  In this paper, we analyze the deflection angle of light by Brane-Dicke
wormhole in the weak field limit approximation to find the effect of the
Brane-Dicke coupling parameter on the weak gravitation lensing. For this
purpose, we consider new geometric techniques, i.e., Gauss-Bonnet theorem and
optical geometry in order to calculate the deflection angle. Furthermore, we
verify our results by considering the most familiar geodesic technique.
Moreover, we establish the quantum corrected metric of Brane-Dicke wormhole by
replacing the classical geodesic with Bohmian trajectories, whose matter source
and anisotropic pressure are influenced by Bohmian quantum effects and
calculate its quantum corrected deflection angle. Then, we calculate the
deflection angle by naked singularities and compare with the result of
wormhole's. Such a novel lensing feature might serve as a way to detect
wormholes, naked singularities and also the evidence of Brane-Dicke theory.
