Abstract

The wavelength dependence of the dominant directional reflective properties of beach sands was demonstrated using principal component analysis and the related correlation matrix. In general, we found that the hyperspectral bidirectional reflectance distribution function (BRDF) of beach sands has weak wavelength dependence. Its BRDF varies slightly in three broad wavelength regions. The variations are more evident in surfaces of greater visual roughness than in smooth surfaces. The weak wavelength dependence of the BRDF of beach sand can be captured using three broad wavelength regions instead of hundreds of individual wavelengths.

© 2015 Optical Society of America

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References

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2014 (2)

Z. Wang, C. A. Coburn, X. Ren, and P. M. Teillet, “Effect of surface roughness, wavelength, illumination, and viewing zenith angles on soil surface BRDF using an imaging BRDF approach,” Int. J. Remote Sens. 35, 6894–6913 (2014).
[Crossref]

C. M. Bachmann, A. Abelev, W. Philpot, K. Z. Doctor, M. J. Montes, R. A. Fusina, R.-R. Li, and E. van Roggen, “Retrieval of sand density from hyperspectral BRDF,” Proc. SPIE 9088, 9 (2014).

2013 (1)

M. Buchhorn, R. Petereit, and B. Heim, “A manual transportable instrument platform for ground-based spectro-directional observations (ManTIS) and the resultant hyperspectral field goniometer system,” Sensors 13, 16105–16128 (2013).
[Crossref]

2012 (2)

C. M. Bachmann, D. Gray, A. Abelev, W. Philpot, M. J. Montes, R. Fusina, J. Musser, R.-R. Li, M. Vermillion, G. Smith, D. R. Korwan, C. Snow, W. D. Miller, J. Gardner, M. Sletten, G. Georgiev, B. Truitt, M. Killmon, J. Sellars, J. Woolard, C. Parrish, and A. Schwarzschild, “Linking goniometer measurements to hyperspectral and multisensor imagery for retrieval of beach properties and coastal characterization,” Proc. SPIE 8390, 1–9 (2012).

C. M. Bachmann, M. J. Montes, C. E. Parrish, R. A. Fusina, C. R. Nichols, R.-R. Li, E. Hallenborg, C. A. Jones, K. Lee, J. Sellars, S. A. White, and J. C. Fry, “A dual-spectrometer approach to reflectance measurements under sub-optimal sky conditions,” Opt. Express 20, 8959–8973 (2012).
[Crossref]

2010 (1)

Z. Wang, C. A. Coburn, X. Ren, D. Mazumdar, S. Myshak, A. Mullin, and P. M. Teillet, “Assessment of soil surface BRDF using an imaging spectrometer,” Proc. SPIE 7830, 783010 (2010).
[Crossref]

2006 (3)

H. Zhang and K. J. Voss, “Bidirectional reflectance study on dry, wet, and submerged particulate layers: effects of pore liquid refractive index and translucent particle concentrations,” Appl. Opt. 45, 8753–8763 (2006).
[Crossref]

G. Schaepman-Strub, M. Schaepman, T. Painter, S. Dangel, and J. Martonchik, “Reflectance quantities in optical remote sensing—definitions and case studies,” Remote Sens. Environ. 103, 27–42 (2006).
[Crossref]

C. S. Bourgeois, A. Ohmura, K. Schroff, H.-J. Frei, and P. Calanca, “IAC ETH goniospectrometer: a tool for hyperspectral HDRF measurements,” J. Atmos. Oceanic Technol. 23, 573–584 (2006).
[Crossref]

2002 (1)

G. Strub, U. Beisl, M. Schaepman, D. Schläpfer, C. Dickerhof, and K. Itten, “Evaluation of diurnal hyperspectral HDRF data acquired with the RSL field goniometer during the DAISEX’99 campaign,” ISPRS J. Photogramm. Remote Sens. 57, 184–193 (2002).
[Crossref]

2000 (2)

J. V. Martonchik, C. J. Bruegge, and A. H. Strahler, “A review of reflectance nomenclature used in remote sensing,” Remote Sens. Rev. 19, 9–20 (2000).
[Crossref]

C. Walthall, J. L. Roujean, and J. Morisette, “Field and landscape BRDF optical wavelength measurements: experience, techniques and the future,” Remote Sens. Rev. 18, 503–531 (2000).
[Crossref]

1999 (1)

S. R. Sandmeier and K. I. Itten, “A field goniometer system (FIGOS) for acquisition of hyperspectral BRDF data,” IEEE Trans. Geosci. Remote Sens 37, 978–986 (1999).
[Crossref]

1998 (1)

S. Sandmeier, C. Müller, B. Hosgood, and G. Andreoli, “Physical mechanisms in hyperspectral BRDF data of grass and watercress,” Remote Sens. Environ. 66, 222–233 (1998).
[Crossref]

1987 (1)

E. J. Milton, “Review article principles of field spectroscopy,” Int. J. Remote Sens. 8, 1807–1827 (1987).
[Crossref]

1965 (1)

Abelev, A.

C. M. Bachmann, A. Abelev, W. Philpot, K. Z. Doctor, M. J. Montes, R. A. Fusina, R.-R. Li, and E. van Roggen, “Retrieval of sand density from hyperspectral BRDF,” Proc. SPIE 9088, 9 (2014).

C. M. Bachmann, D. Gray, A. Abelev, W. Philpot, M. J. Montes, R. Fusina, J. Musser, R.-R. Li, M. Vermillion, G. Smith, D. R. Korwan, C. Snow, W. D. Miller, J. Gardner, M. Sletten, G. Georgiev, B. Truitt, M. Killmon, J. Sellars, J. Woolard, C. Parrish, and A. Schwarzschild, “Linking goniometer measurements to hyperspectral and multisensor imagery for retrieval of beach properties and coastal characterization,” Proc. SPIE 8390, 1–9 (2012).

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Anderson, K.

H. Croft and K. Anderson, “Directional reflectance factors for monitoring spatial changes in soil surface structure and soil organic matter erosion in agricultural systems,” in EGU General Assembly, Vienna, Austria (2012), vol. 14, p. 9089.

Andreoli, G.

S. Sandmeier, C. Müller, B. Hosgood, and G. Andreoli, “Physical mechanisms in hyperspectral BRDF data of grass and watercress,” Remote Sens. Environ. 66, 222–233 (1998).
[Crossref]

Bachmann, C. M.

C. M. Bachmann, A. Abelev, W. Philpot, K. Z. Doctor, M. J. Montes, R. A. Fusina, R.-R. Li, and E. van Roggen, “Retrieval of sand density from hyperspectral BRDF,” Proc. SPIE 9088, 9 (2014).

C. M. Bachmann, D. Gray, A. Abelev, W. Philpot, M. J. Montes, R. Fusina, J. Musser, R.-R. Li, M. Vermillion, G. Smith, D. R. Korwan, C. Snow, W. D. Miller, J. Gardner, M. Sletten, G. Georgiev, B. Truitt, M. Killmon, J. Sellars, J. Woolard, C. Parrish, and A. Schwarzschild, “Linking goniometer measurements to hyperspectral and multisensor imagery for retrieval of beach properties and coastal characterization,” Proc. SPIE 8390, 1–9 (2012).

C. M. Bachmann, M. J. Montes, C. E. Parrish, R. A. Fusina, C. R. Nichols, R.-R. Li, E. Hallenborg, C. A. Jones, K. Lee, J. Sellars, S. A. White, and J. C. Fry, “A dual-spectrometer approach to reflectance measurements under sub-optimal sky conditions,” Opt. Express 20, 8959–8973 (2012).
[Crossref]

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Ball, D.

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Beisl, U.

G. Strub, U. Beisl, M. Schaepman, D. Schläpfer, C. Dickerhof, and K. Itten, “Evaluation of diurnal hyperspectral HDRF data acquired with the RSL field goniometer during the DAISEX’99 campaign,” ISPRS J. Photogramm. Remote Sens. 57, 184–193 (2002).
[Crossref]

Bongiorno, D.

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Bourgeois, C. S.

C. S. Bourgeois, A. Ohmura, K. Schroff, H.-J. Frei, and P. Calanca, “IAC ETH goniospectrometer: a tool for hyperspectral HDRF measurements,” J. Atmos. Oceanic Technol. 23, 573–584 (2006).
[Crossref]

Brady, A.

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Bruegge, C. J.

J. V. Martonchik, C. J. Bruegge, and A. H. Strahler, “A review of reflectance nomenclature used in remote sensing,” Remote Sens. Rev. 19, 9–20 (2000).
[Crossref]

Buchhorn, M.

M. Buchhorn, R. Petereit, and B. Heim, “A manual transportable instrument platform for ground-based spectro-directional observations (ManTIS) and the resultant hyperspectral field goniometer system,” Sensors 13, 16105–16128 (2013).
[Crossref]

Calanca, P.

C. S. Bourgeois, A. Ohmura, K. Schroff, H.-J. Frei, and P. Calanca, “IAC ETH goniospectrometer: a tool for hyperspectral HDRF measurements,” J. Atmos. Oceanic Technol. 23, 573–584 (2006).
[Crossref]

Camacho-de Coca, F.

F. Camacho-de Coca, F. J. Garcia-Haro, and M. A. Gilbert, “Quantitative analysis of cropland’s BRDF anisotropy using airborne POLDER data,” in Proc. 1st International Symposium on Recent Advances in Quantitative Remote Sensing, Torrent (2002), pp. 1–7.

Carr, S.

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Christie, G.

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Coburn, C. A.

Z. Wang, C. A. Coburn, X. Ren, and P. M. Teillet, “Effect of surface roughness, wavelength, illumination, and viewing zenith angles on soil surface BRDF using an imaging BRDF approach,” Int. J. Remote Sens. 35, 6894–6913 (2014).
[Crossref]

Z. Wang, C. A. Coburn, X. Ren, D. Mazumdar, S. Myshak, A. Mullin, and P. M. Teillet, “Assessment of soil surface BRDF using an imaging spectrometer,” Proc. SPIE 7830, 783010 (2010).
[Crossref]

Croft, H.

H. Croft and K. Anderson, “Directional reflectance factors for monitoring spatial changes in soil surface structure and soil organic matter erosion in agricultural systems,” in EGU General Assembly, Vienna, Austria (2012), vol. 14, p. 9089.

Dangel, S.

G. Schaepman-Strub, M. Schaepman, T. Painter, S. Dangel, and J. Martonchik, “Reflectance quantities in optical remote sensing—definitions and case studies,” Remote Sens. Environ. 103, 27–42 (2006).
[Crossref]

Dickerhof, C.

G. Strub, U. Beisl, M. Schaepman, D. Schläpfer, C. Dickerhof, and K. Itten, “Evaluation of diurnal hyperspectral HDRF data acquired with the RSL field goniometer during the DAISEX’99 campaign,” ISPRS J. Photogramm. Remote Sens. 57, 184–193 (2002).
[Crossref]

Doctor, K. Z.

C. M. Bachmann, A. Abelev, W. Philpot, K. Z. Doctor, M. J. Montes, R. A. Fusina, R.-R. Li, and E. van Roggen, “Retrieval of sand density from hyperspectral BRDF,” Proc. SPIE 9088, 9 (2014).

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Eggleton, J.

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Esbensen, K. H.

K. H. Esbensen, D. Guyot, F. Westad, and L. P. Houmoller, Multivariate Data Analysis–in Practice, 5th Ed. (CAMO Software AS, 2004).

Fairley, A.

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Filzmoser, P.

K. Varmuza and P. Filzmoser, Introduction to Multivariate Statistical Analysis in Chemometrics (CRC Press, 2009).

Frei, H.-J.

C. S. Bourgeois, A. Ohmura, K. Schroff, H.-J. Frei, and P. Calanca, “IAC ETH goniospectrometer: a tool for hyperspectral HDRF measurements,” J. Atmos. Oceanic Technol. 23, 573–584 (2006).
[Crossref]

Frick, G.

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Fry, J. C.

Fusina, R.

C. M. Bachmann, D. Gray, A. Abelev, W. Philpot, M. J. Montes, R. Fusina, J. Musser, R.-R. Li, M. Vermillion, G. Smith, D. R. Korwan, C. Snow, W. D. Miller, J. Gardner, M. Sletten, G. Georgiev, B. Truitt, M. Killmon, J. Sellars, J. Woolard, C. Parrish, and A. Schwarzschild, “Linking goniometer measurements to hyperspectral and multisensor imagery for retrieval of beach properties and coastal characterization,” Proc. SPIE 8390, 1–9 (2012).

Fusina, R. A.

C. M. Bachmann, A. Abelev, W. Philpot, K. Z. Doctor, M. J. Montes, R. A. Fusina, R.-R. Li, and E. van Roggen, “Retrieval of sand density from hyperspectral BRDF,” Proc. SPIE 9088, 9 (2014).

C. M. Bachmann, M. J. Montes, C. E. Parrish, R. A. Fusina, C. R. Nichols, R.-R. Li, E. Hallenborg, C. A. Jones, K. Lee, J. Sellars, S. A. White, and J. C. Fry, “A dual-spectrometer approach to reflectance measurements under sub-optimal sky conditions,” Opt. Express 20, 8959–8973 (2012).
[Crossref]

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Garcia-Haro, F. J.

F. Camacho-de Coca, F. J. Garcia-Haro, and M. A. Gilbert, “Quantitative analysis of cropland’s BRDF anisotropy using airborne POLDER data,” in Proc. 1st International Symposium on Recent Advances in Quantitative Remote Sensing, Torrent (2002), pp. 1–7.

Gardner, J.

C. M. Bachmann, D. Gray, A. Abelev, W. Philpot, M. J. Montes, R. Fusina, J. Musser, R.-R. Li, M. Vermillion, G. Smith, D. R. Korwan, C. Snow, W. D. Miller, J. Gardner, M. Sletten, G. Georgiev, B. Truitt, M. Killmon, J. Sellars, J. Woolard, C. Parrish, and A. Schwarzschild, “Linking goniometer measurements to hyperspectral and multisensor imagery for retrieval of beach properties and coastal characterization,” Proc. SPIE 8390, 1–9 (2012).

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Gates, B. Q.

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Georgiev, G.

C. M. Bachmann, D. Gray, A. Abelev, W. Philpot, M. J. Montes, R. Fusina, J. Musser, R.-R. Li, M. Vermillion, G. Smith, D. R. Korwan, C. Snow, W. D. Miller, J. Gardner, M. Sletten, G. Georgiev, B. Truitt, M. Killmon, J. Sellars, J. Woolard, C. Parrish, and A. Schwarzschild, “Linking goniometer measurements to hyperspectral and multisensor imagery for retrieval of beach properties and coastal characterization,” Proc. SPIE 8390, 1–9 (2012).

Gilbert, M. A.

F. Camacho-de Coca, F. J. Garcia-Haro, and M. A. Gilbert, “Quantitative analysis of cropland’s BRDF anisotropy using airborne POLDER data,” in Proc. 1st International Symposium on Recent Advances in Quantitative Remote Sensing, Torrent (2002), pp. 1–7.

Ginsberg, I. W.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” Tech. Rep. (U.S. Department of Commerce, National Bureau of Standards, 1977).

Gray, D.

C. M. Bachmann, D. Gray, A. Abelev, W. Philpot, M. J. Montes, R. Fusina, J. Musser, R.-R. Li, M. Vermillion, G. Smith, D. R. Korwan, C. Snow, W. D. Miller, J. Gardner, M. Sletten, G. Georgiev, B. Truitt, M. Killmon, J. Sellars, J. Woolard, C. Parrish, and A. Schwarzschild, “Linking goniometer measurements to hyperspectral and multisensor imagery for retrieval of beach properties and coastal characterization,” Proc. SPIE 8390, 1–9 (2012).

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Guyot, D.

K. H. Esbensen, D. Guyot, F. Westad, and L. P. Houmoller, Multivariate Data Analysis–in Practice, 5th Ed. (CAMO Software AS, 2004).

Hagen, R.

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Hallenborg, E.

Hamilton, L.

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Hammond, A.

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Hapke, B. W.

B. W. Hapke, Theory of Reflectance and Emittance Spectroscopy, 2nd ed. (Cambridge University, 2012), Vol. 47.

Heath, M. T.

M. T. Heath, Scientific Computing–An Introductory Survey (McGraw Hill, 2002).

Heim, B.

M. Buchhorn, R. Petereit, and B. Heim, “A manual transportable instrument platform for ground-based spectro-directional observations (ManTIS) and the resultant hyperspectral field goniometer system,” Sensors 13, 16105–16128 (2013).
[Crossref]

Hong, K.

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Hosgood, B.

S. Sandmeier, C. Müller, B. Hosgood, and G. Andreoli, “Physical mechanisms in hyperspectral BRDF data of grass and watercress,” Remote Sens. Environ. 66, 222–233 (1998).
[Crossref]

Houmoller, L. P.

K. H. Esbensen, D. Guyot, F. Westad, and L. P. Houmoller, Multivariate Data Analysis–in Practice, 5th Ed. (CAMO Software AS, 2004).

Hsia, J. J.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” Tech. Rep. (U.S. Department of Commerce, National Bureau of Standards, 1977).

Hughes, R. J.

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Itten, K.

G. Strub, U. Beisl, M. Schaepman, D. Schläpfer, C. Dickerhof, and K. Itten, “Evaluation of diurnal hyperspectral HDRF data acquired with the RSL field goniometer during the DAISEX’99 campaign,” ISPRS J. Photogramm. Remote Sens. 57, 184–193 (2002).
[Crossref]

Itten, K. I.

S. R. Sandmeier and K. I. Itten, “A field goniometer system (FIGOS) for acquisition of hyperspectral BRDF data,” IEEE Trans. Geosci. Remote Sens 37, 978–986 (1999).
[Crossref]

Jia, X.

J. A. Richards and X. Jia, Remote Sensing Digital Image Analysis: An Introduction, 4th Ed. (Springer-Verlag, 2006).

Jones, C. A.

Junek, J.

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Kharabash, S.

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Killmon, M.

C. M. Bachmann, D. Gray, A. Abelev, W. Philpot, M. J. Montes, R. Fusina, J. Musser, R.-R. Li, M. Vermillion, G. Smith, D. R. Korwan, C. Snow, W. D. Miller, J. Gardner, M. Sletten, G. Georgiev, B. Truitt, M. Killmon, J. Sellars, J. Woolard, C. Parrish, and A. Schwarzschild, “Linking goniometer measurements to hyperspectral and multisensor imagery for retrieval of beach properties and coastal characterization,” Proc. SPIE 8390, 1–9 (2012).

Korwan, D. R.

C. M. Bachmann, D. Gray, A. Abelev, W. Philpot, M. J. Montes, R. Fusina, J. Musser, R.-R. Li, M. Vermillion, G. Smith, D. R. Korwan, C. Snow, W. D. Miller, J. Gardner, M. Sletten, G. Georgiev, B. Truitt, M. Killmon, J. Sellars, J. Woolard, C. Parrish, and A. Schwarzschild, “Linking goniometer measurements to hyperspectral and multisensor imagery for retrieval of beach properties and coastal characterization,” Proc. SPIE 8390, 1–9 (2012).

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Lee, K.

Li, R.-R.

C. M. Bachmann, A. Abelev, W. Philpot, K. Z. Doctor, M. J. Montes, R. A. Fusina, R.-R. Li, and E. van Roggen, “Retrieval of sand density from hyperspectral BRDF,” Proc. SPIE 9088, 9 (2014).

C. M. Bachmann, D. Gray, A. Abelev, W. Philpot, M. J. Montes, R. Fusina, J. Musser, R.-R. Li, M. Vermillion, G. Smith, D. R. Korwan, C. Snow, W. D. Miller, J. Gardner, M. Sletten, G. Georgiev, B. Truitt, M. Killmon, J. Sellars, J. Woolard, C. Parrish, and A. Schwarzschild, “Linking goniometer measurements to hyperspectral and multisensor imagery for retrieval of beach properties and coastal characterization,” Proc. SPIE 8390, 1–9 (2012).

C. M. Bachmann, M. J. Montes, C. E. Parrish, R. A. Fusina, C. R. Nichols, R.-R. Li, E. Hallenborg, C. A. Jones, K. Lee, J. Sellars, S. A. White, and J. C. Fry, “A dual-spectrometer approach to reflectance measurements under sub-optimal sky conditions,” Opt. Express 20, 8959–8973 (2012).
[Crossref]

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Liang, R.

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Limperis, T.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” Tech. Rep. (U.S. Department of Commerce, National Bureau of Standards, 1977).

Martonchik, J.

G. Schaepman-Strub, M. Schaepman, T. Painter, S. Dangel, and J. Martonchik, “Reflectance quantities in optical remote sensing—definitions and case studies,” Remote Sens. Environ. 103, 27–42 (2006).
[Crossref]

Martonchik, J. V.

J. V. Martonchik, C. J. Bruegge, and A. H. Strahler, “A review of reflectance nomenclature used in remote sensing,” Remote Sens. Rev. 19, 9–20 (2000).
[Crossref]

Mason, G. L.

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Mattis, G.

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Mazumdar, D.

Z. Wang, C. A. Coburn, X. Ren, D. Mazumdar, S. Myshak, A. Mullin, and P. M. Teillet, “Assessment of soil surface BRDF using an imaging spectrometer,” Proc. SPIE 7830, 783010 (2010).
[Crossref]

McCluney, R.

R. McCluney, Introduction to Radiometry and Photometry (Artech House, 1994).

Miller, W. D.

C. M. Bachmann, D. Gray, A. Abelev, W. Philpot, M. J. Montes, R. Fusina, J. Musser, R.-R. Li, M. Vermillion, G. Smith, D. R. Korwan, C. Snow, W. D. Miller, J. Gardner, M. Sletten, G. Georgiev, B. Truitt, M. Killmon, J. Sellars, J. Woolard, C. Parrish, and A. Schwarzschild, “Linking goniometer measurements to hyperspectral and multisensor imagery for retrieval of beach properties and coastal characterization,” Proc. SPIE 8390, 1–9 (2012).

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Milton, E. J.

E. J. Milton, “Review article principles of field spectroscopy,” Int. J. Remote Sens. 8, 1807–1827 (1987).
[Crossref]

Montes, M. J.

C. M. Bachmann, A. Abelev, W. Philpot, K. Z. Doctor, M. J. Montes, R. A. Fusina, R.-R. Li, and E. van Roggen, “Retrieval of sand density from hyperspectral BRDF,” Proc. SPIE 9088, 9 (2014).

C. M. Bachmann, D. Gray, A. Abelev, W. Philpot, M. J. Montes, R. Fusina, J. Musser, R.-R. Li, M. Vermillion, G. Smith, D. R. Korwan, C. Snow, W. D. Miller, J. Gardner, M. Sletten, G. Georgiev, B. Truitt, M. Killmon, J. Sellars, J. Woolard, C. Parrish, and A. Schwarzschild, “Linking goniometer measurements to hyperspectral and multisensor imagery for retrieval of beach properties and coastal characterization,” Proc. SPIE 8390, 1–9 (2012).

C. M. Bachmann, M. J. Montes, C. E. Parrish, R. A. Fusina, C. R. Nichols, R.-R. Li, E. Hallenborg, C. A. Jones, K. Lee, J. Sellars, S. A. White, and J. C. Fry, “A dual-spectrometer approach to reflectance measurements under sub-optimal sky conditions,” Opt. Express 20, 8959–8973 (2012).
[Crossref]

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Morisette, J.

C. Walthall, J. L. Roujean, and J. Morisette, “Field and landscape BRDF optical wavelength measurements: experience, techniques and the future,” Remote Sens. Rev. 18, 503–531 (2000).
[Crossref]

Müller, C.

S. Sandmeier, C. Müller, B. Hosgood, and G. Andreoli, “Physical mechanisms in hyperspectral BRDF data of grass and watercress,” Remote Sens. Environ. 66, 222–233 (1998).
[Crossref]

Mullin, A.

Z. Wang, C. A. Coburn, X. Ren, D. Mazumdar, S. Myshak, A. Mullin, and P. M. Teillet, “Assessment of soil surface BRDF using an imaging spectrometer,” Proc. SPIE 7830, 783010 (2010).
[Crossref]

Musser, J.

C. M. Bachmann, D. Gray, A. Abelev, W. Philpot, M. J. Montes, R. Fusina, J. Musser, R.-R. Li, M. Vermillion, G. Smith, D. R. Korwan, C. Snow, W. D. Miller, J. Gardner, M. Sletten, G. Georgiev, B. Truitt, M. Killmon, J. Sellars, J. Woolard, C. Parrish, and A. Schwarzschild, “Linking goniometer measurements to hyperspectral and multisensor imagery for retrieval of beach properties and coastal characterization,” Proc. SPIE 8390, 1–9 (2012).

Myshak, S.

Z. Wang, C. A. Coburn, X. Ren, D. Mazumdar, S. Myshak, A. Mullin, and P. M. Teillet, “Assessment of soil surface BRDF using an imaging spectrometer,” Proc. SPIE 7830, 783010 (2010).
[Crossref]

Nichols, C. R.

Nicodemus, F. E.

F. E. Nicodemus, “Directional reflectance and emissivity of an opaque surface,” Appl. Opt. 4, 767 (1965).
[Crossref]

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” Tech. Rep. (U.S. Department of Commerce, National Bureau of Standards, 1977).

Ohmura, A.

C. S. Bourgeois, A. Ohmura, K. Schroff, H.-J. Frei, and P. Calanca, “IAC ETH goniospectrometer: a tool for hyperspectral HDRF measurements,” J. Atmos. Oceanic Technol. 23, 573–584 (2006).
[Crossref]

Painter, T.

G. Schaepman-Strub, M. Schaepman, T. Painter, S. Dangel, and J. Martonchik, “Reflectance quantities in optical remote sensing—definitions and case studies,” Remote Sens. Environ. 103, 27–42 (2006).
[Crossref]

Parrish, C.

C. M. Bachmann, D. Gray, A. Abelev, W. Philpot, M. J. Montes, R. Fusina, J. Musser, R.-R. Li, M. Vermillion, G. Smith, D. R. Korwan, C. Snow, W. D. Miller, J. Gardner, M. Sletten, G. Georgiev, B. Truitt, M. Killmon, J. Sellars, J. Woolard, C. Parrish, and A. Schwarzschild, “Linking goniometer measurements to hyperspectral and multisensor imagery for retrieval of beach properties and coastal characterization,” Proc. SPIE 8390, 1–9 (2012).

Parrish, C. E.

Petereit, R.

M. Buchhorn, R. Petereit, and B. Heim, “A manual transportable instrument platform for ground-based spectro-directional observations (ManTIS) and the resultant hyperspectral field goniometer system,” Sensors 13, 16105–16128 (2013).
[Crossref]

Peterson, Z.

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Philpot, W.

C. M. Bachmann, A. Abelev, W. Philpot, K. Z. Doctor, M. J. Montes, R. A. Fusina, R.-R. Li, and E. van Roggen, “Retrieval of sand density from hyperspectral BRDF,” Proc. SPIE 9088, 9 (2014).

C. M. Bachmann, D. Gray, A. Abelev, W. Philpot, M. J. Montes, R. Fusina, J. Musser, R.-R. Li, M. Vermillion, G. Smith, D. R. Korwan, C. Snow, W. D. Miller, J. Gardner, M. Sletten, G. Georgiev, B. Truitt, M. Killmon, J. Sellars, J. Woolard, C. Parrish, and A. Schwarzschild, “Linking goniometer measurements to hyperspectral and multisensor imagery for retrieval of beach properties and coastal characterization,” Proc. SPIE 8390, 1–9 (2012).

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Ren, X.

Z. Wang, C. A. Coburn, X. Ren, and P. M. Teillet, “Effect of surface roughness, wavelength, illumination, and viewing zenith angles on soil surface BRDF using an imaging BRDF approach,” Int. J. Remote Sens. 35, 6894–6913 (2014).
[Crossref]

Z. Wang, C. A. Coburn, X. Ren, D. Mazumdar, S. Myshak, A. Mullin, and P. M. Teillet, “Assessment of soil surface BRDF using an imaging spectrometer,” Proc. SPIE 7830, 783010 (2010).
[Crossref]

Richards, J. A.

J. A. Richards and X. Jia, Remote Sensing Digital Image Analysis: An Introduction, 4th Ed. (Springer-Verlag, 2006).

Richmond, J. C.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” Tech. Rep. (U.S. Department of Commerce, National Bureau of Standards, 1977).

Roujean, J. L.

C. Walthall, J. L. Roujean, and J. Morisette, “Field and landscape BRDF optical wavelength measurements: experience, techniques and the future,” Remote Sens. Rev. 18, 503–531 (2000).
[Crossref]

Sandmeier, S.

S. Sandmeier, C. Müller, B. Hosgood, and G. Andreoli, “Physical mechanisms in hyperspectral BRDF data of grass and watercress,” Remote Sens. Environ. 66, 222–233 (1998).
[Crossref]

Sandmeier, S. R.

S. R. Sandmeier and K. I. Itten, “A field goniometer system (FIGOS) for acquisition of hyperspectral BRDF data,” IEEE Trans. Geosci. Remote Sens 37, 978–986 (1999).
[Crossref]

Schaepman, M.

G. Schaepman-Strub, M. Schaepman, T. Painter, S. Dangel, and J. Martonchik, “Reflectance quantities in optical remote sensing—definitions and case studies,” Remote Sens. Environ. 103, 27–42 (2006).
[Crossref]

G. Strub, U. Beisl, M. Schaepman, D. Schläpfer, C. Dickerhof, and K. Itten, “Evaluation of diurnal hyperspectral HDRF data acquired with the RSL field goniometer during the DAISEX’99 campaign,” ISPRS J. Photogramm. Remote Sens. 57, 184–193 (2002).
[Crossref]

Schaepman-Strub, G.

G. Schaepman-Strub, M. Schaepman, T. Painter, S. Dangel, and J. Martonchik, “Reflectance quantities in optical remote sensing—definitions and case studies,” Remote Sens. Environ. 103, 27–42 (2006).
[Crossref]

G. Schaepman-Strub, “Spectrodirectional reflectance analysis and definition for the estimation of vegetation variables,” Ph.D. thesis, (University of Zurich, 2004).

Schläpfer, D.

G. Strub, U. Beisl, M. Schaepman, D. Schläpfer, C. Dickerhof, and K. Itten, “Evaluation of diurnal hyperspectral HDRF data acquired with the RSL field goniometer during the DAISEX’99 campaign,” ISPRS J. Photogramm. Remote Sens. 57, 184–193 (2002).
[Crossref]

Schott, J. R.

J. R. Schott, Remote Sensing: The Image Chain Approach, 2nd Ed. (Oxford University, 2007).

Schroff, K.

C. S. Bourgeois, A. Ohmura, K. Schroff, H.-J. Frei, and P. Calanca, “IAC ETH goniospectrometer: a tool for hyperspectral HDRF measurements,” J. Atmos. Oceanic Technol. 23, 573–584 (2006).
[Crossref]

Schwarzschild, A.

C. M. Bachmann, D. Gray, A. Abelev, W. Philpot, M. J. Montes, R. Fusina, J. Musser, R.-R. Li, M. Vermillion, G. Smith, D. R. Korwan, C. Snow, W. D. Miller, J. Gardner, M. Sletten, G. Georgiev, B. Truitt, M. Killmon, J. Sellars, J. Woolard, C. Parrish, and A. Schwarzschild, “Linking goniometer measurements to hyperspectral and multisensor imagery for retrieval of beach properties and coastal characterization,” Proc. SPIE 8390, 1–9 (2012).

Sellars, J.

C. M. Bachmann, D. Gray, A. Abelev, W. Philpot, M. J. Montes, R. Fusina, J. Musser, R.-R. Li, M. Vermillion, G. Smith, D. R. Korwan, C. Snow, W. D. Miller, J. Gardner, M. Sletten, G. Georgiev, B. Truitt, M. Killmon, J. Sellars, J. Woolard, C. Parrish, and A. Schwarzschild, “Linking goniometer measurements to hyperspectral and multisensor imagery for retrieval of beach properties and coastal characterization,” Proc. SPIE 8390, 1–9 (2012).

C. M. Bachmann, M. J. Montes, C. E. Parrish, R. A. Fusina, C. R. Nichols, R.-R. Li, E. Hallenborg, C. A. Jones, K. Lee, J. Sellars, S. A. White, and J. C. Fry, “A dual-spectrometer approach to reflectance measurements under sub-optimal sky conditions,” Opt. Express 20, 8959–8973 (2012).
[Crossref]

Sletten, M.

C. M. Bachmann, D. Gray, A. Abelev, W. Philpot, M. J. Montes, R. Fusina, J. Musser, R.-R. Li, M. Vermillion, G. Smith, D. R. Korwan, C. Snow, W. D. Miller, J. Gardner, M. Sletten, G. Georgiev, B. Truitt, M. Killmon, J. Sellars, J. Woolard, C. Parrish, and A. Schwarzschild, “Linking goniometer measurements to hyperspectral and multisensor imagery for retrieval of beach properties and coastal characterization,” Proc. SPIE 8390, 1–9 (2012).

Smith, G.

C. M. Bachmann, D. Gray, A. Abelev, W. Philpot, M. J. Montes, R. Fusina, J. Musser, R.-R. Li, M. Vermillion, G. Smith, D. R. Korwan, C. Snow, W. D. Miller, J. Gardner, M. Sletten, G. Georgiev, B. Truitt, M. Killmon, J. Sellars, J. Woolard, C. Parrish, and A. Schwarzschild, “Linking goniometer measurements to hyperspectral and multisensor imagery for retrieval of beach properties and coastal characterization,” Proc. SPIE 8390, 1–9 (2012).

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Snow, C.

C. M. Bachmann, D. Gray, A. Abelev, W. Philpot, M. J. Montes, R. Fusina, J. Musser, R.-R. Li, M. Vermillion, G. Smith, D. R. Korwan, C. Snow, W. D. Miller, J. Gardner, M. Sletten, G. Georgiev, B. Truitt, M. Killmon, J. Sellars, J. Woolard, C. Parrish, and A. Schwarzschild, “Linking goniometer measurements to hyperspectral and multisensor imagery for retrieval of beach properties and coastal characterization,” Proc. SPIE 8390, 1–9 (2012).

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Strahler, A. H.

J. V. Martonchik, C. J. Bruegge, and A. H. Strahler, “A review of reflectance nomenclature used in remote sensing,” Remote Sens. Rev. 19, 9–20 (2000).
[Crossref]

Strub, G.

G. Strub, U. Beisl, M. Schaepman, D. Schläpfer, C. Dickerhof, and K. Itten, “Evaluation of diurnal hyperspectral HDRF data acquired with the RSL field goniometer during the DAISEX’99 campaign,” ISPRS J. Photogramm. Remote Sens. 57, 184–193 (2002).
[Crossref]

Teillet, P. M.

Z. Wang, C. A. Coburn, X. Ren, and P. M. Teillet, “Effect of surface roughness, wavelength, illumination, and viewing zenith angles on soil surface BRDF using an imaging BRDF approach,” Int. J. Remote Sens. 35, 6894–6913 (2014).
[Crossref]

Z. Wang, C. A. Coburn, X. Ren, D. Mazumdar, S. Myshak, A. Mullin, and P. M. Teillet, “Assessment of soil surface BRDF using an imaging spectrometer,” Proc. SPIE 7830, 783010 (2010).
[Crossref]

Truitt, B.

C. M. Bachmann, D. Gray, A. Abelev, W. Philpot, M. J. Montes, R. Fusina, J. Musser, R.-R. Li, M. Vermillion, G. Smith, D. R. Korwan, C. Snow, W. D. Miller, J. Gardner, M. Sletten, G. Georgiev, B. Truitt, M. Killmon, J. Sellars, J. Woolard, C. Parrish, and A. Schwarzschild, “Linking goniometer measurements to hyperspectral and multisensor imagery for retrieval of beach properties and coastal characterization,” Proc. SPIE 8390, 1–9 (2012).

van Roggen, E.

C. M. Bachmann, A. Abelev, W. Philpot, K. Z. Doctor, M. J. Montes, R. A. Fusina, R.-R. Li, and E. van Roggen, “Retrieval of sand density from hyperspectral BRDF,” Proc. SPIE 9088, 9 (2014).

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Varmuza, K.

K. Varmuza and P. Filzmoser, Introduction to Multivariate Statistical Analysis in Chemometrics (CRC Press, 2009).

Vermillion, M.

C. M. Bachmann, D. Gray, A. Abelev, W. Philpot, M. J. Montes, R. Fusina, J. Musser, R.-R. Li, M. Vermillion, G. Smith, D. R. Korwan, C. Snow, W. D. Miller, J. Gardner, M. Sletten, G. Georgiev, B. Truitt, M. Killmon, J. Sellars, J. Woolard, C. Parrish, and A. Schwarzschild, “Linking goniometer measurements to hyperspectral and multisensor imagery for retrieval of beach properties and coastal characterization,” Proc. SPIE 8390, 1–9 (2012).

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Voss, K. J.

Vrbancich, J.

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Walthall, C.

C. Walthall, J. L. Roujean, and J. Morisette, “Field and landscape BRDF optical wavelength measurements: experience, techniques and the future,” Remote Sens. Rev. 18, 503–531 (2000).
[Crossref]

Wang, Z.

Z. Wang, C. A. Coburn, X. Ren, and P. M. Teillet, “Effect of surface roughness, wavelength, illumination, and viewing zenith angles on soil surface BRDF using an imaging BRDF approach,” Int. J. Remote Sens. 35, 6894–6913 (2014).
[Crossref]

Z. Wang, C. A. Coburn, X. Ren, D. Mazumdar, S. Myshak, A. Mullin, and P. M. Teillet, “Assessment of soil surface BRDF using an imaging spectrometer,” Proc. SPIE 7830, 783010 (2010).
[Crossref]

Westad, F.

K. H. Esbensen, D. Guyot, F. Westad, and L. P. Houmoller, Multivariate Data Analysis–in Practice, 5th Ed. (CAMO Software AS, 2004).

White, S. A.

White, T.

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Wilson, J.

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Winter, R.

C. M. Bachmann, R. J. Hughes, A. Abelev, E. van Roggen, G. Mattis, R. A. Fusina, R.-R. Li, K. Z. Doctor, D. Gray, M. J. Montes, W. Philpot, S. Carr, S. Kharabash, A. Brady, G. Smith, J. Gardner, D. R. Korwan, W. D. Miller, C. Snow, M. Vermillion, R. Liang, D. Ball, R. Hagen, G. Frick, Z. Peterson, R. Winter, J. Vrbancich, J. Eggleton, L. Hamilton, T. White, A. Fairley, D. Bongiorno, K. Hong, J. Wilson, G. L. Mason, B. Q. Gates, A. Hammond, J. Junek, and G. Christie, “Tools for hyperspectral exploitation of multi-angular spectra (THEMAS): May 2012 and June 2013 experiments,” (Naval Research Laboratory, 2015).

Woolard, J.

C. M. Bachmann, D. Gray, A. Abelev, W. Philpot, M. J. Montes, R. Fusina, J. Musser, R.-R. Li, M. Vermillion, G. Smith, D. R. Korwan, C. Snow, W. D. Miller, J. Gardner, M. Sletten, G. Georgiev, B. Truitt, M. Killmon, J. Sellars, J. Woolard, C. Parrish, and A. Schwarzschild, “Linking goniometer measurements to hyperspectral and multisensor imagery for retrieval of beach properties and coastal characterization,” Proc. SPIE 8390, 1–9 (2012).

Zhang, H.

Appl. Opt. (2)

IEEE Trans. Geosci. Remote Sens (1)

S. R. Sandmeier and K. I. Itten, “A field goniometer system (FIGOS) for acquisition of hyperspectral BRDF data,” IEEE Trans. Geosci. Remote Sens 37, 978–986 (1999).
[Crossref]

Int. J. Remote Sens. (2)

E. J. Milton, “Review article principles of field spectroscopy,” Int. J. Remote Sens. 8, 1807–1827 (1987).
[Crossref]

Z. Wang, C. A. Coburn, X. Ren, and P. M. Teillet, “Effect of surface roughness, wavelength, illumination, and viewing zenith angles on soil surface BRDF using an imaging BRDF approach,” Int. J. Remote Sens. 35, 6894–6913 (2014).
[Crossref]

ISPRS J. Photogramm. Remote Sens. (1)

G. Strub, U. Beisl, M. Schaepman, D. Schläpfer, C. Dickerhof, and K. Itten, “Evaluation of diurnal hyperspectral HDRF data acquired with the RSL field goniometer during the DAISEX’99 campaign,” ISPRS J. Photogramm. Remote Sens. 57, 184–193 (2002).
[Crossref]

J. Atmos. Oceanic Technol. (1)

C. S. Bourgeois, A. Ohmura, K. Schroff, H.-J. Frei, and P. Calanca, “IAC ETH goniospectrometer: a tool for hyperspectral HDRF measurements,” J. Atmos. Oceanic Technol. 23, 573–584 (2006).
[Crossref]

Opt. Express (1)

Proc. SPIE (3)

Z. Wang, C. A. Coburn, X. Ren, D. Mazumdar, S. Myshak, A. Mullin, and P. M. Teillet, “Assessment of soil surface BRDF using an imaging spectrometer,” Proc. SPIE 7830, 783010 (2010).
[Crossref]

C. M. Bachmann, A. Abelev, W. Philpot, K. Z. Doctor, M. J. Montes, R. A. Fusina, R.-R. Li, and E. van Roggen, “Retrieval of sand density from hyperspectral BRDF,” Proc. SPIE 9088, 9 (2014).

C. M. Bachmann, D. Gray, A. Abelev, W. Philpot, M. J. Montes, R. Fusina, J. Musser, R.-R. Li, M. Vermillion, G. Smith, D. R. Korwan, C. Snow, W. D. Miller, J. Gardner, M. Sletten, G. Georgiev, B. Truitt, M. Killmon, J. Sellars, J. Woolard, C. Parrish, and A. Schwarzschild, “Linking goniometer measurements to hyperspectral and multisensor imagery for retrieval of beach properties and coastal characterization,” Proc. SPIE 8390, 1–9 (2012).

Remote Sens. Environ. (2)

S. Sandmeier, C. Müller, B. Hosgood, and G. Andreoli, “Physical mechanisms in hyperspectral BRDF data of grass and watercress,” Remote Sens. Environ. 66, 222–233 (1998).
[Crossref]

G. Schaepman-Strub, M. Schaepman, T. Painter, S. Dangel, and J. Martonchik, “Reflectance quantities in optical remote sensing—definitions and case studies,” Remote Sens. Environ. 103, 27–42 (2006).
[Crossref]

Remote Sens. Rev. (2)

C. Walthall, J. L. Roujean, and J. Morisette, “Field and landscape BRDF optical wavelength measurements: experience, techniques and the future,” Remote Sens. Rev. 18, 503–531 (2000).
[Crossref]

J. V. Martonchik, C. J. Bruegge, and A. H. Strahler, “A review of reflectance nomenclature used in remote sensing,” Remote Sens. Rev. 19, 9–20 (2000).
[Crossref]

Sensors (1)

M. Buchhorn, R. Petereit, and B. Heim, “A manual transportable instrument platform for ground-based spectro-directional observations (ManTIS) and the resultant hyperspectral field goniometer system,” Sensors 13, 16105–16128 (2013).
[Crossref]

Other (12)

J. R. Schott, Remote Sensing: The Image Chain Approach, 2nd Ed. (Oxford University, 2007).

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” Tech. Rep. (U.S. Department of Commerce, National Bureau of Standards, 1977).

R. McCluney, Introduction to Radiometry and Photometry (Artech House, 1994).

F. Camacho-de Coca, F. J. Garcia-Haro, and M. A. Gilbert, “Quantitative analysis of cropland’s BRDF anisotropy using airborne POLDER data,” in Proc. 1st International Symposium on Recent Advances in Quantitative Remote Sensing, Torrent (2002), pp. 1–7.

G. Schaepman-Strub, “Spectrodirectional reflectance analysis and definition for the estimation of vegetation variables,” Ph.D. thesis, (University of Zurich, 2004).

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Figures (16)

Fig. 1.
Fig. 1. Concept of incident and reflected angles in spherical coordinate system.
Fig. 2.
Fig. 2. Geometrical aspects of reflectance factor nomenclature used in this study: the bidirectional (BRF) (a), the conical–conical (CCRF) (b), the hemispherical–conical (HCRF) (c), and the hemispherical–directional (HDRF) (d).
Fig. 3.
Fig. 3. Queensland, Australia: Freshwater Beach, Port Clinton Pocket Beach, and Sabina Point Beach.
Fig. 4.
Fig. 4. Sand bubbler crab (Dotilla fenestrate) creates sand balls at low tide (a), and the pattern created from the sand balls on the smooth sand (b).
Fig. 5.
Fig. 5. GOPHER instrument. (a) A schematic drawing of the GOPHER as viewed from above. (b) An example scanning grid pattern, where green dots represent the positions of the spectrometer. (c) The scan cycle starts at the nadir (0° zenith and 0° azimuth angles) and the red arrows show the first few positions of the spectrometer.
Fig. 6.
Fig. 6. Dual spectrometer approach. A spectrometer measuring the radiance of the reference white Spectralon plaque (a) continuously at the base station while the goniospectrometer (b) is taking the hemispherical scan at the GOPHER’s station. The two spectrometers are located close to each other, so the light conditions are similar. Prior to each spectral measurement cycle, radiance from a reference white plaque of standardized material Spectralon (c) was measured from the nadir position, and was used to calculate the reflectance from the measured radiance as a part of the dual-spectrometer algorithm [25].
Fig. 7.
Fig. 7. Example of improved spectra using the dual-spectrometer method. These are plots of spectra from a full hemispherical scan cycle. The gray shows the spectra measured at off-nadir directions, whereas the purple and green indicate the spectra measured while observing at the nadir (perpendicular to the leveled horizontal plane). Reflectance spectra processed using only the GOPHER’s white Spectralon reference obtained prior to the hemispherical ground scan (a) and reflectance spectra that are radiometrically corrected using the dual spectrometer approach (b).
Fig. 8.
Fig. 8. Elements of the GOPHER spectra BRDF rendering. (a) The grid is the goniospectrometer’s hemispherical sampling pattern of the scanning cycle. The solar zenith angle throughout this scan is between 50.3° and 52.5° and the solar azimuth angle is between 319.6° and 316.3° from north in clockwise direction. The range of the sun’s movement during the scan and its position is plotted in magenta. The letter “N” indicates the geographical north direction in relation to goniospectrometer’s grid. (b) The mechanisms responsible when the dominant reflection is in each of the labeled areas.
Fig. 9.
Fig. 9. Beach sand sampling station FWB-1-2. (a) and (c)–(f) show the renderings of nondimensionalized reflectance factor [%] at 450.6, 702.9, 1159.7, 1542, and 2212.8 nm, respectively. (b) Plot of the spectra of the full hemispherical scan cycle. Spectra in gray were measured from off-nadir direction, and teal indicates the spectra measured from nadir direction. The peaks in the BRDF renderings are similar at each selected wavelength.
Fig. 10.
Fig. 10. Beach sand sampling station FWB-6-2. (b): plot of the spectra of the full hemispherical scan cycle. Spectra in gray were measured from off-nadir direction, and teal indicates the spectra measured from nadir direction. (a) and (c)–(f) show the renderings of nondimensionalized reflectance factor [in percent] at 450.6, 702.9, 1159.7, 1542, and 2212.8 nm, respectively. The peaks of renderings (d) and (e) (702.9, 1159.7 nm) are similar. This is also the case for the renderings in (c) and (f) (1542, 2212.8 nm), whereas the rendering at (a) (450.6 nm) also has a prominent forward-scattered peak.
Fig. 11.
Fig. 11. (a) ANIF of FWB-1-2and (b) the ANIF of FWB-6-2, where the colors represent the view zenith angles in degrees. The nondimensionalized reflectance factor in the solar principal plane of these same stations are shown in (c) FWB-1-2 and (d) FWB-6-2, where the colors denote the different wavelengths, of which every tenth is plotted for figure clarity reasons. The 180° represents the backscattering and 0° the forward-scattering direction.
Fig. 12.
Fig. 12. Sampling station SPB-1-1: (a) rendering of nondimensionalized reflectance factor at 1159.7 nm, (b) solar principal plane, and (c) plane of 30 and 210° plot of every tenth of wavelength.
Fig. 13.
Fig. 13. First and second principal components (PC1 and PC2) of (a and b) FWB-1-2 and (c and d): FWB-6-2 sand sampling stations. The scale of PC2 renderings is the same as the corresponding PC1 for comparison. PC1 of FWB-1-2: (a) contains 99.29% of variance from all wavelengths and PC2, and (b) contains 0.48% additional variance, which is 99.77 cumulative % variance. PC1 of FWB-6-2 (c) contains 94.76% of variance from all wavelengths, and PC2 (d) contains 2.67% additional variance, which is 99.77 cumulative % variance.
Fig. 14.
Fig. 14. Correlation matrix from: (a) FWB-1-2 and (b) FWB-6-2 sampling stations. The axes show the wavelengths, which are not equally spaced. The white area represents no data, which is the region of the removed bands due to unacceptable atmospheric absorption (bad bands). The highest correlation is 1 (along the diagonal) and the lowest is 0. Since the correlation at all the sampling stations is very high, the scale on each correlation figure is limited to between 0.8 and 1, so they can be compared.
Fig. 15.
Fig. 15. Examples of sand samples measured at GOPHER stations exhibiting smooth surfaces. The station names are indicated on the left side of the photos. The photos were taken with a portable digital microscope (second column), and the scale bar shown on them is a millimeter scale. The wooden ruler on the photos in the first column is in metric scale. The length of the ruler is 50 cm. The correlation matrices related to the sand samples are in the third column.
Fig. 16.
Fig. 16. Examples of sand samples measured at GOPHER stations exhibiting visually rough surfaces. The station names are indicated on the left side of the photos. The photos in the second column, (a) and (c)–(e), were taken with a portable digital microscope, and the scale bar shown on them is a millimeter scale. The wooden ruler on the photos in the first column is in metric scale. The length of the ruler is 50 cm. The correlation matrices are in the third column.

Tables (2)

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Table 1. Symbols and Notations

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Table 2. Grain Size Distribution

Equations (9)

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f DD ( θ i , ϕ i ; θ r , ϕ r ) = d L r ( θ i , ϕ i ; θ r , ϕ r ) d E i ( θ i , ϕ i ) ,
ANIF = R ( θ i , ϕ i , 2 π ; θ r , ϕ r , ω r ; λ ) R 0 ( θ i , ϕ i , 2 π ; θ r = 0 , ϕ r , ω r ; λ ) ,
BRF ( θ i , ϕ i , ω i 0 ; θ r , ϕ r , ω r ) = d Φ r ( θ i , ϕ i , θ r , ϕ r ) d Φ i id ( θ i , ϕ i ) = cos θ r sin θ r d L r ( θ i , ϕ i ; θ r , ϕ r ) d θ r d ϕ r d A cos θ r sin θ r d L i id ( θ i , ϕ i ) d θ r d ϕ r d A = f DD ( θ i , ϕ i ; θ r , ϕ r ) f id ( θ i , ϕ i ) = π f DD ( θ i , ϕ i ; θ r , ϕ r ) .
HCRF ( θ i , ϕ i , 2 π ; θ r , ϕ r , ω r ) = 1 Ω r 2 π ω r f HC ( θ r , ϕ r ) d Ω r d Ω i .
HCRF ( θ i , ϕ i , 2 π ; θ r , ϕ r , ω r ) = d R ( θ i , ϕ i , ω i 0 ; θ r , ϕ r , ω r 0 ) + ( 1 d ) R ( θ i , ϕ i , 2 π ; θ r , ϕ r , ω r ) ,
HDRF ( θ i , ϕ i , 2 π ; θ r , ϕ r , ω r 0 ) = 2 π f HD ( θ r , ϕ r ) d Ω i = 0 2 π 0 π 2 f HD ( θ r , ϕ r ) cos θ i sin θ i d θ i d ϕ i = 0 2 π 1 2 f HD ( θ r , ϕ r ) d ϕ i = π f HD ( θ r , ϕ r ) .
HDRF ( θ i , ϕ i , 2 π ; θ r , ϕ r , ω r 0 , λ ) = C id , gon ( λ ) 1 n m t = 1 n L r id , base ( t , λ ) L r id , gon ( t , λ ) t = 1 m L r gon ( t , λ ) L r id , base ( t , λ ) ,
f DD ( θ i , ϕ i ; θ r , ϕ r ; λ ) f HD ( θ r , ϕ r ; λ ) = HDRF ( θ i , ϕ i , 2 π ; θ r , ϕ r , ω r 0 ; λ ) π = 1 π C id , gon ( λ ) 1 n m t = 1 n L r id , base ( t , λ ) L r id , gon ( t , λ ) t = 1 m L r gon ( t , λ ) L r id , base ( t , λ ) ,
f HD , nonD ( θ r , ϕ r ; λ ) = R ( θ r , ϕ r ; λ x ) R min ( λ ) R max ( λ ) R min ( λ ) 100 [ % ] = R nonD ( λ ) ,

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