Abstract

We show that the multiple-scatter rejection provided by optical coherence microscopy (low-coherence interferometry) can be incomplete in optically turbid media and that multiple scattering manifests itself in two distinct ways. Multiple small-angle scattering results in an effective probe field that is stronger than expected from a first-order beam extinction model, but that contains a distorted wave front that enhances the apparent reflectance of small structures relative to those that are larger than the unscattered incident beam. Multiple wide-angle scattering produces a broad diffuse haze that reduces the contrast of subsequent features.

© 1995 Optical Society of America

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  1. D. Huang, J. Wand, C. P. Lin, C. A. Puliafito, J. G. Fujimoto, “Micron-resolution ranging of cornea anterior chamber by optical reflectometry,” Lasers Surg. Med. 11, 419–425 (1991).
    [CrossRef] [PubMed]
  2. 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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
    [CrossRef] [PubMed]
  3. C. K. Hitzenberger, “Measurement of corneal thickness by low-coherence interferometry,” Appl. Opt. 31, 6637–6642 (1992).
    [CrossRef] [PubMed]
  4. E. A. Swanson, J. A. Izatt, M. R. Hee, D. Huang, C. P. Lin, J. S. Schuman, C. A. Puliafito, J. G. Fujimoto, “In vivo retinal imaging by optical coherence tomography,” Opt. Lett. 17, 151–153 (1992).
    [CrossRef] [PubMed]
  5. J. M. Schmitt, A. Knüttel, R. F. Bonner, “Measurement of optical properties of biological tissues by low-coherence reflectometry,” Appl. Opt. 32, 6032–6042 (1993).
    [CrossRef] [PubMed]
  6. J. M. Schmitt, A. Knüttel, A. Gandjbakhche, R. F. Bonner, “Optical characterization of dense tissues using low-coherence interferometry,” in Holography, Interferometry, and Optical Pattern Recognition in Biomedicine III, H. Podbielska, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1889, 197–210 (1993).
  7. J. M. Schmitt, A. Knüttel, M. Yadlowsky, M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
    [CrossRef] [PubMed]
  8. J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, J. G. Fujimoto, “Optical coherence microscopy in scattering media,” Opt. Lett. 19, 590–592 (1994).
    [CrossRef] [PubMed]
  9. C. M. Sonnenschein, F. A. Horrigan, “Signal-to-noise relationships for coaxial systems that heterodyne backscatter from the atmosphere,” Appl. Opt. 10, 1600–1604 (1971).
    [CrossRef] [PubMed]
  10. J. M. Schmitt, M. J. Yadlowsky, R. F. Bonner, “Subsurface imaging of living skin with optical coherence microscopy,” Dermatology (to be published).
  11. S. Kimura, T. Wilson, “Confocal scanning microscope using single-mode fiber for signal detection,” Appl. Opt. 30, 2143–2150 (1991).
    [CrossRef] [PubMed]
  12. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  13. J. M. Schmitt, A. Knüttel, M. Yadlowsky, R. F. Bonner, “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. Soc. Photo-Opt. Instrum. Eng.2135, 251–262 (1994).
  14. H. T. Yura, “Signal-to-noise ratio of heterodyne lidar systems in the presence of atmospheric turbulence,” Opt. Acta 26, 627–644 (1979).
    [CrossRef]
  15. J. M. Schmitt, A. Knüttel, M. Yadlowsky, “Confocal microscopy in turbid media,” J. Opt. Soc. Am. A 11, 2226–2235 (1994).
    [CrossRef]
  16. D. L. Fried, “Optical heterodyne detection of an atmospherically distorted signal wave front,” Proc. IEEE 55, 57–67 (1967).
    [CrossRef]

1994

1993

1992

1991

S. Kimura, T. Wilson, “Confocal scanning microscope using single-mode fiber for signal detection,” Appl. Opt. 30, 2143–2150 (1991).
[CrossRef] [PubMed]

D. Huang, J. Wand, C. P. Lin, C. A. Puliafito, J. G. Fujimoto, “Micron-resolution ranging of cornea anterior chamber by optical reflectometry,” Lasers Surg. Med. 11, 419–425 (1991).
[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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

1979

H. T. Yura, “Signal-to-noise ratio of heterodyne lidar systems in the presence of atmospheric turbulence,” Opt. Acta 26, 627–644 (1979).
[CrossRef]

1971

1967

D. L. Fried, “Optical heterodyne detection of an atmospherically distorted signal wave front,” Proc. IEEE 55, 57–67 (1967).
[CrossRef]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Bonner, R. F.

J. M. Schmitt, A. Knüttel, R. F. Bonner, “Measurement of optical properties of biological tissues by low-coherence reflectometry,” Appl. Opt. 32, 6032–6042 (1993).
[CrossRef] [PubMed]

J. M. Schmitt, A. Knüttel, M. Yadlowsky, R. F. Bonner, “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. Soc. Photo-Opt. Instrum. Eng.2135, 251–262 (1994).

J. M. Schmitt, M. J. Yadlowsky, R. F. Bonner, “Subsurface imaging of living skin with optical coherence microscopy,” Dermatology (to be published).

J. M. Schmitt, A. Knüttel, A. Gandjbakhche, R. F. Bonner, “Optical characterization of dense tissues using low-coherence interferometry,” in Holography, Interferometry, and Optical Pattern Recognition in Biomedicine III, H. Podbielska, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1889, 197–210 (1993).

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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Eckhaus, M. A.

J. M. Schmitt, A. Knüttel, M. Yadlowsky, M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
[CrossRef] [PubMed]

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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Fried, D. L.

D. L. Fried, “Optical heterodyne detection of an atmospherically distorted signal wave front,” Proc. IEEE 55, 57–67 (1967).
[CrossRef]

Fujimoto, J. G.

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

E. A. Swanson, J. A. Izatt, M. R. Hee, D. Huang, C. P. Lin, J. S. Schuman, C. A. Puliafito, J. G. Fujimoto, “In vivo retinal imaging by optical coherence tomography,” Opt. Lett. 17, 151–153 (1992).
[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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

D. Huang, J. Wand, C. P. Lin, C. A. Puliafito, J. G. Fujimoto, “Micron-resolution ranging of cornea anterior chamber by optical reflectometry,” Lasers Surg. Med. 11, 419–425 (1991).
[CrossRef] [PubMed]

Gandjbakhche, A.

J. M. Schmitt, A. Knüttel, A. Gandjbakhche, R. F. Bonner, “Optical characterization of dense tissues using low-coherence interferometry,” in Holography, Interferometry, and Optical Pattern Recognition in Biomedicine III, H. Podbielska, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1889, 197–210 (1993).

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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Hee, M. R.

Hitzenberger, C. K.

Horrigan, F. A.

Huang, D.

E. A. Swanson, J. A. Izatt, M. R. Hee, D. Huang, C. P. Lin, J. S. Schuman, C. A. Puliafito, J. G. Fujimoto, “In vivo retinal imaging by optical coherence tomography,” Opt. Lett. 17, 151–153 (1992).
[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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

D. Huang, J. Wand, C. P. Lin, C. A. Puliafito, J. G. Fujimoto, “Micron-resolution ranging of cornea anterior chamber by optical reflectometry,” Lasers Surg. Med. 11, 419–425 (1991).
[CrossRef] [PubMed]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Izatt, J. A.

Kimura, S.

Knüttel, A.

J. M. Schmitt, A. Knüttel, M. Yadlowsky, M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
[CrossRef] [PubMed]

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

J. M. Schmitt, A. Knüttel, R. F. Bonner, “Measurement of optical properties of biological tissues by low-coherence reflectometry,” Appl. Opt. 32, 6032–6042 (1993).
[CrossRef] [PubMed]

J. M. Schmitt, A. Knüttel, M. Yadlowsky, R. F. Bonner, “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. Soc. Photo-Opt. Instrum. Eng.2135, 251–262 (1994).

J. M. Schmitt, A. Knüttel, A. Gandjbakhche, R. F. Bonner, “Optical characterization of dense tissues using low-coherence interferometry,” in Holography, Interferometry, and Optical Pattern Recognition in Biomedicine III, H. Podbielska, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1889, 197–210 (1993).

Lin, C. P.

E. A. Swanson, J. A. Izatt, M. R. Hee, D. Huang, C. P. Lin, J. S. Schuman, C. A. Puliafito, J. G. Fujimoto, “In vivo retinal imaging by optical coherence tomography,” Opt. Lett. 17, 151–153 (1992).
[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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

D. Huang, J. Wand, C. P. Lin, C. A. Puliafito, J. G. Fujimoto, “Micron-resolution ranging of cornea anterior chamber by optical reflectometry,” Lasers Surg. Med. 11, 419–425 (1991).
[CrossRef] [PubMed]

Owen, G. M.

Puliafito, C. A.

E. A. Swanson, J. A. Izatt, M. R. Hee, D. Huang, C. P. Lin, J. S. Schuman, C. A. Puliafito, J. G. Fujimoto, “In vivo retinal imaging by optical coherence tomography,” Opt. Lett. 17, 151–153 (1992).
[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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

D. Huang, J. Wand, C. P. Lin, C. A. Puliafito, J. G. Fujimoto, “Micron-resolution ranging of cornea anterior chamber by optical reflectometry,” Lasers Surg. Med. 11, 419–425 (1991).
[CrossRef] [PubMed]

Schmitt, J. M.

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

J. M. Schmitt, A. Knüttel, M. Yadlowsky, M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
[CrossRef] [PubMed]

J. M. Schmitt, A. Knüttel, R. F. Bonner, “Measurement of optical properties of biological tissues by low-coherence reflectometry,” Appl. Opt. 32, 6032–6042 (1993).
[CrossRef] [PubMed]

J. M. Schmitt, A. Knüttel, M. Yadlowsky, R. F. Bonner, “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. Soc. Photo-Opt. Instrum. Eng.2135, 251–262 (1994).

J. M. Schmitt, A. Knüttel, A. Gandjbakhche, R. F. Bonner, “Optical characterization of dense tissues using low-coherence interferometry,” in Holography, Interferometry, and Optical Pattern Recognition in Biomedicine III, H. Podbielska, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1889, 197–210 (1993).

J. M. Schmitt, M. J. Yadlowsky, R. F. Bonner, “Subsurface imaging of living skin with optical coherence microscopy,” Dermatology (to be published).

Schuman, J. S.

E. A. Swanson, J. A. Izatt, M. R. Hee, D. Huang, C. P. Lin, J. S. Schuman, C. A. Puliafito, J. G. Fujimoto, “In vivo retinal imaging by optical coherence tomography,” Opt. Lett. 17, 151–153 (1992).
[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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Sonnenschein, C. M.

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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Swanson, E. A.

Wand, J.

D. Huang, J. Wand, C. P. Lin, C. A. Puliafito, J. G. Fujimoto, “Micron-resolution ranging of cornea anterior chamber by optical reflectometry,” Lasers Surg. Med. 11, 419–425 (1991).
[CrossRef] [PubMed]

Wilson, T.

Yadlowsky, M.

J. M. Schmitt, A. Knüttel, M. Yadlowsky, M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
[CrossRef] [PubMed]

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

J. M. Schmitt, A. Knüttel, M. Yadlowsky, R. F. Bonner, “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. Soc. Photo-Opt. Instrum. Eng.2135, 251–262 (1994).

Yadlowsky, M. J.

J. M. Schmitt, M. J. Yadlowsky, R. F. Bonner, “Subsurface imaging of living skin with optical coherence microscopy,” Dermatology (to be published).

Yura, H. T.

H. T. Yura, “Signal-to-noise ratio of heterodyne lidar systems in the presence of atmospheric turbulence,” Opt. Acta 26, 627–644 (1979).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am. A

Lasers Surg. Med.

D. Huang, J. Wand, C. P. Lin, C. A. Puliafito, J. G. Fujimoto, “Micron-resolution ranging of cornea anterior chamber by optical reflectometry,” Lasers Surg. Med. 11, 419–425 (1991).
[CrossRef] [PubMed]

Opt. Acta

H. T. Yura, “Signal-to-noise ratio of heterodyne lidar systems in the presence of atmospheric turbulence,” Opt. Acta 26, 627–644 (1979).
[CrossRef]

Opt. Lett.

Phys. Med. Biol.

J. M. Schmitt, A. Knüttel, M. Yadlowsky, M. A. Eckhaus, “Optical-coherence tomography of a dense tissue: statistics of attenuation and backscattering,” Phys. Med. Biol. 39, 1705–1720 (1994).
[CrossRef] [PubMed]

Proc. IEEE

D. L. Fried, “Optical heterodyne detection of an atmospherically distorted signal wave front,” Proc. IEEE 55, 57–67 (1967).
[CrossRef]

Science

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, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Other

J. M. Schmitt, A. Knüttel, A. Gandjbakhche, R. F. Bonner, “Optical characterization of dense tissues using low-coherence interferometry,” in Holography, Interferometry, and Optical Pattern Recognition in Biomedicine III, H. Podbielska, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1889, 197–210 (1993).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

J. M. Schmitt, A. Knüttel, M. Yadlowsky, R. F. Bonner, “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. Soc. Photo-Opt. Instrum. Eng.2135, 251–262 (1994).

J. M. Schmitt, M. J. Yadlowsky, R. F. Bonner, “Subsurface imaging of living skin with optical coherence microscopy,” Dermatology (to be published).

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Figures (11)

Fig. 1
Fig. 1

OCM image of the fingernail and nailfold region of the index finger of a male subject. The gray scale is the log of the reflected intensity, with the dark region representing high reflectance. The exposed portion of the fingernail (upper left) exhibits strong backscatter, whereas the identical contiguous nail (to its right) beneath the eponychium exhibits much lower signal intensity. Strong backscatter from superficial dermal structures beneath the nail form the contiguous dark band across the image (unaffected by overlying eponychium).

Fig. 2
Fig. 2

Schematic diagram of OCM used to make the measurements presented: GRIN, graded index; A/D, analog-to-digital converter.

Fig. 3
Fig. 3

Aberrations and path-length mismatch resulting from refractive index mismatches: (a) Schematic diagram of the sample cell filled with 2.5% (w/v) 0.22-μm PSL. (b) Reflectance profile through the sample taken at full system aperture with the reference arm length set to (i) match the path length of the free space focus of the sample arm and (ii) compensate for aberrations at the end of the cell by shifting the zero-path-length difference match point off of the free-space focus. Curve (iii) shows the ratio of curve (i) to curve (ii) (scale on right). The exponential fit corresponds to a one-way excess loss of 4.4 mm−1. (c) Same as (b) except the objective aperture is limited to 3.8 mm. The excess loss represented by the ratio shown in curve (iii) has been reduced to 1.4 mm−1 because of the smaller aperture.

Fig. 4
Fig. 4

Comparison of the effects of different scattering media of equal strength (total one-way optical depth, τ = 3) on the relative reflectances of a 2.0% volume fraction suspension of 0.3-μm mean-size anatase TiO2 particles suspended in water (in cell 2) and the preceding glass–water interface. (a) Schematic diagram of the sample. (b) Cell 1 filled with 0.48-μm PSL (○), 1.1-μm PSL (×), 1.9-μm PSL (Δ), and 2.8-μm PSL (—). All the curves have been normalized so that the Fresnel reflectance of the beginning of cell 2 is 1.

Fig. 5
Fig. 5

Enlarged view of the reflectance profiles through the beginning of cell 2 of the sample shown in Fig. 4. Cell 1 was filled with PSL’s having the same scatter MFP but consisting of beads of increasing size, and therefore increasingly anisotropic phase functions. (a) PSL samples in cell 1 having a total one-way optical depth of τ = 3. (b) PSL samples in cell 1 having a total one-way optical depth of τ = 1. Each curve has been normalized so that the Fresnel reflection from the beginning of cell 2 is unity.

Fig. 6
Fig. 6

Relative apparent reflectances of the flat interface between glass and the aqueous suspension in cell 2 (Fresnel reflection) and of the 0.3-μm mean-size anatase TiO2 particle suspension adjacent to the interface, as a function of concentration of strongly forward-scattering 2.8-μm PSL in cell 1 (τ = 1–3.5). For comparison, measurement data are also included in which cell 1 was filled with water alone (nonscattering reference) and a 0.48-μm PSL having an optical depth of 1.0. Each curve has been normalized so that the Fresnel reflection from the beginning of cell 2 is unity.

Fig. 7
Fig. 7

Excess backscatter signal from the subwavelength sized TiO2 particles (in cell 2) increases with the optical depth of large scatters in cell 1 for both full (□) and closed (●) aperture settings.

Fig. 8
Fig. 8

Phantom reflectance signals that appear to originate within a transparent glass plate. (a) Schematic diagram of the measurement sample. (b) Reflectance profiles through a sample containing 0.48-μm PSL at (i) 2.5% w/v, (ii) 1.25% w/v, (iii) 0.63% w/v, and (iv) 0.25% w/v. The phantom reflectance within the glass increases with concentration for 0.48-μm PSL. Solid curves are single exponential fits to the reflectance data used to calculate contrast at the interface (see Fig. 11).

Fig. 9
Fig. 9

Reflectance profiles of an enlarged view of the glass portion shown in Fig. 8 for 0.48-μm PSL at 2.5% w/v (-----) and 0.4% w/v (Δ) and for 0.22-μm PSL at 2.5% w/v (—). The phantom reflectance clearly seen with 2.5% w/v, 0.48-μm PSL (MFP = 120 μm) disappears for both an equal volume fraction of 0.22-μm PSL (MFP = 740 μm) and 0.4% w/v, 0.48-μm PSL (MFP = 740 μm).

Fig. 10
Fig. 10

Multiply scattered light responsible for the haze or phantom signals observed in Figs. 7 9 is insensitive to aberrations. Reflectance measurements from 2.5% w/v, 0.48-μm PSL when the reference arm was adjusted to put the zero-path-length difference match point of the sample arm at the free-space focus of the optics (○) exhibit fourfold lower reflectance near the glass interface than measurements obtained with the reference arm adjusted to compensate for the aberrations at the end of the sample cell (×). The haze that appears to arise at this depth in the glass is the same.

Fig. 11
Fig. 11

Contrast decreases with increasing total optical thickness (multiple scattering) of the 0.48-μm PSL-filled cell shown in Fig. 8. Contrast is calculated as the ratio of the PSL backscatter signal extrapolated to the end of the scatter cell to the haze signal in the glass strength extrapolated back to the same point [as indicated in Figs. 8(b) and 10]. The contrast with the full aperture (○) with exponential fit (-----) is roughly threefold greater than contrast with the small aperture (□), (—).

Equations (2)

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i het 2 = ( η P 0 h v ) 2 0 d z R ( z ) exp ( - 2 μ t z ) ( 1 - δ / f ) 2 + ( δ π r 2 / λ f 2 ) 2 γ ( τ ) 2 ,
R ( z ) μ b 4 ( r f ) 2 ,

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