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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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We define the signal-relevant efficiency (SRE) of a diffractive optical element as a measure of the proportion of the incident field power that ends up in the desired output signal. An upper bound for SRE is determined in the presence of arbitrary constraints imposed on the element, such as phase-dependent loss due to absorption within the microstructure and quantization of the surface profile. We apply the theory to the important class of diffractive elements that contain only one desired diffraction order (such as diffractive lenses) and derive the surface profile that provides the highest efficiency allowed by the constraints.