Abstract
The ability of thermal waves to perform non-destructive depth-profiling studies in materials with spatially variable thermal/thermodynamic properties has been exploited mostly qualitatively so far. The lack of appropriate general theoretical models in the literature has been largely responsible for the near absence of quantitative depth-profiling, especially in media with large thermal property variations within depths on the order of the thermal wavelength. As a result of mathematical difficulties, theoretical treatments have been essentially confined to discrete, multilayered solid structures with constant thermal and thermodynamic properties within each thin layer [1,2]. Furthermore, Afromowitz et al. [3] have applied discrete Laplace transformations to the heat conduction equation to treat the production of the photoacoustic signal in a solid with continuously variable optical absorption coefficient as a function of depth, however, the thermal parameters of the solid were assumed constant. Thomas et al. [4] calculated the Green’s function for the three-dimensional heat conduction equation describing thermal wave propagation in a thermally uniform solid with a subsurface discontinuity (“flaw”). More recently, Jaarinen and co-workers [5,6] used Finite Difference and Inverse methods for thermal wave depth-profiling of samples with spatially variant thermal properties from measurements of the surface temperature distribution. Aamodt and Murphy [7] very recently used vector/matrix methods to calculate thermal wave responses from discretely layered samples. These authors further considered the case of continuously varying thermal properties as the limit of infinitely thin layers.
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References
J. Opsal and A. Rosencwaig, J. Appl. Phys. 53, 4240 (1982).
S.D. Campbell, S.S. Yee, and M.A. Afromowitz, IEEE Trans. Biomed. Engn. BME-26, 220 (1979).
M.A. Afromowitz, S.P. Yeh, and S.S. Yee, J. Appl. Phys. 48, 209 (1977).
R.L. Thomas, JJ. Pouch, Y.H. Wong, L.D. Favro, P.K. Kuo, and A. Rosencwaig, J. Appl. Phys. 51, 1152 (1980).
J. Jaarinen and M. Luukkala, J. Phys. (Paris) 44, C6 - 503 (1983).
H.J. Vidberg, J. Jaarinen and D.O. Riska, in “Inverse Determination of the Thermal Conductivity Profile in Steel from the Thermal Wave Surface Data” Res. Inst. Theor. Phys. Univ. Helsinki, Preprint # HU-TFT-85-38 (1985).
L.C. Aamodt and J.C. Murphy, J. Appl. Phys. (in press).
A. Mandelis, J. Math. Phys. 26, 2676 (1985).
H. Goldstein, in “Classical Mechanics”, Addison-Wesley, Reading, MA, (1965).
A. Rosencwaig and A. Gersho, J. Appl. Phys. 47, 64 (1976).
D. Marcuse, in “Light Transmission Optics”, Van Nostrand, New York (1982).
A. Burt, Proc. IEEE Ultrasonics Symp. 815 (1981).
A. Burt, J. Phys. (Paris) 44, C6 - 453 (1983).
A. Burt, Proc. 4th Intern’l Topical Meeting on Photoacoustic, Thermal and Related Sciences Tech. Digest MA10 (1985).
C.A. Bennett and R.R. Patty, Appl. Opt. 21, 49 (1982).
A. Mandelis, E. Siu, and S. Ho, Appl. Phys. A33 153 (1984).
J. Opsal, A. Rosencwaig, and D.L. Willenborg, Appl. Opt. 22, 3169 (1983).
E.T. Whittaker and G.N. Watson, in “A Course of Modern Analysis”, Cambridge Univ. Press, Cambridge (1963).
P. Morse and H. Feshbach, in “Methods of Theoretical Physics”, McGraw-Hill, New York (1953).
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Mandelis, A. (1987). Classical and Quantum Mechanical Aspects of Thermal Wave Physics. In: Thompson, D.O., Chimenti, D.E. (eds) Review of Progress in Quantitative Nondestructive Evaluation. Review of Progress in Quantitative Nondestructive Evaluation, vol 6 A. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1893-4_26
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DOI: https://doi.org/10.1007/978-1-4613-1893-4_26
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