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

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    [CrossRef]
  7. N. M. Amer, M. A. Olmstead, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy of surfaces and thin films,” J. Phys. (Paris) Colloq. 44, 317–319 (1983).
    [CrossRef]
  8. G. Rousset, L. Bertrand, P. Cielo, “A pulsed thermoelastic analysis of photothermal surface displacements in layered materials,” J. Appl. Phys. 57, 4396–4405 (1985).
    [CrossRef]
  9. J. Opsal, A. Rosencwaig, D. L. Willenborg, “Thermal-wave detection and thin-film thickness measurements with laser beam deflection,” Appl. Opt. 22, 3169–3176 (1983).
    [CrossRef] [PubMed]
  10. M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy: an optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
    [CrossRef]
  11. J. C. Cheng, S.-Y. Zhang, “Three-dimensional theory to study photothermal phenomena of semiconductors II. Modulated photothermal deflection,” J. Appl. Phys. 70, 7007–7013 (1991).
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  12. E. Welsch, “Photothermal surface deformation technique–a goal for nondestructive evaluation in thin-film optics,” J. Mod. Opt. 38, 2159–2176 (1991).
    [CrossRef]
  13. D. L. Balageas, D. M. Boscher, A. A. Déom, F. Enguehard, “Photoacoustic microscopy by photodeformation applied to thermal diffusitivity determination,” High Temp.-High Pressures 23, 517–528 (1991).
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    [CrossRef]
  15. M. A. Olmstead, 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).
    [CrossRef]
  16. A. Déom, D. Boscher, 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, B. S. H. Royce, eds. (Springer-VerlagNew York, 1990), pp.13–16.
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    [CrossRef]
  22. P. K. Kuo, M. Munidasa, “Single-beam inteferometry of a thermal bump,” Appl. Opt. 29, 5326–5331 (1990).
    [CrossRef] [PubMed]
  23. P. K. Kuo, S.-Y. Zhang, “A new diffraction theory for the mirage effect and thermal lensing,” in Proceedings 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.
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  25. L. Chen, K. H. Yang, S. Y. Zhang, “New technique of photodisplacement imaging using one laser for both excitation and detection,” Appl. Phys. Lett. 50, 1349–1351 (1987).
    [CrossRef]
  26. J.-P. Pérez,Optique Géométrique et Ondulatoire (Masson, Paris, 1988).
  27. K. Marguerre, H.-T. Woernle, Elastic Plates (Blaisdell Publishing, Waltham, Mass., 1969).
  28. A. Yariv, Quantum Electronics (Wiley, New York, 1989).
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1992 (2)

H. Saito, M. Irikura, M. Haraguchi, M. Fukui, “New type of photothermal spectroscopic technique,” Appl. Opt. 31, 2047–2054 (1992).
[CrossRef] [PubMed]

G. Amato, G. Benedetto, L. Boarino, R. Spagnolo, “Temperature dependence of photothermal displacement signal in silicon,” J. Mod. Opt. 39, 1803–1809 (1992).
[CrossRef]

1991 (4)

J. C. Cheng, S.-Y. Zhang, “Three-dimensional theory to study photothermal phenomena of semiconductors II. Modulated photothermal deflection,” J. Appl. Phys. 70, 7007–7013 (1991).
[CrossRef]

E. Welsch, “Photothermal surface deformation technique–a goal for nondestructive evaluation in thin-film optics,” J. Mod. Opt. 38, 2159–2176 (1991).
[CrossRef]

D. L. Balageas, D. M. Boscher, A. A. Déom, F. Enguehard, “Photoacoustic microscopy by photodeformation applied to thermal diffusitivity determination,” High Temp.-High Pressures 23, 517–528 (1991).

B. Li, Z. Zhen, S. He, “Modulated photothermal deformation in solids,” J. Phys. D 24, 2196–2201 (1991).
[CrossRef]

1990 (2)

1988 (1)

1987 (1)

L. Chen, K. H. Yang, S. Y. Zhang, “New technique of photodisplacement imaging using one laser for both excitation and detection,” Appl. Phys. Lett. 50, 1349–1351 (1987).
[CrossRef]

1986 (1)

A. C. Tam, “Applications of Photoacoustic Sensing Techniques,” Rev. Mod. Phys. 58, 381–431 (1986).
[CrossRef]

1985 (1)

G. Rousset, L. Bertrand, P. Cielo, “A pulsed thermoelastic analysis of photothermal surface displacements in layered materials,” J. Appl. Phys. 57, 4396–4405 (1985).
[CrossRef]

1984 (1)

M. A. Olmstead, 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).
[CrossRef]

1983 (5)

J. Opsal, A. Rosencwaig, D. L. Willenborg, “Thermal-wave detection and thin-film thickness measurements with laser beam deflection,” Appl. Opt. 22, 3169–3176 (1983).
[CrossRef] [PubMed]

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy: an optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
[CrossRef]

L. C. M. Miranda, “Photodisplacement spectroscopy of solids: theory,” Appl. Opt. 22, 2882–2886 (1983).
[CrossRef] [PubMed]

N. M. Amer, “New approaches to photothermal spectroscopy,” J. Phys. (Paris) Colloq. 44, 185–190 (1983).
[CrossRef]

N. M. Amer, M. A. Olmstead, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy of surfaces and thin films,” J. Phys. (Paris) Colloq. 44, 317–319 (1983).
[CrossRef]

1982 (1)

Amato, G.

G. Amato, G. Benedetto, L. Boarino, R. Spagnolo, “Temperature dependence of photothermal displacement signal in silicon,” J. Mod. Opt. 39, 1803–1809 (1992).
[CrossRef]

Amer, N. M.

M. A. Olmstead, 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).
[CrossRef]

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy: an optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
[CrossRef]

N. M. Amer, “New approaches to photothermal spectroscopy,” J. Phys. (Paris) Colloq. 44, 185–190 (1983).
[CrossRef]

N. M. Amer, M. A. Olmstead, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy of surfaces and thin films,” J. Phys. (Paris) Colloq. 44, 317–319 (1983).
[CrossRef]

Balageas, D.

A. Déom, D. Boscher, 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, B. S. H. Royce, eds. (Springer-VerlagNew York, 1990), pp.13–16.
[CrossRef]

Balageas, D. L.

D. L. Balageas, D. M. Boscher, A. A. Déom, F. Enguehard, “Photoacoustic microscopy by photodeformation applied to thermal diffusitivity determination,” High Temp.-High Pressures 23, 517–528 (1991).

Benedetto, G.

G. Amato, G. Benedetto, L. Boarino, R. Spagnolo, “Temperature dependence of photothermal displacement signal in silicon,” J. Mod. Opt. 39, 1803–1809 (1992).
[CrossRef]

Bertrand, L.

G. Rousset, L. Bertrand, P. Cielo, “A pulsed thermoelastic analysis of photothermal surface displacements in layered materials,” J. Appl. Phys. 57, 4396–4405 (1985).
[CrossRef]

Boarino, L.

G. Amato, G. Benedetto, L. Boarino, R. Spagnolo, “Temperature dependence of photothermal displacement signal in silicon,” J. Mod. Opt. 39, 1803–1809 (1992).
[CrossRef]

Boccara, A. C.

N. M. Amer, M. A. Olmstead, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy of surfaces and thin films,” J. Phys. (Paris) Colloq. 44, 317–319 (1983).
[CrossRef]

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy: an optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
[CrossRef]

Boivin, A.

A. Boivin, Théorie et Calcul des Figures de Diffraction de Révolution (Les Presses de l’Université Laval, Québec, 1964).

Boscher, D.

A. Déom, D. Boscher, 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, B. S. H. Royce, eds. (Springer-VerlagNew York, 1990), pp.13–16.
[CrossRef]

Boscher, D. M.

D. L. Balageas, D. M. Boscher, A. A. Déom, F. Enguehard, “Photoacoustic microscopy by photodeformation applied to thermal diffusitivity determination,” High Temp.-High Pressures 23, 517–528 (1991).

Chen, L.

L. Chen, K. H. Yang, S. Y. Zhang, “New technique of photodisplacement imaging using one laser for both excitation and detection,” Appl. Phys. Lett. 50, 1349–1351 (1987).
[CrossRef]

Cheng, J. C.

J. C. Cheng, S.-Y. Zhang, “Three-dimensional theory to study photothermal phenomena of semiconductors II. Modulated photothermal deflection,” J. Appl. Phys. 70, 7007–7013 (1991).
[CrossRef]

Choi, J. G.

Cielo, P.

G. Rousset, L. Bertrand, P. Cielo, “A pulsed thermoelastic analysis of photothermal surface displacements in layered materials,” J. Appl. Phys. 57, 4396–4405 (1985).
[CrossRef]

Déom, A.

A. Déom, D. Boscher, 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, B. S. H. Royce, eds. (Springer-VerlagNew York, 1990), pp.13–16.
[CrossRef]

Déom, A. A.

D. L. Balageas, D. M. Boscher, A. A. Déom, F. Enguehard, “Photoacoustic microscopy by photodeformation applied to thermal diffusitivity determination,” High Temp.-High Pressures 23, 517–528 (1991).

Diebold, G. J.

Enguehard, F.

D. L. Balageas, D. M. Boscher, A. A. Déom, F. Enguehard, “Photoacoustic microscopy by photodeformation applied to thermal diffusitivity determination,” High Temp.-High Pressures 23, 517–528 (1991).

Favro, L. D.

Y. Lu, P. K. Kuo, L. D. Favro, R. L. Thomas, “Diffraction patterns of surface thermal lens,” in Proceedings 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.

L. D. Favro, M. Munidasa, “Single beam interferometry of a thermal bump: II. theory,” in Review of Progress in Quantitative NDE, D. O. Thompson, D. E. Chimenti, eds 8th ed (Plenum, New York, 1989), pp. 635–640.

P. K. Kuo, L. D. Favro, M. Munidasa, R. L. Thomas, “A single beam interferometry of a thermal bump,” in Photoacoustic and Photothermal Phenomena II, Vol. 62 of Springer Series in Optical Sciences, J. C. Murphy, J. W. Maclachlan-Spicer, L. Aamodt, B. S. H. Royce, eds. (Springer-Verlag, New York, 1990), pp.472–478.
[CrossRef]

Fournier, D.

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy: an optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
[CrossRef]

N. M. Amer, M. A. Olmstead, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy of surfaces and thin films,” J. Phys. (Paris) Colloq. 44, 317–319 (1983).
[CrossRef]

Fukui, M.

Gupta, R.

Haraguchi, M.

He, S.

B. Li, Z. Zhen, S. He, “Modulated photothermal deformation in solids,” J. Phys. D 24, 2196–2201 (1991).
[CrossRef]

Irikura, M.

Kohn, S.

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy: an optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
[CrossRef]

Kuo, P. K.

P. K. Kuo, M. Munidasa, “Single-beam inteferometry of a thermal bump,” Appl. Opt. 29, 5326–5331 (1990).
[CrossRef] [PubMed]

P. K. Kuo, L. D. Favro, M. Munidasa, R. L. Thomas, “A single beam interferometry of a thermal bump,” in Photoacoustic and Photothermal Phenomena II, Vol. 62 of Springer Series in Optical Sciences, J. C. Murphy, J. W. Maclachlan-Spicer, L. Aamodt, B. S. H. Royce, eds. (Springer-Verlag, New York, 1990), pp.472–478.
[CrossRef]

P. K. Kuo, and M. Munidasa, “Single beam interferometry of a thermal bump: I. Experiment,” in Review of Progress in Quantitative NDE, D. O. Thompson, D. E. Chimenti, eds. 8th ed. (Plenum, New York, 1989), pp. 627–633.

P. K. Kuo, S.-Y. Zhang, “A new diffraction theory for the mirage effect and thermal lensing,” in Proceedings 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.

Y. Lu, P. K. Kuo, L. D. Favro, R. L. Thomas, “Diffraction patterns of surface thermal lens,” in Proceedings 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.

Li, B.

B. Li, Z. Zhen, S. He, “Modulated photothermal deformation in solids,” J. Phys. D 24, 2196–2201 (1991).
[CrossRef]

Lu, Y.

Y. Lu, P. K. Kuo, L. D. Favro, R. L. Thomas, “Diffraction patterns of surface thermal lens,” in Proceedings 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.

Marguerre, K.

K. Marguerre, H.-T. Woernle, Elastic Plates (Blaisdell Publishing, Waltham, Mass., 1969).

Miranda, L. C. M.

Munidasa, and M.

P. K. Kuo, and M. Munidasa, “Single beam interferometry of a thermal bump: I. Experiment,” in Review of Progress in Quantitative NDE, D. O. Thompson, D. E. Chimenti, eds. 8th ed. (Plenum, New York, 1989), pp. 627–633.

Munidasa, M.

P. K. Kuo, M. Munidasa, “Single-beam inteferometry of a thermal bump,” Appl. Opt. 29, 5326–5331 (1990).
[CrossRef] [PubMed]

P. K. Kuo, L. D. Favro, M. Munidasa, R. L. Thomas, “A single beam interferometry of a thermal bump,” in Photoacoustic and Photothermal Phenomena II, Vol. 62 of Springer Series in Optical Sciences, J. C. Murphy, J. W. Maclachlan-Spicer, L. Aamodt, B. S. H. Royce, eds. (Springer-Verlag, New York, 1990), pp.472–478.
[CrossRef]

L. D. Favro, M. Munidasa, “Single beam interferometry of a thermal bump: II. theory,” in Review of Progress in Quantitative NDE, D. O. Thompson, D. E. Chimenti, eds 8th ed (Plenum, New York, 1989), pp. 635–640.

Olmstead, M. A.

M. A. Olmstead, 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).
[CrossRef]

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy: an optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
[CrossRef]

N. M. Amer, M. A. Olmstead, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy of surfaces and thin films,” J. Phys. (Paris) Colloq. 44, 317–319 (1983).
[CrossRef]

Opsal, J.

Pérez, J.-P.

J.-P. Pérez,Optique Géométrique et Ondulatoire (Masson, Paris, 1988).

Power, J. F.

Rosencwaig, A.

Rousset, G.

G. Rousset, L. Bertrand, P. Cielo, “A pulsed thermoelastic analysis of photothermal surface displacements in layered materials,” J. Appl. Phys. 57, 4396–4405 (1985).
[CrossRef]

Saito, H.

Spagnolo, R.

G. Amato, G. Benedetto, L. Boarino, R. Spagnolo, “Temperature dependence of photothermal displacement signal in silicon,” J. Mod. Opt. 39, 1803–1809 (1992).
[CrossRef]

Tam, A. C.

A. C. Tam, “Applications of Photoacoustic Sensing Techniques,” Rev. Mod. Phys. 58, 381–431 (1986).
[CrossRef]

Thomas, R. L.

P. K. Kuo, L. D. Favro, M. Munidasa, R. L. Thomas, “A single beam interferometry of a thermal bump,” in Photoacoustic and Photothermal Phenomena II, Vol. 62 of Springer Series in Optical Sciences, J. C. Murphy, J. W. Maclachlan-Spicer, L. Aamodt, B. S. H. Royce, eds. (Springer-Verlag, New York, 1990), pp.472–478.
[CrossRef]

Y. Lu, P. K. Kuo, L. D. Favro, R. L. Thomas, “Diffraction patterns of surface thermal lens,” in Proceedings 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.

Vyas, R.

Welsch, E.

E. Welsch, “Photothermal surface deformation technique–a goal for nondestructive evaluation in thin-film optics,” J. Mod. Opt. 38, 2159–2176 (1991).
[CrossRef]

Willenborg, D. L.

Woernle, H.-T.

K. Marguerre, H.-T. Woernle, Elastic Plates (Blaisdell Publishing, Waltham, Mass., 1969).

Yang, K. H.

L. Chen, K. H. Yang, S. Y. Zhang, “New technique of photodisplacement imaging using one laser for both excitation and detection,” Appl. Phys. Lett. 50, 1349–1351 (1987).
[CrossRef]

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, New York, 1989).

Zhang, S. Y.

L. Chen, K. H. Yang, S. Y. Zhang, “New technique of photodisplacement imaging using one laser for both excitation and detection,” Appl. Phys. Lett. 50, 1349–1351 (1987).
[CrossRef]

Zhang, S.-Y.

J. C. Cheng, S.-Y. Zhang, “Three-dimensional theory to study photothermal phenomena of semiconductors II. Modulated photothermal deflection,” J. Appl. Phys. 70, 7007–7013 (1991).
[CrossRef]

P. K. Kuo, S.-Y. Zhang, “A new diffraction theory for the mirage effect and thermal lensing,” in Proceedings 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.

Zhen, Z.

B. Li, Z. Zhen, S. He, “Modulated photothermal deformation in solids,” J. Phys. D 24, 2196–2201 (1991).
[CrossRef]

Appl. Opt. (7)

Appl. Phys. A (1)

M. A. Olmstead, N. M. Amer, S. Kohn, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy: an optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
[CrossRef]

Appl. Phys. Lett. (1)

L. Chen, K. H. Yang, S. Y. Zhang, “New technique of photodisplacement imaging using one laser for both excitation and detection,” Appl. Phys. Lett. 50, 1349–1351 (1987).
[CrossRef]

High Temp.-High Pressures (1)

D. L. Balageas, D. M. Boscher, A. A. Déom, F. Enguehard, “Photoacoustic microscopy by photodeformation applied to thermal diffusitivity determination,” High Temp.-High Pressures 23, 517–528 (1991).

J. Appl. Phys. (2)

J. C. Cheng, S.-Y. Zhang, “Three-dimensional theory to study photothermal phenomena of semiconductors II. Modulated photothermal deflection,” J. Appl. Phys. 70, 7007–7013 (1991).
[CrossRef]

G. Rousset, L. Bertrand, P. Cielo, “A pulsed thermoelastic analysis of photothermal surface displacements in layered materials,” J. Appl. Phys. 57, 4396–4405 (1985).
[CrossRef]

J. Mod. Opt. (2)

E. Welsch, “Photothermal surface deformation technique–a goal for nondestructive evaluation in thin-film optics,” J. Mod. Opt. 38, 2159–2176 (1991).
[CrossRef]

G. Amato, G. Benedetto, L. Boarino, R. Spagnolo, “Temperature dependence of photothermal displacement signal in silicon,” J. Mod. Opt. 39, 1803–1809 (1992).
[CrossRef]

J. Phys. (Paris) Colloq. (2)

N. M. Amer, “New approaches to photothermal spectroscopy,” J. Phys. (Paris) Colloq. 44, 185–190 (1983).
[CrossRef]

N. M. Amer, M. A. Olmstead, D. Fournier, A. C. Boccara, “Photothermal displacement spectroscopy of surfaces and thin films,” J. Phys. (Paris) Colloq. 44, 317–319 (1983).
[CrossRef]

J. Phys. D (1)

B. Li, Z. Zhen, S. He, “Modulated photothermal deformation in solids,” J. Phys. D 24, 2196–2201 (1991).
[CrossRef]

Phys. Rev. Lett. (1)

M. A. Olmstead, 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).
[CrossRef]

Rev. Mod. Phys. (1)

A. C. Tam, “Applications of Photoacoustic Sensing Techniques,” Rev. Mod. Phys. 58, 381–431 (1986).
[CrossRef]

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P. K. Kuo, and M. Munidasa, “Single beam interferometry of a thermal bump: I. Experiment,” in Review of Progress in Quantitative NDE, D. O. Thompson, D. E. Chimenti, eds. 8th ed. (Plenum, New York, 1989), pp. 627–633.

L. D. Favro, M. Munidasa, “Single beam interferometry of a thermal bump: II. theory,” in Review of Progress in Quantitative NDE, D. O. Thompson, D. E. Chimenti, eds 8th ed (Plenum, New York, 1989), pp. 635–640.

P. K. Kuo, L. D. Favro, M. Munidasa, R. L. Thomas, “A single beam interferometry of a thermal bump,” in Photoacoustic and Photothermal Phenomena II, Vol. 62 of Springer Series in Optical Sciences, J. C. Murphy, J. W. Maclachlan-Spicer, L. Aamodt, B. S. H. Royce, eds. (Springer-Verlag, New York, 1990), pp.472–478.
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A. Déom, D. Boscher, 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, B. S. H. Royce, eds. (Springer-VerlagNew York, 1990), pp.13–16.
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P. K. Kuo, S.-Y. Zhang, “A new diffraction theory for the mirage effect and thermal lensing,” in Proceedings 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.

Y. Lu, P. K. Kuo, L. D. Favro, R. L. Thomas, “Diffraction patterns of surface thermal lens,” in Proceedings 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.

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Figures (9)

Fig. 1
Fig. 1

Principle of the schlieren detection of photodeformation. NDPB, nondivergent probe beam; DPB, divergent probe beam.

Fig. 2
Fig. 2

General geometry of the problem. z 1 is the distance between the output of the probe laser and the reflecting surface plane.

Fig. 3
Fig. 3

Geometry of the problem for the case of the geometrical optics formalism. (a) N is the normal vector to the reflecting deformed surface. (b) dΩ is the solid angle.

Fig. 4
Fig. 4

Geometry of the problem for the case of the ABCD law formalism.

Fig. 5
Fig. 5

Geometry of the problem for the case of the Fresnel diffraction formalism. z 1 is the distance between the output of the probe laser and the reflecting surface plane. e is a unit vector.

Fig. 6
Fig. 6

S max as a function of the amplitude u 0 of the photodeformation. (a) Case of a parabolic deformation. Exact calculation, Eq. (5.19); approximate calculation, Eq. (5.23). (b) Case of a Gaussian deformation. Exact calculation, numerical integration of Eq. (5.11); approximate calculation, Eq. (5.40).

Fig. 7
Fig. 7

S max as a function of the distance z between the deformed reflecting surface and the detector. (a) Case of a parabolic deformation. (b) Case of a Gaussian deformation.

Fig. 8
Fig. 8

S as a function of the radius s of the iris placed in front of the detector. z = z 1 = 0.1 m. (a) Case of a parabolic deformation. (b) Case of a Gaussian deformation.

Fig. 9
Fig. 9

S as a function of the radius s of the iris placed in front of the detector. z = 1.5 m, z 1 = 1 m. (a) Case of a parabolic deformation. (b) Case of a Gaussian deformation.

Equations (130)

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pincr=2P0πw02exp-2 r2w02,
dΦincr=pincrdA=pincr2πrdr,
Iα=dΦdΩ=dΦ2π sin αdα,
dΦinc=dΦref+dΦtrans=RdΦinc+TdΦinc,
pdetr=dΦrefdA=RprdAdA=Rprrdrrdr,
Iα=dΦrefdΩ=RprdAdΩ=Rprrdrsin α dα.
tan γ=-ddr ur=-ur,
tan α=-2ur1-[ur]2.
α-2ur.
r=r+z-urtan α,
r=r-2urz-ur1-ur2.
rr-2zur.
drdr=1-2urz-ur-2ur21-ur2 -4ur2urz-ur1-ur22,
drdr1-2zur.
Φdet=02πdθ 0s pdetrrdr=2π 0s rdrRprrdrrdr,
dαdr=-2ur1+ur2
dαdr-2ur
sin α=-2ur1+ur2
sin αα-2ur
ur=u01-r2R02,
ur=-2u0rR02,
ur=-2u0R02,
r=r1+4zu0R02,
drdr=1+4zu0R02.
pdetr=2P0Rπw021+4zu0R022exp-2 r2w021+4zu0R022,
w=w01+4zu0R02.
S=Φdetur=0-Φdetur=0=u0.
S=RP0exp-2 s2w0211+4zu0R022 -exp-2 s2w02.
SRP0 exp-2 s2w02exp16zu0R02s2w02-1.
S16RP0 exp-2 s2w02zu0R02s2w02.
smax=w02,
Smax8e-1RP0zu0R02,
dαdr=4u0R02.
sin αα=4u0R02r
Iα=Rpincr4u0R022.
ur=u0 exp- r2R02.
ur=- 2u0R02 r exp- r2R02,
ur=- 2u0R02exp- r2R021-2r2R02,
r=r1+4zu0R02exp- r2R02,
drdr=1+4zu0R02exp- r2R021-2r2R02,
pdetr=2P0Rπw021+4zu0R02exp- r2R021+4zu0R02exp- r2R02-8zu0R02r2R02exp- r2R02×exp-2 r2w021+4zu0R02exp-r2R022.
pdetr=2P0Rπw021+4zu0R02exp-r2R022×exp-2r2w021+4zu0R02exp-r2R022,
w=w01+4zu0R02exp-r2R02.
ddr-2r2w2-4rw021+4zu0R02exp-r2R022=-4rw2.
S=RP0exp-2s2w021+4zu0R02exp-s2R022exp-2s2w02.
S16RP0 exp-2s2w02zu0R02s2w02exp-s2R02.
smax=2w02+1R02-1/2,
Smax=8e-1RP01+w022R02-1zu0R02.
dαdr4u0R02exp-r2R021-2r2R02,
sin α α=4u0R02 r exp-r2R02,
Iα=Rpincr4u0R02exp-r2R0221-2r2R02.
s<R02.
w0<2R0,
MT=Mt2MrMt1,MT=1z/n00110-V11z1/no01,MT=1-zVz1+z-z1zV-V1-z1V=ABCD,
1qzt=1Rczt-iλπw2zt,
q1zt-zr=Aq0zr+BCq0zr+D,
q0=iπw02λ.
1w12z1+z1w12=-πλIm1q1,
1q1=1-z1V-i πw02λ Vz1+z-z1zV+i πw02λ1-zV,
1w12=1w021-zV2+λ2z1+z2π2w021-z1zz1+zV2.
1w012=1w021+λ2z1+z2π2w04.
ρ=xx+yy+zz=r cos θx+r sin θy+uzrz,
n2v2-n1v1=n2-n1N,
-N=ρrρθρrρθ.
N=αNx+βNy+γNz =1r1+ur21/2r cos θurx +r sin θury-rz.
n2α2β2γ2 - n1α1β1γ1=n2-n1αNβNγN =n2-n1r1+ur21/2×urxuryγNr1+ur21/2.
V-n2-n1urr1+ur21/2.
V2 urr<0.
ur=u01-r2R02,
ur=-2u0rR02,
V=-4u0R02.
1w121w0121-2zVFc,
Fc=1+λ2z1z1+zπ2w041+λ2z1+z2π2w04
1w121w0121+8zu0R02 Fc
w1w011+4zu0R02 Fc.
S=RP0exp-2s2w0121+4zu0R02 Fc2-exp-2s2w012.
S16RP0 exp-2s2w012zu0R02s2w012 Fc.
smax=w012,
Smax=8e-1RP0zu0R02 Fc.
ur=u0 exp-r2R02,
ur=-2u0R02 r exp-r2R02.
V=-4u0R02exp-r2R02,
1w121w0121+8zuR02exp-r2R02Fc.
S=RP0exp-2s2w0121+8zu0R02exp-s2R02Fc-exp-2s2w012.
S16RP0 exp-s22w012+1R02zu0R02s2w012 Fc,
smax=2w012+1R02-1/2,
Smax=8e-1RP01+w0122R02-1zu0R02 Fc.
EP=RSP EMQ|MP¯|expiκ|MP¯|dA,
Ex, y=-iλz--expiκzexp-iκz ×expiκx-x2+y-y22z×Ex, y, zdxdy,
Er, θ=-iλz002π rdrdθexpiκzexp-iκz×expiκ r22zexpiκ r22z×exp-iκ rrzcosθ-θEr, θ, z.
02πexp-iκ rrzcos θdθ=2πJ0κrrz,
Er=-iκzexpiκzexpiκ r22z×0 rdrexp-iκur×expiκ r22zJ0κrrzEr, ur.
Er, z, t=-iE0z0z1-z-iz0expiκz1-z×expiκr22z1-z-iz0×exp-iωt,
z0=w02πλ,
Er, ur=-i E0z0z1-iz0×expiκz1+r22z1-iz0×exp-iκur,
Er-2πλzEozoz12+zo2z1+izo×exp2πiλz+z1+r22z×0 rdrJ02πrrλz×expiπλzz1-izo+zz1-izor2×exp-4πiλur.
pdetr, ur=R2μoc E*r, urEr, ur,
S=2π 0S rdrpdetr, ur =0-pdetr, ur=0=uo.
ur=uo1-r2Ro2.
Er, ur=0=CA,
Er, ur=0=uo=CB
C=-2πλzEozoz12+zo2z1+izo×exp2πiλz+z1+r22z,
A=0 rdrJ02πrrλzexpiπλzz1-izo+zz1-izor2,
B=exp-4πiλ uo0 rdrJ02πrrλz ×expiπλzz1-izo+zz1-izo+4zuoRo2r2.
S=2π R2μ0c rdrCC*AA*-BB*,
S=R2μ0cλ2Eo2zoexp-2πλz×zozz12+zo2z12+zo2+z1z+4zuoRo2z12+zo22+zo2z2 s2-exp-2πλzzozz12+zo2z12+zo2+z1z2+zo2z2 s2.
S16RPo exp-2πλzzozz12+zo2z12+zo2+z1z2+zo2z2s2×zuoRo2s2wo2zo2z12+zo22z12+zo2+z1zz12+zo2+z1z2+z02z22,
Eo22μ0c=2Poπwo2.
smax=λz2πz12+zo2+z1z2+zo2z2zozz12+zo21/2.
Smax=8e-1RPozuoRo2z12+zo2z12+zo2+z1zz12+zo2+z1z2+zo2z2.
Fc=z12+zo2z12+zo2+z1zz12+zo2+z1z2+zo2z2.
ur=uo exp-r2Ro2.
exp-4πiλ ur1-4πiλ ur
Er, ur=0=CA,
Er, ur=0=uo=CA-B,
B=4πiλ uo0 rdrJ02πrrλz×expiπλzz1-izo+zz1-izo-1Ro2r2.
S=2π R2μ0c0s rdrCC*AB*+A*B-BB*.
S=2π R2μ0c0s rdrCC*AB*+A*B.
A*B+AB*=DG costr2+H sintr2expqr2,
D=2λuoπz2z12+zo22z12+zo2+z1z2+zo2z2z12+zo2+z1z2+zoz+λzπRo2z12+zo22,
G=λzπRo2z12+zo2z12+zo2+z1z,
H=-z12+zo2+z1z2+zo2z2+λzoz2πRo2z12+zo2,
t=1Ro2z12+zo22z12+zo2+z1z2zoz+λzπRo2z12+zo2z12+zo2+z1z2+zo2z2z12+zo2+z1z2+zoz+λzπRo2z12+zo22,
q=-πλzz12+zo22zoz+λzπRo2z12+zo2z12+zo2+z1z2+zo2z2+λzoz2πRo2z12+zo2z12+zo2+z1z2+zo2z2z12+zo2+z1z2+zoz+λzπRo2z12+zo22.
S=4Rπ3μ0cλ2z2Eo2z02z12+zo2 D×G 0s rdr expqr2costr2+H 0s rdr expqr2sintr2.
S=2Rπ3μ0cλ2z2Eo2zo2z12+zo2DtG+qHt2+q2expqs2sints2.
S=16RPo expqs2zuosints2wo2×zo22zoz+λzπRo2z12+zo2.
smax=1tarctan-tq1/2.
smax-1q1/2.
Smax8e-1RPozuoRo21+λzo2-z122πRo2zo-1×zo2+z12z12+zo2+z1zzo2+z12+z1z2+zo2z21+λzo2+z12πRo2zo.

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