Resonance-Matched Excitation: A General Overlap Model for Beam–Target Spectroscopy, Identifiability, and Optimal Design

We formulate a general spectral-overlap functional for beam–target excitation and show how it yields closed-form measurement models, parameter identifiability, and experiment design strategies. A Gaussian source spectrum overlapped with Lorentzian target resonances produces Voigt-type responses with analytic derivatives. We derive Fisher information matrices and Cramér–Rao bounds for spectral parameters and demonstrate parameter recovery on synthetic and benchmark datasets. The framework applies to microwave cavities, mechanical resonators, optical transitions, and other linear spectroscopy systems.