Asymptotic methods in design and characterization ofdiffractive axicons

Abstract: This thesis addresses the subject of diffractive axicons inpartially coherent or oblique illumination. Design andcharacterization of the axicons are performed using asymptoticwave optics, employing the stationary-phase method to obtainapproximations of the diffraction integrals.A design method for axicons in partially coherentillumination is derived. The method can be applied to anyincident illumination on radially symmetric Schell-model form.It provides analytical solutions for some specific cases, butfor most incident intensity and coherence distributions it canbe solved numerically to yield the desired on-axis intensity.In addition, a method for estimating the width of the focalline is provided. For coherent light, the design method isidentical to the old one based on energy conservation in raybundles. Since the new method is derived entirely from waveoptics, it both clarifies the old method and extends it topartially coherent light.Oblique illumination of axicons, frequently encountered inapplications, causes degradation of the focal line. This changeis characterized, and from the asymptotic theory it is foundthat the focal line is described by an asteroid curve. Thewidth of the focal segment in oblique illumination isaccurately predicted, as confirmed by simulations andexperiments. It is also found that at a fixed angle, anelliptical axicon may be used to compensate for the adverseeffects of oblique illumination.Keywords:axicons, diffractive optics, coherence,asymptotic methods