= Solution
Let $x^a(\lambda,s)$ be a smooth family of affinely parametrized <null geodesics>. The tangent is $U=\partial x/\partial\lambda$, and the <deviation vector> is $Z=\partial x/\partial s$, comparing nearby rays at the same <affine parameter>. The two parameter derivatives commute, so
$$
\boxed{[U,Z]=0,\qquad\nabla_UZ=\nabla_ZU.}
$$
Thus the separation vector is Lie-transported along the <null geodesic congruence>; it is not required to be parallel-transported. Differentiating once more gives the <geodesic deviation> equation. With curvature convention $[\nabla_c,\nabla_d]V^a=R^a{}_{bcd}V^b$,
$$
\nabla_U\nabla_UZ^a=R^a{}_{bcd}U^bU^cZ^d.
$$
For optical measurements one uses transverse deviations with $U\cdot Z=0$ and identifies longitudinal additions proportional to $U$. The scalar $U\cdot Z$ is constant along affine null rays by the displayed transport relation, so an initially transverse deviation remains transverse.
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