Eikonal Aberrations in Gradient Cylindrical Lenses

Approximate formulas are derived for eikonal on the output surface of a cylindrical dielectric lens with a gradient of refractive index along the Cartesian coordinate for a source that is displaced from the focal point on the symmetry axis of the lens. The first formula is obtained for the paraxial region and represents an expansion in powers of the longitudinal and transverse displacement of the source including terms of the first and second orders of smallness, and the second (integral) formula has no limitations on the numerical aperture. The first formula is used to obtain an equation of the focal curve. Errors of the formulas in the calculations of the eikonal and its aberrations on the output surface of the lens are analyzed. The second formula is used to find optimal parameters of the lens with parabolic variation in permittivity that provides minimum aberrations.