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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 41, Iss. 6 — Feb. 20, 2002
  • pp: 1128–1144

Mathematical Formulations for the Schlieren Detection Method Applied to the Measurement of Photodeformation

Alain Cournoyer, Pierre Baulaigue, Jacques Bures, Lionel Bertrand, and Roland Occelli  »View Author Affiliations


Applied Optics, Vol. 41, Issue 6, pp. 1128-1144 (2002)
http://dx.doi.org/10.1364/AO.41.001128


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Abstract

In a schlieren detection scheme for photodeformation measurements, the divergence of the probe beam that is induced by the axisymmetric but radially inhomogeneous periodic photothermal displacement of the surface of a sample is transformed into an intensity variation by insertion of an iris in front of the detection photodiode. We present three expressions for the intensity profile of a Gaussian laser beam that is reflected by the inhomogeneous photodeformation of a solid. The first expression proceeds from geometrical optics (or photometry), whereas the second one derives from the use of the well-known ABCD law and the third one from diffraction principles. Comparing these formulations of the schlieren signal with their behavior as a function of different geometrical parameters, we obtain the domain of validity of each expression, and we deduce the advantages of the different formalisms.

© 2002 Optical Society of America

OCIS Codes
(260.1960) Physical optics : Diffraction theory
(350.5340) Other areas of optics : Photothermal effects

Citation
Alain Cournoyer, Pierre Baulaigue, Jacques Bures, Lionel Bertrand, and Roland Occelli, "Mathematical Formulations for the Schlieren Detection Method Applied to the Measurement of Photodeformation," Appl. Opt. 41, 1128-1144 (2002)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-41-6-1128


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References

  1. J. G. Choi and G. J. Diebold, “Laser schlieren microphone for optoacoustic spectroscopy,”Appl. Opt. 21, 4087–4091 (1982).
  2. H. Saito, M. Irikura, M. Haraguchi, and M. Fukui, “New type of photothermal spectroscopic technique,”Appl. Opt. 31, 2047–2054 (1992).
  3. R. Vyas and R. Gupta, “Photothermal lensing spectroscopy in a flowing medium: theory,”Appl. Opt. 27, 4701–4711 (1988).
  4. J. F. Power, “Pulsed mode thermal lens effect detection in the near field via thermally induced probe bean spatial phase modulation: a theory,”Appl. Opt. 29, 52–63 (1990).
  5. L. C. M. Miranda, “Photodisplacement spectroscopy of solids: theory,”Appl. Opt. 22, 2882–2886 (1983).
  6. N. M. Amer, “New approaches to photothermal spectroscopy,”J. Phys. (Paris) Colloq. 44, 185–190 (1983).
  7. N. M. Amer, M. A. Olmstead, D. Fournier, and A. C. Boccara, “Photothermal displacement spectroscopy of surfaces and thin films,”J. Phys. (Paris) Colloq. 44, 317–319 (1983).
  8. G. Rousset, L. Bertrand, and P. Cielo, “A pulsed thermoelastic analysis of photothermal surface displacements in layered materials,”J. Appl. Phys. 57, 4396–4405 (1985).
  9. J. Opsal, A. Rosencwaig, and D. L. Willenborg, “Thermal-wave detection and thin-film thickness measurements with laser beam deflection,”Appl. Opt. 22, 3169–3176 (1983).
  10. M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, and A. C. Boccara, “Photothermal displacement spectroscopy: an optical probe for solids and surfaces,”Appl. Phys. A 32, 141–154 (1983).
  11. J. C. Cheng and S.-Y. Zhang, “Three-dimensional theory to study photothermal phenomena of semiconductors II. Modulated photothermal deflection,”J. Appl. Phys. 70, 7007–7013 (1991).
  12. E. Welsch, “Photothermal surface deformation technique–a goal for nondestructive evaluation in thin-film optics,”J. Mod. Opt. 38, 2159–2176 (1991).
  13. D. L. Balageas, D. M. Boscher, A. A. Déom, and F. Enguehard, “Photoacoustic microscopy by photodeformation applied to thermal diffusitivity determination,”High Temp.-High Pressures 23, 517–528 (1991).
  14. B. Li, Z. Zhen, and S. He, “Modulated photothermal deformation in solids,”J. Phys. D 24, 2196–2201 (1991).
  15. M. A. Olmstead, and N. M. Amer, “Direct measurement of the photothermal displacement of Si(111) 2 × 1 surface-state absorption by use of photothermal displacement spectroscopy,”Phys. Rev. Lett. 52, 1148–1151 (1984).
  16. A. Déom, D. Boscher, and D. Balageas, “Micrometer photoacoustic imaging by photodeformation: application to carbon-carbon composites,”Photoacoustic and Photothermal0 Phenomena II, Vol. 62 of Springer Series in Optical Sciences, J. C. Murphy, J. W. Maclachlan-Spicer, L. Aamodt, and B. S. H. Royce, eds. (Springer-VerlagNew York, 1990), pp.13–16.
  17. G. Amato, G. Benedetto, L. Boarino, and R. Spagnolo, “Temperature dependence of photothermal displacement signal in silicon,”J. Mod. Opt. 39, 1803–1809 (1992).
  18. A. C. Tam, “Applications of Photoacoustic Sensing Techniques,”Rev. Mod. Phys. 58, 381–431 (1986).
  19. P. K. Kuo and M. Munidasa, “Single beam interferometry of a thermal bump: I. Experiment,” inReview of Progress in Quantitative NDE, D. O. Thompson and D. E. Chimenti, eds. 8th ed. (Plenum, New York, 1989), pp.627–633.
  20. L. D. Favro and M. Munidasa, “Single beam interferometry of a thermal bump: II. theory,” inReview of Progress in Quantitative NDE, D. O. Thompson and D. E. Chimenti, eds 8th ed (Plenum, New York, 1989), pp.635–640.
  21. P. K. Kuo, L. D. Favro, M. Munidasa, and R. L. Thomas, “A single beam interferometry of a thermal bump,” inPhotoacoustic and Photothermal Phenomena II, Vol. 62 of Springer Series in Optical Sciences, J. C. Murphy, J. W. Maclachlan-Spicer, L. Aamodt, and B. S. H. Royce, eds. (Springer-Verlag, New York, 1990), pp.472–478.
  22. P. K. Kuo and M. Munidasa, “Single-beam inteferometry of a thermal bump,”Appl. Opt. 29, 5326–5331 (1990).
  23. P. K. Kuo and S.-Y. Zhang, “A new diffraction theory for the mirage effect and thermal lensing,” inProceedings of the 9th International Conference on Photoacoustic and Photothermal Phenomena, Nanjing, China, 27–30 June, 1996 (suppl. to Prog. Nat. Sci. vol. 6), S.-Y. Zhangm, ed. (Taylor & Francis, London, 1996), pp. S191–S197.
  24. Y. Lu, P. K. Kuo, L. D. Favro, and R. L. Thomas, “Diffraction patterns of surface thermal lens,” inProceedings of the 9th International Conference on Photoacoustic and Photothermal Phenomena, Nanjing, China, 27–30 June, 1996 (suppl. to Prog. Nat. Sci. vol. 6), S.-Y. Zhang, ed. (Taylor & Francis, London, 1996), pp.S202–S205.
  25. L. Chen, K. H. Yang, and S. Y. Zhang, “New technique of photodisplacement imaging using one laser for both excitation and detection,”Appl. Phys. Lett. 50, 1349–1351 (1987).
  26. J.-P. Pérez, Optique Géométrique et Ondulatoire (Masson, Paris, 1988).
  27. K. Marguerre and H.-T. Woernle, Elastic Plates (Blaisdell Publishing, Waltham, Mass., 1969).
  28. A. Yariv, Quantum Electronics (Wiley, New York, 1989).
  29. A. Boivin, Théorie et Calcul des Figures de Diffraction de Révolution (Les Presses de l’Université Laval, Québec, 1964).
  30. M. Abramowitz, and I. A. Stegun, eds., Handbook of Mathematical Functions, Dover, New York, 1970).

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