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The metrological characterization of a Fresnel method for measuring the dimensions of objects is investigated. In this method, free space, as an optical element, transforms the input image of the inspected object into its Fresnel image with great accuracy. The major sources of systematic measurement error are estimated analytically including non-uniform illumination of the object, the interference effect of the edge images of the diffracting object, the integration properties of the linear multi-element photodetector, the influence of the extended size of a partially coherent light source and the volumetric properties of a 3D object. It is proposed that algorithms are used to account for any error components; effective algorithms for this are proposed.

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We present a numerical technique for solving evolution equations, such as the wave equation, in the description of rotating astrophysical compact objects in comoving coordinates, which avoids the problems associated with the light cylinder. The technique implements a fast spectral matching between two domains in relative rotation: an inner spherical domain, comoving with the sources and lying strictly inside the light cylinder, and an outer inertial spherical shell. Even though the emphasis is placed on spectral techniques, the matching is independent of the specific manner in which equations are solved inside each domain, and can be adapted to different schemes. We illustrate the strategy with some simple but representative examples.