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Invited Article: Linearization and signal recovery in photoacoustic infrared spectroscopy
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10.1063/1.2735447
/content/aip/journal/rsi/78/5/10.1063/1.2735447
http://aip.metastore.ingenta.com/content/aip/journal/rsi/78/5/10.1063/1.2735447
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Experimental layout for lock-in demodulation of step-scan phase-modulation PA signals.

Image of FIG. 2.
FIG. 2.

Double-sided interferogram for thimble solids, a clay/hydrocarbon mixture obtained from oil sand by means of distillation extraction.

Image of FIG. 3.
FIG. 3.

Rotation and zero filling of the interferogram in Fig. 2.

Image of FIG. 4.
FIG. 4.

Apodization of the positive-path-difference points in Fig. 3 using Eq. (9).

Image of FIG. 5.
FIG. 5.

Central regions of measured interferograms for carbon black (solid line) and thimble solids (dashed line). The scale for the upper axis refers to the dashed line.

Image of FIG. 6.
FIG. 6.

Phase spectra for thimble solids (noisy curve) and carbon black (smooth curve).

Image of FIG. 7.
FIG. 7.

Phase spectra for thimble solids and carbon black. The origin of the carbon black interferogram was shifted in the positive-path-difference direction by one or two points (middle and top curves, respectively).

Image of FIG. 8.
FIG. 8.

PA infrared spectra of thimble solids. (a) Linearized, (b) amplitude, and (c) linearized and corrected for scattering through multiplication by wave number. for the reference interferogram was shifted two points in the positive-path-difference direction, corresponding to the top phase curve in Fig. 7. The linearized spectrum was calculated using Eq. (5).

Image of FIG. 9.
FIG. 9.

Comparison of the linearization factors in Sec. IV. Open circles, Eq. (2); filled circles, Eq. (4).

Image of FIG. 10.
FIG. 10.

Third-order polynomial fit of the carbon black phase spectrum in Fig. 6. The fitted (smooth) curve is given by .

Image of FIG. 11.
FIG. 11.

Comparison of the phase difference terms in Eqs. (10) and (14). Upper curve, ; lower curve, . The first argument for the upper curve corresponds to a one-point shift of the reference interferogram. The subtraction of inverts the bands in both curves with respect to those in Figs. 6 and 7.

Image of FIG. 12.
FIG. 12.

Central regions of original interferograms for carbon black (solid line) and kaolin (dashed line) measured at .

Image of FIG. 13.
FIG. 13.

(a) Linearized and (b) amplitude PA infrared spectra of kaolin. for the sample interferogram was shifted one point in the negative-path-difference direction. The linearized spectrum was calculated using Eq. (5) and corrected for scattering. Low-wave-number bands are located at about 645, 695, 754, 793, 916, 937, 1013, 1035, and . Hydroxyl stretching bands occur at 3620, 3652, 3669, and .

Image of FIG. 14.
FIG. 14.

Central regions of original interferograms for carbon black (solid line) and illite (dashed line) measured at .

Image of FIG. 15.
FIG. 15.

(a) Linearized and (b) amplitude PA infrared spectra of illite. for the sample interferogram was shifted two points in the negative-path-difference direction.

Image of FIG. 16.
FIG. 16.

First-order Bessel function for phase modulation. The line at zero intensity is drawn as an aid to the reader.

Image of FIG. 17.
FIG. 17.

Model phase-modulation PA spectrum of carbon black, calculated as product of rapid-scan spectrum and with . The minimum occurs at , i.e., .

Image of FIG. 18.
FIG. 18.

Central region of (a) real and (b) imaginary interferograms obtained for carbon black using a modulation frequency of and lock-in demodulation.

Image of FIG. 19.
FIG. 19.

PA spectra calculated from the interferograms in Fig. 18. Upper curve, real spectrum; lower curve, imaginary spectrum.

Image of FIG. 20.
FIG. 20.

Central region of (a) real and (b) imaginary interferograms obtained for carbon black using a modulation frequency of and DSP demodulation.

Image of FIG. 21.
FIG. 21.

Phase calculated from the real interferogram in Fig. 20 using OPUS.

Image of FIG. 22.
FIG. 22.

PA spectra calculated from the interferograms in Fig. 20. (a) Real spectrum; (b) imaginary spectrum calculated using standard Mertz phase correction; (c) imaginary spectrum calculated using the phase in Fig. 21 and Mertz/stored-phase correction; (d) modulus (power) spectrum calculated from the real and imaginary spectra in (a) and (c).

Image of FIG. 23.
FIG. 23.

Central region of (a) real and (b) imaginary interferograms obtained for carbon black using a modulation frequency of and DSP demodulation.

Image of FIG. 24.
FIG. 24.

PA spectra calculated from the interferograms in Fig. 23. Upper curve, real spectrum (standard Mertz phase correction); lower curve, imaginary spectrum (signed-Mertz phase correction).

Image of FIG. 25.
FIG. 25.

Central region of imaginary interferograms observed for kaolin using a modulation frequency of and lock-in demodulation. The lock-in phase was adjusted to maximize the intensity of the real interferogram at points (a) 226, (b) 224, (c) 222, and (d) 220 (see text).

Image of FIG. 26.
FIG. 26.

Spectra calculated from the interferograms in Fig. 25 using the Mertz/stored-phase procedure. Curves (a)–(d) correspond to the interferograms with the same labels in Fig. 25.

Image of FIG. 27.
FIG. 27.

(a) Central region of real interferogram acquired for kaolin with lock in optimized at point 226; (b) spectrum calculated from interferogram in (a); (c) phase spectrum calculated from Figs. 26(a) and 27(b).

Image of FIG. 28.
FIG. 28.

Central region of (a) real and (b) imaginary interferograms obtained for kaolin using a modulation frequency of and DSP demodulation.

Image of FIG. 29.
FIG. 29.

(a) Spectra and (b) phase calculated from the interferograms in Fig. 28 using standard Mertz phase correction. The upper and lower curves in (a) are the real and imaginary spectra, respectively.

Image of FIG. 30.
FIG. 30.

(a) Spectra and (b) phase derived from the interferograms in Fig. 28. The Mertz/stored-phase procedure was used to calculate the spectra. The two curves in (a) have the same significance as in Fig. 29.

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2007-05-15
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Invited Article: Linearization and signal recovery in photoacoustic infrared spectroscopy
http://aip.metastore.ingenta.com/content/aip/journal/rsi/78/5/10.1063/1.2735447
10.1063/1.2735447
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