Abstract
Diffractive axicons operating in spatially partially coherent light can be designed non-iteratively, on the basis of asymptotic wave theory, to produce focal lines with prescribed on-axis intensity profiles. In this paper we analyse the transverse intensity variation of these axicon lines, concentrating on relatively coherent beams. By Taylor expansion, a way is found to approximate the transverse intensity profile, without the demanding numerical integration otherwise needed. From this expression, also the width of the focal line as a function of position on the optical axis can be easily found. As now both this width profile and the on-axis intensity profile can be determined, the two most important features of the partially coherent axicon focal line have been characterized.
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