With uniform partially coherent illumination of a sufficiently small coherence width, linear holographic axicons produce an extended axial line image of a desired length and a nearly uniform intensity. This result is demonstrated by numerical diffractive simulations based on generalized axicon phase functions and the space-frequency theory of optical coherence. The conclusions are also verified through analytical calculations employing the asymptotic method of stationary phase.
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A 1995 study studied this question.