Abstract

We describe how sky luminance can be derived from a newly developed hemispherical sky imager (HSI) system. The system contains a commercial compact charge coupled device (CCD) camera equipped with a fish-eye lens. The projection of the camera system has been found to be nearly equidistant. The luminance from the high dynamic range images has been calculated and then validated with luminance data measured by a CCD array spectroradiometer. The deviation between both datasets is less than 10% for cloudless and completely overcast skies, and differs by no more than 20% for all sky conditions. The global illuminance derived from the HSI pictures deviates by less than 5% and 20% under cloudless and cloudy skies for solar zenith angles less than 80°, respectively. This system is therefore capable of measuring sky luminance with the high spatial and temporal resolution of more than a million pixels and every 20 s respectively.

© 2013 Optical Society of America

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2012 (1)

R. Román, M. Antón, A. Cazorla, A. de Miquel, F. J. Olmo, J. Bilbao, and L. Alados-Arboledas, “Calibration of an all-sky camera for obtaining sky radiance at three wavelengths,” Atmos. Meas. Tech. 5, 2013–2024 (2012).
[CrossRef]

2011 (1)

V. Ferraro, M. Mele, and V. Malinelli, “Sky luminance measurements and comparison with models,” J. Atmos. Sol.-Terr. Phys. 73, 1780–1789 (2011).
[CrossRef]

2010 (3)

I. H. Yang and E. J. Nam, “Economic analysis of the daylight-linked lighting control system in office buildings,” Solar Energy 84, 1513–1525 (2010).
[CrossRef]

A. Heinle, A. Macke, and A. Srivastav, “Automatic cloud classification of whole sky images,” Atmos. Meas. Tech. 3, 557–567 (2010).
[CrossRef]

J. Estrada, R. Alvarez, T. Abbott, J. Annis, M. Bonati, E. Buckley-Geer, J. Campa, H. Cease, S. Chappa, D. Depoy, G. Derylo, H. T. Diehl, B. Flaugher, J. Hao, S. Holland, D. Huffman, I. Karliner, D. Kubik, S. Kuhlmann, K. Kuk, H. Lin, N. Roe, V. Scarpine, R. Schmidt, K. Schultz, T. Shaw, V. Simaitis, H. Spinka, W. Stuermer, D. Tucker, A. Walker, and W. Wester, “Focal plane detectors for dark energy camera (DECam),” Proc. SPIE 7735, 77351R (2010).
[CrossRef]

2009 (4)

D. Schneider, E. Schwalbe, and H. G. Maas, “Validation of geometric models for fisheye lenses,” ISPRS J. Photogramm. Remote Sens. 64, 259–266 (2009).

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

D. Pissulla, G. Seckmeyer, R. R. Cordero, M. Blumthaler, B. Schallhart, A. Webb, R. Kift, A. Smedley, A. F. Bais, N. Kouremeti, A. Cede, J. Herman, and M. Kowalewski, “Comparison of atmospheric spectral radiance measurement from five independently calibrated systems,” Photochem. Photobiol. Sci. 8, 516–527 (2009).
[CrossRef]

A. Kreuter, M. Zangerl, M. Schwarzmann, and M. Blumthaler, “All-sky imaging: a simple, versatile system for atmospheric research,” Appl. Opt. 48, 1091–1097 (2009).
[CrossRef]

2008 (7)

F. J. Olmo, A. Cazorla, L. Alados-Arboledas, M. A. López-Álvarez, J. Hernández-Andrés, and J. Romero, “Retrieval of the optical depth using an all-sky CCD camera,” Appl. Opt. 47, H182–H189 (2008).
[CrossRef]

S. Janjai, I. Masiri, M. Nunez, and J. Laksanaboonsong, “Modeling sky luminance using satellite data to classify sky conditions,” Build. Environ. 43, 2059–2073 (2008).
[CrossRef]

R. R. Cordero, G. Seckmeyer, D. Pissulla, and F. Labbe, “Uncertainty of experimental integrals: application to the UV index calculation,” Metrologia 45, 1–10 (2008).
[CrossRef]

A. Ansko, K. Eerme, S. Lätt, M. Noorma, and U. Veismann, “Study of suitability of AvaSpec array spectrometer for solar UV field measurements,” Atmos. Chem. Phys. 8, 3247–3253 (2008).
[CrossRef]

N. Kouremeti, A. Bais, S. Kazadzis, M. Blumthaler, and R. Schmitt, “Charge-coupled device spectrograph for direct solar irradiance and sky radiance measurements,” Appl. Opt. 47, 1594–1607 (2008).
[CrossRef]

A. Cazorla, F. J. Olmo, and L. Alados-Arboledas, “Development of a sky imager for cloud cover assessment,” J. Opt. Soc. Am. A 25, 29–39 (2008).
[CrossRef]

R. R. Cordero, G. Seckmeyer, D. Pissulla, and F. Labbe, “Uncertainty evaluation of spectral UV irradiance measurements,” Meas. Sci. Technol. 19, 045104 (2008).
[CrossRef]

2007 (1)

E. G. Rossini and A. Krenzinger, “Maps of sky relative radiance and luminance distributions acquired with a monochromatic CCD camera,” Sol. Energy 81, 1323–1332 (2007).
[CrossRef]

2006 (2)

S. Wuttke and G. Seckmeyer, “Spectral radiance and sky luminance in Antarctica: a case study,” Theor. Appl. Climatol. 85, 131–148 (2006).
[CrossRef]

S. Wuttke, G. Bernhard, J. Ehramjian, R. McKenzie, P. Johnston, M. O’Neil, and G. Seckmeyer, “New spectroradiometers complying with NDSC standards,” J. Atmos. Ocean. Technol. 23, 241–251 (2006).
[CrossRef]

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]

2004 (3)

M. Yamashita, M. Yoshimura, and T. Nakashizaka, “Cloud cover estimation using multitemporal hemispherical imageries,” Int. Arch. Photogram. Rem. Sens. Spatial Inform. Sci. 35, 826–829 (2004).
[CrossRef]

W. J. M. Van Bommel and G. J. Van den Beld, “Lighting for work: a review of visual and biological effects,” Lighting Res. Technol. 36, 255–269 (2004).
[CrossRef]

N. Igawa, Y. Koga, T. Matsuzawa, and H. Nakamura, “Models of sky radiance distribution and sky luminance distribution,” Sol. Energy 77, 137–157 (2004).
[CrossRef]

2003 (1)

M. A. Robertson, S. Borman, and R. L. Stevenson, “Estimation-theoretic approach to dynamic range enhancement using multi exposures,” J. Electron. Imaging 12, 219–228 (2003).
[CrossRef]

2002 (1)

L. Heschong, “Daylighting and human performance,” ASHRAE J. 44, 65–67 (2002).

2001 (1)

E. Vartiainen, “Electricity benefits of daylighting and photovoltaics for various solar facade layouts in office buildings,” Energy Build. 33, 113–120 (2001).
[CrossRef]

1999 (2)

D. Kinghorn and T. Muneer, “All-sky zenith luminance models for the UK,” Lighting Res. Technol. 31, 49–56(1999).
[CrossRef]

G. Bernhard and G. Seckmeyer, “Uncertainty of measurements of spectral solar UV irradiance,” J. Geophys. Res. 104, 14321–14345 (1999).
[CrossRef]

1995 (1)

P. J. Starks, E. A. Walter-Shea, F. R. Schiebe, and B. L. Markham, “Temperature sensitivity characterization of a silicon diode array spectroradiometer,” Remote Sens. Environ. 51, 385–389 (1995).
[CrossRef]

1993 (1)

R. Perez, R. Seals, and J. Michalsky, “All-weather model for sky luminance distribution—preliminary configuration and validation,” Sol. Energy 50, 235–245 (1993).

1991 (1)

M. Hietanen, “Ocular exposure to solar ultraviolet and visible radiation at high latitudes,” Scand. J. Work Environ. Health 17, 398–403 (1991).
[CrossRef]

1989 (1)

K. J. Voss and G. Zibordi, “Radiometric and geometric calibration of a visible spectral electro-optic “fisheye” camera radiance distribution system,” J. Atmos. Oceanic Technol. 6, 652–662 (1989).
[CrossRef]

1984 (1)

M. Karayel, M. Navvab, E. Ne’eman, and S. Selkowitz, “Zenith luminance and sky luminance distributions for daylighting calculations,” Energy Build. 6, 283–291 (1984).
[CrossRef]

1983 (1)

P. R. Tregenza and I. M. Waters, “Daylight coefficients,” Lighting Res. Technol. 15, 65–71 (1983).
[CrossRef]

1974 (1)

J. Krochmann and M. Seidl, “Quantitative data on daylight for illuminating engineering,” Lighting Res. Technol. 6, 165–171 (1974).
[CrossRef]

Abbott, T.

J. Estrada, R. Alvarez, T. Abbott, J. Annis, M. Bonati, E. Buckley-Geer, J. Campa, H. Cease, S. Chappa, D. Depoy, G. Derylo, H. T. Diehl, B. Flaugher, J. Hao, S. Holland, D. Huffman, I. Karliner, D. Kubik, S. Kuhlmann, K. Kuk, H. Lin, N. Roe, V. Scarpine, R. Schmidt, K. Schultz, T. Shaw, V. Simaitis, H. Spinka, W. Stuermer, D. Tucker, A. Walker, and W. Wester, “Focal plane detectors for dark energy camera (DECam),” Proc. SPIE 7735, 77351R (2010).
[CrossRef]

Alados-Arboledas, L.

Alvarez, R.

J. Estrada, R. Alvarez, T. Abbott, J. Annis, M. Bonati, E. Buckley-Geer, J. Campa, H. Cease, S. Chappa, D. Depoy, G. Derylo, H. T. Diehl, B. Flaugher, J. Hao, S. Holland, D. Huffman, I. Karliner, D. Kubik, S. Kuhlmann, K. Kuk, H. Lin, N. Roe, V. Scarpine, R. Schmidt, K. Schultz, T. Shaw, V. Simaitis, H. Spinka, W. Stuermer, D. Tucker, A. Walker, and W. Wester, “Focal plane detectors for dark energy camera (DECam),” Proc. SPIE 7735, 77351R (2010).
[CrossRef]

Annis, J.

J. Estrada, R. Alvarez, T. Abbott, J. Annis, M. Bonati, E. Buckley-Geer, J. Campa, H. Cease, S. Chappa, D. Depoy, G. Derylo, H. T. Diehl, B. Flaugher, J. Hao, S. Holland, D. Huffman, I. Karliner, D. Kubik, S. Kuhlmann, K. Kuk, H. Lin, N. Roe, V. Scarpine, R. Schmidt, K. Schultz, T. Shaw, V. Simaitis, H. Spinka, W. Stuermer, D. Tucker, A. Walker, and W. Wester, “Focal plane detectors for dark energy camera (DECam),” Proc. SPIE 7735, 77351R (2010).
[CrossRef]

Ansko, A.

A. Ansko, K. Eerme, S. Lätt, M. Noorma, and U. Veismann, “Study of suitability of AvaSpec array spectrometer for solar UV field measurements,” Atmos. Chem. Phys. 8, 3247–3253 (2008).
[CrossRef]

Antón, M.

R. Román, M. Antón, A. Cazorla, A. de Miquel, F. J. Olmo, J. Bilbao, and L. Alados-Arboledas, “Calibration of an all-sky camera for obtaining sky radiance at three wavelengths,” Atmos. Meas. Tech. 5, 2013–2024 (2012).
[CrossRef]

Bais, A.

N. Kouremeti, A. Bais, S. Kazadzis, M. Blumthaler, and R. Schmitt, “Charge-coupled device spectrograph for direct solar irradiance and sky radiance measurements,” Appl. Opt. 47, 1594–1607 (2008).
[CrossRef]

G. Seckmeyer, A. Bais, G. Bernhard, M. Blumthaler, S. Drüke, P. Kiedron, K. Lantz, R. L. McKenzie, and S. Riechelmann, “Instruments to measure solar ultraviolet radiation, part 4: array spectroradiometers,” in WMO, Global Atmospheric Watch (World Meteorological Organization, 2010), p. 43.

Bais, A. F.

D. Pissulla, G. Seckmeyer, R. R. Cordero, M. Blumthaler, B. Schallhart, A. Webb, R. Kift, A. Smedley, A. F. Bais, N. Kouremeti, A. Cede, J. Herman, and M. Kowalewski, “Comparison of atmospheric spectral radiance measurement from five independently calibrated systems,” Photochem. Photobiol. Sci. 8, 516–527 (2009).
[CrossRef]

Bernhard, G.

S. Wuttke, G. Bernhard, J. Ehramjian, R. McKenzie, P. Johnston, M. O’Neil, and G. Seckmeyer, “New spectroradiometers complying with NDSC standards,” J. Atmos. Ocean. Technol. 23, 241–251 (2006).
[CrossRef]

G. Bernhard and G. Seckmeyer, “Uncertainty of measurements of spectral solar UV irradiance,” J. Geophys. Res. 104, 14321–14345 (1999).
[CrossRef]

G. Seckmeyer, A. Bais, G. Bernhard, M. Blumthaler, S. Drüke, P. Kiedron, K. Lantz, R. L. McKenzie, and S. Riechelmann, “Instruments to measure solar ultraviolet radiation, part 4: array spectroradiometers,” in WMO, Global Atmospheric Watch (World Meteorological Organization, 2010), p. 43.

Bilbao, J.

R. Román, M. Antón, A. Cazorla, A. de Miquel, F. J. Olmo, J. Bilbao, and L. Alados-Arboledas, “Calibration of an all-sky camera for obtaining sky radiance at three wavelengths,” Atmos. Meas. Tech. 5, 2013–2024 (2012).
[CrossRef]

Blumthaler, M.

A. Kreuter, M. Zangerl, M. Schwarzmann, and M. Blumthaler, “All-sky imaging: a simple, versatile system for atmospheric research,” Appl. Opt. 48, 1091–1097 (2009).
[CrossRef]

D. Pissulla, G. Seckmeyer, R. R. Cordero, M. Blumthaler, B. Schallhart, A. Webb, R. Kift, A. Smedley, A. F. Bais, N. Kouremeti, A. Cede, J. Herman, and M. Kowalewski, “Comparison of atmospheric spectral radiance measurement from five independently calibrated systems,” Photochem. Photobiol. Sci. 8, 516–527 (2009).
[CrossRef]

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

N. Kouremeti, A. Bais, S. Kazadzis, M. Blumthaler, and R. Schmitt, “Charge-coupled device spectrograph for direct solar irradiance and sky radiance measurements,” Appl. Opt. 47, 1594–1607 (2008).
[CrossRef]

G. Seckmeyer, A. Bais, G. Bernhard, M. Blumthaler, S. Drüke, P. Kiedron, K. Lantz, R. L. McKenzie, and S. Riechelmann, “Instruments to measure solar ultraviolet radiation, part 4: array spectroradiometers,” in WMO, Global Atmospheric Watch (World Meteorological Organization, 2010), p. 43.

Bonati, M.

J. Estrada, R. Alvarez, T. Abbott, J. Annis, M. Bonati, E. Buckley-Geer, J. Campa, H. Cease, S. Chappa, D. Depoy, G. Derylo, H. T. Diehl, B. Flaugher, J. Hao, S. Holland, D. Huffman, I. Karliner, D. Kubik, S. Kuhlmann, K. Kuk, H. Lin, N. Roe, V. Scarpine, R. Schmidt, K. Schultz, T. Shaw, V. Simaitis, H. Spinka, W. Stuermer, D. Tucker, A. Walker, and W. Wester, “Focal plane detectors for dark energy camera (DECam),” Proc. SPIE 7735, 77351R (2010).
[CrossRef]

Borman, S.

M. A. Robertson, S. Borman, and R. L. Stevenson, “Estimation-theoretic approach to dynamic range enhancement using multi exposures,” J. Electron. Imaging 12, 219–228 (2003).
[CrossRef]

Buckley-Geer, E.

J. Estrada, R. Alvarez, T. Abbott, J. Annis, M. Bonati, E. Buckley-Geer, J. Campa, H. Cease, S. Chappa, D. Depoy, G. Derylo, H. T. Diehl, B. Flaugher, J. Hao, S. Holland, D. Huffman, I. Karliner, D. Kubik, S. Kuhlmann, K. Kuk, H. Lin, N. Roe, V. Scarpine, R. Schmidt, K. Schultz, T. Shaw, V. Simaitis, H. Spinka, W. Stuermer, D. Tucker, A. Walker, and W. Wester, “Focal plane detectors for dark energy camera (DECam),” Proc. SPIE 7735, 77351R (2010).
[CrossRef]

Campa, J.

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D. Pissulla, G. Seckmeyer, R. R. Cordero, M. Blumthaler, B. Schallhart, A. Webb, R. Kift, A. Smedley, A. F. Bais, N. Kouremeti, A. Cede, J. Herman, and M. Kowalewski, “Comparison of atmospheric spectral radiance measurement from five independently calibrated systems,” Photochem. Photobiol. Sci. 8, 516–527 (2009).
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R. R. Cordero, G. Seckmeyer, D. Pissulla, and F. Labbe, “Uncertainty of experimental integrals: application to the UV index calculation,” Metrologia 45, 1–10 (2008).
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R. R. Cordero, G. Seckmeyer, D. Pissulla, and F. Labbe, “Uncertainty evaluation of spectral UV irradiance measurements,” Meas. Sci. Technol. 19, 045104 (2008).
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J. Estrada, R. Alvarez, T. Abbott, J. Annis, M. Bonati, E. Buckley-Geer, J. Campa, H. Cease, S. Chappa, D. Depoy, G. Derylo, H. T. Diehl, B. Flaugher, J. Hao, S. Holland, D. Huffman, I. Karliner, D. Kubik, S. Kuhlmann, K. Kuk, H. Lin, N. Roe, V. Scarpine, R. Schmidt, K. Schultz, T. Shaw, V. Simaitis, H. Spinka, W. Stuermer, D. Tucker, A. Walker, and W. Wester, “Focal plane detectors for dark energy camera (DECam),” Proc. SPIE 7735, 77351R (2010).
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D. Pissulla, G. Seckmeyer, R. R. Cordero, M. Blumthaler, B. Schallhart, A. Webb, R. Kift, A. Smedley, A. F. Bais, N. Kouremeti, A. Cede, J. Herman, and M. Kowalewski, “Comparison of atmospheric spectral radiance measurement from five independently calibrated systems,” Photochem. Photobiol. Sci. 8, 516–527 (2009).
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A. Ansko, K. Eerme, S. Lätt, M. Noorma, and U. Veismann, “Study of suitability of AvaSpec array spectrometer for solar UV field measurements,” Atmos. Chem. Phys. 8, 3247–3253 (2008).
[CrossRef]

Nunez, M.

S. Janjai, I. Masiri, M. Nunez, and J. Laksanaboonsong, “Modeling sky luminance using satellite data to classify sky conditions,” Build. Environ. 43, 2059–2073 (2008).
[CrossRef]

O’Neil, M.

S. Wuttke, G. Bernhard, J. Ehramjian, R. McKenzie, P. Johnston, M. O’Neil, and G. Seckmeyer, “New spectroradiometers complying with NDSC standards,” J. Atmos. Ocean. Technol. 23, 241–251 (2006).
[CrossRef]

Olmo, F. J.

Perez, R.

R. Perez, R. Seals, and J. Michalsky, “All-weather model for sky luminance distribution—preliminary configuration and validation,” Sol. Energy 50, 235–245 (1993).

Pissulla, D.

D. Pissulla, G. Seckmeyer, R. R. Cordero, M. Blumthaler, B. Schallhart, A. Webb, R. Kift, A. Smedley, A. F. Bais, N. Kouremeti, A. Cede, J. Herman, and M. Kowalewski, “Comparison of atmospheric spectral radiance measurement from five independently calibrated systems,” Photochem. Photobiol. Sci. 8, 516–527 (2009).
[CrossRef]

R. R. Cordero, G. Seckmeyer, D. Pissulla, and F. Labbe, “Uncertainty of experimental integrals: application to the UV index calculation,” Metrologia 45, 1–10 (2008).
[CrossRef]

R. R. Cordero, G. Seckmeyer, D. Pissulla, and F. Labbe, “Uncertainty evaluation of spectral UV irradiance measurements,” Meas. Sci. Technol. 19, 045104 (2008).
[CrossRef]

Riechelmann, S.

G. Seckmeyer, A. Bais, G. Bernhard, M. Blumthaler, S. Drüke, P. Kiedron, K. Lantz, R. L. McKenzie, and S. Riechelmann, “Instruments to measure solar ultraviolet radiation, part 4: array spectroradiometers,” in WMO, Global Atmospheric Watch (World Meteorological Organization, 2010), p. 43.

Robertson, M. A.

M. A. Robertson, S. Borman, and R. L. Stevenson, “Estimation-theoretic approach to dynamic range enhancement using multi exposures,” J. Electron. Imaging 12, 219–228 (2003).
[CrossRef]

Roe, N.

J. Estrada, R. Alvarez, T. Abbott, J. Annis, M. Bonati, E. Buckley-Geer, J. Campa, H. Cease, S. Chappa, D. Depoy, G. Derylo, H. T. Diehl, B. Flaugher, J. Hao, S. Holland, D. Huffman, I. Karliner, D. Kubik, S. Kuhlmann, K. Kuk, H. Lin, N. Roe, V. Scarpine, R. Schmidt, K. Schultz, T. Shaw, V. Simaitis, H. Spinka, W. Stuermer, D. Tucker, A. Walker, and W. Wester, “Focal plane detectors for dark energy camera (DECam),” Proc. SPIE 7735, 77351R (2010).
[CrossRef]

Román, R.

R. Román, M. Antón, A. Cazorla, A. de Miquel, F. J. Olmo, J. Bilbao, and L. Alados-Arboledas, “Calibration of an all-sky camera for obtaining sky radiance at three wavelengths,” Atmos. Meas. Tech. 5, 2013–2024 (2012).
[CrossRef]

Romero, J.

Rossini, E. G.

E. G. Rossini and A. Krenzinger, “Maps of sky relative radiance and luminance distributions acquired with a monochromatic CCD camera,” Sol. Energy 81, 1323–1332 (2007).
[CrossRef]

Roy, G. G.

G. G. Roy, S. Hayman, and W. Julian, “Sky modeling from digital imagery,” ARC Project A89530177, Final Report (The University of Sydney and Murdoch University, 1998).

Scarpine, V.

J. Estrada, R. Alvarez, T. Abbott, J. Annis, M. Bonati, E. Buckley-Geer, J. Campa, H. Cease, S. Chappa, D. Depoy, G. Derylo, H. T. Diehl, B. Flaugher, J. Hao, S. Holland, D. Huffman, I. Karliner, D. Kubik, S. Kuhlmann, K. Kuk, H. Lin, N. Roe, V. Scarpine, R. Schmidt, K. Schultz, T. Shaw, V. Simaitis, H. Spinka, W. Stuermer, D. Tucker, A. Walker, and W. Wester, “Focal plane detectors for dark energy camera (DECam),” Proc. SPIE 7735, 77351R (2010).
[CrossRef]

Schallhart, B.

D. Pissulla, G. Seckmeyer, R. R. Cordero, M. Blumthaler, B. Schallhart, A. Webb, R. Kift, A. Smedley, A. F. Bais, N. Kouremeti, A. Cede, J. Herman, and M. Kowalewski, “Comparison of atmospheric spectral radiance measurement from five independently calibrated systems,” Photochem. Photobiol. Sci. 8, 516–527 (2009).
[CrossRef]

Schiebe, F. R.

P. J. Starks, E. A. Walter-Shea, F. R. Schiebe, and B. L. Markham, “Temperature sensitivity characterization of a silicon diode array spectroradiometer,” Remote Sens. Environ. 51, 385–389 (1995).
[CrossRef]

Schmidt, R.

J. Estrada, R. Alvarez, T. Abbott, J. Annis, M. Bonati, E. Buckley-Geer, J. Campa, H. Cease, S. Chappa, D. Depoy, G. Derylo, H. T. Diehl, B. Flaugher, J. Hao, S. Holland, D. Huffman, I. Karliner, D. Kubik, S. Kuhlmann, K. Kuk, H. Lin, N. Roe, V. Scarpine, R. Schmidt, K. Schultz, T. Shaw, V. Simaitis, H. Spinka, W. Stuermer, D. Tucker, A. Walker, and W. Wester, “Focal plane detectors for dark energy camera (DECam),” Proc. SPIE 7735, 77351R (2010).
[CrossRef]

Schmitt, R.

Schneider, D.

D. Schneider, E. Schwalbe, and H. G. Maas, “Validation of geometric models for fisheye lenses,” ISPRS J. Photogramm. Remote Sens. 64, 259–266 (2009).

Schultz, K.

J. Estrada, R. Alvarez, T. Abbott, J. Annis, M. Bonati, E. Buckley-Geer, J. Campa, H. Cease, S. Chappa, D. Depoy, G. Derylo, H. T. Diehl, B. Flaugher, J. Hao, S. Holland, D. Huffman, I. Karliner, D. Kubik, S. Kuhlmann, K. Kuk, H. Lin, N. Roe, V. Scarpine, R. Schmidt, K. Schultz, T. Shaw, V. Simaitis, H. Spinka, W. Stuermer, D. Tucker, A. Walker, and W. Wester, “Focal plane detectors for dark energy camera (DECam),” Proc. SPIE 7735, 77351R (2010).
[CrossRef]

Schwalbe, E.

D. Schneider, E. Schwalbe, and H. G. Maas, “Validation of geometric models for fisheye lenses,” ISPRS J. Photogramm. Remote Sens. 64, 259–266 (2009).

Schwarzmann, M.

Seals, R.

R. Perez, R. Seals, and J. Michalsky, “All-weather model for sky luminance distribution—preliminary configuration and validation,” Sol. Energy 50, 235–245 (1993).

Seckmeyer, G.

D. Pissulla, G. Seckmeyer, R. R. Cordero, M. Blumthaler, B. Schallhart, A. Webb, R. Kift, A. Smedley, A. F. Bais, N. Kouremeti, A. Cede, J. Herman, and M. Kowalewski, “Comparison of atmospheric spectral radiance measurement from five independently calibrated systems,” Photochem. Photobiol. Sci. 8, 516–527 (2009).
[CrossRef]

R. R. Cordero, G. Seckmeyer, D. Pissulla, and F. Labbe, “Uncertainty evaluation of spectral UV irradiance measurements,” Meas. Sci. Technol. 19, 045104 (2008).
[CrossRef]

R. R. Cordero, G. Seckmeyer, D. Pissulla, and F. Labbe, “Uncertainty of experimental integrals: application to the UV index calculation,” Metrologia 45, 1–10 (2008).
[CrossRef]

S. Wuttke, G. Bernhard, J. Ehramjian, R. McKenzie, P. Johnston, M. O’Neil, and G. Seckmeyer, “New spectroradiometers complying with NDSC standards,” J. Atmos. Ocean. Technol. 23, 241–251 (2006).
[CrossRef]

S. Wuttke and G. Seckmeyer, “Spectral radiance and sky luminance in Antarctica: a case study,” Theor. Appl. Climatol. 85, 131–148 (2006).
[CrossRef]

G. Bernhard and G. Seckmeyer, “Uncertainty of measurements of spectral solar UV irradiance,” J. Geophys. Res. 104, 14321–14345 (1999).
[CrossRef]

G. Seckmeyer, A. Bais, G. Bernhard, M. Blumthaler, S. Drüke, P. Kiedron, K. Lantz, R. L. McKenzie, and S. Riechelmann, “Instruments to measure solar ultraviolet radiation, part 4: array spectroradiometers,” in WMO, Global Atmospheric Watch (World Meteorological Organization, 2010), p. 43.

Seidl, M.

J. Krochmann and M. Seidl, “Quantitative data on daylight for illuminating engineering,” Lighting Res. Technol. 6, 165–171 (1974).
[CrossRef]

Selkowitz, S.

M. Karayel, M. Navvab, E. Ne’eman, and S. Selkowitz, “Zenith luminance and sky luminance distributions for daylighting calculations,” Energy Build. 6, 283–291 (1984).
[CrossRef]

Shaw, T.

J. Estrada, R. Alvarez, T. Abbott, J. Annis, M. Bonati, E. Buckley-Geer, J. Campa, H. Cease, S. Chappa, D. Depoy, G. Derylo, H. T. Diehl, B. Flaugher, J. Hao, S. Holland, D. Huffman, I. Karliner, D. Kubik, S. Kuhlmann, K. Kuk, H. Lin, N. Roe, V. Scarpine, R. Schmidt, K. Schultz, T. Shaw, V. Simaitis, H. Spinka, W. Stuermer, D. Tucker, A. Walker, and W. Wester, “Focal plane detectors for dark energy camera (DECam),” Proc. SPIE 7735, 77351R (2010).
[CrossRef]

Shields, J.

U. Feister, J. Shields, M. Karr, R. Johnson, K. Dehne, and M. Woldt, “Ground-based cloud images and sky radiance in the visible and near infrared region from whole sky image measurement,” in EUMETSAT Satellite Application Facility Workshop (German Weather Service and World Meteorological Organization, 2000), pp. 79–88.

Shields, J. E.

J. E. Shields, R. W. Johnson, M. E. Karr, and J. L. Wertz, “Automated day/night whole sky imagers for field assessment of cloud cover distributions and radiance distribution,” in Tenth Symposium on Meteorological Observations and Instrument (American Meteorological Society, 1998).

Simaitis, V.

J. Estrada, R. Alvarez, T. Abbott, J. Annis, M. Bonati, E. Buckley-Geer, J. Campa, H. Cease, S. Chappa, D. Depoy, G. Derylo, H. T. Diehl, B. Flaugher, J. Hao, S. Holland, D. Huffman, I. Karliner, D. Kubik, S. Kuhlmann, K. Kuk, H. Lin, N. Roe, V. Scarpine, R. Schmidt, K. Schultz, T. Shaw, V. Simaitis, H. Spinka, W. Stuermer, D. Tucker, A. Walker, and W. Wester, “Focal plane detectors for dark energy camera (DECam),” Proc. SPIE 7735, 77351R (2010).
[CrossRef]

Smedley, A.

D. Pissulla, G. Seckmeyer, R. R. Cordero, M. Blumthaler, B. Schallhart, A. Webb, R. Kift, A. Smedley, A. F. Bais, N. Kouremeti, A. Cede, J. Herman, and M. Kowalewski, “Comparison of atmospheric spectral radiance measurement from five independently calibrated systems,” Photochem. Photobiol. Sci. 8, 516–527 (2009).
[CrossRef]

Spinka, H.

J. Estrada, R. Alvarez, T. Abbott, J. Annis, M. Bonati, E. Buckley-Geer, J. Campa, H. Cease, S. Chappa, D. Depoy, G. Derylo, H. T. Diehl, B. Flaugher, J. Hao, S. Holland, D. Huffman, I. Karliner, D. Kubik, S. Kuhlmann, K. Kuk, H. Lin, N. Roe, V. Scarpine, R. Schmidt, K. Schultz, T. Shaw, V. Simaitis, H. Spinka, W. Stuermer, D. Tucker, A. Walker, and W. Wester, “Focal plane detectors for dark energy camera (DECam),” Proc. SPIE 7735, 77351R (2010).
[CrossRef]

Srivastav, A.

A. Heinle, A. Macke, and A. Srivastav, “Automatic cloud classification of whole sky images,” Atmos. Meas. Tech. 3, 557–567 (2010).
[CrossRef]

Starks, P. J.

P. J. Starks, E. A. Walter-Shea, F. R. Schiebe, and B. L. Markham, “Temperature sensitivity characterization of a silicon diode array spectroradiometer,” Remote Sens. Environ. 51, 385–389 (1995).
[CrossRef]

Stevenson, R. L.

M. A. Robertson, S. Borman, and R. L. Stevenson, “Estimation-theoretic approach to dynamic range enhancement using multi exposures,” J. Electron. Imaging 12, 219–228 (2003).
[CrossRef]

Stuermer, W.

J. Estrada, R. Alvarez, T. Abbott, J. Annis, M. Bonati, E. Buckley-Geer, J. Campa, H. Cease, S. Chappa, D. Depoy, G. Derylo, H. T. Diehl, B. Flaugher, J. Hao, S. Holland, D. Huffman, I. Karliner, D. Kubik, S. Kuhlmann, K. Kuk, H. Lin, N. Roe, V. Scarpine, R. Schmidt, K. Schultz, T. Shaw, V. Simaitis, H. Spinka, W. Stuermer, D. Tucker, A. Walker, and W. Wester, “Focal plane detectors for dark energy camera (DECam),” Proc. SPIE 7735, 77351R (2010).
[CrossRef]

Sun, N.

N. Sun, H. Mansour, and R. Ward, “HDR image construction from multi-exposed stereo LDR images,” in Proceedings of IEEE 17th International Conference on Image Processing (IEEE, 2010), pp. 2973–2976.

Tregenza, P. R.

P. R. Tregenza and I. M. Waters, “Daylight coefficients,” Lighting Res. Technol. 15, 65–71 (1983).
[CrossRef]

Tucker, D.

J. Estrada, R. Alvarez, T. Abbott, J. Annis, M. Bonati, E. Buckley-Geer, J. Campa, H. Cease, S. Chappa, D. Depoy, G. Derylo, H. T. Diehl, B. Flaugher, J. Hao, S. Holland, D. Huffman, I. Karliner, D. Kubik, S. Kuhlmann, K. Kuk, H. Lin, N. Roe, V. Scarpine, R. Schmidt, K. Schultz, T. Shaw, V. Simaitis, H. Spinka, W. Stuermer, D. Tucker, A. Walker, and W. Wester, “Focal plane detectors for dark energy camera (DECam),” Proc. SPIE 7735, 77351R (2010).
[CrossRef]

Van Bommel, W. J. M.

W. J. M. Van Bommel and G. J. Van den Beld, “Lighting for work: a review of visual and biological effects,” Lighting Res. Technol. 36, 255–269 (2004).
[CrossRef]

Van den Beld, G. J.

W. J. M. Van Bommel and G. J. Van den Beld, “Lighting for work: a review of visual and biological effects,” Lighting Res. Technol. 36, 255–269 (2004).
[CrossRef]

Vartiainen, E.

E. Vartiainen, “Electricity benefits of daylighting and photovoltaics for various solar facade layouts in office buildings,” Energy Build. 33, 113–120 (2001).
[CrossRef]

Veismann, U.

A. Ansko, K. Eerme, S. Lätt, M. Noorma, and U. Veismann, “Study of suitability of AvaSpec array spectrometer for solar UV field measurements,” Atmos. Chem. Phys. 8, 3247–3253 (2008).
[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]

Voss, K. J.

K. J. Voss and G. Zibordi, “Radiometric and geometric calibration of a visible spectral electro-optic “fisheye” camera radiance distribution system,” J. Atmos. Oceanic Technol. 6, 652–662 (1989).
[CrossRef]

Walker, A.

J. Estrada, R. Alvarez, T. Abbott, J. Annis, M. Bonati, E. Buckley-Geer, J. Campa, H. Cease, S. Chappa, D. Depoy, G. Derylo, H. T. Diehl, B. Flaugher, J. Hao, S. Holland, D. Huffman, I. Karliner, D. Kubik, S. Kuhlmann, K. Kuk, H. Lin, N. Roe, V. Scarpine, R. Schmidt, K. Schultz, T. Shaw, V. Simaitis, H. Spinka, W. Stuermer, D. Tucker, A. Walker, and W. Wester, “Focal plane detectors for dark energy camera (DECam),” Proc. SPIE 7735, 77351R (2010).
[CrossRef]

Walter-Shea, E. A.

P. J. Starks, E. A. Walter-Shea, F. R. Schiebe, and B. L. Markham, “Temperature sensitivity characterization of a silicon diode array spectroradiometer,” Remote Sens. Environ. 51, 385–389 (1995).
[CrossRef]

Ward, R.

N. Sun, H. Mansour, and R. Ward, “HDR image construction from multi-exposed stereo LDR images,” in Proceedings of IEEE 17th International Conference on Image Processing (IEEE, 2010), pp. 2973–2976.

Waters, I. M.

P. R. Tregenza and I. M. Waters, “Daylight coefficients,” Lighting Res. Technol. 15, 65–71 (1983).
[CrossRef]

Webb, A.

D. Pissulla, G. Seckmeyer, R. R. Cordero, M. Blumthaler, B. Schallhart, A. Webb, R. Kift, A. Smedley, A. F. Bais, N. Kouremeti, A. Cede, J. Herman, and M. Kowalewski, “Comparison of atmospheric spectral radiance measurement from five independently calibrated systems,” Photochem. Photobiol. Sci. 8, 516–527 (2009).
[CrossRef]

Wertz, J. L.

J. E. Shields, R. W. Johnson, M. E. Karr, and J. L. Wertz, “Automated day/night whole sky imagers for field assessment of cloud cover distributions and radiance distribution,” in Tenth Symposium on Meteorological Observations and Instrument (American Meteorological Society, 1998).

Wester, W.

J. Estrada, R. Alvarez, T. Abbott, J. Annis, M. Bonati, E. Buckley-Geer, J. Campa, H. Cease, S. Chappa, D. Depoy, G. Derylo, H. T. Diehl, B. Flaugher, J. Hao, S. Holland, D. Huffman, I. Karliner, D. Kubik, S. Kuhlmann, K. Kuk, H. Lin, N. Roe, V. Scarpine, R. Schmidt, K. Schultz, T. Shaw, V. Simaitis, H. Spinka, W. Stuermer, D. Tucker, A. Walker, and W. Wester, “Focal plane detectors for dark energy camera (DECam),” Proc. SPIE 7735, 77351R (2010).
[CrossRef]

Woldt, M.

U. Feister, J. Shields, M. Karr, R. Johnson, K. Dehne, and M. Woldt, “Ground-based cloud images and sky radiance in the visible and near infrared region from whole sky image measurement,” in EUMETSAT Satellite Application Facility Workshop (German Weather Service and World Meteorological Organization, 2000), pp. 79–88.

Wuttke, S.

S. Wuttke, G. Bernhard, J. Ehramjian, R. McKenzie, P. Johnston, M. O’Neil, and G. Seckmeyer, “New spectroradiometers complying with NDSC standards,” J. Atmos. Ocean. Technol. 23, 241–251 (2006).
[CrossRef]

S. Wuttke and G. Seckmeyer, “Spectral radiance and sky luminance in Antarctica: a case study,” Theor. Appl. Climatol. 85, 131–148 (2006).
[CrossRef]

Yamashita, M.

M. Yamashita, M. Yoshimura, and T. Nakashizaka, “Cloud cover estimation using multitemporal hemispherical imageries,” Int. Arch. Photogram. Rem. Sens. Spatial Inform. Sci. 35, 826–829 (2004).
[CrossRef]

Yang, I. H.

I. H. Yang and E. J. Nam, “Economic analysis of the daylight-linked lighting control system in office buildings,” Solar Energy 84, 1513–1525 (2010).
[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]

Yoshimura, M.

M. Yamashita, M. Yoshimura, and T. Nakashizaka, “Cloud cover estimation using multitemporal hemispherical imageries,” Int. Arch. Photogram. Rem. Sens. Spatial Inform. Sci. 35, 826–829 (2004).
[CrossRef]

Zangerl, M.

Zibordi, G.

K. J. Voss and G. Zibordi, “Radiometric and geometric calibration of a visible spectral electro-optic “fisheye” camera radiance distribution system,” J. Atmos. Oceanic Technol. 6, 652–662 (1989).
[CrossRef]

Appl. Opt. (3)

ASHRAE J. (1)

L. Heschong, “Daylighting and human performance,” ASHRAE J. 44, 65–67 (2002).

Atmos. Chem. Phys. (1)

A. Ansko, K. Eerme, S. Lätt, M. Noorma, and U. Veismann, “Study of suitability of AvaSpec array spectrometer for solar UV field measurements,” Atmos. Chem. Phys. 8, 3247–3253 (2008).
[CrossRef]

Atmos. Meas. Tech. (2)

R. Román, M. Antón, A. Cazorla, A. de Miquel, F. J. Olmo, J. Bilbao, and L. Alados-Arboledas, “Calibration of an all-sky camera for obtaining sky radiance at three wavelengths,” Atmos. Meas. Tech. 5, 2013–2024 (2012).
[CrossRef]

A. Heinle, A. Macke, and A. Srivastav, “Automatic cloud classification of whole sky images,” Atmos. Meas. Tech. 3, 557–567 (2010).
[CrossRef]

Build. Environ. (1)

S. Janjai, I. Masiri, M. Nunez, and J. Laksanaboonsong, “Modeling sky luminance using satellite data to classify sky conditions,” Build. Environ. 43, 2059–2073 (2008).
[CrossRef]

Energy Build. (2)

E. Vartiainen, “Electricity benefits of daylighting and photovoltaics for various solar facade layouts in office buildings,” Energy Build. 33, 113–120 (2001).
[CrossRef]

M. Karayel, M. Navvab, E. Ne’eman, and S. Selkowitz, “Zenith luminance and sky luminance distributions for daylighting calculations,” Energy Build. 6, 283–291 (1984).
[CrossRef]

Int. Arch. Photogram. Rem. Sens. Spatial Inform. Sci. (1)

M. Yamashita, M. Yoshimura, and T. Nakashizaka, “Cloud cover estimation using multitemporal hemispherical imageries,” Int. Arch. Photogram. Rem. Sens. Spatial Inform. Sci. 35, 826–829 (2004).
[CrossRef]

ISPRS J. Photogramm. Remote Sens. (1)

D. Schneider, E. Schwalbe, and H. G. Maas, “Validation of geometric models for fisheye lenses,” ISPRS J. Photogramm. Remote Sens. 64, 259–266 (2009).

J. Atmos. Ocean. Technol. (1)

S. Wuttke, G. Bernhard, J. Ehramjian, R. McKenzie, P. Johnston, M. O’Neil, and G. Seckmeyer, “New spectroradiometers complying with NDSC standards,” J. Atmos. Ocean. Technol. 23, 241–251 (2006).
[CrossRef]

J. Atmos. Oceanic Technol. (1)

K. J. Voss and G. Zibordi, “Radiometric and geometric calibration of a visible spectral electro-optic “fisheye” camera radiance distribution system,” J. Atmos. Oceanic Technol. 6, 652–662 (1989).
[CrossRef]

J. Atmos. Sol.-Terr. Phys. (1)

V. Ferraro, M. Mele, and V. Malinelli, “Sky luminance measurements and comparison with models,” J. Atmos. Sol.-Terr. Phys. 73, 1780–1789 (2011).
[CrossRef]

J. Electron. Imaging (1)

M. A. Robertson, S. Borman, and R. L. Stevenson, “Estimation-theoretic approach to dynamic range enhancement using multi exposures,” J. Electron. Imaging 12, 219–228 (2003).
[CrossRef]

J. Geophys. Res. (1)

G. Bernhard and G. Seckmeyer, “Uncertainty of measurements of spectral solar UV irradiance,” J. Geophys. Res. 104, 14321–14345 (1999).
[CrossRef]

J. Opt. Soc. Am. A (1)

Lighting Res. Technol. (4)

D. Kinghorn and T. Muneer, “All-sky zenith luminance models for the UK,” Lighting Res. Technol. 31, 49–56(1999).
[CrossRef]

J. Krochmann and M. Seidl, “Quantitative data on daylight for illuminating engineering,” Lighting Res. Technol. 6, 165–171 (1974).
[CrossRef]

W. J. M. Van Bommel and G. J. Van den Beld, “Lighting for work: a review of visual and biological effects,” Lighting Res. Technol. 36, 255–269 (2004).
[CrossRef]

P. R. Tregenza and I. M. Waters, “Daylight coefficients,” Lighting Res. Technol. 15, 65–71 (1983).
[CrossRef]

Meas. Sci. Technol. (1)

R. R. Cordero, G. Seckmeyer, D. Pissulla, and F. Labbe, “Uncertainty evaluation of spectral UV irradiance measurements,” Meas. Sci. Technol. 19, 045104 (2008).
[CrossRef]

Metrologia (1)

R. R. Cordero, G. Seckmeyer, D. Pissulla, and F. Labbe, “Uncertainty of experimental integrals: application to the UV index calculation,” Metrologia 45, 1–10 (2008).
[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]

Photochem. Photobiol. Sci. (1)

D. Pissulla, G. Seckmeyer, R. R. Cordero, M. Blumthaler, B. Schallhart, A. Webb, R. Kift, A. Smedley, A. F. Bais, N. Kouremeti, A. Cede, J. Herman, and M. Kowalewski, “Comparison of atmospheric spectral radiance measurement from five independently calibrated systems,” Photochem. Photobiol. Sci. 8, 516–527 (2009).
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Proc. SPIE (1)

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Figures (9)

Fig. 1.
Fig. 1.

Image (a) shows the setup for the camera distortion determination and (b) shows an image of the nighttime sky taken on April 19th, 2010 at 21.55 UTC with an exposure time of 15 s. Despite the fact that the horizon is light contaminated by street illumination and the moon can clearly be recognized in the picture, 18 bright stars (marked with circles) could be identified and are used for the star calibration.

Fig. 2.
Fig. 2.

Reflectance plaque is illuminated perpendicularly by a 1000 W tungsten halogen lamp. The plaque provides uniform radiance for the luminance calibration in the center of the HSI image. Images of the plaque were acquired with different exposure times varied from 1/2000s to 1/20s.

Fig. 3.
Fig. 3.

Counts (left axis) of the red channel measured during the luminance calibration for seven different exposure times as a function of the distance between the reflectance plaque and the calibration lamp. The black solid line represents the luminance (right axis) emitted by the reflectance plaque.

Fig. 4.
Fig. 4.

Radial distance from optical axis to image center or zenith point, r in millimeter and zenith angle of the 18 reference stars with the square of correlation coefficient (R2) of 0.998.

Fig. 5.
Fig. 5.

Deviation of different measurements to the equidistant geometry determined in degrees (left axis) and pixels (right axis) for the camera distortion determination (diamond) and star calibration (triangle). Both calibration methods agree well with the equidistant geometry.

Fig. 6.
Fig. 6.

(a)–(d) Diurnal variation of zenith sky luminance measured with CCD spectroradiometer (black line) and HSI (gray line). (a) Comparison of zenith sky luminance on March 28th 2012 under clear sky conditions and (b) the corresponding ratio. (c) Comparison of zenith sky luminance on May 12th 2012 for broken cloud conditions and (d) the corresponding ratio. (e) HSI image for a broken cloud condition from May 12th 2012 at 15:31 UTC and (f) HSI image of a clear sky condition from March 28th 2012 at 11:50 UTC. The black circles on the images (e) and (f) mark the corresponding FOV of the CCD spectroradiometer entrance optics. The sky luminance in the morning is only 1% of the noon sky luminance. The figure shows that the deviation between both measurements is less than ±10% for these instantaneous measurements that are not averaged.

Fig. 7.
Fig. 7.

(a) Daily averaged zenith luminance measured by the CCD spectroradiometer (star) compared with HSI (diamond) calculation on different dates in February–May 2012. (b) Ratio of daily averaged zenith luminance derived from HSI images to the measurement of CCD spectroradiometer.

Fig. 8.
Fig. 8.

Diurnal variation of global illuminance on (a) March 28th and (c) May 12th 2012. Plot (a) shows the comparisons between the measured illuminance from the luxmeter (black line) and the illuminance derived from the HSI system (gray line) on March 28th. Plot (c) presents the illuminance from the luxmeter on May 12th 2012. The corresponding ratios of HSI’s illuminance to illuminance from the luxmeter for both days are shown in plots (b) and (d).

Fig. 9.
Fig. 9.

(a) Comparison between daily averaged global illuminance measured from the luxmeter (star) and HSI (diamond) calculation on different dates in May 2012. (b) Ratio of daily average global illuminance from HSI images to the measured values from the luxmeter.

Tables (1)

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Table 1. Definition of Radiometric (Radiance, Irradiance) and Photometric (Luminance, Illuminance) Quantities According to [38]

Equations (10)

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r=c·α(Equidistant projection),r=2c·sinα2(Equisolid-angle projection),r=c·sinα(Orthographic projection),
Lph=Km380780R(λ)·V(λ)dλ,
Lcam=VaTbT·Ev,
V=0.2125R+0.7154G+0.0721B,
Ev=179200·π·S·Tf2,
Edh=02π0π/2Lγ,φsinγcosγdγdφ,
Es=130·sinγs·exp(0.2/sinγs),
ri=0.0187683+0.0196850·θi,
xi=x0+ri(θi)·cos(φi),
yi=y0+ri(θi)·sin(φi),

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