= Solution
Choose the affine tangent $k^a$ to a <null geodesic congruence>, and an auxiliary <null vector> $\ell^a$ with $k\cdot\ell=-1$. The <screen-space projector>
$$
q_{ab}=g_{ab}+k_a\ell_b+\ell_ak_b
$$
annihilates $k$ and $\ell$ and restricts to a positive-definite two-dimensional metric in four spacetime dimensions. Neighboring transverse rays have relative displacement governed by the <optical tensor>
$$
B_{ab}=q_a{}^cq_b{}^d\nabla_dk_c.
$$
Its irreducible decomposition defines the three requested optical quantities:
$$
\boxed{\theta=q^{ab}B_{ab},\qquad
\sigma_{ab}=B_{(ab)}-\frac12\theta q_{ab},\qquad
\omega_{ab}=B_{[ab]}.}
$$
The <null expansion> $\theta$ is the fractional rate of change of transverse area, $d\log A/d\lambda$. The <null shear> $\sigma$ changes a beam's shape at fixed area to first order; it is symmetric and trace-free. The <null twist> $\omega$ is antisymmetric and measures local rotation of the transverse rays; it vanishes for a hypersurface-orthogonal <null geodesic congruence>. In $D$ dimensions replace $1/2$ by $1/(D-2)$. These definitions use the trace convention for <null expansion>, rather than the alternative screen-averaged convention.
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