Abstract

The detection of ballistic and diffuse light in confocal and heterodyne imaging systems in transillumination is studied experimentally and theoretically. We find an optimum pinhole size for ballistic light detection and diffuse light rejection for confocal imaging. The ratio of ballistic and diffuse light is found to be determined primarily by sample parameters and aberrations introduced by the sample. For sample and illumination characteristics that are typical for biomedical imaging, the limits of ballistic light detection in confocal imaging are close to the noise limits of standard detectors. Heterodyne detection with narrow-bandwidth light can extend these limits, depending on the spatial and the temporal coherence properties of the transmitted scattered light.

© 1997 Optical Society of America

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    [CrossRef]
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  19. J. H. Li, A. A. Lisyansky, T. D. Cheung, D. Livdan, A. Z. Genack, “Transmission and surface intensity profiles in random media,” Europhys. Lett. 22, 675–680 (1993).
    [CrossRef]
  20. J. M. Schmitt, A. Knuettel, M. Yadlowsky, “Confocal microscopy in turbid media,” J. Opt. Soc. Am. A 11, 2226–2235 (1994).
    [CrossRef]

1996 (2)

1995 (3)

1994 (3)

1993 (2)

J. H. Li, A. A. Lisyansky, T. D. Cheung, D. Livdan, A. Z. Genack, “Transmission and surface intensity profiles in random media,” Europhys. Lett. 22, 675–680 (1993).
[CrossRef]

M. R. Hee, J. A. Izatt, J. M. Jacobson, J. G. Fujimoto, E. A. Swanson, “Femtosecond transillumination optical coherence tomography,” Opt. Lett. 18, 950–952 (1993).
[CrossRef] [PubMed]

1991 (1)

1978 (1)

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

Alfano, R. R.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1989).

Chan, K. P.

Cheung, T. D.

J. H. Li, A. A. Lisyansky, T. D. Cheung, D. Livdan, A. Z. Genack, “Transmission and surface intensity profiles in random media,” Europhys. Lett. 22, 675–680 (1993).
[CrossRef]

Cho, Y.

Demos, S. G.

Devaraj, B.

Frehlich, R. G.

Fujimoto, J. G.

Genack, A. Z.

J. H. Li, A. A. Lisyansky, T. D. Cheung, D. Livdan, A. Z. Genack, “Transmission and surface intensity profiles in random media,” Europhys. Lett. 22, 675–680 (1993).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

Hashimoto, K.

Hee, M. R.

Ho, P. P.

Horinaka, H.

Inaba, H.

Izatt, J. A.

Jacobson, J. M.

Kavaya, M. K.

Kempe, M.

Knuettel, A.

J. M. Schmitt, A. Knuettel, M. Yadlowsky, “Confocal microscopy in turbid media,” J. Opt. Soc. Am. A 11, 2226–2235 (1994).
[CrossRef]

J. M. Schmitt, A. Knuettel, M. Yadlowsky, “Interferometric versus confocal techniques for imaging microstructures in turbid biological media,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE2135, 251–262 (1994).
[CrossRef]

Li, J. H.

J. H. Li, A. A. Lisyansky, T. D. Cheung, D. Livdan, A. Z. Genack, “Transmission and surface intensity profiles in random media,” Europhys. Lett. 22, 675–680 (1993).
[CrossRef]

Liang, X.

Lisyansky, A. A.

J. H. Li, A. A. Lisyansky, T. D. Cheung, D. Livdan, A. Z. Genack, “Transmission and surface intensity profiles in random media,” Europhys. Lett. 22, 675–680 (1993).
[CrossRef]

Livdan, D.

J. H. Li, A. A. Lisyansky, T. D. Cheung, D. Livdan, A. Z. Genack, “Transmission and surface intensity profiles in random media,” Europhys. Lett. 22, 675–680 (1993).
[CrossRef]

Osawa, M.

Owen, G. M.

Rudolph, W.

Schmitt, J. M.

J. M. Schmitt, A. Knuettel, M. Yadlowsky, “Confocal microscopy in turbid media,” J. Opt. Soc. Am. A 11, 2226–2235 (1994).
[CrossRef]

J. M. Schmitt, A. Knuettel, M. Yadlowsky, “Interferometric versus confocal techniques for imaging microstructures in turbid biological media,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE2135, 251–262 (1994).
[CrossRef]

Sheppard, C. J. R.

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

T. Wilson, C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, London, 1984).

Swanson, E. A.

Wada, K.

Wang, L.

Wang, Q. Z.

Welsch, E.

Wilson, T.

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

T. Wilson, C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, London, 1984).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1989).

Yadlowsky, M.

J. M. Schmitt, A. Knuettel, M. Yadlowsky, “Confocal microscopy in turbid media,” J. Opt. Soc. Am. A 11, 2226–2235 (1994).
[CrossRef]

J. M. Schmitt, A. Knuettel, M. Yadlowsky, “Interferometric versus confocal techniques for imaging microstructures in turbid biological media,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE2135, 251–262 (1994).
[CrossRef]

Yamada, M.

Appl. Opt. (1)

Europhys. Lett. (1)

J. H. Li, A. A. Lisyansky, T. D. Cheung, D. Livdan, A. Z. Genack, “Transmission and surface intensity profiles in random media,” Europhys. Lett. 22, 675–680 (1993).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Acta (1)

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. Lett. (7)

Other (8)

M. Kempe, W. Rudolph, “Analysis of heterodyne laser scanning microscopy for illumination with broad bandwidth light,“ J. Mod. Opt. (to be published).

J. P. Pawley, ed., Handbook of Biological Confocal Microscopy (Plenum, New York, 1990).

T. Wilson, C. J. R. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, London, 1984).

T. Wilson, ed., Confocal Microscopy (Academic, London, 1991).

J. M. Schmitt, A. Knuettel, M. Yadlowsky, “Interferometric versus confocal techniques for imaging microstructures in turbid biological media,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE2135, 251–262 (1994).
[CrossRef]

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1989).

R. R. Alfano, ed., Advances in Optical Imaging and Photon Migration, Vol. 21 of OSA Proceedings Series (Optical Society of America, Washington, DC, 1994).

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Figures (9)

Fig. 1
Fig. 1

Experimental setup: BS’s beam splitters; ai, aperture radius of lens Li; D, detector (photomultiplier tube).

Fig. 2
Fig. 2

Semilogarithmic plot of the signal as a function of sample thickness for a suspension with ls=74 µm. Shown is the signal obtained with a NA of 0.10 for a pinhole with vp=1.24 and for a NA of 0.015 with vp=1.16. The solid line is the fit to the part of the curves that exhibits an exponential falloff.

Fig. 3
Fig. 3

(a) Log–log plot of the pinhole transmission for ballistic light (at L=0.47 mm) and (b) semilogarithmic plot of the maximum sample thickness Lmax as a function of the normalized pinhole size. The NA is 0.015. The suspension had a scattering mean free path of 74 µm. The pinhole had a diameter of 10 µm (squares) and 50 µm (circles), respectively. The focal length of lens L3 was varied from 32 to 200 mm. The solid and the dashed curves result from calculations explained in the text.

Fig. 4
Fig. 4

Semilogarithmic plots of (a) the pinhole transmission for ballistic light (at L=0.47 mm) and (b) the maximum sample thickness Lmax as a function of the NA. We increased the NA by increasing the beam radius a. The solid curve is the theoretical curve of the pinhole transmission in the absence of aberrations. The dashed lines connecting the measured points are only guides for the eye.

Fig. 5
Fig. 5

Maximum sample thickness Lmax/ls as a function of ls. The theoretical results (solid and dashed curves) are explained in the text.

Fig. 6
Fig. 6

Diffuse-light signal as a function of the distance between the back surface of the sample and the focal plane of the collector lens. The sample was alumina with a scattering mean free path of ls=8 µm and a thickness of 70 µm. The result according to Eq. (18) is shown as a solid curve.

Fig. 7
Fig. 7

Semilogarithmic plot of the normalized confocal and heterodyne signals. In these measurements latex spheres with diameters of 135 µm (σs=3.10×10-12cm2, g=0.14 according to Mie theory) were used. The power in the reference arm was 100 µW, and the power incident upon the sample was 1 mW.

Fig. 8
Fig. 8

Geometry of the confocal imaging system (a) with objective and collector lenses only and (b) with a third lens used to focus into the pinhole in front of the detector.

Fig. 9
Fig. 9

Calculated normalized ratio of ballistic to diffuse light as a function of the normalized distance between the collector lens and the lens focusing into the pinhole.

Equations (21)

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Kb=exp(-L/ls).
Kdl/L,
SconfP0=exp(-L/ls)+2λ2 lL3,
RbdL22λ2Llexp(-L/ls).
Shet=QD D d2rd2rMo(r, r)Mr*(r, r)1/2,
Shet,b0.73QPrPo exp(-0.5L/ls),
Shet,dQ 2λπ1LlLPrPo.
Rhet,bd0.37 πLλLlTτc exp(-0.5L/ls).
Rhet,bd(Rbd=1)1.6T/τc.
U(r1)=2π2λ20 dr0r0h(x1-x0, y1-y0)U(r0),
Iinc(r1)=4π3λ20 dr0r0|h(x1-x0, y1-y0)|2I(r0).
Ic(r1)=4π4λ40 dr0r0h(x1-x0, y1-y0)U(r0)2.
U(r0)=-jπa2λd1h(v, Φ)I0Kb,
h(v, Φ)=2 exp[-jd1v2λ/(4πa2)]×01 drrJ0(rv)exp[-jΦ(r)],
Ib(v1)=π2d124λ2IinKb×0dvvh(x1-x0, y1-y0, Φb)h(v, Φb)2,
Id(v1)=4πd12L2FI0Kd 0 dvvf(v)×|h(x1-x0, y1-y0, Φd)|2.
Idet=0vp dv1v1Ib,d(v1).
Rbd=Ib(0)Id(0)=πL216λ2KbKdF |0 dvvh(v, Φb)2|20 dvvf(v)|h(v, Φd)|2.
Rbd=πL22λ2Llexp(-L/ls).
Ic(0)Iinc(0)=πλ2IcIi0adr0r0h(r0, u)20adr0r0|h(r0, u)|2=πa2λ2u2IcIi0udvvh(v, u)20udvv|h(v, u)|2,
Ic(0)Iic(0)=πa2λ2u2IcIi×0udvv 01drrJ0(rv)exp{-ju/2[r2+(v/u)2]}20udvv01drrJ0(rv)exp(-jur2/2)2.

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