Fixed-Detector Tilt--Defocus Sensing by Upstream Source Coding in a Time-Reversed Young Interferometer

We propose a physically explicit sensing application of a time-reversed Young (TRY) interferometer: simultaneous monitoring of beam tilt and focus drift with a fixed detector. The task is relevant to compact optical relays, free-space links, fiber-coupling stages, and micro-optical alignment modules, where continuous tracking of pointing and focus is needed but downstream wavefront cameras or multiport analyzers are undesirable. Using a finite-width double-slit Fresnel model, we derive the exact local TRY response functions for tilt-like and defocus-like phase perturbations and compute the corresponding optimal upstream source codes numerically. The physical optimal codes are fringe-locked and differ qualitatively from the simple odd/even modes suggested by Gaussian toy models. Two source-coded scalar channels recover essentially all local Fisher information in the full source-resolved TRY record for the physical model considered here. Compared with downstream direct intensity sensing, TRY provides first-order access to the mixed tilt--defocus task with fixed detection; compared with ideal downstream matched-mode sorting, its advantage is architectural rather than fundamental.