Beyond Direct Imaging: Quantum Measurement Design for Small-Target Detection in UAV Hyperspectral Sensing

Abstract

Small mineral patches can be spectrally distinct yet difficult to detect when diffraction mixes their light with the surrounding rock. Conventional hyperspectral detectors analyze recorded intensities, leaving an opportunity to recover target evidence through the optical measurement itself. We develop a quantum-assisted framework for exploiting this opportunity in prospective unmanned aerial vehicle (UAV) hyperspectral sensing. A common radiometric and diffraction model describes direct imaging and spatial-mode measurements of the same light. The theory identifies target changes that survive background fitting and explains when mode measurements retain more detection information. It quantifies losses from mode mismatch and unresolved outputs, linking the quantum benchmark to finite receiver design. A common-basis result identifies when material spectra can share a spatial measurement at fixed geometry. An adaptive receiver uses an imaging pilot to select candidate modes and combines both stages in a full-region presence test. Simulations based on measured mineral spectra and published UAV acquisition scales demonstrate gains over complete direct imaging at a shared active-exposure budget, including pilot cost and optical loss. At matched empirical 1\% region-level false alarms, detection increases from 62.95\% to 69.65\% for a representative target. Paired analysis supports gains with registration uncertainty and, separately, under controlled nonuniform backgrounds. Calibrated mode errors reveal where measurement losses weaken or reverse the benefit. These results connect background identifiability to receiver choices and their operating conditions. They provide a framework for designing spatial measurements alongside spectral channels to detect small material features.

Can spatial-mode measurements improve detection of an unresolved, spectrally distinct material patch within a bright reflecting background when its position and background brightness are unknown? This paper studies that question using a shared radiometric, diffraction, and Poisson-count model for direct imaging (DI) and passive optical mode sorting, with UAV mineral sensing as the application. The analysis projects target perturbations away from nuisance directions and identifies residual-SLD eigenmodes attaining scalar local quantum Fisher information. For a uniform background, spectral-residual formulas weight pupil overlap by $H$ for quantum information versus $H^2$ for DI. Finite-output loss identities quantify mode mismatch and aggregation. An adaptive receiver spends 70% of its exposure on imaging, selects eight candidate PSF modes, and combines pilot and subsequent mode counts in a full-region presence test. Simulations use measured calcite/dolomite spectra and published acquisition scales, rather than UAV measurements. For a 6.5-mm patch, an aligned reference PSF retains 97.21% of the quantum information, whose ratio to DI is 2.1395. At matched empirical 1% region-level false alarms, adaptive detection rises from 62.95% to 69.65%, including pilot cost and 80% mode-stage efficiency; the threshold-inclusive paired 95% difference interval is 3.40–10.20 percentage points. Gains remain supported with 2-mm interstage registration uncertainty, but become statistically unresolved when combined with smooth illumination variation or a prescribed 1-ms control delay. Larger calibrated mode errors reverse the advantage. The model omits electronic noise, turbulence, motion blur, and instrument-specific aberrations; broadband hardware performance is not demonstrated, and receiver allocation is not optimized.