ABSTRACT
Chapter 8 Fresnel Equations describes polarization changes which occur at dielectric interfaces, total internal reflection, and reflection from metal mirrors. This chapter focuses on the polarization effects, the consequences of Fresnel equations, their magnitudes and forms, and how to integrate these polarization effects into optical design. Incident light is analyzed into s and p-polarized components, with separate s and p-amplitude reflection and transmission coefficients derived from Maxwell’s equations applied to a homogeneous and isotropic interface. At Brewster’s angle the reflected light is completely s-polarized and all the p-polarized light is transmitted. For internal reflection, for the light incident beyond the critical angle, all of the light is internally reflected with substantial retardance between the s and p-components. Very large polarization effects occur at the critical angle where the derivative of the retardance becomes infinite. The change of amplitude and phase for reflection from a smooth metal surface is calculated using the same Fresnel equations which apply to dielectrics, except the metal’s complex refractive index is used. The complex Fresnel coefficients are used during polarization ray tracing to calculate the changes in polarization, the diattenuation and retardance associated with ray intercepts and ray paths through optical systems. When wavefronts propagate through optical systems, the resulting polarization effects generate diattenuation aberrations and retardance aberrations. It is useful to take complex equations, like the Fresnel equations, and replace them with polynomial functions, which, although approximate, maintain a high degree of accuracy. Then by reasoning with these approximate functions, methods for polarization aberration compensation more easily constructed. The resulting polarization aberrations are described in several example optical systems, such as a Cassegrain telescope in Chapter 12 and an astronomical telescope in Chapter 27.
