Abstract

The response of a Fourier-transform infrared (FTIR) instrument to changes in absorbance is inherently nonlinear for a number of reasons. One is that the interferogram acquired by the FTIR is truncated and then apodized before further processing of the data is accomplished. A commonly used apodization function in open-path FTIR research is triangular apodization, and all the research presented here has been done with that function. We calculated a set of absorption spectra by using the HITRAN database, covering ranges in both concentration and temperature for water, ammonia, and methane. Plots of these data reveal nonlinear results. The commonly used analysis technique, classical least squares, assumes that the response is linear. We describe some of the effects of this nonlinearity and present ways to address these effects.

© 1999 Optical Society of America

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References

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  1. R. L. Spellicy, W. L. Crow, J. A. Draves, W. F. Buchholtz, W. F. Herget, “Spectroscopic remote sensing addressing requirements of the Clean Air Act,” Spectroscopy 6, 24–34 (1991).
  2. P. R. Griffiths, R. L. Richardson, D. Qin, C. Zhu, “Open path atmospheric monitoring with a low resolution FT-IR spectrometer,” in Optical Sensing for Environmental and Process Monitoring, O. A. Simpson, ed., Proc. SPIE2365, 274–284 (1995).
    [CrossRef]
  3. P. M. Chu, F. R. Guenther, G. C. Rhoderick, W. J. Lafferty, “The NIST quantitative database,” J. Res. Natl. Inst. Stand. Technol. 104, 59–81 (1999).
    [CrossRef]
  4. P. M. Chu, National Institute of Standards and Technology, Gaithersburg, Md. 20899 (personal communication, 1999).
  5. The U.S. Air Force Geophysics Laboratory HITRAN molecular absorption parameters database. See, for example, L. S. Rothman, R. R. Gamache, A. Goldman, R. A. Toth, H. M. Pickett, R. L. Poynter, J. M. Flaud, C. Camy-Peyret, A. Barbe, N. Hussen, C. P. Rinsland, M. A. H. Smith, “The HITRAN database: 1986 edition,” Appl. Opt. 26, 4058–4096 (1987).
  6. H. Happ, L. Genzel, “Interfernz-Modulation mit monochromatischen millimeter-wellen,” Infrared Phys. 1, 39–48 (1961).
    [CrossRef]
  7. A. S. Filler, “Apodization and interpolation in Fourier-transform spectroscopy,” J. Opt. Soc. Am. 54, 762–767 (1964).
    [CrossRef]
  8. R. H. Norton, R. Beer, “New apodizing functions for Fourier spectrometry,” J. Opt. Soc. Am. 66, 259–264 (1976).
    [CrossRef]
  9. J. K. Kauppinen, D. J. Moffatt, D. G. Cameron, H. H. Mantsch, “Noise in Fourier self-deconvolution,” Appl. Opt. 20, 1866–1879 (1981).
    [CrossRef] [PubMed]
  10. G. M. Russwurm, J. W. Childers, FT-IR Open-Path Monitoring Guidance Document, 2nd. ed. SP-4420-95-04 (ManTech Environmental Technology, Inc., Research Triangle Park, N.C., 1995).
  11. G. M. Russwurm, “Compendium method TO-16: long-path open-path Fourier transform infrared method monitoring of atmospheric gases,” in Compendium of Methods for the Determination of Toxic Organic Compounds in Ambient Air, 2nd ed., EPA/625/R-96/010b (U.S. Environmental Protection Agency, Research Triangle Park, N.C., 1996), pp. 16-1–16-42.
  12. A. Ropertz, “Kalibrierung eines FTIR langwegabsorptions-Spektrometeres in Verbindung mit einer einstelbaren Infrarot-Multi-Reflexionsgaszelle und Validerung der Ergebnisse wahrend einer Messkampagne bei einer Raffinerie” (Diplomatarbeit im Fachbereich Maschienen und Vefahrenstechnik an der Fachhochschule Dusseldorf, Matrikel-Nr 240415, Dusseldorf, 1997).

1999 (1)

P. M. Chu, F. R. Guenther, G. C. Rhoderick, W. J. Lafferty, “The NIST quantitative database,” J. Res. Natl. Inst. Stand. Technol. 104, 59–81 (1999).
[CrossRef]

1991 (1)

R. L. Spellicy, W. L. Crow, J. A. Draves, W. F. Buchholtz, W. F. Herget, “Spectroscopic remote sensing addressing requirements of the Clean Air Act,” Spectroscopy 6, 24–34 (1991).

1987 (1)

1981 (1)

1976 (1)

1964 (1)

1961 (1)

H. Happ, L. Genzel, “Interfernz-Modulation mit monochromatischen millimeter-wellen,” Infrared Phys. 1, 39–48 (1961).
[CrossRef]

Barbe, A.

Beer, R.

Buchholtz, W. F.

R. L. Spellicy, W. L. Crow, J. A. Draves, W. F. Buchholtz, W. F. Herget, “Spectroscopic remote sensing addressing requirements of the Clean Air Act,” Spectroscopy 6, 24–34 (1991).

Cameron, D. G.

Camy-Peyret, C.

Childers, J. W.

G. M. Russwurm, J. W. Childers, FT-IR Open-Path Monitoring Guidance Document, 2nd. ed. SP-4420-95-04 (ManTech Environmental Technology, Inc., Research Triangle Park, N.C., 1995).

Chu, P. M.

P. M. Chu, F. R. Guenther, G. C. Rhoderick, W. J. Lafferty, “The NIST quantitative database,” J. Res. Natl. Inst. Stand. Technol. 104, 59–81 (1999).
[CrossRef]

P. M. Chu, National Institute of Standards and Technology, Gaithersburg, Md. 20899 (personal communication, 1999).

Crow, W. L.

R. L. Spellicy, W. L. Crow, J. A. Draves, W. F. Buchholtz, W. F. Herget, “Spectroscopic remote sensing addressing requirements of the Clean Air Act,” Spectroscopy 6, 24–34 (1991).

Draves, J. A.

R. L. Spellicy, W. L. Crow, J. A. Draves, W. F. Buchholtz, W. F. Herget, “Spectroscopic remote sensing addressing requirements of the Clean Air Act,” Spectroscopy 6, 24–34 (1991).

Filler, A. S.

Flaud, J. M.

Gamache, R. R.

Genzel, L.

H. Happ, L. Genzel, “Interfernz-Modulation mit monochromatischen millimeter-wellen,” Infrared Phys. 1, 39–48 (1961).
[CrossRef]

Goldman, A.

Griffiths, P. R.

P. R. Griffiths, R. L. Richardson, D. Qin, C. Zhu, “Open path atmospheric monitoring with a low resolution FT-IR spectrometer,” in Optical Sensing for Environmental and Process Monitoring, O. A. Simpson, ed., Proc. SPIE2365, 274–284 (1995).
[CrossRef]

Guenther, F. R.

P. M. Chu, F. R. Guenther, G. C. Rhoderick, W. J. Lafferty, “The NIST quantitative database,” J. Res. Natl. Inst. Stand. Technol. 104, 59–81 (1999).
[CrossRef]

Happ, H.

H. Happ, L. Genzel, “Interfernz-Modulation mit monochromatischen millimeter-wellen,” Infrared Phys. 1, 39–48 (1961).
[CrossRef]

Herget, W. F.

R. L. Spellicy, W. L. Crow, J. A. Draves, W. F. Buchholtz, W. F. Herget, “Spectroscopic remote sensing addressing requirements of the Clean Air Act,” Spectroscopy 6, 24–34 (1991).

Hussen, N.

Kauppinen, J. K.

Lafferty, W. J.

P. M. Chu, F. R. Guenther, G. C. Rhoderick, W. J. Lafferty, “The NIST quantitative database,” J. Res. Natl. Inst. Stand. Technol. 104, 59–81 (1999).
[CrossRef]

Mantsch, H. H.

Moffatt, D. J.

Norton, R. H.

Pickett, H. M.

Poynter, R. L.

Qin, D.

P. R. Griffiths, R. L. Richardson, D. Qin, C. Zhu, “Open path atmospheric monitoring with a low resolution FT-IR spectrometer,” in Optical Sensing for Environmental and Process Monitoring, O. A. Simpson, ed., Proc. SPIE2365, 274–284 (1995).
[CrossRef]

Rhoderick, G. C.

P. M. Chu, F. R. Guenther, G. C. Rhoderick, W. J. Lafferty, “The NIST quantitative database,” J. Res. Natl. Inst. Stand. Technol. 104, 59–81 (1999).
[CrossRef]

Richardson, R. L.

P. R. Griffiths, R. L. Richardson, D. Qin, C. Zhu, “Open path atmospheric monitoring with a low resolution FT-IR spectrometer,” in Optical Sensing for Environmental and Process Monitoring, O. A. Simpson, ed., Proc. SPIE2365, 274–284 (1995).
[CrossRef]

Rinsland, C. P.

Ropertz, A.

A. Ropertz, “Kalibrierung eines FTIR langwegabsorptions-Spektrometeres in Verbindung mit einer einstelbaren Infrarot-Multi-Reflexionsgaszelle und Validerung der Ergebnisse wahrend einer Messkampagne bei einer Raffinerie” (Diplomatarbeit im Fachbereich Maschienen und Vefahrenstechnik an der Fachhochschule Dusseldorf, Matrikel-Nr 240415, Dusseldorf, 1997).

Rothman, L. S.

Russwurm, G. M.

G. M. Russwurm, J. W. Childers, FT-IR Open-Path Monitoring Guidance Document, 2nd. ed. SP-4420-95-04 (ManTech Environmental Technology, Inc., Research Triangle Park, N.C., 1995).

G. M. Russwurm, “Compendium method TO-16: long-path open-path Fourier transform infrared method monitoring of atmospheric gases,” in Compendium of Methods for the Determination of Toxic Organic Compounds in Ambient Air, 2nd ed., EPA/625/R-96/010b (U.S. Environmental Protection Agency, Research Triangle Park, N.C., 1996), pp. 16-1–16-42.

Smith, M. A. H.

Spellicy, R. L.

R. L. Spellicy, W. L. Crow, J. A. Draves, W. F. Buchholtz, W. F. Herget, “Spectroscopic remote sensing addressing requirements of the Clean Air Act,” Spectroscopy 6, 24–34 (1991).

Toth, R. A.

Zhu, C.

P. R. Griffiths, R. L. Richardson, D. Qin, C. Zhu, “Open path atmospheric monitoring with a low resolution FT-IR spectrometer,” in Optical Sensing for Environmental and Process Monitoring, O. A. Simpson, ed., Proc. SPIE2365, 274–284 (1995).
[CrossRef]

Appl. Opt. (2)

Infrared Phys. (1)

H. Happ, L. Genzel, “Interfernz-Modulation mit monochromatischen millimeter-wellen,” Infrared Phys. 1, 39–48 (1961).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Res. Natl. Inst. Stand. Technol. (1)

P. M. Chu, F. R. Guenther, G. C. Rhoderick, W. J. Lafferty, “The NIST quantitative database,” J. Res. Natl. Inst. Stand. Technol. 104, 59–81 (1999).
[CrossRef]

Spectroscopy (1)

R. L. Spellicy, W. L. Crow, J. A. Draves, W. F. Buchholtz, W. F. Herget, “Spectroscopic remote sensing addressing requirements of the Clean Air Act,” Spectroscopy 6, 24–34 (1991).

Other (5)

P. R. Griffiths, R. L. Richardson, D. Qin, C. Zhu, “Open path atmospheric monitoring with a low resolution FT-IR spectrometer,” in Optical Sensing for Environmental and Process Monitoring, O. A. Simpson, ed., Proc. SPIE2365, 274–284 (1995).
[CrossRef]

P. M. Chu, National Institute of Standards and Technology, Gaithersburg, Md. 20899 (personal communication, 1999).

G. M. Russwurm, J. W. Childers, FT-IR Open-Path Monitoring Guidance Document, 2nd. ed. SP-4420-95-04 (ManTech Environmental Technology, Inc., Research Triangle Park, N.C., 1995).

G. M. Russwurm, “Compendium method TO-16: long-path open-path Fourier transform infrared method monitoring of atmospheric gases,” in Compendium of Methods for the Determination of Toxic Organic Compounds in Ambient Air, 2nd ed., EPA/625/R-96/010b (U.S. Environmental Protection Agency, Research Triangle Park, N.C., 1996), pp. 16-1–16-42.

A. Ropertz, “Kalibrierung eines FTIR langwegabsorptions-Spektrometeres in Verbindung mit einer einstelbaren Infrarot-Multi-Reflexionsgaszelle und Validerung der Ergebnisse wahrend einer Messkampagne bei einer Raffinerie” (Diplomatarbeit im Fachbereich Maschienen und Vefahrenstechnik an der Fachhochschule Dusseldorf, Matrikel-Nr 240415, Dusseldorf, 1997).

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Figures (16)

Fig. 1
Fig. 1

Schematic of actual and assumed FTIR responses. The actual response was calculated by use of triangular apodization.

Fig. 2
Fig. 2

Measured concentration of methane versus the experimental response of the FTIR (reprinted with the permission of A. Ropertz).

Fig. 3
Fig. 3

Methane absorbance (ABS) at 2927 cm-1. (a) 0.25-cm-1 resolution, (b) 0.50-cm-1 resolution, (c) 1-cm-1 resolution, and (d) 4-cm-1 resolution. CL, concentration path length.

Fig. 4
Fig. 4

Ammonia absorbance (ABS) at 967 cm-1. (a) 0.25-cm-1 resolution, (b) 0.50-cm-1 resolution, (c) 1-cm-1 resolution, and (d) 4-cm-1 resolution. CL, concentration path length.

Fig. 5
Fig. 5

Water absorbance (ABS) at 1014.5 cm-1. (a) 0.25-cm-1 resolution, (b) 0.50-cm-1 resolution, (c) 1-cm-1 resolution, and (d) 4-cm-1 resolution.

Fig. 6
Fig. 6

Methane absorbance (ABS) versus concentration path length (CL) at 2927 cm-1. (a) 0.25-cm-1 resolution, ABS = -2.766 × 10-4 + 2.491 × 10-4 (CL) - 1.052386 × 10-8 (CL)2; (b) 0.50-cm-1 resolution, ABS = -2.766 × 10-4 + 2.491 × 10-4 (CL) - 1.052386 × 10-8 (CL)2; (c) 1-cm-1 resolution, ABS = -2.766 × 10-4 + 2.491 × 10-4 (CL) - 1.052386 × 10-8 (CL)2; and (d) 4-cm-1 resolution, ABS = -2.766 × 10-4 + 2.491 × 10-4 (CL) - 1.052386 × 10-8 (CL)2.

Fig. 7
Fig. 7

Ammonia absorbance (ABS) versus concentration path length (CL) at 967 cm-1. (a) 0.25-cm-1 resolution, ABS = 1.9424 × 10-3 + 1.7394 × 10-3 (CL) - 5.672623 × 10-7 (CL)2; (b) 0.50-cm-1 resolution, ABS = 2.4923 × 10-3 + 1.2273 × 10-3 (CL) - 3.713544 × 10-7 (CL)2; (c) 1-cm-1 resolution, ABS = 1.4744 × 10-3 + 1.077 × 10-3 (CL) - 3.15021 × 10-7 (CL)2; and (d) 4-cm-1 resolution, ABS = 1.2571 × 10-3 + 6.847 × 10-3 (CL) - 2.246147 × 10-7 (CL)2.

Fig. 8
Fig. 8

Water absorbance (ABS) versus pressure (P) at 1014.5 cm-1. (a) 0.25-cm-1 resolution, ABS = 2.0092 × 10-4 + 1.27711 × 10-3 P - 2.66 × 10-5 P2; (b) 0.50-cm-1 resolution, ABS = 2.0458 × 10-3 + 6.6919 × 10-3 P + 1.02 × 10-5 P2; (c) 1-cm-1 resolution, ABS = 2.0458 × 10-3 + 6.6919 × 10-3 P - 1.02 × 10-5 P2; and (d) 4-cm-1 resolution, ABS = 9.127 × 10-4 + 1.4907 × 10-3 P + 2.53 × 10-5 P2.

Fig. 9
Fig. 9

Water absorbance (ABS) for 0.5 Torr at 1014.5 cm-1. (a) 0.25-cm-1 resolution, ABS = 3.05685 × 10-2 - 2.843 × 10-4 Torr + 6.8172 × 10-7 (Torr)2; (b) 0.50-cm-1 resolution, ABS = 1.78549 × 10-2 - 1.661 × 10-4 Torr + 4.004795 × 10-7 (Torr)2; (c) 1-cm-1 resolution, ABS = 1.02741 × 10-2 - 9.39 × 10-5 Torr + 2.245754 × 10-7 (Torr)2; and (d) 4-cm-1 resolution, ABS = 4.1819 × 10-3 - 3.39 × 10-5 Torr + 7.706049 × 10-8 (Torr)2.

Fig. 10
Fig. 10

Water absorbance (ABS) for 35 Torr at 1014.5 cm-1. (a) 0.25-cm-1 resolution, ABS = 3.941383 - 2.68651 × 10-2 Torr + 5.01 × 10-5 Torr2; (b) 0.50-cm-1 resolution, ABS = 3.952566 - 2.57658 × 10-2 Torr + 4.48 × 10-5 Torr2; (c) 1-cm-1 resolution, ABS = 4.06909 - 2.59501 × 10-2 Torr + 4.31 × 10-5 Torr2; and (d) 4-cm-1 resolution, ABS = 4.21752 - 2.65233 - 10-2 Torr + 4.26 × 10-5 Torr2.

Fig. 11
Fig. 11

Match of water absorbance at 1014.5 cm-1.

Fig. 12
Fig. 12

Analysis results for methane from 2915 to 2929 cm-1. The field spectrum concentration (CONC) of methane is 6 ppm.

Fig. 13
Fig. 13

Analysis results for methane from 2900 to 3000 cm-1. The field spectrum concentration (CONC) of methane is 6 ppm.

Fig. 14
Fig. 14

Methane analysis allowing the water reference concentration to vary. The field spectrum of methane is 6 ppm and water is 15 Torr.

Fig. 15
Fig. 15

Plot of regression slopes versus temperature. The partial pressure of water is fixed at 15 Torr for all spectra. The field spectrum is at 275 K and the analysis is performed from 1008 to 1019 cm-1.

Fig. 16
Fig. 16

Difference of two spectra after the regression coefficients are applied to the reference spectrum. The field spectrum is at 275 K and the reference spectrum is at 255 K.

Tables (1)

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Table 1 Maximum Values Over which Response can be Considered Linear and Associated Errors

Equations (14)

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Trω= Tω-xSxdx.
Trω= Tω-xFAxdx.
Trω=FF-1 Tω-xFAxdx.
Trω=FF-1TωAω,
Imω=Dω  Iω+δSδ, Rdδ.
Im0ω=Dω  I0ω+δSδ, Rdδ,
Iω=I0ωTω,
Trω=ImωIm0ω=Dω  I0ω+δTω+δSδ, RdδDω  I0ω+δSδ, Rdδ.
Trω= Tω+δSδ, Rdδ Sδ, Rdδ.
Trω= Tω+δSδ, Rdδ.
Amω=-log exp-cαω+δSδ, Rdδ.
Amω-log 1-cαω+δSδ, Rdδ.
Amω=c  αω+δSδ, Rdδ,
Amω=-logexp-cαω=cαω,

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