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Chapter 3:
Scatter Calculations and Diffraction Theory
This chapter outlines the important elements of diffraction theory and gives several key results that pertain to the interpretation of measured scatter data. These results are employed in Chapters 4 and 7 to relate measured scatter from reflective surfaces to the corresponding surface roughness and to consider various methods of scatter prediction. In Chapter 8, the diffraction theory results presented here are combined with the polarization concepts found in Chapter 5 and used to outline a technique for separating surface scatter from that due to subsurface defects and contamination. A complete development of diffraction theory is well beyond the scope of this book; however, excellent texts on the subject are available, and these will be referenced in the review presented in the next four sections. The following discussions assume that the reader has some familiarity with electromagnetic field theory and the required complex math notation. Appendix A is a brief review of the elements of field theory and Appendix B gives details of some diffraction calculations. 3.1 Overview When light from a point source passes through an aperture or past an edge, it expands slightly into the shadowed region. The result is that the shadow borders appear fuzzy instead of well defined. The effect is different from the one obtained by illuminating an object with an extended light source (such as the shadow of your head on this book) where the width of the reading lamp also contributes to an indistinct shadow. Well-collimated light sources (sunlight for example) also produce fuzzy shadow edges. This bending effect, which illustrates the failure of light to travel in exactly straight lines, is called diffraction and is analyzed through the wave description of light. As explained in Appendix A, the propagation of light is described in terms of the transverse electric field E(t,r), where r denotes position and t is time. The value k is 2π/λ, and ν is the light frequency. The expression in Eq. (3.1) is for a wave traveling in the direction of increasing r.
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