From the schwarzchild metric,
\[\begin{split} e = -\xi \cdot u &= W_{\rm{eff}}(r) \frac{d t}{d \lambda} \\ l = \eta \cdot u &= r^2 \sin^2 \theta \frac{d \phi}{d \lambda} \end{split}\]
are conserved quantities along the path of the photon.
setting \(u \cdot u = 0\) since its a light ray with \(\theta = \frac{\pi}{2}\) gives
\[\begin{split} u \cdot u = g_{\alpha \beta} \frac{d x^\alpha}{d \lambda}\frac{d x^\alpha}{d \lambda} \\ \frac{1}{b^2} = \frac{1}{l^2}\left( \frac{dr}{\lambda}\right)^2 + W_{\rm{eff}}(r) \end{split}\]
where
\[\begin{split} b^2 &= \frac{l^2}{e^2} \\ W_{\rm{eff}}(r) &= \frac{1}{r^2}(1-\frac{2M}{r}) \end{split}\]
Another useful equation:
\[\delta \phi_{\rm{def}} = \frac{4 G M }{c^2 b}\]
where b is the impact parameter