The well-known central-slice, or projection-slice, theorem states that the Radon transform can be used to reduce a two-dimensional Fourier transform to a series of one-dimensional Fourier transforms. In this paper we describe a practical system for implementing this theorem. The Radon transform is carried out with a rotating prism and a flying-line scanner, while the one-dimensional Fourier transforms are performed with surface acoustic wave filters. Both real and imaginary parts of the complex Fourier transform can be obtained. A method of displaying the two-dimensional Fourier transforms is described, and representative transforms are shown. Application of this approach to Labeyrie speckle interferometry is demonstrated.
Anthony J. Ticknor,
Roger L. Easton,
Harrison H. Barrett,
"Two-Dimensional Radon-Fourier Transformer," Optical Engineering 24(1), 240182 (1 February 1985). https://doi.org/10.1117/12.7973429