# Inverse Transformation of s-Reflection Coefficient between Oblique and Normal Incidence

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If denotes an interface Fresnel reflection or transmission coefficient for - or -polarized light at an oblique angle of incidence , and *z* denotes the same coefficient at normal incidence, then it can be shown that *w* is an analytic function of , that depends parametrically on the angle of incidence . The inverse mapping between the complex and planes is illustrated here by one of the Fresnel coefficients (for *s* reflection) at one oblique angle of incidence (45°) and normal incidence. Here , where and are the oblique-incidence amplitude reflectance and phase shift.

Contributed by: Siva Perla (March 2011)

Open content licensed under CC BY-NC-SA

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R. M. A. Azzam, "Transformation of Fresnel's interface reflection and transmission coefficients between normal and oblique incidence," *Journal of Optical Society of America*, 69(4), 1979 pp. 590-596.

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