Confocal laser endoscopy for diagnosing intraepithelial neoplasias and colorectal cancer in vivo,” Gastroenterology 127, 706-713 (2004).
[CrossRef] [PubMed]

Nafe, B.

R. Kiesslich, J. Burg, M. Vieth, J. Gnaendiger, M. Enders, P. Delaney, A. Polglase, W. McLaren, D. Janell, S. Thomas, B. Nafe, P. R. Galle, and M. F. Neurath, “Confocal laser endoscopy for diagnosing intraepithelial neoplasias and colorectal cancer in vivo,” Gastroenterology 127, 706-713 (2004).
[CrossRef] [PubMed]

Neurath, M. F.

R. Kiesslich, J. Burg, M. Vieth, J. Gnaendiger, M. Enders, P. Delaney, A. Polglase, W. McLaren, D. Janell, S. Thomas, B. Nafe, P. R. Galle, and M. F. Neurath, “Confocal laser endoscopy for diagnosing intraepithelial neoplasias and colorectal cancer in vivo,” Gastroenterology 127, 706-713 (2004).
[CrossRef] [PubMed]

Polglase, A.

R. Kiesslich, J. Burg, M. Vieth, J. Gnaendiger, M. Enders, P. Delaney, A. Polglase, W. McLaren, D. Janell, S. Thomas, B. Nafe, P. R. Galle, and M. F. Neurath, “Confocal laser endoscopy for diagnosing intraepithelial neoplasias and colorectal cancer in vivo,” Gastroenterology 127, 706-713 (2004).
[CrossRef] [PubMed]

Rajadhyaksha, M.

Sharma, M. D.

C. J. R. Sheppard and M. D. Sharma, “Integrated intensity, and imaging through scattering media,” J. Mod. Opt. 48, 1517-1525 (2001).

Sheppard, C. J. R.

K. Si, W. Gong, and C. J. R. Sheppard, “Three-dimensional coherent transfer function for a confocal microscope with two D-shaped pupils,” Appl. Opt. 48, 810-817 (2009).
[CrossRef] [PubMed]

W. Gong, K. Si, and C. J. R. Sheppard, “Optimization of axial resolution in confocal microscope with D-shaped apertures,” Appl. Opt. 48, 3998-4002 (2009).
[CrossRef] [PubMed]

W. Gong, K. Si, and C. J. R. Sheppard, “Improvements in confocal microscopy imaging using serrated divided apertures,” Opt. Commun. 282, 3846-3849 (2009).
[CrossRef]

C. J. R. Sheppard, W. Gong, and K. Si, “The divided aperture technique for microscopy through scattering media,” Opt. Express 16, 17031-17038 (2008).
[CrossRef] [PubMed]

C. J. R. Sheppard and M. D. Sharma, “Integrated intensity, and imaging through scattering media,” J. Mod. Opt. 48, 1517-1525 (2001).

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

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

M. Gu and C. J. R. Sheppard, “Three-dimensional imaging in confocal fluorescent microscopy with annular lenses,” J. Mod. Opt. 38, 2247-2263 (1991).
[CrossRef]

C. J. R. Sheppard and T. Wilson, “Depth of field in the scanning microscope,” Opt. Lett. 3, 115-117 (1978).
[CrossRef] [PubMed]

Si, K.

Siedentopf, H.

H. Siedentopf and R. Zsigmondy, “Uber Sichtbarmachung und Grössenbestimmung ultramikroskopischer Teilchen, mit besonderer Anwendung auf Goldrubingläser,” Ann. Phys. 10, 1-39 (1903).

Tannous, T.

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

Thomas, S.

R. Kiesslich, J. Burg, M. Vieth, J. Gnaendiger, M. Enders, P. Delaney, A. Polglase, W. McLaren, D. Janell, S. Thomas, B. Nafe, P. R. Galle, and M. F. Neurath, “Confocal laser endoscopy for diagnosing intraepithelial neoplasias and colorectal cancer in vivo,” Gastroenterology 127, 706-713 (2004).
[CrossRef] [PubMed]

Vieth, M.

R. Kiesslich, J. Burg, M. Vieth, J. Gnaendiger, M. Enders, P. Delaney, A. Polglase, W. McLaren, D. Janell, S. Thomas, B. Nafe, P. R. Galle, and M. F. Neurath, “Confocal laser endoscopy for diagnosing intraepithelial neoplasias and colorectal cancer in vivo,” Gastroenterology 127, 706-713 (2004).
[CrossRef] [PubMed]

Wilson, T.

T. Wilson, “Optical sectioning in confocal fluorescent microscopes,” J. Microsc. 154, 143-156 (1989).
[CrossRef]

C. J. R. Sheppard and T. Wilson, “Depth of field in the scanning microscope,” Opt. Lett. 3, 115-117 (1978).
[CrossRef] [PubMed]

Zsigmondy, R.

H. Siedentopf and R. Zsigmondy, “Uber Sichtbarmachung und Grössenbestimmung ultramikroskopischer Teilchen, mit besonderer Anwendung auf Goldrubingläser,” Ann. Phys. 10, 1-39 (1903).

Ann. Phys.

H. Siedentopf and R. Zsigmondy, “Uber Sichtbarmachung und Grössenbestimmung ultramikroskopischer Teilchen, mit besonderer Anwendung auf Goldrubingläser,” Ann. Phys. 10, 1-39 (1903).

Appl. Opt.

Experientia

D. M. Maurice, “Cellular membrane activity in the corneal endothelium of the intact eye,” Experientia 24, 1094-1095(1968).
[CrossRef] [PubMed]

Gastroenterology

R. Kiesslich, J. Burg, M. Vieth, J. Gnaendiger, M. Enders, P. Delaney, A. Polglase, W. McLaren, D. Janell, S. Thomas, B. Nafe, P. R. Galle, and M. F. Neurath, “Confocal laser endoscopy for diagnosing intraepithelial neoplasias and colorectal cancer in vivo,” Gastroenterology 127, 706-713 (2004).
[CrossRef] [PubMed]

J. Microsc.

T. Wilson, “Optical sectioning in confocal fluorescent microscopes,” J. Microsc. 154, 143-156 (1989).
[CrossRef]

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

J. Mod. Opt.

M. Gu and C. J. R. Sheppard, “Three-dimensional imaging in confocal fluorescent microscopy with annular lenses,” J. Mod. Opt. 38, 2247-2263 (1991).
[CrossRef]

C. J. R. Sheppard and M. D. Sharma, “Integrated intensity, and imaging through scattering media,” J. Mod. Opt. 48, 1517-1525 (2001).

Ophthalmologica

H. Goldman, “Spaltlampenphotographie und -photometrie,” Ophthalmologica 98, 257-270 (1940).
[CrossRef]

Opt. Commun.

W. Gong, K. Si, and C. J. R. Sheppard, “Improvements in confocal microscopy imaging using serrated divided apertures,” Opt. Commun. 282, 3846-3849 (2009).
[CrossRef]

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

Opt. Express

Opt. Lett.

Other

C. J. Koester, “Comparison of optical sectioning methods: the scanning slit confocal microscope,” in Handbook of Confocal Microscopy, J. Pawley, ed. (Plenum, 1990).

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Figures (10)

Fig. 1
Fig. 1

3D OTFs for confocal single-photon fluorescence microscopy with a point detector. (a)  C ( l , s ) for circular apertures, (b)  C ( m = 0 , n , s ) for D-shaped apertures with d = 0 , (c)  C ( m , n = 0 , s ) for D-shaped apertures with d = 0 , (d)  C ( m = 0 , n , s ) for D-shaped apertures with d = 0.4 , and (e)  C ( m , n = 0 , s ) for D-shaped apertures with d = 0.4 .

Fig. 2
Fig. 2

(a) Transverse and (b) axial cross sections of the 3D OTF for confocal microscopy with circular apertures and D-shaped apertures with a point detector.

Fig. 3
Fig. 3

3D OTFs for confocal one-photon fluorescence microscopy with a finite-size detector v d = 6 . (a)  C ( l , s ) for circular apertures, (b)  C ( m = 0 , n , s ) for D-shaped apertures with d = 0 , (c)  C ( m , n = 0 , s ) for D-shaped apertures with d = 0 , (d)  C ( m = 0 , n , s ) for D-shaped apertures with d = 0.4 , and (e)  C ( m , n = 0 , s ) for D-shaped apertures with d = 0.4 .

Fig. 4
Fig. 4

Transverse and axial cross sections of the 3D OTF for CM (dashed curves) and DCM with d = 0 (solid curves) for v d = 0 and v d = 4 , respectively. (a)  C ( n , m = 0 , s = 0 ) and (b)  C ( l = 0 , s ) .

Fig. 5
Fig. 5

Intensity of the axial response to a thin fluorescence sheet for different values of divider strip width d in the cases of v d = 0 and v d = 6 .

Fig. 6
Fig. 6

Optimum and equivalent width of the divider strip d as a function of detector size v d to achieve the best axial resolution (solid curve) or the best transverse resolution (dashed curve).

Fig. 7
Fig. 7

Image of a thick fluorescence layer scanning in the axial direction for DCM and CM with various of detector size. (a)  v d = 0 and (b)  v d = 6 .

Fig. 8
Fig. 8

Images of a thick, straight, and sharp edge placed perpendicular to the divided strip for CM (dashed curves) and DCM (solid curves), respectively, (a) given d = 0 , but with different values of detector size v d , and (b) given v d = 6 , but with different values of the width of the divider strip d.

Fig. 9
Fig. 9

Integrated intensities of CM (solid curves) and DCM (dash curves) for (a)  v d = 0 and (b)  v d = 4 .

Fig. 10
Fig. 10

S/B as a function of the width of divider strip d for various values of detector size v d .

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

h ( v x , v y , u ) = | h ill ( v x , v y , u ) | 2 ( | h dec ( v x , v y , u ) | 2 2 D ( v x , v y ) ) ,
h ill , dec ( v x , v y , u ) = 1 π P P ill , dec ( ρ x , ρ y ) exp { i [ v x ρ x + v y ρ y 1 2 u ( ρ x 2 + ρ y 2 ) ] } d ρ x d ρ y ,
I ( u ) = C ( l = 0 , s ) exp ( i u s ) d s .
o f ( x , y , z ) = { 1 , z 0 , 0 , z < 0.
I ( u ) = O f ( s ) C ( l = 0 , s ) exp ( i u s ) d s = 1 2 + 1 π 0 C ( l = 0 , s ) sin ( u s ) s d s ,
I ( u = 0 ) = 1 π 0 C ( l = 0 , s ) d s .
o f ( x , y , z ) = { 1 , y 0 , 0 , y < 0.
I ( v y ) = 1 2 + 1 π 0 C ( m = 0 , n , s = 0 ) sin ( v y n ) n d n .
I ( v y = 0 ) = 1 π 0 C ( m = 0 , n , s = 0 ) d n .
I int ( u ) = I ( v x , v y , u ) d v x d v y ,

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