Diffraction ring pattern at the focal plane of a spherical lens – axicon doublet

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Abstract
A spherical lens and an axicon are combined to form an optical system producing a ring-shaped focalization pattern. The diameter of the ring in the focal plane depends on the angle of the axicon, on its dielectric index, and on the focal length of the spherical lens. The diffractional analysis of the lens–axicon combination, when illuminated by a plane wave, is presented. In particular, we show that, when the aperture is large, the Kirchhoff–Fresnel integral can be reduced to a known function. A close examination of the function reveals that the diffractional width of the ring is equal to approximately twice the width of the Airy pattern of the lens alone. This type of focalization is well suited for a system where a laser beam is used to drill holes.

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