Abstract

A simple, practical method has been developed to correct a spectroradiometer's response for measurement errors arising from the instrument's spectral stray light. By characterizing the instrument's response to a set of monochromatic laser sources that cover the instrument's spectral range, one obtains a spectral stray light signal distribution matrix that quantifies the magnitude of the spectral stray light signal within the instrument. By use of these data, a spectral stray light correction matrix is derived and the instrument's response can be corrected with a simple matrix multiplication. The method has been implemented and validated with a commercial CCD-array spectrograph. Spectral stray light errors after the correction was applied were reduced by 1–2 orders of magnitude to a level of approximately 105 for a broadband source measurement, equivalent to less than one count of the 15-bit-resolution instrument. This method is fast enough to be integrated into an instrument's software to perform real-time corrections with minimal effect on acquisition speed. Using instruments that have been corrected for spectral stray light, we expect significant reductions in overall measurement uncertainties in many applications in which spectrometers are commonly used, including radiometry, colorimetry, photometry, and biotechnology.

© 2006 Optical Society of America

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References

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  1. T. N. Woods R.T Wrigley III, G. J. Rottman, and R. E. Haring, "Scattered light properties of diffraction gratings," Appl. Opt. 33, 4273-4285 (1994).
    [CrossRef] [PubMed]
  2. H. J. Kostkowski, ed., "Spectral scattering," in Reliable Spectroradiometry (Spectroradiometry Consulting, La Plata, Md., 1997), pp. 57-87.
  3. S. W. 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, S81-83 (2003).
    [CrossRef]
  4. S. W. Brown, D. K. Clark, B. C. Johnson, H. Yoon, K. R. Lykke, S. J. Flora, M. E. Feinholz, N. Souaidia, C. Pietras, T. C. Stone, M. A. Yarbrough, Y. S. Kim, R. A. Barnes, and J. L. Mueller, "Advances in radiometry for ocean color," Chap. 7 of Special Topics in Ocean Optics Protocols, Part 2 of Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Rev. 5, Vol. VI, J. L. Mueller, G. S. Fargion, and C. R. McClain, eds. (NASA Goddard Space Flight Center, 2004), pp. 8-35.
  5. C. B. Moler, ed., "Linear equations," in Numerical Computing with Matlab (Society for Industrial and Applied Mathematics, 2004), pp. 53-92.
  6. S. W. Brown, G. P. Eppeldauer, and K. R. Lykke, "NIST facility for spectral irradiance and radiance responsivity calibrations with uniform sources," Metrologia 37, 579-582 (2000).
    [CrossRef]
  7. Richard Young, Optronic Laboratories, Inc., 4632 36th Street, Orlando, Fla. 32811 (personal communication, 2004).
  8. Dennis K. Clark, National Oceanic and Atmospheric Administration, NOAA/NESDIS, 5200 Auth Rd., Camp Springs, MD 20746 (personal communication, 2004).
  9. CIE Technical Committee 1-48, "Recommendations concerning the calculation of tristimulus values and chromaticity coordinates," in Colorimetry, CIE Tech. Rep. CIE 15:2004, 3rd ed. (Commission Internationale de l'Eclairage, 2004), pp. 12-16.
  10. Y. Zong, C. C. Miller, K. R. Lykke, and Y. Ohno, "Measurement of total radiant flux of UV LEDs," in Proceedings of the CIE Symposium '04, LED Light Sources: Physical Measurement and Visual and Photobiological Assessment, CIE publ. x026:2004 (Commission Internationale de l'Eclairage, 2004), pp. 107-110.

2003

S. W. 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, S81-83 (2003).
[CrossRef]

2000

S. W. Brown, G. P. Eppeldauer, and K. R. Lykke, "NIST facility for spectral irradiance and radiance responsivity calibrations with uniform sources," Metrologia 37, 579-582 (2000).
[CrossRef]

1994

Barnes, R. A.

S. W. Brown, D. K. Clark, B. C. Johnson, H. Yoon, K. R. Lykke, S. J. Flora, M. E. Feinholz, N. Souaidia, C. Pietras, T. C. Stone, M. A. Yarbrough, Y. S. Kim, R. A. Barnes, and J. L. Mueller, "Advances in radiometry for ocean color," Chap. 7 of Special Topics in Ocean Optics Protocols, Part 2 of Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Rev. 5, Vol. VI, J. L. Mueller, G. S. Fargion, and C. R. McClain, eds. (NASA Goddard Space Flight Center, 2004), pp. 8-35.

Brown, S. W.

S. W. 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, S81-83 (2003).
[CrossRef]

S. W. Brown, G. P. Eppeldauer, and K. R. Lykke, "NIST facility for spectral irradiance and radiance responsivity calibrations with uniform sources," Metrologia 37, 579-582 (2000).
[CrossRef]

S. W. Brown, D. K. Clark, B. C. Johnson, H. Yoon, K. R. Lykke, S. J. Flora, M. E. Feinholz, N. Souaidia, C. Pietras, T. C. Stone, M. A. Yarbrough, Y. S. Kim, R. A. Barnes, and J. L. Mueller, "Advances in radiometry for ocean color," Chap. 7 of Special Topics in Ocean Optics Protocols, Part 2 of Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Rev. 5, Vol. VI, J. L. Mueller, G. S. Fargion, and C. R. McClain, eds. (NASA Goddard Space Flight Center, 2004), pp. 8-35.

Clark, D. K.

S. W. 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, S81-83 (2003).
[CrossRef]

S. W. Brown, D. K. Clark, B. C. Johnson, H. Yoon, K. R. Lykke, S. J. Flora, M. E. Feinholz, N. Souaidia, C. Pietras, T. C. Stone, M. A. Yarbrough, Y. S. Kim, R. A. Barnes, and J. L. Mueller, "Advances in radiometry for ocean color," Chap. 7 of Special Topics in Ocean Optics Protocols, Part 2 of Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Rev. 5, Vol. VI, J. L. Mueller, G. S. Fargion, and C. R. McClain, eds. (NASA Goddard Space Flight Center, 2004), pp. 8-35.

Clark, Dennis K.

Dennis K. Clark, National Oceanic and Atmospheric Administration, NOAA/NESDIS, 5200 Auth Rd., Camp Springs, MD 20746 (personal communication, 2004).

Eppeldauer, G. P.

S. W. Brown, G. P. Eppeldauer, and K. R. Lykke, "NIST facility for spectral irradiance and radiance responsivity calibrations with uniform sources," Metrologia 37, 579-582 (2000).
[CrossRef]

Feinholz, M. E.

S. W. 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, S81-83 (2003).
[CrossRef]

S. W. Brown, D. K. Clark, B. C. Johnson, H. Yoon, K. R. Lykke, S. J. Flora, M. E. Feinholz, N. Souaidia, C. Pietras, T. C. Stone, M. A. Yarbrough, Y. S. Kim, R. A. Barnes, and J. L. Mueller, "Advances in radiometry for ocean color," Chap. 7 of Special Topics in Ocean Optics Protocols, Part 2 of Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Rev. 5, Vol. VI, J. L. Mueller, G. S. Fargion, and C. R. McClain, eds. (NASA Goddard Space Flight Center, 2004), pp. 8-35.

Flora, S. J.

S. W. 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, S81-83 (2003).
[CrossRef]

S. W. Brown, D. K. Clark, B. C. Johnson, H. Yoon, K. R. Lykke, S. J. Flora, M. E. Feinholz, N. Souaidia, C. Pietras, T. C. Stone, M. A. Yarbrough, Y. S. Kim, R. A. Barnes, and J. L. Mueller, "Advances in radiometry for ocean color," Chap. 7 of Special Topics in Ocean Optics Protocols, Part 2 of Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Rev. 5, Vol. VI, J. L. Mueller, G. S. Fargion, and C. R. McClain, eds. (NASA Goddard Space Flight Center, 2004), pp. 8-35.

Haring, R. E.

Johnson, B. C.

S. W. 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, S81-83 (2003).
[CrossRef]

S. W. Brown, D. K. Clark, B. C. Johnson, H. Yoon, K. R. Lykke, S. J. Flora, M. E. Feinholz, N. Souaidia, C. Pietras, T. C. Stone, M. A. Yarbrough, Y. S. Kim, R. A. Barnes, and J. L. Mueller, "Advances in radiometry for ocean color," Chap. 7 of Special Topics in Ocean Optics Protocols, Part 2 of Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Rev. 5, Vol. VI, J. L. Mueller, G. S. Fargion, and C. R. McClain, eds. (NASA Goddard Space Flight Center, 2004), pp. 8-35.

Kim, Y. S.

S. W. Brown, D. K. Clark, B. C. Johnson, H. Yoon, K. R. Lykke, S. J. Flora, M. E. Feinholz, N. Souaidia, C. Pietras, T. C. Stone, M. A. Yarbrough, Y. S. Kim, R. A. Barnes, and J. L. Mueller, "Advances in radiometry for ocean color," Chap. 7 of Special Topics in Ocean Optics Protocols, Part 2 of Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Rev. 5, Vol. VI, J. L. Mueller, G. S. Fargion, and C. R. McClain, eds. (NASA Goddard Space Flight Center, 2004), pp. 8-35.

Kostkowski, H. J.

H. J. Kostkowski, ed., "Spectral scattering," in Reliable Spectroradiometry (Spectroradiometry Consulting, La Plata, Md., 1997), pp. 57-87.

Lykke, K. R.

S. W. 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, S81-83 (2003).
[CrossRef]

S. W. Brown, G. P. Eppeldauer, and K. R. Lykke, "NIST facility for spectral irradiance and radiance responsivity calibrations with uniform sources," Metrologia 37, 579-582 (2000).
[CrossRef]

Y. Zong, C. C. Miller, K. R. Lykke, and Y. Ohno, "Measurement of total radiant flux of UV LEDs," in Proceedings of the CIE Symposium '04, LED Light Sources: Physical Measurement and Visual and Photobiological Assessment, CIE publ. x026:2004 (Commission Internationale de l'Eclairage, 2004), pp. 107-110.

S. W. Brown, D. K. Clark, B. C. Johnson, H. Yoon, K. R. Lykke, S. J. Flora, M. E. Feinholz, N. Souaidia, C. Pietras, T. C. Stone, M. A. Yarbrough, Y. S. Kim, R. A. Barnes, and J. L. Mueller, "Advances in radiometry for ocean color," Chap. 7 of Special Topics in Ocean Optics Protocols, Part 2 of Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Rev. 5, Vol. VI, J. L. Mueller, G. S. Fargion, and C. R. McClain, eds. (NASA Goddard Space Flight Center, 2004), pp. 8-35.

Miller, C. C.

Y. Zong, C. C. Miller, K. R. Lykke, and Y. Ohno, "Measurement of total radiant flux of UV LEDs," in Proceedings of the CIE Symposium '04, LED Light Sources: Physical Measurement and Visual and Photobiological Assessment, CIE publ. x026:2004 (Commission Internationale de l'Eclairage, 2004), pp. 107-110.

Moler, C. B.

C. B. Moler, ed., "Linear equations," in Numerical Computing with Matlab (Society for Industrial and Applied Mathematics, 2004), pp. 53-92.

Mueller, J. L.

S. W. Brown, D. K. Clark, B. C. Johnson, H. Yoon, K. R. Lykke, S. J. Flora, M. E. Feinholz, N. Souaidia, C. Pietras, T. C. Stone, M. A. Yarbrough, Y. S. Kim, R. A. Barnes, and J. L. Mueller, "Advances in radiometry for ocean color," Chap. 7 of Special Topics in Ocean Optics Protocols, Part 2 of Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Rev. 5, Vol. VI, J. L. Mueller, G. S. Fargion, and C. R. McClain, eds. (NASA Goddard Space Flight Center, 2004), pp. 8-35.

Ohno, Y.

Y. Zong, C. C. Miller, K. R. Lykke, and Y. Ohno, "Measurement of total radiant flux of UV LEDs," in Proceedings of the CIE Symposium '04, LED Light Sources: Physical Measurement and Visual and Photobiological Assessment, CIE publ. x026:2004 (Commission Internationale de l'Eclairage, 2004), pp. 107-110.

Pietras, C.

S. W. Brown, D. K. Clark, B. C. Johnson, H. Yoon, K. R. Lykke, S. J. Flora, M. E. Feinholz, N. Souaidia, C. Pietras, T. C. Stone, M. A. Yarbrough, Y. S. Kim, R. A. Barnes, and J. L. Mueller, "Advances in radiometry for ocean color," Chap. 7 of Special Topics in Ocean Optics Protocols, Part 2 of Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Rev. 5, Vol. VI, J. L. Mueller, G. S. Fargion, and C. R. McClain, eds. (NASA Goddard Space Flight Center, 2004), pp. 8-35.

Rottman, G. J.

Souaidia, N.

S. W. Brown, D. K. Clark, B. C. Johnson, H. Yoon, K. R. Lykke, S. J. Flora, M. E. Feinholz, N. Souaidia, C. Pietras, T. C. Stone, M. A. Yarbrough, Y. S. Kim, R. A. Barnes, and J. L. Mueller, "Advances in radiometry for ocean color," Chap. 7 of Special Topics in Ocean Optics Protocols, Part 2 of Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Rev. 5, Vol. VI, J. L. Mueller, G. S. Fargion, and C. R. McClain, eds. (NASA Goddard Space Flight Center, 2004), pp. 8-35.

Stone, T. C.

S. W. Brown, D. K. Clark, B. C. Johnson, H. Yoon, K. R. Lykke, S. J. Flora, M. E. Feinholz, N. Souaidia, C. Pietras, T. C. Stone, M. A. Yarbrough, Y. S. Kim, R. A. Barnes, and J. L. Mueller, "Advances in radiometry for ocean color," Chap. 7 of Special Topics in Ocean Optics Protocols, Part 2 of Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Rev. 5, Vol. VI, J. L. Mueller, G. S. Fargion, and C. R. McClain, eds. (NASA Goddard Space Flight Center, 2004), pp. 8-35.

Woods, T. N.

Yarbrough, M. A.

S. W. 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, S81-83 (2003).
[CrossRef]

S. W. Brown, D. K. Clark, B. C. Johnson, H. Yoon, K. R. Lykke, S. J. Flora, M. E. Feinholz, N. Souaidia, C. Pietras, T. C. Stone, M. A. Yarbrough, Y. S. Kim, R. A. Barnes, and J. L. Mueller, "Advances in radiometry for ocean color," Chap. 7 of Special Topics in Ocean Optics Protocols, Part 2 of Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Rev. 5, Vol. VI, J. L. Mueller, G. S. Fargion, and C. R. McClain, eds. (NASA Goddard Space Flight Center, 2004), pp. 8-35.

Yoon, H.

S. W. Brown, D. K. Clark, B. C. Johnson, H. Yoon, K. R. Lykke, S. J. Flora, M. E. Feinholz, N. Souaidia, C. Pietras, T. C. Stone, M. A. Yarbrough, Y. S. Kim, R. A. Barnes, and J. L. Mueller, "Advances in radiometry for ocean color," Chap. 7 of Special Topics in Ocean Optics Protocols, Part 2 of Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Rev. 5, Vol. VI, J. L. Mueller, G. S. Fargion, and C. R. McClain, eds. (NASA Goddard Space Flight Center, 2004), pp. 8-35.

Zong, Y.

Y. Zong, C. C. Miller, K. R. Lykke, and Y. Ohno, "Measurement of total radiant flux of UV LEDs," in Proceedings of the CIE Symposium '04, LED Light Sources: Physical Measurement and Visual and Photobiological Assessment, CIE publ. x026:2004 (Commission Internationale de l'Eclairage, 2004), pp. 107-110.

Appl. Opt.

Metrologia

S. W. 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, S81-83 (2003).
[CrossRef]

S. W. Brown, G. P. Eppeldauer, and K. R. Lykke, "NIST facility for spectral irradiance and radiance responsivity calibrations with uniform sources," Metrologia 37, 579-582 (2000).
[CrossRef]

Other

Richard Young, Optronic Laboratories, Inc., 4632 36th Street, Orlando, Fla. 32811 (personal communication, 2004).

Dennis K. Clark, National Oceanic and Atmospheric Administration, NOAA/NESDIS, 5200 Auth Rd., Camp Springs, MD 20746 (personal communication, 2004).

CIE Technical Committee 1-48, "Recommendations concerning the calculation of tristimulus values and chromaticity coordinates," in Colorimetry, CIE Tech. Rep. CIE 15:2004, 3rd ed. (Commission Internationale de l'Eclairage, 2004), pp. 12-16.

Y. Zong, C. C. Miller, K. R. Lykke, and Y. Ohno, "Measurement of total radiant flux of UV LEDs," in Proceedings of the CIE Symposium '04, LED Light Sources: Physical Measurement and Visual and Photobiological Assessment, CIE publ. x026:2004 (Commission Internationale de l'Eclairage, 2004), pp. 107-110.

S. W. Brown, D. K. Clark, B. C. Johnson, H. Yoon, K. R. Lykke, S. J. Flora, M. E. Feinholz, N. Souaidia, C. Pietras, T. C. Stone, M. A. Yarbrough, Y. S. Kim, R. A. Barnes, and J. L. Mueller, "Advances in radiometry for ocean color," Chap. 7 of Special Topics in Ocean Optics Protocols, Part 2 of Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Rev. 5, Vol. VI, J. L. Mueller, G. S. Fargion, and C. R. McClain, eds. (NASA Goddard Space Flight Center, 2004), pp. 8-35.

C. B. Moler, ed., "Linear equations," in Numerical Computing with Matlab (Society for Industrial and Applied Mathematics, 2004), pp. 53-92.

H. J. Kostkowski, ed., "Spectral scattering," in Reliable Spectroradiometry (Spectroradiometry Consulting, La Plata, Md., 1997), pp. 57-87.

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Figures (8)

Fig. 1
Fig. 1

Illustration of an array spectrometer composed of a fixed imaging grating and a fixed multipixel array detector.

Fig. 2
Fig. 2

(a) Illustration of a LSF of a spectrograph with a 1024-pixel array detector. The wavelength of the spectral line source is λ j , centered on pixel j of the array. (b) Plot of the corresponding SDF derived from the LSF shown in (a). The top x axis is in pixel space, and the bottom x axis is in wavelength space.

Fig. 3
Fig. 3

Representative LSFs spanning the test spectrograph's detector array.

Fig. 4
Fig. 4

Three representative columns of the spectrograph's 1024 × 1024 SDF matrix D.

Fig. 5
Fig. 5

Three representative rows of SDF matrix D.

Fig. 6
Fig. 6

Result of validation of the spectral stray light correction for a broadband source with a bandpass filter: measured raw signals from the spectrograph, spectral stray light corrected signals, and the one-count level of the 15 bit spectrograph are shown.

Fig. 7
Fig. 7

Result of the spectral stray light correction for a monochromatic laser source at 516 nm. Measured raw signals from the spectrograph, spectral stray light-corrected signals, and the one-count level of the 15-bit spectrograph are shown.

Fig. 8
Fig. 8

Plots of the raw and the spectral stray light corrected signals of the three LEDs, normalized to the respective raw peak signals: red, green, and blue LEDs are shown. Thicker curves, measured relative spectral signal distribution; thinner curves, spectral stray light corrected spectral signal distribution.

Equations (14)

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d i , J = f LSF,   i , J i IB f LSF,   i , J , i   IB   ( pixel   i   outside   IB ) ,
d i , J = 0 , i   IB   ( pixel   i   inside   IB ) ,
i = 1 n .
D = d 1 , 1 d 1 , 2 d 1 , J d 1 , n 1 d 1 , n d 2 , 1 d 2 , 2 d 2 , J d 2 , n 1 d 2 , n d i , 1 d i , 2 d i , J d i , n 1 d i , n d n 1 , 1 d n 1 , 2 d n 1 , J d n 1 , n 1 d n 1 , n d n , 1 d n , 2 d n , J d n , n 1 d n , n .
y s _ spec , i = j = 1 n d i , j y IB,   j , true j = 1 n d i , j y IB,   j ,
y s _ spec , i = j = 1 n ( d i , j y IB,   j ) + δ spec , i ,
y meas , i = y IB , i + y s _ spec , i = y IB , i + j = 1 n ( d i , j y IB , j ) + δ spec , i ,
Y s _ spec = D Y IB ,
Y meas = Y IB + Y s _ spec = Y IB + D Y IB ,
Y meas = [ I + D ] Y IB = A Y IB ,
Y IB = A 1 Y meas = C   Y meas .
Y IB ( k + 1 ) = Y m e a s - DY IB ( k ) ,
k = 0 , 1 , 2 , ,
Y IB ( 0 ) = Y meas .

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