Abstract

We examine the performance of confocal microscopes designed for probing structures embedded in turbid media. A heuristic scheme is described that combines a numerical Monte Carlo simulation of photon transport in a turbid medium with a geometrical ray trace through the confocal optics. To show the effects of multiple scattering on depth discrimination, we compare results from the Monte Carlo simulations and scalar diffraction theory. Experimental results showing the effects of the pinhole diameter and other variables on imaging performance at various optical depths in suspensions of polystyrene microspheres were found to correspond well with the Monte Carlo simulations. The major conclusion of the paper is that the trade-off between signal level and background scattered-light rejection places a fundamental limit on the sectioning capability of the microscope.

© 1994 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

1993

1991

P. A. Andrews, W. M. Petroll, H. D. Cavanagh, J. V. Jester, “Tandem scanning confocal microscopy (TSCM) of normal and ischemic living kidneys,” J. Anat. 191, 95–102 (1991).
[CrossRef]

1990

W. F. Cheong, S. A. Prahl, A. J. Walsh, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

1989

S. T. Flock, M. S. Patterson, B. C. Wilson, Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues—1: model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1167 (1989).
[CrossRef] [PubMed]

C. J. R. Sheppard, X. Q. Mao, “Three-dimensional imaging in a microscope,” J. Opt. Soc. Am. A 6, 1260–1269 (1989).
[CrossRef]

1988

T. Wilson, “Optical sectioning in confocal fluorescent microscopes,” J. Microsc. 154, 143–156 (1988).
[CrossRef]

1987

T. Wilson, A. R. Carlini, “Size of the detector in confocal imaging systems,” Opt. Lett. 12, 227–229 (1987).
[CrossRef] [PubMed]

S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14, 835–841 (1987).
[CrossRef] [PubMed]

1986

1981

Y. Fujii, H. Takimoto, T. Igarashi, “Optimum resolution of laser microscope by using optical heterodyne detection,” Opt. Commun. 38, 85–90 (1981).
[CrossRef]

1980

P. Bruscaglioni, G. Milloni, G. Zaccanti, “On the contribution of multiple scattering to lidar returns from homogeneous fogs and its dependence on the receiver angular aperture,” Opt. Acta 27, 1229–1242 (1980).
[CrossRef]

S. E. Moran, “On the transport theory of mutual intensity function propagation in a multiple scattering medium,” Radio Sci. 15, 1195–1205 (1980).
[CrossRef]

1978

C. J. R. Sheppard, T. Wilson, “Image formation in scanning microscopes with partially coherent source and detector,” Opt. Acta 25, 315–325 (1978).
[CrossRef]

1977

C. J. R. Sheppard, A. Choudhury, “Image formation in the scanning microscope,” Opt. Acta 24, 1051–1073 (1977).
[CrossRef]

1976

E. Wolf, “New theory of radiative energy transfer in free electromagnetic fields,” Phys. Rev. D 13, 869–886 (1976).
[CrossRef]

1973

1941

L. Henyey, J. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Andrews, P. A.

P. A. Andrews, W. M. Petroll, H. D. Cavanagh, J. V. Jester, “Tandem scanning confocal microscopy (TSCM) of normal and ischemic living kidneys,” J. Anat. 191, 95–102 (1991).
[CrossRef]

Binder, S.

A. J. Cochran, S. Binder, F. Remotti, “The role of microscopic evaluation in the management of cutaneous melanoma,” in Current Research and Clinical Management of Melanoma, L. Nathanson, ed. (Kluwer, Boston, Mass., 1993), Chap. 4.
[CrossRef]

Bonner, R. F.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1983).

Bruscaglioni, P.

P. Bruscaglioni, G. Milloni, G. Zaccanti, “On the contribution of multiple scattering to lidar returns from homogeneous fogs and its dependence on the receiver angular aperture,” Opt. Acta 27, 1229–1242 (1980).
[CrossRef]

Bucher, E. A.

Carlini, A. R.

Cassis, L. A.

L. A. Cassis, R. A. Loddor, “Near-IR imaging of atheromas in living arterial tissue,” Anal. Chem. 65, 1247–1256 (1993).
[CrossRef] [PubMed]

Cavanagh, H. D.

P. A. Andrews, W. M. Petroll, H. D. Cavanagh, J. V. Jester, “Tandem scanning confocal microscopy (TSCM) of normal and ischemic living kidneys,” J. Anat. 191, 95–102 (1991).
[CrossRef]

Cheong, W. F.

W. F. Cheong, S. A. Prahl, A. J. Walsh, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Chou, C. H.

Choudhury, A.

C. J. R. Sheppard, A. Choudhury, “Image formation in the scanning microscope,” Opt. Acta 24, 1051–1073 (1977).
[CrossRef]

Cochran, A. J.

A. J. Cochran, S. Binder, F. Remotti, “The role of microscopic evaluation in the management of cutaneous melanoma,” in Current Research and Clinical Management of Melanoma, L. Nathanson, ed. (Kluwer, Boston, Mass., 1993), Chap. 4.
[CrossRef]

Corle, T. R.

Flock, S. T.

S. T. Flock, M. S. Patterson, B. C. Wilson, Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues—1: model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1167 (1989).
[CrossRef] [PubMed]

S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14, 835–841 (1987).
[CrossRef] [PubMed]

Fujii, Y.

Y. Fujii, H. Takimoto, T. Igarashi, “Optimum resolution of laser microscope by using optical heterodyne detection,” Opt. Commun. 38, 85–90 (1981).
[CrossRef]

Goodman, J.

J. Goodman, Fourier Optics (McGraw-Hill, New York, 1968).

Greenstein, J.

L. Henyey, J. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Henyey, L.

L. Henyey, J. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Igarashi, T.

Y. Fujii, H. Takimoto, T. Igarashi, “Optimum resolution of laser microscope by using optical heterodyne detection,” Opt. Commun. 38, 85–90 (1981).
[CrossRef]

Ishimaru, A.

Jester, J. V.

P. A. Andrews, W. M. Petroll, H. D. Cavanagh, J. V. Jester, “Tandem scanning confocal microscopy (TSCM) of normal and ischemic living kidneys,” J. Anat. 191, 95–102 (1991).
[CrossRef]

Kino, G. S.

Knüttel, A.

Kuga, Y.

Loddor, R. A.

L. A. Cassis, R. A. Loddor, “Near-IR imaging of atheromas in living arterial tissue,” Anal. Chem. 65, 1247–1256 (1993).
[CrossRef] [PubMed]

Mao, X. Q.

Milloni, G.

P. Bruscaglioni, G. Milloni, G. Zaccanti, “On the contribution of multiple scattering to lidar returns from homogeneous fogs and its dependence on the receiver angular aperture,” Opt. Acta 27, 1229–1242 (1980).
[CrossRef]

Moran, S. E.

S. E. Moran, “On the transport theory of mutual intensity function propagation in a multiple scattering medium,” Radio Sci. 15, 1195–1205 (1980).
[CrossRef]

Patterson, M. S.

S. T. Flock, M. S. Patterson, B. C. Wilson, Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues—1: model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1167 (1989).
[CrossRef] [PubMed]

S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14, 835–841 (1987).
[CrossRef] [PubMed]

Petroll, W. M.

P. A. Andrews, W. M. Petroll, H. D. Cavanagh, J. V. Jester, “Tandem scanning confocal microscopy (TSCM) of normal and ischemic living kidneys,” J. Anat. 191, 95–102 (1991).
[CrossRef]

Prahl, S. A.

W. F. Cheong, S. A. Prahl, A. J. Walsh, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Remotti, F.

A. J. Cochran, S. Binder, F. Remotti, “The role of microscopic evaluation in the management of cutaneous melanoma,” in Current Research and Clinical Management of Melanoma, L. Nathanson, ed. (Kluwer, Boston, Mass., 1993), Chap. 4.
[CrossRef]

Schmitt, J. M.

Sheppard, C. J. R.

C. J. R. Sheppard, X. Q. Mao, “Three-dimensional imaging in a microscope,” J. Opt. Soc. Am. A 6, 1260–1269 (1989).
[CrossRef]

C. J. R. Sheppard, T. Wilson, “Image formation in scanning microscopes with partially coherent source and detector,” Opt. Acta 25, 315–325 (1978).
[CrossRef]

C. J. R. Sheppard, A. Choudhury, “Image formation in the scanning microscope,” Opt. Acta 24, 1051–1073 (1977).
[CrossRef]

Takimoto, H.

Y. Fujii, H. Takimoto, T. Igarashi, “Optimum resolution of laser microscope by using optical heterodyne detection,” Opt. Commun. 38, 85–90 (1981).
[CrossRef]

Walsh, A. J.

W. F. Cheong, S. A. Prahl, A. J. Walsh, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Walther, A.

Wilson, B. C.

S. T. Flock, M. S. Patterson, B. C. Wilson, Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues—1: model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1167 (1989).
[CrossRef] [PubMed]

S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14, 835–841 (1987).
[CrossRef] [PubMed]

Wilson, T.

T. Wilson, “Optical sectioning in confocal fluorescent microscopes,” J. Microsc. 154, 143–156 (1988).
[CrossRef]

T. Wilson, A. R. Carlini, “Size of the detector in confocal imaging systems,” Opt. Lett. 12, 227–229 (1987).
[CrossRef] [PubMed]

C. J. R. Sheppard, T. Wilson, “Image formation in scanning microscopes with partially coherent source and detector,” Opt. Acta 25, 315–325 (1978).
[CrossRef]

Wolf, E.

E. Wolf, “New theory of radiative energy transfer in free electromagnetic fields,” Phys. Rev. D 13, 869–886 (1976).
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1983).

Wyman,

S. T. Flock, M. S. Patterson, B. C. Wilson, Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues—1: model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1167 (1989).
[CrossRef] [PubMed]

Zaccanti, G.

P. Bruscaglioni, G. Milloni, G. Zaccanti, “On the contribution of multiple scattering to lidar returns from homogeneous fogs and its dependence on the receiver angular aperture,” Opt. Acta 27, 1229–1242 (1980).
[CrossRef]

Anal. Chem.

L. A. Cassis, R. A. Loddor, “Near-IR imaging of atheromas in living arterial tissue,” Anal. Chem. 65, 1247–1256 (1993).
[CrossRef] [PubMed]

Appl. Opt.

Astrophys. J.

L. Henyey, J. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

IEEE J. Quantum Electron.

W. F. Cheong, S. A. Prahl, A. J. Walsh, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

IEEE Trans. Biomed. Eng.

S. T. Flock, M. S. Patterson, B. C. Wilson, Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues—1: model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1167 (1989).
[CrossRef] [PubMed]

J. Anat.

P. A. Andrews, W. M. Petroll, H. D. Cavanagh, J. V. Jester, “Tandem scanning confocal microscopy (TSCM) of normal and ischemic living kidneys,” J. Anat. 191, 95–102 (1991).
[CrossRef]

J. Microsc.

T. Wilson, “Optical sectioning in confocal fluorescent microscopes,” J. Microsc. 154, 143–156 (1988).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Med. Phys.

S. T. Flock, B. C. Wilson, M. S. Patterson, “Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm,” Med. Phys. 14, 835–841 (1987).
[CrossRef] [PubMed]

Opt. Acta

P. Bruscaglioni, G. Milloni, G. Zaccanti, “On the contribution of multiple scattering to lidar returns from homogeneous fogs and its dependence on the receiver angular aperture,” Opt. Acta 27, 1229–1242 (1980).
[CrossRef]

C. J. R. Sheppard, A. Choudhury, “Image formation in the scanning microscope,” Opt. Acta 24, 1051–1073 (1977).
[CrossRef]

C. J. R. Sheppard, T. Wilson, “Image formation in scanning microscopes with partially coherent source and detector,” Opt. Acta 25, 315–325 (1978).
[CrossRef]

Opt. Commun.

Y. Fujii, H. Takimoto, T. Igarashi, “Optimum resolution of laser microscope by using optical heterodyne detection,” Opt. Commun. 38, 85–90 (1981).
[CrossRef]

Opt. Lett.

Phys. Rev. D

E. Wolf, “New theory of radiative energy transfer in free electromagnetic fields,” Phys. Rev. D 13, 869–886 (1976).
[CrossRef]

Radio Sci.

S. E. Moran, “On the transport theory of mutual intensity function propagation in a multiple scattering medium,” Radio Sci. 15, 1195–1205 (1980).
[CrossRef]

Other

J. Goodman, Fourier Optics (McGraw-Hill, New York, 1968).

T. Wilson, ed., Confocal Microscopy (Academic, London, 1990).

A. J. Cochran, S. Binder, F. Remotti, “The role of microscopic evaluation in the management of cutaneous melanoma,” in Current Research and Clinical Management of Melanoma, L. Nathanson, ed. (Kluwer, Boston, Mass., 1993), Chap. 4.
[CrossRef]

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1983).

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Figures (11)

Fig. 1
Fig. 1

Geometry of a confocal scanning microscope viewing a turbid medium. Here only one of the two orthogonal planes (the xz plane) of the system is shown. The distance labels in this figure define the variables used throughout the text. zm, Depth in the medium; n1, n2, indices of refraction outside and inside the medium, respectively. Inset: Geometry of the equivalent 4f confocal system.

Fig. 2
Fig. 2

Experimental setup used to evaluate the performance of a confocal microscope viewing objects embedded in highly scattering media. The incident beam was chopped at frequency f0 = 1.5 KHz for synchronous detection.

Fig. 3
Fig. 3

Comparison of the axial focusing profiles of a confocal microscope predicted by use of the analytical [single-backscatter, Eq. (4)] and the numerical (Monte Carlo) models. For this example, the following model parameters were assumed: λ = 632.8 nm, D = 6.0 mm, f = 8.6 mm, d = 7.85 mm, dp = 5 μm, n1 = n2 = 1. A mirror was used as a reflector in the Monte Carlo simulations, and the backscattered light was normalized to 1 for both models for μs = 0. The x coordinates are given in units of optical depth, defined as τ = μszm, where zm is the depth measured from the surface of the scattering medium.

Fig. 4
Fig. 4

Measured and predicted responses of the experimental confocal microscope to a mirror located at different depths in turbid suspensions of polystyrene microspheres. In these experiments a pinhole with a diameter of 5 μm was used. Solid curves, experimental data; symbols, data calculated with the Monte Carlo model. The constants used in the model were measured from the experimental setup: D = 6.0 mm, f = 8.6 mm, d = 8.036 mm, nI = 1.0, and n2 = 1.33. The optical coefficients marked on the curves were obtained from Mie theory; the same values were used in the Monte Carlo simulations.

Fig. 5
Fig. 5

Measured and predicted responses of the experimental confocal microscope to a mirror located at different depths in turbid suspensions of polystyrene microspheres. Solid curves, experimental data; symbols, data calculated with the Monte Carlo model. The conditions were the same as those under which the data in Fig. 4 were obtained, except that the diameter of the pinhole used in these experiments was 10 μm.

Fig. 6
Fig. 6

Detector signal recorded from the experimental confocal microscope as a 10-lines/mm Ronchi ruling embedded in suspensions of microspheres, translated perpendicular to the focused beam. The legend gives the scattering coefficients of the suspensions. The setup of the microscope was the same as that used for obtaining the data plotted in Fig. 4. Refer to Section 4 of the text for details about the experimental procedures.

Fig. 7
Fig. 7

Transverse contrast measured with the 10-line/mm Ronchi ruling for suspensions containing microspheres with two different diameters. The contrast measured in these experiments is defined in Section 4. Inset: the peak of the detected signal, plotted as a function of the optical depth of the microsphere suspensions.

Fig. 8
Fig. 8

Fraction of the incident power backscatted from different depths and captured by the detector of a simulated confocal microscope probing a turbid suspension. Solid curves, axial profiles for pinholes of different diameters; dotted curve, profile for a 10-μm-diameter pinhole that resulted from a selection of only the single-backscattered photons. These data were obtained from Monte Carlo simulations of a microscope focused at a depth of 300 μm in a random suspension of 1.05-μm-diameter spherical particles. The scattering mean-free path was assumed to be 230 μm. The other constants used in this model were D = 6.0 mm, f = 8.6 mm, d = 8.37 mm, n1 = 1.0, and n2 = 1.33.

Fig. 9
Fig. 9

Fraction of the incident power backscattered from different depths and captured by the detector of a simulated confocal microscope probing a turbid suspension. Solid curves, axial profiles for pinholes of different diameters; dotted curve, profile for a 10-μm-diameter pinhole that resulted from selection of only the single-backscattered photons. These data were obtained from Monte Carlo simulations of a microscope focused at a depth of 300 μm. in a random suspension of 0.22-μm-diameter spherical particles. The other simulations conditions were the same as those listed in the caption for Fig. 8.

Fig. 10
Fig. 10

Fraction of the incident power backscattered from different depths and captured by the detector of a simulated confocal microscope probing a turbid suspension. Solid curves, axial profiles for pinholes of different diameters; dotted curve, profile for a 10-μm-diameter pinhole that resulted from selection of only the single-backscattered photons. These data were obtained from Monte Carlo simulations of a microscope focused at a depth of 700 μm in a random suspension of 1.05-μm-diameter spherical particles. The scattering mean free path was assumed to be 230 μm. The other constants used in the model were D = 6.0 mm, f = 8.6 mm, d = 8.07 mm, n1 = 1.0, and n2 = 1.33.

Fig. 11
Fig. 11

Relationship between the background-rejection ratio R and the normalized detected signal power ΣPs/P0 as a function of pinhole size, derived from the data plotted in Figs. 8 and 10. The background-rejection ratio is defined in Section 4 of the text.

Equations (11)

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h I lens ( x d , y d ; x m , y m ; δ ) = π 2 4 λ 4 f 4 × | 0 D d r r exp ( i π κ r 2 / λ ) J 0 ( 2 π r ρ ) | 2 ,
ρ = [ ( x d x m ) 2 + ( y d y m ) 2 ] 1 / 2 2 λ f , κ = δ 4 f 2
S i = I 0 A h I lens ( 0 , 0 ; , x m , y m ; δ ) .
P s ( x m , y m ; δ ) = S i pinhole h I lens ( x d y d ; x m , y m ; δ ) d x d d y d .
P axial ( δ ) = P s ( x m , y m ; δ ) d x m d y m ,
x d = x m + α x [ f ( n 1 / n 2 ) ( z m + n 1 d / n 2 ) ]
y d = y m + α y [ f ( n 1 / n 2 ) ( z m + n 1 d / n 2 ) ] ,
cos ( θ ) = 1 + g 2 2 g ( 1 g 2 ) 2 2 g ( 1 g + 2 g υ ) 2 0 < θ < π ,
R = Σ P ideal Σ P s Σ P ideal ,
Σ P ideal 0 exp [ 2 μ s ( f d ) ] 1 + d p 2 / [ 2 ( f d z m ) α ] 2 d z m ,
Σ P s 0 exp [ 2 μ s z m ) 1 + d p 2 / [ 2 ( f d z m ) α ] 2 d z m ,

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