The local plane-interface approximation (LPIA) is a method for propagating electromagnetic fields through the inhomogeneous regions (e.g., elements) of an optical system. The LPIA is the superclass of all approximations that replace the usually curved optical interfaces with local tangential planes. Therefore the LPIA is restricted to smooth optical surfaces. A maximum radius of curvature of the optical interface of the order of a few wavelengths is a rough estimate for the validity of the LPIA. Two important approximation levels of the LPIA are the thin-element approximation (TEA) and a geometric-optical version of the LPIA (LPIA(ray)). The latter combines the wave-optical propagation of an electromagnetic field in the homogeneous region of an optical system with a ray-tracing step in the inhomogeneous region. We discuss the regions of validity of the LPIA in general and the approximation levels LPIA(ray) and TEA in detail.

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The design of an optical element profile with specified transmission function for a given incident wave is of fundamental concern in optical design. A well-known example is the design of an aspherical surface in order to realize a spherical phase-only transmission. Various wave-optical system design methods lead to transmission functions as a first step. Then, often the thin-element approximation is applied in a second step to obtain an element structure with the desired transmission. However, if the refraction at the optical interface cannot be neglected, the thin-element approximation is not valid. In this case, a higher version of the local plane-interface approximation can be used for the element structure design. An algorithm for this model is introduced and its characteristics are discussed for the example of a non-paraxial Gaussian-to-tophat beam shaping element

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