Abstract

Polarization sensitivity is a critical property that must be characterized for spaceborne remote sensing instruments designed to measure reflected solar radiation. Broadband testing of the first Joint Polar-orbiting Satellite System (JPSS-1) Visible Infrared Imaging Radiometer Suite (VIIRS) showed unexpectedly large polarization sensitivities for the bluest bands on VIIRS (centered between 400 and 600 nm). Subsequent ray trace modeling indicated that large diattenuation on the edges of the bandpass for these spectral bands was the driver behind these large sensitivities. Additional testing using the National Institute of Standards and Technology’s Traveling Spectral Irradiance and Radiance Responsivity Calibrations Using Uniform Sources was added to the test program to verify and enhance the model. The testing was limited in scope to two spectral bands at two scan angles; nonetheless, this additional testing provided valuable insight into the polarization sensitivity. Analysis has shown that the derived diattenuation agreed with the broadband measurements to within an absolute difference of about 0.4% and that the ray trace model reproduced the general features of the measured data. Additionally, by deriving the spectral responsivity, the linear diattenuation is shown to be explicitly dependent on the changes in bandwidth with polarization state.

© 2016 Optical Society of America

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  1. H. Oudrari, J. McIntire, X. Xiong, J. Butler, Q. Ji, T. Schwarting, S. Lee, and B. Efremova, “JPSS-1 VIIRS radiometric characterization and calibration based on pre-launch testing,” Remote Sens. 8, 41 (2016).
    [Crossref]
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  3. E. Waluschka, J. McCorkel, J. McIntire, D. Moyer, B. McAndrew, S. W. Brown, K. R. Lykke, J. B. Young, E. Fest, J. Butler, T. R. Wang, E. O. Monroy, K. Turpie, G. Meister, and K. J. Thome, “VIIRS polarization narrative,” Proc. SPIE 9607, 960712 (2015).
    [Crossref]
  4. S. W. Brown, G. P. Eppeldauer, and K. R. Lykke, “Facility for spectral irradiance and radiance responsivity calibrations using uniform sources,” Appl. Opt. 45, 8218–8237 (2006).
    [Crossref]
  5. J. McIntire, J. B. Young, D. Moyer, E. Waluschka, H. Oudrari, and X. Xiong, “Analysis of JPSS J1 VIIRS polarization sensitivity using the NIST T-SIRCUS,” Proc. SPIE 9607, 960713 (2015).
    [Crossref]
  6. R. A. Barnes, S. W. Brown, K. R. Lykke, B. Guenther, J. J. Butler, T. Schwarting, K. Turpie, D. Moyer, F. De Luccia, and C. Moeller, “Comparison of two methodologies for calibrating satellite instruments in the visible and near-infrared,” Appl. Opt. 54, 10376 (2015).
    [Crossref]
  7. J. McIntire, J. B. Young, D. Moyer, E. Waluschka, and X. Xiong, “Measured polarized spectral responsivity of JPSS J1 VIIRS using the NIST T-SIRCUS,” Proc. SPIE 9607, 96072D (2015).
    [Crossref]
  8. X. Xiong, J. Butler, K. Chiang, B. Efremova, N. Lei, J. McIntire, H. Oudrari, Z. Wang, and A. Wu, “Assessment of SNPP VIIRS on-orbit calibration methodology and performance,” Remote Sens. 8, 84 (2016).
    [Crossref]
  9. C. Cao, F. De Luccia, X. Xiong, R. Wolfe, and F. Weng, “Early on-orbit performance of the visible infrared imaging radiometer suite (VIIRS) onboard the suomi national polar-orbiting partnership (S-NPP) satellite,” IEEE Trans. Geosci. Remote Sens. 52, 1142–1156 (2014).
    [Crossref]
  10. W. Barnes and V. Salomonson, “MODIS: a global image spectroradiometer for the earth observing system,” Crit. Rev. Opt. Sci. Technol. CR47, 285–307 (1993).
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    [Crossref]
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    [Crossref]
  17. G. Meister, E. J. Kwiatkowska, B. A. Franz, F. S. Pratt, G. C. Feldman, and C. R. McClain, “Moderate-resolution imaging spectroradiometer ocean color polarization correction,” Appl. Opt. 44, 5524–5535 (2005).
    [Crossref]
  18. C. Moeller, T. Schwarting, J. McIntire, D. Moyer, and J. Zeng, “JPSS-1 VIIRS version 2 at-launch relative spectral response characterization,” Proc. SPIE 9972, 99722 (2016).
  19. B. N. Taylor and C. E. Kuyatt, Guidelines for evaluating and expressing the uncertainty of NIST measurement results, NIST, Technical Note 1297 (1994).

2016 (3)

H. Oudrari, J. McIntire, X. Xiong, J. Butler, Q. Ji, T. Schwarting, S. Lee, and B. Efremova, “JPSS-1 VIIRS radiometric characterization and calibration based on pre-launch testing,” Remote Sens. 8, 41 (2016).
[Crossref]

X. Xiong, J. Butler, K. Chiang, B. Efremova, N. Lei, J. McIntire, H. Oudrari, Z. Wang, and A. Wu, “Assessment of SNPP VIIRS on-orbit calibration methodology and performance,” Remote Sens. 8, 84 (2016).
[Crossref]

C. Moeller, T. Schwarting, J. McIntire, D. Moyer, and J. Zeng, “JPSS-1 VIIRS version 2 at-launch relative spectral response characterization,” Proc. SPIE 9972, 99722 (2016).

2015 (4)

E. Waluschka, J. McCorkel, J. McIntire, D. Moyer, B. McAndrew, S. W. Brown, K. R. Lykke, J. B. Young, E. Fest, J. Butler, T. R. Wang, E. O. Monroy, K. Turpie, G. Meister, and K. J. Thome, “VIIRS polarization narrative,” Proc. SPIE 9607, 960712 (2015).
[Crossref]

J. McIntire, J. B. Young, D. Moyer, E. Waluschka, H. Oudrari, and X. Xiong, “Analysis of JPSS J1 VIIRS polarization sensitivity using the NIST T-SIRCUS,” Proc. SPIE 9607, 960713 (2015).
[Crossref]

R. A. Barnes, S. W. Brown, K. R. Lykke, B. Guenther, J. J. Butler, T. Schwarting, K. Turpie, D. Moyer, F. De Luccia, and C. Moeller, “Comparison of two methodologies for calibrating satellite instruments in the visible and near-infrared,” Appl. Opt. 54, 10376 (2015).
[Crossref]

J. McIntire, J. B. Young, D. Moyer, E. Waluschka, and X. Xiong, “Measured polarized spectral responsivity of JPSS J1 VIIRS using the NIST T-SIRCUS,” Proc. SPIE 9607, 96072D (2015).
[Crossref]

2014 (1)

C. Cao, F. De Luccia, X. Xiong, R. Wolfe, and F. Weng, “Early on-orbit performance of the visible infrared imaging radiometer suite (VIIRS) onboard the suomi national polar-orbiting partnership (S-NPP) satellite,” IEEE Trans. Geosci. Remote Sens. 52, 1142–1156 (2014).
[Crossref]

2006 (2)

S. W. Brown, G. P. Eppeldauer, and K. R. Lykke, “Facility for spectral irradiance and radiance responsivity calibrations using uniform sources,” Appl. Opt. 45, 8218–8237 (2006).
[Crossref]

C. McClain, S. Hooker, G. Feldman, and P. Bontempi, “Satellite data for ocean biology, biogeochemistry, and climate research,” Eos Trans. Am. Geophys. Union 87, 337–339 (2006).
[Crossref]

2005 (1)

2003 (1)

M. D. King, W. P. Menzel, Y. J. Kaufman, D. Tanre, B.-C. Gao, S. Platnick, S. A. Ackerman, L. A. Remer, R. Pincus, and P. A. Hubanks, “Cloud and aerosol and water vapor properties, precipitable water, and profiles of temperature and humidity from MODIS,” IEEE Trans. Geosci. Remote Sens. 41, 442–458 (2003).
[Crossref]

1998 (1)

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. P. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Mynemi, P. Lewis, and M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[Crossref]

1993 (1)

W. Barnes and V. Salomonson, “MODIS: a global image spectroradiometer for the earth observing system,” Crit. Rev. Opt. Sci. Technol. CR47, 285–307 (1993).

1974 (1)

R. Miller and G. Hennessey, “Infrared coatings for 2-15 micron,” Proc. SPIE 0050, 119–142 (1974).
[Crossref]

Ackerman, S. A.

M. D. King, W. P. Menzel, Y. J. Kaufman, D. Tanre, B.-C. Gao, S. Platnick, S. A. Ackerman, L. A. Remer, R. Pincus, and P. A. Hubanks, “Cloud and aerosol and water vapor properties, precipitable water, and profiles of temperature and humidity from MODIS,” IEEE Trans. Geosci. Remote Sens. 41, 442–458 (2003).
[Crossref]

Barnes, R. A.

Barnes, W.

W. Barnes and V. Salomonson, “MODIS: a global image spectroradiometer for the earth observing system,” Crit. Rev. Opt. Sci. Technol. CR47, 285–307 (1993).

Barnsley, M. J.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. P. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Mynemi, P. Lewis, and M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[Crossref]

Bontempi, P.

C. McClain, S. Hooker, G. Feldman, and P. Bontempi, “Satellite data for ocean biology, biogeochemistry, and climate research,” Eos Trans. Am. Geophys. Union 87, 337–339 (2006).
[Crossref]

Brown, S. W.

Butler, J.

H. Oudrari, J. McIntire, X. Xiong, J. Butler, Q. Ji, T. Schwarting, S. Lee, and B. Efremova, “JPSS-1 VIIRS radiometric characterization and calibration based on pre-launch testing,” Remote Sens. 8, 41 (2016).
[Crossref]

X. Xiong, J. Butler, K. Chiang, B. Efremova, N. Lei, J. McIntire, H. Oudrari, Z. Wang, and A. Wu, “Assessment of SNPP VIIRS on-orbit calibration methodology and performance,” Remote Sens. 8, 84 (2016).
[Crossref]

E. Waluschka, J. McCorkel, J. McIntire, D. Moyer, B. McAndrew, S. W. Brown, K. R. Lykke, J. B. Young, E. Fest, J. Butler, T. R. Wang, E. O. Monroy, K. Turpie, G. Meister, and K. J. Thome, “VIIRS polarization narrative,” Proc. SPIE 9607, 960712 (2015).
[Crossref]

Butler, J. J.

Cao, C.

C. Cao, F. De Luccia, X. Xiong, R. Wolfe, and F. Weng, “Early on-orbit performance of the visible infrared imaging radiometer suite (VIIRS) onboard the suomi national polar-orbiting partnership (S-NPP) satellite,” IEEE Trans. Geosci. Remote Sens. 52, 1142–1156 (2014).
[Crossref]

Chiang, K.

X. Xiong, J. Butler, K. Chiang, B. Efremova, N. Lei, J. McIntire, H. Oudrari, Z. Wang, and A. Wu, “Assessment of SNPP VIIRS on-orbit calibration methodology and performance,” Remote Sens. 8, 84 (2016).
[Crossref]

De Luccia, F.

R. A. Barnes, S. W. Brown, K. R. Lykke, B. Guenther, J. J. Butler, T. Schwarting, K. Turpie, D. Moyer, F. De Luccia, and C. Moeller, “Comparison of two methodologies for calibrating satellite instruments in the visible and near-infrared,” Appl. Opt. 54, 10376 (2015).
[Crossref]

C. Cao, F. De Luccia, X. Xiong, R. Wolfe, and F. Weng, “Early on-orbit performance of the visible infrared imaging radiometer suite (VIIRS) onboard the suomi national polar-orbiting partnership (S-NPP) satellite,” IEEE Trans. Geosci. Remote Sens. 52, 1142–1156 (2014).
[Crossref]

D. Moyer, J. McIntire, E. Waluschka, X. Xiong, and F. De Luccia, “JPSS-1 VIIRS pre-launch polarization testing and performance,” IEEE Trans. Geosci. Remote Sens. (to be published).

Defries, R.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. P. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Mynemi, P. Lewis, and M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[Crossref]

Efremova, B.

H. Oudrari, J. McIntire, X. Xiong, J. Butler, Q. Ji, T. Schwarting, S. Lee, and B. Efremova, “JPSS-1 VIIRS radiometric characterization and calibration based on pre-launch testing,” Remote Sens. 8, 41 (2016).
[Crossref]

X. Xiong, J. Butler, K. Chiang, B. Efremova, N. Lei, J. McIntire, H. Oudrari, Z. Wang, and A. Wu, “Assessment of SNPP VIIRS on-orbit calibration methodology and performance,” Remote Sens. 8, 84 (2016).
[Crossref]

Eppeldauer, G. P.

Feldman, G.

C. McClain, S. Hooker, G. Feldman, and P. Bontempi, “Satellite data for ocean biology, biogeochemistry, and climate research,” Eos Trans. Am. Geophys. Union 87, 337–339 (2006).
[Crossref]

Feldman, G. C.

Fest, E.

E. Waluschka, J. McCorkel, J. McIntire, D. Moyer, B. McAndrew, S. W. Brown, K. R. Lykke, J. B. Young, E. Fest, J. Butler, T. R. Wang, E. O. Monroy, K. Turpie, G. Meister, and K. J. Thome, “VIIRS polarization narrative,” Proc. SPIE 9607, 960712 (2015).
[Crossref]

Franz, B. A.

Gao, B.-C.

M. D. King, W. P. Menzel, Y. J. Kaufman, D. Tanre, B.-C. Gao, S. Platnick, S. A. Ackerman, L. A. Remer, R. Pincus, and P. A. Hubanks, “Cloud and aerosol and water vapor properties, precipitable water, and profiles of temperature and humidity from MODIS,” IEEE Trans. Geosci. Remote Sens. 41, 442–458 (2003).
[Crossref]

Guenther, B.

Hall, D. K.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. P. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Mynemi, P. Lewis, and M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[Crossref]

Hennessey, G.

R. Miller and G. Hennessey, “Infrared coatings for 2-15 micron,” Proc. SPIE 0050, 119–142 (1974).
[Crossref]

Hooker, S.

C. McClain, S. Hooker, G. Feldman, and P. Bontempi, “Satellite data for ocean biology, biogeochemistry, and climate research,” Eos Trans. Am. Geophys. Union 87, 337–339 (2006).
[Crossref]

Hubanks, P. A.

M. D. King, W. P. Menzel, Y. J. Kaufman, D. Tanre, B.-C. Gao, S. Platnick, S. A. Ackerman, L. A. Remer, R. Pincus, and P. A. Hubanks, “Cloud and aerosol and water vapor properties, precipitable water, and profiles of temperature and humidity from MODIS,” IEEE Trans. Geosci. Remote Sens. 41, 442–458 (2003).
[Crossref]

Ji, Q.

H. Oudrari, J. McIntire, X. Xiong, J. Butler, Q. Ji, T. Schwarting, S. Lee, and B. Efremova, “JPSS-1 VIIRS radiometric characterization and calibration based on pre-launch testing,” Remote Sens. 8, 41 (2016).
[Crossref]

Justice, C. O.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. P. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Mynemi, P. Lewis, and M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[Crossref]

Kaufman, Y. J.

M. D. King, W. P. Menzel, Y. J. Kaufman, D. Tanre, B.-C. Gao, S. Platnick, S. A. Ackerman, L. A. Remer, R. Pincus, and P. A. Hubanks, “Cloud and aerosol and water vapor properties, precipitable water, and profiles of temperature and humidity from MODIS,” IEEE Trans. Geosci. Remote Sens. 41, 442–458 (2003).
[Crossref]

King, M. D.

M. D. King, W. P. Menzel, Y. J. Kaufman, D. Tanre, B.-C. Gao, S. Platnick, S. A. Ackerman, L. A. Remer, R. Pincus, and P. A. Hubanks, “Cloud and aerosol and water vapor properties, precipitable water, and profiles of temperature and humidity from MODIS,” IEEE Trans. Geosci. Remote Sens. 41, 442–458 (2003).
[Crossref]

Kuyatt, C. E.

B. N. Taylor and C. E. Kuyatt, Guidelines for evaluating and expressing the uncertainty of NIST measurement results, NIST, Technical Note 1297 (1994).

Kwiatkowska, E. J.

Lee, S.

H. Oudrari, J. McIntire, X. Xiong, J. Butler, Q. Ji, T. Schwarting, S. Lee, and B. Efremova, “JPSS-1 VIIRS radiometric characterization and calibration based on pre-launch testing,” Remote Sens. 8, 41 (2016).
[Crossref]

Lei, N.

X. Xiong, J. Butler, K. Chiang, B. Efremova, N. Lei, J. McIntire, H. Oudrari, Z. Wang, and A. Wu, “Assessment of SNPP VIIRS on-orbit calibration methodology and performance,” Remote Sens. 8, 84 (2016).
[Crossref]

Lewis, P.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. P. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Mynemi, P. Lewis, and M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[Crossref]

Lucht, W.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. P. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Mynemi, P. Lewis, and M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[Crossref]

Lykke, K. R.

McAndrew, B.

E. Waluschka, J. McCorkel, J. McIntire, D. Moyer, B. McAndrew, S. W. Brown, K. R. Lykke, J. B. Young, E. Fest, J. Butler, T. R. Wang, E. O. Monroy, K. Turpie, G. Meister, and K. J. Thome, “VIIRS polarization narrative,” Proc. SPIE 9607, 960712 (2015).
[Crossref]

McClain, C.

C. McClain, S. Hooker, G. Feldman, and P. Bontempi, “Satellite data for ocean biology, biogeochemistry, and climate research,” Eos Trans. Am. Geophys. Union 87, 337–339 (2006).
[Crossref]

McClain, C. R.

McCorkel, J.

E. Waluschka, J. McCorkel, J. McIntire, D. Moyer, B. McAndrew, S. W. Brown, K. R. Lykke, J. B. Young, E. Fest, J. Butler, T. R. Wang, E. O. Monroy, K. Turpie, G. Meister, and K. J. Thome, “VIIRS polarization narrative,” Proc. SPIE 9607, 960712 (2015).
[Crossref]

McIntire, J.

H. Oudrari, J. McIntire, X. Xiong, J. Butler, Q. Ji, T. Schwarting, S. Lee, and B. Efremova, “JPSS-1 VIIRS radiometric characterization and calibration based on pre-launch testing,” Remote Sens. 8, 41 (2016).
[Crossref]

X. Xiong, J. Butler, K. Chiang, B. Efremova, N. Lei, J. McIntire, H. Oudrari, Z. Wang, and A. Wu, “Assessment of SNPP VIIRS on-orbit calibration methodology and performance,” Remote Sens. 8, 84 (2016).
[Crossref]

C. Moeller, T. Schwarting, J. McIntire, D. Moyer, and J. Zeng, “JPSS-1 VIIRS version 2 at-launch relative spectral response characterization,” Proc. SPIE 9972, 99722 (2016).

E. Waluschka, J. McCorkel, J. McIntire, D. Moyer, B. McAndrew, S. W. Brown, K. R. Lykke, J. B. Young, E. Fest, J. Butler, T. R. Wang, E. O. Monroy, K. Turpie, G. Meister, and K. J. Thome, “VIIRS polarization narrative,” Proc. SPIE 9607, 960712 (2015).
[Crossref]

J. McIntire, J. B. Young, D. Moyer, E. Waluschka, H. Oudrari, and X. Xiong, “Analysis of JPSS J1 VIIRS polarization sensitivity using the NIST T-SIRCUS,” Proc. SPIE 9607, 960713 (2015).
[Crossref]

J. McIntire, J. B. Young, D. Moyer, E. Waluschka, and X. Xiong, “Measured polarized spectral responsivity of JPSS J1 VIIRS using the NIST T-SIRCUS,” Proc. SPIE 9607, 96072D (2015).
[Crossref]

D. Moyer, J. McIntire, E. Waluschka, X. Xiong, and F. De Luccia, “JPSS-1 VIIRS pre-launch polarization testing and performance,” IEEE Trans. Geosci. Remote Sens. (to be published).

Meister, G.

E. Waluschka, J. McCorkel, J. McIntire, D. Moyer, B. McAndrew, S. W. Brown, K. R. Lykke, J. B. Young, E. Fest, J. Butler, T. R. Wang, E. O. Monroy, K. Turpie, G. Meister, and K. J. Thome, “VIIRS polarization narrative,” Proc. SPIE 9607, 960712 (2015).
[Crossref]

G. Meister, E. J. Kwiatkowska, B. A. Franz, F. S. Pratt, G. C. Feldman, and C. R. McClain, “Moderate-resolution imaging spectroradiometer ocean color polarization correction,” Appl. Opt. 44, 5524–5535 (2005).
[Crossref]

Menzel, W. P.

M. D. King, W. P. Menzel, Y. J. Kaufman, D. Tanre, B.-C. Gao, S. Platnick, S. A. Ackerman, L. A. Remer, R. Pincus, and P. A. Hubanks, “Cloud and aerosol and water vapor properties, precipitable water, and profiles of temperature and humidity from MODIS,” IEEE Trans. Geosci. Remote Sens. 41, 442–458 (2003).
[Crossref]

Miller, R.

R. Miller and G. Hennessey, “Infrared coatings for 2-15 micron,” Proc. SPIE 0050, 119–142 (1974).
[Crossref]

Moeller, C.

Monroy, E. O.

E. Waluschka, J. McCorkel, J. McIntire, D. Moyer, B. McAndrew, S. W. Brown, K. R. Lykke, J. B. Young, E. Fest, J. Butler, T. R. Wang, E. O. Monroy, K. Turpie, G. Meister, and K. J. Thome, “VIIRS polarization narrative,” Proc. SPIE 9607, 960712 (2015).
[Crossref]

Moyer, D.

C. Moeller, T. Schwarting, J. McIntire, D. Moyer, and J. Zeng, “JPSS-1 VIIRS version 2 at-launch relative spectral response characterization,” Proc. SPIE 9972, 99722 (2016).

R. A. Barnes, S. W. Brown, K. R. Lykke, B. Guenther, J. J. Butler, T. Schwarting, K. Turpie, D. Moyer, F. De Luccia, and C. Moeller, “Comparison of two methodologies for calibrating satellite instruments in the visible and near-infrared,” Appl. Opt. 54, 10376 (2015).
[Crossref]

J. McIntire, J. B. Young, D. Moyer, E. Waluschka, H. Oudrari, and X. Xiong, “Analysis of JPSS J1 VIIRS polarization sensitivity using the NIST T-SIRCUS,” Proc. SPIE 9607, 960713 (2015).
[Crossref]

E. Waluschka, J. McCorkel, J. McIntire, D. Moyer, B. McAndrew, S. W. Brown, K. R. Lykke, J. B. Young, E. Fest, J. Butler, T. R. Wang, E. O. Monroy, K. Turpie, G. Meister, and K. J. Thome, “VIIRS polarization narrative,” Proc. SPIE 9607, 960712 (2015).
[Crossref]

J. McIntire, J. B. Young, D. Moyer, E. Waluschka, and X. Xiong, “Measured polarized spectral responsivity of JPSS J1 VIIRS using the NIST T-SIRCUS,” Proc. SPIE 9607, 96072D (2015).
[Crossref]

D. Moyer, J. McIntire, E. Waluschka, X. Xiong, and F. De Luccia, “JPSS-1 VIIRS pre-launch polarization testing and performance,” IEEE Trans. Geosci. Remote Sens. (to be published).

Mynemi, R. B.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. P. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Mynemi, P. Lewis, and M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[Crossref]

Oudrari, H.

H. Oudrari, J. McIntire, X. Xiong, J. Butler, Q. Ji, T. Schwarting, S. Lee, and B. Efremova, “JPSS-1 VIIRS radiometric characterization and calibration based on pre-launch testing,” Remote Sens. 8, 41 (2016).
[Crossref]

X. Xiong, J. Butler, K. Chiang, B. Efremova, N. Lei, J. McIntire, H. Oudrari, Z. Wang, and A. Wu, “Assessment of SNPP VIIRS on-orbit calibration methodology and performance,” Remote Sens. 8, 84 (2016).
[Crossref]

J. McIntire, J. B. Young, D. Moyer, E. Waluschka, H. Oudrari, and X. Xiong, “Analysis of JPSS J1 VIIRS polarization sensitivity using the NIST T-SIRCUS,” Proc. SPIE 9607, 960713 (2015).
[Crossref]

Pincus, R.

M. D. King, W. P. Menzel, Y. J. Kaufman, D. Tanre, B.-C. Gao, S. Platnick, S. A. Ackerman, L. A. Remer, R. Pincus, and P. A. Hubanks, “Cloud and aerosol and water vapor properties, precipitable water, and profiles of temperature and humidity from MODIS,” IEEE Trans. Geosci. Remote Sens. 41, 442–458 (2003).
[Crossref]

Platnick, S.

M. D. King, W. P. Menzel, Y. J. Kaufman, D. Tanre, B.-C. Gao, S. Platnick, S. A. Ackerman, L. A. Remer, R. Pincus, and P. A. Hubanks, “Cloud and aerosol and water vapor properties, precipitable water, and profiles of temperature and humidity from MODIS,” IEEE Trans. Geosci. Remote Sens. 41, 442–458 (2003).
[Crossref]

Pratt, F. S.

Privette, J. L.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. P. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Mynemi, P. Lewis, and M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[Crossref]

Remer, L. A.

M. D. King, W. P. Menzel, Y. J. Kaufman, D. Tanre, B.-C. Gao, S. Platnick, S. A. Ackerman, L. A. Remer, R. Pincus, and P. A. Hubanks, “Cloud and aerosol and water vapor properties, precipitable water, and profiles of temperature and humidity from MODIS,” IEEE Trans. Geosci. Remote Sens. 41, 442–458 (2003).
[Crossref]

Riggs, G.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. P. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Mynemi, P. Lewis, and M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[Crossref]

Roy, D. P.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. P. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Mynemi, P. Lewis, and M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[Crossref]

Salomonson, V.

W. Barnes and V. Salomonson, “MODIS: a global image spectroradiometer for the earth observing system,” Crit. Rev. Opt. Sci. Technol. CR47, 285–307 (1993).

Salomonson, V. V.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. P. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Mynemi, P. Lewis, and M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[Crossref]

Schwarting, T.

C. Moeller, T. Schwarting, J. McIntire, D. Moyer, and J. Zeng, “JPSS-1 VIIRS version 2 at-launch relative spectral response characterization,” Proc. SPIE 9972, 99722 (2016).

H. Oudrari, J. McIntire, X. Xiong, J. Butler, Q. Ji, T. Schwarting, S. Lee, and B. Efremova, “JPSS-1 VIIRS radiometric characterization and calibration based on pre-launch testing,” Remote Sens. 8, 41 (2016).
[Crossref]

R. A. Barnes, S. W. Brown, K. R. Lykke, B. Guenther, J. J. Butler, T. Schwarting, K. Turpie, D. Moyer, F. De Luccia, and C. Moeller, “Comparison of two methodologies for calibrating satellite instruments in the visible and near-infrared,” Appl. Opt. 54, 10376 (2015).
[Crossref]

Strahler, A.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. P. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Mynemi, P. Lewis, and M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[Crossref]

Tanre, D.

M. D. King, W. P. Menzel, Y. J. Kaufman, D. Tanre, B.-C. Gao, S. Platnick, S. A. Ackerman, L. A. Remer, R. Pincus, and P. A. Hubanks, “Cloud and aerosol and water vapor properties, precipitable water, and profiles of temperature and humidity from MODIS,” IEEE Trans. Geosci. Remote Sens. 41, 442–458 (2003).
[Crossref]

Taylor, B. N.

B. N. Taylor and C. E. Kuyatt, Guidelines for evaluating and expressing the uncertainty of NIST measurement results, NIST, Technical Note 1297 (1994).

Thome, K. J.

E. Waluschka, J. McCorkel, J. McIntire, D. Moyer, B. McAndrew, S. W. Brown, K. R. Lykke, J. B. Young, E. Fest, J. Butler, T. R. Wang, E. O. Monroy, K. Turpie, G. Meister, and K. J. Thome, “VIIRS polarization narrative,” Proc. SPIE 9607, 960712 (2015).
[Crossref]

Townshend, J. R. G.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. P. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Mynemi, P. Lewis, and M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[Crossref]

Turpie, K.

E. Waluschka, J. McCorkel, J. McIntire, D. Moyer, B. McAndrew, S. W. Brown, K. R. Lykke, J. B. Young, E. Fest, J. Butler, T. R. Wang, E. O. Monroy, K. Turpie, G. Meister, and K. J. Thome, “VIIRS polarization narrative,” Proc. SPIE 9607, 960712 (2015).
[Crossref]

R. A. Barnes, S. W. Brown, K. R. Lykke, B. Guenther, J. J. Butler, T. Schwarting, K. Turpie, D. Moyer, F. De Luccia, and C. Moeller, “Comparison of two methodologies for calibrating satellite instruments in the visible and near-infrared,” Appl. Opt. 54, 10376 (2015).
[Crossref]

Vermote, E.

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. P. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Mynemi, P. Lewis, and M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[Crossref]

Waluschka, E.

J. McIntire, J. B. Young, D. Moyer, E. Waluschka, and X. Xiong, “Measured polarized spectral responsivity of JPSS J1 VIIRS using the NIST T-SIRCUS,” Proc. SPIE 9607, 96072D (2015).
[Crossref]

J. McIntire, J. B. Young, D. Moyer, E. Waluschka, H. Oudrari, and X. Xiong, “Analysis of JPSS J1 VIIRS polarization sensitivity using the NIST T-SIRCUS,” Proc. SPIE 9607, 960713 (2015).
[Crossref]

E. Waluschka, J. McCorkel, J. McIntire, D. Moyer, B. McAndrew, S. W. Brown, K. R. Lykke, J. B. Young, E. Fest, J. Butler, T. R. Wang, E. O. Monroy, K. Turpie, G. Meister, and K. J. Thome, “VIIRS polarization narrative,” Proc. SPIE 9607, 960712 (2015).
[Crossref]

D. Moyer, J. McIntire, E. Waluschka, X. Xiong, and F. De Luccia, “JPSS-1 VIIRS pre-launch polarization testing and performance,” IEEE Trans. Geosci. Remote Sens. (to be published).

Wang, T. R.

E. Waluschka, J. McCorkel, J. McIntire, D. Moyer, B. McAndrew, S. W. Brown, K. R. Lykke, J. B. Young, E. Fest, J. Butler, T. R. Wang, E. O. Monroy, K. Turpie, G. Meister, and K. J. Thome, “VIIRS polarization narrative,” Proc. SPIE 9607, 960712 (2015).
[Crossref]

Wang, Z.

X. Xiong, J. Butler, K. Chiang, B. Efremova, N. Lei, J. McIntire, H. Oudrari, Z. Wang, and A. Wu, “Assessment of SNPP VIIRS on-orbit calibration methodology and performance,” Remote Sens. 8, 84 (2016).
[Crossref]

Weng, F.

C. Cao, F. De Luccia, X. Xiong, R. Wolfe, and F. Weng, “Early on-orbit performance of the visible infrared imaging radiometer suite (VIIRS) onboard the suomi national polar-orbiting partnership (S-NPP) satellite,” IEEE Trans. Geosci. Remote Sens. 52, 1142–1156 (2014).
[Crossref]

Wolfe, R.

C. Cao, F. De Luccia, X. Xiong, R. Wolfe, and F. Weng, “Early on-orbit performance of the visible infrared imaging radiometer suite (VIIRS) onboard the suomi national polar-orbiting partnership (S-NPP) satellite,” IEEE Trans. Geosci. Remote Sens. 52, 1142–1156 (2014).
[Crossref]

Wu, A.

X. Xiong, J. Butler, K. Chiang, B. Efremova, N. Lei, J. McIntire, H. Oudrari, Z. Wang, and A. Wu, “Assessment of SNPP VIIRS on-orbit calibration methodology and performance,” Remote Sens. 8, 84 (2016).
[Crossref]

Xiong, X.

X. Xiong, J. Butler, K. Chiang, B. Efremova, N. Lei, J. McIntire, H. Oudrari, Z. Wang, and A. Wu, “Assessment of SNPP VIIRS on-orbit calibration methodology and performance,” Remote Sens. 8, 84 (2016).
[Crossref]

H. Oudrari, J. McIntire, X. Xiong, J. Butler, Q. Ji, T. Schwarting, S. Lee, and B. Efremova, “JPSS-1 VIIRS radiometric characterization and calibration based on pre-launch testing,” Remote Sens. 8, 41 (2016).
[Crossref]

J. McIntire, J. B. Young, D. Moyer, E. Waluschka, H. Oudrari, and X. Xiong, “Analysis of JPSS J1 VIIRS polarization sensitivity using the NIST T-SIRCUS,” Proc. SPIE 9607, 960713 (2015).
[Crossref]

J. McIntire, J. B. Young, D. Moyer, E. Waluschka, and X. Xiong, “Measured polarized spectral responsivity of JPSS J1 VIIRS using the NIST T-SIRCUS,” Proc. SPIE 9607, 96072D (2015).
[Crossref]

C. Cao, F. De Luccia, X. Xiong, R. Wolfe, and F. Weng, “Early on-orbit performance of the visible infrared imaging radiometer suite (VIIRS) onboard the suomi national polar-orbiting partnership (S-NPP) satellite,” IEEE Trans. Geosci. Remote Sens. 52, 1142–1156 (2014).
[Crossref]

D. Moyer, J. McIntire, E. Waluschka, X. Xiong, and F. De Luccia, “JPSS-1 VIIRS pre-launch polarization testing and performance,” IEEE Trans. Geosci. Remote Sens. (to be published).

Young, J. B.

E. Waluschka, J. McCorkel, J. McIntire, D. Moyer, B. McAndrew, S. W. Brown, K. R. Lykke, J. B. Young, E. Fest, J. Butler, T. R. Wang, E. O. Monroy, K. Turpie, G. Meister, and K. J. Thome, “VIIRS polarization narrative,” Proc. SPIE 9607, 960712 (2015).
[Crossref]

J. McIntire, J. B. Young, D. Moyer, E. Waluschka, and X. Xiong, “Measured polarized spectral responsivity of JPSS J1 VIIRS using the NIST T-SIRCUS,” Proc. SPIE 9607, 96072D (2015).
[Crossref]

J. McIntire, J. B. Young, D. Moyer, E. Waluschka, H. Oudrari, and X. Xiong, “Analysis of JPSS J1 VIIRS polarization sensitivity using the NIST T-SIRCUS,” Proc. SPIE 9607, 960713 (2015).
[Crossref]

Zeng, J.

C. Moeller, T. Schwarting, J. McIntire, D. Moyer, and J. Zeng, “JPSS-1 VIIRS version 2 at-launch relative spectral response characterization,” Proc. SPIE 9972, 99722 (2016).

Appl. Opt. (3)

Crit. Rev. Opt. Sci. Technol. (1)

W. Barnes and V. Salomonson, “MODIS: a global image spectroradiometer for the earth observing system,” Crit. Rev. Opt. Sci. Technol. CR47, 285–307 (1993).

Eos Trans. Am. Geophys. Union (1)

C. McClain, S. Hooker, G. Feldman, and P. Bontempi, “Satellite data for ocean biology, biogeochemistry, and climate research,” Eos Trans. Am. Geophys. Union 87, 337–339 (2006).
[Crossref]

IEEE Trans. Geosci. Remote Sens. (3)

M. D. King, W. P. Menzel, Y. J. Kaufman, D. Tanre, B.-C. Gao, S. Platnick, S. A. Ackerman, L. A. Remer, R. Pincus, and P. A. Hubanks, “Cloud and aerosol and water vapor properties, precipitable water, and profiles of temperature and humidity from MODIS,” IEEE Trans. Geosci. Remote Sens. 41, 442–458 (2003).
[Crossref]

C. O. Justice, E. Vermote, J. R. G. Townshend, R. Defries, D. P. Roy, D. K. Hall, V. V. Salomonson, J. L. Privette, G. Riggs, A. Strahler, W. Lucht, R. B. Mynemi, P. Lewis, and M. J. Barnsley, “The moderate resolution imaging spectroradiometer (MODIS): land remote sensing for global change research,” IEEE Trans. Geosci. Remote Sens. 36, 1228–1249 (1998).
[Crossref]

C. Cao, F. De Luccia, X. Xiong, R. Wolfe, and F. Weng, “Early on-orbit performance of the visible infrared imaging radiometer suite (VIIRS) onboard the suomi national polar-orbiting partnership (S-NPP) satellite,” IEEE Trans. Geosci. Remote Sens. 52, 1142–1156 (2014).
[Crossref]

Proc. SPIE (5)

E. Waluschka, J. McCorkel, J. McIntire, D. Moyer, B. McAndrew, S. W. Brown, K. R. Lykke, J. B. Young, E. Fest, J. Butler, T. R. Wang, E. O. Monroy, K. Turpie, G. Meister, and K. J. Thome, “VIIRS polarization narrative,” Proc. SPIE 9607, 960712 (2015).
[Crossref]

J. McIntire, J. B. Young, D. Moyer, E. Waluschka, and X. Xiong, “Measured polarized spectral responsivity of JPSS J1 VIIRS using the NIST T-SIRCUS,” Proc. SPIE 9607, 96072D (2015).
[Crossref]

J. McIntire, J. B. Young, D. Moyer, E. Waluschka, H. Oudrari, and X. Xiong, “Analysis of JPSS J1 VIIRS polarization sensitivity using the NIST T-SIRCUS,” Proc. SPIE 9607, 960713 (2015).
[Crossref]

C. Moeller, T. Schwarting, J. McIntire, D. Moyer, and J. Zeng, “JPSS-1 VIIRS version 2 at-launch relative spectral response characterization,” Proc. SPIE 9972, 99722 (2016).

R. Miller and G. Hennessey, “Infrared coatings for 2-15 micron,” Proc. SPIE 0050, 119–142 (1974).
[Crossref]

Remote Sens. (2)

H. Oudrari, J. McIntire, X. Xiong, J. Butler, Q. Ji, T. Schwarting, S. Lee, and B. Efremova, “JPSS-1 VIIRS radiometric characterization and calibration based on pre-launch testing,” Remote Sens. 8, 41 (2016).
[Crossref]

X. Xiong, J. Butler, K. Chiang, B. Efremova, N. Lei, J. McIntire, H. Oudrari, Z. Wang, and A. Wu, “Assessment of SNPP VIIRS on-orbit calibration methodology and performance,” Remote Sens. 8, 84 (2016).
[Crossref]

Other (4)

D. Moyer, J. McIntire, E. Waluschka, X. Xiong, and F. De Luccia, “JPSS-1 VIIRS pre-launch polarization testing and performance,” IEEE Trans. Geosci. Remote Sens. (to be published).

B. N. Taylor and C. E. Kuyatt, Guidelines for evaluating and expressing the uncertainty of NIST measurement results, NIST, Technical Note 1297 (1994).

Bolder Vision Optik, 4730 Walnut Street, Suite 102, Boulder, Colorado, USA.

Sonoma C165-210-JB NIR Blocking Filter, Sonoma Photonic Incorporated, 1750 Northpoint Parkway, Santa Rosa, CA.

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Figures (15)

Fig. 1.
Fig. 1. Measured dn versus polarizer angle for band M1 at 408 nm (a), band M1 at 417 nm (b), band M4 at 547 nm (c), and band M4 at 555 nm (d). The legend defines the different symbol/color combinations which correspond to each detector.
Fig. 2.
Fig. 2. Measured weighted diattenuation versus wavelength for band M1 (a) and modeled weighted diattenuation versus wavelength for band M1 (b). The legend defines the different symbol/color combinations which correspond to each detector.
Fig. 3.
Fig. 3. Measured weighted diattenuation versus wavelength for band M4 (a) and modeled weighted diattenuation versus wavelength for band M4 (b). The legend defines the different symbol/color combinations which correspond to each detector.
Fig. 4.
Fig. 4. Plots of the diattenuation showing band M1 at 8° scan angle, HAM side 1. Black “+” indicates T-SIRCUS measurements, red “*” denote broadband measurements, and blue “◊” refer to the model. Dashed lines indicate the extent on the k=2 uncertainties.
Fig. 5.
Fig. 5. Plots of the diattenuation showing band M4 at 8° scan angle, HAM side 1. Black “+” indicates T-SIRCUS measurements, red “*” denote broadband measurements, and blue “◊” refer to the model. Dashed lines indicate the extent on the k=2 uncertainties.
Fig. 6.
Fig. 6. Band M1 ASR shown for detector 9. The legend defines the different symbol/color combinations which correspond to each polarization state (and “un” refers to the unpolarized ASR).
Fig. 7.
Fig. 7. Band M4 ASR shown for detector 9. The legend defines the different symbol/color combinations which correspond to each polarization state (and “un” refers to the unpolarized ASR).
Fig. 8.
Fig. 8. Band M1 ASR shown for detector 9. The legend defines the different symbol/color combinations which correspond to the unpolarized ASR for different input spectra.
Fig. 9.
Fig. 9. Band M4 ASR shown for detector 9. The legend defines the different symbol/color combinations which correspond to the unpolarized ASR for different input spectra.
Fig. 10.
Fig. 10. Plots are shown of the band centroid for band M1 (a) and for band M4 (b) versus polarization state. The legend defines the different symbol/color combinations which correspond to each detector. Note that the unconnected data at 195° in each plot represents the centroid derived from unpolarized data.
Fig. 11.
Fig. 11. Plots are shown of the bandwidth for band M1 (a) and for band M4 (b) versus polarization state. The legend defines the different symbol/color combinations which correspond to each detector. Note that the unconnected data at 195° in each plot represents the bandwidth derived from unpolarized data.
Fig. 12.
Fig. 12. Plots of the band centroid versus polarization state for band M1 using the flat spectrum (a), the SIS spectrum (b), and the TOA spectrum (c). The legend defines the different symbol/color combinations which correspond to each detector. Note that the unconnected data at 195° in each plot represents the centroid derived from unpolarized data.
Fig. 13.
Fig. 13. Plots of the bandwidth versus polarization state for band M4 using the flat spectrum (a), the SIS spectrum (b), and the TOA spectrum (c). The legend defines the different symbol/color combinations which correspond to each detector. Note that the unconnected data at 195° in each plot represents the bandwidth derived from unpolarized data.
Fig. 14.
Fig. 14. Plots are shown of the responsivity versus polarization state for band M1 (a) and for band M4 (b). The responsivity is in units of [dn/(W/m2/sr/μm)]. The legend defines the different symbol/color combinations which correspond to each detector. Note that the unconnected data at 195° in each plot represents the responsivity derived from unpolarized data.
Fig. 15.
Fig. 15. Plots are shown of the diattenuation (in %) versus detector derived from the Fourier and ASR analysis for band M1 (a) and for band M4 (c). Black “+” indicates the Fourier analysis and red “*” denote the ASR analysis. The difference between the two methods is plotted for the same data for band M1 (b) and band M4 (d), represented by the blue “◊”.

Tables (3)

Tables Icon

Table 1. Center Wavelengths (λC) and Bandwidths (BW) for the Bands Measured in T-SIRCUS Polarization Testing

Tables Icon

Table 2. T-SIRCUS Polarization Measurements Performed as a Function of Wavelength, HAM Side, Scan Angle, and Test Type (Stray Light, Polarizer Efficiency, or Polarization Sensitivity)a

Tables Icon

Table 3. Measured Band Average Centroids, Bandwidths, and Responsivities Determined from the Unpolarized ASR Compared to Spectral Testing Results [18]a

Equations (22)

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

dn(λ,θ)=12c0(λ)+c2(λ)cos(2θ)+d2(λ)sin(2θ),
12c0(λ)=1π0πdθdn(λ,θ),
C2(λ)=2c2(λ)c0(λ)=4πc0(λ)0πdθdn(λ,θ)cos(2θ),
D2(λ)=2d2(λ)c0(λ)=4πc0(λ)0πdθdn(λ,θ)sin(2θ).
dn(λ,θ)=12c0(λ){1+a2(λ)cos[2θ+2δn(λ)]},
a2(λ)=C22(λ)+D22(λ)a2eff(λ),
δ2(λ)=12tan1[D2(λ)C2(λ)].
a2eff(λ)=C22(λ)+D22(λ),
C2(B)=dλC2(λ)RSR(λ)Lsource(λ)dλRSR(λ)Lsource(λ),
D2(B)=dλD2(λ)RSR(λ)Lsource(λ)dλRSR(λ)Lsource(λ),
a2(B)=C22(B)+D22(B)a2eff(B),
δ2(B)=12arctan[D2(B)C2(B)].
ASR(λ,θ)=dn(λ,θ)L(λ,θ),
R(θ)=dλASR(λ,θ),
λc(θ)=dλλASR(λ,θ)dλASR(λ,θ)=dλλASR(λ,θ)R(θ),
BW(θ)=dλASR(λ,θ)max[ASR(λ,θ)]λ=R(θ)max[ASR(λ,θ)]λ.
ASR(λ,θ)=ASR(λ,θ)Lsource(λ)LsourceAVG,
LsourceAVG=dλLsource(λ)ASR(λ,θ)R(θ).
C2(B)=2πR(B)0πdθcos(2θ)R(θ),
D2(B)=2πR(B)0πdθsin(2θ)R(θ),
a2(B)=2πR(B)1a2eff(B)×[0πdθ1R(θ1)0πdθ2R(θ2)cos(2θ12θ2)]12.
δ2(B)=12tan1[0πdθsin(2θ)R(θ)0πdθcos(2θ)R(θ)].

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