Abstract

Optical imaging of intrinsic signals detects neural activation patterns by taking video images of the local activity-related changes in the light intensity reflected from neural tissue (intrinsic signals). At red light (605 nm), these signals are caused mainly by local variations of the tissue absorption following deoxygenation of blood. We characterize the image generation process during optical imaging by Monte Carlo simulations of light propagation through a homogeneous model tissue equipped with a local absorber. Conventional video imaging and scanning laser imaging are compared. We find that, compared with video imaging, scanning laser techniques drastically increase both the contrast and the lateral resolution of optical recordings. Also, the maximum depth up to which the signals can be detected is increased by roughly a factor of 2 when scanning laser optical imaging is used. Further, the radial profile of the diffuse-reflectance pattern for each pixel is subject to changes that correlate with the depth of the absorber within the tissue. We suggest a detection geometry for the online measurement of these radial profiles that can be realized by modifying a standard scanning laser ophthalmoscope.

© 1999 Optical Society of America

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1998 (1)

L. Ostergaard, D. F. Smith, P. Vestergaard-Poulsen, S. B. Hansen, A. D. Gjedde, C. Gyldensted, “Absolute cerebral blood-flow and blood volume measured by magnetic resonance imaging bolus tracking: comparison with positron emission tomography,” J. Cereb. Blood Flow Metab. 18, 425–432 (1998).
[CrossRef]

1997 (10)

S. C. Rao, L. J. Toth, M. Sur, “Optically imaged maps of orientation preference in primary visual cortex of cats and ferrets,” J. Comp. Neurol. 387, 358–370 (1997).
[CrossRef] [PubMed]

W. H. Bosking, Y. Zhang, B. Schofield, D. Fitzpatrick, “Orientation selectivity and the arrangement of horizontal connections in tree shrew striate cortex,” J. Neurosci. 17, 2112–2127 (1997).
[PubMed]

T. Yoshioka, G. G. Blasdel, J. B. Levitt, J. S. Lund, “Relation between patterns of intrinsic lateral connectivity, ocular dominance and cytochrome oxidase-reactive regions in macaque monkey striate cortex,” Cereb. Cortex 6, 297–310 (1997).
[CrossRef]

M. Hübener, D. Shoham, A. Grinvald, T. Bonhoeffer, “Spatial relationships among three columnar systems in cat area 17,” J. Neurosci. 17, 9270–9284 (1997).
[PubMed]

H. R. Dinse, G. Reuter, S. M. Cords, B. Godde, T. Hilger, T. Lenarz, “Optical imaging of cat auditory cortical organization after electrical stimulation of a multi-channel cochlear implant: differential effects of acute and chronic stimulation,” Am. J. Otol. 18, S17–S18 (1997).
[PubMed]

I. Goedecke, D.-S. Kim, T. Bonhoeffer, W. Singer, “Development of orientation preference maps in area 18 of kitten visual cortex,” Eur. J. Neurosci. 9, 1754–1762 (1997).
[CrossRef]

M. B. Dalva, M. Weliky, L. C. Katz, “Relationships between local synaptic connections and orientation domains in primary visual cortex,” Neuron 19, 871–880 (1997).
[CrossRef] [PubMed]

N. P. McLoughlin, G. G. Blasdel, “Effect of wavelength on differential images of ocular dominance and orientation in monkey striate cortex,” Soc. Neurosci. Abstr. 23, 13 (1997).

S. Marcos, R. P. Tornow, A. E. Elsner, R. Navarro, “Foveal cone spacing and cone photopigment density difference: objective measurement in the same subjects,” Vision Res. 37, 1909–1915 (1997).
[CrossRef] [PubMed]

R.-P. Tornow, S. Beuel, E. Zrenner, “Modifying a Rodenstock scanning laser ophthalmoscope for imaging densitometry,” Appl. Opt. 36, 5621–5629 (1997).
[CrossRef] [PubMed]

1996 (9)

J. M. Schmitt, K. Ben-Letaief, “Efficient Monte Carlo simulation of confocal microscopy in biological tissue,” J. Opt. Soc. Am. A 13, 952–961 (1996).
[CrossRef]

M. Stetter, R. A. Sendtner, G. T. Timberlake, “A novel method for measuring saccade profiles using the scanning laser ophthalmoscope,” Vision Res. 36, 1987–1994 (1996).
[CrossRef] [PubMed]

B. Chapman, M. P. Stryker, T. Bonhoeffer, “Development of orientation preference maps in ferret primary visual cortex,” J. Neurosci. 16, 6443–6453 (1996).
[PubMed]

B. Godde, F. Spengler, H. R. Dinse, “Associative pairing of tactile stimulation induces somatosensory cortical reorganization in rats and humans,” Neuroreport 8, 281–285 (1996).
[CrossRef] [PubMed]

I. Gödecke, T. Bonhoeffer, “Development of identical orientation maps for two eyes without common visual experience,” Nature 379, 251–254 (1996).
[CrossRef] [PubMed]

A. Hess, H. Scheich, “Optical and fdg mapping of frequency-specific activity in auditory cortex,” Neuroreport 7, 2643–2647 (1996).
[CrossRef] [PubMed]

A. Shmuel, A. Grinvald, “Functional organization for direction of motion and its relationship to orientation maps in cat area 18,” J. Neurosci. 16, 6945–6964 (1996).
[PubMed]

M. Weliky, W. H. Bosking, D. Fitzpatrick, “A systematic map of direction preference in primary visual cortex,” Nature 379, 725–728 (1996).
[CrossRef] [PubMed]

T. Yoshioka, G. G. Blasdel, J. B. Levitt, J. S. Lund, “Relation between patterns of intrinsic lateral connectivity, ocular dominance, and cytochrome oxidase-reactive regions in macaque monkey striate cortex,” Cereb. Cortex 6, 297–310 (1996).
[CrossRef] [PubMed]

1995 (4)

T. Bonhoeffer, D. S. Kim, D. Malonek, D. Shoham, A. Grinvald, “Optical imaging of the layout of functional domains in area 17 and across the area 17/18 border in cat visual cortex,” Eur. J. Neurosci. 7, 1973–1988 (1995).
[CrossRef] [PubMed]

A. Das, C. D. Gilbert, “Long-range horizontal connections and their role in cortical reorganization revealed by optical recording of cat primary visual cortex,” Nature 375, 780–784 (1995).
[CrossRef] [PubMed]

N. R. Kreisman, J. C. LaManna, S.-C. Liao, E. R. Teh, J. R. Alcala, “Light transmittance as an index of cell volume in hippocampus slices: optical differences of interfaced and submerged positions,” Brain Res. 693, 179–186 (1995).
[CrossRef] [PubMed]

M. Stetter, R. A. Sendtner, F. W. Fitzke, V. P. Gabel, “Development of a kinetic SLO microperimetry module for functional macular diagnostics,” Vision Res. 35, S43 (1995).

1994 (5)

R. D. Andrew, B. A. MacVicar, “Imaging cell volume changes and neuronal excitation in the hippocampal slice,” Neuroscience 62, 371–383 (1994).
[CrossRef] [PubMed]

R. Malach, R. B. Tootell, D. Malonek, “Relationship between orientation domains, cytochrome oxidase stripes, and intrinsic horntal connections in squirrel monkey area v2.nizo,” Cereb. Cortex 4, 151–165 (1994).
[CrossRef] [PubMed]

Z. F. Kisvarday, D. S. Kim, U. T. Eysel, T. Bonhoeffer, “Relationship between lateral inhibitory connections and the topography of the orientation map in cat visual cortex,” Eur. J. Neurosci. 6, 1619–1632 (1994).
[CrossRef] [PubMed]

D. S. Kim, T. Bonhoeffer, “Reverse occlusion leads to a precise restoration of orientation preference maps in visual cortex,” Nature 370, 370–372 (1994).
[CrossRef] [PubMed]

M. S. Cohen, S. Y. Bookheimer, “Localization of brain function using magnetic resonance imaging,” Trends Neurosci. 17, 268–277 (1994).
[CrossRef] [PubMed]

1993 (5)

T. Bonhoeffer, A. Grinvald, “The layout of iso-orientation domains in area 18 of cat visual cortex: optical imaging reveals a pinwheel-like organization,” J. Neurosci. 13, 4157–4180 (1993).
[PubMed]

K. Obermayer, G. G. Blasdel, “Geometry of orientation and ocular dominance columns in monkey striate cortex,” J. Neurosci. 13, 4114–4129 (1993).
[PubMed]

R. Malach, Y. Amir, M. Harel, A. Grinvald, “Relationship between intrinsic connections and functional architecture revealed by optical imaging and in vivo targeted biocytin injections in primate striate cortex,” Proc. Natl. Acad. Sci. USA 90, 10469–10473 (1993).
[CrossRef] [PubMed]

F. W. Fitzke, B. R. Masters, “Three-dimensional visualization of confocal sections of in vivo human fundus and optic nerve,” Curr. Eye Res. 12, 1015–1018 (1993).
[CrossRef] [PubMed]

R. Graaf, M. H. Koelink, F. F. M. de Mul, W. G. Zijlstra, A. C. M. Dassel, J. G. Arnoudse, “Condensed Monte Carlo simulations for the description of light transport,” Appl. Opt. 32, 426–435 (1993).
[CrossRef]

1992 (2)

G. G. Blasdel, “Differential imaging of ocular dominance and orientation selectivity in monkey striate cortex,” J. Neurosci. 12, 3115–3138 (1992).
[PubMed]

G. G. Blasdel, “Orientation selectivity, preference, and continuity in monkey striate cortex,” J. Neurosci. 12, 3139–3161 (1992).
[PubMed]

1991 (3)

T. Bonhoeffer, A. Grinvald, “Iso-orientation domains in cat visual cortex are arranged in pinwheel-like patterns,” Nature 353, 429–431 (1991).
[CrossRef] [PubMed]

B. A. MacVicar, D. Hochman, “Imaging of synaptically evoked intrinsic optical signals in hippocampal slices,” J. Neurosci. 11, 1458–1469 (1991).
[PubMed]

F. W. Fitzke, H. Woon, G. Timberlake, L. Robinson, J. Marshall, A. C. Bird, “Optical modifications to a scanning laser ophthalmoscope for high magnification, narrow optical section imaging,” Lasers Light Ophthalmol. 4, 7–14 (1991).

1990 (2)

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

B. C. Wilson, S. L. Jacques, “Optical reflectance and transmittance of tissues: principles and applications,” IEEE J. Quantum Electron. 26, 2186–2199 (1990).
[CrossRef]

1989 (3)

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues—i: predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1163–1168 (1989).

M. J. C. van Gemert, S. L. Jacques, H. J. C. M. Sterenborg, W. M. Star, “Skin optics,” IEEE Trans. Biomed. Eng. 36, 1146–1154 (1989).
[CrossRef] [PubMed]

S. T. Flock, B. C. Wilson, M. S. Patterson, “Monte Carlo modeling of light propagation in highly scattering tissues—ii: comparison with measurements in phantoms,” IEEE Trans. Biomed. Eng. 36, 1169–1173 (1989).
[CrossRef] [PubMed]

1988 (1)

M. J. Hawken, A. J. Parker, J. S. Lund, “Laminar organization and contrast sensitivity of direction-selective cells in the striate cortex of the old world monkey,” J. Neurosci. 8, 3541–3548 (1988).
[PubMed]

1986 (2)

G. G. Blasdel, G. Salama, “Voltage-sensitive dyes reveal a modular organization in monkey striate cortex,” Nature 321, 579–585 (1986).
[CrossRef] [PubMed]

A. Grinvald, E. Lieke, R. D. Frostig, C. D. Gilbert, T. N. Wiesel, “Functional architecture of cortex revealed by optical imaging of intrinsic signals,” Nature 324, 361–364 (1986).
[CrossRef] [PubMed]

1985 (1)

H. S. Orbach, L. B. Cohen, A. Grinvald, “Optical mapping of electrical activity in rat somatosensory and visual cortex,” J. Neurosci. 5, 1886–1895 (1985).
[PubMed]

1983 (1)

K. S. Rockland, J. S. Lund, “Intrinsic laminar lattice connections in primate visual cortex,” J. Comp. Neurol. 216, 303–318 (1983).
[CrossRef] [PubMed]

1981 (1)

R. H. Webb, G. W. Hughes, “Scanning laser ophthalmoscope,” IEEE Trans. Biomed. Eng. 28, 488–492 (1981).
[CrossRef] [PubMed]

1977 (1)

D. H. Hubel, T. N. Wiesel, “Functional architecture of macaque monkey visual cortex,” Proc. R. Soc. London, Ser. B 198, 1–59 (1977).
[CrossRef]

1972 (1)

1968 (1)

D. H. Hubel, T. N. Wiesel, “Receptive fields and functional architecture of monkey striate cortex,” J. Physiol. 195, 215–243 (1968).
[PubMed]

1941 (1)

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

Aarnoudse, J. G.

R. Graaf, A. C. M. Dassel, M. H. Koelink, J. G. Aarnoudse, F. F. M. de Mul, W. G. Zijlstra, J. Greve, “Condensed Monte Carlo simulations applied to reflectance pulse oximetry,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alvano, eds., Proc. SPIE1888, 201–213 (1993).
[CrossRef]

Alcala, J. R.

N. R. Kreisman, J. C. LaManna, S.-C. Liao, E. R. Teh, J. R. Alcala, “Light transmittance as an index of cell volume in hippocampus slices: optical differences of interfaced and submerged positions,” Brain Res. 693, 179–186 (1995).
[CrossRef] [PubMed]

Amir, Y.

R. Malach, Y. Amir, M. Harel, A. Grinvald, “Relationship between intrinsic connections and functional architecture revealed by optical imaging and in vivo targeted biocytin injections in primate striate cortex,” Proc. Natl. Acad. Sci. USA 90, 10469–10473 (1993).
[CrossRef] [PubMed]

Andrew, R. D.

R. D. Andrew, B. A. MacVicar, “Imaging cell volume changes and neuronal excitation in the hippocampal slice,” Neuroscience 62, 371–383 (1994).
[CrossRef] [PubMed]

Arnoudse, J. G.

Ben-Letaief, K.

Beuel, S.

Bird, A. C.

F. W. Fitzke, H. Woon, G. Timberlake, L. Robinson, J. Marshall, A. C. Bird, “Optical modifications to a scanning laser ophthalmoscope for high magnification, narrow optical section imaging,” Lasers Light Ophthalmol. 4, 7–14 (1991).

Blasdel, G. G.

T. Yoshioka, G. G. Blasdel, J. B. Levitt, J. S. Lund, “Relation between patterns of intrinsic lateral connectivity, ocular dominance and cytochrome oxidase-reactive regions in macaque monkey striate cortex,” Cereb. Cortex 6, 297–310 (1997).
[CrossRef]

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H. S. Orbach, L. B. Cohen, A. Grinvald, “Optical mapping of electrical activity in rat somatosensory and visual cortex,” J. Neurosci. 5, 1886–1895 (1985).
[PubMed]

Ostergaard, L.

L. Ostergaard, D. F. Smith, P. Vestergaard-Poulsen, S. B. Hansen, A. D. Gjedde, C. Gyldensted, “Absolute cerebral blood-flow and blood volume measured by magnetic resonance imaging bolus tracking: comparison with positron emission tomography,” J. Cereb. Blood Flow Metab. 18, 425–432 (1998).
[CrossRef]

Parker, A. J.

M. J. Hawken, A. J. Parker, J. S. Lund, “Laminar organization and contrast sensitivity of direction-selective cells in the striate cortex of the old world monkey,” J. Neurosci. 8, 3541–3548 (1988).
[PubMed]

Patterson, M. S.

S. T. Flock, B. C. Wilson, M. S. Patterson, “Monte Carlo modeling of light propagation in highly scattering tissues—ii: comparison with measurements in phantoms,” IEEE Trans. Biomed. Eng. 36, 1169–1173 (1989).
[CrossRef] [PubMed]

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues—i: predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1163–1168 (1989).

Prahl, S. A.

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

Rao, S. C.

S. C. Rao, L. J. Toth, M. Sur, “Optically imaged maps of orientation preference in primary visual cortex of cats and ferrets,” J. Comp. Neurol. 387, 358–370 (1997).
[CrossRef] [PubMed]

Reuter, G.

H. R. Dinse, G. Reuter, S. M. Cords, B. Godde, T. Hilger, T. Lenarz, “Optical imaging of cat auditory cortical organization after electrical stimulation of a multi-channel cochlear implant: differential effects of acute and chronic stimulation,” Am. J. Otol. 18, S17–S18 (1997).
[PubMed]

Robinson, L.

F. W. Fitzke, H. Woon, G. Timberlake, L. Robinson, J. Marshall, A. C. Bird, “Optical modifications to a scanning laser ophthalmoscope for high magnification, narrow optical section imaging,” Lasers Light Ophthalmol. 4, 7–14 (1991).

Rockland, K. S.

K. S. Rockland, J. S. Lund, “Intrinsic laminar lattice connections in primate visual cortex,” J. Comp. Neurol. 216, 303–318 (1983).
[CrossRef] [PubMed]

Salama, G.

G. G. Blasdel, G. Salama, “Voltage-sensitive dyes reveal a modular organization in monkey striate cortex,” Nature 321, 579–585 (1986).
[CrossRef] [PubMed]

Scheich, H.

A. Hess, H. Scheich, “Optical and fdg mapping of frequency-specific activity in auditory cortex,” Neuroreport 7, 2643–2647 (1996).
[CrossRef] [PubMed]

Schmitt, J. M.

Schofield, B.

W. H. Bosking, Y. Zhang, B. Schofield, D. Fitzpatrick, “Orientation selectivity and the arrangement of horizontal connections in tree shrew striate cortex,” J. Neurosci. 17, 2112–2127 (1997).
[PubMed]

Sendtner, R. A.

M. Stetter, R. A. Sendtner, G. T. Timberlake, “A novel method for measuring saccade profiles using the scanning laser ophthalmoscope,” Vision Res. 36, 1987–1994 (1996).
[CrossRef] [PubMed]

M. Stetter, R. A. Sendtner, F. W. Fitzke, V. P. Gabel, “Development of a kinetic SLO microperimetry module for functional macular diagnostics,” Vision Res. 35, S43 (1995).

M. Stetter, G. T. Timberlake, R. A. Sendtner, R. H. Webb, “SLO saccade profile measurements and the effects of retinal raster size and distortion,” in Proceedings of the European Biomedical Optics Symposium, R. Birngruber, A. F. Fercher, eds., Proc. SPIE2632, 98–109 (1995).
[CrossRef]

Shmuel, A.

A. Shmuel, A. Grinvald, “Functional organization for direction of motion and its relationship to orientation maps in cat area 18,” J. Neurosci. 16, 6945–6964 (1996).
[PubMed]

Shoham, D.

M. Hübener, D. Shoham, A. Grinvald, T. Bonhoeffer, “Spatial relationships among three columnar systems in cat area 17,” J. Neurosci. 17, 9270–9284 (1997).
[PubMed]

T. Bonhoeffer, D. S. Kim, D. Malonek, D. Shoham, A. Grinvald, “Optical imaging of the layout of functional domains in area 17 and across the area 17/18 border in cat visual cortex,” Eur. J. Neurosci. 7, 1973–1988 (1995).
[CrossRef] [PubMed]

Singer, W.

I. Goedecke, D.-S. Kim, T. Bonhoeffer, W. Singer, “Development of orientation preference maps in area 18 of kitten visual cortex,” Eur. J. Neurosci. 9, 1754–1762 (1997).
[CrossRef]

Sliney, D.

D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sources (Plenum, New York, 1980).

Smith, D. F.

L. Ostergaard, D. F. Smith, P. Vestergaard-Poulsen, S. B. Hansen, A. D. Gjedde, C. Gyldensted, “Absolute cerebral blood-flow and blood volume measured by magnetic resonance imaging bolus tracking: comparison with positron emission tomography,” J. Cereb. Blood Flow Metab. 18, 425–432 (1998).
[CrossRef]

Spengler, F.

B. Godde, F. Spengler, H. R. Dinse, “Associative pairing of tactile stimulation induces somatosensory cortical reorganization in rats and humans,” Neuroreport 8, 281–285 (1996).
[CrossRef] [PubMed]

Star, W. M.

M. J. C. van Gemert, S. L. Jacques, H. J. C. M. Sterenborg, W. M. Star, “Skin optics,” IEEE Trans. Biomed. Eng. 36, 1146–1154 (1989).
[CrossRef] [PubMed]

Sterenborg, H. J. C. M.

M. J. C. van Gemert, S. L. Jacques, H. J. C. M. Sterenborg, W. M. Star, “Skin optics,” IEEE Trans. Biomed. Eng. 36, 1146–1154 (1989).
[CrossRef] [PubMed]

Stetter, M.

M. Stetter, R. A. Sendtner, G. T. Timberlake, “A novel method for measuring saccade profiles using the scanning laser ophthalmoscope,” Vision Res. 36, 1987–1994 (1996).
[CrossRef] [PubMed]

M. Stetter, R. A. Sendtner, F. W. Fitzke, V. P. Gabel, “Development of a kinetic SLO microperimetry module for functional macular diagnostics,” Vision Res. 35, S43 (1995).

M. Stetter, G. T. Timberlake, R. A. Sendtner, R. H. Webb, “SLO saccade profile measurements and the effects of retinal raster size and distortion,” in Proceedings of the European Biomedical Optics Symposium, R. Birngruber, A. F. Fercher, eds., Proc. SPIE2632, 98–109 (1995).
[CrossRef]

M. Stetter, K. Obermayer, “Tissue optics simulations of scanning laser techniques for optical imaging,” in N. Elsner, R. Wehner, eds., New Neuroethology on the Move: Proceedings of the 26th Göttingen Neurobiology Conference 1998 (Thieme, Stuttgart, Germany, 1998), p. 779.

Stryker, M. P.

B. Chapman, M. P. Stryker, T. Bonhoeffer, “Development of orientation preference maps in ferret primary visual cortex,” J. Neurosci. 16, 6443–6453 (1996).
[PubMed]

Sur, M.

S. C. Rao, L. J. Toth, M. Sur, “Optically imaged maps of orientation preference in primary visual cortex of cats and ferrets,” J. Comp. Neurol. 387, 358–370 (1997).
[CrossRef] [PubMed]

Teh, E. R.

N. R. Kreisman, J. C. LaManna, S.-C. Liao, E. R. Teh, J. R. Alcala, “Light transmittance as an index of cell volume in hippocampus slices: optical differences of interfaced and submerged positions,” Brain Res. 693, 179–186 (1995).
[CrossRef] [PubMed]

Timberlake, G.

F. W. Fitzke, H. Woon, G. Timberlake, L. Robinson, J. Marshall, A. C. Bird, “Optical modifications to a scanning laser ophthalmoscope for high magnification, narrow optical section imaging,” Lasers Light Ophthalmol. 4, 7–14 (1991).

Timberlake, G. T.

M. Stetter, R. A. Sendtner, G. T. Timberlake, “A novel method for measuring saccade profiles using the scanning laser ophthalmoscope,” Vision Res. 36, 1987–1994 (1996).
[CrossRef] [PubMed]

M. Stetter, G. T. Timberlake, R. A. Sendtner, R. H. Webb, “SLO saccade profile measurements and the effects of retinal raster size and distortion,” in Proceedings of the European Biomedical Optics Symposium, R. Birngruber, A. F. Fercher, eds., Proc. SPIE2632, 98–109 (1995).
[CrossRef]

Tootell, R. B.

R. Malach, R. B. Tootell, D. Malonek, “Relationship between orientation domains, cytochrome oxidase stripes, and intrinsic horntal connections in squirrel monkey area v2.nizo,” Cereb. Cortex 4, 151–165 (1994).
[CrossRef] [PubMed]

Tornow, R. P.

S. Marcos, R. P. Tornow, A. E. Elsner, R. Navarro, “Foveal cone spacing and cone photopigment density difference: objective measurement in the same subjects,” Vision Res. 37, 1909–1915 (1997).
[CrossRef] [PubMed]

Tornow, R.-P.

Toth, L. J.

S. C. Rao, L. J. Toth, M. Sur, “Optically imaged maps of orientation preference in primary visual cortex of cats and ferrets,” J. Comp. Neurol. 387, 358–370 (1997).
[CrossRef] [PubMed]

van Gemert, M. J. C.

M. J. C. van Gemert, S. L. Jacques, H. J. C. M. Sterenborg, W. M. Star, “Skin optics,” IEEE Trans. Biomed. Eng. 36, 1146–1154 (1989).
[CrossRef] [PubMed]

Vestergaard-Poulsen, P.

L. Ostergaard, D. F. Smith, P. Vestergaard-Poulsen, S. B. Hansen, A. D. Gjedde, C. Gyldensted, “Absolute cerebral blood-flow and blood volume measured by magnetic resonance imaging bolus tracking: comparison with positron emission tomography,” J. Cereb. Blood Flow Metab. 18, 425–432 (1998).
[CrossRef]

Webb, R. H.

R. H. Webb, G. W. Hughes, “Scanning laser ophthalmoscope,” IEEE Trans. Biomed. Eng. 28, 488–492 (1981).
[CrossRef] [PubMed]

M. Stetter, G. T. Timberlake, R. A. Sendtner, R. H. Webb, “SLO saccade profile measurements and the effects of retinal raster size and distortion,” in Proceedings of the European Biomedical Optics Symposium, R. Birngruber, A. F. Fercher, eds., Proc. SPIE2632, 98–109 (1995).
[CrossRef]

Welch, A. J.

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

Weliky, M.

M. B. Dalva, M. Weliky, L. C. Katz, “Relationships between local synaptic connections and orientation domains in primary visual cortex,” Neuron 19, 871–880 (1997).
[CrossRef] [PubMed]

M. Weliky, W. H. Bosking, D. Fitzpatrick, “A systematic map of direction preference in primary visual cortex,” Nature 379, 725–728 (1996).
[CrossRef] [PubMed]

Wiesel, T. N.

A. Grinvald, E. Lieke, R. D. Frostig, C. D. Gilbert, T. N. Wiesel, “Functional architecture of cortex revealed by optical imaging of intrinsic signals,” Nature 324, 361–364 (1986).
[CrossRef] [PubMed]

D. H. Hubel, T. N. Wiesel, “Functional architecture of macaque monkey visual cortex,” Proc. R. Soc. London, Ser. B 198, 1–59 (1977).
[CrossRef]

D. H. Hubel, T. N. Wiesel, “Receptive fields and functional architecture of monkey striate cortex,” J. Physiol. 195, 215–243 (1968).
[PubMed]

Wilson, B. C.

B. C. Wilson, S. L. Jacques, “Optical reflectance and transmittance of tissues: principles and applications,” IEEE J. Quantum Electron. 26, 2186–2199 (1990).
[CrossRef]

S. T. Flock, B. C. Wilson, M. S. Patterson, “Monte Carlo modeling of light propagation in highly scattering tissues—ii: comparison with measurements in phantoms,” IEEE Trans. Biomed. Eng. 36, 1169–1173 (1989).
[CrossRef] [PubMed]

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues—i: predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1163–1168 (1989).

Wolbarsht, M.

D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sources (Plenum, New York, 1980).

Woon, H.

F. W. Fitzke, H. Woon, G. Timberlake, L. Robinson, J. Marshall, A. C. Bird, “Optical modifications to a scanning laser ophthalmoscope for high magnification, narrow optical section imaging,” Lasers Light Ophthalmol. 4, 7–14 (1991).

Wyman, D. R.

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues—i: predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1163–1168 (1989).

Yoshioka, T.

T. Yoshioka, G. G. Blasdel, J. B. Levitt, J. S. Lund, “Relation between patterns of intrinsic lateral connectivity, ocular dominance and cytochrome oxidase-reactive regions in macaque monkey striate cortex,” Cereb. Cortex 6, 297–310 (1997).
[CrossRef]

T. Yoshioka, G. G. Blasdel, J. B. Levitt, J. S. Lund, “Relation between patterns of intrinsic lateral connectivity, ocular dominance, and cytochrome oxidase-reactive regions in macaque monkey striate cortex,” Cereb. Cortex 6, 297–310 (1996).
[CrossRef] [PubMed]

Zhang, Y.

W. H. Bosking, Y. Zhang, B. Schofield, D. Fitzpatrick, “Orientation selectivity and the arrangement of horizontal connections in tree shrew striate cortex,” J. Neurosci. 17, 2112–2127 (1997).
[PubMed]

Zheng, Y.

J. E. W. Mayhew, Y. Zheng, “A model for the intrinsic image signal and an evaluation of the methodology of intrinsic image signal analysis,” (Artificial Intelligence Vision Research Unit AIVRU, University of Sheffield, Sheffield, UK, 1996).

Zijlstra, W. G.

R. Graaf, M. H. Koelink, F. F. M. de Mul, W. G. Zijlstra, A. C. M. Dassel, J. G. Arnoudse, “Condensed Monte Carlo simulations for the description of light transport,” Appl. Opt. 32, 426–435 (1993).
[CrossRef]

R. Graaf, A. C. M. Dassel, M. H. Koelink, J. G. Aarnoudse, F. F. M. de Mul, W. G. Zijlstra, J. Greve, “Condensed Monte Carlo simulations applied to reflectance pulse oximetry,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alvano, eds., Proc. SPIE1888, 201–213 (1993).
[CrossRef]

Zrenner, E.

Am. J. Otol. (1)

H. R. Dinse, G. Reuter, S. M. Cords, B. Godde, T. Hilger, T. Lenarz, “Optical imaging of cat auditory cortical organization after electrical stimulation of a multi-channel cochlear implant: differential effects of acute and chronic stimulation,” Am. J. Otol. 18, S17–S18 (1997).
[PubMed]

Appl. Opt. (2)

Astrophys. J. (1)

L. G. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
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Brain Res. (1)

N. R. Kreisman, J. C. LaManna, S.-C. Liao, E. R. Teh, J. R. Alcala, “Light transmittance as an index of cell volume in hippocampus slices: optical differences of interfaced and submerged positions,” Brain Res. 693, 179–186 (1995).
[CrossRef] [PubMed]

Cereb. Cortex (3)

R. Malach, R. B. Tootell, D. Malonek, “Relationship between orientation domains, cytochrome oxidase stripes, and intrinsic horntal connections in squirrel monkey area v2.nizo,” Cereb. Cortex 4, 151–165 (1994).
[CrossRef] [PubMed]

T. Yoshioka, G. G. Blasdel, J. B. Levitt, J. S. Lund, “Relation between patterns of intrinsic lateral connectivity, ocular dominance, and cytochrome oxidase-reactive regions in macaque monkey striate cortex,” Cereb. Cortex 6, 297–310 (1996).
[CrossRef] [PubMed]

T. Yoshioka, G. G. Blasdel, J. B. Levitt, J. S. Lund, “Relation between patterns of intrinsic lateral connectivity, ocular dominance and cytochrome oxidase-reactive regions in macaque monkey striate cortex,” Cereb. Cortex 6, 297–310 (1997).
[CrossRef]

Curr. Eye Res. (1)

F. W. Fitzke, B. R. Masters, “Three-dimensional visualization of confocal sections of in vivo human fundus and optic nerve,” Curr. Eye Res. 12, 1015–1018 (1993).
[CrossRef] [PubMed]

Eur. J. Neurosci. (3)

T. Bonhoeffer, D. S. Kim, D. Malonek, D. Shoham, A. Grinvald, “Optical imaging of the layout of functional domains in area 17 and across the area 17/18 border in cat visual cortex,” Eur. J. Neurosci. 7, 1973–1988 (1995).
[CrossRef] [PubMed]

Z. F. Kisvarday, D. S. Kim, U. T. Eysel, T. Bonhoeffer, “Relationship between lateral inhibitory connections and the topography of the orientation map in cat visual cortex,” Eur. J. Neurosci. 6, 1619–1632 (1994).
[CrossRef] [PubMed]

I. Goedecke, D.-S. Kim, T. Bonhoeffer, W. Singer, “Development of orientation preference maps in area 18 of kitten visual cortex,” Eur. J. Neurosci. 9, 1754–1762 (1997).
[CrossRef]

IEEE J. Quantum Electron. (2)

B. C. Wilson, S. L. Jacques, “Optical reflectance and transmittance of tissues: principles and applications,” IEEE J. Quantum Electron. 26, 2186–2199 (1990).
[CrossRef]

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

IEEE Trans. Biomed. Eng. (4)

R. H. Webb, G. W. Hughes, “Scanning laser ophthalmoscope,” IEEE Trans. Biomed. Eng. 28, 488–492 (1981).
[CrossRef] [PubMed]

M. J. C. van Gemert, S. L. Jacques, H. J. C. M. Sterenborg, W. M. Star, “Skin optics,” IEEE Trans. Biomed. Eng. 36, 1146–1154 (1989).
[CrossRef] [PubMed]

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues—i: predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1163–1168 (1989).

S. T. Flock, B. C. Wilson, M. S. Patterson, “Monte Carlo modeling of light propagation in highly scattering tissues—ii: comparison with measurements in phantoms,” IEEE Trans. Biomed. Eng. 36, 1169–1173 (1989).
[CrossRef] [PubMed]

J. Cereb. Blood Flow Metab. (1)

L. Ostergaard, D. F. Smith, P. Vestergaard-Poulsen, S. B. Hansen, A. D. Gjedde, C. Gyldensted, “Absolute cerebral blood-flow and blood volume measured by magnetic resonance imaging bolus tracking: comparison with positron emission tomography,” J. Cereb. Blood Flow Metab. 18, 425–432 (1998).
[CrossRef]

J. Comp. Neurol. (2)

S. C. Rao, L. J. Toth, M. Sur, “Optically imaged maps of orientation preference in primary visual cortex of cats and ferrets,” J. Comp. Neurol. 387, 358–370 (1997).
[CrossRef] [PubMed]

K. S. Rockland, J. S. Lund, “Intrinsic laminar lattice connections in primate visual cortex,” J. Comp. Neurol. 216, 303–318 (1983).
[CrossRef] [PubMed]

J. Neurosci. (11)

W. H. Bosking, Y. Zhang, B. Schofield, D. Fitzpatrick, “Orientation selectivity and the arrangement of horizontal connections in tree shrew striate cortex,” J. Neurosci. 17, 2112–2127 (1997).
[PubMed]

A. Shmuel, A. Grinvald, “Functional organization for direction of motion and its relationship to orientation maps in cat area 18,” J. Neurosci. 16, 6945–6964 (1996).
[PubMed]

K. Obermayer, G. G. Blasdel, “Geometry of orientation and ocular dominance columns in monkey striate cortex,” J. Neurosci. 13, 4114–4129 (1993).
[PubMed]

M. Hübener, D. Shoham, A. Grinvald, T. Bonhoeffer, “Spatial relationships among three columnar systems in cat area 17,” J. Neurosci. 17, 9270–9284 (1997).
[PubMed]

G. G. Blasdel, “Differential imaging of ocular dominance and orientation selectivity in monkey striate cortex,” J. Neurosci. 12, 3115–3138 (1992).
[PubMed]

G. G. Blasdel, “Orientation selectivity, preference, and continuity in monkey striate cortex,” J. Neurosci. 12, 3139–3161 (1992).
[PubMed]

B. Chapman, M. P. Stryker, T. Bonhoeffer, “Development of orientation preference maps in ferret primary visual cortex,” J. Neurosci. 16, 6443–6453 (1996).
[PubMed]

M. J. Hawken, A. J. Parker, J. S. Lund, “Laminar organization and contrast sensitivity of direction-selective cells in the striate cortex of the old world monkey,” J. Neurosci. 8, 3541–3548 (1988).
[PubMed]

H. S. Orbach, L. B. Cohen, A. Grinvald, “Optical mapping of electrical activity in rat somatosensory and visual cortex,” J. Neurosci. 5, 1886–1895 (1985).
[PubMed]

B. A. MacVicar, D. Hochman, “Imaging of synaptically evoked intrinsic optical signals in hippocampal slices,” J. Neurosci. 11, 1458–1469 (1991).
[PubMed]

T. Bonhoeffer, A. Grinvald, “The layout of iso-orientation domains in area 18 of cat visual cortex: optical imaging reveals a pinwheel-like organization,” J. Neurosci. 13, 4157–4180 (1993).
[PubMed]

J. Opt. Soc. Am. (1)

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

J. Physiol. (1)

D. H. Hubel, T. N. Wiesel, “Receptive fields and functional architecture of monkey striate cortex,” J. Physiol. 195, 215–243 (1968).
[PubMed]

Lasers Light Ophthalmol. (1)

F. W. Fitzke, H. Woon, G. Timberlake, L. Robinson, J. Marshall, A. C. Bird, “Optical modifications to a scanning laser ophthalmoscope for high magnification, narrow optical section imaging,” Lasers Light Ophthalmol. 4, 7–14 (1991).

Nature (7)

I. Gödecke, T. Bonhoeffer, “Development of identical orientation maps for two eyes without common visual experience,” Nature 379, 251–254 (1996).
[CrossRef] [PubMed]

A. Das, C. D. Gilbert, “Long-range horizontal connections and their role in cortical reorganization revealed by optical recording of cat primary visual cortex,” Nature 375, 780–784 (1995).
[CrossRef] [PubMed]

D. S. Kim, T. Bonhoeffer, “Reverse occlusion leads to a precise restoration of orientation preference maps in visual cortex,” Nature 370, 370–372 (1994).
[CrossRef] [PubMed]

T. Bonhoeffer, A. Grinvald, “Iso-orientation domains in cat visual cortex are arranged in pinwheel-like patterns,” Nature 353, 429–431 (1991).
[CrossRef] [PubMed]

G. G. Blasdel, G. Salama, “Voltage-sensitive dyes reveal a modular organization in monkey striate cortex,” Nature 321, 579–585 (1986).
[CrossRef] [PubMed]

A. Grinvald, E. Lieke, R. D. Frostig, C. D. Gilbert, T. N. Wiesel, “Functional architecture of cortex revealed by optical imaging of intrinsic signals,” Nature 324, 361–364 (1986).
[CrossRef] [PubMed]

M. Weliky, W. H. Bosking, D. Fitzpatrick, “A systematic map of direction preference in primary visual cortex,” Nature 379, 725–728 (1996).
[CrossRef] [PubMed]

Neuron (1)

M. B. Dalva, M. Weliky, L. C. Katz, “Relationships between local synaptic connections and orientation domains in primary visual cortex,” Neuron 19, 871–880 (1997).
[CrossRef] [PubMed]

Neuroreport (2)

B. Godde, F. Spengler, H. R. Dinse, “Associative pairing of tactile stimulation induces somatosensory cortical reorganization in rats and humans,” Neuroreport 8, 281–285 (1996).
[CrossRef] [PubMed]

A. Hess, H. Scheich, “Optical and fdg mapping of frequency-specific activity in auditory cortex,” Neuroreport 7, 2643–2647 (1996).
[CrossRef] [PubMed]

Neuroscience (1)

R. D. Andrew, B. A. MacVicar, “Imaging cell volume changes and neuronal excitation in the hippocampal slice,” Neuroscience 62, 371–383 (1994).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. USA (1)

R. Malach, Y. Amir, M. Harel, A. Grinvald, “Relationship between intrinsic connections and functional architecture revealed by optical imaging and in vivo targeted biocytin injections in primate striate cortex,” Proc. Natl. Acad. Sci. USA 90, 10469–10473 (1993).
[CrossRef] [PubMed]

Proc. R. Soc. London, Ser. B (1)

D. H. Hubel, T. N. Wiesel, “Functional architecture of macaque monkey visual cortex,” Proc. R. Soc. London, Ser. B 198, 1–59 (1977).
[CrossRef]

Soc. Neurosci. Abstr. (1)

N. P. McLoughlin, G. G. Blasdel, “Effect of wavelength on differential images of ocular dominance and orientation in monkey striate cortex,” Soc. Neurosci. Abstr. 23, 13 (1997).

Trends Neurosci. (1)

M. S. Cohen, S. Y. Bookheimer, “Localization of brain function using magnetic resonance imaging,” Trends Neurosci. 17, 268–277 (1994).
[CrossRef] [PubMed]

Vision Res. (3)

M. Stetter, R. A. Sendtner, G. T. Timberlake, “A novel method for measuring saccade profiles using the scanning laser ophthalmoscope,” Vision Res. 36, 1987–1994 (1996).
[CrossRef] [PubMed]

M. Stetter, R. A. Sendtner, F. W. Fitzke, V. P. Gabel, “Development of a kinetic SLO microperimetry module for functional macular diagnostics,” Vision Res. 35, S43 (1995).

S. Marcos, R. P. Tornow, A. E. Elsner, R. Navarro, “Foveal cone spacing and cone photopigment density difference: objective measurement in the same subjects,” Vision Res. 37, 1909–1915 (1997).
[CrossRef] [PubMed]

Other (7)

J. B. Pawley, ed., Handbook of Biological Confocal Microscopy (Plenum, New York, 1995).

R. Graaf, A. C. M. Dassel, M. H. Koelink, J. G. Aarnoudse, F. F. M. de Mul, W. G. Zijlstra, J. Greve, “Condensed Monte Carlo simulations applied to reflectance pulse oximetry,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alvano, eds., Proc. SPIE1888, 201–213 (1993).
[CrossRef]

M. Stetter, K. Obermayer, “Tissue optics simulations of scanning laser techniques for optical imaging,” in N. Elsner, R. Wehner, eds., New Neuroethology on the Move: Proceedings of the 26th Göttingen Neurobiology Conference 1998 (Thieme, Stuttgart, Germany, 1998), p. 779.

M. Stetter, G. T. Timberlake, R. A. Sendtner, R. H. Webb, “SLO saccade profile measurements and the effects of retinal raster size and distortion,” in Proceedings of the European Biomedical Optics Symposium, R. Birngruber, A. F. Fercher, eds., Proc. SPIE2632, 98–109 (1995).
[CrossRef]

D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sources (Plenum, New York, 1980).

J. E. W. Mayhew, Y. Zheng, “A model for the intrinsic image signal and an evaluation of the methodology of intrinsic image signal analysis,” (Artificial Intelligence Vision Research Unit AIVRU, University of Sheffield, Sheffield, UK, 1996).

T. Bonhoeffer, A. Grinvald, “Optical imaging based on intrinsic signals: the methodology,” in Brain Mapping: The Methods, A. Toga, J. C. Maziotta, eds. (Academic, San Diego, Calif., 1996), pp. 55–97.

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Figures (9)

Fig. 1
Fig. 1

Phase function p(r, s, s) describing the probability density for a photon to be scattered from propagation direction s into direction s at r. For isotropic media the phase function depends only on position r and on scattering angle θ.

Fig. 2
Fig. 2

(a) Model tissue is assumed to be an isotropic, semi-infinite medium with constant optic parameters μa, μs, and g. Within a small sphere with radius ρ centered around R=(0, 0,-Z) the absorption coefficient is increased by μA. This spheric absorber models a localized blood-related intrinsic signal source caused by a small neural activation blob. (b) Behavior of the survival probability Pa(l) of a photon along a trajectory r0+ls for the three practically different cases, namely, (i) the photon misses the sphere, (ii) the photon leaves the sphere, and (iii) the photon penetrates the sphere.

Fig. 3
Fig. 3

Detection of the diffuse-reflectance pattern. The region around the photon injection point is divided into a raster of (2na+1)×(2na+1) pixels of Δa on a side. If a photon exits at a given square, its maximum penetration depth is stored in a corresponding penetration-depth histogram with nz bins and penetration-depth intervals Δz. Similarly, the exit angle α between the surface normal and its exit direction is stored.

Fig. 4
Fig. 4

Simulated video images (left column) and scanning laser images (right column) for a homogeneous tissue with a local absorber at Z=0.2 mm (top row) and Z=0.6 mm (bottom row). Scanning laser images are much less blurred and show a higher contrast than video images. Gray level shows number of remitted photons per pixel.

Fig. 5
Fig. 5

Contrast of the image of the local absorber obtained with conventional video optical imaging and with scanning laser optical imaging. Scanning laser images are less strongly blurred than video images and show a considerably higher contrast, which decreases less steeply with increasing absorber depth.

Fig. 6
Fig. 6

(a) Normalized penetration-depth histograms for 108 photons injected into a homogeneous medium, averaged over annuli with inner radii r1=0, 0.2, 0.4, and 0.6 mm and outer radii r2=r1+0.2 mm [see inset in (b)]. The most frequent penetration depth increases systematically with the radius of the annulus. Maximum photon counts: 0–0.2 mm; 77,900; 0.2–0.4 mm, 25,014; 0.4–0.6 mm, 12,285; 0.6–0.8 mm, 7472. (b) The peak penetration depth depends approximately linearly on the radius ra=(r1+r2)/2 of the detection annulus. Solid line shows the linear least-squares fit, offset -0.02 mm, slope 1.30; circles represent data. Inset: calculation of the penetration-depth histograms versus the lateral spread of the photons. The histogram is built from all photons that were exiting the medium within an annulus between r1 and r2 (detection annulus). For these photons the different possible maximum penetration depths were counted to determine the penetration-depth histogram.

Fig. 7
Fig. 7

Differences between the radial-reflectance patterns (photon exit angles <30 deg) obtained in the presence of an absorber and those obtained for the homogeneous medium for depths Z=0.2, 0.4, 0.6, and 0.8 mm of the absorber. Gray levels indicate the difference in photon count per raster square. With increasing depth of the absorber the signal amplitude strongly decreases, while the fraction of darkening at the periphery of the diffuse-reflectance pattern (far from the origin) increases.

Fig. 8
Fig. 8

Normalized change in the curve shape SZ(ra)/max(|SZ(ra)|), where SZ(ra) is the difference between the normalized radial-reflectance pattern for the tissue with absorber and that obtained from the same tissue without absorber. The four functions correspond to absorber depths of Z=0.2, 0.4, 0.6, and 0.8 mm. With increasing Z the changes in the curve shape shift to higher radii (i.e., to the periphery of the reflectance pattern). Absolute minima of S: Z=0.2 mm, -0.58; Z=0.4 mm, -0.35; Z=0.6 mm, -0.19; Z=0.8 mm, -0.10.

Fig. 9
Fig. 9

Schematic illustration of online detection of the radial reflectance function. An optical setup forms a low-depth-of-focus image of the diffuse-reflectance pattern. This image propagates through a set of reflecting annuli with systematically decreasing radii. Each annulus reflects a ring-shaped part of the diffusely reflected light onto one of n detectors D1, , Dn, which thereby detects light to form a single annulus within the reflectance pattern.

Equations (21)

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dn(l)dl=-μ(r(l))n(l),
dn(l)dl=-[μa(r(l))+μs(r(l))]n(l)=:-μt(r(l))n(l),
n(l)=n0 exp-0lμ(r(l))dl,
Pt(l)=limn0 n(l)n0=exp-0lμt(r(l))dl.
Pa(l)=exp-0lμa(r(l))dl,
Ps(l)=exp-0lμs(r(l))dl.
Pa(l)=exp(-μal),
Ps(l)=exp(-μsl),
g(r)=0πp(r, θ)cos(θ)dθ.
p(r, θ)=14π1-g(r)2[1+g(r)2-2g(r)cos(θ)]3/2.
δeff={3μa[μa+μs(1-g)]}-1/2.
D(σ)=1σ2exp(-σ/δeff),
μa,sphere=μa+μA.
|ls-(R-r0)|2=ρ2,
l1,2=sT·Δr±[(s·Δr)2-(Δr2-ρ2)]1/2,
Pa(l)=exp(-μal).
Pa(l)=exp(-μal)exp(-μAl),l<l1exp(-μal)exp(-μAl1)ll1,
Pa(l)=exp(-μal),l<l1exp(-μal)exp[-μA(l-l1)],l1l<l2exp(-μal)exp[-μA(l2-l1)],ll2.
Pa(l0)=exp(-μal0)m=1M exp(-μA,mΔlm).
c=maxx, y[I(x, y)]-minx, y[I(x, y)]maxx, y[I(x, y)].
hζ(ra)={x,y|r1x2+y2r2}hζ(x, y),ζ=0, , nz-1,

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