Book contents
- Frontmatter
- Contents
- Acknowledgments
- 1 Introduction
- 2 Electromagnetic wave propagation
- 3 The absorption of light
- 4 Specular reflection
- 5 Single-particle scattering: perfect spheres
- 6 Single-particle scattering: irregular particles
- 7 Propagation in a nonuniform medium: the equation of radiative transfer
- 8 The bidirectional reflectance of a semi-infinite medium
- 9 The opposition effect
- 10 A miscellany of bidirectional reflectances and related quantities
- 11 Integrated reflectances and planetary photometry
- 12 Photometric effects of large-scale roughness
- 13 Polarization of light scattered by a particulate medium
- 14 Reflectance spectroscopy
- 15 Thermal emission and emittance spectroscopy
- 16 Simultaneous transport of energy by radiation and thermal conduction
- Appendix A A brief review of vector calculus
- Appendix B Functions of a complex variable
- Appendix C The wave equation in spherical coordinates
- Appendix D Fraunhofer diffraction by a circular hole
- Appendix E Table of symbols
- Bibliography
- Index
8 - The bidirectional reflectance of a semi-infinite medium
Published online by Cambridge University Press: 05 January 2012
- Frontmatter
- Contents
- Acknowledgments
- 1 Introduction
- 2 Electromagnetic wave propagation
- 3 The absorption of light
- 4 Specular reflection
- 5 Single-particle scattering: perfect spheres
- 6 Single-particle scattering: irregular particles
- 7 Propagation in a nonuniform medium: the equation of radiative transfer
- 8 The bidirectional reflectance of a semi-infinite medium
- 9 The opposition effect
- 10 A miscellany of bidirectional reflectances and related quantities
- 11 Integrated reflectances and planetary photometry
- 12 Photometric effects of large-scale roughness
- 13 Polarization of light scattered by a particulate medium
- 14 Reflectance spectroscopy
- 15 Thermal emission and emittance spectroscopy
- 16 Simultaneous transport of energy by radiation and thermal conduction
- Appendix A A brief review of vector calculus
- Appendix B Functions of a complex variable
- Appendix C The wave equation in spherical coordinates
- Appendix D Fraunhofer diffraction by a circular hole
- Appendix E Table of symbols
- Bibliography
- Index
Summary
Introduction
In the following chapters a variety of expressions for several different types of reflectances and related quantities frequently encountered in remote sensing and diffuse reflectance spectroscopy will be given, including empirical formulae, and solutions to the equation of radiative transfer. Approximate analytic solutions to the radiative-transfer equation will be developed. As was discussed in Chapter 1, even though such analytic solutions are not exact, they are useful because there is little point in doing a detailed, exact calculation of the reflectance from a medium when the scattering properties of the particles that make up the medium are unknown and the absolute accuracy of the measurement is not high. In most of the cases encountered in remote sensing an approximate analytic solution is much more convenient and not necessarily less accurate than a numerical computer calculation.
In keeping with this discussion, polarization will be ignored in the derivations. This neglect is justified because most of the applications of interest involve the interpretation of remote-sensing or laboratory measurements in which the polarization of the incident irradiance is usually small. Although certain particles, such as Rayleigh scatterers or perfect spheres, may polarize the light strongly at some angles, the particles encountered in most applications are large, rough, and irregular, and the polarization of the light scattered by them is relatively small (Liou and Schotland, 1971; see also Chapter 6). Hence, to first order, both the incident radiation and scattered radiation may be assumed to be unpolarized.
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- Information
- Theory of Reflectance and Emittance Spectroscopy , pp. 180 - 220Publisher: Cambridge University PressPrint publication year: 2012