Abstract

The bidirectional reflectance factor (BRF) is commonly used to study the structure of a particulate surface based on photometric measurements. In this paper, we describe the bidirectional reflectance factor distribution of natural particulate surfaces with particles sizes varying from 0.15 mm to 0.9 mm. Two types of natural particulate surfaces (one with low reflectance and the other with moderate reflectance) were measured at visible and near-infrared wavelengths using the Northeast Normal University Laboratory Goniospectrometer System (NENULGS). Both the BRFs and anisotropic reflectance factors (ARFs) at selected wavelengths were compared with previously published results to verify the accuracy of our measurements, and we also quantitatively analyzed the effects of particle size on the BRF. It was found that the maximum reflectance difference, which was more distinct for the low-reflectance samples, between particulate surfaces with particle sizes of 0.15 mm and 0.9 mm occurred in the forward scattering direction for all samples, and the value of this maximum difference reached 59% for the low-reflectance samples. Then, we conducted a test of a photometric model to determine which parameters could be confidently linked to the surfaces’ reflectance behavior. The inverted parameters were compared with the known physical parameters of our samples, such as the particle size. We found that the single-scattering albedo could be empirically used to determine the particle sizes of our samples when measurements of particulate surfaces with different particle sizes were performed under the same incidence conditions and with wide viewing angles. The potential applications of our results appear very promising for empirically resolving the spatial distribution of particle size within a given particulate sample as well as for deepening our understanding of the scattering properties of particulate media.

© 2016 Optical Society of America

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    [Crossref]

2015 (4)

J. Cierniewski, C. Kazmierowski, and S. Krolewicz, “Evaluation of the effects of surface roughness on the relationship between soil BRF data and broadban albedo,” IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 8(4), 1528–1533 (2015).
[Crossref]

Z. Sun, Y. Lv, and S. Lu, “An assessment of the bidirectional reflectance models basing on laboratory experiment of natural particulate surfaces,” J. Quant. Spectrosc. Ra. 163, 102–119 (2015).
[Crossref]

O. Kemppinen, T. Nousiainen, and H. Lindqvist, “The impact of surface roughness on scattering by realistically shaped wavelength-scale dust particles,” J. Quant. Spectrosc. Ra. 150, 55–67 (2015).
[Crossref]

G. Videen and K. Muinonen, “Light-scattering evolution from particles to regolith,” J. Quant. Spectrosc. Ra. 150, 87–94 (2015).
[Crossref]

2014 (5)

J. Peltoniemi, T. Hakala, J. Suomalainen, E. Honkavaara, L. Markelin, M. Gritsevich, J. Eskelinen, P. Jaanson, and E. Ikonen, “Technical notes: A detailed study for the provision of measurement uncertainty and traceability for goniospectrometers,” J. Quant. Spectrosc. Ra. 146, 376–390 (2014).
[Crossref]

Z. Sun, J. Zhang, Z. Tong, and Y. Zhao, “Particle size effects on the reflectance and negative polarization of light backscattered from natural surface particulate medium: Soil and sand,” J. Quant. Spectrosc. Ra. 133, 1–12 (2014).
[Crossref]

Z. Q. Sun, Z. F. Wu, and Y. S. Zhao, “Semi-automatic laboratory goniospectrometer system for performing multi-angular reflectance and polarization measurements for natural surfaces,” Rev. Sci. Instrum. 85(1), 014503 (2014).
[Crossref] [PubMed]

C. M. Bachmann, W. Philpot, A. Abelev, and D. Korwan, “Phase angle dependence of sand density observable in hyperspectral reflectance,” Remote Sens. Environ. 150, 53–65 (2014).
[Crossref]

H. Croft, K. Anderson, and N. Kuhn, “Evaluating the influence of surface soil moisture and soil surface roughness on optical directional reflectance factors,” Eur. J. Soil Sci. 65(4), 605–612 (2014).
[Crossref]

2013 (1)

Z. Sun, J. Zhang, and Y. Zhao, “Laboratory studies of polarized light reflection from sea ice and lake ice in visible and near infrared,” IEEE Geosci. Remote Sens. Lett. 10(1), 170–173 (2013).
[Crossref]

2012 (3)

P. Litvinov, O. Hasekamp, O. Dubovik, and B. Cairns, “Model for land surface reflectance treatment: physical derivation application for bare soil and evaluation on airborne and satellite measurements,” J. Quant. Spectrosc. Ra. 113(16), 2023–2039 (2012).
[Crossref]

Y. Shkuratov, V. Kaydash, V. Korokhin, Y. Velikodsky, D. Petrov, E. Zubko, D. Stankevich, and G. Videen, “A critical assessment of the Hapke photometric model,” J. Quant. Spectrosc. Ra. 113(18), 2431–2456 (2012).
[Crossref]

H. Croft, K. Anderson, and N. Kuhn, “Reflectance anisotropy for measuring soil surface roughness of multiple soil types,” Catena 93, 87–96 (2012).
[Crossref]

2011 (4)

A. L. Souchon, P. C. Pinet, S. D. Chevrel, Y. H. Daydou, D. Baratoux, K. Kurita, M. K. Shepard, and P. Helfenstein, “An experimental study of Hapke’s modeling of natural granular surfaces samples,” Icarus 215(1), 313–331 (2011).
[Crossref]

Z. Sun and Y. Zhao, “The effects of grain size on bidirectional polarized reflectance factor measurements of snow,” J. Quant. Spectrosc. Ra. 112(14), 2372–2383 (2011).
[Crossref]

H. Zhang and K. J. Voss, “On Hapke photometric model predictions on reflectance of closely packed particulate surfaces,” Icarus 215(1), 27–33 (2011).
[Crossref]

P. Litvinov, O. Hasekamp, and B. Cairns, “Models for surface reflection of radiance and polarized radiance: comparison with airborne multi-angle photopolarimetric measurements and implications for modeling top-of-atmosphere measurements,” Remote Sens. Environ. 115(2), 781–792 (2011).
[Crossref]

2010 (2)

A. Chappell, S. V. Pelt, T. Zobeck, and Z. Dong, “Estimating aerodynamic resistance of rough surfaces using angular reflectance,” Remote Sens. Environ. 114(7), 1462–1470 (2010).
[Crossref]

J. Cierniewski and M. Gulinski, “Furrow microrelief influence on the directional hyperspectral reflectance of soil at various illumination and observation conditions,” IEEE Trans. Geosci. Rem. Sens. 48(11), 4143–4148 (2010).

2009 (5)

J. Peltoniemi, T. Hakala, J. Suomalainen, and E. Puttonen, “Polarised bidirectional reflectance factor measurements from soil, stones, and snow,” J. Quant. Spectrosc. Ra. 110(17), 1940–1953 (2009).
[Crossref]

K. Muinonen, T. Nousiainen, H. Lindqvist, O. Munoz, and G. Videen, “Light scattering by Gaussian particles with internal inclusions and roughened surfaces using ray optics,” J. Quant. Spectrosc. Ra. 110(14-16), 1628–1639 (2009).
[Crossref]

C. Wu, A. R. Jacobson, M. Laba, and P. C. Baveye, “Accounting for surface roughness effects in the near-infrared reflectance sensing of soils,” Geoderma 152(1-2), 171–180 (2009).
[Crossref]

K. Anderson and H. Croft, “Remote sensing of soil surface properties,” Prog. Phys. Geogr. 33(4), 457–473 (2009).
[Crossref]

M. E. Schaepman, S. L. Ustin, A. J. Plaza, T. H. Painter, J. Verrelst, and S. Liang, “Earth system science related imaging spectroscopy-An assessment,” Remote Sens. Environ. 113, S123–S137 (2009).
[Crossref]

2008 (2)

M. I. Mishchenko, “Multiple scattering radiative transfer, and weak localization in discrete random medium: unified microphysical approach,” Rev. Geophys. 46(2), RG2003 (2008).
[Crossref]

B. Hapke, “Bidirectional reflectance spectroscopy. 6. Effects of porosity,” Icarus 195(2), 918–926 (2008).
[Crossref]

2007 (6)

J. Peltoniemi, J. Piironen, J. Naranen, J. Suomalainen, R. Kuittinen, L. Markelin, and E. Honkavaara, “Bidirectional reflectance spectrometry of gravel at the Sjokulla test field,” ISPRS J. Photogramm. Remote Sens. 62(6), 434–446 (2007).
[Crossref]

Y. Shkuratov, S. Bondarenko, V. Kaydash, G. Videen, O. Munoz, and H. Volten, “Photometry and polarimetry of particulate surfaces and aerosol particles over a wide range of phase angles,” J. Quant. Spectrosc. Ra. 106(1-3), 487–508 (2007).
[Crossref]

H. A. Ghrefat, P. C. Goodell, B. E. Hubbard, R. P. Langford, and R. E. Aldouri, “Modeling grain size variations of aeolian gypsum deposits at White Sands, New Mexico, using AVIRIS imagery,” Geomorphology 88(1-2), 57–68 (2007).
[Crossref]

A. Chappell, C. Strong, G. McTainsh, and J. Leys, “Detecting induced in situ erodibility of a dust-producing playa in Australia using a bi-directional soil spectral reflectance model,” Remote Sens. Environ. 106(4), 508–524 (2007).
[Crossref]

M. K. Shepard and P. A. Helfenstein, “A test of the Hapke photometric model,” J. Geophys. Res. 112(E3), E03001 (2007).
[Crossref]

T. Nousiainen and K. Muinonen, “Surface-roughness effects on single-scattering properties of wavelength-scale particles,” J. Quant. Spectrosc. Ra. 106(1-3), 389–397 (2007).
[Crossref]

2006 (3)

A. Chappell, T. M. Zobeck, and G. Brunner, “Using bi-directional soil spectral reflectance to model soil surface changes induced by rainfall and wind-tunnel abrasion,” Remote Sens. Environ. 102(3-4), 328–343 (2006).
[Crossref]

G. S. Okin, D. A. Gillette, and J. E. Herrick, “Multi-scale controls on and consequences of aeolian processes in landscape change in arid and semi-arid environments,” J. Arid Environ. 65(2), 253–275 (2006).
[Crossref]

Y. Shkuratov, S. Bondarenko, A. Ovcharenko, C. Pieters, T. Hiroi, H. Volten, O. Munoz, and G. Videen, “Comparative studies of the reflectance and degree of linear polarization of particulate surfaces and independently scattering particles,” J. Quant. Spectrosc. Ra. 100(1-3), 340–358 (2006).
[Crossref]

2005 (1)

2004 (3)

C. Li, G. W. Kattawar, and P. Yang, “Effects of surface roughness on light scattering by small particles,” J. Quant. Spectrosc. Ra. 89(1-4), 123–131 (2004).
[Crossref]

G. S. Okin and T. H. Painter, “Effect of grain size on remeotely sensed spectral reflectance of desert sandy desert surfaces,” Remote Sens. Environ. 89(3), 272–280 (2004).
[Crossref]

J. Cierniewski, T. Gdala, and A. Karnieli, “A hemispherical-directional reflectance model as a tool for understanding image distinctions between cultivated and uncultivated bare surfaces,” Remote Sens. Environ. 90(4), 505–523 (2004).
[Crossref]

2003 (3)

H. Zhang, K. J. Voss, R. P. Reid, and M. Louchard, “Bidirectional reflectance measurements of sediments in the vicinity of Lee Stocking Island, Bahamas,” Limnol. Oceanogr. 48(1), 380–389 (2003).
[Crossref]

A. M. Cord, P. C. Pinet, Y. Daydou, and S. D. Chevrel, “Planetary regolith surface analogs: optimized determination of Hapke parameters using multi-angular spectro-imaging laboratory data,” Icarus 165(2), 414–427 (2003).
[Crossref]

T. Nousiainen, K. Muinonen, and P. Raisanen, “Scattering of light by large Saharan dust particles in a modified ray optics approximation,” J. Geophys. Res. 108(D1), 4025 (2003).
[Crossref]

2002 (5)

K. D. Shepherd and M. G. Walsh, “Development of reflectance spectral libraries for characterization of soil properties,” Soil Sci. Soc. Am. J. 66(3), 988–998 (2002).
[Crossref]

Y. Shkuratov, A. Ovcharenko, E. Zubko, O. Miloslavskaya, K. Muinonen, J. Piironen, R. Nelson, W. Smythe, V. Rosenbush, and P. Helfenstein, “The opposition effect and negative polarization of structural analogs for planetary regoliths,” Icarus 159(2), 396–416 (2002).
[Crossref]

B. Hapke, “Bidirectional reflectance spectroscopy. 5. The coherent backscatter opposition effect and anisotropic scattering,” Icarus 157(2), 523–534 (2002).
[Crossref]

J. Cierniewski and A. Karnieli, “Virtual surfaces simulating the bidirectional reflectance of semi-arid soils,” Int. J. Remote Sens. 23(19), 4019–4037 (2002).
[Crossref]

A. Kamei and A. M. Nakamura, “Laboratory study of the bidirectional reflectance of powdered surfaces: on the asymmetry parameter of asteroid photometric data,” Icarus 156(2), 551–561 (2002).
[Crossref]

2000 (1)

A. W. Nolin and S. Liang, “Progress in bidirectional reflectance modeling and applications for surface particulate media: snow and soils,” Remote Sens. Rev. 18(2-4), 307–342 (2000).
[Crossref]

1999 (4)

Y. Shkuratov, L. Starukina, H. Hoffman, and G. Arnold, “A model of spectral albedo of particulate surfaces: Implications for optical properties of the Moon,” Icarus 137(2), 235–246 (1999).
[Crossref]

M. I. Mishchenko, J. M. Dlugach, E. G. Yanovitskij, and N. T. Zakharova, “Bidirectional reflectance of flat, optically thick particulate layers: an efficient radiative transfer solution and applications to snow and soil surfaces,” J. Quant. Spectrosc. Ra. 63(2-6), 409–432 (1999).
[Crossref]

D. J. Diner, G. P. Asner, R. Davies, Y. Knyazikhin, J. Muller, A. W. Nolin, B. Pinty, C. B. Schaaf, and J. Stroeve, “New directions in earth observing: scientific applications of multiangle remote sensing,” Bull. Am. Meteorol. Soc. 80(11), 2209–2228 (1999).
[Crossref]

B. Cairns, E. E. Russell, and L. D. Travis, “The research scanning polarimeter: Calibration and ground-based measurements,” Proc. SPIE 3745, 186–196 (1999).
[Crossref]

1998 (1)

St. Sandmeier, Ch. Muller, B. Hosgood, and G. Andreoli, “Physical mechanisms in hyperspectral BRDF data of grass and watercress,” Remote Sens. Environ. 66(2), 222–233 (1998).
[Crossref]

1997 (1)

M. I. Mishchenko and A. Macke, “Asymmetry parameters of the phase function for isolated and densely packed spherical particles with multiple internal inclusions in the geometric optics limit,” J. Quant. Spectrosc. Ra. 57(6), 767–794 (1997).
[Crossref]

1995 (1)

A. F. McGuire and B. Hapke, “An experimental study of light scattering by large, irregular particles,” Icarus 113(1), 134–155 (1995).
[Crossref]

1994 (1)

M. I. Mishchenko, “Asymmetry parameters of the phase function for densely packed scattering grains,” J. Quant. Spectrosc. Ra. 52(1), 95–110 (1994).
[Crossref]

1993 (2)

F. Baret, S. Jacquemoud, and J. F. Hanocq, “About the soil line concept in remote sensing,” Adv. Space Res. 13(5), 281–284 (1993).
[Crossref]

F. Baret, S. Jacquemoud, and J. F. Hanocq, “The soil line concept in remote sensing,” Remote Sens. Rev. 7(1), 65–82 (1993).
[Crossref]

1992 (2)

S. Jacquemound, F. Bater, and J. F. Hanocq, “Modeling spectral and bidirectional soil reflectance,” Remote Sens. Environ. 41(2-3), 123–132 (1992).
[Crossref]

P. E. Johnson, M. O. Smith, and J. B. Adams, “Simple algorithms for remote determination of mineral abundances and particles from reflectance spectra,” J. Geophys. Res. 97(E2), 3649–3657 (1992).
[Crossref]

1991 (1)

E. C. I. Paisley, N. Lancaster, L. R. Gaddis, and R. Greeley, “Discrimination of active and inactive desert sand from remote sensing: Kelso dunes, Mojave Desert, California,” Remote Sens. Environ. 37(3), 153–166 (1991).
[Crossref]

1990 (1)

G. Blount, M. O. Smith, J. B. Adams, R. Greeley, and P. R. Christensen, “Regional Aeolian dynamics and desert mixing in the Gran Desierto: evidence from Landsat Thematic Mapper images,” J. Geophys. Res. 95(B10), 15463–15482 (1990).
[Crossref]

1989 (1)

B. Pinty, M. M. Verstraete, and R. E. Dickinson, “A physical model for predicting bidirectional reflectance over bare soil,” Remote Sens. Environ. 27(3), 273–288 (1989).
[Crossref]

1986 (1)

B. Hapke, “Bidirectional reflectance spectroscopy. 4. The extinction coefficient and the opposition effect,” Icarus 67(2), 264–280 (1986).
[Crossref]

1984 (1)

B. Hapke, “Bidirectional reflectance spectroscopy. 3. Correction for macroscopic roughness,” Icarus 59(1), 41–59 (1984).
[Crossref]

1981 (1)

B. Hapke, “Bidirectional reflectance spectroscopy. 1. Theory,” J. Geophys. Res. 86(B4), 3039–3054 (1981).
[Crossref]

1977 (1)

G. Hunt, “Spectral signatures of particulate minerals in the visible and near infrared,” Geophysics 42(3), 501–513 (1977).
[Crossref]

1968 (1)

J. W. Salisbury and G. R. Hunt, “Martian surface materials: effect of particle size on spectral behavior,” Science 161(3839), 365–366 (1968).
[Crossref] [PubMed]

Abelev, A.

C. M. Bachmann, W. Philpot, A. Abelev, and D. Korwan, “Phase angle dependence of sand density observable in hyperspectral reflectance,” Remote Sens. Environ. 150, 53–65 (2014).
[Crossref]

Adams, J. B.

P. E. Johnson, M. O. Smith, and J. B. Adams, “Simple algorithms for remote determination of mineral abundances and particles from reflectance spectra,” J. Geophys. Res. 97(E2), 3649–3657 (1992).
[Crossref]

G. Blount, M. O. Smith, J. B. Adams, R. Greeley, and P. R. Christensen, “Regional Aeolian dynamics and desert mixing in the Gran Desierto: evidence from Landsat Thematic Mapper images,” J. Geophys. Res. 95(B10), 15463–15482 (1990).
[Crossref]

Aldouri, R. E.

H. A. Ghrefat, P. C. Goodell, B. E. Hubbard, R. P. Langford, and R. E. Aldouri, “Modeling grain size variations of aeolian gypsum deposits at White Sands, New Mexico, using AVIRIS imagery,” Geomorphology 88(1-2), 57–68 (2007).
[Crossref]

Anderson, K.

H. Croft, K. Anderson, and N. Kuhn, “Evaluating the influence of surface soil moisture and soil surface roughness on optical directional reflectance factors,” Eur. J. Soil Sci. 65(4), 605–612 (2014).
[Crossref]

H. Croft, K. Anderson, and N. Kuhn, “Reflectance anisotropy for measuring soil surface roughness of multiple soil types,” Catena 93, 87–96 (2012).
[Crossref]

K. Anderson and H. Croft, “Remote sensing of soil surface properties,” Prog. Phys. Geogr. 33(4), 457–473 (2009).
[Crossref]

Andreoli, G.

St. Sandmeier, Ch. Muller, B. Hosgood, and G. Andreoli, “Physical mechanisms in hyperspectral BRDF data of grass and watercress,” Remote Sens. Environ. 66(2), 222–233 (1998).
[Crossref]

Arnold, G.

Y. Shkuratov, L. Starukina, H. Hoffman, and G. Arnold, “A model of spectral albedo of particulate surfaces: Implications for optical properties of the Moon,” Icarus 137(2), 235–246 (1999).
[Crossref]

Asner, G. P.

D. J. Diner, G. P. Asner, R. Davies, Y. Knyazikhin, J. Muller, A. W. Nolin, B. Pinty, C. B. Schaaf, and J. Stroeve, “New directions in earth observing: scientific applications of multiangle remote sensing,” Bull. Am. Meteorol. Soc. 80(11), 2209–2228 (1999).
[Crossref]

Bachmann, C. M.

C. M. Bachmann, W. Philpot, A. Abelev, and D. Korwan, “Phase angle dependence of sand density observable in hyperspectral reflectance,” Remote Sens. Environ. 150, 53–65 (2014).
[Crossref]

Baratoux, D.

A. L. Souchon, P. C. Pinet, S. D. Chevrel, Y. H. Daydou, D. Baratoux, K. Kurita, M. K. Shepard, and P. Helfenstein, “An experimental study of Hapke’s modeling of natural granular surfaces samples,” Icarus 215(1), 313–331 (2011).
[Crossref]

Baret, F.

F. Baret, S. Jacquemoud, and J. F. Hanocq, “About the soil line concept in remote sensing,” Adv. Space Res. 13(5), 281–284 (1993).
[Crossref]

F. Baret, S. Jacquemoud, and J. F. Hanocq, “The soil line concept in remote sensing,” Remote Sens. Rev. 7(1), 65–82 (1993).
[Crossref]

Bater, F.

S. Jacquemound, F. Bater, and J. F. Hanocq, “Modeling spectral and bidirectional soil reflectance,” Remote Sens. Environ. 41(2-3), 123–132 (1992).
[Crossref]

Baveye, P. C.

C. Wu, A. R. Jacobson, M. Laba, and P. C. Baveye, “Accounting for surface roughness effects in the near-infrared reflectance sensing of soils,” Geoderma 152(1-2), 171–180 (2009).
[Crossref]

Blount, G.

G. Blount, M. O. Smith, J. B. Adams, R. Greeley, and P. R. Christensen, “Regional Aeolian dynamics and desert mixing in the Gran Desierto: evidence from Landsat Thematic Mapper images,” J. Geophys. Res. 95(B10), 15463–15482 (1990).
[Crossref]

Bondarenko, S.

Y. Shkuratov, S. Bondarenko, V. Kaydash, G. Videen, O. Munoz, and H. Volten, “Photometry and polarimetry of particulate surfaces and aerosol particles over a wide range of phase angles,” J. Quant. Spectrosc. Ra. 106(1-3), 487–508 (2007).
[Crossref]

Y. Shkuratov, S. Bondarenko, A. Ovcharenko, C. Pieters, T. Hiroi, H. Volten, O. Munoz, and G. Videen, “Comparative studies of the reflectance and degree of linear polarization of particulate surfaces and independently scattering particles,” J. Quant. Spectrosc. Ra. 100(1-3), 340–358 (2006).
[Crossref]

Brunner, G.

A. Chappell, T. M. Zobeck, and G. Brunner, “Using bi-directional soil spectral reflectance to model soil surface changes induced by rainfall and wind-tunnel abrasion,” Remote Sens. Environ. 102(3-4), 328–343 (2006).
[Crossref]

Cairns, B.

P. Litvinov, O. Hasekamp, O. Dubovik, and B. Cairns, “Model for land surface reflectance treatment: physical derivation application for bare soil and evaluation on airborne and satellite measurements,” J. Quant. Spectrosc. Ra. 113(16), 2023–2039 (2012).
[Crossref]

P. Litvinov, O. Hasekamp, and B. Cairns, “Models for surface reflection of radiance and polarized radiance: comparison with airborne multi-angle photopolarimetric measurements and implications for modeling top-of-atmosphere measurements,” Remote Sens. Environ. 115(2), 781–792 (2011).
[Crossref]

B. Cairns, E. E. Russell, and L. D. Travis, “The research scanning polarimeter: Calibration and ground-based measurements,” Proc. SPIE 3745, 186–196 (1999).
[Crossref]

Chappell, A.

A. Chappell, S. V. Pelt, T. Zobeck, and Z. Dong, “Estimating aerodynamic resistance of rough surfaces using angular reflectance,” Remote Sens. Environ. 114(7), 1462–1470 (2010).
[Crossref]

A. Chappell, C. Strong, G. McTainsh, and J. Leys, “Detecting induced in situ erodibility of a dust-producing playa in Australia using a bi-directional soil spectral reflectance model,” Remote Sens. Environ. 106(4), 508–524 (2007).
[Crossref]

A. Chappell, T. M. Zobeck, and G. Brunner, “Using bi-directional soil spectral reflectance to model soil surface changes induced by rainfall and wind-tunnel abrasion,” Remote Sens. Environ. 102(3-4), 328–343 (2006).
[Crossref]

Chevrel, S. D.

A. L. Souchon, P. C. Pinet, S. D. Chevrel, Y. H. Daydou, D. Baratoux, K. Kurita, M. K. Shepard, and P. Helfenstein, “An experimental study of Hapke’s modeling of natural granular surfaces samples,” Icarus 215(1), 313–331 (2011).
[Crossref]

A. M. Cord, P. C. Pinet, Y. Daydou, and S. D. Chevrel, “Planetary regolith surface analogs: optimized determination of Hapke parameters using multi-angular spectro-imaging laboratory data,” Icarus 165(2), 414–427 (2003).
[Crossref]

Christensen, P. R.

G. Blount, M. O. Smith, J. B. Adams, R. Greeley, and P. R. Christensen, “Regional Aeolian dynamics and desert mixing in the Gran Desierto: evidence from Landsat Thematic Mapper images,” J. Geophys. Res. 95(B10), 15463–15482 (1990).
[Crossref]

Cierniewski, J.

J. Cierniewski, C. Kazmierowski, and S. Krolewicz, “Evaluation of the effects of surface roughness on the relationship between soil BRF data and broadban albedo,” IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 8(4), 1528–1533 (2015).
[Crossref]

J. Cierniewski and M. Gulinski, “Furrow microrelief influence on the directional hyperspectral reflectance of soil at various illumination and observation conditions,” IEEE Trans. Geosci. Rem. Sens. 48(11), 4143–4148 (2010).

J. Cierniewski, T. Gdala, and A. Karnieli, “A hemispherical-directional reflectance model as a tool for understanding image distinctions between cultivated and uncultivated bare surfaces,” Remote Sens. Environ. 90(4), 505–523 (2004).
[Crossref]

J. Cierniewski and A. Karnieli, “Virtual surfaces simulating the bidirectional reflectance of semi-arid soils,” Int. J. Remote Sens. 23(19), 4019–4037 (2002).
[Crossref]

Cord, A. M.

A. M. Cord, P. C. Pinet, Y. Daydou, and S. D. Chevrel, “Planetary regolith surface analogs: optimized determination of Hapke parameters using multi-angular spectro-imaging laboratory data,” Icarus 165(2), 414–427 (2003).
[Crossref]

Croft, H.

H. Croft, K. Anderson, and N. Kuhn, “Evaluating the influence of surface soil moisture and soil surface roughness on optical directional reflectance factors,” Eur. J. Soil Sci. 65(4), 605–612 (2014).
[Crossref]

H. Croft, K. Anderson, and N. Kuhn, “Reflectance anisotropy for measuring soil surface roughness of multiple soil types,” Catena 93, 87–96 (2012).
[Crossref]

K. Anderson and H. Croft, “Remote sensing of soil surface properties,” Prog. Phys. Geogr. 33(4), 457–473 (2009).
[Crossref]

Davies, R.

D. J. Diner, G. P. Asner, R. Davies, Y. Knyazikhin, J. Muller, A. W. Nolin, B. Pinty, C. B. Schaaf, and J. Stroeve, “New directions in earth observing: scientific applications of multiangle remote sensing,” Bull. Am. Meteorol. Soc. 80(11), 2209–2228 (1999).
[Crossref]

Daydou, Y.

A. M. Cord, P. C. Pinet, Y. Daydou, and S. D. Chevrel, “Planetary regolith surface analogs: optimized determination of Hapke parameters using multi-angular spectro-imaging laboratory data,” Icarus 165(2), 414–427 (2003).
[Crossref]

Daydou, Y. H.

A. L. Souchon, P. C. Pinet, S. D. Chevrel, Y. H. Daydou, D. Baratoux, K. Kurita, M. K. Shepard, and P. Helfenstein, “An experimental study of Hapke’s modeling of natural granular surfaces samples,” Icarus 215(1), 313–331 (2011).
[Crossref]

Dickinson, R. E.

B. Pinty, M. M. Verstraete, and R. E. Dickinson, “A physical model for predicting bidirectional reflectance over bare soil,” Remote Sens. Environ. 27(3), 273–288 (1989).
[Crossref]

Diner, D. J.

D. J. Diner, G. P. Asner, R. Davies, Y. Knyazikhin, J. Muller, A. W. Nolin, B. Pinty, C. B. Schaaf, and J. Stroeve, “New directions in earth observing: scientific applications of multiangle remote sensing,” Bull. Am. Meteorol. Soc. 80(11), 2209–2228 (1999).
[Crossref]

Dlugach, J. M.

M. I. Mishchenko, J. M. Dlugach, E. G. Yanovitskij, and N. T. Zakharova, “Bidirectional reflectance of flat, optically thick particulate layers: an efficient radiative transfer solution and applications to snow and soil surfaces,” J. Quant. Spectrosc. Ra. 63(2-6), 409–432 (1999).
[Crossref]

Dong, Z.

A. Chappell, S. V. Pelt, T. Zobeck, and Z. Dong, “Estimating aerodynamic resistance of rough surfaces using angular reflectance,” Remote Sens. Environ. 114(7), 1462–1470 (2010).
[Crossref]

Dubovik, O.

P. Litvinov, O. Hasekamp, O. Dubovik, and B. Cairns, “Model for land surface reflectance treatment: physical derivation application for bare soil and evaluation on airborne and satellite measurements,” J. Quant. Spectrosc. Ra. 113(16), 2023–2039 (2012).
[Crossref]

Eskelinen, J.

J. Peltoniemi, T. Hakala, J. Suomalainen, E. Honkavaara, L. Markelin, M. Gritsevich, J. Eskelinen, P. Jaanson, and E. Ikonen, “Technical notes: A detailed study for the provision of measurement uncertainty and traceability for goniospectrometers,” J. Quant. Spectrosc. Ra. 146, 376–390 (2014).
[Crossref]

Gaddis, L. R.

E. C. I. Paisley, N. Lancaster, L. R. Gaddis, and R. Greeley, “Discrimination of active and inactive desert sand from remote sensing: Kelso dunes, Mojave Desert, California,” Remote Sens. Environ. 37(3), 153–166 (1991).
[Crossref]

Gdala, T.

J. Cierniewski, T. Gdala, and A. Karnieli, “A hemispherical-directional reflectance model as a tool for understanding image distinctions between cultivated and uncultivated bare surfaces,” Remote Sens. Environ. 90(4), 505–523 (2004).
[Crossref]

Ghrefat, H. A.

H. A. Ghrefat, P. C. Goodell, B. E. Hubbard, R. P. Langford, and R. E. Aldouri, “Modeling grain size variations of aeolian gypsum deposits at White Sands, New Mexico, using AVIRIS imagery,” Geomorphology 88(1-2), 57–68 (2007).
[Crossref]

Gillette, D. A.

G. S. Okin, D. A. Gillette, and J. E. Herrick, “Multi-scale controls on and consequences of aeolian processes in landscape change in arid and semi-arid environments,” J. Arid Environ. 65(2), 253–275 (2006).
[Crossref]

Goodell, P. C.

H. A. Ghrefat, P. C. Goodell, B. E. Hubbard, R. P. Langford, and R. E. Aldouri, “Modeling grain size variations of aeolian gypsum deposits at White Sands, New Mexico, using AVIRIS imagery,” Geomorphology 88(1-2), 57–68 (2007).
[Crossref]

Greeley, R.

E. C. I. Paisley, N. Lancaster, L. R. Gaddis, and R. Greeley, “Discrimination of active and inactive desert sand from remote sensing: Kelso dunes, Mojave Desert, California,” Remote Sens. Environ. 37(3), 153–166 (1991).
[Crossref]

G. Blount, M. O. Smith, J. B. Adams, R. Greeley, and P. R. Christensen, “Regional Aeolian dynamics and desert mixing in the Gran Desierto: evidence from Landsat Thematic Mapper images,” J. Geophys. Res. 95(B10), 15463–15482 (1990).
[Crossref]

Gritsevich, M.

J. Peltoniemi, T. Hakala, J. Suomalainen, E. Honkavaara, L. Markelin, M. Gritsevich, J. Eskelinen, P. Jaanson, and E. Ikonen, “Technical notes: A detailed study for the provision of measurement uncertainty and traceability for goniospectrometers,” J. Quant. Spectrosc. Ra. 146, 376–390 (2014).
[Crossref]

Gulinski, M.

J. Cierniewski and M. Gulinski, “Furrow microrelief influence on the directional hyperspectral reflectance of soil at various illumination and observation conditions,” IEEE Trans. Geosci. Rem. Sens. 48(11), 4143–4148 (2010).

Hakala, T.

J. Peltoniemi, T. Hakala, J. Suomalainen, E. Honkavaara, L. Markelin, M. Gritsevich, J. Eskelinen, P. Jaanson, and E. Ikonen, “Technical notes: A detailed study for the provision of measurement uncertainty and traceability for goniospectrometers,” J. Quant. Spectrosc. Ra. 146, 376–390 (2014).
[Crossref]

J. Peltoniemi, T. Hakala, J. Suomalainen, and E. Puttonen, “Polarised bidirectional reflectance factor measurements from soil, stones, and snow,” J. Quant. Spectrosc. Ra. 110(17), 1940–1953 (2009).
[Crossref]

Hanocq, J. F.

F. Baret, S. Jacquemoud, and J. F. Hanocq, “The soil line concept in remote sensing,” Remote Sens. Rev. 7(1), 65–82 (1993).
[Crossref]

F. Baret, S. Jacquemoud, and J. F. Hanocq, “About the soil line concept in remote sensing,” Adv. Space Res. 13(5), 281–284 (1993).
[Crossref]

S. Jacquemound, F. Bater, and J. F. Hanocq, “Modeling spectral and bidirectional soil reflectance,” Remote Sens. Environ. 41(2-3), 123–132 (1992).
[Crossref]

Hapke, B.

B. Hapke, “Bidirectional reflectance spectroscopy. 6. Effects of porosity,” Icarus 195(2), 918–926 (2008).
[Crossref]

B. Hapke, “Bidirectional reflectance spectroscopy. 5. The coherent backscatter opposition effect and anisotropic scattering,” Icarus 157(2), 523–534 (2002).
[Crossref]

A. F. McGuire and B. Hapke, “An experimental study of light scattering by large, irregular particles,” Icarus 113(1), 134–155 (1995).
[Crossref]

B. Hapke, “Bidirectional reflectance spectroscopy. 4. The extinction coefficient and the opposition effect,” Icarus 67(2), 264–280 (1986).
[Crossref]

B. Hapke, “Bidirectional reflectance spectroscopy. 3. Correction for macroscopic roughness,” Icarus 59(1), 41–59 (1984).
[Crossref]

B. Hapke, “Bidirectional reflectance spectroscopy. 1. Theory,” J. Geophys. Res. 86(B4), 3039–3054 (1981).
[Crossref]

Hasekamp, O.

P. Litvinov, O. Hasekamp, O. Dubovik, and B. Cairns, “Model for land surface reflectance treatment: physical derivation application for bare soil and evaluation on airborne and satellite measurements,” J. Quant. Spectrosc. Ra. 113(16), 2023–2039 (2012).
[Crossref]

P. Litvinov, O. Hasekamp, and B. Cairns, “Models for surface reflection of radiance and polarized radiance: comparison with airborne multi-angle photopolarimetric measurements and implications for modeling top-of-atmosphere measurements,” Remote Sens. Environ. 115(2), 781–792 (2011).
[Crossref]

Helfenstein, P.

A. L. Souchon, P. C. Pinet, S. D. Chevrel, Y. H. Daydou, D. Baratoux, K. Kurita, M. K. Shepard, and P. Helfenstein, “An experimental study of Hapke’s modeling of natural granular surfaces samples,” Icarus 215(1), 313–331 (2011).
[Crossref]

Y. Shkuratov, A. Ovcharenko, E. Zubko, O. Miloslavskaya, K. Muinonen, J. Piironen, R. Nelson, W. Smythe, V. Rosenbush, and P. Helfenstein, “The opposition effect and negative polarization of structural analogs for planetary regoliths,” Icarus 159(2), 396–416 (2002).
[Crossref]

Helfenstein, P. A.

M. K. Shepard and P. A. Helfenstein, “A test of the Hapke photometric model,” J. Geophys. Res. 112(E3), E03001 (2007).
[Crossref]

Herrick, J. E.

G. S. Okin, D. A. Gillette, and J. E. Herrick, “Multi-scale controls on and consequences of aeolian processes in landscape change in arid and semi-arid environments,” J. Arid Environ. 65(2), 253–275 (2006).
[Crossref]

Hiroi, T.

Y. Shkuratov, S. Bondarenko, A. Ovcharenko, C. Pieters, T. Hiroi, H. Volten, O. Munoz, and G. Videen, “Comparative studies of the reflectance and degree of linear polarization of particulate surfaces and independently scattering particles,” J. Quant. Spectrosc. Ra. 100(1-3), 340–358 (2006).
[Crossref]

Hoffman, H.

Y. Shkuratov, L. Starukina, H. Hoffman, and G. Arnold, “A model of spectral albedo of particulate surfaces: Implications for optical properties of the Moon,” Icarus 137(2), 235–246 (1999).
[Crossref]

Honkavaara, E.

J. Peltoniemi, T. Hakala, J. Suomalainen, E. Honkavaara, L. Markelin, M. Gritsevich, J. Eskelinen, P. Jaanson, and E. Ikonen, “Technical notes: A detailed study for the provision of measurement uncertainty and traceability for goniospectrometers,” J. Quant. Spectrosc. Ra. 146, 376–390 (2014).
[Crossref]

J. Peltoniemi, J. Piironen, J. Naranen, J. Suomalainen, R. Kuittinen, L. Markelin, and E. Honkavaara, “Bidirectional reflectance spectrometry of gravel at the Sjokulla test field,” ISPRS J. Photogramm. Remote Sens. 62(6), 434–446 (2007).
[Crossref]

Hosgood, B.

St. Sandmeier, Ch. Muller, B. Hosgood, and G. Andreoli, “Physical mechanisms in hyperspectral BRDF data of grass and watercress,” Remote Sens. Environ. 66(2), 222–233 (1998).
[Crossref]

Hubbard, B. E.

H. A. Ghrefat, P. C. Goodell, B. E. Hubbard, R. P. Langford, and R. E. Aldouri, “Modeling grain size variations of aeolian gypsum deposits at White Sands, New Mexico, using AVIRIS imagery,” Geomorphology 88(1-2), 57–68 (2007).
[Crossref]

Hunt, G.

G. Hunt, “Spectral signatures of particulate minerals in the visible and near infrared,” Geophysics 42(3), 501–513 (1977).
[Crossref]

Hunt, G. R.

J. W. Salisbury and G. R. Hunt, “Martian surface materials: effect of particle size on spectral behavior,” Science 161(3839), 365–366 (1968).
[Crossref] [PubMed]

Ikonen, E.

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Y. Shkuratov, V. Kaydash, V. Korokhin, Y. Velikodsky, D. Petrov, E. Zubko, D. Stankevich, and G. Videen, “A critical assessment of the Hapke photometric model,” J. Quant. Spectrosc. Ra. 113(18), 2431–2456 (2012).
[Crossref]

Y. Shkuratov, S. Bondarenko, V. Kaydash, G. Videen, O. Munoz, and H. Volten, “Photometry and polarimetry of particulate surfaces and aerosol particles over a wide range of phase angles,” J. Quant. Spectrosc. Ra. 106(1-3), 487–508 (2007).
[Crossref]

Y. Shkuratov, S. Bondarenko, A. Ovcharenko, C. Pieters, T. Hiroi, H. Volten, O. Munoz, and G. Videen, “Comparative studies of the reflectance and degree of linear polarization of particulate surfaces and independently scattering particles,” J. Quant. Spectrosc. Ra. 100(1-3), 340–358 (2006).
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Y. Shkuratov, A. Ovcharenko, E. Zubko, O. Miloslavskaya, K. Muinonen, J. Piironen, R. Nelson, W. Smythe, V. Rosenbush, and P. Helfenstein, “The opposition effect and negative polarization of structural analogs for planetary regoliths,” Icarus 159(2), 396–416 (2002).
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Y. Shkuratov, L. Starukina, H. Hoffman, and G. Arnold, “A model of spectral albedo of particulate surfaces: Implications for optical properties of the Moon,” Icarus 137(2), 235–246 (1999).
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P. E. Johnson, M. O. Smith, and J. B. Adams, “Simple algorithms for remote determination of mineral abundances and particles from reflectance spectra,” J. Geophys. Res. 97(E2), 3649–3657 (1992).
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Y. Shkuratov, A. Ovcharenko, E. Zubko, O. Miloslavskaya, K. Muinonen, J. Piironen, R. Nelson, W. Smythe, V. Rosenbush, and P. Helfenstein, “The opposition effect and negative polarization of structural analogs for planetary regoliths,” Icarus 159(2), 396–416 (2002).
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A. L. Souchon, P. C. Pinet, S. D. Chevrel, Y. H. Daydou, D. Baratoux, K. Kurita, M. K. Shepard, and P. Helfenstein, “An experimental study of Hapke’s modeling of natural granular surfaces samples,” Icarus 215(1), 313–331 (2011).
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Y. Shkuratov, V. Kaydash, V. Korokhin, Y. Velikodsky, D. Petrov, E. Zubko, D. Stankevich, and G. Videen, “A critical assessment of the Hapke photometric model,” J. Quant. Spectrosc. Ra. 113(18), 2431–2456 (2012).
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Y. Shkuratov, L. Starukina, H. Hoffman, and G. Arnold, “A model of spectral albedo of particulate surfaces: Implications for optical properties of the Moon,” Icarus 137(2), 235–246 (1999).
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Z. Sun, Y. Lv, and S. Lu, “An assessment of the bidirectional reflectance models basing on laboratory experiment of natural particulate surfaces,” J. Quant. Spectrosc. Ra. 163, 102–119 (2015).
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Z. Sun, J. Zhang, Z. Tong, and Y. Zhao, “Particle size effects on the reflectance and negative polarization of light backscattered from natural surface particulate medium: Soil and sand,” J. Quant. Spectrosc. Ra. 133, 1–12 (2014).
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Z. Sun, J. Zhang, and Y. Zhao, “Laboratory studies of polarized light reflection from sea ice and lake ice in visible and near infrared,” IEEE Geosci. Remote Sens. Lett. 10(1), 170–173 (2013).
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Z. Sun and Y. Zhao, “The effects of grain size on bidirectional polarized reflectance factor measurements of snow,” J. Quant. Spectrosc. Ra. 112(14), 2372–2383 (2011).
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Z. Q. Sun, Z. F. Wu, and Y. S. Zhao, “Semi-automatic laboratory goniospectrometer system for performing multi-angular reflectance and polarization measurements for natural surfaces,” Rev. Sci. Instrum. 85(1), 014503 (2014).
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Y. Shkuratov, S. Bondarenko, A. Ovcharenko, C. Pieters, T. Hiroi, H. Volten, O. Munoz, and G. Videen, “Comparative studies of the reflectance and degree of linear polarization of particulate surfaces and independently scattering particles,” J. Quant. Spectrosc. Ra. 100(1-3), 340–358 (2006).
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Y. Shkuratov, S. Bondarenko, V. Kaydash, G. Videen, O. Munoz, and H. Volten, “Photometry and polarimetry of particulate surfaces and aerosol particles over a wide range of phase angles,” J. Quant. Spectrosc. Ra. 106(1-3), 487–508 (2007).
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Y. Shkuratov, S. Bondarenko, A. Ovcharenko, C. Pieters, T. Hiroi, H. Volten, O. Munoz, and G. Videen, “Comparative studies of the reflectance and degree of linear polarization of particulate surfaces and independently scattering particles,” J. Quant. Spectrosc. Ra. 100(1-3), 340–358 (2006).
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Z. Q. Sun, Z. F. Wu, and Y. S. Zhao, “Semi-automatic laboratory goniospectrometer system for performing multi-angular reflectance and polarization measurements for natural surfaces,” Rev. Sci. Instrum. 85(1), 014503 (2014).
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K. Muinonen, T. Nousiainen, H. Lindqvist, O. Munoz, and G. Videen, “Light scattering by Gaussian particles with internal inclusions and roughened surfaces using ray optics,” J. Quant. Spectrosc. Ra. 110(14-16), 1628–1639 (2009).
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Z. Sun and Y. Zhao, “The effects of grain size on bidirectional polarized reflectance factor measurements of snow,” J. Quant. Spectrosc. Ra. 112(14), 2372–2383 (2011).
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J. Peltoniemi, T. Hakala, J. Suomalainen, E. Honkavaara, L. Markelin, M. Gritsevich, J. Eskelinen, P. Jaanson, and E. Ikonen, “Technical notes: A detailed study for the provision of measurement uncertainty and traceability for goniospectrometers,” J. Quant. Spectrosc. Ra. 146, 376–390 (2014).
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H. Zhang, K. J. Voss, R. P. Reid, and M. Louchard, “Bidirectional reflectance measurements of sediments in the vicinity of Lee Stocking Island, Bahamas,” Limnol. Oceanogr. 48(1), 380–389 (2003).
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Figures (18)

Fig. 1
Fig. 1 The photomicrographs of our samples, A corresponding to 0.375 mm desert sand, B corresponding to 0.375 mm cultivated soil, and the small-scale surface structure of A and B are designated as C and D, respectively.
Fig. 2
Fig. 2 The reflectance curves of particulate surfaces with a particle size of 0.9 mm at different viewing zenith angles in the principal plane, where the incident zenith angle was 60°. For both types of particulate surfaces, the minimum reflectance was observed in the forward scattering direction (−60°) and the maximum reflectance was observed in the backward scattering direction (52°).
Fig. 3
Fig. 3 The reflectance curves of particulate surfaces with a particle size of 0.45 mm measured in the nadir direction, for incident zenith angles of 45° and 60°, respectively. The upper two curves correspond to the desert sand surface, and the lower two curves correspond to the cultivated soil surface.
Fig. 4
Fig. 4 The reflectance curves of particulate surfaces with different particle sizes measured in the nadir direction for an incident zenith angle of 45°
Fig. 5
Fig. 5 The ARFs of desert sand surfaces with different particle sizes measured at different viewing zenith angles in the principal plane; the incident angle was 45°, and the wavelength was 670 nm.
Fig. 6
Fig. 6 The ARFs of particulate surfaces with different particle sizes measured at different viewing zenith angles; the incident zenith angle was 45°, and the wavelength was 1589 nm. The negative viewing angles correspond to the forward scattering direction.
Fig. 7
Fig. 7 Polar plots of the BRFs of cultivated soil surfaces with different particle sizes for all viewing zenith angles at 1589 nm; the incident angle was 60°. The radial distance from the center of each plot represents the viewing zenith angle, with a maximum value of 70°. Rotation about the center represents a change in azimuth. An azimuthal angle of 0° corresponds to backward reflectance in half of the illumination principal plane. Near the hot spot (from 52° to 68°), the absent values were replaced with the values corresponding to a viewing zenith angle of 68°.
Fig. 8
Fig. 8 Polar plots of the BRFs of desert sand surfaces with different particle sizes for all viewing zenith angles at 1589 nm; the incident angle was 60°.
Fig. 9
Fig. 9 The polar plots of ARFs of cultivated soil with different particle size for all viewing zenith angles at 1589 nm; the incident angle was 60°.
Fig. 10
Fig. 10 The polar plots of ARFs of desert sand with different particle size for all viewing zenith angles at 1589 nm; the incident angle was 60°.
Fig. 11
Fig. 11 The change in the sample BRF from a particle size of 0.9 mm to a particle size of 0.15 mm ((BRF0.15mm-BRF0.9mm)/BRF0.9mm) for an incident zenith angle of 45° at 1589 nm; the cultivated soil results are shown on the left, and the desert sand results are shown on the right.
Fig. 12
Fig. 12 The change in the sample BRF from a particle size of 0.9 mm to a particle size of 0.15 mm ((BRF0.15mm-BRF0.9mm)/BRF0.9mm) for an incident zenith angle of 60°; the cultivated soil results are shown on the left, and the desert sand results are shown on the right.
Fig. 13
Fig. 13 Comparison between the measured and modeled BRFs of cultivated soil surfaces with particle sizes of 0.9 mm, 0.45 mm and 0.3 mm at 1589 nm for an incident zenith angle of 60°.
Fig. 14
Fig. 14 The values of the difference (R-Rm)/Rm between the measured and modeled BRFs of desert sand surfaces with particle sizes of 0.9 mm, 0.45 mm and 0.3 mm at 1589 nm for an incident zenith angle of 45°.
Fig. 15
Fig. 15 Polar plots of R2 that represent the logarithmic regression relationship between the BRF of a cultivated soil surface and the particle size at 1589 nm (left) and the linear regression relationship between the BRF of a desert sand surface and the particle size at 1589 nm (right), for an incident zenith angle of 45°.
Fig. 16
Fig. 16 The logarithmic relationship between the BRF of a cultivated soil surface and the particle size at 1589 nm and the linear relationship between the BRF of a desert sand surface and the particle size at 1589 nm; the incident zenith angle was 45°, and the BRF was measured in the nadir direction.
Fig. 17
Fig. 17 The regression relationship between the single-scattering albedo (SSA) inverted based on all viewing directions and the particle size for both types of samples, for an incident zenith angle of 45°.
Fig. 18
Fig. 18 The regression relationship between the single-scattering albedo (SSA) inverted based on all viewing directions and the particle size for both types of samples, for an incident zenith angle of 60°.

Tables (14)

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Table 1 The average value from 10 samples was used to characteristic each soil property considered in this study. N indicates that we did not measure this parameter. C-soil stands for cultivated soil.

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Table 2 The best-fit parameters of the model for the cultivated soil at 1589 nm with an incident zenith angle of 45°.

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Table 3 The best-fit parameters of the model for the desert sand at 1589 nm with an incident zenith angle of 45°.

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Table 4 The best-fit parameters of the model for the cultivated soil at 1589 nm with an incident zenith angle of 60°.

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Table 5 The best-fit parameters of the model for the desert sand at 1589 nm with an incident zenith angle of 60°.

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Table 6 The best-fit parameters of the model for the cultivated soil at 865 nm with an incident zenith angle of 45°.

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Table 7 The best fitted parameters of model for desert sand at 865 nm, the incident zenith angle was 45°.

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Table 8 The best fitted parameters of model for cultivated soil at 865 nm, the incident zenith angle was 60°.

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Table 9 The best fitted parameters of model for desert sand at 865 nm, the incident zenith angle was 60°.

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Table 10 The best fitted parameters of model for cultivated soil at 1589 nm in the principal plane, the incident zenith angle was 45°.

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Table 11 The best fitted parameters of model for dessert sand at 1589 nm in the principal plane, the incident zenith angle was 45°.

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Table 12 The best fitted parameters of model for cultivated soil at 865 nm in the principal plane, the incident zenith angle was 45°.

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Table 13 The best fitted parameters of model for desert sand at 865 nm in the principal plane, the incident zenith angle was 45°.

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Table 14 The best fitted parameters of model for dessert sand at 1589 nm in the principal plane, the incident zenith angle was 60°.

Equations (11)

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R= ω 4 μ 0 μ 0 +μ {[1+B(α,h)]P(α,α')+H( μ 0 )H(μ)1}
cosα'=cosicosesinisinecosφ
cosα=cosicose+sinisinecosφ
B(α,h)= 1 1+(1/h)tan(α/2)
P(α,α')=1+bcosα+c 3 cos 2 α1 2 +b'cosα'+c' 3 cos 2 α'1 2
H(x)= 1+2x 1+2 x(1ω)
R eff = i n R i 3 ( ΔN ΔR ) i i n R i 2 ( ΔN ΔR ) i
( ΔN ΔR )i= 3 4πρ R i 3 Δ M i Δ R i
BRF= dL'(i, φ i ;e, φ e ) dL(i, φ i ;e, φ e )
ARF= BRF(λ,i, φ i ;e, φ e ) BR F nadir (λ,i, φ i )
RMSE= k=1 n ( R m R) 2 N f

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