  We explicitly derive the Christoffel symbols in terms of adapted frame fields
for the Levi-Civita connection of a Lorentzian $n$-manifold $(M, g)$, equipped
with a prescribed optical geometry of K\"ahler-Sasaki type. The formulas found
in this paper have several important applications, such as determining the
geometric invariants of Lorentzian manifolds with prescribed optical geometries
or solving curvature constraints.
