Bidirectional transmittance and reflectance models for soil signature analysis.

The propagation of radiation in an absorbing-scattering soil with constant or spatial variation of the refractive index is investigated. The soil consists of a plane parallel with Fresnel reflection at the boundaries and is exposed at one boundary to a diffuse or collimated incident radiation. The discrete spherical harmonics method using Marshak boundary conditions is introduced to approximate the directional hemispherical reflectance and transmittance as well as the bidirectional reflectance. The effect in spatial variation of the refractive index on the reflectance and transmittance predictions is examined. A comparison of the directional transmittance and reflectance with the literature results demonstrates that the present method gives accurate results for optically thin and thick soil with a maximum relative error in all cases less than 1%. The bidirectional radiance for variable refractive index soils also shows excellent agreement as compared to the literature results. The results demonstrated that the anisotropic soil interfaces cause a significant decrease of energy reflected and transmitted as well as the bidirectional reflectance.

[1]  W. Verhoef,et al.  Coupled soil–leaf-canopy and atmosphere radiative transfer modeling to simulate hyperspectral multi-angular surface reflectance and TOA radiance data , 2007 .

[2]  G. Campbell,et al.  Simple equation to approximate the bidirectional reflectance from vegetative canopies and bare soil surfaces. , 1985, Applied optics.

[3]  William R. Reynolds,et al.  Theory and measurement of bidirectional reflectance for signature analysis , 1999, Defense, Security, and Sensing.

[4]  S. Fujimura,et al.  Nondestructive measurement of chlorophyll pigment content in plant leaves from three-color reflectance and transmittance. , 1991, Applied optics.

[5]  Bruce Hapke,et al.  Bidirectional Reflectance Spectroscopy: 5. The Coherent Backscatter Opposition Effect and Anisotropic Scattering , 2002 .

[6]  James C. Jafolla,et al.  Phenomenological BRDF modeling for engineering applications , 1997, Optics & Photonics.

[7]  Michael I. Mishchenko,et al.  Asymmetry parameters of the phase function for densely packed scattering grains , 1994 .

[8]  Hao Zhang,et al.  Comparisons of bidirectional reflectance distribution function measurements on prepared particulate surfaces and radiative-transfer models. , 2005, Applied optics.

[9]  F. Baret,et al.  MARMIT: A multilayer radiative transfer model of soil reflectance to estimate surface soil moisture content in the solar domain (400–2500 nm) , 2018, Remote Sensing of Environment.

[10]  Shenglu Zhou,et al.  Analysis of soil chronosequence studies using reflectance spectroscopy , 2016 .

[11]  A. Huete,et al.  Assessment of biophysical soil properties through spectral decomposition techniques , 1991 .

[12]  Chih-Yang Wu,et al.  Discrete ordinates solution of radiative heat transfer in a refractive two-layer slab with collimated irradiation , 2011 .

[13]  W. Lipiński,et al.  COMBINED TWO-FLUX APPROXIMATION AND MONTE CARLO MODEL FOR IDENTIFICATION OF RADIATIVE PROPERTIES OF HIGHLY SCATTERING DISPERSED MATERIALS , 2012 .

[14]  Stephen J. Wright,et al.  Reconstruction in optical tomography using the PN approximations , 2006 .

[15]  D. Yemele,et al.  Discrete spherical harmonics method for radiative transfer in scalar planar inhomogeneous atmosphere. , 2018, Journal of the Optical Society of America. A, Optics, image science, and vision.

[16]  K. Stamnes,et al.  Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media. , 1988, Applied optics.

[17]  Ming Xie,et al.  Analysis of transient radiative transfer induced by an incident short-pulsed laser in a graded-index medium with Fresnel boundaries. , 2017, Applied optics.

[18]  Dmitry Yudovsky,et al.  Simple and accurate expressions for diffuse reflectance of semi-infinite and two-layer absorbing and scattering media. , 2009, Applied optics.

[19]  Y. Hong,et al.  Monte Carlo simulation of radiative transfer in a medium with varying refractive index specified at discrete points , 2017 .

[20]  Dominique Baillis,et al.  Use of Mie theory to analyze experimental data to identify infrared properties of fused quartz containing bubbles. , 2005, Applied optics.

[21]  Chih-Yang Wu,et al.  Radiative transfer in a two-layer slab with Fresnel interfaces , 1996 .

[22]  K. Shepherd,et al.  Development of Reflectance Spectral Libraries for Characterization of Soil Properties , 2002 .

[23]  Viacheslav I. Adamchuk,et al.  A global spectral library to characterize the world’s soil , 2016 .

[24]  David W. Graham,et al.  Prediction and measurement of soil bidirectional reflectance , 1992, IEEE Trans. Geosci. Remote. Sens..

[25]  Chih-Yang Wu,et al.  Modified differential approximation for radiative transfer in a scattering medium with specularly reflecting boundaries , 1991 .

[26]  Hervé Thierry Tagne Kamdem,et al.  A discrete spherical harmonics method for radiative transfer analysis in inhomogeneous polarized planar atmosphere , 2018, 1802.01631.

[27]  K. Shepherd,et al.  Application of mid-infrared spectroscopy for rapid characterization of key soil properties for engineering land use , 2015 .

[28]  H. Tan,et al.  Short-pulsed laser transport in two-dimensional scattering media by natural element method. , 2014, Journal of the Optical Society of America. A, Optics, image science, and vision.

[29]  J. Hillier.  Scattering of Light by Composite Particles in a Planetary Surface , 1997 .

[30]  H. Kamdem,et al.  The Discrete Ordinates Characteristics Solution to the One-Dimensional Radiative Transfer Equation , 2017 .

[31]  H. Tan,et al.  Least-squares natural element method for radiative heat transfer in graded index medium with semitransparent surfaces , 2013 .

[32]  L. Dombrovsky.  THE USE OF TRANSPORT APPROXIMATION AND DIFFUSION-BASED MODELS IN RADIATIVE TRANSFER CALCULATIONS , 2012 .

[33]  Antoine Karam,et al.  Visible near infrared reflectance spectroscopy prediction of soil heavy metal concentrations in paper mill biosolid- and liming by-product-amended agricultural soils , 2017 .

[34]  Peter N. Raven,et al.  Bidirectional reflectance from pigmented coatings , 1999, Optics & Photonics.

[35]  B. Hapke.  Bidirectional reflectance spectroscopy: 1. Theory , 1981 .

[36]  H. Tan,et al.  Simultaneous radiation and conduction heat transfer in a graded index semitransparent slab with gray boundaries , 2002 .

[37]  Z. Shi,et al.  Measurement and simulation of bi‐directional reflectance on three zonal soils in the south‐east of China , 2007 .

[38]  INFLUENCE OF REFRACTIVE INDEX ON REFLECTANCE FROM A SEMI-INFINITE ABSORBING-SCATTERING MEDIUM WITH COLLIMATED INCIDENT RADIATION* , 1975 .

[39]  J. Randrianalisoa,et al.  Modified two-flux approximation for identification of radiative properties of absorbing and scattering media from directional-hemispherical measurements. , 2006, Journal of the Optical Society of America. A, Optics, image science, and vision.

[40]  Chih-Yang Wu,et al.  Azimuthally dependent radiative transfer in a slab with variable refractive index , 2008 .

[41]  Chih-Yang Wu.  Monte Carlo simulation of radiative transfer in a refractive layered medium , 2010 .

[42]  H. Kamdem,et al.  Hyperbolic Conduction–Radiation in Participating and Inhomogeneous Slab With Double Spherical Harmonics and Lattice Boltzmann Methods , 2017 .

[43]  K. Cooper,et al.  A Monte Carlo Reflectance Model for Soil Surfaces with Three-Dimensional Structure , 1985, IEEE Transactions on Geoscience and Remote Sensing.

[44]  Simon R. Arridge,et al.  Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements , 2011, J. Comput. Phys..

[45]  Yufeng Ge,et al.  Mid-infrared attenuated total reflectance spectroscopy for soil carbon and particle size determination , 2014 .

[46]  Qin Chen,et al.  Fast method of retrieving the asymmetry factor and scattering albedo from the maximum time-resolved reflectance of participating media. , 2015, Applied optics.

[47]  R. Dickinson,et al.  A physical model for predicting bidirectional reflectances over bare soil , 1989 .

[48]  M. Fukuhara,et al.  Estimation of complex refractive index of soil particles and its dependence on soil chemical properties , 1991 .

[49]  Jacqueline Lenoble,et al.  A MODEL FOR THE BIDIRECTIONAL POLARIZED REFLECTANCE OF SNOW , 1999 .

[50]  D. Courault,et al.  Bidirectional reflectance of bare soil surfaces in the visible and near‐infrared range , 1993 .

[51]  Wenjiang Huang,et al.  Extension of the Hapke bidirectional reflectance model to retrieve soil water content , 2011 .

[52]  D. Kimes.  Modeling the directional reflectance from complete homogeneous vegetation canopies with various leaf-orientation distributions , 1984 .

[53]  Simon Arridge,et al.  Incorporating reflection boundary conditions in the Neumann series radiative transport equation: application to photon propagation and reconstruction in diffuse optical imaging. , 2018, Biomedical optics express.

[54]  F. Baret,et al.  Modeling Spectral and Bidirectional Soil Reflectance , 1992 .

[55]  Simple and accurate expressions for diffuse reflectance of semi-infinite and two-layer absorbing and scattering media: erratum. , 2015, Applied optics.

[56]  Subir Das,et al.  Numerical Solution of Two-Dimensional Solute Transport System Using Operational Matrices , 2018, Transport in Porous Media.