ADORA: a differentiable optical modeling and astrometric retrieval framework for SHERA
Searching for Habitable Exoplanets with Relative Astrometry (SHERA) is a proposed Small Explorer mission concept designed to measure the separation of nearby binary stars at microarcsecond-class precision. Recovering this signal requires separating astrophysical motion from coupled changes in pointing, plate scale, wavefront error, spectral response, and detector calibration. We present the Astrometric Differentiable Optics and Retrieval Algorithm (ADORA), an image-domain framework that combines a three-plane differentiable physical-optics model with a layered astrometric inference algorithm. The forward model includes a diffractive pupil, mirror-specific wavefront error and beamwalk, polychromatic source and throughput models, and configurable detector effects. Per-frame registration states are treated locally and eliminated through Schur reduction before the slower astrometric and instrument state is updated in a prior-whitened Fisher eigenbasis. Five-minute matched-model simulations show no detected separation bias at the current Monte Carlo depth and approximately 11 uas realization-to-realization scatter. A SHERA target sweep reveals a more-than-fivefold variation in astrometric information between Alpha Centauri and 61 Cygni, motivating future target-dependent accumulation and update cadence. High-order-wavefront knowledge error can drive the retrieval toward a strongly biased astrometric solution while leaving the local posterior sigma nearly unchanged, demonstrating that statistical curvature alone does not capture unmodeled bias. Pixel-position errors across the tested range remain near the matched-model recovery scale indicating robustness to certain detector calibration errors. ADORA provides a flexible framework for studying astrometric extraction, calibration-bias diagnosis, and future SHERA requirements.