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The inversion of the one-dimensional Radon transform on the rotation group SO(3) is an ill posed inverse problem which applies to X-ray tomography with polycrystalline materials. This communication presents a novel approach to the numerical inversion of the one-dimensional Radon transform on SO(3). Based on a Fourier slice theorem the discrete inverse Radon transform of a function sampled on the product space S 2 × S 2 of two two-dimensional spheres is determined as the solution of adoi:10.1088/0266-5611/24/2/025011 fatcat:3oq2efczhvgvpjctiakr3acjia