Abstract

A procedure for calibration of a spectral bandwidth standard for high-resolution spectrophotometers is described. Symmetrical absorption bands for a crystal standard are adopted. The method relies on spectral band shape fitting followed by a convolution with the slit function of the spectrophotometer. A reference spectrophotometer is used to calibrate the spectral bandwidth standard. Bandwidth calibration curves for a minimum spectral transmission factor relative to the spectral bandwidth of the reference spectrophotometer are derived for the absorption bands at the wavelength of the band absorption maximum. The family of these calibration curves characterizes the spectral bandwidth standard. We calibrate the spectral bandwidth of a spectrophotometer with respect to the reference spectrophotometer by determining the spectral transmission factor minimum at every calibrated absorption band of the bandwidth standard for the nominal instrument values of the spectral bandwidth. With reference to the standard spectral bandwidth calibration curves, the relation of the spectral bandwidth to the reference spectrophotometer is determined. We determine the discrepancy in the spectrophotometers’ spectral bandwidths by averaging the spectral bandwidth discrepancies relative to the standard calibrated values found at the absorption bands considered. A weighted average of the uncertainties is taken.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. F. Verrill, “Advances in spectrophotometric transfer standards at National Physical Laboratory” in Spectrophotometry, Luminescence and Colour, Sciences and Compliance, C. Burgess, D. C. Jones, eds. (Elsevier, Amsterdam, 1995), pp. 49–63.
  2. McCrone wavelength standards with calibration certificates can be ordered from the National Physical Laboratory, Teddington, UK.
  3. National Physical Laboratory, “Certificate of calibration, one wavelength standard,” (National Physical Laboratory, Teddington, UK, 1994), pp. 1–3.
  4. O. Svelto, Principles of Lasers (Plenum, New York, 1989).
  5. S. Brodersen, “Resolving power and noise in infrared spectroscopes,” J. Opt. Soc. Am. 43, 877–881 (1953);“Slit-width effects,” J. Opt. Soc. Am. A 43, 22–25 (1954).
    [CrossRef]
  6. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986).
  7. O. D. D. Soares, J. L. Costa, “Spectral bandwidth standard based on symmetrical absorption bands of a crystal standard,” in Applications of Photonic Technology 3: Closing the Gap between Theory, Development, and Application, G. A. Lampropoulos, R. A. Lessard, eds., Proc. SPIE3491, 854–859 (1998).
  8. O. D. D. Soares, J. L. Costa, “Spectrocolorimetric scale harmonisation,” in Applications of Photonic Technology 3: Closing the Gap between Theory, Development, and Application, G. A. Lampropoulos, R. A. Lessard, eds., Proc. SPIE3491, 818–825 (1998).
  9. ISO/IEC/OIML/BIPM, Guide to the Expression of Uncertainty in Measurements, ISO/TAG 4/WG3 (International Organization for Standardization, Geneva, 1993).
  10. National Physical Laboratory, “Certification of calibration, a set of 5 reflectance standards, BN97” (National Physical Laboratory, Teddington, UK, May1997), pp. 1–17.
  11. Central Bureau of CIE, Colourimetry 15.2 (Commission International de Eclairage, Vienna, 1986).
  12. J. F. Verrill, “Harmonization of national scales of surface colour measurements,” (National Physical Laboratory, Teddington, UK, 1998), pp. 1–52.

1953 (1)

Brodersen, S.

Costa, J. L.

O. D. D. Soares, J. L. Costa, “Spectral bandwidth standard based on symmetrical absorption bands of a crystal standard,” in Applications of Photonic Technology 3: Closing the Gap between Theory, Development, and Application, G. A. Lampropoulos, R. A. Lessard, eds., Proc. SPIE3491, 854–859 (1998).

O. D. D. Soares, J. L. Costa, “Spectrocolorimetric scale harmonisation,” in Applications of Photonic Technology 3: Closing the Gap between Theory, Development, and Application, G. A. Lampropoulos, R. A. Lessard, eds., Proc. SPIE3491, 818–825 (1998).

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986).

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986).

Soares, O. D. D.

O. D. D. Soares, J. L. Costa, “Spectrocolorimetric scale harmonisation,” in Applications of Photonic Technology 3: Closing the Gap between Theory, Development, and Application, G. A. Lampropoulos, R. A. Lessard, eds., Proc. SPIE3491, 818–825 (1998).

O. D. D. Soares, J. L. Costa, “Spectral bandwidth standard based on symmetrical absorption bands of a crystal standard,” in Applications of Photonic Technology 3: Closing the Gap between Theory, Development, and Application, G. A. Lampropoulos, R. A. Lessard, eds., Proc. SPIE3491, 854–859 (1998).

Svelto, O.

O. Svelto, Principles of Lasers (Plenum, New York, 1989).

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986).

Verrill, J. F.

J. F. Verrill, “Advances in spectrophotometric transfer standards at National Physical Laboratory” in Spectrophotometry, Luminescence and Colour, Sciences and Compliance, C. Burgess, D. C. Jones, eds. (Elsevier, Amsterdam, 1995), pp. 49–63.

J. F. Verrill, “Harmonization of national scales of surface colour measurements,” (National Physical Laboratory, Teddington, UK, 1998), pp. 1–52.

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986).

J. Opt. Soc. Am. (1)

Other (11)

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986).

O. D. D. Soares, J. L. Costa, “Spectral bandwidth standard based on symmetrical absorption bands of a crystal standard,” in Applications of Photonic Technology 3: Closing the Gap between Theory, Development, and Application, G. A. Lampropoulos, R. A. Lessard, eds., Proc. SPIE3491, 854–859 (1998).

O. D. D. Soares, J. L. Costa, “Spectrocolorimetric scale harmonisation,” in Applications of Photonic Technology 3: Closing the Gap between Theory, Development, and Application, G. A. Lampropoulos, R. A. Lessard, eds., Proc. SPIE3491, 818–825 (1998).

ISO/IEC/OIML/BIPM, Guide to the Expression of Uncertainty in Measurements, ISO/TAG 4/WG3 (International Organization for Standardization, Geneva, 1993).

National Physical Laboratory, “Certification of calibration, a set of 5 reflectance standards, BN97” (National Physical Laboratory, Teddington, UK, May1997), pp. 1–17.

Central Bureau of CIE, Colourimetry 15.2 (Commission International de Eclairage, Vienna, 1986).

J. F. Verrill, “Harmonization of national scales of surface colour measurements,” (National Physical Laboratory, Teddington, UK, 1998), pp. 1–52.

J. F. Verrill, “Advances in spectrophotometric transfer standards at National Physical Laboratory” in Spectrophotometry, Luminescence and Colour, Sciences and Compliance, C. Burgess, D. C. Jones, eds. (Elsevier, Amsterdam, 1995), pp. 49–63.

McCrone wavelength standards with calibration certificates can be ordered from the National Physical Laboratory, Teddington, UK.

National Physical Laboratory, “Certificate of calibration, one wavelength standard,” (National Physical Laboratory, Teddington, UK, 1994), pp. 1–3.

O. Svelto, Principles of Lasers (Plenum, New York, 1989).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Transmission spectrum of wavelength standard JS93.

Fig. 2
Fig. 2

Variation in the transmission spectrum of the JS93 wavelength standard with changes in the reference instruments’ bandwidth. Absorption peaks at (a) 353.92 nm, (b) 588.45 nm, (c) 748.20 nm. SBW, spectral bandwidth.

Fig. 3
Fig. 3

Calibration curves derived by the Levenberg–Marquardt method6 for three absorption peaks of bandwidth standard JS93. Absorption peaks are at (a) 353.92 nm, (b) 588.45 nm, and (c) 748.20 nm.

Fig. 4
Fig. 4

Bandwidth discrepancies and corresponding uncertainties for use of bandwidth standard JS93 to calibrate a spectrophotometer. Absorption peaks are at (a) 353.92 nm, (b) 588.45 nm, and (c) 748.20 nm.

Fig. 5
Fig. 5

Spectrophotometer bandwidth calibration with reference to the bandwidth standard JS93.

Fig. 6
Fig. 6

Calibration of bandwidth scales for a set of instruments at 23 laboratories. The spectral bandwidth discrepancies are weighted averages with uncertainties including the values at calibrated bandwidth standard absorption peaks: 353.92, 588.45, and 748.20 nm. The three bandwidth nominal values from left to right correspond to bandwidth nominal values of 0.5, 1, and 2 nm or more (for instruments with fixed bandwidths).

Fig. 7
Fig. 7

Variations in spectral reflection factor R of the orange tile color standard for variable spectral bandwidth S.

Tables (3)

Tables Icon

Table 1 Wavelength Values of Six Absorption Peaks of Wavelength Standard JS93 for Bandwidths of 0.5, 1.0, and 2 nm measured at 25 °C)a

Tables Icon

Table 2 Model Design Parameters from the Levenberg–Marquardt Method of Adjustmentsa

Tables Icon

Table 3 Color Coordinate Discrepancies Owing to Spectral Bandwidth Variations Near a Set Value of 2 nma

Equations (6)

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

D=D0 exp-ν-ν022σ2,
Gλ, λ0, B, C=10-B exp-C λ-λ02λ2,
Mλ, λ0, A, S=A exp-λ-λ02/S2/4ln2,
Tλ0=1Sλ0-3Sλ0+3S Gλ, λ0, B, CMλ, λ0, A, Sdλ.
σΔS2=σSmeasured2+σScalibrated2.
σScalibrated2=σT2γT2+σA2γA2+σB2γB2+σC2γC2+σλ02γλ02+2σAB2γAB+2σBC2γBC+2σAC2γAC,

Metrics