Abstract

A distance-scan method to determine the distance between the probe beam and sample, which is not easily measured exactly, in photothermal deflection (PD) was reported, with which the distance and thermal diffusivity of the deflecting medium can be simultaneously measured. Probe beam size effect (PBSE) on PD phase signal was quantitatively analyzed to clearly show its physical meaning. The measured distance was experimentally verified as correct and reliable, and the measured thermal diffusivities of N2 and CO2 are in good agreement with the literature values. They could not be precisely measured by phase signal without considering the PBSE.

© 2006 Optical Society of America

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References

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  1. J. P. Roger, F. Lepoutre, D. Fournier, and A. C. Boccara, Thin Solid Films 155, 165 (1987).
    [CrossRef]
  2. M. Bertolotti, R. Li Voti, G. Liakhou, and C. Sibilia, Rev. Sci. Instrum. 64, 1576 (1993).
    [CrossRef]
  3. M. Bertolotti, S. Ligia, G. Liakhou, R. Li Voti, S. Paoloni, and C. Sibilia, J. Appl. Phys. 85, 2881 (1999).
    [CrossRef]
  4. J. Zhao, J. Shen, and C. Hu, Opt. Lett. 27, 1755 (2002).
    [CrossRef]
  5. J. Zhao, J. Zhou, and J. Shen, Appl. Phys. Lett. 84, 5332 (2004).
    [CrossRef]
  6. T. R. Anthony, W. F. Banholzer, J. F. Fleischer, L. Wei, P. K. Kou, R. L. Thomas, and R. W. Pryor, Phys. Rev. B 42, 1104 (1990).
    [CrossRef]
  7. E. L. Lasalle, F. Lepotre, and J. R. Roger, J. Appl. Phys. 64, 1 (1988).
    [CrossRef]
  8. C. Hu, J. Zhao, and J. Shen, Rev. Sci. Instrum. 74, 459 (2003).
    [CrossRef]
  9. J. Shen, R. D. Lowe, and R. D. Snook, Chem. Phys. 165, 385 (1992).
    [CrossRef]
  10. A. Rosencwaig and A. Gersho, J. Appl. Phys. 47, 64 (1976).
    [CrossRef]
  11. J. Shen, A. Mandelis, and T. Ashe, Int. J. Thermophys. 19, 579 (1998).
    [CrossRef]
  12. S. E. Bialkowski, Photothermal Spectroscopy Methods for Chemical Analysis (Wiley, 1996).

2004 (1)

J. Zhao, J. Zhou, and J. Shen, Appl. Phys. Lett. 84, 5332 (2004).
[CrossRef]

2003 (1)

C. Hu, J. Zhao, and J. Shen, Rev. Sci. Instrum. 74, 459 (2003).
[CrossRef]

2002 (1)

1999 (1)

M. Bertolotti, S. Ligia, G. Liakhou, R. Li Voti, S. Paoloni, and C. Sibilia, J. Appl. Phys. 85, 2881 (1999).
[CrossRef]

1998 (1)

J. Shen, A. Mandelis, and T. Ashe, Int. J. Thermophys. 19, 579 (1998).
[CrossRef]

1993 (1)

M. Bertolotti, R. Li Voti, G. Liakhou, and C. Sibilia, Rev. Sci. Instrum. 64, 1576 (1993).
[CrossRef]

1992 (1)

J. Shen, R. D. Lowe, and R. D. Snook, Chem. Phys. 165, 385 (1992).
[CrossRef]

1990 (1)

T. R. Anthony, W. F. Banholzer, J. F. Fleischer, L. Wei, P. K. Kou, R. L. Thomas, and R. W. Pryor, Phys. Rev. B 42, 1104 (1990).
[CrossRef]

1988 (1)

E. L. Lasalle, F. Lepotre, and J. R. Roger, J. Appl. Phys. 64, 1 (1988).
[CrossRef]

1987 (1)

J. P. Roger, F. Lepoutre, D. Fournier, and A. C. Boccara, Thin Solid Films 155, 165 (1987).
[CrossRef]

1976 (1)

A. Rosencwaig and A. Gersho, J. Appl. Phys. 47, 64 (1976).
[CrossRef]

Anthony, T. R.

T. R. Anthony, W. F. Banholzer, J. F. Fleischer, L. Wei, P. K. Kou, R. L. Thomas, and R. W. Pryor, Phys. Rev. B 42, 1104 (1990).
[CrossRef]

Ashe, T.

J. Shen, A. Mandelis, and T. Ashe, Int. J. Thermophys. 19, 579 (1998).
[CrossRef]

Banholzer, W. F.

T. R. Anthony, W. F. Banholzer, J. F. Fleischer, L. Wei, P. K. Kou, R. L. Thomas, and R. W. Pryor, Phys. Rev. B 42, 1104 (1990).
[CrossRef]

Bertolotti, M.

M. Bertolotti, S. Ligia, G. Liakhou, R. Li Voti, S. Paoloni, and C. Sibilia, J. Appl. Phys. 85, 2881 (1999).
[CrossRef]

M. Bertolotti, R. Li Voti, G. Liakhou, and C. Sibilia, Rev. Sci. Instrum. 64, 1576 (1993).
[CrossRef]

Bialkowski, S. E.

S. E. Bialkowski, Photothermal Spectroscopy Methods for Chemical Analysis (Wiley, 1996).

Boccara, A. C.

J. P. Roger, F. Lepoutre, D. Fournier, and A. C. Boccara, Thin Solid Films 155, 165 (1987).
[CrossRef]

Fleischer, J. F.

T. R. Anthony, W. F. Banholzer, J. F. Fleischer, L. Wei, P. K. Kou, R. L. Thomas, and R. W. Pryor, Phys. Rev. B 42, 1104 (1990).
[CrossRef]

Fournier, D.

J. P. Roger, F. Lepoutre, D. Fournier, and A. C. Boccara, Thin Solid Films 155, 165 (1987).
[CrossRef]

Gersho, A.

A. Rosencwaig and A. Gersho, J. Appl. Phys. 47, 64 (1976).
[CrossRef]

Hu, C.

C. Hu, J. Zhao, and J. Shen, Rev. Sci. Instrum. 74, 459 (2003).
[CrossRef]

J. Zhao, J. Shen, and C. Hu, Opt. Lett. 27, 1755 (2002).
[CrossRef]

Kou, P. K.

T. R. Anthony, W. F. Banholzer, J. F. Fleischer, L. Wei, P. K. Kou, R. L. Thomas, and R. W. Pryor, Phys. Rev. B 42, 1104 (1990).
[CrossRef]

Lasalle, E. L.

E. L. Lasalle, F. Lepotre, and J. R. Roger, J. Appl. Phys. 64, 1 (1988).
[CrossRef]

Lepotre, F.

E. L. Lasalle, F. Lepotre, and J. R. Roger, J. Appl. Phys. 64, 1 (1988).
[CrossRef]

Lepoutre, F.

J. P. Roger, F. Lepoutre, D. Fournier, and A. C. Boccara, Thin Solid Films 155, 165 (1987).
[CrossRef]

Li Voti, R.

M. Bertolotti, S. Ligia, G. Liakhou, R. Li Voti, S. Paoloni, and C. Sibilia, J. Appl. Phys. 85, 2881 (1999).
[CrossRef]

M. Bertolotti, R. Li Voti, G. Liakhou, and C. Sibilia, Rev. Sci. Instrum. 64, 1576 (1993).
[CrossRef]

Liakhou, G.

M. Bertolotti, S. Ligia, G. Liakhou, R. Li Voti, S. Paoloni, and C. Sibilia, J. Appl. Phys. 85, 2881 (1999).
[CrossRef]

M. Bertolotti, R. Li Voti, G. Liakhou, and C. Sibilia, Rev. Sci. Instrum. 64, 1576 (1993).
[CrossRef]

Ligia, S.

M. Bertolotti, S. Ligia, G. Liakhou, R. Li Voti, S. Paoloni, and C. Sibilia, J. Appl. Phys. 85, 2881 (1999).
[CrossRef]

Lowe, R. D.

J. Shen, R. D. Lowe, and R. D. Snook, Chem. Phys. 165, 385 (1992).
[CrossRef]

Mandelis, A.

J. Shen, A. Mandelis, and T. Ashe, Int. J. Thermophys. 19, 579 (1998).
[CrossRef]

Paoloni, S.

M. Bertolotti, S. Ligia, G. Liakhou, R. Li Voti, S. Paoloni, and C. Sibilia, J. Appl. Phys. 85, 2881 (1999).
[CrossRef]

Pryor, R. W.

T. R. Anthony, W. F. Banholzer, J. F. Fleischer, L. Wei, P. K. Kou, R. L. Thomas, and R. W. Pryor, Phys. Rev. B 42, 1104 (1990).
[CrossRef]

Roger, J. P.

J. P. Roger, F. Lepoutre, D. Fournier, and A. C. Boccara, Thin Solid Films 155, 165 (1987).
[CrossRef]

Roger, J. R.

E. L. Lasalle, F. Lepotre, and J. R. Roger, J. Appl. Phys. 64, 1 (1988).
[CrossRef]

Rosencwaig, A.

A. Rosencwaig and A. Gersho, J. Appl. Phys. 47, 64 (1976).
[CrossRef]

Shen, J.

J. Zhao, J. Zhou, and J. Shen, Appl. Phys. Lett. 84, 5332 (2004).
[CrossRef]

C. Hu, J. Zhao, and J. Shen, Rev. Sci. Instrum. 74, 459 (2003).
[CrossRef]

J. Zhao, J. Shen, and C. Hu, Opt. Lett. 27, 1755 (2002).
[CrossRef]

J. Shen, A. Mandelis, and T. Ashe, Int. J. Thermophys. 19, 579 (1998).
[CrossRef]

J. Shen, R. D. Lowe, and R. D. Snook, Chem. Phys. 165, 385 (1992).
[CrossRef]

Sibilia, C.

M. Bertolotti, S. Ligia, G. Liakhou, R. Li Voti, S. Paoloni, and C. Sibilia, J. Appl. Phys. 85, 2881 (1999).
[CrossRef]

M. Bertolotti, R. Li Voti, G. Liakhou, and C. Sibilia, Rev. Sci. Instrum. 64, 1576 (1993).
[CrossRef]

Snook, R. D.

J. Shen, R. D. Lowe, and R. D. Snook, Chem. Phys. 165, 385 (1992).
[CrossRef]

Thomas, R. L.

T. R. Anthony, W. F. Banholzer, J. F. Fleischer, L. Wei, P. K. Kou, R. L. Thomas, and R. W. Pryor, Phys. Rev. B 42, 1104 (1990).
[CrossRef]

Wei, L.

T. R. Anthony, W. F. Banholzer, J. F. Fleischer, L. Wei, P. K. Kou, R. L. Thomas, and R. W. Pryor, Phys. Rev. B 42, 1104 (1990).
[CrossRef]

Zhao, J.

J. Zhao, J. Zhou, and J. Shen, Appl. Phys. Lett. 84, 5332 (2004).
[CrossRef]

C. Hu, J. Zhao, and J. Shen, Rev. Sci. Instrum. 74, 459 (2003).
[CrossRef]

J. Zhao, J. Shen, and C. Hu, Opt. Lett. 27, 1755 (2002).
[CrossRef]

Zhou, J.

J. Zhao, J. Zhou, and J. Shen, Appl. Phys. Lett. 84, 5332 (2004).
[CrossRef]

Appl. Phys. Lett. (1)

J. Zhao, J. Zhou, and J. Shen, Appl. Phys. Lett. 84, 5332 (2004).
[CrossRef]

Chem. Phys. (1)

J. Shen, R. D. Lowe, and R. D. Snook, Chem. Phys. 165, 385 (1992).
[CrossRef]

Int. J. Thermophys. (1)

J. Shen, A. Mandelis, and T. Ashe, Int. J. Thermophys. 19, 579 (1998).
[CrossRef]

J. Appl. Phys. (3)

A. Rosencwaig and A. Gersho, J. Appl. Phys. 47, 64 (1976).
[CrossRef]

E. L. Lasalle, F. Lepotre, and J. R. Roger, J. Appl. Phys. 64, 1 (1988).
[CrossRef]

M. Bertolotti, S. Ligia, G. Liakhou, R. Li Voti, S. Paoloni, and C. Sibilia, J. Appl. Phys. 85, 2881 (1999).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (1)

T. R. Anthony, W. F. Banholzer, J. F. Fleischer, L. Wei, P. K. Kou, R. L. Thomas, and R. W. Pryor, Phys. Rev. B 42, 1104 (1990).
[CrossRef]

Rev. Sci. Instrum. (2)

C. Hu, J. Zhao, and J. Shen, Rev. Sci. Instrum. 74, 459 (2003).
[CrossRef]

M. Bertolotti, R. Li Voti, G. Liakhou, and C. Sibilia, Rev. Sci. Instrum. 64, 1576 (1993).
[CrossRef]

Thin Solid Films (1)

J. P. Roger, F. Lepoutre, D. Fournier, and A. C. Boccara, Thin Solid Films 155, 165 (1987).
[CrossRef]

Other (1)

S. E. Bialkowski, Photothermal Spectroscopy Methods for Chemical Analysis (Wiley, 1996).

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Figures (3)

Fig. 1
Fig. 1

Typical amplitude and phase signals in a PD distance-scan experiment ( f = 93 Hz ) . Points, experimental data; solid curves, the best curve fitting. Deflecting medium: nitrogen.

Fig. 2
Fig. 2

Typical curves of C ( x 01 , f ) and E ( x 01 , f ) versus frequency f. Points, C ( x 01 , f ) and E ( x 01 , f ) data; solid curves, the best curve fitting. Deflecting medium, nitrogen.

Fig. 3
Fig. 3

Dependence of measured x 0 on L: (a) from phase, (b) from amplitude. Points, experimental data; solid curves, the best linear curve fitting with correlation coefficient R > 0.999 . Deflecting medium, nitrogen.

Tables (1)

Tables Icon

Table 1 Comparison of Measurement Results at 20°C with Diffraction (Considering the PBSE) and Ray (Without Considering the PBSE) Theories

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

V 1 ( x ) = 2 θ d d n d T exp ( x μ g ) z D μ g sin ( 2 π f t + ξ 1 ) ,
ξ 1 = φ x μ g + 3 π 4 + ( q i 2 + q r 2 ) λ 4 π μ g 2 q i ,
( q i 2 + q r 2 ) λ 4 π μ g 2 q i ( ω 1 2 μ g ) 2 .
A ( x , f ) = 2 θ d d n d T exp ( x 0 + x μ g ) z D μ g = C ( x 0 , f ) exp ( x μ g ) ,
ξ 1 ( x , f ) = φ x 0 + x μ g + 3 π 4 + ( ω 1 2 μ g ) 2 = E ( x 0 , f ) x μ g .
C ( x 0 , f ) = D α g exp ( π f α g x 0 ) ,
E ( x 0 , f ) = π 2 π f α g x 0 + ( ω 1 2 4 π f α g ) ,

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