Axicons in oblique illumination produce broadened focal lines, a problem, e.g., in scanning applications. A compact mathematical description of the focal segment is presented, for the first time, to our knowledge, and the results are compared with elliptical axicons in normal illumination. In both cases, analytical expressions in the form of asteroid curves are obtained from asymptotic wave theory and caustic surfaces. The results are confirmed by direct diffraction simulations and by experiments. In addition we show that at a fixed angle an elliptical axicon can be used to compensate for the adverse effects of oblique illumination.

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We present a design method for diffractive axicons in spatially partially coherent Gaussian Schell-model illumination. The method of stationary phase applied to the Fresnel diffraction integral for on-axis intensity leads, on requiring a uniform axial image profile, to a second-order differential equation for the optimal axicon phase function. The first integral can be formally performed, and the phase function is subsequently obtained numerically. The correctness of the synthesized phase profiles is confirmed by numerical simulations using partially coherent Fresnel diffraction theory. The effects of input-beam spot size and coherence width are assessed, and influences of different forms of apodization, including asymmetric functions for narrow incident beams, in annular-aperture diffractive axicons are examined.

A general, noniterative method for designing diffractive axicons is derived. This new technique clarifies the earlier phenomenological design principle that was used for coherent light and extends it to the domain of partial coherence. The approach is based on the method of stationary phase in fluctuating diffracted wave fields, and it applies to arbitrary axially symmetric radiation of the Schell-model type. It is shown that the general design equation can be solved numerically, in a straightforward way, for any reasonable illumination and image specifications.

Di ractive 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 pro®les. 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 pro®le, 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 pro®le and the on-axis intensity pro®le can be determined, the two most important features of the partially coherent axicon focal line have been characterized.