Apodized annular-aperture logarithmic axicons that form uniform-intensity axial line images with coherent light are studied in Gaussian-correlated illumination. Diffractive assessment of the line-image distributions and spatial coherence properties involves a highly oscillating double two-dimensional integral. The on-axis behavior depends only on radial integrals that can be computed with special-purpose routines. We show that at all correlation levels the images at off-axis points can be evaluated by using a technique based on spline approximations. We also demonstrate that the method of stationary phase can be sequentially applied to the four-dimensional diffraction integral, yielding accurate three-dimensional closed-form results. The stationary-phase formulas find applications in fast image evaluation, in intensity balancing by varying the irradiance, and in designing axicon phase profiles. The results complement our earlier study of partially coherent axicon images by radiometric transport techniques.

© 1999 Optical Society of America

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