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We present in this paper a new application of the geodesic light-cone (GLC)gauge for weak lensing calculations. Using interesting properties of thisgauge, we derive an exact expression of the amplification matrix - involvingconvergence, magnification and shear - and of the deformation matrix -involving the optical scalars. These expressions are simple andnon-perturbative as long as no caustics are created on the past light-cone andare, by construction, free from the thin lens approximation. We apply thesegeneral expressions on the example of an Lema\^itre-Tolman-Bondi (LTB) modelwith an off-center observer and obtain explicit forms for the lensingquantities as a direct consequence of the non-perturbative transformationbetween GLC and LTB coordinates. We show their evolution in redshift after anumerical integration, for underdense and overdense LTB models, and interprettheir respective variations in the simple non-curvature case.

Lensing in the Geodesic Light-Cone coordinates and its (exact) illustration to an off-center observer in Lema\^itre-Tolman-Bondi models