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We investigate the validity of the approximate method to describe a stronggravitational lensing which was extended by Alard on the basis of aperturbative approach to an Einstein ring. Adopting an ellipticalNavarro-Frenk-White (NFW) lens model, we demonstrate how the approximate methodworks, focusing on the shape of the image, the magnification, caustics, and thecritical line. Simplicity of the approximate method enables us to investigatethe lensing phenomena in an analytic way. We derive simple approximate formulaswhich characterise a lens system near the Einstein ring.

Analytic approach to perturbed Einstein ring with elliptical NFW lens model