Abstract

We present a guide to the implementation and uncertainty evaluation for spectral stray light corrections according to the widely used method as proposed by Zong et al. [Appl. Opt. 45, 1111 (2006) [CrossRef]  ]. The uncertainty analysis is based on the Monte Carlo approach in accordance with the Guide to the Expression of Uncertainty in Measurement (JCGM, Paris, 2008). We show that significant uncertainty contributions result from drifts of the spectrometer’s dark signal and the width of the in-band region selected for shaping stray light distribution functions. Additionally, a simplified method for estimating these uncertainty contributions is presented, which does not require a complex Monte Carlo analysis. We also show that stray light correction may introduce correlations with respect to wavelength.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Stray light correction of array spectroradiometers for solar UV measurements

Saulius Nevas, Julian Gröbner, Luca Egli, and Mario Blumthaler
Appl. Opt. 53(19) 4313-4319 (2014)

Simple spectral stray light correction method for array spectroradiometers

Yuqin Zong, Steven W. Brown, B. Carol Johnson, Keith R. Lykke, and Yoshi Ohno
Appl. Opt. 45(6) 1111-1119 (2006)

Uncertainty evaluation for the spectroradiometric measurement of the averaged light-emitting diode intensity

Seongchong Park, Dong-Hoon Lee, Yong-Wan Kim, and Seung-Nam Park
Appl. Opt. 46(15) 2851-2858 (2007)

References

  • View by:
  • |
  • |
  • |

  1. H. J. Kostkowski, Reliable Spectroradiometry (La Plata, 1997).
  2. S. Brown, B. C. Johnson, M. E. Feinholz, M. A. Yarbrough, S. J. Flora, K. R. Lykke, and D. K. Clark, “Stray-light correction algorithm for spectrographs,” Metrologia 40, S81–S84 (2003).
    [Crossref]
  3. L. Ylianttila, R. Visuri, L. Huurto, and K. Jokela, “Evaluation of a single-monochromator diode array spectroradiometer for sunbed UV-radiation measurements,” Photochem. Photobiol. 81, 333–341 (2005).
    [Crossref]
  4. Y. Zong, S. W. Brown, B. C. Johnson, K. R. Lykke, and Y. Ohno, “Simple spectral stray light correction method for array spectroradiometers,” Appl. Opt. 45, 1111–1119 (2006).
    [Crossref]
  5. M. Shaw and T. Goodman, “Array-based goniospectroradiometer for measurement of spectral radiant intensity and spectral total flux of light sources,” Appl. Opt. 47, 2637–2647 (2008).
    [Crossref]
  6. K. Lenhard, P. Gege, and M. Damm, “Implementation of algorithmic correction of stray light in a pushbroom hyperspectral sensor,” in 6th EARSeL Imaging Spectroscopy SIG Workshop (2009).
  7. H. Shen, J. Pan, H. Feng, and M. Liu, “Stray light errors in spectral colour measurement and two rejection methods,” Metrologia 46, 129 (2009).
    [Crossref]
  8. A. Kreuter and M. Blumthaler, “Stray light correction for solar measurements using array spectrometers,” Rev. Sci. Instrum. 80, 096108 (2009).
    [Crossref]
  9. E. R. Wooliams, R. Baribeau, A. Bialek, and M. G. Cox, “Spectrometer bandwidth correction for generalized bandpass functions,” Metrologia 48, 164–172 (2011).
    [Crossref]
  10. S. G. R. Salim, N. P. Fox, W. S. Hartree, E. R. Woolliams, T. Sun, and K. T. V. Grattan, “Stray light correction for diode-array-based spectrometers using a monochromator,” Appl. Opt. 50, 5130–5138 (2011).
    [Crossref]
  11. M. E. Feinholz, S. J. Flora, S. W. Brown, Y. Zong, K. R. Lykke, M. A. Yarbrough, B. C. Johnson, and D. K. Clark, “Stray light correction algorithm for multichannel hyperspectral spectrographs,” Appl. Opt. 51, 3631–3641 (2012).
    [Crossref]
  12. J. L. Gardner, “Spectral deconvolution applications for colorimetry,” Color Res. Appl. 39, 430–435 (2013).
    [Crossref]
  13. S. Nevas, J. Gröbner, L. Egli, and M. Blumthaler, “Stray light correction of array spectroradiometers for solar UV measurements,” Appl. Opt. 53, 4313–4319 (2014).
    [Crossref]
  14. B. Bohn and I. Lohse, “Calibration and evaluation of CCD spectroradiometers for ground-based and airborne measurements of spectral actinic flux densities,” Atmos. Meas. Tech. 10, 3151–3174 (2017).
    [Crossref]
  15. D. R. Thompson, J. W. Boardman, M. L. Eastwood, R. O. Green, J. M. Haag, P. Mouroulis, and B. V. Gorp, “Imaging spectrometer stray spectral response: in-flight characterization, correction, and validation,” Remote Sens. Environ. 204, 850–860 (2018).
    [Crossref]
  16. F. Schmähling, G. Wübbeler, U. Krüger, B. Ruggaber, F. Schmidt, R. D. Taubert, A. Sperling, and C. Elster, “Uncertainty evaluation and propagation for spectral measurements,” Color Res. Appl. 43, 6–16 (2018).
    [Crossref]
  17. S. Park, D.-H. Lee, Y.-W. Kim, and S.-N. Park, “Uncertainty evaluation for the spectroradiometric measurement of the averaged light-emitting diode intensity,” Appl. Opt. 46, 2851–2858 (2007).
    [Crossref]
  18. Y. Zong, “Uncertainty analysis of stray-light correction,” in Proc. CIE Expert Symposium on Spectral and Imaging Methods for Photometry and Radiometry (2010).
  19. J. Dubard and R. Etienne, “A guide for the evaluation of the solar spectrum measurement uncertainty using array spectroradiometers,” in Technical report (EURAMET, 2013).
  20. J. Dubard, R. Etienne, and T. Valin, “Uncertainty evaluation of spectrally resolved source output measurement using array spectroradiometer,” in Proc. CIE Expert Symposium on Measurement Uncertainties in Photometry and Radiometry for Industry (2014).
  21. Joint Committee for Guides in Metrology, Guide to the Expression of Uncertainty in Measurement (BIPM, 2008).
  22. J. Kuusk, I. Ansko, A. Bialek, R. Vendt, and N. Fox, “Implication of illumination beam geometry on stray light and bandpass characteristics of diode array spectrometer,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sensing 11, 2925–2932 (2018).
    [Crossref]
  23. S. Nevas, M. Lindemann, A. Sperling, A. Teuber, and R. Maass, “Colorimetry of LEDs with array spectroradiometers,” Mapan 24, 153 (2009).
    [Crossref]
  24. Joint Committee for Guides in Metrology, Evaluation of measurement data-Supplement 1 to the “Guide to the expression of uncertainty in measurement”-Propagation of distributions using a Monte Carlo method (BIPM, 2008).
  25. Joint Committee for Guides in Metrology, International vocabulary of metrology-Basic and general concepts and associated terms (VIM) (BIPM, 2008).
  26. J. L. Gardner, “Uncertainties in interpolated spectral data,” J. Res. Natl. Inst. Stand. Technol. 108, 69 (2003).
    [Crossref]
  27. E. R. Woolliams, “Determining the uncertainty associated with integrals of spectral quantities,” in Technical report (National Physical Laboratory, 2013).
  28. K. Pearson, “VII. Mathematical contributions to the theory of evolution.-iii. Regression, heredity, and panmixia,” Philos. Trans. R. Soc. London, Ser. A 187, 253–318 (1896).
    [Crossref]
  29. J. L. Rodgers and W. A. Nicewander, “Thirteen ways to look at the correlation coefficient,” Amer. Statist. 42, 59–66 (1988).
    [Crossref]
  30. S. Nevas, G. Wübbeler, A. Sperling, C. Elster, and A. Teuber, “Simultaneous correction of bandpass and stray-light effects in array spectroradiometer data,” Metrologia 49, S43–S47 (2012).
    [Crossref]
  31. E. I. Stearns and R. E. Stearns, “An example of a method for correcting radiance data for bandpass error,” Color Res. Appl. 13, 257–259 (1988).
    [Crossref]
  32. J. L. Gardner, “Bandwidth correction for LED chromaticity,” Color Res. Appl. 31, 374–380 (2006).
    [Crossref]
  33. S. Eichstädt, F. Schmähling, G. Wübbeler, K. Anhalt, L. Bünger, U. Krüger, and C. Elster, “Comparison of the Richardson-Lucy method and a classical approach for spectrometer bandpass correction,” Metrologia 50, 107 (2013).
    [Crossref]

2018 (3)

J. Kuusk, I. Ansko, A. Bialek, R. Vendt, and N. Fox, “Implication of illumination beam geometry on stray light and bandpass characteristics of diode array spectrometer,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sensing 11, 2925–2932 (2018).
[Crossref]

D. R. Thompson, J. W. Boardman, M. L. Eastwood, R. O. Green, J. M. Haag, P. Mouroulis, and B. V. Gorp, “Imaging spectrometer stray spectral response: in-flight characterization, correction, and validation,” Remote Sens. Environ. 204, 850–860 (2018).
[Crossref]

F. Schmähling, G. Wübbeler, U. Krüger, B. Ruggaber, F. Schmidt, R. D. Taubert, A. Sperling, and C. Elster, “Uncertainty evaluation and propagation for spectral measurements,” Color Res. Appl. 43, 6–16 (2018).
[Crossref]

2017 (1)

B. Bohn and I. Lohse, “Calibration and evaluation of CCD spectroradiometers for ground-based and airborne measurements of spectral actinic flux densities,” Atmos. Meas. Tech. 10, 3151–3174 (2017).
[Crossref]

2014 (1)

2013 (2)

J. L. Gardner, “Spectral deconvolution applications for colorimetry,” Color Res. Appl. 39, 430–435 (2013).
[Crossref]

S. Eichstädt, F. Schmähling, G. Wübbeler, K. Anhalt, L. Bünger, U. Krüger, and C. Elster, “Comparison of the Richardson-Lucy method and a classical approach for spectrometer bandpass correction,” Metrologia 50, 107 (2013).
[Crossref]

2012 (2)

S. Nevas, G. Wübbeler, A. Sperling, C. Elster, and A. Teuber, “Simultaneous correction of bandpass and stray-light effects in array spectroradiometer data,” Metrologia 49, S43–S47 (2012).
[Crossref]

M. E. Feinholz, S. J. Flora, S. W. Brown, Y. Zong, K. R. Lykke, M. A. Yarbrough, B. C. Johnson, and D. K. Clark, “Stray light correction algorithm for multichannel hyperspectral spectrographs,” Appl. Opt. 51, 3631–3641 (2012).
[Crossref]

2011 (2)

E. R. Wooliams, R. Baribeau, A. Bialek, and M. G. Cox, “Spectrometer bandwidth correction for generalized bandpass functions,” Metrologia 48, 164–172 (2011).
[Crossref]

S. G. R. Salim, N. P. Fox, W. S. Hartree, E. R. Woolliams, T. Sun, and K. T. V. Grattan, “Stray light correction for diode-array-based spectrometers using a monochromator,” Appl. Opt. 50, 5130–5138 (2011).
[Crossref]

2009 (3)

H. Shen, J. Pan, H. Feng, and M. Liu, “Stray light errors in spectral colour measurement and two rejection methods,” Metrologia 46, 129 (2009).
[Crossref]

A. Kreuter and M. Blumthaler, “Stray light correction for solar measurements using array spectrometers,” Rev. Sci. Instrum. 80, 096108 (2009).
[Crossref]

S. Nevas, M. Lindemann, A. Sperling, A. Teuber, and R. Maass, “Colorimetry of LEDs with array spectroradiometers,” Mapan 24, 153 (2009).
[Crossref]

2008 (1)

2007 (1)

2006 (2)

2005 (1)

L. Ylianttila, R. Visuri, L. Huurto, and K. Jokela, “Evaluation of a single-monochromator diode array spectroradiometer for sunbed UV-radiation measurements,” Photochem. Photobiol. 81, 333–341 (2005).
[Crossref]

2003 (2)

S. Brown, B. C. Johnson, M. E. Feinholz, M. A. Yarbrough, S. J. Flora, K. R. Lykke, and D. K. Clark, “Stray-light correction algorithm for spectrographs,” Metrologia 40, S81–S84 (2003).
[Crossref]

J. L. Gardner, “Uncertainties in interpolated spectral data,” J. Res. Natl. Inst. Stand. Technol. 108, 69 (2003).
[Crossref]

1988 (2)

J. L. Rodgers and W. A. Nicewander, “Thirteen ways to look at the correlation coefficient,” Amer. Statist. 42, 59–66 (1988).
[Crossref]

E. I. Stearns and R. E. Stearns, “An example of a method for correcting radiance data for bandpass error,” Color Res. Appl. 13, 257–259 (1988).
[Crossref]

1896 (1)

K. Pearson, “VII. Mathematical contributions to the theory of evolution.-iii. Regression, heredity, and panmixia,” Philos. Trans. R. Soc. London, Ser. A 187, 253–318 (1896).
[Crossref]

Anhalt, K.

S. Eichstädt, F. Schmähling, G. Wübbeler, K. Anhalt, L. Bünger, U. Krüger, and C. Elster, “Comparison of the Richardson-Lucy method and a classical approach for spectrometer bandpass correction,” Metrologia 50, 107 (2013).
[Crossref]

Ansko, I.

J. Kuusk, I. Ansko, A. Bialek, R. Vendt, and N. Fox, “Implication of illumination beam geometry on stray light and bandpass characteristics of diode array spectrometer,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sensing 11, 2925–2932 (2018).
[Crossref]

Baribeau, R.

E. R. Wooliams, R. Baribeau, A. Bialek, and M. G. Cox, “Spectrometer bandwidth correction for generalized bandpass functions,” Metrologia 48, 164–172 (2011).
[Crossref]

Bialek, A.

J. Kuusk, I. Ansko, A. Bialek, R. Vendt, and N. Fox, “Implication of illumination beam geometry on stray light and bandpass characteristics of diode array spectrometer,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sensing 11, 2925–2932 (2018).
[Crossref]

E. R. Wooliams, R. Baribeau, A. Bialek, and M. G. Cox, “Spectrometer bandwidth correction for generalized bandpass functions,” Metrologia 48, 164–172 (2011).
[Crossref]

Blumthaler, M.

S. Nevas, J. Gröbner, L. Egli, and M. Blumthaler, “Stray light correction of array spectroradiometers for solar UV measurements,” Appl. Opt. 53, 4313–4319 (2014).
[Crossref]

A. Kreuter and M. Blumthaler, “Stray light correction for solar measurements using array spectrometers,” Rev. Sci. Instrum. 80, 096108 (2009).
[Crossref]

Boardman, J. W.

D. R. Thompson, J. W. Boardman, M. L. Eastwood, R. O. Green, J. M. Haag, P. Mouroulis, and B. V. Gorp, “Imaging spectrometer stray spectral response: in-flight characterization, correction, and validation,” Remote Sens. Environ. 204, 850–860 (2018).
[Crossref]

Bohn, B.

B. Bohn and I. Lohse, “Calibration and evaluation of CCD spectroradiometers for ground-based and airborne measurements of spectral actinic flux densities,” Atmos. Meas. Tech. 10, 3151–3174 (2017).
[Crossref]

Brown, S.

S. Brown, B. C. Johnson, M. E. Feinholz, M. A. Yarbrough, S. J. Flora, K. R. Lykke, and D. K. Clark, “Stray-light correction algorithm for spectrographs,” Metrologia 40, S81–S84 (2003).
[Crossref]

Brown, S. W.

Bünger, L.

S. Eichstädt, F. Schmähling, G. Wübbeler, K. Anhalt, L. Bünger, U. Krüger, and C. Elster, “Comparison of the Richardson-Lucy method and a classical approach for spectrometer bandpass correction,” Metrologia 50, 107 (2013).
[Crossref]

Clark, D. K.

M. E. Feinholz, S. J. Flora, S. W. Brown, Y. Zong, K. R. Lykke, M. A. Yarbrough, B. C. Johnson, and D. K. Clark, “Stray light correction algorithm for multichannel hyperspectral spectrographs,” Appl. Opt. 51, 3631–3641 (2012).
[Crossref]

S. Brown, B. C. Johnson, M. E. Feinholz, M. A. Yarbrough, S. J. Flora, K. R. Lykke, and D. K. Clark, “Stray-light correction algorithm for spectrographs,” Metrologia 40, S81–S84 (2003).
[Crossref]

Cox, M. G.

E. R. Wooliams, R. Baribeau, A. Bialek, and M. G. Cox, “Spectrometer bandwidth correction for generalized bandpass functions,” Metrologia 48, 164–172 (2011).
[Crossref]

Damm, M.

K. Lenhard, P. Gege, and M. Damm, “Implementation of algorithmic correction of stray light in a pushbroom hyperspectral sensor,” in 6th EARSeL Imaging Spectroscopy SIG Workshop (2009).

Dubard, J.

J. Dubard, R. Etienne, and T. Valin, “Uncertainty evaluation of spectrally resolved source output measurement using array spectroradiometer,” in Proc. CIE Expert Symposium on Measurement Uncertainties in Photometry and Radiometry for Industry (2014).

J. Dubard and R. Etienne, “A guide for the evaluation of the solar spectrum measurement uncertainty using array spectroradiometers,” in Technical report (EURAMET, 2013).

Eastwood, M. L.

D. R. Thompson, J. W. Boardman, M. L. Eastwood, R. O. Green, J. M. Haag, P. Mouroulis, and B. V. Gorp, “Imaging spectrometer stray spectral response: in-flight characterization, correction, and validation,” Remote Sens. Environ. 204, 850–860 (2018).
[Crossref]

Egli, L.

Eichstädt, S.

S. Eichstädt, F. Schmähling, G. Wübbeler, K. Anhalt, L. Bünger, U. Krüger, and C. Elster, “Comparison of the Richardson-Lucy method and a classical approach for spectrometer bandpass correction,” Metrologia 50, 107 (2013).
[Crossref]

Elster, C.

F. Schmähling, G. Wübbeler, U. Krüger, B. Ruggaber, F. Schmidt, R. D. Taubert, A. Sperling, and C. Elster, “Uncertainty evaluation and propagation for spectral measurements,” Color Res. Appl. 43, 6–16 (2018).
[Crossref]

S. Eichstädt, F. Schmähling, G. Wübbeler, K. Anhalt, L. Bünger, U. Krüger, and C. Elster, “Comparison of the Richardson-Lucy method and a classical approach for spectrometer bandpass correction,” Metrologia 50, 107 (2013).
[Crossref]

S. Nevas, G. Wübbeler, A. Sperling, C. Elster, and A. Teuber, “Simultaneous correction of bandpass and stray-light effects in array spectroradiometer data,” Metrologia 49, S43–S47 (2012).
[Crossref]

Etienne, R.

J. Dubard and R. Etienne, “A guide for the evaluation of the solar spectrum measurement uncertainty using array spectroradiometers,” in Technical report (EURAMET, 2013).

J. Dubard, R. Etienne, and T. Valin, “Uncertainty evaluation of spectrally resolved source output measurement using array spectroradiometer,” in Proc. CIE Expert Symposium on Measurement Uncertainties in Photometry and Radiometry for Industry (2014).

Feinholz, M. E.

M. E. Feinholz, S. J. Flora, S. W. Brown, Y. Zong, K. R. Lykke, M. A. Yarbrough, B. C. Johnson, and D. K. Clark, “Stray light correction algorithm for multichannel hyperspectral spectrographs,” Appl. Opt. 51, 3631–3641 (2012).
[Crossref]

S. Brown, B. C. Johnson, M. E. Feinholz, M. A. Yarbrough, S. J. Flora, K. R. Lykke, and D. K. Clark, “Stray-light correction algorithm for spectrographs,” Metrologia 40, S81–S84 (2003).
[Crossref]

Feng, H.

H. Shen, J. Pan, H. Feng, and M. Liu, “Stray light errors in spectral colour measurement and two rejection methods,” Metrologia 46, 129 (2009).
[Crossref]

Flora, S. J.

M. E. Feinholz, S. J. Flora, S. W. Brown, Y. Zong, K. R. Lykke, M. A. Yarbrough, B. C. Johnson, and D. K. Clark, “Stray light correction algorithm for multichannel hyperspectral spectrographs,” Appl. Opt. 51, 3631–3641 (2012).
[Crossref]

S. Brown, B. C. Johnson, M. E. Feinholz, M. A. Yarbrough, S. J. Flora, K. R. Lykke, and D. K. Clark, “Stray-light correction algorithm for spectrographs,” Metrologia 40, S81–S84 (2003).
[Crossref]

Fox, N.

J. Kuusk, I. Ansko, A. Bialek, R. Vendt, and N. Fox, “Implication of illumination beam geometry on stray light and bandpass characteristics of diode array spectrometer,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sensing 11, 2925–2932 (2018).
[Crossref]

Fox, N. P.

Gardner, J. L.

J. L. Gardner, “Spectral deconvolution applications for colorimetry,” Color Res. Appl. 39, 430–435 (2013).
[Crossref]

J. L. Gardner, “Bandwidth correction for LED chromaticity,” Color Res. Appl. 31, 374–380 (2006).
[Crossref]

J. L. Gardner, “Uncertainties in interpolated spectral data,” J. Res. Natl. Inst. Stand. Technol. 108, 69 (2003).
[Crossref]

Gege, P.

K. Lenhard, P. Gege, and M. Damm, “Implementation of algorithmic correction of stray light in a pushbroom hyperspectral sensor,” in 6th EARSeL Imaging Spectroscopy SIG Workshop (2009).

Goodman, T.

Gorp, B. V.

D. R. Thompson, J. W. Boardman, M. L. Eastwood, R. O. Green, J. M. Haag, P. Mouroulis, and B. V. Gorp, “Imaging spectrometer stray spectral response: in-flight characterization, correction, and validation,” Remote Sens. Environ. 204, 850–860 (2018).
[Crossref]

Grattan, K. T. V.

Green, R. O.

D. R. Thompson, J. W. Boardman, M. L. Eastwood, R. O. Green, J. M. Haag, P. Mouroulis, and B. V. Gorp, “Imaging spectrometer stray spectral response: in-flight characterization, correction, and validation,” Remote Sens. Environ. 204, 850–860 (2018).
[Crossref]

Gröbner, J.

Haag, J. M.

D. R. Thompson, J. W. Boardman, M. L. Eastwood, R. O. Green, J. M. Haag, P. Mouroulis, and B. V. Gorp, “Imaging spectrometer stray spectral response: in-flight characterization, correction, and validation,” Remote Sens. Environ. 204, 850–860 (2018).
[Crossref]

Hartree, W. S.

Huurto, L.

L. Ylianttila, R. Visuri, L. Huurto, and K. Jokela, “Evaluation of a single-monochromator diode array spectroradiometer for sunbed UV-radiation measurements,” Photochem. Photobiol. 81, 333–341 (2005).
[Crossref]

Johnson, B. C.

Jokela, K.

L. Ylianttila, R. Visuri, L. Huurto, and K. Jokela, “Evaluation of a single-monochromator diode array spectroradiometer for sunbed UV-radiation measurements,” Photochem. Photobiol. 81, 333–341 (2005).
[Crossref]

Kim, Y.-W.

Kostkowski, H. J.

H. J. Kostkowski, Reliable Spectroradiometry (La Plata, 1997).

Kreuter, A.

A. Kreuter and M. Blumthaler, “Stray light correction for solar measurements using array spectrometers,” Rev. Sci. Instrum. 80, 096108 (2009).
[Crossref]

Krüger, U.

F. Schmähling, G. Wübbeler, U. Krüger, B. Ruggaber, F. Schmidt, R. D. Taubert, A. Sperling, and C. Elster, “Uncertainty evaluation and propagation for spectral measurements,” Color Res. Appl. 43, 6–16 (2018).
[Crossref]

S. Eichstädt, F. Schmähling, G. Wübbeler, K. Anhalt, L. Bünger, U. Krüger, and C. Elster, “Comparison of the Richardson-Lucy method and a classical approach for spectrometer bandpass correction,” Metrologia 50, 107 (2013).
[Crossref]

Kuusk, J.

J. Kuusk, I. Ansko, A. Bialek, R. Vendt, and N. Fox, “Implication of illumination beam geometry on stray light and bandpass characteristics of diode array spectrometer,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sensing 11, 2925–2932 (2018).
[Crossref]

Lee, D.-H.

Lenhard, K.

K. Lenhard, P. Gege, and M. Damm, “Implementation of algorithmic correction of stray light in a pushbroom hyperspectral sensor,” in 6th EARSeL Imaging Spectroscopy SIG Workshop (2009).

Lindemann, M.

S. Nevas, M. Lindemann, A. Sperling, A. Teuber, and R. Maass, “Colorimetry of LEDs with array spectroradiometers,” Mapan 24, 153 (2009).
[Crossref]

Liu, M.

H. Shen, J. Pan, H. Feng, and M. Liu, “Stray light errors in spectral colour measurement and two rejection methods,” Metrologia 46, 129 (2009).
[Crossref]

Lohse, I.

B. Bohn and I. Lohse, “Calibration and evaluation of CCD spectroradiometers for ground-based and airborne measurements of spectral actinic flux densities,” Atmos. Meas. Tech. 10, 3151–3174 (2017).
[Crossref]

Lykke, K. R.

Maass, R.

S. Nevas, M. Lindemann, A. Sperling, A. Teuber, and R. Maass, “Colorimetry of LEDs with array spectroradiometers,” Mapan 24, 153 (2009).
[Crossref]

Mouroulis, P.

D. R. Thompson, J. W. Boardman, M. L. Eastwood, R. O. Green, J. M. Haag, P. Mouroulis, and B. V. Gorp, “Imaging spectrometer stray spectral response: in-flight characterization, correction, and validation,” Remote Sens. Environ. 204, 850–860 (2018).
[Crossref]

Nevas, S.

S. Nevas, J. Gröbner, L. Egli, and M. Blumthaler, “Stray light correction of array spectroradiometers for solar UV measurements,” Appl. Opt. 53, 4313–4319 (2014).
[Crossref]

S. Nevas, G. Wübbeler, A. Sperling, C. Elster, and A. Teuber, “Simultaneous correction of bandpass and stray-light effects in array spectroradiometer data,” Metrologia 49, S43–S47 (2012).
[Crossref]

S. Nevas, M. Lindemann, A. Sperling, A. Teuber, and R. Maass, “Colorimetry of LEDs with array spectroradiometers,” Mapan 24, 153 (2009).
[Crossref]

Nicewander, W. A.

J. L. Rodgers and W. A. Nicewander, “Thirteen ways to look at the correlation coefficient,” Amer. Statist. 42, 59–66 (1988).
[Crossref]

Ohno, Y.

Pan, J.

H. Shen, J. Pan, H. Feng, and M. Liu, “Stray light errors in spectral colour measurement and two rejection methods,” Metrologia 46, 129 (2009).
[Crossref]

Park, S.

Park, S.-N.

Pearson, K.

K. Pearson, “VII. Mathematical contributions to the theory of evolution.-iii. Regression, heredity, and panmixia,” Philos. Trans. R. Soc. London, Ser. A 187, 253–318 (1896).
[Crossref]

Rodgers, J. L.

J. L. Rodgers and W. A. Nicewander, “Thirteen ways to look at the correlation coefficient,” Amer. Statist. 42, 59–66 (1988).
[Crossref]

Ruggaber, B.

F. Schmähling, G. Wübbeler, U. Krüger, B. Ruggaber, F. Schmidt, R. D. Taubert, A. Sperling, and C. Elster, “Uncertainty evaluation and propagation for spectral measurements,” Color Res. Appl. 43, 6–16 (2018).
[Crossref]

Salim, S. G. R.

Schmähling, F.

F. Schmähling, G. Wübbeler, U. Krüger, B. Ruggaber, F. Schmidt, R. D. Taubert, A. Sperling, and C. Elster, “Uncertainty evaluation and propagation for spectral measurements,” Color Res. Appl. 43, 6–16 (2018).
[Crossref]

S. Eichstädt, F. Schmähling, G. Wübbeler, K. Anhalt, L. Bünger, U. Krüger, and C. Elster, “Comparison of the Richardson-Lucy method and a classical approach for spectrometer bandpass correction,” Metrologia 50, 107 (2013).
[Crossref]

Schmidt, F.

F. Schmähling, G. Wübbeler, U. Krüger, B. Ruggaber, F. Schmidt, R. D. Taubert, A. Sperling, and C. Elster, “Uncertainty evaluation and propagation for spectral measurements,” Color Res. Appl. 43, 6–16 (2018).
[Crossref]

Shaw, M.

Shen, H.

H. Shen, J. Pan, H. Feng, and M. Liu, “Stray light errors in spectral colour measurement and two rejection methods,” Metrologia 46, 129 (2009).
[Crossref]

Sperling, A.

F. Schmähling, G. Wübbeler, U. Krüger, B. Ruggaber, F. Schmidt, R. D. Taubert, A. Sperling, and C. Elster, “Uncertainty evaluation and propagation for spectral measurements,” Color Res. Appl. 43, 6–16 (2018).
[Crossref]

S. Nevas, G. Wübbeler, A. Sperling, C. Elster, and A. Teuber, “Simultaneous correction of bandpass and stray-light effects in array spectroradiometer data,” Metrologia 49, S43–S47 (2012).
[Crossref]

S. Nevas, M. Lindemann, A. Sperling, A. Teuber, and R. Maass, “Colorimetry of LEDs with array spectroradiometers,” Mapan 24, 153 (2009).
[Crossref]

Stearns, E. I.

E. I. Stearns and R. E. Stearns, “An example of a method for correcting radiance data for bandpass error,” Color Res. Appl. 13, 257–259 (1988).
[Crossref]

Stearns, R. E.

E. I. Stearns and R. E. Stearns, “An example of a method for correcting radiance data for bandpass error,” Color Res. Appl. 13, 257–259 (1988).
[Crossref]

Sun, T.

Taubert, R. D.

F. Schmähling, G. Wübbeler, U. Krüger, B. Ruggaber, F. Schmidt, R. D. Taubert, A. Sperling, and C. Elster, “Uncertainty evaluation and propagation for spectral measurements,” Color Res. Appl. 43, 6–16 (2018).
[Crossref]

Teuber, A.

S. Nevas, G. Wübbeler, A. Sperling, C. Elster, and A. Teuber, “Simultaneous correction of bandpass and stray-light effects in array spectroradiometer data,” Metrologia 49, S43–S47 (2012).
[Crossref]

S. Nevas, M. Lindemann, A. Sperling, A. Teuber, and R. Maass, “Colorimetry of LEDs with array spectroradiometers,” Mapan 24, 153 (2009).
[Crossref]

Thompson, D. R.

D. R. Thompson, J. W. Boardman, M. L. Eastwood, R. O. Green, J. M. Haag, P. Mouroulis, and B. V. Gorp, “Imaging spectrometer stray spectral response: in-flight characterization, correction, and validation,” Remote Sens. Environ. 204, 850–860 (2018).
[Crossref]

Valin, T.

J. Dubard, R. Etienne, and T. Valin, “Uncertainty evaluation of spectrally resolved source output measurement using array spectroradiometer,” in Proc. CIE Expert Symposium on Measurement Uncertainties in Photometry and Radiometry for Industry (2014).

Vendt, R.

J. Kuusk, I. Ansko, A. Bialek, R. Vendt, and N. Fox, “Implication of illumination beam geometry on stray light and bandpass characteristics of diode array spectrometer,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sensing 11, 2925–2932 (2018).
[Crossref]

Visuri, R.

L. Ylianttila, R. Visuri, L. Huurto, and K. Jokela, “Evaluation of a single-monochromator diode array spectroradiometer for sunbed UV-radiation measurements,” Photochem. Photobiol. 81, 333–341 (2005).
[Crossref]

Wooliams, E. R.

E. R. Wooliams, R. Baribeau, A. Bialek, and M. G. Cox, “Spectrometer bandwidth correction for generalized bandpass functions,” Metrologia 48, 164–172 (2011).
[Crossref]

Woolliams, E. R.

S. G. R. Salim, N. P. Fox, W. S. Hartree, E. R. Woolliams, T. Sun, and K. T. V. Grattan, “Stray light correction for diode-array-based spectrometers using a monochromator,” Appl. Opt. 50, 5130–5138 (2011).
[Crossref]

E. R. Woolliams, “Determining the uncertainty associated with integrals of spectral quantities,” in Technical report (National Physical Laboratory, 2013).

Wübbeler, G.

F. Schmähling, G. Wübbeler, U. Krüger, B. Ruggaber, F. Schmidt, R. D. Taubert, A. Sperling, and C. Elster, “Uncertainty evaluation and propagation for spectral measurements,” Color Res. Appl. 43, 6–16 (2018).
[Crossref]

S. Eichstädt, F. Schmähling, G. Wübbeler, K. Anhalt, L. Bünger, U. Krüger, and C. Elster, “Comparison of the Richardson-Lucy method and a classical approach for spectrometer bandpass correction,” Metrologia 50, 107 (2013).
[Crossref]

S. Nevas, G. Wübbeler, A. Sperling, C. Elster, and A. Teuber, “Simultaneous correction of bandpass and stray-light effects in array spectroradiometer data,” Metrologia 49, S43–S47 (2012).
[Crossref]

Yarbrough, M. A.

M. E. Feinholz, S. J. Flora, S. W. Brown, Y. Zong, K. R. Lykke, M. A. Yarbrough, B. C. Johnson, and D. K. Clark, “Stray light correction algorithm for multichannel hyperspectral spectrographs,” Appl. Opt. 51, 3631–3641 (2012).
[Crossref]

S. Brown, B. C. Johnson, M. E. Feinholz, M. A. Yarbrough, S. J. Flora, K. R. Lykke, and D. K. Clark, “Stray-light correction algorithm for spectrographs,” Metrologia 40, S81–S84 (2003).
[Crossref]

Ylianttila, L.

L. Ylianttila, R. Visuri, L. Huurto, and K. Jokela, “Evaluation of a single-monochromator diode array spectroradiometer for sunbed UV-radiation measurements,” Photochem. Photobiol. 81, 333–341 (2005).
[Crossref]

Zong, Y.

Amer. Statist. (1)

J. L. Rodgers and W. A. Nicewander, “Thirteen ways to look at the correlation coefficient,” Amer. Statist. 42, 59–66 (1988).
[Crossref]

Appl. Opt. (6)

Atmos. Meas. Tech. (1)

B. Bohn and I. Lohse, “Calibration and evaluation of CCD spectroradiometers for ground-based and airborne measurements of spectral actinic flux densities,” Atmos. Meas. Tech. 10, 3151–3174 (2017).
[Crossref]

Color Res. Appl. (4)

F. Schmähling, G. Wübbeler, U. Krüger, B. Ruggaber, F. Schmidt, R. D. Taubert, A. Sperling, and C. Elster, “Uncertainty evaluation and propagation for spectral measurements,” Color Res. Appl. 43, 6–16 (2018).
[Crossref]

J. L. Gardner, “Spectral deconvolution applications for colorimetry,” Color Res. Appl. 39, 430–435 (2013).
[Crossref]

E. I. Stearns and R. E. Stearns, “An example of a method for correcting radiance data for bandpass error,” Color Res. Appl. 13, 257–259 (1988).
[Crossref]

J. L. Gardner, “Bandwidth correction for LED chromaticity,” Color Res. Appl. 31, 374–380 (2006).
[Crossref]

IEEE J. Sel. Top. Appl. Earth Observ. Remote Sensing (1)

J. Kuusk, I. Ansko, A. Bialek, R. Vendt, and N. Fox, “Implication of illumination beam geometry on stray light and bandpass characteristics of diode array spectrometer,” IEEE J. Sel. Top. Appl. Earth Observ. Remote Sensing 11, 2925–2932 (2018).
[Crossref]

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

J. L. Gardner, “Uncertainties in interpolated spectral data,” J. Res. Natl. Inst. Stand. Technol. 108, 69 (2003).
[Crossref]

Mapan (1)

S. Nevas, M. Lindemann, A. Sperling, A. Teuber, and R. Maass, “Colorimetry of LEDs with array spectroradiometers,” Mapan 24, 153 (2009).
[Crossref]

Metrologia (5)

S. Nevas, G. Wübbeler, A. Sperling, C. Elster, and A. Teuber, “Simultaneous correction of bandpass and stray-light effects in array spectroradiometer data,” Metrologia 49, S43–S47 (2012).
[Crossref]

S. Eichstädt, F. Schmähling, G. Wübbeler, K. Anhalt, L. Bünger, U. Krüger, and C. Elster, “Comparison of the Richardson-Lucy method and a classical approach for spectrometer bandpass correction,” Metrologia 50, 107 (2013).
[Crossref]

E. R. Wooliams, R. Baribeau, A. Bialek, and M. G. Cox, “Spectrometer bandwidth correction for generalized bandpass functions,” Metrologia 48, 164–172 (2011).
[Crossref]

S. Brown, B. C. Johnson, M. E. Feinholz, M. A. Yarbrough, S. J. Flora, K. R. Lykke, and D. K. Clark, “Stray-light correction algorithm for spectrographs,” Metrologia 40, S81–S84 (2003).
[Crossref]

H. Shen, J. Pan, H. Feng, and M. Liu, “Stray light errors in spectral colour measurement and two rejection methods,” Metrologia 46, 129 (2009).
[Crossref]

Philos. Trans. R. Soc. London, Ser. A (1)

K. Pearson, “VII. Mathematical contributions to the theory of evolution.-iii. Regression, heredity, and panmixia,” Philos. Trans. R. Soc. London, Ser. A 187, 253–318 (1896).
[Crossref]

Photochem. Photobiol. (1)

L. Ylianttila, R. Visuri, L. Huurto, and K. Jokela, “Evaluation of a single-monochromator diode array spectroradiometer for sunbed UV-radiation measurements,” Photochem. Photobiol. 81, 333–341 (2005).
[Crossref]

Remote Sens. Environ. (1)

D. R. Thompson, J. W. Boardman, M. L. Eastwood, R. O. Green, J. M. Haag, P. Mouroulis, and B. V. Gorp, “Imaging spectrometer stray spectral response: in-flight characterization, correction, and validation,” Remote Sens. Environ. 204, 850–860 (2018).
[Crossref]

Rev. Sci. Instrum. (1)

A. Kreuter and M. Blumthaler, “Stray light correction for solar measurements using array spectrometers,” Rev. Sci. Instrum. 80, 096108 (2009).
[Crossref]

Other (9)

K. Lenhard, P. Gege, and M. Damm, “Implementation of algorithmic correction of stray light in a pushbroom hyperspectral sensor,” in 6th EARSeL Imaging Spectroscopy SIG Workshop (2009).

H. J. Kostkowski, Reliable Spectroradiometry (La Plata, 1997).

E. R. Woolliams, “Determining the uncertainty associated with integrals of spectral quantities,” in Technical report (National Physical Laboratory, 2013).

Joint Committee for Guides in Metrology, Evaluation of measurement data-Supplement 1 to the “Guide to the expression of uncertainty in measurement”-Propagation of distributions using a Monte Carlo method (BIPM, 2008).

Joint Committee for Guides in Metrology, International vocabulary of metrology-Basic and general concepts and associated terms (VIM) (BIPM, 2008).

Y. Zong, “Uncertainty analysis of stray-light correction,” in Proc. CIE Expert Symposium on Spectral and Imaging Methods for Photometry and Radiometry (2010).

J. Dubard and R. Etienne, “A guide for the evaluation of the solar spectrum measurement uncertainty using array spectroradiometers,” in Technical report (EURAMET, 2013).

J. Dubard, R. Etienne, and T. Valin, “Uncertainty evaluation of spectrally resolved source output measurement using array spectroradiometer,” in Proc. CIE Expert Symposium on Measurement Uncertainties in Photometry and Radiometry for Industry (2014).

Joint Committee for Guides in Metrology, Guide to the Expression of Uncertainty in Measurement (BIPM, 2008).

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 (14)

Fig. 1.
Fig. 1. Fraction of stray light in spectral signals of five different array spectroradiometers (left axis) when a spectrum of a quartz–tungsten–halogen lamp (right axis) is measured.
Fig.
					2.
Fig. 2. Dynamic range of an exemplary LSF measurement.
Fig.
					3.
Fig. 3. Example of generating a combined LSF at 750 nm from two measurements with different integration times (${t_{{\rm int,sat}}}=90\times {t_{{\rm int,norm}}}$).
Fig.
						4.
Fig. 4. Schematic of the setup used for the LSF measurements at PTB.
Fig. 5.
Fig. 5. Top: visualization of experimentally determined LSFs of the silicon-CCD array spectrometer considered in the uncertainty analysis. Bottom: spectrometer signal caused by a test source (250 W QTH lamp) before (black line) and after (blue dotted line) application of the stray light correction.
Fig.
						6.
Fig. 6. Maximum SDF offsets resulting from the analysis of the dark signal drift.
Fig.
						7.
Fig. 7. Estimation of OOR stray light.
Fig. 8.
Fig. 8. Impact of number of LSFs on the corrected data of the QTH lamp measurement. Bottom: result of the stray light correction (${S_{{\rm corr}}}$) when using different numbers of LSFs. Top: zoom on the wavelength region 180 nm to 230 nm.
Fig. 9.
Fig. 9. Top: histogram for the corrected signal at 220 nm as resulting from the MC analysis. Bottom: uncertainty of the correction due to uncertainty contributions a to d (solid lines) and as resulting from the simplified estimation (dashed line).
Fig.
					10.
Fig. 10. Expanded uncertainty ${U_{{\rm corr}}}$ ($k=2$) of the corrected signal ${S_{{\rm corr}}}$.
Fig.
					11.
Fig. 11. Linear correlation coefficient $r$ for the corrected spectral data obtained from the MC analysis.
Fig.
				12.
Fig. 12. Uncertainty analysis for different spectral distributions: (a) class A solar simulator, (b) halogen lamp with OG550 edge filter, (c) diode laser at 635 nm, and (d) white LED. Symbols represent measured signal ${S_{{\rm meas}}}$, dashed lines represent corrected signal ${S_{{\rm corr}}}$, and solid lines represent expanded uncertainty ${U_{{\rm corr}}}$ ($k=2$) of corrected signal. The bottom plot compares the uncertainties following from the MC analysis to the simplified estimation.
Fig.
				13.
Fig. 13. Determination of the scaling factor for normal and saturated LSF in the near-peak region (blue shaded areas).
Fig.
					14.
Fig. 14. Condition number of the correction matrix following from the LSF matrix shown in Fig. 5 (top) and corrected detector signal for different widths of the IB region (bottom).

Equations (15)

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

 S c o r r =  C c o r r  S m e a s .
S m e a s , i = S i l l , i S d r k , i .
 LSF i =  S m e a s , m o n , i .
SDF i = { 0   , i IB LSF i / IB LSF i , i IB   .
S j , stray = i IB d i , j S i , IB i IB d i , j S i   .
S j = S j , I B + S j , s t r a y .
 S m e a s =  S I B +  S s t r a y .
 S m e a s =  S I B +  D  S I B = (  I +  D )  S I B ,
 C c o r r = (  I +  D ) 1 .
S d r k = S d r k , 1 + S d r k , 2 2 .
σ d i f f = σ i l l 2 + σ d r k 2 N ,
σ d r k = σ d r k , 1 2 + σ d r k , 2 2 4 σ d r k , 1 2 2 ,
u m c 2 = ( a / 2 ) 2 3 ,
u c o r r 2 = u m c 2 + u o o r 2 + u l s f 2 ,
u 2 ( S c o r r S c o r r ) 2 / 3.

Metrics