Abstract

We report on the application of pulsed photothermal radiometry (PPTR) to determine the depth of in-vitro and in-vivo subsurface chromophores in biological materials. Measurements provided by PPTR in combination with a nonnegative constrained conjugate-gradient algorithm are used to determine the initial temperature distribution in a biological material immediately following pulsed laser irradiation. Within the experimental error, chromophore depths (50–450 μm) in 55 in-vitro collagen phantoms determined by PPTR and optical low-coherence reflectometry are equivalent. The depths of port-wine-stain blood vessels determined by PPTR correlate very well with their locations found by computer-assisted microscopic observation of histologic sections. The mean blood-vessel depth deduced from PPTR and histologic observation is statistically indistinguishable (p > 0.94).

© 1996 Optical Society of America

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  1. J. A. Bauer, Th. Sauer, “Cutaneous 10-MHz ultrasound B scan allows the quantitative assessment of burn depth,” Burns Therm. Injury 15, 49–51 (1989).
    [CrossRef]
  2. J. M. Schmitt, A. Knuttel, R. F. Bonner, “Measurement of optical properties of biological tissues by low-coherence reflectometry,” Appl. Opt. 32, 6032–6042 (1993).
    [CrossRef] [PubMed]
  3. M. Rajadhyaksha, M. Grossman, D. Esterowitz, R. H. Webb, R. R. Anderson, “In vivo confocal scanning laser microscopy of human skin: melanin provides strong contrast,” J. Invest. Dermatol. 104, 946–952 (1995).
    [CrossRef] [PubMed]
  4. H.-A. Crostack, W. Jahnel, E. H. Meyer, K.-J. Pohl, “Recent developments in non-destructive testing of coated components,” Thin Solid Films 181, 295–304 (1989).
    [CrossRef]
  5. D. J. Crowther, L. D. Favro, P. K. Kuo, R. L. Thomas, “Inverse scattering algorithm applied to infrared thermal wave images,” J. Appl. Phys. 74, 5828–5835 (1993).
    [CrossRef]
  6. F. H. Long, T. F. Deutsch, “Pulsed photothermal radiometry of human artery,” IEEE J. Quantum Electron. 23, 1821–1826 (1987).
    [CrossRef]
  7. F. H. Long, N. S. Nishioka, T. F. Deutsch, “Measurement of the optical and thermal properties of biliary calculi using pulsed photothermal radiometry,” Lasers Surg. Med. 7, 461– 466 (1987).
    [CrossRef] [PubMed]
  8. S. L. Jacques, J. S. Nelson, W. H. Wright, T. E. Milner, “Pulsed photothermal radiometry of port-wine-stain lesions,” Appl. Opt. 32, 2439–2446 (1993).
    [CrossRef] [PubMed]
  9. R. R. Anderson, H. Beck, U. Bruggeman, W. Farinelli, S. L. Jacques, J. A. Parish, “Pulsed photothermal radiometry in turbid media: internal reflection of backscattered radiation strongly influences optical dosimetry,” Appl. Opt. 28, 2256–2262 (1989).
    [CrossRef] [PubMed]
  10. S. A. Prahl, I. A. Vitkin, U. Bruggemann, B. C. Wilson, R. R. Anderson, “Determination of optical properties of turbid media using pulsed photothermal radiometry,” Phys. Med. Biol. 37, 1203–1217 (1992).
    [CrossRef] [PubMed]
  11. I. A. Vitkin, B. C. Wilson, R. R. Anderson, S. A. Prahl, “Pulsed photothermal radiometry in optically transparent media containing discrete optical absorbers,” Phys. Med. Biol. 39, 1721–1744 (1994).
    [CrossRef] [PubMed]
  12. T. E. Milner, D. M. Goodman, B. S. Tanenbaum, J. S. Nelson, “Depth profiling of laser-heated chromophores in biological tissues by pulsed photothermal radiometry,” J. Opt. Soc. Am. A 12, 1479–1488 (1995).
    [CrossRef]
  13. W. J. Cody, “Rational Chebyshev approximations for the error function,” Math. Comput. 23, 631–638 (1969).
    [CrossRef]
  14. C. W. Groetsch, The Theory of Tichonov Regularization for Fredholm Equations of the First Kind (Pitman, New York, 1984).
  15. D. M. Goodman, E. M. Johansson, T. W. Lawrence, “On applying the conjugate-gradient algorithm to image processing problems,” in Multivariate Analysis: Future Directions, C. R. Rao, ed. (North-Holland, Amsterdam, 1993).
  16. I. E. Frank, J. H. Friedman, “A statistical view of some chemometrics regression tools,” Technometrics 35, 109–148 (1993).
    [CrossRef]
  17. M. Stone, R. J. Brooks, “Continuum regression: cross-validated sequentially constructed prediction embracing ordinary least squares, partial least squares, and principal components regression,” J. R. Stat. Soc. B 52, 237–269 (1990).
  18. A. Björck, “A bidiagonalization algorithm for solving large and sparse ill-posed systems of linear equations,” BIT 28, 658–670 (1988).
  19. P. C. Hansen, D. P. O'Leary, “The use of the L-curve in the regularization of discrete ill-posed problems,” SIAM J. Sci. Comput. 14, 1487–1503 (1993).
    [CrossRef]
  20. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafato, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
    [CrossRef] [PubMed]
  21. X. Clivaz, F. Marquis-Weible, R. P. Salathé, R. P. Novàk, H. H. Gilgen, “High-resolution reflectometry in biological tissues,” Opt. Lett. 17, 4–6 (1992).
    [CrossRef] [PubMed]
  22. X. J. Wang, T. E. Milner, R. P. Dhond, W. V. Sorin, S. A. Newton, J. S. Nelson, “Characterization of human scalp hairs by optical low-coherence reflectometry,” Opt. Lett. 20, 524–526 (1995).
    [CrossRef] [PubMed]
  23. F. A. Duck, Physical Properties of Tissue: A Comprehensive Reference Book (Academic, London, 1990).
  24. D. M. Wieliczka, S. Weng, M. R. Querry, “Wedge shaped cell for highly absorbant liquids: infrared optical constants of water,” App. Opt. 28, 1714–1719 (1989).
    [CrossRef]
  25. G. M. Hale, M. R. Querry, “Optical constants of water in the 200-nm to 200-μm wavelength region,” App. Opt. 12, 555–563 (1973).
    [CrossRef]
  26. B. B. Doyle, E. R. Blout, “Infrared spectroscopy of collagen and collagen-like peptides,” Biopolymers 14, 937–957 (1975).
    [CrossRef] [PubMed]
  27. F. P. Incropera, D. P. DeWitt, Fundamentals of Heat Transfer (Wiley, New York, 1985), p. 8.
  28. X. J. Wang, T. E. Milner, M. C. Chang, J. S. Nelson, “Group refractive index measurement of dry and hydrated collagen films using optical low-coherence reflectometry,” J. Bio. Opt. 1, 212–216 (1996).
    [CrossRef]
  29. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1988).
  30. D. J. Smithies, P. H. Butler, “Modeling the distribution of laser light in port-wine stains with the Monte Carlo method,” Phys. Med. Bio. 40, 701–731 (1995).
    [CrossRef]
  31. X. J. Wang, T. E. Milner, J. S. Nelson, “Characterization of fluid flow velocity by optical Doppler tomography,” Opt. Lett. 20, 1337–1339 (1995).
    [CrossRef] [PubMed]

1996

X. J. Wang, T. E. Milner, M. C. Chang, J. S. Nelson, “Group refractive index measurement of dry and hydrated collagen films using optical low-coherence reflectometry,” J. Bio. Opt. 1, 212–216 (1996).
[CrossRef]

1995

1994

I. A. Vitkin, B. C. Wilson, R. R. Anderson, S. A. Prahl, “Pulsed photothermal radiometry in optically transparent media containing discrete optical absorbers,” Phys. Med. Biol. 39, 1721–1744 (1994).
[CrossRef] [PubMed]

1993

D. J. Crowther, L. D. Favro, P. K. Kuo, R. L. Thomas, “Inverse scattering algorithm applied to infrared thermal wave images,” J. Appl. Phys. 74, 5828–5835 (1993).
[CrossRef]

I. E. Frank, J. H. Friedman, “A statistical view of some chemometrics regression tools,” Technometrics 35, 109–148 (1993).
[CrossRef]

P. C. Hansen, D. P. O'Leary, “The use of the L-curve in the regularization of discrete ill-posed problems,” SIAM J. Sci. Comput. 14, 1487–1503 (1993).
[CrossRef]

S. L. Jacques, J. S. Nelson, W. H. Wright, T. E. Milner, “Pulsed photothermal radiometry of port-wine-stain lesions,” Appl. Opt. 32, 2439–2446 (1993).
[CrossRef] [PubMed]

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

1992

X. Clivaz, F. Marquis-Weible, R. P. Salathé, R. P. Novàk, H. H. Gilgen, “High-resolution reflectometry in biological tissues,” Opt. Lett. 17, 4–6 (1992).
[CrossRef] [PubMed]

S. A. Prahl, I. A. Vitkin, U. Bruggemann, B. C. Wilson, R. R. Anderson, “Determination of optical properties of turbid media using pulsed photothermal radiometry,” Phys. Med. Biol. 37, 1203–1217 (1992).
[CrossRef] [PubMed]

1991

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafato, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

1990

M. Stone, R. J. Brooks, “Continuum regression: cross-validated sequentially constructed prediction embracing ordinary least squares, partial least squares, and principal components regression,” J. R. Stat. Soc. B 52, 237–269 (1990).

1989

R. R. Anderson, H. Beck, U. Bruggeman, W. Farinelli, S. L. Jacques, J. A. Parish, “Pulsed photothermal radiometry in turbid media: internal reflection of backscattered radiation strongly influences optical dosimetry,” Appl. Opt. 28, 2256–2262 (1989).
[CrossRef] [PubMed]

D. M. Wieliczka, S. Weng, M. R. Querry, “Wedge shaped cell for highly absorbant liquids: infrared optical constants of water,” App. Opt. 28, 1714–1719 (1989).
[CrossRef]

J. A. Bauer, Th. Sauer, “Cutaneous 10-MHz ultrasound B scan allows the quantitative assessment of burn depth,” Burns Therm. Injury 15, 49–51 (1989).
[CrossRef]

H.-A. Crostack, W. Jahnel, E. H. Meyer, K.-J. Pohl, “Recent developments in non-destructive testing of coated components,” Thin Solid Films 181, 295–304 (1989).
[CrossRef]

1988

A. Björck, “A bidiagonalization algorithm for solving large and sparse ill-posed systems of linear equations,” BIT 28, 658–670 (1988).

1987

F. H. Long, T. F. Deutsch, “Pulsed photothermal radiometry of human artery,” IEEE J. Quantum Electron. 23, 1821–1826 (1987).
[CrossRef]

F. H. Long, N. S. Nishioka, T. F. Deutsch, “Measurement of the optical and thermal properties of biliary calculi using pulsed photothermal radiometry,” Lasers Surg. Med. 7, 461– 466 (1987).
[CrossRef] [PubMed]

1975

B. B. Doyle, E. R. Blout, “Infrared spectroscopy of collagen and collagen-like peptides,” Biopolymers 14, 937–957 (1975).
[CrossRef] [PubMed]

1973

G. M. Hale, M. R. Querry, “Optical constants of water in the 200-nm to 200-μm wavelength region,” App. Opt. 12, 555–563 (1973).
[CrossRef]

1969

W. J. Cody, “Rational Chebyshev approximations for the error function,” Math. Comput. 23, 631–638 (1969).
[CrossRef]

Anderson, R. R.

M. Rajadhyaksha, M. Grossman, D. Esterowitz, R. H. Webb, R. R. Anderson, “In vivo confocal scanning laser microscopy of human skin: melanin provides strong contrast,” J. Invest. Dermatol. 104, 946–952 (1995).
[CrossRef] [PubMed]

I. A. Vitkin, B. C. Wilson, R. R. Anderson, S. A. Prahl, “Pulsed photothermal radiometry in optically transparent media containing discrete optical absorbers,” Phys. Med. Biol. 39, 1721–1744 (1994).
[CrossRef] [PubMed]

S. A. Prahl, I. A. Vitkin, U. Bruggemann, B. C. Wilson, R. R. Anderson, “Determination of optical properties of turbid media using pulsed photothermal radiometry,” Phys. Med. Biol. 37, 1203–1217 (1992).
[CrossRef] [PubMed]

R. R. Anderson, H. Beck, U. Bruggeman, W. Farinelli, S. L. Jacques, J. A. Parish, “Pulsed photothermal radiometry in turbid media: internal reflection of backscattered radiation strongly influences optical dosimetry,” Appl. Opt. 28, 2256–2262 (1989).
[CrossRef] [PubMed]

Bauer, J. A.

J. A. Bauer, Th. Sauer, “Cutaneous 10-MHz ultrasound B scan allows the quantitative assessment of burn depth,” Burns Therm. Injury 15, 49–51 (1989).
[CrossRef]

Beck, H.

Björck, A.

A. Björck, “A bidiagonalization algorithm for solving large and sparse ill-posed systems of linear equations,” BIT 28, 658–670 (1988).

Blout, E. R.

B. B. Doyle, E. R. Blout, “Infrared spectroscopy of collagen and collagen-like peptides,” Biopolymers 14, 937–957 (1975).
[CrossRef] [PubMed]

Bonner, R. F.

Brooks, R. J.

M. Stone, R. J. Brooks, “Continuum regression: cross-validated sequentially constructed prediction embracing ordinary least squares, partial least squares, and principal components regression,” J. R. Stat. Soc. B 52, 237–269 (1990).

Bruggeman, U.

Bruggemann, U.

S. A. Prahl, I. A. Vitkin, U. Bruggemann, B. C. Wilson, R. R. Anderson, “Determination of optical properties of turbid media using pulsed photothermal radiometry,” Phys. Med. Biol. 37, 1203–1217 (1992).
[CrossRef] [PubMed]

Butler, P. H.

D. J. Smithies, P. H. Butler, “Modeling the distribution of laser light in port-wine stains with the Monte Carlo method,” Phys. Med. Bio. 40, 701–731 (1995).
[CrossRef]

Chang, M. C.

X. J. Wang, T. E. Milner, M. C. Chang, J. S. Nelson, “Group refractive index measurement of dry and hydrated collagen films using optical low-coherence reflectometry,” J. Bio. Opt. 1, 212–216 (1996).
[CrossRef]

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafato, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Clivaz, X.

Cody, W. J.

W. J. Cody, “Rational Chebyshev approximations for the error function,” Math. Comput. 23, 631–638 (1969).
[CrossRef]

Crostack, H.-A.

H.-A. Crostack, W. Jahnel, E. H. Meyer, K.-J. Pohl, “Recent developments in non-destructive testing of coated components,” Thin Solid Films 181, 295–304 (1989).
[CrossRef]

Crowther, D. J.

D. J. Crowther, L. D. Favro, P. K. Kuo, R. L. Thomas, “Inverse scattering algorithm applied to infrared thermal wave images,” J. Appl. Phys. 74, 5828–5835 (1993).
[CrossRef]

Deutsch, T. F.

F. H. Long, N. S. Nishioka, T. F. Deutsch, “Measurement of the optical and thermal properties of biliary calculi using pulsed photothermal radiometry,” Lasers Surg. Med. 7, 461– 466 (1987).
[CrossRef] [PubMed]

F. H. Long, T. F. Deutsch, “Pulsed photothermal radiometry of human artery,” IEEE J. Quantum Electron. 23, 1821–1826 (1987).
[CrossRef]

DeWitt, D. P.

F. P. Incropera, D. P. DeWitt, Fundamentals of Heat Transfer (Wiley, New York, 1985), p. 8.

Dhond, R. P.

Doyle, B. B.

B. B. Doyle, E. R. Blout, “Infrared spectroscopy of collagen and collagen-like peptides,” Biopolymers 14, 937–957 (1975).
[CrossRef] [PubMed]

Duck, F. A.

F. A. Duck, Physical Properties of Tissue: A Comprehensive Reference Book (Academic, London, 1990).

Esterowitz, D.

M. Rajadhyaksha, M. Grossman, D. Esterowitz, R. H. Webb, R. R. Anderson, “In vivo confocal scanning laser microscopy of human skin: melanin provides strong contrast,” J. Invest. Dermatol. 104, 946–952 (1995).
[CrossRef] [PubMed]

Farinelli, W.

Favro, L. D.

D. J. Crowther, L. D. Favro, P. K. Kuo, R. L. Thomas, “Inverse scattering algorithm applied to infrared thermal wave images,” J. Appl. Phys. 74, 5828–5835 (1993).
[CrossRef]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1988).

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafato, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Frank, I. E.

I. E. Frank, J. H. Friedman, “A statistical view of some chemometrics regression tools,” Technometrics 35, 109–148 (1993).
[CrossRef]

Friedman, J. H.

I. E. Frank, J. H. Friedman, “A statistical view of some chemometrics regression tools,” Technometrics 35, 109–148 (1993).
[CrossRef]

Fujimoto, J. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafato, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Gilgen, H. H.

Goodman, D. M.

T. E. Milner, D. M. Goodman, B. S. Tanenbaum, J. S. Nelson, “Depth profiling of laser-heated chromophores in biological tissues by pulsed photothermal radiometry,” J. Opt. Soc. Am. A 12, 1479–1488 (1995).
[CrossRef]

D. M. Goodman, E. M. Johansson, T. W. Lawrence, “On applying the conjugate-gradient algorithm to image processing problems,” in Multivariate Analysis: Future Directions, C. R. Rao, ed. (North-Holland, Amsterdam, 1993).

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafato, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Groetsch, C. W.

C. W. Groetsch, The Theory of Tichonov Regularization for Fredholm Equations of the First Kind (Pitman, New York, 1984).

Grossman, M.

M. Rajadhyaksha, M. Grossman, D. Esterowitz, R. H. Webb, R. R. Anderson, “In vivo confocal scanning laser microscopy of human skin: melanin provides strong contrast,” J. Invest. Dermatol. 104, 946–952 (1995).
[CrossRef] [PubMed]

Hale, G. M.

G. M. Hale, M. R. Querry, “Optical constants of water in the 200-nm to 200-μm wavelength region,” App. Opt. 12, 555–563 (1973).
[CrossRef]

Hansen, P. C.

P. C. Hansen, D. P. O'Leary, “The use of the L-curve in the regularization of discrete ill-posed problems,” SIAM J. Sci. Comput. 14, 1487–1503 (1993).
[CrossRef]

Hee, M. R.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafato, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafato, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Incropera, F. P.

F. P. Incropera, D. P. DeWitt, Fundamentals of Heat Transfer (Wiley, New York, 1985), p. 8.

Jacques, S. L.

Jahnel, W.

H.-A. Crostack, W. Jahnel, E. H. Meyer, K.-J. Pohl, “Recent developments in non-destructive testing of coated components,” Thin Solid Films 181, 295–304 (1989).
[CrossRef]

Johansson, E. M.

D. M. Goodman, E. M. Johansson, T. W. Lawrence, “On applying the conjugate-gradient algorithm to image processing problems,” in Multivariate Analysis: Future Directions, C. R. Rao, ed. (North-Holland, Amsterdam, 1993).

Knuttel, A.

Kuo, P. K.

D. J. Crowther, L. D. Favro, P. K. Kuo, R. L. Thomas, “Inverse scattering algorithm applied to infrared thermal wave images,” J. Appl. Phys. 74, 5828–5835 (1993).
[CrossRef]

Lawrence, T. W.

D. M. Goodman, E. M. Johansson, T. W. Lawrence, “On applying the conjugate-gradient algorithm to image processing problems,” in Multivariate Analysis: Future Directions, C. R. Rao, ed. (North-Holland, Amsterdam, 1993).

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafato, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Long, F. H.

F. H. Long, N. S. Nishioka, T. F. Deutsch, “Measurement of the optical and thermal properties of biliary calculi using pulsed photothermal radiometry,” Lasers Surg. Med. 7, 461– 466 (1987).
[CrossRef] [PubMed]

F. H. Long, T. F. Deutsch, “Pulsed photothermal radiometry of human artery,” IEEE J. Quantum Electron. 23, 1821–1826 (1987).
[CrossRef]

Marquis-Weible, F.

Meyer, E. H.

H.-A. Crostack, W. Jahnel, E. H. Meyer, K.-J. Pohl, “Recent developments in non-destructive testing of coated components,” Thin Solid Films 181, 295–304 (1989).
[CrossRef]

Milner, T. E.

Nelson, J. S.

Newton, S. A.

Nishioka, N. S.

F. H. Long, N. S. Nishioka, T. F. Deutsch, “Measurement of the optical and thermal properties of biliary calculi using pulsed photothermal radiometry,” Lasers Surg. Med. 7, 461– 466 (1987).
[CrossRef] [PubMed]

Novàk, R. P.

O'Leary, D. P.

P. C. Hansen, D. P. O'Leary, “The use of the L-curve in the regularization of discrete ill-posed problems,” SIAM J. Sci. Comput. 14, 1487–1503 (1993).
[CrossRef]

Parish, J. A.

Pohl, K.-J.

H.-A. Crostack, W. Jahnel, E. H. Meyer, K.-J. Pohl, “Recent developments in non-destructive testing of coated components,” Thin Solid Films 181, 295–304 (1989).
[CrossRef]

Prahl, S. A.

I. A. Vitkin, B. C. Wilson, R. R. Anderson, S. A. Prahl, “Pulsed photothermal radiometry in optically transparent media containing discrete optical absorbers,” Phys. Med. Biol. 39, 1721–1744 (1994).
[CrossRef] [PubMed]

S. A. Prahl, I. A. Vitkin, U. Bruggemann, B. C. Wilson, R. R. Anderson, “Determination of optical properties of turbid media using pulsed photothermal radiometry,” Phys. Med. Biol. 37, 1203–1217 (1992).
[CrossRef] [PubMed]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1988).

Puliafato, C.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafato, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Querry, M. R.

D. M. Wieliczka, S. Weng, M. R. Querry, “Wedge shaped cell for highly absorbant liquids: infrared optical constants of water,” App. Opt. 28, 1714–1719 (1989).
[CrossRef]

G. M. Hale, M. R. Querry, “Optical constants of water in the 200-nm to 200-μm wavelength region,” App. Opt. 12, 555–563 (1973).
[CrossRef]

Rajadhyaksha, M.

M. Rajadhyaksha, M. Grossman, D. Esterowitz, R. H. Webb, R. R. Anderson, “In vivo confocal scanning laser microscopy of human skin: melanin provides strong contrast,” J. Invest. Dermatol. 104, 946–952 (1995).
[CrossRef] [PubMed]

Salathé, R. P.

Sauer, Th.

J. A. Bauer, Th. Sauer, “Cutaneous 10-MHz ultrasound B scan allows the quantitative assessment of burn depth,” Burns Therm. Injury 15, 49–51 (1989).
[CrossRef]

Schmitt, J. M.

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafato, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Smithies, D. J.

D. J. Smithies, P. H. Butler, “Modeling the distribution of laser light in port-wine stains with the Monte Carlo method,” Phys. Med. Bio. 40, 701–731 (1995).
[CrossRef]

Sorin, W. V.

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafato, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Stone, M.

M. Stone, R. J. Brooks, “Continuum regression: cross-validated sequentially constructed prediction embracing ordinary least squares, partial least squares, and principal components regression,” J. R. Stat. Soc. B 52, 237–269 (1990).

Swanson, E. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafato, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Tanenbaum, B. S.

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1988).

Thomas, R. L.

D. J. Crowther, L. D. Favro, P. K. Kuo, R. L. Thomas, “Inverse scattering algorithm applied to infrared thermal wave images,” J. Appl. Phys. 74, 5828–5835 (1993).
[CrossRef]

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1988).

Vitkin, I. A.

I. A. Vitkin, B. C. Wilson, R. R. Anderson, S. A. Prahl, “Pulsed photothermal radiometry in optically transparent media containing discrete optical absorbers,” Phys. Med. Biol. 39, 1721–1744 (1994).
[CrossRef] [PubMed]

S. A. Prahl, I. A. Vitkin, U. Bruggemann, B. C. Wilson, R. R. Anderson, “Determination of optical properties of turbid media using pulsed photothermal radiometry,” Phys. Med. Biol. 37, 1203–1217 (1992).
[CrossRef] [PubMed]

Wang, X. J.

Webb, R. H.

M. Rajadhyaksha, M. Grossman, D. Esterowitz, R. H. Webb, R. R. Anderson, “In vivo confocal scanning laser microscopy of human skin: melanin provides strong contrast,” J. Invest. Dermatol. 104, 946–952 (1995).
[CrossRef] [PubMed]

Weng, S.

D. M. Wieliczka, S. Weng, M. R. Querry, “Wedge shaped cell for highly absorbant liquids: infrared optical constants of water,” App. Opt. 28, 1714–1719 (1989).
[CrossRef]

Wieliczka, D. M.

D. M. Wieliczka, S. Weng, M. R. Querry, “Wedge shaped cell for highly absorbant liquids: infrared optical constants of water,” App. Opt. 28, 1714–1719 (1989).
[CrossRef]

Wilson, B. C.

I. A. Vitkin, B. C. Wilson, R. R. Anderson, S. A. Prahl, “Pulsed photothermal radiometry in optically transparent media containing discrete optical absorbers,” Phys. Med. Biol. 39, 1721–1744 (1994).
[CrossRef] [PubMed]

S. A. Prahl, I. A. Vitkin, U. Bruggemann, B. C. Wilson, R. R. Anderson, “Determination of optical properties of turbid media using pulsed photothermal radiometry,” Phys. Med. Biol. 37, 1203–1217 (1992).
[CrossRef] [PubMed]

Wright, W. H.

App. Opt.

D. M. Wieliczka, S. Weng, M. R. Querry, “Wedge shaped cell for highly absorbant liquids: infrared optical constants of water,” App. Opt. 28, 1714–1719 (1989).
[CrossRef]

G. M. Hale, M. R. Querry, “Optical constants of water in the 200-nm to 200-μm wavelength region,” App. Opt. 12, 555–563 (1973).
[CrossRef]

Appl. Opt.

Biopolymers

B. B. Doyle, E. R. Blout, “Infrared spectroscopy of collagen and collagen-like peptides,” Biopolymers 14, 937–957 (1975).
[CrossRef] [PubMed]

BIT

A. Björck, “A bidiagonalization algorithm for solving large and sparse ill-posed systems of linear equations,” BIT 28, 658–670 (1988).

Burns Therm. Injury

J. A. Bauer, Th. Sauer, “Cutaneous 10-MHz ultrasound B scan allows the quantitative assessment of burn depth,” Burns Therm. Injury 15, 49–51 (1989).
[CrossRef]

IEEE J. Quantum Electron.

F. H. Long, T. F. Deutsch, “Pulsed photothermal radiometry of human artery,” IEEE J. Quantum Electron. 23, 1821–1826 (1987).
[CrossRef]

J. Appl. Phys.

D. J. Crowther, L. D. Favro, P. K. Kuo, R. L. Thomas, “Inverse scattering algorithm applied to infrared thermal wave images,” J. Appl. Phys. 74, 5828–5835 (1993).
[CrossRef]

J. Bio. Opt.

X. J. Wang, T. E. Milner, M. C. Chang, J. S. Nelson, “Group refractive index measurement of dry and hydrated collagen films using optical low-coherence reflectometry,” J. Bio. Opt. 1, 212–216 (1996).
[CrossRef]

J. Invest. Dermatol.

M. Rajadhyaksha, M. Grossman, D. Esterowitz, R. H. Webb, R. R. Anderson, “In vivo confocal scanning laser microscopy of human skin: melanin provides strong contrast,” J. Invest. Dermatol. 104, 946–952 (1995).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

J. R. Stat. Soc. B

M. Stone, R. J. Brooks, “Continuum regression: cross-validated sequentially constructed prediction embracing ordinary least squares, partial least squares, and principal components regression,” J. R. Stat. Soc. B 52, 237–269 (1990).

Lasers Surg. Med.

F. H. Long, N. S. Nishioka, T. F. Deutsch, “Measurement of the optical and thermal properties of biliary calculi using pulsed photothermal radiometry,” Lasers Surg. Med. 7, 461– 466 (1987).
[CrossRef] [PubMed]

Math. Comput.

W. J. Cody, “Rational Chebyshev approximations for the error function,” Math. Comput. 23, 631–638 (1969).
[CrossRef]

Opt. Lett.

Phys. Med. Bio.

D. J. Smithies, P. H. Butler, “Modeling the distribution of laser light in port-wine stains with the Monte Carlo method,” Phys. Med. Bio. 40, 701–731 (1995).
[CrossRef]

Phys. Med. Biol.

S. A. Prahl, I. A. Vitkin, U. Bruggemann, B. C. Wilson, R. R. Anderson, “Determination of optical properties of turbid media using pulsed photothermal radiometry,” Phys. Med. Biol. 37, 1203–1217 (1992).
[CrossRef] [PubMed]

I. A. Vitkin, B. C. Wilson, R. R. Anderson, S. A. Prahl, “Pulsed photothermal radiometry in optically transparent media containing discrete optical absorbers,” Phys. Med. Biol. 39, 1721–1744 (1994).
[CrossRef] [PubMed]

Science

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. Puliafato, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

SIAM J. Sci. Comput.

P. C. Hansen, D. P. O'Leary, “The use of the L-curve in the regularization of discrete ill-posed problems,” SIAM J. Sci. Comput. 14, 1487–1503 (1993).
[CrossRef]

Technometrics

I. E. Frank, J. H. Friedman, “A statistical view of some chemometrics regression tools,” Technometrics 35, 109–148 (1993).
[CrossRef]

Thin Solid Films

H.-A. Crostack, W. Jahnel, E. H. Meyer, K.-J. Pohl, “Recent developments in non-destructive testing of coated components,” Thin Solid Films 181, 295–304 (1989).
[CrossRef]

Other

C. W. Groetsch, The Theory of Tichonov Regularization for Fredholm Equations of the First Kind (Pitman, New York, 1984).

D. M. Goodman, E. M. Johansson, T. W. Lawrence, “On applying the conjugate-gradient algorithm to image processing problems,” in Multivariate Analysis: Future Directions, C. R. Rao, ed. (North-Holland, Amsterdam, 1993).

F. P. Incropera, D. P. DeWitt, Fundamentals of Heat Transfer (Wiley, New York, 1985), p. 8.

F. A. Duck, Physical Properties of Tissue: A Comprehensive Reference Book (Academic, London, 1990).

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1988).

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Figures (6)

Fig. 1
Fig. 1

Three-dimensional phantom geometry approximated as a one-dimensional model with the initial temperature distribution ΔT(z, t = 0). The oval shaded region represents the laser-irradiation spot.

Fig. 2
Fig. 2

Schematic of the apparatus used to record PPTR signals in experiments involving phantoms.

Fig. 3
Fig. 3

Representative signals from an in-vitro collagen phantom: (a) PPTR signal amplitude ΔS(t), and (b) computed initial temperature distribution ΔT(z, t = 0), with zc = 0.33 mm.

Fig. 4
Fig. 4

Depth of the upper surface (zc ) of a stained collagen film deduced from the inversion of the PPTR signal and the OLCR measurement: The solid line represents the case of PPTRzc = OLCRzc ; the center-dot circles represent individual data points.

Fig. 5
Fig. 5

Representative signals from three skin types exposed to equivalent laser irradiance: solid curves, type I skin; dashed curves, type II skin; short-dash–long-dash curves, type III skin. The plots show the (a) PPTR signal amplitude ΔS(t), and (b) computed initial temperature distribution ΔT(z, t = 0).

Fig. 6
Fig. 6

Hemoglobin distribution (hi , bars) deduced from microscopic observation of histologic sections and the corresponding initial temperature distribution [ΔT(z, t = 0), solid line] in a type I skin site.

Equations (9)

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Δ S ( t ) = z Δ T ( z , t = 0 ) K ( z , t ) d z + n ( t ) , K ( z , t ) = μ ir 2 exp ( z 2 / 4 D t ) × { erfcx ( u + ) + erfcx ( u ) 2 h / κ h / κ μ ir × [ erfcx ( u + ) erfcx ( u 1 ) ] } .
u ± = μ ir D t ± z / 2 D t , u 1 = h κ D t + z / D t ,
f ( Δ T , Λ ) = min { K Δ T Δ S 2 + Λ Δ T 2 } .
z c = min { z : Δ T ( z , t = 0 ) = 0.85 Δ T max } ,
x c = x min + x max 2 , z c = z min + z max 2 .
Δ T ( z , t = 0 ) = Δ T m ( z , t = 0 ) + Δ T b ( z , t = 0 ) .
b i = z i Δ / 2 z i + Δ / 2 Δ T b ( z , t = 0 ) d z z 1 Δ / 2 z 20 + Δ / 2 Δ T b ( z , t = 0 ) d z .
z h = i = 1 i = 20 z i h i , z b = i = 1 i = 20 z i b i .
σ = [ i = 1 20 ( h i b i ) 2 20 ] 1 / 2 .

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