Abstract

The properties of many three-dimensional radiographic imaging systems are examined within a common analytic framework. It is found, by performing an important coordinate transformation, that the projection data of these systems can be transformed to a form amenable to analysis by the central-slice theorem. Therefore, a clear relationship between the measured data set and the three-dimensional Fourier transform of the object can be established. For the Fourier aperture system, each measurement in the detector plane gives directly one point in the three-dimensional Fourier transform of the object. The limited view angle of these systems manifests itself in the incomplete collection of the Fourier transform of the object. This “missing cones” region in the Fourier space produces a point-spread function that has long-range conical ridges radiating from the central core. It is shown that degradations in linear reconstructions of extended objects are not as disastrous as might have been expected.

© 1979 Optical Society of America

Three-dimensional reconstruction from planar projections

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