Numerical Computation of the Discrete 2D Fourier Transform in Polar Coordinates

Abstract

The discrete Fourier transform in Cartesian coordinates has proven to be invaluable in many disciplines. However, in application such as photoacoustics and tomography, a discrete 2D-Fourier transform in polar coordinates is needed. In this paper, a discrete 2D-Fourier transform in polar coordinates is presented. It is shown that numerical implementation is best achieved by interpreting the transform as a 1D-discrete Fourier transform (DFT), a 1D-discrete Hankel transform (DHT) and a 1D-discrete inverse transform (IDFT) in sequence. The transform is tested by numerical simulations with respect to accuracy and precision for computation of the continuous 2D transform at specific discrete points. It was found that both the forward and inverse transform showed good accuracy to approximate the continuous Fourier transform. Moreover, good precision results were obtained, which indicate that the proposed transform itself does not add much error.