Abstract

All-sky night brightness maps (calibrated images of the night sky with hemispherical field-of-view (FOV) taken at standard photometric bands) provide useful data to assess the light pollution levels at any ground site. We show that these maps can be efficiently described and analyzed using Zernike circle polynomials. The relevant image information can be compressed into a low-dimensional coefficients vector, giving an analytical expression for the sky brightness and alleviating the effects of noise. Moreover, the Zernike expansions allow us to quantify in a straightforward way the average and zenithal sky brightness and its variation across the FOV, providing a convenient framework to study the time course of these magnitudes. We apply this framework to analyze the results of a one-year campaign of night sky brightness measurements made at the UCM observatory in Madrid.

© 2014 Optical Society of America

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    [CrossRef]
  3. F. Hölker, C. Wolter, E. K. Perkin, and K. Tockner, “Light pollution as a biodiversity threat,” Trends Ecol. Evol. 25, 681–682 (2010).
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  4. K. Thapan, J. Arendt, and D. J. Skene, “An action spectrum for melatonin suppression: evidence for a novel non-rod, non-cone photoreceptor system in humans,” J. Physiol. 535, 261–267 (2001).
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  5. D. M. Berson, F. A. Dunn, and M. Takao, “Phototransduction by retinal ganglion cells that set the circadian clock,” Science 295, 1070–1073 (2002).
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  6. M. S. Rea, M. G. Figueiro, A. Bierman, and R. Hamner, “Modeling the spectral sensitivity of the human circadian system,” Lighting Res. Technol. 44, 386–396 (2012).
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  8. M. Kocifaj, “Light pollution simulations for planar ground-based light sources,” Appl. Opt. 47, 792–798 (2008).
    [CrossRef]
  9. P. Cinzano and F. Falchi, “The propagation of light pollution in the atmosphere,” Mon. Not. R. Astron. Soc. 427, 3337–3357 (2012).
    [CrossRef]
  10. R. H. Garstang, “Model for artificial night-sky illumination,” Publ. Astron. Soc. Pac. 98, 364–375 (1986).
    [CrossRef]
  11. M. Kocifaj, “A numerical experiment on light pollution from distant sources,” Mon. Not. R. Astron. Soc. 415, 3609–3615 (2011).
    [CrossRef]
  12. M. Aube and M. Kocifaj, “Using two light-pollution models to investigate artificial sky radiances at Canary Islands observatories,” Mon. Not. R. Astron. Soc. 422, 819–830 (2012).
    [CrossRef]
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    [CrossRef]
  14. O. Rabaza, D. Galadí-Enríquez, A. Espín-Estrella, and F. Aznar-Dols, “All-sky brightness monitoring of light pollution with astronomical methods,” J. Environ. Manage. 91, 1278–1287 (2010).
  15. D. M. Duriscoe, C. B. Luginbuhl, and C. A. Moore, “Measuring night-sky brightness with a wide-field CCD camera,” Publ. Astron. Soc. Pac. 119, 192–213 (2007).
    [CrossRef]
  16. J. Aceituno, S. F. Sánchez, F. J. Aceituno, D. Galadí-Enríquez, J. J. Negro, R. C. Soriguer, and G. Sanchez-Gomez, “An all-sky transmission monitor: ASTMON,” Publ. Astron. Soc. Pac. 123, 1076–1086 (2011).
    [CrossRef]
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  22. M. R. Calabretta and E. W. Greisen, “Representation of celestial coordinates in FITS,” Astronomy and Astrophysics 395, 1077–1122 (2002).
    [CrossRef]
  23. M. Nievas Rosillo, “Absolute photometry and night sky brightness with all-sky cameras,” Master’s thesis, (Universidad Complutense de Madrid, 2013), http://eprints.ucm.es/24626/ .
  24. J. Herrmann, “Least-squares wave front errors of minimum norm,” J. Opt. Soc. Am. 70, 28–35 (1980).
    [CrossRef]
  25. P. B. Liebelt, An Introduction to Optimal Estimation (Addison-Wesley, 1967).
  26. M. S. Bessell, “UBVRI photometry II: the Cousings VRI syatem, its temperature and absolute flux calibration, and relevance for two-dimensional photometry,” Publ. Astron. Soc. Pac. 91, 589–607 (1979).
    [CrossRef]
  27. M. Nievas Rosillo, “Fotometría absoluta y brillo de fondo de cielo con AstMon-UCM,” (Universidad Complutense de Madrid, 2012), http://eprints.ucm.es/16974/
  28. S. Darula, “Windows in buildings: potential source of light pollution,” in Proceedings of the International Conference on Light Pollution Theory, Modelling and Measurements, Smolenice, Slovak Republic (2013) pp. 51–56.
  29. A. Sánchez de Miguel, “Variación del brillo del fondo de cielo en el cénit con la fase y altura de la Luna,” (Universidad Complutense de Madrid, 2013), http://guaix.fis.ucm.es/~alex/TFG_Alex_v3.pdf .
  30. J. Puschnig, T. Posch, and S. Uttenthaler, “Night sky photometry and spectroscopy performed at the Vienna University Observatory,” J. Quant. Spectrosc. Radiat. Transfer (2013). Available online 4September2013.
  31. C. C. M. Kyba, T. Ruhtz, J. Fischer, and F. Hölker, “Red is the new black: how the colour of urban skyglow varies with cloud cover,” Mon. Not. R. Astron. Soc. 425, 701–708 (2012).
    [CrossRef]
  32. C. S. J. Pun and C. W. So, “Night-sky brightness monitoring in Hong Kong. A city-wide light pollution assessment,” Environ. Monit. Assess. 184, 2537–2557 (2012).
    [CrossRef]
  33. J. Zamorano, A. Sánchez de Miguel, J. Gómez Castaño, F. Ocaña, J. Gallego, B. Pila Díez, M. Nievas, C. Tapia, A. Fernández, and S. Pascual, “Night sky brightness and light pollution in Comunidad de Madrid,” in International Conference on Light Pollution Theory, Modelling, and Measurements, Smolenice, Slovak Republic, 15-18 April2013, http://eprints.ucm.es/24201/ ).

2013

2012

M. S. Rea, M. G. Figueiro, A. Bierman, and R. Hamner, “Modeling the spectral sensitivity of the human circadian system,” Lighting Res. Technol. 44, 386–396 (2012).
[CrossRef]

P. Cinzano and F. Falchi, “The propagation of light pollution in the atmosphere,” Mon. Not. R. Astron. Soc. 427, 3337–3357 (2012).
[CrossRef]

M. Aube and M. Kocifaj, “Using two light-pollution models to investigate artificial sky radiances at Canary Islands observatories,” Mon. Not. R. Astron. Soc. 422, 819–830 (2012).
[CrossRef]

C. C. M. Kyba, T. Ruhtz, J. Fischer, and F. Hölker, “Red is the new black: how the colour of urban skyglow varies with cloud cover,” Mon. Not. R. Astron. Soc. 425, 701–708 (2012).
[CrossRef]

C. S. J. Pun and C. W. So, “Night-sky brightness monitoring in Hong Kong. A city-wide light pollution assessment,” Environ. Monit. Assess. 184, 2537–2557 (2012).
[CrossRef]

2011

V. Lakshminarayanan and A. Flecka, “Zernike polynomials: a guide,” J. Mod. Opt. 58, 545–561 (2011).

J. Aceituno, S. F. Sánchez, F. J. Aceituno, D. Galadí-Enríquez, J. J. Negro, R. C. Soriguer, and G. Sanchez-Gomez, “An all-sky transmission monitor: ASTMON,” Publ. Astron. Soc. Pac. 123, 1076–1086 (2011).
[CrossRef]

M. Kocifaj, “A numerical experiment on light pollution from distant sources,” Mon. Not. R. Astron. Soc. 415, 3609–3615 (2011).
[CrossRef]

2010

F. Hölker, C. Wolter, E. K. Perkin, and K. Tockner, “Light pollution as a biodiversity threat,” Trends Ecol. Evol. 25, 681–682 (2010).
[CrossRef]

O. Rabaza, D. Galadí-Enríquez, A. Espín-Estrella, and F. Aznar-Dols, “All-sky brightness monitoring of light pollution with astronomical methods,” J. Environ. Manage. 91, 1278–1287 (2010).

2008

2007

M. Kocifaj, “Light-pollution model for cloudy and cloudless night skies with ground-based light sources,” Appl. Opt. 46, 3013–3022 (2007).
[CrossRef]

D. M. Duriscoe, C. B. Luginbuhl, and C. A. Moore, “Measuring night-sky brightness with a wide-field CCD camera,” Publ. Astron. Soc. Pac. 119, 192–213 (2007).
[CrossRef]

2002

M. R. Calabretta and E. W. Greisen, “Representation of celestial coordinates in FITS,” Astronomy and Astrophysics 395, 1077–1122 (2002).
[CrossRef]

D. M. Berson, F. A. Dunn, and M. Takao, “Phototransduction by retinal ganglion cells that set the circadian clock,” Science 295, 1070–1073 (2002).
[CrossRef]

2001

K. Thapan, J. Arendt, and D. J. Skene, “An action spectrum for melatonin suppression: evidence for a novel non-rod, non-cone photoreceptor system in humans,” J. Physiol. 535, 261–267 (2001).
[CrossRef]

P. Cinzano, F. Falchi, and C. Elvidge, “The first world atlas of the artificial night sky brightness,” Mon. Not. R. Astron. Soc. 328, 689–707 (2001).
[CrossRef]

1986

R. H. Garstang, “Model for artificial night-sky illumination,” Publ. Astron. Soc. Pac. 98, 364–375 (1986).
[CrossRef]

1980

1979

M. S. Bessell, “UBVRI photometry II: the Cousings VRI syatem, its temperature and absolute flux calibration, and relevance for two-dimensional photometry,” Publ. Astron. Soc. Pac. 91, 589–607 (1979).
[CrossRef]

1970

M. F. Walker, “The California site survey,” Publ. Astron. Soc. Pac. 82, 672–698 (1970).
[CrossRef]

1934

F. Zernike, “Beugungstheorie des Schneidenverfahrens und seiner verbesserten Form, der Phasenkontrastmethode,” Physica 1, 689–704 (1934).
[CrossRef]

Aceituno, F. J.

J. Aceituno, S. F. Sánchez, F. J. Aceituno, D. Galadí-Enríquez, J. J. Negro, R. C. Soriguer, and G. Sanchez-Gomez, “An all-sky transmission monitor: ASTMON,” Publ. Astron. Soc. Pac. 123, 1076–1086 (2011).
[CrossRef]

Aceituno, J.

J. Aceituno, S. F. Sánchez, F. J. Aceituno, D. Galadí-Enríquez, J. J. Negro, R. C. Soriguer, and G. Sanchez-Gomez, “An all-sky transmission monitor: ASTMON,” Publ. Astron. Soc. Pac. 123, 1076–1086 (2011).
[CrossRef]

Applegate, R. A.

L. N. Thibos, R. A. Applegate, J. T. Schwiegerling, and R. Webb, and VSIA Standards Taskforce Members, “Standards for reporting the optical aberrations of eyes,” in Vision Science and Its Applications 2000, V. Lakshminarayanan, ed., OSA Trends in Optics and Photonics Series (Optical Society of America, 2000), Vol. 35, pp. 232–244.

Arendt, J.

K. Thapan, J. Arendt, and D. J. Skene, “An action spectrum for melatonin suppression: evidence for a novel non-rod, non-cone photoreceptor system in humans,” J. Physiol. 535, 261–267 (2001).
[CrossRef]

Aube, M.

M. Aube and M. Kocifaj, “Using two light-pollution models to investigate artificial sky radiances at Canary Islands observatories,” Mon. Not. R. Astron. Soc. 422, 819–830 (2012).
[CrossRef]

Aznar-Dols, F.

O. Rabaza, D. Galadí-Enríquez, A. Espín-Estrella, and F. Aznar-Dols, “All-sky brightness monitoring of light pollution with astronomical methods,” J. Environ. Manage. 91, 1278–1287 (2010).

Berson, D. M.

D. M. Berson, F. A. Dunn, and M. Takao, “Phototransduction by retinal ganglion cells that set the circadian clock,” Science 295, 1070–1073 (2002).
[CrossRef]

Bessell, M. S.

M. S. Bessell, “UBVRI photometry II: the Cousings VRI syatem, its temperature and absolute flux calibration, and relevance for two-dimensional photometry,” Publ. Astron. Soc. Pac. 91, 589–607 (1979).
[CrossRef]

Bierman, A.

M. S. Rea, M. G. Figueiro, A. Bierman, and R. Hamner, “Modeling the spectral sensitivity of the human circadian system,” Lighting Res. Technol. 44, 386–396 (2012).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1998), pp. 464–466, 767–772.

Calabretta, M. R.

M. R. Calabretta and E. W. Greisen, “Representation of celestial coordinates in FITS,” Astronomy and Astrophysics 395, 1077–1122 (2002).
[CrossRef]

Cinzano, P.

P. Cinzano and F. Falchi, “The propagation of light pollution in the atmosphere,” Mon. Not. R. Astron. Soc. 427, 3337–3357 (2012).
[CrossRef]

P. Cinzano, F. Falchi, and C. Elvidge, “The first world atlas of the artificial night sky brightness,” Mon. Not. R. Astron. Soc. 328, 689–707 (2001).
[CrossRef]

Darula, S.

S. Darula, “Windows in buildings: potential source of light pollution,” in Proceedings of the International Conference on Light Pollution Theory, Modelling and Measurements, Smolenice, Slovak Republic (2013) pp. 51–56.

Dunn, F. A.

D. M. Berson, F. A. Dunn, and M. Takao, “Phototransduction by retinal ganglion cells that set the circadian clock,” Science 295, 1070–1073 (2002).
[CrossRef]

Duriscoe, D. M.

D. M. Duriscoe, C. B. Luginbuhl, and C. A. Moore, “Measuring night-sky brightness with a wide-field CCD camera,” Publ. Astron. Soc. Pac. 119, 192–213 (2007).
[CrossRef]

Elvidge, C.

P. Cinzano, F. Falchi, and C. Elvidge, “The first world atlas of the artificial night sky brightness,” Mon. Not. R. Astron. Soc. 328, 689–707 (2001).
[CrossRef]

Espín-Estrella, A.

O. Rabaza, D. Galadí-Enríquez, A. Espín-Estrella, and F. Aznar-Dols, “All-sky brightness monitoring of light pollution with astronomical methods,” J. Environ. Manage. 91, 1278–1287 (2010).

Falchi, F.

P. Cinzano and F. Falchi, “The propagation of light pollution in the atmosphere,” Mon. Not. R. Astron. Soc. 427, 3337–3357 (2012).
[CrossRef]

P. Cinzano, F. Falchi, and C. Elvidge, “The first world atlas of the artificial night sky brightness,” Mon. Not. R. Astron. Soc. 328, 689–707 (2001).
[CrossRef]

Fernández, A.

J. Zamorano, A. Sánchez de Miguel, J. Gómez Castaño, F. Ocaña, J. Gallego, B. Pila Díez, M. Nievas, C. Tapia, A. Fernández, and S. Pascual, “Night sky brightness and light pollution in Comunidad de Madrid,” in International Conference on Light Pollution Theory, Modelling, and Measurements, Smolenice, Slovak Republic, 15-18 April2013, http://eprints.ucm.es/24201/ ).

Figueiro, M. G.

M. S. Rea, M. G. Figueiro, A. Bierman, and R. Hamner, “Modeling the spectral sensitivity of the human circadian system,” Lighting Res. Technol. 44, 386–396 (2012).
[CrossRef]

Fischer, J.

C. C. M. Kyba, T. Ruhtz, J. Fischer, and F. Hölker, “Red is the new black: how the colour of urban skyglow varies with cloud cover,” Mon. Not. R. Astron. Soc. 425, 701–708 (2012).
[CrossRef]

Flecka, A.

V. Lakshminarayanan and A. Flecka, “Zernike polynomials: a guide,” J. Mod. Opt. 58, 545–561 (2011).

Galadí-Enríquez, D.

J. Aceituno, S. F. Sánchez, F. J. Aceituno, D. Galadí-Enríquez, J. J. Negro, R. C. Soriguer, and G. Sanchez-Gomez, “An all-sky transmission monitor: ASTMON,” Publ. Astron. Soc. Pac. 123, 1076–1086 (2011).
[CrossRef]

O. Rabaza, D. Galadí-Enríquez, A. Espín-Estrella, and F. Aznar-Dols, “All-sky brightness monitoring of light pollution with astronomical methods,” J. Environ. Manage. 91, 1278–1287 (2010).

Gallego, J.

J. Zamorano, A. Sánchez de Miguel, J. Gómez Castaño, F. Ocaña, J. Gallego, B. Pila Díez, M. Nievas, C. Tapia, A. Fernández, and S. Pascual, “Night sky brightness and light pollution in Comunidad de Madrid,” in International Conference on Light Pollution Theory, Modelling, and Measurements, Smolenice, Slovak Republic, 15-18 April2013, http://eprints.ucm.es/24201/ ).

Garstang, R. H.

R. H. Garstang, “Model for artificial night-sky illumination,” Publ. Astron. Soc. Pac. 98, 364–375 (1986).
[CrossRef]

Gómez Castaño, J.

J. Zamorano, A. Sánchez de Miguel, J. Gómez Castaño, F. Ocaña, J. Gallego, B. Pila Díez, M. Nievas, C. Tapia, A. Fernández, and S. Pascual, “Night sky brightness and light pollution in Comunidad de Madrid,” in International Conference on Light Pollution Theory, Modelling, and Measurements, Smolenice, Slovak Republic, 15-18 April2013, http://eprints.ucm.es/24201/ ).

Greisen, E. W.

M. R. Calabretta and E. W. Greisen, “Representation of celestial coordinates in FITS,” Astronomy and Astrophysics 395, 1077–1122 (2002).
[CrossRef]

Hamner, R.

M. S. Rea, M. G. Figueiro, A. Bierman, and R. Hamner, “Modeling the spectral sensitivity of the human circadian system,” Lighting Res. Technol. 44, 386–396 (2012).
[CrossRef]

Herrmann, J.

Hölker, F.

C. C. M. Kyba, T. Ruhtz, J. Fischer, and F. Hölker, “Red is the new black: how the colour of urban skyglow varies with cloud cover,” Mon. Not. R. Astron. Soc. 425, 701–708 (2012).
[CrossRef]

F. Hölker, C. Wolter, E. K. Perkin, and K. Tockner, “Light pollution as a biodiversity threat,” Trends Ecol. Evol. 25, 681–682 (2010).
[CrossRef]

Kocifaj, M.

M. Aube and M. Kocifaj, “Using two light-pollution models to investigate artificial sky radiances at Canary Islands observatories,” Mon. Not. R. Astron. Soc. 422, 819–830 (2012).
[CrossRef]

M. Kocifaj, “A numerical experiment on light pollution from distant sources,” Mon. Not. R. Astron. Soc. 415, 3609–3615 (2011).
[CrossRef]

M. Kocifaj, “Light pollution simulations for planar ground-based light sources,” Appl. Opt. 47, 792–798 (2008).
[CrossRef]

M. Kocifaj, “Light-pollution model for cloudy and cloudless night skies with ground-based light sources,” Appl. Opt. 46, 3013–3022 (2007).
[CrossRef]

Kyba, C. C. M.

C. C. M. Kyba, T. Ruhtz, J. Fischer, and F. Hölker, “Red is the new black: how the colour of urban skyglow varies with cloud cover,” Mon. Not. R. Astron. Soc. 425, 701–708 (2012).
[CrossRef]

Lakshminarayanan, V.

V. Lakshminarayanan and A. Flecka, “Zernike polynomials: a guide,” J. Mod. Opt. 58, 545–561 (2011).

Liebelt, P. B.

P. B. Liebelt, An Introduction to Optimal Estimation (Addison-Wesley, 1967).

Luginbuhl, C. B.

D. M. Duriscoe, C. B. Luginbuhl, and C. A. Moore, “Measuring night-sky brightness with a wide-field CCD camera,” Publ. Astron. Soc. Pac. 119, 192–213 (2007).
[CrossRef]

Moore, C. A.

D. M. Duriscoe, C. B. Luginbuhl, and C. A. Moore, “Measuring night-sky brightness with a wide-field CCD camera,” Publ. Astron. Soc. Pac. 119, 192–213 (2007).
[CrossRef]

Negro, J. J.

J. Aceituno, S. F. Sánchez, F. J. Aceituno, D. Galadí-Enríquez, J. J. Negro, R. C. Soriguer, and G. Sanchez-Gomez, “An all-sky transmission monitor: ASTMON,” Publ. Astron. Soc. Pac. 123, 1076–1086 (2011).
[CrossRef]

Nievas, M.

J. Zamorano, A. Sánchez de Miguel, J. Gómez Castaño, F. Ocaña, J. Gallego, B. Pila Díez, M. Nievas, C. Tapia, A. Fernández, and S. Pascual, “Night sky brightness and light pollution in Comunidad de Madrid,” in International Conference on Light Pollution Theory, Modelling, and Measurements, Smolenice, Slovak Republic, 15-18 April2013, http://eprints.ucm.es/24201/ ).

Nievas Rosillo, M.

M. Nievas Rosillo, “Fotometría absoluta y brillo de fondo de cielo con AstMon-UCM,” (Universidad Complutense de Madrid, 2012), http://eprints.ucm.es/16974/

M. Nievas Rosillo, “Absolute photometry and night sky brightness with all-sky cameras,” Master’s thesis, (Universidad Complutense de Madrid, 2013), http://eprints.ucm.es/24626/ .

Ocaña, F.

J. Zamorano, A. Sánchez de Miguel, J. Gómez Castaño, F. Ocaña, J. Gallego, B. Pila Díez, M. Nievas, C. Tapia, A. Fernández, and S. Pascual, “Night sky brightness and light pollution in Comunidad de Madrid,” in International Conference on Light Pollution Theory, Modelling, and Measurements, Smolenice, Slovak Republic, 15-18 April2013, http://eprints.ucm.es/24201/ ).

Pascual, S.

J. Zamorano, A. Sánchez de Miguel, J. Gómez Castaño, F. Ocaña, J. Gallego, B. Pila Díez, M. Nievas, C. Tapia, A. Fernández, and S. Pascual, “Night sky brightness and light pollution in Comunidad de Madrid,” in International Conference on Light Pollution Theory, Modelling, and Measurements, Smolenice, Slovak Republic, 15-18 April2013, http://eprints.ucm.es/24201/ ).

Perkin, E. K.

F. Hölker, C. Wolter, E. K. Perkin, and K. Tockner, “Light pollution as a biodiversity threat,” Trends Ecol. Evol. 25, 681–682 (2010).
[CrossRef]

Pila Díez, B.

J. Zamorano, A. Sánchez de Miguel, J. Gómez Castaño, F. Ocaña, J. Gallego, B. Pila Díez, M. Nievas, C. Tapia, A. Fernández, and S. Pascual, “Night sky brightness and light pollution in Comunidad de Madrid,” in International Conference on Light Pollution Theory, Modelling, and Measurements, Smolenice, Slovak Republic, 15-18 April2013, http://eprints.ucm.es/24201/ ).

Posch, T.

J. Puschnig, T. Posch, and S. Uttenthaler, “Night sky photometry and spectroscopy performed at the Vienna University Observatory,” J. Quant. Spectrosc. Radiat. Transfer (2013). Available online 4September2013.

Pun, C. S. J.

C. S. J. Pun and C. W. So, “Night-sky brightness monitoring in Hong Kong. A city-wide light pollution assessment,” Environ. Monit. Assess. 184, 2537–2557 (2012).
[CrossRef]

Puschnig, J.

J. Puschnig, T. Posch, and S. Uttenthaler, “Night sky photometry and spectroscopy performed at the Vienna University Observatory,” J. Quant. Spectrosc. Radiat. Transfer (2013). Available online 4September2013.

Rabaza, O.

O. Rabaza, D. Galadí-Enríquez, A. Espín-Estrella, and F. Aznar-Dols, “All-sky brightness monitoring of light pollution with astronomical methods,” J. Environ. Manage. 91, 1278–1287 (2010).

Rea, M. S.

M. S. Rea, M. G. Figueiro, A. Bierman, and R. Hamner, “Modeling the spectral sensitivity of the human circadian system,” Lighting Res. Technol. 44, 386–396 (2012).
[CrossRef]

Riechelmann, S.

Ruhtz, T.

C. C. M. Kyba, T. Ruhtz, J. Fischer, and F. Hölker, “Red is the new black: how the colour of urban skyglow varies with cloud cover,” Mon. Not. R. Astron. Soc. 425, 701–708 (2012).
[CrossRef]

Sánchez, S. F.

J. Aceituno, S. F. Sánchez, F. J. Aceituno, D. Galadí-Enríquez, J. J. Negro, R. C. Soriguer, and G. Sanchez-Gomez, “An all-sky transmission monitor: ASTMON,” Publ. Astron. Soc. Pac. 123, 1076–1086 (2011).
[CrossRef]

Sánchez de Miguel, A.

A. Sánchez de Miguel, “Variación del brillo del fondo de cielo en el cénit con la fase y altura de la Luna,” (Universidad Complutense de Madrid, 2013), http://guaix.fis.ucm.es/~alex/TFG_Alex_v3.pdf .

J. Zamorano, A. Sánchez de Miguel, J. Gómez Castaño, F. Ocaña, J. Gallego, B. Pila Díez, M. Nievas, C. Tapia, A. Fernández, and S. Pascual, “Night sky brightness and light pollution in Comunidad de Madrid,” in International Conference on Light Pollution Theory, Modelling, and Measurements, Smolenice, Slovak Republic, 15-18 April2013, http://eprints.ucm.es/24201/ ).

Sanchez-Gomez, G.

J. Aceituno, S. F. Sánchez, F. J. Aceituno, D. Galadí-Enríquez, J. J. Negro, R. C. Soriguer, and G. Sanchez-Gomez, “An all-sky transmission monitor: ASTMON,” Publ. Astron. Soc. Pac. 123, 1076–1086 (2011).
[CrossRef]

Schilke, H.

Schrempf, M.

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Figures (7)

Fig. 1.
Fig. 1.

All-sky night brightness map taken in the Johnson–Cousin’s V-band at the astronomical observatory of Universidad Complutense, Madrid, in December 8, 2012, at 21:28 (UT) using an ASTMON camera. The observatory domes can be seen at the lower rim of the image. Gray scale in units mJy/arcsec2.

Fig. 2.
Fig. 2.

From left to right and top to bottom: Plots of the Zernike modes of indices k(n,m): 1 (0,0); 3(1,+1); 4 (2,2); 5 (2,0); 10 (3,+3); 13 (4,0); 21 (5,+5); 25 (6,0); and 45 (8,+8).

Fig. 3.
Fig. 3.

Values of the first 45 estimated Zernike coefficients (in mJy/arcsec2), corresponding to the all-sky night brightness maps taken at the astronomical observatory of Universidad Complutense, Madrid, on December 8, 2012, at 21:28 (UT), in the Johnson–Cousin’s B, V (see Fig. 1), and R bands, plotted versus the Zernike mode index k.

Fig. 4.
Fig. 4.

Top to bottom: Color-coded versions of the original all-sky night brightness maps in the B, V and R bands (left) and reconstructed ones (right) with an expansion up to the Zernike radial order nmax=10 (M=66 modes). The scale units are mJy/arsec2. Note the different amplitude of the scale for each band.

Fig. 5.
Fig. 5.

Original (thin black line) and reconstructed (thick red line) profiles of the night sky brightness measured on the B-band image across an horizontal row, using sampled sky maps with resolution 500×500 pixels. Isolated point-like sources (Jupiter) do not show in the low-order Zernike fitting of the continuous sky brightness distribution.

Fig. 6.
Fig. 6.

Average values a^k of the first 15 Zernike modes for the ensemble of cloudless and moonless nights (see text) in the B, V and R bands. Error bars correspond to one standard deviation of the mean (80 images for each band).

Fig. 7.
Fig. 7.

Top: P(k), power spectrum in the Zernike space of the ensemble of all-sky maps analyzed in this work (B, V and R bands). Bottom: Spectral power distribution aggregated by whole radial orders, P(n).

Tables (1)

Tables Icon

Table 1. Average and Zenithal Brightness

Equations (19)

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

Zn,m(r)=Nn,mRn,m(r)Am(θ),
Rn,m(r)=l=0(n|m|)/2(1)l(nl)!l![0.5(n+|m|)l]![0.5(n|m|)l]!rn2l
Am(θ)={cosmθ,form0sin|m|θ,form<0
Nn,m=(2δm0)(n+1),
1πr=01θ=02πZn,m(r)Zn,m(r)rdrdθ=δnnδmm.
k=[n(n+2)+m]/2+1.
B(r)=n=0m=nnan,mZn,m(r)k=1akZk(r),
ak=1πr=01θ=02πB(r)Zk(r)rdrdθ,
S(r)=B(r)+ν(r),
B(0)=n=0(1)n2(n+1)an,0.
1πr=01θ=02π|B(r)|2rdrdθ=k=1ak2n=0m=nnan,m2.
σ2=k=2ak2n=1m=nnan,m2.
P(k)=ak2an,m2,
P(n)=m=nnan,m2.
B^(r)=k=1Ma^kZk(r),
s=Za+ν.
b^=Za^,
a^=Rs.
R=(ZMTZM)1ZMT,

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