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Chapter 6:
Polarimetric Bidirectional Reflectance Distribution Functions (pBRDF)
In this chapter, we begin by introducing the scalar bidirectional reflectance distribution function (BRDF) used to describe directional reflectance. This treatment draws extensively from Schott (2007). We then proceed to describe a polar form of the BRDF or pBRDF and ways to measure and model the pBRDFs of materials. This treatment draws heavily from Shell (2005). 6.1 Bidirectional Reflectance Distribution Functions In Chapter 2, we introduced the concept of radiance and the constancy of radiance during propagation in a lossless medium. This ease of propagation of radiance makes it the most convenient term to study for most remote sensing applications. However, what we often know is the irradiance onto a target we wish to observe. In order to convert the irradiance onto the target into radiance toward the detector, we need to consider the reflectance properties of materials. In general the reflectance properties are a function of wavelength, illumination angle, viewing angle and the polarization state of the incident flux. We need to develop a means to express the full impact of these dependencies on the reflected radiance and to develop a simpler expression for cases when full angular reflectance data are not available. 6.1.1 Ways to characterize reflectance In Chapter 2, we introduced what we will now define to be the total spectral reflectance as: r(λ)=M λ E λ .
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