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The modeling of source distributions of finite spatial extent in ultrasound and medical imaging applications is a problem of longstanding interest. In time domain methods, such as the finite difference time domain or pseudospectral approaches, one requirement is the representation of such distributions over a grid, normally Cartesian. Various artefacts, including staircasing errors, can arise. In this short contribution, the problem of the representation of a distribution over a grid is framed as an optimisation problem in the Fourier do
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