  The utility of transmission measurement has made it a target for quantum
enhanced measurement strategies. Here we find if the length of an absorbing
object is a controllable variable, then via the Beer-Lambert law, classical
strategies can be optimised to reach within 83% of the absolute quantum limit.
Our analysis includes experimental losses, detector noise, and input states
with arbitrary photon statistics. We derive optimal operating conditions for
both classical and quantum sources, and observe experimental agreement with
theory using Fock and thermal states.
