Lensing convergence ($\kappa =\frac{1}{2}{\nabla }_{\theta }\cdot \mathbf{\alpha }$)

The trace of the angular derivative of the reduced deflection defines convergence in the standard thin gravitational lens equation convention. It equals projected surface mass density divided by the critical surface density, ${\Sigma }_{\mathrm{crit}}=c^2{D}_s/(4\pi G{D}_d{D}_{ds})$. If deflection is instead defined as source minus image angle, the divergence relation has a minus sign.

The geometrical projected density scale converting a thin lens surface mass density into convergence. Its value depends on the angular-diameter distances to lens and source, not only on lens matter.