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We advance a phase-space theory of partially coherent accelerating, non-diffracting beams employing the Wigner distribution function (WDF). We derive a general expression for the WDF of any accelerating, diffraction-free beam of arbitrary degree of spatial coherence and find an elegant closed-form expression for the WDF of such a beam with a Gaussian energy spectrum of noise. We also show how partially coherent accelerating beams of finite power can be constructed within the Wigner picture.
Ponomarenko et al. (Wed,) studied this question.