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 is the index of refraction in the medium in which the wave is propagating (often air) and 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 . For the more general case of radiation incident from an arbitrary angle, we must take into account the polarized nature of radiation.