Fast Fourier method for the accurate rotation of sampled images

At present the best methods for rotation of discrete sampled images use a combination of (fast) Fourier interpolation followed by cubic interpolation onto a rotated grid. A method is presented which uses only Fourier interpolation. The new method has a similar computational complexity to the old, and is exactly reversible. The method uses the well-known decomposition of rotation into three pure shears. Each shear is performed using a 2D extension of the 1D Fourier shift theorem. This allows the fast Fourier transform (FFT) to be used, With appropriate data padding (such as zero padding) in both the real and Fourier domains, the procedure gives near perfect results and minimal loss of information in multiple rotation tests.