Full- and minimal-scan reconstruction algorithms for fan-beam diffraction tomography

Diffraction tomography (DT) is a tomographic inversion technique that reconstructs the spatially variant refractive-index distribution of a scattering object. In fan-beam DT, the interrogating radiation is not a plane wave but rather a cylindrical wave front emanating from a line source located a finite distance from the scattering object. We reveal and examine the redundant information that is inherent in the fan-beam DT data function. Such redundant information can be exploited to reduce the reconstructed image variance or, alternatively, to reduce the angular scanning requirements of the fan-beam DT experiment. We develop novel filtered backpropagation and estimate–combination reconstruction algorithms for full-scan and minimal-scan fan-beam DT. The full-scan algorithms utilize measurements taken over the angular range 0 ≤ ϕ ≤ 2Π, whereas the minimal-scan reconstruction algorithms utilize only measurements taken over the angular range 0 ≤ f ≤ ϕ_min, where Π ≤ ϕ_min ≤ 3Π/2 is a specified function that describes the fan-beam geometry. We demonstrate that the full-and minimal-scan fanbeam algorithms are mathematically equivalent. An implementation of the algorithms and numerical results obtained with noiseless and noisy simulated data are presented.