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In this work we analyze the theory of gravitational weak lenses on a flat background. We obtain explicit expressions for the optical scalars at the second order in the flat metric perturbation in a general way in the sense that we do not mention neither the extension of the lens nor the shape thereof. We explicitly calculate the optical scalars in the generalized Poisson gauge. Finally, considering axially symmetrical lenses in the approximation of thin lens obtain an expression for the deflection angle at the second order in the flat metric perturbation.