Abstract

The uncertainty of the radiometric calibration affects the accuracy of the earth observation (EO) radiance restored from the remote sensing digital number (DN) data. However, it has not been intensively analyzed whether they are equivalent to each other. The algorithm to deduce the uncertainty of the restored EO radiance in the solar-reflective spectral range (400-2500 nm) along the uncertainty propagation chain in the radiometric calibration process is proposed. It was validated compared with the traditional calibration uncertainty algorithm through an example of calibrating an imaging spectrometer. The interval about the real EO radiance and the corresponding level of confidence was reported as a result, which shows the possibility to accurately expressing the quality of the restored EO radiance following the rules used in the field of metrology.

© 2014 Optical Society of America

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References

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  1. G. Chander, T. J. Hewison, N. Fox, X. Wu, X. Xiong, W. J. Blackwell, “Overview of Intercalibration of Satellite Instruments,” IEEE Trans. Geosci. Rem. Sens. 51(3), 1056–1080 (2013).
    [CrossRef]
  2. R. V. Datla, R. Kessel, A. W. Smith, R. N. Kacker, D. B. Pollock, “Review Article: Uncertainty analysis of remote sensing optical sensor data: guiding principles to achieve metrological consistency,” Int. J. Remote Sens. 31(4), 867–880 (2010).
    [CrossRef]
  3. N. P. Fox, “Improving the accuracy and traceability to SI of space-based radiometric measurements, both pre-flight and post-launch,” Adv. Space Res. 23(8), 1471–1476 (1999).
    [CrossRef]
  4. P. N. Slater, S. F. Biggar, J. M. Palmer, K. J. Thome, “Unified approach to absolute radiometric calibration in the solar-reflective range,” Remote Sens. Environ. 77(3), 293–303 (2001).
    [CrossRef]
  5. K. Thome, J. Czapla-Myers, M. Kuester, N. Anderson, “Accuracy assessment for the radiometric calibration of imaging sensors using preflight techniques relying on the sun as a source,” Proc. SPIE 7081, 708118 (2008).
    [CrossRef]
  6. T. G. Chrien, R. O. Green, M. L. Eastwood, “Accuracy of the spectral and radiometric laboratory calibration of the Airborne Visible/Infrared Imaging Spectrometer,” Proc. SPIE 1298, 37–49 (1990).
    [CrossRef]
  7. C. J. Bruegge, N. L. Chrien, D. J. Diner, R. A. Kahn, J. V. Martonchik, “MISR radiometric uncertainty analyses and their utilization within geophysical retrievals,” Metrologia 35(4), 571–579 (1998).
    [CrossRef]
  8. M. Dinguirard, J. Mueller, F. Sirou, T. Tremas, “Comparison of ScaRaB ground calibration in the short-wave and long-wave spectral domains,” Metrologia 35(4), 597–601 (1998).
    [CrossRef]
  9. BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, and OIML, “Evaluation of measurement data - Guide to the expression of uncertainty in measurement” (2008), http://www.bipm.org/utils/common/documents/jcgm/JCGM_100_2008_E.pdf .
  10. L. Kirkup and B. Frenkel, An introduction to uncertainty in measurement (Cambridge University, Cambridge, 2006).
  11. P. Zhou, H. Zhao, Y. Zhang, and C. Li, “Accurate optical design of an acousto-optic tunable filter imaging spectrometer,” in Proceedings of IEEE International Conference on Imaging Systems and Techniques (IST), (Institute of Electrical and Electronics Engineers, Manchester, 2012), pp. 249–253.
    [CrossRef]

2013

G. Chander, T. J. Hewison, N. Fox, X. Wu, X. Xiong, W. J. Blackwell, “Overview of Intercalibration of Satellite Instruments,” IEEE Trans. Geosci. Rem. Sens. 51(3), 1056–1080 (2013).
[CrossRef]

2010

R. V. Datla, R. Kessel, A. W. Smith, R. N. Kacker, D. B. Pollock, “Review Article: Uncertainty analysis of remote sensing optical sensor data: guiding principles to achieve metrological consistency,” Int. J. Remote Sens. 31(4), 867–880 (2010).
[CrossRef]

2008

K. Thome, J. Czapla-Myers, M. Kuester, N. Anderson, “Accuracy assessment for the radiometric calibration of imaging sensors using preflight techniques relying on the sun as a source,” Proc. SPIE 7081, 708118 (2008).
[CrossRef]

2001

P. N. Slater, S. F. Biggar, J. M. Palmer, K. J. Thome, “Unified approach to absolute radiometric calibration in the solar-reflective range,” Remote Sens. Environ. 77(3), 293–303 (2001).
[CrossRef]

1999

N. P. Fox, “Improving the accuracy and traceability to SI of space-based radiometric measurements, both pre-flight and post-launch,” Adv. Space Res. 23(8), 1471–1476 (1999).
[CrossRef]

1998

C. J. Bruegge, N. L. Chrien, D. J. Diner, R. A. Kahn, J. V. Martonchik, “MISR radiometric uncertainty analyses and their utilization within geophysical retrievals,” Metrologia 35(4), 571–579 (1998).
[CrossRef]

M. Dinguirard, J. Mueller, F. Sirou, T. Tremas, “Comparison of ScaRaB ground calibration in the short-wave and long-wave spectral domains,” Metrologia 35(4), 597–601 (1998).
[CrossRef]

1990

T. G. Chrien, R. O. Green, M. L. Eastwood, “Accuracy of the spectral and radiometric laboratory calibration of the Airborne Visible/Infrared Imaging Spectrometer,” Proc. SPIE 1298, 37–49 (1990).
[CrossRef]

Anderson, N.

K. Thome, J. Czapla-Myers, M. Kuester, N. Anderson, “Accuracy assessment for the radiometric calibration of imaging sensors using preflight techniques relying on the sun as a source,” Proc. SPIE 7081, 708118 (2008).
[CrossRef]

Biggar, S. F.

P. N. Slater, S. F. Biggar, J. M. Palmer, K. J. Thome, “Unified approach to absolute radiometric calibration in the solar-reflective range,” Remote Sens. Environ. 77(3), 293–303 (2001).
[CrossRef]

Blackwell, W. J.

G. Chander, T. J. Hewison, N. Fox, X. Wu, X. Xiong, W. J. Blackwell, “Overview of Intercalibration of Satellite Instruments,” IEEE Trans. Geosci. Rem. Sens. 51(3), 1056–1080 (2013).
[CrossRef]

Bruegge, C. J.

C. J. Bruegge, N. L. Chrien, D. J. Diner, R. A. Kahn, J. V. Martonchik, “MISR radiometric uncertainty analyses and their utilization within geophysical retrievals,” Metrologia 35(4), 571–579 (1998).
[CrossRef]

Chander, G.

G. Chander, T. J. Hewison, N. Fox, X. Wu, X. Xiong, W. J. Blackwell, “Overview of Intercalibration of Satellite Instruments,” IEEE Trans. Geosci. Rem. Sens. 51(3), 1056–1080 (2013).
[CrossRef]

Chrien, N. L.

C. J. Bruegge, N. L. Chrien, D. J. Diner, R. A. Kahn, J. V. Martonchik, “MISR radiometric uncertainty analyses and their utilization within geophysical retrievals,” Metrologia 35(4), 571–579 (1998).
[CrossRef]

Chrien, T. G.

T. G. Chrien, R. O. Green, M. L. Eastwood, “Accuracy of the spectral and radiometric laboratory calibration of the Airborne Visible/Infrared Imaging Spectrometer,” Proc. SPIE 1298, 37–49 (1990).
[CrossRef]

Czapla-Myers, J.

K. Thome, J. Czapla-Myers, M. Kuester, N. Anderson, “Accuracy assessment for the radiometric calibration of imaging sensors using preflight techniques relying on the sun as a source,” Proc. SPIE 7081, 708118 (2008).
[CrossRef]

Datla, R. V.

R. V. Datla, R. Kessel, A. W. Smith, R. N. Kacker, D. B. Pollock, “Review Article: Uncertainty analysis of remote sensing optical sensor data: guiding principles to achieve metrological consistency,” Int. J. Remote Sens. 31(4), 867–880 (2010).
[CrossRef]

Diner, D. J.

C. J. Bruegge, N. L. Chrien, D. J. Diner, R. A. Kahn, J. V. Martonchik, “MISR radiometric uncertainty analyses and their utilization within geophysical retrievals,” Metrologia 35(4), 571–579 (1998).
[CrossRef]

Dinguirard, M.

M. Dinguirard, J. Mueller, F. Sirou, T. Tremas, “Comparison of ScaRaB ground calibration in the short-wave and long-wave spectral domains,” Metrologia 35(4), 597–601 (1998).
[CrossRef]

Eastwood, M. L.

T. G. Chrien, R. O. Green, M. L. Eastwood, “Accuracy of the spectral and radiometric laboratory calibration of the Airborne Visible/Infrared Imaging Spectrometer,” Proc. SPIE 1298, 37–49 (1990).
[CrossRef]

Fox, N.

G. Chander, T. J. Hewison, N. Fox, X. Wu, X. Xiong, W. J. Blackwell, “Overview of Intercalibration of Satellite Instruments,” IEEE Trans. Geosci. Rem. Sens. 51(3), 1056–1080 (2013).
[CrossRef]

Fox, N. P.

N. P. Fox, “Improving the accuracy and traceability to SI of space-based radiometric measurements, both pre-flight and post-launch,” Adv. Space Res. 23(8), 1471–1476 (1999).
[CrossRef]

Green, R. O.

T. G. Chrien, R. O. Green, M. L. Eastwood, “Accuracy of the spectral and radiometric laboratory calibration of the Airborne Visible/Infrared Imaging Spectrometer,” Proc. SPIE 1298, 37–49 (1990).
[CrossRef]

Hewison, T. J.

G. Chander, T. J. Hewison, N. Fox, X. Wu, X. Xiong, W. J. Blackwell, “Overview of Intercalibration of Satellite Instruments,” IEEE Trans. Geosci. Rem. Sens. 51(3), 1056–1080 (2013).
[CrossRef]

Kacker, R. N.

R. V. Datla, R. Kessel, A. W. Smith, R. N. Kacker, D. B. Pollock, “Review Article: Uncertainty analysis of remote sensing optical sensor data: guiding principles to achieve metrological consistency,” Int. J. Remote Sens. 31(4), 867–880 (2010).
[CrossRef]

Kahn, R. A.

C. J. Bruegge, N. L. Chrien, D. J. Diner, R. A. Kahn, J. V. Martonchik, “MISR radiometric uncertainty analyses and their utilization within geophysical retrievals,” Metrologia 35(4), 571–579 (1998).
[CrossRef]

Kessel, R.

R. V. Datla, R. Kessel, A. W. Smith, R. N. Kacker, D. B. Pollock, “Review Article: Uncertainty analysis of remote sensing optical sensor data: guiding principles to achieve metrological consistency,” Int. J. Remote Sens. 31(4), 867–880 (2010).
[CrossRef]

Kuester, M.

K. Thome, J. Czapla-Myers, M. Kuester, N. Anderson, “Accuracy assessment for the radiometric calibration of imaging sensors using preflight techniques relying on the sun as a source,” Proc. SPIE 7081, 708118 (2008).
[CrossRef]

Martonchik, J. V.

C. J. Bruegge, N. L. Chrien, D. J. Diner, R. A. Kahn, J. V. Martonchik, “MISR radiometric uncertainty analyses and their utilization within geophysical retrievals,” Metrologia 35(4), 571–579 (1998).
[CrossRef]

Mueller, J.

M. Dinguirard, J. Mueller, F. Sirou, T. Tremas, “Comparison of ScaRaB ground calibration in the short-wave and long-wave spectral domains,” Metrologia 35(4), 597–601 (1998).
[CrossRef]

Palmer, J. M.

P. N. Slater, S. F. Biggar, J. M. Palmer, K. J. Thome, “Unified approach to absolute radiometric calibration in the solar-reflective range,” Remote Sens. Environ. 77(3), 293–303 (2001).
[CrossRef]

Pollock, D. B.

R. V. Datla, R. Kessel, A. W. Smith, R. N. Kacker, D. B. Pollock, “Review Article: Uncertainty analysis of remote sensing optical sensor data: guiding principles to achieve metrological consistency,” Int. J. Remote Sens. 31(4), 867–880 (2010).
[CrossRef]

Sirou, F.

M. Dinguirard, J. Mueller, F. Sirou, T. Tremas, “Comparison of ScaRaB ground calibration in the short-wave and long-wave spectral domains,” Metrologia 35(4), 597–601 (1998).
[CrossRef]

Slater, P. N.

P. N. Slater, S. F. Biggar, J. M. Palmer, K. J. Thome, “Unified approach to absolute radiometric calibration in the solar-reflective range,” Remote Sens. Environ. 77(3), 293–303 (2001).
[CrossRef]

Smith, A. W.

R. V. Datla, R. Kessel, A. W. Smith, R. N. Kacker, D. B. Pollock, “Review Article: Uncertainty analysis of remote sensing optical sensor data: guiding principles to achieve metrological consistency,” Int. J. Remote Sens. 31(4), 867–880 (2010).
[CrossRef]

Thome, K.

K. Thome, J. Czapla-Myers, M. Kuester, N. Anderson, “Accuracy assessment for the radiometric calibration of imaging sensors using preflight techniques relying on the sun as a source,” Proc. SPIE 7081, 708118 (2008).
[CrossRef]

Thome, K. J.

P. N. Slater, S. F. Biggar, J. M. Palmer, K. J. Thome, “Unified approach to absolute radiometric calibration in the solar-reflective range,” Remote Sens. Environ. 77(3), 293–303 (2001).
[CrossRef]

Tremas, T.

M. Dinguirard, J. Mueller, F. Sirou, T. Tremas, “Comparison of ScaRaB ground calibration in the short-wave and long-wave spectral domains,” Metrologia 35(4), 597–601 (1998).
[CrossRef]

Wu, X.

G. Chander, T. J. Hewison, N. Fox, X. Wu, X. Xiong, W. J. Blackwell, “Overview of Intercalibration of Satellite Instruments,” IEEE Trans. Geosci. Rem. Sens. 51(3), 1056–1080 (2013).
[CrossRef]

Xiong, X.

G. Chander, T. J. Hewison, N. Fox, X. Wu, X. Xiong, W. J. Blackwell, “Overview of Intercalibration of Satellite Instruments,” IEEE Trans. Geosci. Rem. Sens. 51(3), 1056–1080 (2013).
[CrossRef]

Adv. Space Res.

N. P. Fox, “Improving the accuracy and traceability to SI of space-based radiometric measurements, both pre-flight and post-launch,” Adv. Space Res. 23(8), 1471–1476 (1999).
[CrossRef]

IEEE Trans. Geosci. Rem. Sens.

G. Chander, T. J. Hewison, N. Fox, X. Wu, X. Xiong, W. J. Blackwell, “Overview of Intercalibration of Satellite Instruments,” IEEE Trans. Geosci. Rem. Sens. 51(3), 1056–1080 (2013).
[CrossRef]

Int. J. Remote Sens.

R. V. Datla, R. Kessel, A. W. Smith, R. N. Kacker, D. B. Pollock, “Review Article: Uncertainty analysis of remote sensing optical sensor data: guiding principles to achieve metrological consistency,” Int. J. Remote Sens. 31(4), 867–880 (2010).
[CrossRef]

Metrologia

C. J. Bruegge, N. L. Chrien, D. J. Diner, R. A. Kahn, J. V. Martonchik, “MISR radiometric uncertainty analyses and their utilization within geophysical retrievals,” Metrologia 35(4), 571–579 (1998).
[CrossRef]

M. Dinguirard, J. Mueller, F. Sirou, T. Tremas, “Comparison of ScaRaB ground calibration in the short-wave and long-wave spectral domains,” Metrologia 35(4), 597–601 (1998).
[CrossRef]

Proc. SPIE

K. Thome, J. Czapla-Myers, M. Kuester, N. Anderson, “Accuracy assessment for the radiometric calibration of imaging sensors using preflight techniques relying on the sun as a source,” Proc. SPIE 7081, 708118 (2008).
[CrossRef]

T. G. Chrien, R. O. Green, M. L. Eastwood, “Accuracy of the spectral and radiometric laboratory calibration of the Airborne Visible/Infrared Imaging Spectrometer,” Proc. SPIE 1298, 37–49 (1990).
[CrossRef]

Remote Sens. Environ.

P. N. Slater, S. F. Biggar, J. M. Palmer, K. J. Thome, “Unified approach to absolute radiometric calibration in the solar-reflective range,” Remote Sens. Environ. 77(3), 293–303 (2001).
[CrossRef]

Other

BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, and OIML, “Evaluation of measurement data - Guide to the expression of uncertainty in measurement” (2008), http://www.bipm.org/utils/common/documents/jcgm/JCGM_100_2008_E.pdf .

L. Kirkup and B. Frenkel, An introduction to uncertainty in measurement (Cambridge University, Cambridge, 2006).

P. Zhou, H. Zhao, Y. Zhang, and C. Li, “Accurate optical design of an acousto-optic tunable filter imaging spectrometer,” in Proceedings of IEEE International Conference on Imaging Systems and Techniques (IST), (Institute of Electrical and Electronics Engineers, Manchester, 2012), pp. 249–253.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Sketch of the standard-lamp-based radiometric calibration setup.

Fig. 2
Fig. 2

Radiometric calibration system for the AOTF imaging spectrometer. 1 – Standard lamp, 2 – Diffusing panel, 3 – Spectroradiometer, 4 – Fiber optic probe, 5 – Integrating sphere, 6 – Guideway.

Fig. 3
Fig. 3

Illustration of the radiometric response characteristic of the AOTF imaging spectrometer.

Tables (4)

Tables Icon

Table 1 The IS radiance and the corresponding DNs at 700 nm

Tables Icon

Table 2 The uncertainty sources affecting the retrieved IS radiance

Tables Icon

Table 3 The uncertainty sources contributing to the DNs of the imaging spectrometer

Tables Icon

Table 4 The calibration parameters and their uncertainties

Equations (13)

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

L=bDN+a,
L IS (λ)= E SL (λ) π ρ DP (λ) R SR_IS (λ) R SR_DP (λ) ,
u c ( L IS ) L IS = [ u( E SL ) E SL ] 2 + [ u( ρ DP ) ρ DP ] 2 + [ u( R SR_IS ) R SR_IS ] 2 + [ u( R SR_DP ) R SR_DP ] 2 2u( R SR_IS , R SR_DP ) R SR_IS R SR_DP ,
L IS ˜ ~N( L IS , σ L IS 2 ),
σ L IS = u c ( L IS ) L IS L IS .
{ b= N i=1 N (D N IS,i L IS,i ) i=1 N D N IS,i i=1 N L IS,i N i=1 N D N IS,i 2 ( i=1 N D N IS,i ) 2 a= i=1 N L IS,i N b i=1 N D N IS,i N .
σ b 2 = N 2 i=1 N (D N IS,i 2 σ L IS,i 2 ) + ( i=1 N D N IS,i ) 2 i=1 N σ L IS,i 2 [ N i=1 N D N IS,i 2 ( i=1 N D N IS,i ) 2 ] 2 .
σ a 2 = i=1 N σ L IS,i 2 N 2 + σ b 2 ( i=1 N D N IS,i N ) 2 .
u c (D N EO ) D N EO = [ u(D N S ) D N S ] 2 + [ u(D N L ) D N L ] 2 + [ u(D N N ) D N N ] 2 + [ u(D N SC ) D N SC ] 2 ,
σ D N EO 2 = [ u c (D N EO ) D N EO D N EO ] 2 .
L EO =bD N EO +a
σ L EO 2 = σ b 2 σ D N EO 2 + b 2 σ D N EO 2 +D N EO 2 σ b 2 + σ a 2 .
u c ( L EO ) L EO = σ L EO L EO = σ b 2 σ D N EO 2 + b 2 σ D N EO 2 +D N EO 2 σ b 2 + σ a 2 bD N EO +a ,

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