chapter 5, Polarimetric Interactions: Reflection and Transmission

from: Fundamentals of Polarimetric Remote Sensing

Author(s): John R. Schott

Author(s): John R. Schott

Published: 30 March 2009

Chapter DOI: 10.1117/3.817304.ch5

Chapter Page Count: 11 pages

Previous Chapter | Next Chapter

Front Matter

1. Introduction

2. Review of Radiometry

3. The Wave Nature of EM Energy and an Introduction of the Polarization Ellipse

4. Representation of the Polarimetric State of a Beam

5. Polarimetric Interactions: Reflection and Transmission

6. Polarimetric Bidirectional Reflectance Distribution Functions (pBRDF)

7. Polarized Form of the Governing Equation Including Atmospheric Scattering Terms

Color Plate Section

8. Sensors for Measuring the Polarized State of a Beam

9. Processing and Display Algorithms

10. Measurements and Modeling of the pBRDF of Materials

11. Longwave Infrared pBRDF Principles

12. LWIR pBRDF Measurements and Modeling

Back Matter

Preview

Chapter Contents

5.1 Fresnel Specular Reflection
5.2 Polarized Transmission and Polarizing Materials
5.3 The Mueller Matrix: Polarimetric Energy-Matter Interactions
References

Excerpt

This chapter introduces the formalism we need to describe the interaction of a polarized beam with a reflective or transmissive medium. To simplify the discussion, we begin in this chapter with simple optically flat surfaces and move, in Chapter 6, to consideration of the more complex surfaces that represent the surfaces we wish to remotely sense. This chapter draws on classic texts on optics and polarization [e.g., Hecht (1990) and Goldstein (2003)], to which the reader is referred for a more thorough treatment.

5.1 Fresnel Specular Reflection

In Chapter 2 we introduced the concept of total reflection as the ratio of the exittance from a surface to the irradiance onto a surface and a similar term for the transmission. Fresnel (1866) showed that for radiation normally incident onto a planar dielectric surface (i.e., an optically flat surface), the reflectivity is a function only of the index of refraction of the two media and can be expressed as

where n₁ is the index of refraction in the medium in which the wave is propagating (often air) and n₂ is the index of refraction of the second medium (i.e., the reflecting surface). If the medium is opaque, then the remainder of the energy is absorbed (i.e., 1-r). If the medium is transmissive, the transmission through the interface is simply τ = 1−r. For the more general case of radiation incident from an arbitrary angle, we must take into account the polarized nature of radiation.

DOI: 10.1117/3.817304.ch5

Your library does not subscribe to the eBooks portion of the SPIE Digital Library.