Abstract

We have investigated the ordinate scale accuracy of ambient temperature transmittance measurements made with a Fourier transform infrared (FT-IR) spectrophotometer over the wavelength range of 2–10 µm. Two approaches are used: (1) measurements of Si wafers whose index of refraction are well known from 2 to 5 µm, in which case the FT-IR result is compared with calculated values; (2) comparison of FT-IR and laser transmittance measurements at 3.39 and 10.6 µm on nominally neutral-density filters that are free of etaloning effects. Various schemes are employed to estimate and reduce systematic error sources in both the FT-IR and laser measurements, and quantitative uncertainty analyses are performed.

© 1997 Optical Society of America

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References

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  1. P. R. Griffiths, J. A. de Haseth, Fourier Transform Infrared Spectroscopy (Wiley-Interscience, New York, 1986); D. R. Mattson, “Sensitivity of a Fourier transform infrared spectrometer,” Appl. Spectrosc. 32, 335–338 (1978); D. A. C. Compton, J. Drab, H. S. Barr, “Accurate infrared transmittance measurements on optical filters using an FT-IR spectrometer,” Appl. Opt. 29, 2908–2912 (1980).
    [CrossRef]
  2. D. B. Chase, “Nonlinear detector response in FT-IR,” Appl. Spectrosc. 38, 491–494 (1984).
    [CrossRef]
  3. H. W. H. M. Jongbloets, M. J. H. Van de Steeg, E. J. C. M. Van der Werf, J. H. M. Stoelinga, P. Wyder, “Spectrum distortion in far-infrared Fourier spectroscopy by multiple reflections between sample and Michelson interferometer,” Infrared Phys. 20, 185–192 (1980).
    [CrossRef]
  4. M. A. Ford, “Dispersive vs. FTIR photometric accuracy—can it be measured?” in Advances in Standards and Methodology in Spectrophotometry, C. Burgess, K. D. Mielenz, eds. (Elsevier, Amsterdam, 1987), pp. 359–366.
    [CrossRef]
  5. J. R. Birch, E. A. Nicol, “The removal of detector port radiation effects in power transmission or reflection Fourier transform spectroscopy,” Infrared Phys. 27, 159–165 (1987); D. B. Tanner, R. P. McCall, “Source of a problem with Fourier transform spectroscopy,” Appl. Opt. 23, 2363–2368 (1984).
    [CrossRef] [PubMed]
  6. J. R. Birch, F. J. J. Clarke, “Fifty categories of ordinate error in Fourier transform spectroscopy,” Spectrosc. Europe 7, 16–22 (1995).
  7. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), p. 277.
  8. M. I. Flik, Z. M. Zhang, “Influence of nonequivalent detector responsivity on FT-IR photometric accuracy,” J. Quant. Spectrosc. Radiat. Transfer 47, 293–303 (1992).
    [CrossRef]
  9. E. D. Palik, Handbook of Optical Constants of Solids (Academic, Orlando, Fla., 1985), p. 566.
  10. H. W. Icenogle, B. C. Platt, W. L. Wolfe, “Refractive indexes and temperature coefficients of germanium and silicon,” Appl. Opt. 15, 2348–2351 (1976); W. Primak, “Refractive index of silicon,” Appl. Opt. 10, 759–763 (1971); C. D. Salzberg, J. J. Villa, “Infrared refractive indices of silicon, germanium, and modified selenium glass,” J. Opt. Soc. Am. 47, 244–246 (1957).
    [CrossRef] [PubMed]
  11. D. F. Edwards, E. Ochoa, “Infrared refractive index of silicon,” Appl. Opt. 19, 4130–4131 (1980).
    [CrossRef] [PubMed]
  12. A. Frenkel, Z. M. Zhang, “Broadband high-optical-density filters in the infrared,” Opt. Lett. 19, 1495–1497 (1994).
    [CrossRef] [PubMed]
  13. A. L. Migdall, B. Roop, Y. C. Zheng, J. E. Hardis, G. J. Xia, “Use of heterodyne detection to measure optical transmittance over a wide range,” Appl. Opt. 29, 5136–5144 (1990).
    [CrossRef] [PubMed]
  14. B. N. Taylor, C. E. Kuyatt, “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” (U.S. GPO, Washington, DC, 1994).
  15. Z. M. Zhang, L. M. Hanssen, R. U. Datla, “High-optical-density out-of-band spectral transmittance measurements of bandpass filters,” Opt. Lett. 20, 1077–1079 (1995).
    [CrossRef] [PubMed]
  16. K. D. Mielenz, “Physical parameters in high-accuracy spectrophotometry,” (U.S. GPO, Washington, DC, 1973).
  17. Z. M. Zhang, C. J. Zhu, L. M. Hanssen, “Methods for correcting nonlinearity errors in Fourier transform infrared spectrometers,” Appl. Spectrosc. 51, 576–579 (1997).
    [CrossRef]

1997 (1)

1995 (2)

J. R. Birch, F. J. J. Clarke, “Fifty categories of ordinate error in Fourier transform spectroscopy,” Spectrosc. Europe 7, 16–22 (1995).

Z. M. Zhang, L. M. Hanssen, R. U. Datla, “High-optical-density out-of-band spectral transmittance measurements of bandpass filters,” Opt. Lett. 20, 1077–1079 (1995).
[CrossRef] [PubMed]

1994 (1)

1992 (1)

M. I. Flik, Z. M. Zhang, “Influence of nonequivalent detector responsivity on FT-IR photometric accuracy,” J. Quant. Spectrosc. Radiat. Transfer 47, 293–303 (1992).
[CrossRef]

1990 (1)

1987 (1)

J. R. Birch, E. A. Nicol, “The removal of detector port radiation effects in power transmission or reflection Fourier transform spectroscopy,” Infrared Phys. 27, 159–165 (1987); D. B. Tanner, R. P. McCall, “Source of a problem with Fourier transform spectroscopy,” Appl. Opt. 23, 2363–2368 (1984).
[CrossRef] [PubMed]

1984 (1)

1980 (2)

H. W. H. M. Jongbloets, M. J. H. Van de Steeg, E. J. C. M. Van der Werf, J. H. M. Stoelinga, P. Wyder, “Spectrum distortion in far-infrared Fourier spectroscopy by multiple reflections between sample and Michelson interferometer,” Infrared Phys. 20, 185–192 (1980).
[CrossRef]

D. F. Edwards, E. Ochoa, “Infrared refractive index of silicon,” Appl. Opt. 19, 4130–4131 (1980).
[CrossRef] [PubMed]

1976 (1)

Birch, J. R.

J. R. Birch, F. J. J. Clarke, “Fifty categories of ordinate error in Fourier transform spectroscopy,” Spectrosc. Europe 7, 16–22 (1995).

J. R. Birch, E. A. Nicol, “The removal of detector port radiation effects in power transmission or reflection Fourier transform spectroscopy,” Infrared Phys. 27, 159–165 (1987); D. B. Tanner, R. P. McCall, “Source of a problem with Fourier transform spectroscopy,” Appl. Opt. 23, 2363–2368 (1984).
[CrossRef] [PubMed]

Chase, D. B.

Clarke, F. J. J.

J. R. Birch, F. J. J. Clarke, “Fifty categories of ordinate error in Fourier transform spectroscopy,” Spectrosc. Europe 7, 16–22 (1995).

Datla, R. U.

de Haseth, J. A.

P. R. Griffiths, J. A. de Haseth, Fourier Transform Infrared Spectroscopy (Wiley-Interscience, New York, 1986); D. R. Mattson, “Sensitivity of a Fourier transform infrared spectrometer,” Appl. Spectrosc. 32, 335–338 (1978); D. A. C. Compton, J. Drab, H. S. Barr, “Accurate infrared transmittance measurements on optical filters using an FT-IR spectrometer,” Appl. Opt. 29, 2908–2912 (1980).
[CrossRef]

Edwards, D. F.

Flik, M. I.

M. I. Flik, Z. M. Zhang, “Influence of nonequivalent detector responsivity on FT-IR photometric accuracy,” J. Quant. Spectrosc. Radiat. Transfer 47, 293–303 (1992).
[CrossRef]

Ford, M. A.

M. A. Ford, “Dispersive vs. FTIR photometric accuracy—can it be measured?” in Advances in Standards and Methodology in Spectrophotometry, C. Burgess, K. D. Mielenz, eds. (Elsevier, Amsterdam, 1987), pp. 359–366.
[CrossRef]

Frenkel, A.

Griffiths, P. R.

P. R. Griffiths, J. A. de Haseth, Fourier Transform Infrared Spectroscopy (Wiley-Interscience, New York, 1986); D. R. Mattson, “Sensitivity of a Fourier transform infrared spectrometer,” Appl. Spectrosc. 32, 335–338 (1978); D. A. C. Compton, J. Drab, H. S. Barr, “Accurate infrared transmittance measurements on optical filters using an FT-IR spectrometer,” Appl. Opt. 29, 2908–2912 (1980).
[CrossRef]

Hanssen, L. M.

Hardis, J. E.

Icenogle, H. W.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), p. 277.

Jongbloets, H. W. H. M.

H. W. H. M. Jongbloets, M. J. H. Van de Steeg, E. J. C. M. Van der Werf, J. H. M. Stoelinga, P. Wyder, “Spectrum distortion in far-infrared Fourier spectroscopy by multiple reflections between sample and Michelson interferometer,” Infrared Phys. 20, 185–192 (1980).
[CrossRef]

Kuyatt, C. E.

B. N. Taylor, C. E. Kuyatt, “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” (U.S. GPO, Washington, DC, 1994).

Mielenz, K. D.

K. D. Mielenz, “Physical parameters in high-accuracy spectrophotometry,” (U.S. GPO, Washington, DC, 1973).

Migdall, A. L.

Nicol, E. A.

J. R. Birch, E. A. Nicol, “The removal of detector port radiation effects in power transmission or reflection Fourier transform spectroscopy,” Infrared Phys. 27, 159–165 (1987); D. B. Tanner, R. P. McCall, “Source of a problem with Fourier transform spectroscopy,” Appl. Opt. 23, 2363–2368 (1984).
[CrossRef] [PubMed]

Ochoa, E.

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, Orlando, Fla., 1985), p. 566.

Platt, B. C.

Roop, B.

Stoelinga, J. H. M.

H. W. H. M. Jongbloets, M. J. H. Van de Steeg, E. J. C. M. Van der Werf, J. H. M. Stoelinga, P. Wyder, “Spectrum distortion in far-infrared Fourier spectroscopy by multiple reflections between sample and Michelson interferometer,” Infrared Phys. 20, 185–192 (1980).
[CrossRef]

Taylor, B. N.

B. N. Taylor, C. E. Kuyatt, “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” (U.S. GPO, Washington, DC, 1994).

Van de Steeg, M. J. H.

H. W. H. M. Jongbloets, M. J. H. Van de Steeg, E. J. C. M. Van der Werf, J. H. M. Stoelinga, P. Wyder, “Spectrum distortion in far-infrared Fourier spectroscopy by multiple reflections between sample and Michelson interferometer,” Infrared Phys. 20, 185–192 (1980).
[CrossRef]

Van der Werf, E. J. C. M.

H. W. H. M. Jongbloets, M. J. H. Van de Steeg, E. J. C. M. Van der Werf, J. H. M. Stoelinga, P. Wyder, “Spectrum distortion in far-infrared Fourier spectroscopy by multiple reflections between sample and Michelson interferometer,” Infrared Phys. 20, 185–192 (1980).
[CrossRef]

Wolfe, W. L.

Wyder, P.

H. W. H. M. Jongbloets, M. J. H. Van de Steeg, E. J. C. M. Van der Werf, J. H. M. Stoelinga, P. Wyder, “Spectrum distortion in far-infrared Fourier spectroscopy by multiple reflections between sample and Michelson interferometer,” Infrared Phys. 20, 185–192 (1980).
[CrossRef]

Xia, G. J.

Zhang, Z. M.

Zheng, Y. C.

Zhu, C. J.

Appl. Opt. (3)

Appl. Spectrosc. (2)

Infrared Phys. (2)

H. W. H. M. Jongbloets, M. J. H. Van de Steeg, E. J. C. M. Van der Werf, J. H. M. Stoelinga, P. Wyder, “Spectrum distortion in far-infrared Fourier spectroscopy by multiple reflections between sample and Michelson interferometer,” Infrared Phys. 20, 185–192 (1980).
[CrossRef]

J. R. Birch, E. A. Nicol, “The removal of detector port radiation effects in power transmission or reflection Fourier transform spectroscopy,” Infrared Phys. 27, 159–165 (1987); D. B. Tanner, R. P. McCall, “Source of a problem with Fourier transform spectroscopy,” Appl. Opt. 23, 2363–2368 (1984).
[CrossRef] [PubMed]

J. Quant. Spectrosc. Radiat. Transfer (1)

M. I. Flik, Z. M. Zhang, “Influence of nonequivalent detector responsivity on FT-IR photometric accuracy,” J. Quant. Spectrosc. Radiat. Transfer 47, 293–303 (1992).
[CrossRef]

Opt. Lett. (2)

Spectrosc. Europe (1)

J. R. Birch, F. J. J. Clarke, “Fifty categories of ordinate error in Fourier transform spectroscopy,” Spectrosc. Europe 7, 16–22 (1995).

Other (6)

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), p. 277.

M. A. Ford, “Dispersive vs. FTIR photometric accuracy—can it be measured?” in Advances in Standards and Methodology in Spectrophotometry, C. Burgess, K. D. Mielenz, eds. (Elsevier, Amsterdam, 1987), pp. 359–366.
[CrossRef]

E. D. Palik, Handbook of Optical Constants of Solids (Academic, Orlando, Fla., 1985), p. 566.

P. R. Griffiths, J. A. de Haseth, Fourier Transform Infrared Spectroscopy (Wiley-Interscience, New York, 1986); D. R. Mattson, “Sensitivity of a Fourier transform infrared spectrometer,” Appl. Spectrosc. 32, 335–338 (1978); D. A. C. Compton, J. Drab, H. S. Barr, “Accurate infrared transmittance measurements on optical filters using an FT-IR spectrometer,” Appl. Opt. 29, 2908–2912 (1980).
[CrossRef]

B. N. Taylor, C. E. Kuyatt, “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” (U.S. GPO, Washington, DC, 1994).

K. D. Mielenz, “Physical parameters in high-accuracy spectrophotometry,” (U.S. GPO, Washington, DC, 1973).

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Figures (5)

Fig. 1
Fig. 1

Schematic optical layout for the FT-IR transmittance measurements: G, globar source; A1, source aperture; BS, beam splitter; M1, moving mirror; M2, fixed mirror; M3, off-axis paraboloidal mirror; HB, half-beam block; MM, metal mesh filter; A2, field stop; S, sample; M4, off-axis ellipsoidal mirror; D, DTGS pyroelectric detector. The transmittance is measured by our switching the sample in and out of the beam and comparing to either an empty path or a reference sample. The half-blocks, metal mesh, and field stop are used to reduce the systematic errors that are due to interreflections, detector nonequivalence, and source aperture radiation, as described in the text.

Fig. 2
Fig. 2

Effects of sample–interferometer and sample–detector interreflections on the apparent transmittance of (a) a 0.25-mm-thick Si wafer and (b) a 27-nm-thick NiCr film on a 120-nm-thick Lexan substrate, tested by ratioing of the measured transmittance at normal incidence to that at 10° incidence. Curve A, transmittance ratio versus wavelength with no beam blocks; curve B, ratio with a half-block between sample and detector; curve C, ratio with a half-block between the sample and interferometer; curve D, ratio with both half-blocks in place.

Fig. 3
Fig. 3

Transmittance of a 15-mm diameter aperture with a nominal beam diameter of 3 mm at the sample position. The solid curve shows the measured transmittance without field stop A2 (Fig. 1), and the dashed curve shows the results with A2. The reduced transmittance observed at longer wavelengths without A2 is attributed to overfilling of the aperture as a result of thermal radiation from the heated source aperture.

Fig. 4
Fig. 4

Measured transmittance of a 0.25-mm-thick Si wafer versus wavelength for different incident power levels. (a) Measured transmittance curves from 2 to 5 µm for different values of the empty beam detector signal at ZPD, compared with the predicted transmittance based on handbook values for the index of refraction. (b) Dependence of the apparent transmittance at 3.4 µm on ZPD signal (open circles, data; solid line, quadratic fit). The measured transmittance approaches the expected value as the incident power level is decreased, reducing the temperature change of the detector.

Fig. 5
Fig. 5

Comparison of FT-IR and laser transmittance measurements of three metallic thin-film neutral-density filters on 100-nm Lexan substrates: (a) 25-nm NiCr, (b) 104-nm NiCr, and (c) 89-nm NiCr/24-nm Au coatings. Curves, FT-IR data; filled circles, laser data at 3.39 µm and 10.6 µm with expanded uncertainty error bars as described in the text. The laser and FT-IR data appear to agree within the expanded uncertainties.

Tables (4)

Tables Icon

Table 1 FT-IR Transmittance Relative Standard Uncertainty Components (% Measured Value)

Tables Icon

Table 2 3.39-µm He–Ne Laser Transmittance Relative Standard Uncertainty Components (% Measured Value)

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Table 3 10.6-µm CO2 Laser Transmittance Relative Standard Uncertainty Components (% Measured Value)

Tables Icon

Table 4 Comparison of the FT-IR and Laser Transmittance Values for the Three Samples Discussed in the Texta

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T=1-r1+r,

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