Abstract
We consider the inverse source problem for time-harmonic acoustic or electromagnetic wave propagation in the two-dimensional free space. Given the radiated far field pattern of the solution to the Helmholtz equation for a certain source term, we find that the windowed Fourier transform of this far field is related to an exponential Radon transform with purely imaginary exponent of a smoothed approximation of the source. Based on this observation we set up a filtered backprojection algorithm to recover information on the unknown source term from a single far field measurement. We analyze this algorithm and provide extensive numerical results that illustrate our theoretical findings. As one outcome the method is shown to work better the larger the wave number. Possible extensions of the reconstruction method to limited aperture data and to inverse obstacle scattering problems are briefly sketched.
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