Abstract

A discussion of the photoacoustic spectroscopy of condensed matter is presented with emphasis on the role of the sample and the sample cell in the photoacoustic signal waveform. The spectrometer and sample cell are described, and an experimental evaluation of the system performance is given. Data on various samples are reported, and sample geometry, signal saturation, and scattered light effects are analyzed. The relationship between photoacoustic spectra and absorption and reflection spectra is developed.

© 1976 Optical Society of America

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References

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  1. A. Rosencwaig, Opt. Commun. 7, 305 (1973).
    [CrossRef]
  2. A. Rosencwaig, Anal. Chem. 47, 592A (1975).
    [CrossRef]
  3. A. Rosencwaig, Phys. Today 28, 23 (1975).
    [CrossRef]
  4. T. H. Maugh, Science 188, 38 (1975).
    [CrossRef] [PubMed]
  5. A. Rosencwaig, Science 181, 657 (1973).
    [CrossRef] [PubMed]
  6. A. Rosencwaig, Anal. Chem. 47, 548 (1975).
    [CrossRef]
  7. A. Rosencwaig, A. Gersho, Science 190, 556 (1975).
    [CrossRef]
  8. A. Rosencwaig, A. Gersho, J. Appl. Phys. 47, 64 (1976).
    [CrossRef]
  9. The cell does not completely isolate the microphone from acoustical excitation originating outside the cell. The microphone o-ring seal can allow vibrations from the cable and preamplifier to be conducted into the cell unless care is taken to secure and isolate these components. In addition the microphone may pick up sound generated by the slotted chopper blades which often have resonances, especially at high chopping frequencies. This problem can often be controlled by using higher slot count blades at lower angular velocity or by using a solid transparent disk with an opaque chopping pattern.
  10. Recently significantly higher efficiency has been reported by Parker in Ref. 11 for the conversion of absorbed beam power to signal by using He or H2 as the coupling gas.
  11. J. G. Parker, Anal. Chem. 47, 1189A (1975).
  12. J. G. Parker, Appl. Opt. 12, 2974 (1973).
    [CrossRef] [PubMed]
  13. S. A. Schleusener, J. O. Lindberg, K. O. White, Appl. Opt. 14, 2564 (1975).
    [CrossRef] [PubMed]
  14. H. S. Bennett, R. A. Forman, Appl. Opt. 14, 3031 (1975); Appl. Opt. 15, 347 (1976).
    [CrossRef] [PubMed]
  15. J. F. McClelland, R. N. Kniseley, Appl. Phys. Lett. 28, 467 (1976).
    [CrossRef]
  16. Under the assumptions described, the power through a plane perpendicular to the beam is proportional to exp(−βl) at any value of l in the sample. The power absorbed in a layer dl is proportional to {exp(−βl) − exp[−β(l + dl)]} ≃ [exp(−βl) − exp(−βl) (1 − βdl + …)] = βdl exp(−βl). Hence the heat energy developed before conduction per unit time and length is proportional to β exp(−βl).
  17. H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Oxford U. P., London, 1959).
  18. The sample’s thermal diffusivity α is related to the thermal conductivity k, density ρ, and specific heat C by α = k/ρC.

1976

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

J. F. McClelland, R. N. Kniseley, Appl. Phys. Lett. 28, 467 (1976).
[CrossRef]

1975

S. A. Schleusener, J. O. Lindberg, K. O. White, Appl. Opt. 14, 2564 (1975).
[CrossRef] [PubMed]

H. S. Bennett, R. A. Forman, Appl. Opt. 14, 3031 (1975); Appl. Opt. 15, 347 (1976).
[CrossRef] [PubMed]

J. G. Parker, Anal. Chem. 47, 1189A (1975).

A. Rosencwaig, Anal. Chem. 47, 548 (1975).
[CrossRef]

A. Rosencwaig, A. Gersho, Science 190, 556 (1975).
[CrossRef]

A. Rosencwaig, Anal. Chem. 47, 592A (1975).
[CrossRef]

A. Rosencwaig, Phys. Today 28, 23 (1975).
[CrossRef]

T. H. Maugh, Science 188, 38 (1975).
[CrossRef] [PubMed]

1973

A. Rosencwaig, Science 181, 657 (1973).
[CrossRef] [PubMed]

J. G. Parker, Appl. Opt. 12, 2974 (1973).
[CrossRef] [PubMed]

A. Rosencwaig, Opt. Commun. 7, 305 (1973).
[CrossRef]

Bennett, H. S.

Carslaw, H. S.

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Oxford U. P., London, 1959).

Forman, R. A.

Gersho, A.

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

A. Rosencwaig, A. Gersho, Science 190, 556 (1975).
[CrossRef]

Jaeger, J. C.

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Oxford U. P., London, 1959).

Kniseley, R. N.

J. F. McClelland, R. N. Kniseley, Appl. Phys. Lett. 28, 467 (1976).
[CrossRef]

Lindberg, J. O.

Maugh, T. H.

T. H. Maugh, Science 188, 38 (1975).
[CrossRef] [PubMed]

McClelland, J. F.

J. F. McClelland, R. N. Kniseley, Appl. Phys. Lett. 28, 467 (1976).
[CrossRef]

Parker, J. G.

J. G. Parker, Anal. Chem. 47, 1189A (1975).

J. G. Parker, Appl. Opt. 12, 2974 (1973).
[CrossRef] [PubMed]

Rosencwaig, A.

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

A. Rosencwaig, Anal. Chem. 47, 548 (1975).
[CrossRef]

A. Rosencwaig, A. Gersho, Science 190, 556 (1975).
[CrossRef]

A. Rosencwaig, Anal. Chem. 47, 592A (1975).
[CrossRef]

A. Rosencwaig, Phys. Today 28, 23 (1975).
[CrossRef]

A. Rosencwaig, Science 181, 657 (1973).
[CrossRef] [PubMed]

A. Rosencwaig, Opt. Commun. 7, 305 (1973).
[CrossRef]

Schleusener, S. A.

White, K. O.

Anal. Chem.

A. Rosencwaig, Anal. Chem. 47, 592A (1975).
[CrossRef]

A. Rosencwaig, Anal. Chem. 47, 548 (1975).
[CrossRef]

J. G. Parker, Anal. Chem. 47, 1189A (1975).

Appl. Opt.

Appl. Phys. Lett.

J. F. McClelland, R. N. Kniseley, Appl. Phys. Lett. 28, 467 (1976).
[CrossRef]

J. Appl. Phys.

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

Opt. Commun.

A. Rosencwaig, Opt. Commun. 7, 305 (1973).
[CrossRef]

Phys. Today

A. Rosencwaig, Phys. Today 28, 23 (1975).
[CrossRef]

Science

T. H. Maugh, Science 188, 38 (1975).
[CrossRef] [PubMed]

A. Rosencwaig, Science 181, 657 (1973).
[CrossRef] [PubMed]

A. Rosencwaig, A. Gersho, Science 190, 556 (1975).
[CrossRef]

Other

The cell does not completely isolate the microphone from acoustical excitation originating outside the cell. The microphone o-ring seal can allow vibrations from the cable and preamplifier to be conducted into the cell unless care is taken to secure and isolate these components. In addition the microphone may pick up sound generated by the slotted chopper blades which often have resonances, especially at high chopping frequencies. This problem can often be controlled by using higher slot count blades at lower angular velocity or by using a solid transparent disk with an opaque chopping pattern.

Recently significantly higher efficiency has been reported by Parker in Ref. 11 for the conversion of absorbed beam power to signal by using He or H2 as the coupling gas.

Under the assumptions described, the power through a plane perpendicular to the beam is proportional to exp(−βl) at any value of l in the sample. The power absorbed in a layer dl is proportional to {exp(−βl) − exp[−β(l + dl)]} ≃ [exp(−βl) − exp(−βl) (1 − βdl + …)] = βdl exp(−βl). Hence the heat energy developed before conduction per unit time and length is proportional to β exp(−βl).

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Oxford U. P., London, 1959).

The sample’s thermal diffusivity α is related to the thermal conductivity k, density ρ, and specific heat C by α = k/ρC.

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Figures (6)

Fig. 1
Fig. 1

Photoacoustic cell showing sample chamber, microphone port with Cenco seal. The studs are used to clamp the windows which are removed in this figure.

Fig. 2
Fig. 2

Photoacoustic signal and SNR vs chopper frequency for a carbon black sample.

Fig. 3
Fig. 3

Photoacoustic signal waveform for carbon black (black velvet paint) on cardboard (full line) and copper (dashed line) substrates at a chopping frequency of 5 Hz. The ordinate scale is 0.05 V/div and 0.02 V/div for the cardboard and copper substrates, respectively. The upper square wave corresponds to the intermittent illumination of the sample by the copper.

Fig. 4
Fig. 4

Photoacoustic signal for carbon black on cardboard and copper substrates as a function of chopper frequency. The incident beam intensity is lower than in Fig. 3.

Fig. 5
Fig. 5

Schematic of the sample and the initial heat distributions as described for the model with β1 corresponding to nonzero transmission, β2 to the transmission approaching zero but before saturation, β3 = as to the onset of saturation, and finally β4 nearing full saturation.

Fig. 6
Fig. 6

Photoacoustic signal for methylene blue dye in water. The full lines represent experimental data, while the broken lines indicate the signal calculated form the optical power absorbed by the sample assuming a constant thermal coupling efficiency as a function of β and by normalizing to the experimental saturation level. The decrease in signal level at higher chopper frequencies is due to the thermal response of the sample-gas system.

Tables (1)

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Table I Photoacoustic Parameters

Equations (2)

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a s = [ ( π f ) / α ] 1 / 2
L = 2 π / a s .

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