Abstract

In order to perform quantitative photoacoustic spectroscopy (PAS) it is desirable to have a method of obtaining the absolute absorption coefficient of a sample from PAS measurements alone. The photoacoustic signal contains both amplitude and phase data and this paper discusses a method by which this information may be used to determine the absolute absorption coefficient of condensed samples. Experimental results on ions in aqueous solution are also presented.

© 1980 Optical Society of America

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References

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  1. A. Mandelis and B. S. H. Royce. “Relaxation Time Measurements in Frequency and Time Domain PAS of Condensed Phases,” Paper W. A. 6 of the Topical Meeting on Photoacoustic Spectroscopy Ames, Iowa, 1979 (unpublished).
  2. A. Rosencwaig and A. Gersho. “Theory of the photoacoustic effect with solids,” J. Appl. Phys. 47, 64–69 (1976).
    [Crossref]
  3. L. C. Aamodt, J. C. Murphy, and J. G. Parker. “Size considerations in the design of cells for PAS,” J. Appl. Phys. 48, 927–933 (1977).
    [Crossref]
  4. J. C. Roark, R. A. Palmer, and J. S. Hutchinson. “Quantitative Absorption Spectra via Photoacoustic Phase Angle Spectroscopy (ΦAS),” Chem. Phys. Lett. 60112–116 (1978).
    [Crossref]
  5. A. Mandelís, Y. C. Teng, and B. S. H. Royce. “Phase measurements in frequency domain PAS of solids,” J. Appl. Phys. 50, 7138–7146 (1979).
    [Crossref]
  6. A. Silversmith, T. D. Wakefield, and R. Blank. “Phase Measurements and Verification of Theory in Photoacoustic Spectroscopy,” Paper 184Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy (1979) (unpublished); (private communication).
  7. G. C. Wetsel and F. A. McDonald. “PAS determination of absolute optical absorption coefficients,” Appl. Phys. Lett. 30, 252–254 (1977).
    [Crossref]
  8. F. A. McDonald and G. C. Wetsel, “General theory of the photoacoustic effect.” J. Appl. Phys. 49, 2313 (1978).
    [Crossref]
  9. See, for example, T. R. McCalla, Introduction to Numerical Metnods and fortran Programming (Wiley, New York, 1967), pp. 255–260.

1979 (1)

A. Mandelís, Y. C. Teng, and B. S. H. Royce. “Phase measurements in frequency domain PAS of solids,” J. Appl. Phys. 50, 7138–7146 (1979).
[Crossref]

1978 (2)

J. C. Roark, R. A. Palmer, and J. S. Hutchinson. “Quantitative Absorption Spectra via Photoacoustic Phase Angle Spectroscopy (ΦAS),” Chem. Phys. Lett. 60112–116 (1978).
[Crossref]

F. A. McDonald and G. C. Wetsel, “General theory of the photoacoustic effect.” J. Appl. Phys. 49, 2313 (1978).
[Crossref]

1977 (2)

G. C. Wetsel and F. A. McDonald. “PAS determination of absolute optical absorption coefficients,” Appl. Phys. Lett. 30, 252–254 (1977).
[Crossref]

L. C. Aamodt, J. C. Murphy, and J. G. Parker. “Size considerations in the design of cells for PAS,” J. Appl. Phys. 48, 927–933 (1977).
[Crossref]

1976 (1)

A. Rosencwaig and A. Gersho. “Theory of the photoacoustic effect with solids,” J. Appl. Phys. 47, 64–69 (1976).
[Crossref]

Aamodt, L. C.

L. C. Aamodt, J. C. Murphy, and J. G. Parker. “Size considerations in the design of cells for PAS,” J. Appl. Phys. 48, 927–933 (1977).
[Crossref]

Blank, R.

A. Silversmith, T. D. Wakefield, and R. Blank. “Phase Measurements and Verification of Theory in Photoacoustic Spectroscopy,” Paper 184Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy (1979) (unpublished); (private communication).

Gersho, A.

A. Rosencwaig and A. Gersho. “Theory of the photoacoustic effect with solids,” J. Appl. Phys. 47, 64–69 (1976).
[Crossref]

Hutchinson, J. S.

J. C. Roark, R. A. Palmer, and J. S. Hutchinson. “Quantitative Absorption Spectra via Photoacoustic Phase Angle Spectroscopy (ΦAS),” Chem. Phys. Lett. 60112–116 (1978).
[Crossref]

Mandelis, A.

A. Mandelis and B. S. H. Royce. “Relaxation Time Measurements in Frequency and Time Domain PAS of Condensed Phases,” Paper W. A. 6 of the Topical Meeting on Photoacoustic Spectroscopy Ames, Iowa, 1979 (unpublished).

Mandelís, A.

A. Mandelís, Y. C. Teng, and B. S. H. Royce. “Phase measurements in frequency domain PAS of solids,” J. Appl. Phys. 50, 7138–7146 (1979).
[Crossref]

McCalla, T. R.

See, for example, T. R. McCalla, Introduction to Numerical Metnods and fortran Programming (Wiley, New York, 1967), pp. 255–260.

McDonald, F. A.

F. A. McDonald and G. C. Wetsel, “General theory of the photoacoustic effect.” J. Appl. Phys. 49, 2313 (1978).
[Crossref]

G. C. Wetsel and F. A. McDonald. “PAS determination of absolute optical absorption coefficients,” Appl. Phys. Lett. 30, 252–254 (1977).
[Crossref]

Murphy, J. C.

L. C. Aamodt, J. C. Murphy, and J. G. Parker. “Size considerations in the design of cells for PAS,” J. Appl. Phys. 48, 927–933 (1977).
[Crossref]

Palmer, R. A.

J. C. Roark, R. A. Palmer, and J. S. Hutchinson. “Quantitative Absorption Spectra via Photoacoustic Phase Angle Spectroscopy (ΦAS),” Chem. Phys. Lett. 60112–116 (1978).
[Crossref]

Parker, J. G.

L. C. Aamodt, J. C. Murphy, and J. G. Parker. “Size considerations in the design of cells for PAS,” J. Appl. Phys. 48, 927–933 (1977).
[Crossref]

Roark, J. C.

J. C. Roark, R. A. Palmer, and J. S. Hutchinson. “Quantitative Absorption Spectra via Photoacoustic Phase Angle Spectroscopy (ΦAS),” Chem. Phys. Lett. 60112–116 (1978).
[Crossref]

Rosencwaig, A.

A. Rosencwaig and A. Gersho. “Theory of the photoacoustic effect with solids,” J. Appl. Phys. 47, 64–69 (1976).
[Crossref]

Royce, B. S. H.

A. Mandelís, Y. C. Teng, and B. S. H. Royce. “Phase measurements in frequency domain PAS of solids,” J. Appl. Phys. 50, 7138–7146 (1979).
[Crossref]

A. Mandelis and B. S. H. Royce. “Relaxation Time Measurements in Frequency and Time Domain PAS of Condensed Phases,” Paper W. A. 6 of the Topical Meeting on Photoacoustic Spectroscopy Ames, Iowa, 1979 (unpublished).

Silversmith, A.

A. Silversmith, T. D. Wakefield, and R. Blank. “Phase Measurements and Verification of Theory in Photoacoustic Spectroscopy,” Paper 184Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy (1979) (unpublished); (private communication).

Teng, Y. C.

A. Mandelís, Y. C. Teng, and B. S. H. Royce. “Phase measurements in frequency domain PAS of solids,” J. Appl. Phys. 50, 7138–7146 (1979).
[Crossref]

Wakefield, T. D.

A. Silversmith, T. D. Wakefield, and R. Blank. “Phase Measurements and Verification of Theory in Photoacoustic Spectroscopy,” Paper 184Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy (1979) (unpublished); (private communication).

Wetsel, G. C.

F. A. McDonald and G. C. Wetsel, “General theory of the photoacoustic effect.” J. Appl. Phys. 49, 2313 (1978).
[Crossref]

G. C. Wetsel and F. A. McDonald. “PAS determination of absolute optical absorption coefficients,” Appl. Phys. Lett. 30, 252–254 (1977).
[Crossref]

Appl. Phys. Lett. (1)

G. C. Wetsel and F. A. McDonald. “PAS determination of absolute optical absorption coefficients,” Appl. Phys. Lett. 30, 252–254 (1977).
[Crossref]

Chem. Phys. Lett. (1)

J. C. Roark, R. A. Palmer, and J. S. Hutchinson. “Quantitative Absorption Spectra via Photoacoustic Phase Angle Spectroscopy (ΦAS),” Chem. Phys. Lett. 60112–116 (1978).
[Crossref]

J. Appl. Phys. (4)

A. Mandelís, Y. C. Teng, and B. S. H. Royce. “Phase measurements in frequency domain PAS of solids,” J. Appl. Phys. 50, 7138–7146 (1979).
[Crossref]

A. Rosencwaig and A. Gersho. “Theory of the photoacoustic effect with solids,” J. Appl. Phys. 47, 64–69 (1976).
[Crossref]

L. C. Aamodt, J. C. Murphy, and J. G. Parker. “Size considerations in the design of cells for PAS,” J. Appl. Phys. 48, 927–933 (1977).
[Crossref]

F. A. McDonald and G. C. Wetsel, “General theory of the photoacoustic effect.” J. Appl. Phys. 49, 2313 (1978).
[Crossref]

Other (3)

See, for example, T. R. McCalla, Introduction to Numerical Metnods and fortran Programming (Wiley, New York, 1967), pp. 255–260.

A. Mandelis and B. S. H. Royce. “Relaxation Time Measurements in Frequency and Time Domain PAS of Condensed Phases,” Paper W. A. 6 of the Topical Meeting on Photoacoustic Spectroscopy Ames, Iowa, 1979 (unpublished).

A. Silversmith, T. D. Wakefield, and R. Blank. “Phase Measurements and Verification of Theory in Photoacoustic Spectroscopy,” Paper 184Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy (1979) (unpublished); (private communication).

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Figures (5)

FIG. 1
FIG. 1

Photoacoustic amplitude and phase for thermally thick samples.

FIG. 2
FIG. 2

Effects of precision of PHASE on determination of optical absorption coefficient.

FIG. 3
FIG. 3

Photoacoustic spectrum of KMnO4 solution.

FIG. 4
FIG. 4

Fit of experimental data on theoretical amplitude curve.

FIG. 5
FIG. 5

Comparison between PAS and optical data.

Equations (7)

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

Q = Q 1 + i Q 2 = q exp ( i ψ ) ,
ψ = tan 1 [ ( Q 2 / Q 1 ) ] .
ψ ( β ) = tan 1 ( 1 + 2 / β μ s )
ϕ ( β ) = [ ( π / 4 ) + ψ ( β ) ] .
q | Q | = ( Q 1 2 + Q 2 2 ) = ( B f ) cos ψ
ψ exp = ψ ( β ) + ϕ 0 ,
q exp = B cos ( ψ exp ϕ 0 )