Abstract

We present numerical simulations predicting the directional diffuse reflectance and autofluorescence from human skin. Skin is modeled as a seven-layered medium, with each layer having its own optical properties and fluorophore concentrations. Both collimated and diffuse monochromatic excitation at 442  nm are considered. In addition, the effect of an index-matching cream used to eliminate total internal reflection within the skin is assessed. We compute the intensity distributions of the excitation and fluorescence light in the skin by solving the radiative transfer equation using the modified method of characteristics. It was found that the use of an index-matching cream reduces the directional fluorescence signal while increasing the directional diffuse reflectance from the skin for collimated excitation. On the other hand, both the fluorescence and diffuse reflectance increase for diffuse excitation with an index-matching cream. Moreover, the directional fluorescence intensity obtained by use of collimated excitation is larger than that obtained by use of diffuse excitation light. This computational tool could be valuable in designing optical devices for biomedical applications.

© 2006 Optical Society of America

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    [CrossRef]

2006

K. Katika and L. Pilon, "Modified method of characteristics in transient radiative transfer," J. Quant. Spectrosc. Radiat. Transfer 98, 220-237 (2006).
[CrossRef]

2004

J. Sandby-Moller, E. Thieden, P. A. Philipsen, J. Heydenreich, and H. C. Wulf, "Skin autofluorescence as a biological UVR dosimeter," Photodermatol. Photoimmunol. Photomed. 20, 33-40 (2004).
[CrossRef]

R. Meerwaldt, R. Graaff, P. H. N. Oomen, T. P. Links, J. J. Jager, N. L. Alderson, S. R. Thorpe, J. W. Baynes, R. O. B. Gans, and A. J. Smit, "Simple non-invasive assessment of advanced glycation endproduct accumulation," Diabetologia 47, 1324-1330 (2004).
[CrossRef]

D. Y. Churmakov, I. V. Meglinski, and D. A. Greenhalgh, "Amending of fluorescence sensor signal localization in human skin by matching of the refractive index," J. Biomed. Opt. 9, 339-346 (2004).
[CrossRef]

D. Y. Churmakov, I. V. Meglinski, S. A. Piletsky, and D. A. Greenhalgh, "Automatic enhancement of skin fluorescence localization due to refractive index matching," in ALT'03 International Conference on Advanced Laser Technologies: Bio-medical Optics, R. K. Wang, J. C. Hebden, A. V. Priezzhev, and V. V. Tuchin, eds., Proc. SPIE 5486, 16-27 (2004).
[CrossRef]

2003

T. Vo-Dinh, M. Panjehpour, B. F. Overholt, C. E. Julius, S. Overholt, and M. N. Phan, "Laser-induced fluorescence for the detection of esophageal and skin cancer," in Advanced Biomedical and Clinical Diagnostic Systems, T. Vo-Dinh, W. S. Grundfest, D. A. Benaron, and G. E. Cohn, eds., Proc. SPIE 4958, 67-70 (2003).
[CrossRef]

D. Y. Churmakov, I. V. Meglinski, and D. A. Greenhalgh, "Automatic amending of the tattoo sensor fluorescence localization by refractive index matching," in Diagnostic Optical Spectroscopy in Biomedicine II, G. A. Wagnieres, ed., Proc. SPIE 5141, 122-132 (2003).
[CrossRef]

I. V. Meglinski and D. Y. Churmakov, "A novel Monte Carlo method for the optical diagnostics of skin," in Diagnostic Optical Spectroscopy in Biomedicine II, G. A. Wagnieres, ed., Proc. SPIE 5141, 133-141 (2003).
[CrossRef]

I. V. Meglinski, "Monte Carlo method in optical diagnostics of skin and skin tissues," in Third International Conference on Photonics and Imaging in Biology and Medicine, Q. Luo, V. V. Tuchin, M. Gu, and L. V. Wang, eds., Proc. SPIE 5254, 30-43 (2003).
[CrossRef]

D. Y. Churmakov, I. V. Meglinski, S. A. Piletsky, and D. A. Greenhalgh, "Skin fluorescence model based on the Monte Carlo technique," in Saratov Fall Meeting 2002: Optical Technologies in Biophysics and Medicine IV, V. V. Tuchin, ed., Proc. SPIE 5068, 326-333 (2003).
[CrossRef]

2002

M. Panjehpour, C. E. Julius, M. N. Phan, T. Vo-Dinh, and B. F. Overholt, "In-vivo fluorescence spectroscopy for diagnosis of skin cancer," in Biomedical Diagnostic, Guidance, and Surgical-Assist Systems IV, T. Vo-Dinh, D. A. Benaron, and W. S. Grundfest, eds., Proc. SPIE 4615, 20-31 (2002).
[CrossRef]

N. Kollias, G. Zonios, and G. N. Stamatas, "Fluorescence spectroscopy of skin," Vib. Spectrosc. 28, 17-23 (2002).
[CrossRef]

2001

R. H. Na, I. M. Stender, M. Henriksen, and H. C. Wulf, "Autofluorescence of human skin is age-related after correction for skin pigmentation and redness," J. Invest. Dermatol. 116, 536-540 (2001).
[CrossRef]

L. Brancaleon, A. J. Durkin, J. H. Tu, G. Menaker, J. D. Fallon, and N. Kollias, "In vivo fluorescence spectroscopy of nonmelanoma skin cancer," Photochem. Photobiol. 73, 178-183 (2001).
[CrossRef]

I. V. Meglinski and S. J. Matcher, "Modeling of skin reflectance spectra," in Saratov Fall Meeting 2000: Optical Technologies in Biophysics and Medicine II, V. V. Tuchin, ed., Proc. SPIE 4241, 78-87 (2001).
[CrossRef]

2000

R. Gillies, G. Zonios, R. R. Anderson, and N. Kollias, "Fluorescence excitation spectroscopy provides information about human skin in vivo," J. Invest. Dermatology 115, 704-707 (2000).
[CrossRef]

H. Zeng, D. I. McLean, C. E. MacAulay, and H. Lui, "Autofluorescence properties of skin and applications in dermatology," in Biomedical Photonics and Optoelectronic Imaging, H. Liu and Q. Luo, eds., Proc. SPIE 4224, 366-373 (2000).
[CrossRef]

J. Q. Lu, X.-H. Hu, and K. Dong, "Modeling of the rough-interface effect on a converging light beam propagating in a skin tissue phantom," Appl. Opt. 39, 5890-5897 (2000).

T. Spott and L. O. Svaasand, "Collimated light sources in the diffusion approximation," Appl. Opt. 39, 6453-6465 (2000).

1998

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, "Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues," Phys. Med. Biol. 43, 1285-1302 (1998).
[CrossRef]

H. Zeng, D. I. McLean, C. E. MacAulay, B. Palcic, and H. Lui, "Autofluorescence of basal cell carcinoma," in Lasers in Surgery: Advanced Characterization, Therapeutics, and Systems VIII, R. R. Anderson, K. E. Bartels, L. S. Bass, C. G. Garrett, K. W. Gregory, H. Lui, R. S. Malek, A. P. Perlmutter, L. Reinisch, P. J. Smalley, L. P. Tate, S. L. Thomsen, and G. M. Watson, eds., Proc. SPIE 3245, 314-317 (1998).
[CrossRef]

N. Kollias, R. Gillies, M. Moran, I. E. Kochevar, and R. R. Anderson, "Endogenous skin fluorescence includes bands that may serve as quantitative markers of aging and photoaging," J. Invest. Dermatol. 111, 776-776 (1998).
[CrossRef]

1997

Y. Takema, Y. Yorimoto, H. Ohsu, O. Osanai, and M. Kawai, "Age-related discontinuous changes in the in vivo fluorescence of human facial skin," J. Dermatolog. Sci. 24, 55-58 (1997).
[CrossRef]

H. Zeng, C. MacAulay, D. I. McLean, and B. Palcic, "Reconstruction of in vivo skin autofluorescence spectrum from microscopic properties by Monte Carlo simulation," J. Photochem. Photobiol. B 38, 234-240 (1997).
[CrossRef]

1996

H. Zeng, H. Lui, D. I. McLean, C. E. MacAulay, and B. Palcic, "Optical spectroscopy studies of diseased skin: preliminary results," in Optical and Imaging Techniques for Biomonitoring, H.-J. Foth, R. Marchesini, H. Podbielska, M. R. Nicoud, and H. Schneckenburger, eds., Proc. SPIE 2628, 281-285 (1996).

R. Richards-Kortum and E. Sevick-Muraca, "Quantitative optical spectroscopy for tissue diagnostics," Annu. Rev. Phys. Chem. 47, 555-606 (1996).
[CrossRef]

1995

Y. P. Sinichkin, S. R. Utz, P. M. Yudin, and H. A. Pilipenko, "Investigation of formation and dynamics of human skin erythema and pigmentation by in vivo fluorescence spectroscopy," in Optical Biopsy and Fluorescence Spectroscopy and Imaging, R. Cubeddu, R. Marchesini, S. R. Mordon, K. Svanberg, H. H. Rinneberg, and G. A. Wagnieres, eds., Proc. SPIE 2324, 259-268 (1995).
[CrossRef]

S. R. Utz, Y. P. Sinichkin, I. V. Meglinski, and H. A. Pilipenko, "Fluorescence spectroscopy in combination with reflectance measurements in human skin examination: what for and how," in Optical Biopsy and Fluorescence Spectroscopy and Imaging, R. Cubeddu, R. Marchesini, S. R. Mordon, K. Svanberg, H. H. Rinneberg, and G. A. Wagnieres, eds., Proc. SPIE 2324, 125-136 (1995).
[CrossRef]

H. Zeng, C. MacAulay, D. I. McLean, and B. Palcic, "Spectroscopic and microscopic characteristics of human skin autofluorescence emission," Photochem. Photobiol. 61, 639-645 (1995).

H. Zeng, C. E. MacAulay, D. I. McLean, and B. Palcic, "Spectroscopy and microscopy studies of skin tissue autofluorescence emission," in Optical Biopsy and Fluorescence Spectroscopy and Imaging, R. Cubeddu, R. Marchesini, S. R. Mordon, K. Svanberg, H. H. Rinneberg, and G. A. Wagnieres, eds., Proc. SPIE 2324, 198-207 (1995).
[CrossRef]

1994

H. Zeng, C. E. MacAulay, B. Palcic, and D. I. McLean, "Monte Carlo modeling of tissue autofluorescence measurement and imaging," in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE 2135, 94-104 (1994).
[CrossRef]

K. Koenig, H. Schneckenburger, J. Hemmer, B. J. Tromberg, and R. W. Steiner, "In-vivo fluorescence detection and imaging of porphyrin-producing bacteria in the human skin and in the oral cavity for diagnosis of acne vulgaris, caries, and squamous cell carcinoma," in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE 2135, 129-138 (1994).
[CrossRef]

Y. P. Sinichkin, S. R. Utz, and H. A. Pilipenko, "Laser-induced fluorescence of the human skin in vivo: influence of the erythema," in Optical Biopsy, R. Cubeddu, S. Svanberg, and H. van den Bergh, eds., Proc. SPIE 2081, 41-47 (1994).
[CrossRef]

1993

H. Zeng, C. E. MacAulay, B. Palcic, and D. I. McLean, "Autofluorescence distribution in skin tissue revealed by microspectrophotometer measurements," in Lasers in Otolaryngology, Dermatology, and Tissue Welding, R. R. Anderson, L. S. Bass, S. M. Shapshay, J. V. White, and R. A. White, eds., Proc. SPIE 1876, 129-135 (1993).
[CrossRef]

H. Zeng, C. E. MacAulay, B. Palcic, and D. I. McLean, "Laser-induced changes in autofluorescence of in-vivo skin," in Laser-Tissue Interaction IV, S. L. Jacques and A. Katzir, eds., Proc. SPIE 1882, 278-290 (1993).
[CrossRef]

1989

Alcouffe, R. E.

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, "Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues," Phys. Med. Biol. 43, 1285-1302 (1998).
[CrossRef]

Alderson, N. L.

R. Meerwaldt, R. Graaff, P. H. N. Oomen, T. P. Links, J. J. Jager, N. L. Alderson, S. R. Thorpe, J. W. Baynes, R. O. B. Gans, and A. J. Smit, "Simple non-invasive assessment of advanced glycation endproduct accumulation," Diabetologia 47, 1324-1330 (2004).
[CrossRef]

and, L.-H. Wang

L.-H. Wang andS. L. Jacques, Monte Carlo Modeling of Light Transport in Multi-Layered Tissues in Standard C (University of Texas M. D. Anderson Cancer Center, 1992).

Anderson, R. R.

R. Gillies, G. Zonios, R. R. Anderson, and N. Kollias, "Fluorescence excitation spectroscopy provides information about human skin in vivo," J. Invest. Dermatology 115, 704-707 (2000).
[CrossRef]

N. Kollias, R. Gillies, M. Moran, I. E. Kochevar, and R. R. Anderson, "Endogenous skin fluorescence includes bands that may serve as quantitative markers of aging and photoaging," J. Invest. Dermatol. 111, 776-776 (1998).
[CrossRef]

Barbour, R. L.

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, "Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues," Phys. Med. Biol. 43, 1285-1302 (1998).
[CrossRef]

Baynes, J. W.

R. Meerwaldt, R. Graaff, P. H. N. Oomen, T. P. Links, J. J. Jager, N. L. Alderson, S. R. Thorpe, J. W. Baynes, R. O. B. Gans, and A. J. Smit, "Simple non-invasive assessment of advanced glycation endproduct accumulation," Diabetologia 47, 1324-1330 (2004).
[CrossRef]

Brancaleon, L.

L. Brancaleon, A. J. Durkin, J. H. Tu, G. Menaker, J. D. Fallon, and N. Kollias, "In vivo fluorescence spectroscopy of nonmelanoma skin cancer," Photochem. Photobiol. 73, 178-183 (2001).
[CrossRef]

Churmakov, D. Y.

D. Y. Churmakov, I. V. Meglinski, and D. A. Greenhalgh, "Amending of fluorescence sensor signal localization in human skin by matching of the refractive index," J. Biomed. Opt. 9, 339-346 (2004).
[CrossRef]

D. Y. Churmakov, I. V. Meglinski, S. A. Piletsky, and D. A. Greenhalgh, "Automatic enhancement of skin fluorescence localization due to refractive index matching," in ALT'03 International Conference on Advanced Laser Technologies: Bio-medical Optics, R. K. Wang, J. C. Hebden, A. V. Priezzhev, and V. V. Tuchin, eds., Proc. SPIE 5486, 16-27 (2004).
[CrossRef]

I. V. Meglinski and D. Y. Churmakov, "A novel Monte Carlo method for the optical diagnostics of skin," in Diagnostic Optical Spectroscopy in Biomedicine II, G. A. Wagnieres, ed., Proc. SPIE 5141, 133-141 (2003).
[CrossRef]

D. Y. Churmakov, I. V. Meglinski, S. A. Piletsky, and D. A. Greenhalgh, "Skin fluorescence model based on the Monte Carlo technique," in Saratov Fall Meeting 2002: Optical Technologies in Biophysics and Medicine IV, V. V. Tuchin, ed., Proc. SPIE 5068, 326-333 (2003).
[CrossRef]

D. Y. Churmakov, I. V. Meglinski, and D. A. Greenhalgh, "Automatic amending of the tattoo sensor fluorescence localization by refractive index matching," in Diagnostic Optical Spectroscopy in Biomedicine II, G. A. Wagnieres, ed., Proc. SPIE 5141, 122-132 (2003).
[CrossRef]

Dong, K.

Durkin, A. J.

L. Brancaleon, A. J. Durkin, J. H. Tu, G. Menaker, J. D. Fallon, and N. Kollias, "In vivo fluorescence spectroscopy of nonmelanoma skin cancer," Photochem. Photobiol. 73, 178-183 (2001).
[CrossRef]

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L. Brancaleon, A. J. Durkin, J. H. Tu, G. Menaker, J. D. Fallon, and N. Kollias, "In vivo fluorescence spectroscopy of nonmelanoma skin cancer," Photochem. Photobiol. 73, 178-183 (2001).
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T. J. Farrell and M. S. Patterson, "Diffusion modeling of fluorescence in tissue," in Handbook of Biomedical Fluorescence (Marcel Dekker, 2003), pp. 29-60.

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Gans, R. O. B.

R. Meerwaldt, R. Graaff, P. H. N. Oomen, T. P. Links, J. J. Jager, N. L. Alderson, S. R. Thorpe, J. W. Baynes, R. O. B. Gans, and A. J. Smit, "Simple non-invasive assessment of advanced glycation endproduct accumulation," Diabetologia 47, 1324-1330 (2004).
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R. Gillies, G. Zonios, R. R. Anderson, and N. Kollias, "Fluorescence excitation spectroscopy provides information about human skin in vivo," J. Invest. Dermatology 115, 704-707 (2000).
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N. Kollias, R. Gillies, M. Moran, I. E. Kochevar, and R. R. Anderson, "Endogenous skin fluorescence includes bands that may serve as quantitative markers of aging and photoaging," J. Invest. Dermatol. 111, 776-776 (1998).
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R. Meerwaldt, R. Graaff, P. H. N. Oomen, T. P. Links, J. J. Jager, N. L. Alderson, S. R. Thorpe, J. W. Baynes, R. O. B. Gans, and A. J. Smit, "Simple non-invasive assessment of advanced glycation endproduct accumulation," Diabetologia 47, 1324-1330 (2004).
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D. Y. Churmakov, I. V. Meglinski, S. A. Piletsky, and D. A. Greenhalgh, "Automatic enhancement of skin fluorescence localization due to refractive index matching," in ALT'03 International Conference on Advanced Laser Technologies: Bio-medical Optics, R. K. Wang, J. C. Hebden, A. V. Priezzhev, and V. V. Tuchin, eds., Proc. SPIE 5486, 16-27 (2004).
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D. Y. Churmakov, I. V. Meglinski, and D. A. Greenhalgh, "Amending of fluorescence sensor signal localization in human skin by matching of the refractive index," J. Biomed. Opt. 9, 339-346 (2004).
[CrossRef]

D. Y. Churmakov, I. V. Meglinski, S. A. Piletsky, and D. A. Greenhalgh, "Skin fluorescence model based on the Monte Carlo technique," in Saratov Fall Meeting 2002: Optical Technologies in Biophysics and Medicine IV, V. V. Tuchin, ed., Proc. SPIE 5068, 326-333 (2003).
[CrossRef]

D. Y. Churmakov, I. V. Meglinski, and D. A. Greenhalgh, "Automatic amending of the tattoo sensor fluorescence localization by refractive index matching," in Diagnostic Optical Spectroscopy in Biomedicine II, G. A. Wagnieres, ed., Proc. SPIE 5141, 122-132 (2003).
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R. H. Na, I. M. Stender, M. Henriksen, and H. C. Wulf, "Autofluorescence of human skin is age-related after correction for skin pigmentation and redness," J. Invest. Dermatol. 116, 536-540 (2001).
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Ishimaru, A.

Jacques, S.

Jacques, S. L.

M. J. C. V. Gemert, S. L. Jacques, H. J. C. M. Sterenborg, and W. M. Star, "Skin optics," IEEE Trans. Biomed. Eng. 36, 1146-1154 (1989).
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R. Meerwaldt, R. Graaff, P. H. N. Oomen, T. P. Links, J. J. Jager, N. L. Alderson, S. R. Thorpe, J. W. Baynes, R. O. B. Gans, and A. J. Smit, "Simple non-invasive assessment of advanced glycation endproduct accumulation," Diabetologia 47, 1324-1330 (2004).
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T. Vo-Dinh, M. Panjehpour, B. F. Overholt, C. E. Julius, S. Overholt, and M. N. Phan, "Laser-induced fluorescence for the detection of esophageal and skin cancer," in Advanced Biomedical and Clinical Diagnostic Systems, T. Vo-Dinh, W. S. Grundfest, D. A. Benaron, and G. E. Cohn, eds., Proc. SPIE 4958, 67-70 (2003).
[CrossRef]

M. Panjehpour, C. E. Julius, M. N. Phan, T. Vo-Dinh, and B. F. Overholt, "In-vivo fluorescence spectroscopy for diagnosis of skin cancer," in Biomedical Diagnostic, Guidance, and Surgical-Assist Systems IV, T. Vo-Dinh, D. A. Benaron, and W. S. Grundfest, eds., Proc. SPIE 4615, 20-31 (2002).
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Y. Takema, Y. Yorimoto, H. Ohsu, O. Osanai, and M. Kawai, "Age-related discontinuous changes in the in vivo fluorescence of human facial skin," J. Dermatolog. Sci. 24, 55-58 (1997).
[CrossRef]

Keijzer, M.

Kochevar, I. E.

N. Kollias, R. Gillies, M. Moran, I. E. Kochevar, and R. R. Anderson, "Endogenous skin fluorescence includes bands that may serve as quantitative markers of aging and photoaging," J. Invest. Dermatol. 111, 776-776 (1998).
[CrossRef]

Koenig, K.

K. Koenig, H. Schneckenburger, J. Hemmer, B. J. Tromberg, and R. W. Steiner, "In-vivo fluorescence detection and imaging of porphyrin-producing bacteria in the human skin and in the oral cavity for diagnosis of acne vulgaris, caries, and squamous cell carcinoma," in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE 2135, 129-138 (1994).
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Kollias, N.

N. Kollias, G. Zonios, and G. N. Stamatas, "Fluorescence spectroscopy of skin," Vib. Spectrosc. 28, 17-23 (2002).
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L. Brancaleon, A. J. Durkin, J. H. Tu, G. Menaker, J. D. Fallon, and N. Kollias, "In vivo fluorescence spectroscopy of nonmelanoma skin cancer," Photochem. Photobiol. 73, 178-183 (2001).
[CrossRef]

R. Gillies, G. Zonios, R. R. Anderson, and N. Kollias, "Fluorescence excitation spectroscopy provides information about human skin in vivo," J. Invest. Dermatology 115, 704-707 (2000).
[CrossRef]

N. Kollias, R. Gillies, M. Moran, I. E. Kochevar, and R. R. Anderson, "Endogenous skin fluorescence includes bands that may serve as quantitative markers of aging and photoaging," J. Invest. Dermatol. 111, 776-776 (1998).
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R. Meerwaldt, R. Graaff, P. H. N. Oomen, T. P. Links, J. J. Jager, N. L. Alderson, S. R. Thorpe, J. W. Baynes, R. O. B. Gans, and A. J. Smit, "Simple non-invasive assessment of advanced glycation endproduct accumulation," Diabetologia 47, 1324-1330 (2004).
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Lu, J. Q.

Lui, H.

H. Zeng, D. I. McLean, C. E. MacAulay, and H. Lui, "Autofluorescence properties of skin and applications in dermatology," in Biomedical Photonics and Optoelectronic Imaging, H. Liu and Q. Luo, eds., Proc. SPIE 4224, 366-373 (2000).
[CrossRef]

H. Zeng, D. I. McLean, C. E. MacAulay, B. Palcic, and H. Lui, "Autofluorescence of basal cell carcinoma," in Lasers in Surgery: Advanced Characterization, Therapeutics, and Systems VIII, R. R. Anderson, K. E. Bartels, L. S. Bass, C. G. Garrett, K. W. Gregory, H. Lui, R. S. Malek, A. P. Perlmutter, L. Reinisch, P. J. Smalley, L. P. Tate, S. L. Thomsen, and G. M. Watson, eds., Proc. SPIE 3245, 314-317 (1998).
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H. Zeng, H. Lui, D. I. McLean, C. E. MacAulay, and B. Palcic, "Optical spectroscopy studies of diseased skin: preliminary results," in Optical and Imaging Techniques for Biomonitoring, H.-J. Foth, R. Marchesini, H. Podbielska, M. R. Nicoud, and H. Schneckenburger, eds., Proc. SPIE 2628, 281-285 (1996).

MacAulay, C.

H. Zeng, C. MacAulay, D. I. McLean, and B. Palcic, "Reconstruction of in vivo skin autofluorescence spectrum from microscopic properties by Monte Carlo simulation," J. Photochem. Photobiol. B 38, 234-240 (1997).
[CrossRef]

H. Zeng, C. MacAulay, D. I. McLean, and B. Palcic, "Spectroscopic and microscopic characteristics of human skin autofluorescence emission," Photochem. Photobiol. 61, 639-645 (1995).

H. Zeng and C. MacAulay, "Fluorescence spectroscopy and imaging for skin cancer detection and evaluation," in Handbook of Biomedical Fluorescence (Marcel Dekker, 2003), pp. 315-360.

MacAulay, C. E.

H. Zeng, D. I. McLean, C. E. MacAulay, and H. Lui, "Autofluorescence properties of skin and applications in dermatology," in Biomedical Photonics and Optoelectronic Imaging, H. Liu and Q. Luo, eds., Proc. SPIE 4224, 366-373 (2000).
[CrossRef]

H. Zeng, D. I. McLean, C. E. MacAulay, B. Palcic, and H. Lui, "Autofluorescence of basal cell carcinoma," in Lasers in Surgery: Advanced Characterization, Therapeutics, and Systems VIII, R. R. Anderson, K. E. Bartels, L. S. Bass, C. G. Garrett, K. W. Gregory, H. Lui, R. S. Malek, A. P. Perlmutter, L. Reinisch, P. J. Smalley, L. P. Tate, S. L. Thomsen, and G. M. Watson, eds., Proc. SPIE 3245, 314-317 (1998).
[CrossRef]

H. Zeng, H. Lui, D. I. McLean, C. E. MacAulay, and B. Palcic, "Optical spectroscopy studies of diseased skin: preliminary results," in Optical and Imaging Techniques for Biomonitoring, H.-J. Foth, R. Marchesini, H. Podbielska, M. R. Nicoud, and H. Schneckenburger, eds., Proc. SPIE 2628, 281-285 (1996).

H. Zeng, C. E. MacAulay, D. I. McLean, and B. Palcic, "Spectroscopy and microscopy studies of skin tissue autofluorescence emission," in Optical Biopsy and Fluorescence Spectroscopy and Imaging, R. Cubeddu, R. Marchesini, S. R. Mordon, K. Svanberg, H. H. Rinneberg, and G. A. Wagnieres, eds., Proc. SPIE 2324, 198-207 (1995).
[CrossRef]

H. Zeng, C. E. MacAulay, B. Palcic, and D. I. McLean, "Monte Carlo modeling of tissue autofluorescence measurement and imaging," in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE 2135, 94-104 (1994).
[CrossRef]

H. Zeng, C. E. MacAulay, B. Palcic, and D. I. McLean, "Laser-induced changes in autofluorescence of in-vivo skin," in Laser-Tissue Interaction IV, S. L. Jacques and A. Katzir, eds., Proc. SPIE 1882, 278-290 (1993).
[CrossRef]

H. Zeng, C. E. MacAulay, B. Palcic, and D. I. McLean, "Autofluorescence distribution in skin tissue revealed by microspectrophotometer measurements," in Lasers in Otolaryngology, Dermatology, and Tissue Welding, R. R. Anderson, L. S. Bass, S. M. Shapshay, J. V. White, and R. A. White, eds., Proc. SPIE 1876, 129-135 (1993).
[CrossRef]

Matcher, S. J.

I. V. Meglinski and S. J. Matcher, "Modeling of skin reflectance spectra," in Saratov Fall Meeting 2000: Optical Technologies in Biophysics and Medicine II, V. V. Tuchin, ed., Proc. SPIE 4241, 78-87 (2001).
[CrossRef]

McLean, D. I.

H. Zeng, D. I. McLean, C. E. MacAulay, and H. Lui, "Autofluorescence properties of skin and applications in dermatology," in Biomedical Photonics and Optoelectronic Imaging, H. Liu and Q. Luo, eds., Proc. SPIE 4224, 366-373 (2000).
[CrossRef]

H. Zeng, D. I. McLean, C. E. MacAulay, B. Palcic, and H. Lui, "Autofluorescence of basal cell carcinoma," in Lasers in Surgery: Advanced Characterization, Therapeutics, and Systems VIII, R. R. Anderson, K. E. Bartels, L. S. Bass, C. G. Garrett, K. W. Gregory, H. Lui, R. S. Malek, A. P. Perlmutter, L. Reinisch, P. J. Smalley, L. P. Tate, S. L. Thomsen, and G. M. Watson, eds., Proc. SPIE 3245, 314-317 (1998).
[CrossRef]

H. Zeng, C. MacAulay, D. I. McLean, and B. Palcic, "Reconstruction of in vivo skin autofluorescence spectrum from microscopic properties by Monte Carlo simulation," J. Photochem. Photobiol. B 38, 234-240 (1997).
[CrossRef]

H. Zeng, H. Lui, D. I. McLean, C. E. MacAulay, and B. Palcic, "Optical spectroscopy studies of diseased skin: preliminary results," in Optical and Imaging Techniques for Biomonitoring, H.-J. Foth, R. Marchesini, H. Podbielska, M. R. Nicoud, and H. Schneckenburger, eds., Proc. SPIE 2628, 281-285 (1996).

H. Zeng, C. MacAulay, D. I. McLean, and B. Palcic, "Spectroscopic and microscopic characteristics of human skin autofluorescence emission," Photochem. Photobiol. 61, 639-645 (1995).

H. Zeng, C. E. MacAulay, D. I. McLean, and B. Palcic, "Spectroscopy and microscopy studies of skin tissue autofluorescence emission," in Optical Biopsy and Fluorescence Spectroscopy and Imaging, R. Cubeddu, R. Marchesini, S. R. Mordon, K. Svanberg, H. H. Rinneberg, and G. A. Wagnieres, eds., Proc. SPIE 2324, 198-207 (1995).
[CrossRef]

H. Zeng, C. E. MacAulay, B. Palcic, and D. I. McLean, "Monte Carlo modeling of tissue autofluorescence measurement and imaging," in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE 2135, 94-104 (1994).
[CrossRef]

H. Zeng, C. E. MacAulay, B. Palcic, and D. I. McLean, "Laser-induced changes in autofluorescence of in-vivo skin," in Laser-Tissue Interaction IV, S. L. Jacques and A. Katzir, eds., Proc. SPIE 1882, 278-290 (1993).
[CrossRef]

H. Zeng, C. E. MacAulay, B. Palcic, and D. I. McLean, "Autofluorescence distribution in skin tissue revealed by microspectrophotometer measurements," in Lasers in Otolaryngology, Dermatology, and Tissue Welding, R. R. Anderson, L. S. Bass, S. M. Shapshay, J. V. White, and R. A. White, eds., Proc. SPIE 1876, 129-135 (1993).
[CrossRef]

Meerwaldt, R.

R. Meerwaldt, R. Graaff, P. H. N. Oomen, T. P. Links, J. J. Jager, N. L. Alderson, S. R. Thorpe, J. W. Baynes, R. O. B. Gans, and A. J. Smit, "Simple non-invasive assessment of advanced glycation endproduct accumulation," Diabetologia 47, 1324-1330 (2004).
[CrossRef]

Meglinski, I. V.

D. Y. Churmakov, I. V. Meglinski, and D. A. Greenhalgh, "Amending of fluorescence sensor signal localization in human skin by matching of the refractive index," J. Biomed. Opt. 9, 339-346 (2004).
[CrossRef]

D. Y. Churmakov, I. V. Meglinski, S. A. Piletsky, and D. A. Greenhalgh, "Automatic enhancement of skin fluorescence localization due to refractive index matching," in ALT'03 International Conference on Advanced Laser Technologies: Bio-medical Optics, R. K. Wang, J. C. Hebden, A. V. Priezzhev, and V. V. Tuchin, eds., Proc. SPIE 5486, 16-27 (2004).
[CrossRef]

I. V. Meglinski and D. Y. Churmakov, "A novel Monte Carlo method for the optical diagnostics of skin," in Diagnostic Optical Spectroscopy in Biomedicine II, G. A. Wagnieres, ed., Proc. SPIE 5141, 133-141 (2003).
[CrossRef]

D. Y. Churmakov, I. V. Meglinski, S. A. Piletsky, and D. A. Greenhalgh, "Skin fluorescence model based on the Monte Carlo technique," in Saratov Fall Meeting 2002: Optical Technologies in Biophysics and Medicine IV, V. V. Tuchin, ed., Proc. SPIE 5068, 326-333 (2003).
[CrossRef]

D. Y. Churmakov, I. V. Meglinski, and D. A. Greenhalgh, "Automatic amending of the tattoo sensor fluorescence localization by refractive index matching," in Diagnostic Optical Spectroscopy in Biomedicine II, G. A. Wagnieres, ed., Proc. SPIE 5141, 122-132 (2003).
[CrossRef]

I. V. Meglinski, "Monte Carlo method in optical diagnostics of skin and skin tissues," in Third International Conference on Photonics and Imaging in Biology and Medicine, Q. Luo, V. V. Tuchin, M. Gu, and L. V. Wang, eds., Proc. SPIE 5254, 30-43 (2003).
[CrossRef]

I. V. Meglinski and S. J. Matcher, "Modeling of skin reflectance spectra," in Saratov Fall Meeting 2000: Optical Technologies in Biophysics and Medicine II, V. V. Tuchin, ed., Proc. SPIE 4241, 78-87 (2001).
[CrossRef]

S. R. Utz, Y. P. Sinichkin, I. V. Meglinski, and H. A. Pilipenko, "Fluorescence spectroscopy in combination with reflectance measurements in human skin examination: what for and how," in Optical Biopsy and Fluorescence Spectroscopy and Imaging, R. Cubeddu, R. Marchesini, S. R. Mordon, K. Svanberg, H. H. Rinneberg, and G. A. Wagnieres, eds., Proc. SPIE 2324, 125-136 (1995).
[CrossRef]

Menaker, G.

L. Brancaleon, A. J. Durkin, J. H. Tu, G. Menaker, J. D. Fallon, and N. Kollias, "In vivo fluorescence spectroscopy of nonmelanoma skin cancer," Photochem. Photobiol. 73, 178-183 (2001).
[CrossRef]

Modest, M. F.

M. F. Modest, Radiative Heat Transfer (Academic, 2002).

Moran, M.

N. Kollias, R. Gillies, M. Moran, I. E. Kochevar, and R. R. Anderson, "Endogenous skin fluorescence includes bands that may serve as quantitative markers of aging and photoaging," J. Invest. Dermatol. 111, 776-776 (1998).
[CrossRef]

Na, R. H.

R. H. Na, I. M. Stender, M. Henriksen, and H. C. Wulf, "Autofluorescence of human skin is age-related after correction for skin pigmentation and redness," J. Invest. Dermatol. 116, 536-540 (2001).
[CrossRef]

Ohsu, H.

Y. Takema, Y. Yorimoto, H. Ohsu, O. Osanai, and M. Kawai, "Age-related discontinuous changes in the in vivo fluorescence of human facial skin," J. Dermatolog. Sci. 24, 55-58 (1997).
[CrossRef]

Oomen, P. H. N.

R. Meerwaldt, R. Graaff, P. H. N. Oomen, T. P. Links, J. J. Jager, N. L. Alderson, S. R. Thorpe, J. W. Baynes, R. O. B. Gans, and A. J. Smit, "Simple non-invasive assessment of advanced glycation endproduct accumulation," Diabetologia 47, 1324-1330 (2004).
[CrossRef]

Osanai, O.

Y. Takema, Y. Yorimoto, H. Ohsu, O. Osanai, and M. Kawai, "Age-related discontinuous changes in the in vivo fluorescence of human facial skin," J. Dermatolog. Sci. 24, 55-58 (1997).
[CrossRef]

Overholt, B. F.

T. Vo-Dinh, M. Panjehpour, B. F. Overholt, C. E. Julius, S. Overholt, and M. N. Phan, "Laser-induced fluorescence for the detection of esophageal and skin cancer," in Advanced Biomedical and Clinical Diagnostic Systems, T. Vo-Dinh, W. S. Grundfest, D. A. Benaron, and G. E. Cohn, eds., Proc. SPIE 4958, 67-70 (2003).
[CrossRef]

M. Panjehpour, C. E. Julius, M. N. Phan, T. Vo-Dinh, and B. F. Overholt, "In-vivo fluorescence spectroscopy for diagnosis of skin cancer," in Biomedical Diagnostic, Guidance, and Surgical-Assist Systems IV, T. Vo-Dinh, D. A. Benaron, and W. S. Grundfest, eds., Proc. SPIE 4615, 20-31 (2002).
[CrossRef]

Overholt, S.

T. Vo-Dinh, M. Panjehpour, B. F. Overholt, C. E. Julius, S. Overholt, and M. N. Phan, "Laser-induced fluorescence for the detection of esophageal and skin cancer," in Advanced Biomedical and Clinical Diagnostic Systems, T. Vo-Dinh, W. S. Grundfest, D. A. Benaron, and G. E. Cohn, eds., Proc. SPIE 4958, 67-70 (2003).
[CrossRef]

Palcic, B.

H. Zeng, D. I. McLean, C. E. MacAulay, B. Palcic, and H. Lui, "Autofluorescence of basal cell carcinoma," in Lasers in Surgery: Advanced Characterization, Therapeutics, and Systems VIII, R. R. Anderson, K. E. Bartels, L. S. Bass, C. G. Garrett, K. W. Gregory, H. Lui, R. S. Malek, A. P. Perlmutter, L. Reinisch, P. J. Smalley, L. P. Tate, S. L. Thomsen, and G. M. Watson, eds., Proc. SPIE 3245, 314-317 (1998).
[CrossRef]

H. Zeng, C. MacAulay, D. I. McLean, and B. Palcic, "Reconstruction of in vivo skin autofluorescence spectrum from microscopic properties by Monte Carlo simulation," J. Photochem. Photobiol. B 38, 234-240 (1997).
[CrossRef]

H. Zeng, H. Lui, D. I. McLean, C. E. MacAulay, and B. Palcic, "Optical spectroscopy studies of diseased skin: preliminary results," in Optical and Imaging Techniques for Biomonitoring, H.-J. Foth, R. Marchesini, H. Podbielska, M. R. Nicoud, and H. Schneckenburger, eds., Proc. SPIE 2628, 281-285 (1996).

H. Zeng, C. MacAulay, D. I. McLean, and B. Palcic, "Spectroscopic and microscopic characteristics of human skin autofluorescence emission," Photochem. Photobiol. 61, 639-645 (1995).

H. Zeng, C. E. MacAulay, D. I. McLean, and B. Palcic, "Spectroscopy and microscopy studies of skin tissue autofluorescence emission," in Optical Biopsy and Fluorescence Spectroscopy and Imaging, R. Cubeddu, R. Marchesini, S. R. Mordon, K. Svanberg, H. H. Rinneberg, and G. A. Wagnieres, eds., Proc. SPIE 2324, 198-207 (1995).
[CrossRef]

H. Zeng, C. E. MacAulay, B. Palcic, and D. I. McLean, "Monte Carlo modeling of tissue autofluorescence measurement and imaging," in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE 2135, 94-104 (1994).
[CrossRef]

H. Zeng, C. E. MacAulay, B. Palcic, and D. I. McLean, "Laser-induced changes in autofluorescence of in-vivo skin," in Laser-Tissue Interaction IV, S. L. Jacques and A. Katzir, eds., Proc. SPIE 1882, 278-290 (1993).
[CrossRef]

H. Zeng, C. E. MacAulay, B. Palcic, and D. I. McLean, "Autofluorescence distribution in skin tissue revealed by microspectrophotometer measurements," in Lasers in Otolaryngology, Dermatology, and Tissue Welding, R. R. Anderson, L. S. Bass, S. M. Shapshay, J. V. White, and R. A. White, eds., Proc. SPIE 1876, 129-135 (1993).
[CrossRef]

Panjehpour, M.

T. Vo-Dinh, M. Panjehpour, B. F. Overholt, C. E. Julius, S. Overholt, and M. N. Phan, "Laser-induced fluorescence for the detection of esophageal and skin cancer," in Advanced Biomedical and Clinical Diagnostic Systems, T. Vo-Dinh, W. S. Grundfest, D. A. Benaron, and G. E. Cohn, eds., Proc. SPIE 4958, 67-70 (2003).
[CrossRef]

M. Panjehpour, C. E. Julius, M. N. Phan, T. Vo-Dinh, and B. F. Overholt, "In-vivo fluorescence spectroscopy for diagnosis of skin cancer," in Biomedical Diagnostic, Guidance, and Surgical-Assist Systems IV, T. Vo-Dinh, D. A. Benaron, and W. S. Grundfest, eds., Proc. SPIE 4615, 20-31 (2002).
[CrossRef]

Patterson, M. S.

T. J. Farrell and M. S. Patterson, "Diffusion modeling of fluorescence in tissue," in Handbook of Biomedical Fluorescence (Marcel Dekker, 2003), pp. 29-60.

Phan, M. N.

T. Vo-Dinh, M. Panjehpour, B. F. Overholt, C. E. Julius, S. Overholt, and M. N. Phan, "Laser-induced fluorescence for the detection of esophageal and skin cancer," in Advanced Biomedical and Clinical Diagnostic Systems, T. Vo-Dinh, W. S. Grundfest, D. A. Benaron, and G. E. Cohn, eds., Proc. SPIE 4958, 67-70 (2003).
[CrossRef]

M. Panjehpour, C. E. Julius, M. N. Phan, T. Vo-Dinh, and B. F. Overholt, "In-vivo fluorescence spectroscopy for diagnosis of skin cancer," in Biomedical Diagnostic, Guidance, and Surgical-Assist Systems IV, T. Vo-Dinh, D. A. Benaron, and W. S. Grundfest, eds., Proc. SPIE 4615, 20-31 (2002).
[CrossRef]

Philipsen, P. A.

J. Sandby-Moller, E. Thieden, P. A. Philipsen, J. Heydenreich, and H. C. Wulf, "Skin autofluorescence as a biological UVR dosimeter," Photodermatol. Photoimmunol. Photomed. 20, 33-40 (2004).
[CrossRef]

Piletsky, S. A.

D. Y. Churmakov, I. V. Meglinski, S. A. Piletsky, and D. A. Greenhalgh, "Automatic enhancement of skin fluorescence localization due to refractive index matching," in ALT'03 International Conference on Advanced Laser Technologies: Bio-medical Optics, R. K. Wang, J. C. Hebden, A. V. Priezzhev, and V. V. Tuchin, eds., Proc. SPIE 5486, 16-27 (2004).
[CrossRef]

D. Y. Churmakov, I. V. Meglinski, S. A. Piletsky, and D. A. Greenhalgh, "Skin fluorescence model based on the Monte Carlo technique," in Saratov Fall Meeting 2002: Optical Technologies in Biophysics and Medicine IV, V. V. Tuchin, ed., Proc. SPIE 5068, 326-333 (2003).
[CrossRef]

Pilipenko, H. A.

Y. P. Sinichkin, S. R. Utz, P. M. Yudin, and H. A. Pilipenko, "Investigation of formation and dynamics of human skin erythema and pigmentation by in vivo fluorescence spectroscopy," in Optical Biopsy and Fluorescence Spectroscopy and Imaging, R. Cubeddu, R. Marchesini, S. R. Mordon, K. Svanberg, H. H. Rinneberg, and G. A. Wagnieres, eds., Proc. SPIE 2324, 259-268 (1995).
[CrossRef]

S. R. Utz, Y. P. Sinichkin, I. V. Meglinski, and H. A. Pilipenko, "Fluorescence spectroscopy in combination with reflectance measurements in human skin examination: what for and how," in Optical Biopsy and Fluorescence Spectroscopy and Imaging, R. Cubeddu, R. Marchesini, S. R. Mordon, K. Svanberg, H. H. Rinneberg, and G. A. Wagnieres, eds., Proc. SPIE 2324, 125-136 (1995).
[CrossRef]

Y. P. Sinichkin, S. R. Utz, and H. A. Pilipenko, "Laser-induced fluorescence of the human skin in vivo: influence of the erythema," in Optical Biopsy, R. Cubeddu, S. Svanberg, and H. van den Bergh, eds., Proc. SPIE 2081, 41-47 (1994).
[CrossRef]

Pilon, L.

K. Katika and L. Pilon, "Modified method of characteristics in transient radiative transfer," J. Quant. Spectrosc. Radiat. Transfer 98, 220-237 (2006).
[CrossRef]

Prahl, S. A.

Richards-Kortum, R.

R. Richards-Kortum and E. Sevick-Muraca, "Quantitative optical spectroscopy for tissue diagnostics," Annu. Rev. Phys. Chem. 47, 555-606 (1996).
[CrossRef]

M. Keijzer, R. Richards-Kortum, S. Jacques, and M. Feld, "Fluorescence spectroscopy of turbid media: autofluorescence of the human aorta," Appl. Opt. 28, 4286-4292 (1989).

Sandby-Moller, J.

J. Sandby-Moller, E. Thieden, P. A. Philipsen, J. Heydenreich, and H. C. Wulf, "Skin autofluorescence as a biological UVR dosimeter," Photodermatol. Photoimmunol. Photomed. 20, 33-40 (2004).
[CrossRef]

Schneckenburger, H.

K. Koenig, H. Schneckenburger, J. Hemmer, B. J. Tromberg, and R. W. Steiner, "In-vivo fluorescence detection and imaging of porphyrin-producing bacteria in the human skin and in the oral cavity for diagnosis of acne vulgaris, caries, and squamous cell carcinoma," in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE 2135, 129-138 (1994).
[CrossRef]

Sevick-Muraca, E.

R. Richards-Kortum and E. Sevick-Muraca, "Quantitative optical spectroscopy for tissue diagnostics," Annu. Rev. Phys. Chem. 47, 555-606 (1996).
[CrossRef]

Sinichkin, Y. P.

S. R. Utz, Y. P. Sinichkin, I. V. Meglinski, and H. A. Pilipenko, "Fluorescence spectroscopy in combination with reflectance measurements in human skin examination: what for and how," in Optical Biopsy and Fluorescence Spectroscopy and Imaging, R. Cubeddu, R. Marchesini, S. R. Mordon, K. Svanberg, H. H. Rinneberg, and G. A. Wagnieres, eds., Proc. SPIE 2324, 125-136 (1995).
[CrossRef]

Y. P. Sinichkin, S. R. Utz, P. M. Yudin, and H. A. Pilipenko, "Investigation of formation and dynamics of human skin erythema and pigmentation by in vivo fluorescence spectroscopy," in Optical Biopsy and Fluorescence Spectroscopy and Imaging, R. Cubeddu, R. Marchesini, S. R. Mordon, K. Svanberg, H. H. Rinneberg, and G. A. Wagnieres, eds., Proc. SPIE 2324, 259-268 (1995).
[CrossRef]

Y. P. Sinichkin, S. R. Utz, and H. A. Pilipenko, "Laser-induced fluorescence of the human skin in vivo: influence of the erythema," in Optical Biopsy, R. Cubeddu, S. Svanberg, and H. van den Bergh, eds., Proc. SPIE 2081, 41-47 (1994).
[CrossRef]

Smit, A. J.

R. Meerwaldt, R. Graaff, P. H. N. Oomen, T. P. Links, J. J. Jager, N. L. Alderson, S. R. Thorpe, J. W. Baynes, R. O. B. Gans, and A. J. Smit, "Simple non-invasive assessment of advanced glycation endproduct accumulation," Diabetologia 47, 1324-1330 (2004).
[CrossRef]

Spott, T.

Stamatas, G. N.

N. Kollias, G. Zonios, and G. N. Stamatas, "Fluorescence spectroscopy of skin," Vib. Spectrosc. 28, 17-23 (2002).
[CrossRef]

Star, W. M.

M. J. C. V. Gemert, S. L. Jacques, H. J. C. M. Sterenborg, and W. M. Star, "Skin optics," IEEE Trans. Biomed. Eng. 36, 1146-1154 (1989).
[CrossRef]

Steiner, R. W.

K. Koenig, H. Schneckenburger, J. Hemmer, B. J. Tromberg, and R. W. Steiner, "In-vivo fluorescence detection and imaging of porphyrin-producing bacteria in the human skin and in the oral cavity for diagnosis of acne vulgaris, caries, and squamous cell carcinoma," in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE 2135, 129-138 (1994).
[CrossRef]

Stender, I. M.

R. H. Na, I. M. Stender, M. Henriksen, and H. C. Wulf, "Autofluorescence of human skin is age-related after correction for skin pigmentation and redness," J. Invest. Dermatol. 116, 536-540 (2001).
[CrossRef]

Sterenborg, H. J. C. M.

M. J. C. V. Gemert, S. L. Jacques, H. J. C. M. Sterenborg, and W. M. Star, "Skin optics," IEEE Trans. Biomed. Eng. 36, 1146-1154 (1989).
[CrossRef]

Svaasand, L. O.

Takema, Y.

Y. Takema, Y. Yorimoto, H. Ohsu, O. Osanai, and M. Kawai, "Age-related discontinuous changes in the in vivo fluorescence of human facial skin," J. Dermatolog. Sci. 24, 55-58 (1997).
[CrossRef]

Thieden, E.

J. Sandby-Moller, E. Thieden, P. A. Philipsen, J. Heydenreich, and H. C. Wulf, "Skin autofluorescence as a biological UVR dosimeter," Photodermatol. Photoimmunol. Photomed. 20, 33-40 (2004).
[CrossRef]

Thorpe, S. R.

R. Meerwaldt, R. Graaff, P. H. N. Oomen, T. P. Links, J. J. Jager, N. L. Alderson, S. R. Thorpe, J. W. Baynes, R. O. B. Gans, and A. J. Smit, "Simple non-invasive assessment of advanced glycation endproduct accumulation," Diabetologia 47, 1324-1330 (2004).
[CrossRef]

Tromberg, B. J.

K. Koenig, H. Schneckenburger, J. Hemmer, B. J. Tromberg, and R. W. Steiner, "In-vivo fluorescence detection and imaging of porphyrin-producing bacteria in the human skin and in the oral cavity for diagnosis of acne vulgaris, caries, and squamous cell carcinoma," in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE 2135, 129-138 (1994).
[CrossRef]

Tu, J. H.

L. Brancaleon, A. J. Durkin, J. H. Tu, G. Menaker, J. D. Fallon, and N. Kollias, "In vivo fluorescence spectroscopy of nonmelanoma skin cancer," Photochem. Photobiol. 73, 178-183 (2001).
[CrossRef]

Utz, S. R.

Y. P. Sinichkin, S. R. Utz, P. M. Yudin, and H. A. Pilipenko, "Investigation of formation and dynamics of human skin erythema and pigmentation by in vivo fluorescence spectroscopy," in Optical Biopsy and Fluorescence Spectroscopy and Imaging, R. Cubeddu, R. Marchesini, S. R. Mordon, K. Svanberg, H. H. Rinneberg, and G. A. Wagnieres, eds., Proc. SPIE 2324, 259-268 (1995).
[CrossRef]

S. R. Utz, Y. P. Sinichkin, I. V. Meglinski, and H. A. Pilipenko, "Fluorescence spectroscopy in combination with reflectance measurements in human skin examination: what for and how," in Optical Biopsy and Fluorescence Spectroscopy and Imaging, R. Cubeddu, R. Marchesini, S. R. Mordon, K. Svanberg, H. H. Rinneberg, and G. A. Wagnieres, eds., Proc. SPIE 2324, 125-136 (1995).
[CrossRef]

Y. P. Sinichkin, S. R. Utz, and H. A. Pilipenko, "Laser-induced fluorescence of the human skin in vivo: influence of the erythema," in Optical Biopsy, R. Cubeddu, S. Svanberg, and H. van den Bergh, eds., Proc. SPIE 2081, 41-47 (1994).
[CrossRef]

Vo-Dinh, T.

T. Vo-Dinh, M. Panjehpour, B. F. Overholt, C. E. Julius, S. Overholt, and M. N. Phan, "Laser-induced fluorescence for the detection of esophageal and skin cancer," in Advanced Biomedical and Clinical Diagnostic Systems, T. Vo-Dinh, W. S. Grundfest, D. A. Benaron, and G. E. Cohn, eds., Proc. SPIE 4958, 67-70 (2003).
[CrossRef]

M. Panjehpour, C. E. Julius, M. N. Phan, T. Vo-Dinh, and B. F. Overholt, "In-vivo fluorescence spectroscopy for diagnosis of skin cancer," in Biomedical Diagnostic, Guidance, and Surgical-Assist Systems IV, T. Vo-Dinh, D. A. Benaron, and W. S. Grundfest, eds., Proc. SPIE 4615, 20-31 (2002).
[CrossRef]

Welch, A. J.

Wulf, H. C.

J. Sandby-Moller, E. Thieden, P. A. Philipsen, J. Heydenreich, and H. C. Wulf, "Skin autofluorescence as a biological UVR dosimeter," Photodermatol. Photoimmunol. Photomed. 20, 33-40 (2004).
[CrossRef]

R. H. Na, I. M. Stender, M. Henriksen, and H. C. Wulf, "Autofluorescence of human skin is age-related after correction for skin pigmentation and redness," J. Invest. Dermatol. 116, 536-540 (2001).
[CrossRef]

Yoon, G.

Yorimoto, Y.

Y. Takema, Y. Yorimoto, H. Ohsu, O. Osanai, and M. Kawai, "Age-related discontinuous changes in the in vivo fluorescence of human facial skin," J. Dermatolog. Sci. 24, 55-58 (1997).
[CrossRef]

Yudin, P. M.

Y. P. Sinichkin, S. R. Utz, P. M. Yudin, and H. A. Pilipenko, "Investigation of formation and dynamics of human skin erythema and pigmentation by in vivo fluorescence spectroscopy," in Optical Biopsy and Fluorescence Spectroscopy and Imaging, R. Cubeddu, R. Marchesini, S. R. Mordon, K. Svanberg, H. H. Rinneberg, and G. A. Wagnieres, eds., Proc. SPIE 2324, 259-268 (1995).
[CrossRef]

Zeng, H.

H. Zeng, D. I. McLean, C. E. MacAulay, and H. Lui, "Autofluorescence properties of skin and applications in dermatology," in Biomedical Photonics and Optoelectronic Imaging, H. Liu and Q. Luo, eds., Proc. SPIE 4224, 366-373 (2000).
[CrossRef]

H. Zeng, D. I. McLean, C. E. MacAulay, B. Palcic, and H. Lui, "Autofluorescence of basal cell carcinoma," in Lasers in Surgery: Advanced Characterization, Therapeutics, and Systems VIII, R. R. Anderson, K. E. Bartels, L. S. Bass, C. G. Garrett, K. W. Gregory, H. Lui, R. S. Malek, A. P. Perlmutter, L. Reinisch, P. J. Smalley, L. P. Tate, S. L. Thomsen, and G. M. Watson, eds., Proc. SPIE 3245, 314-317 (1998).
[CrossRef]

H. Zeng, C. MacAulay, D. I. McLean, and B. Palcic, "Reconstruction of in vivo skin autofluorescence spectrum from microscopic properties by Monte Carlo simulation," J. Photochem. Photobiol. B 38, 234-240 (1997).
[CrossRef]

H. Zeng, H. Lui, D. I. McLean, C. E. MacAulay, and B. Palcic, "Optical spectroscopy studies of diseased skin: preliminary results," in Optical and Imaging Techniques for Biomonitoring, H.-J. Foth, R. Marchesini, H. Podbielska, M. R. Nicoud, and H. Schneckenburger, eds., Proc. SPIE 2628, 281-285 (1996).

H. Zeng, C. MacAulay, D. I. McLean, and B. Palcic, "Spectroscopic and microscopic characteristics of human skin autofluorescence emission," Photochem. Photobiol. 61, 639-645 (1995).

H. Zeng, C. E. MacAulay, D. I. McLean, and B. Palcic, "Spectroscopy and microscopy studies of skin tissue autofluorescence emission," in Optical Biopsy and Fluorescence Spectroscopy and Imaging, R. Cubeddu, R. Marchesini, S. R. Mordon, K. Svanberg, H. H. Rinneberg, and G. A. Wagnieres, eds., Proc. SPIE 2324, 198-207 (1995).
[CrossRef]

H. Zeng, C. E. MacAulay, B. Palcic, and D. I. McLean, "Monte Carlo modeling of tissue autofluorescence measurement and imaging," in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE 2135, 94-104 (1994).
[CrossRef]

H. Zeng, C. E. MacAulay, B. Palcic, and D. I. McLean, "Laser-induced changes in autofluorescence of in-vivo skin," in Laser-Tissue Interaction IV, S. L. Jacques and A. Katzir, eds., Proc. SPIE 1882, 278-290 (1993).
[CrossRef]

H. Zeng, C. E. MacAulay, B. Palcic, and D. I. McLean, "Autofluorescence distribution in skin tissue revealed by microspectrophotometer measurements," in Lasers in Otolaryngology, Dermatology, and Tissue Welding, R. R. Anderson, L. S. Bass, S. M. Shapshay, J. V. White, and R. A. White, eds., Proc. SPIE 1876, 129-135 (1993).
[CrossRef]

H. Zeng and C. MacAulay, "Fluorescence spectroscopy and imaging for skin cancer detection and evaluation," in Handbook of Biomedical Fluorescence (Marcel Dekker, 2003), pp. 315-360.

Zonios, G.

N. Kollias, G. Zonios, and G. N. Stamatas, "Fluorescence spectroscopy of skin," Vib. Spectrosc. 28, 17-23 (2002).
[CrossRef]

R. Gillies, G. Zonios, R. R. Anderson, and N. Kollias, "Fluorescence excitation spectroscopy provides information about human skin in vivo," J. Invest. Dermatology 115, 704-707 (2000).
[CrossRef]

Annu. Rev. Phys. Chem.

R. Richards-Kortum and E. Sevick-Muraca, "Quantitative optical spectroscopy for tissue diagnostics," Annu. Rev. Phys. Chem. 47, 555-606 (1996).
[CrossRef]

Appl. Opt.

Diabetologia

R. Meerwaldt, R. Graaff, P. H. N. Oomen, T. P. Links, J. J. Jager, N. L. Alderson, S. R. Thorpe, J. W. Baynes, R. O. B. Gans, and A. J. Smit, "Simple non-invasive assessment of advanced glycation endproduct accumulation," Diabetologia 47, 1324-1330 (2004).
[CrossRef]

IEEE Trans. Biomed. Eng.

M. J. C. V. Gemert, S. L. Jacques, H. J. C. M. Sterenborg, and W. M. Star, "Skin optics," IEEE Trans. Biomed. Eng. 36, 1146-1154 (1989).
[CrossRef]

J. Biomed. Opt.

D. Y. Churmakov, I. V. Meglinski, and D. A. Greenhalgh, "Amending of fluorescence sensor signal localization in human skin by matching of the refractive index," J. Biomed. Opt. 9, 339-346 (2004).
[CrossRef]

J. Dermatolog. Sci.

Y. Takema, Y. Yorimoto, H. Ohsu, O. Osanai, and M. Kawai, "Age-related discontinuous changes in the in vivo fluorescence of human facial skin," J. Dermatolog. Sci. 24, 55-58 (1997).
[CrossRef]

J. Invest. Dermatol.

N. Kollias, R. Gillies, M. Moran, I. E. Kochevar, and R. R. Anderson, "Endogenous skin fluorescence includes bands that may serve as quantitative markers of aging and photoaging," J. Invest. Dermatol. 111, 776-776 (1998).
[CrossRef]

R. H. Na, I. M. Stender, M. Henriksen, and H. C. Wulf, "Autofluorescence of human skin is age-related after correction for skin pigmentation and redness," J. Invest. Dermatol. 116, 536-540 (2001).
[CrossRef]

J. Invest. Dermatology

R. Gillies, G. Zonios, R. R. Anderson, and N. Kollias, "Fluorescence excitation spectroscopy provides information about human skin in vivo," J. Invest. Dermatology 115, 704-707 (2000).
[CrossRef]

J. Photochem. Photobiol. B

H. Zeng, C. MacAulay, D. I. McLean, and B. Palcic, "Reconstruction of in vivo skin autofluorescence spectrum from microscopic properties by Monte Carlo simulation," J. Photochem. Photobiol. B 38, 234-240 (1997).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer

K. Katika and L. Pilon, "Modified method of characteristics in transient radiative transfer," J. Quant. Spectrosc. Radiat. Transfer 98, 220-237 (2006).
[CrossRef]

Photochem. Photobiol.

L. Brancaleon, A. J. Durkin, J. H. Tu, G. Menaker, J. D. Fallon, and N. Kollias, "In vivo fluorescence spectroscopy of nonmelanoma skin cancer," Photochem. Photobiol. 73, 178-183 (2001).
[CrossRef]

H. Zeng, C. MacAulay, D. I. McLean, and B. Palcic, "Spectroscopic and microscopic characteristics of human skin autofluorescence emission," Photochem. Photobiol. 61, 639-645 (1995).

Photodermatol. Photoimmunol. Photomed.

J. Sandby-Moller, E. Thieden, P. A. Philipsen, J. Heydenreich, and H. C. Wulf, "Skin autofluorescence as a biological UVR dosimeter," Photodermatol. Photoimmunol. Photomed. 20, 33-40 (2004).
[CrossRef]

Phys. Med. Biol.

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, "Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues," Phys. Med. Biol. 43, 1285-1302 (1998).
[CrossRef]

Proc. SPIE

K. Koenig, H. Schneckenburger, J. Hemmer, B. J. Tromberg, and R. W. Steiner, "In-vivo fluorescence detection and imaging of porphyrin-producing bacteria in the human skin and in the oral cavity for diagnosis of acne vulgaris, caries, and squamous cell carcinoma," in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE 2135, 129-138 (1994).
[CrossRef]

D. Y. Churmakov, I. V. Meglinski, and D. A. Greenhalgh, "Automatic amending of the tattoo sensor fluorescence localization by refractive index matching," in Diagnostic Optical Spectroscopy in Biomedicine II, G. A. Wagnieres, ed., Proc. SPIE 5141, 122-132 (2003).
[CrossRef]

D. Y. Churmakov, I. V. Meglinski, S. A. Piletsky, and D. A. Greenhalgh, "Automatic enhancement of skin fluorescence localization due to refractive index matching," in ALT'03 International Conference on Advanced Laser Technologies: Bio-medical Optics, R. K. Wang, J. C. Hebden, A. V. Priezzhev, and V. V. Tuchin, eds., Proc. SPIE 5486, 16-27 (2004).
[CrossRef]

H. Zeng, C. E. MacAulay, D. I. McLean, and B. Palcic, "Spectroscopy and microscopy studies of skin tissue autofluorescence emission," in Optical Biopsy and Fluorescence Spectroscopy and Imaging, R. Cubeddu, R. Marchesini, S. R. Mordon, K. Svanberg, H. H. Rinneberg, and G. A. Wagnieres, eds., Proc. SPIE 2324, 198-207 (1995).
[CrossRef]

H. Zeng, H. Lui, D. I. McLean, C. E. MacAulay, and B. Palcic, "Optical spectroscopy studies of diseased skin: preliminary results," in Optical and Imaging Techniques for Biomonitoring, H.-J. Foth, R. Marchesini, H. Podbielska, M. R. Nicoud, and H. Schneckenburger, eds., Proc. SPIE 2628, 281-285 (1996).

H. Zeng, C. E. MacAulay, B. Palcic, and D. I. McLean, "Monte Carlo modeling of tissue autofluorescence measurement and imaging," in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE 2135, 94-104 (1994).
[CrossRef]

H. Zeng, C. E. MacAulay, B. Palcic, and D. I. McLean, "Autofluorescence distribution in skin tissue revealed by microspectrophotometer measurements," in Lasers in Otolaryngology, Dermatology, and Tissue Welding, R. R. Anderson, L. S. Bass, S. M. Shapshay, J. V. White, and R. A. White, eds., Proc. SPIE 1876, 129-135 (1993).
[CrossRef]

I. V. Meglinski and D. Y. Churmakov, "A novel Monte Carlo method for the optical diagnostics of skin," in Diagnostic Optical Spectroscopy in Biomedicine II, G. A. Wagnieres, ed., Proc. SPIE 5141, 133-141 (2003).
[CrossRef]

I. V. Meglinski, "Monte Carlo method in optical diagnostics of skin and skin tissues," in Third International Conference on Photonics and Imaging in Biology and Medicine, Q. Luo, V. V. Tuchin, M. Gu, and L. V. Wang, eds., Proc. SPIE 5254, 30-43 (2003).
[CrossRef]

H. Zeng, D. I. McLean, C. E. MacAulay, B. Palcic, and H. Lui, "Autofluorescence of basal cell carcinoma," in Lasers in Surgery: Advanced Characterization, Therapeutics, and Systems VIII, R. R. Anderson, K. E. Bartels, L. S. Bass, C. G. Garrett, K. W. Gregory, H. Lui, R. S. Malek, A. P. Perlmutter, L. Reinisch, P. J. Smalley, L. P. Tate, S. L. Thomsen, and G. M. Watson, eds., Proc. SPIE 3245, 314-317 (1998).
[CrossRef]

H. Zeng, D. I. McLean, C. E. MacAulay, and H. Lui, "Autofluorescence properties of skin and applications in dermatology," in Biomedical Photonics and Optoelectronic Imaging, H. Liu and Q. Luo, eds., Proc. SPIE 4224, 366-373 (2000).
[CrossRef]

M. Panjehpour, C. E. Julius, M. N. Phan, T. Vo-Dinh, and B. F. Overholt, "In-vivo fluorescence spectroscopy for diagnosis of skin cancer," in Biomedical Diagnostic, Guidance, and Surgical-Assist Systems IV, T. Vo-Dinh, D. A. Benaron, and W. S. Grundfest, eds., Proc. SPIE 4615, 20-31 (2002).
[CrossRef]

T. Vo-Dinh, M. Panjehpour, B. F. Overholt, C. E. Julius, S. Overholt, and M. N. Phan, "Laser-induced fluorescence for the detection of esophageal and skin cancer," in Advanced Biomedical and Clinical Diagnostic Systems, T. Vo-Dinh, W. S. Grundfest, D. A. Benaron, and G. E. Cohn, eds., Proc. SPIE 4958, 67-70 (2003).
[CrossRef]

Y. P. Sinichkin, S. R. Utz, and H. A. Pilipenko, "Laser-induced fluorescence of the human skin in vivo: influence of the erythema," in Optical Biopsy, R. Cubeddu, S. Svanberg, and H. van den Bergh, eds., Proc. SPIE 2081, 41-47 (1994).
[CrossRef]

Y. P. Sinichkin, S. R. Utz, P. M. Yudin, and H. A. Pilipenko, "Investigation of formation and dynamics of human skin erythema and pigmentation by in vivo fluorescence spectroscopy," in Optical Biopsy and Fluorescence Spectroscopy and Imaging, R. Cubeddu, R. Marchesini, S. R. Mordon, K. Svanberg, H. H. Rinneberg, and G. A. Wagnieres, eds., Proc. SPIE 2324, 259-268 (1995).
[CrossRef]

S. R. Utz, Y. P. Sinichkin, I. V. Meglinski, and H. A. Pilipenko, "Fluorescence spectroscopy in combination with reflectance measurements in human skin examination: what for and how," in Optical Biopsy and Fluorescence Spectroscopy and Imaging, R. Cubeddu, R. Marchesini, S. R. Mordon, K. Svanberg, H. H. Rinneberg, and G. A. Wagnieres, eds., Proc. SPIE 2324, 125-136 (1995).
[CrossRef]

H. Zeng, C. E. MacAulay, B. Palcic, and D. I. McLean, "Laser-induced changes in autofluorescence of in-vivo skin," in Laser-Tissue Interaction IV, S. L. Jacques and A. Katzir, eds., Proc. SPIE 1882, 278-290 (1993).
[CrossRef]

D. Y. Churmakov, I. V. Meglinski, S. A. Piletsky, and D. A. Greenhalgh, "Skin fluorescence model based on the Monte Carlo technique," in Saratov Fall Meeting 2002: Optical Technologies in Biophysics and Medicine IV, V. V. Tuchin, ed., Proc. SPIE 5068, 326-333 (2003).
[CrossRef]

I. V. Meglinski and S. J. Matcher, "Modeling of skin reflectance spectra," in Saratov Fall Meeting 2000: Optical Technologies in Biophysics and Medicine II, V. V. Tuchin, ed., Proc. SPIE 4241, 78-87 (2001).
[CrossRef]

Vib. Spectrosc.

N. Kollias, G. Zonios, and G. N. Stamatas, "Fluorescence spectroscopy of skin," Vib. Spectrosc. 28, 17-23 (2002).
[CrossRef]

Other

H. Zeng and C. MacAulay, "Fluorescence spectroscopy and imaging for skin cancer detection and evaluation," in Handbook of Biomedical Fluorescence (Marcel Dekker, 2003), pp. 315-360.

M. F. Modest, Radiative Heat Transfer (Academic, 2002).

T. J. Farrell and M. S. Patterson, "Diffusion modeling of fluorescence in tissue," in Handbook of Biomedical Fluorescence (Marcel Dekker, 2003), pp. 29-60.

J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Kluwer Academic/Plenum, 1999).

L.-H. Wang andS. L. Jacques, Monte Carlo Modeling of Light Transport in Multi-Layered Tissues in Standard C (University of Texas M. D. Anderson Cancer Center, 1992).

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Figures (7)

Fig. 1
Fig. 1

Excitation light fluence as a function of depth inside skin for λ x = 442 nm for collimated excitation light with and without index-matching cream.

Fig. 2
Fig. 2

Steady-state directional diffuse reflectance of skin at λ x = 442 nm for collimated excitation light with and without index-matching cream.

Fig. 3
Fig. 3

Steady-state directional fluorescence of skin at λ F = 520 nm for collimated excitation light at λ x = 442 nm with and without index-matching cream.

Fig. 4
Fig. 4

Angular distribution of the normalized reflectance and autofluorescence intensities from skin exposed to collimated excitation with an index-matching cream along with the profile of the cosine law.

Fig. 5
Fig. 5

Excitation light fluence distribution as a function of depth inside skin for λ x = 442 nm for diffuse excitation light with and without index-matching cream.

Fig. 6
Fig. 6

Steady-state directional reflectance of skin at λ x = 442 nm for diffuse excitation light with and without index-matching cream.

Fig. 7
Fig. 7

Steady-state directional fluorescence of skin at λ F = 520 nm for diffuse excitation light at λ x = 442 nm with and without index-matching cream.

Tables (2)

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Table 1 Summary of Experimental Studies of Steady-State In Vivo Fluorescence Spectroscopy of Human Skin

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Table 2 Optical Properties Used in the Seven-Layer Skin Model at 442 and 520 nm a

Equations (104)

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442   nm
( 330 400   nm )
( 400 700   nm )
( 280 330   nm )
407   nm
375   nm
330   nm
85 %
75 %
410   nm
350   nm
600   nm
λ x
( 2   mm )
I λ x
λ x
s ^
( s ^ ) I λ x = κ λ x I λ x σ s , λ x I λ x + σ s , λ x 4 π 4 π I λ x ( s ^ i ) Φ λ x ( s ^ i , s ^ ) d Ω i ,
κ λ x
σ s , λ x
Φ λ x ( s ^ i , s ^ )
s ^ i
d Ω
s ^
37 ° C
λ F
( s ^ ) I λ F = κ λ F I λ F σ s , λ F I λ F + σ s , λ F 4 π ×   4 π I λ F ( s ^ i ) Φ λ F ( s ^ i , s ^ ) d Ω i + β λ x G λ x / 4 π .
G λ x
4 π I λ x d Ω
β λ x
λ λ x
κ λ x F
QY λ x
β λ x = κ λ x F QY λ x
Φ λ ( Θ ) = 1 g λ     2 ( 1 + g λ     2 2 g λ cos Θ ) 3 / 2 ,
g λ
s ^ i
s ^
β λ x
520   nm
θ c = arcsin ( 1 / n sc )
n sc
ρ ( θ i ) = 1 2 [ sin 2 ( θ i θ t ) sin 2 ( θ i + θ t ) + tan 2 ( θ i θ t ) tan 2 ( θ i + θ t ) ]   for   θ i θ c ,
ρ ( θ i ) = 1   for   θ i > θ c ,
θ i
θ t
θ t = n sc sin θ i
c = c 0 / n
N z
N θ
N z = 226
N θ = 181
N z = 311
N θ = 181
1 %
G λ x
N z = 226
N θ = 241
2 %
G λ x
10 , 000 W / m 2
G λ x ( z )
λ x = 442   nm
G λ x
5 %
10 %
G λ x
5 %
65   μm
ρ ( 0 ) = ( n sc 1 ) 2 / ( n sc + 1 ) 2 = 3.4 %
442   nm
337 W / m 2   sr
θ = 0 °
λ x = 442   nm
250   μm
100   μm
442   nm
520   nm
442   nm
G λ x
R λ F = 2 π π / 2 π I λ F ( 0 , θ ) cos θ sin θ d θ ,
R λ F
520   nm
106.25 W / m 2
I λ x ( z = 0 , 0 θ π / 2 ) = 10 , 000 / π W / m 2   sr
G λ x ( z )
65 %
G λ x
G λ x
90 %
30 %
λ x = 442   nm
π / 2
π / 2
G λ x
G λ x
38.5 %
61 %
θ = 0 °
442   nm
520   nm
442   nm
g = 0.9
θ = π / 2

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