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Decoherence arises from a fluctuating spin environment, captured by its noise spectrum S ( ω ). Dynamical decoupling (DD) with n π pulses extends the dephasing time if the associated filter function attenuates S ( ω ). Inversely, DD noise spectroscopy (DDNS) reconstructs S ( ω ) from DD data by approximating the filters pass band by a δ -function. This restricts application to qubit-like spin systems with inherently long dephasing times and/or many applicable pulses. We introduce regularized DDNS to lift this limitation and thereby infer S ( ω ) from DD traces of paramagnetic centers in glassy o -terphenyl and water-glycerol matrices recorded with n ≤ 5. For nitroxide radicals at low temperatures, we utilize deuteration to identify distinct matrix- and spin center-induced spectral features. The former extends up to a matrix-specific cut-off frequency and characterizes nuclear spin diffusion. We demonstrate that rotational tunneling of intramolecular methyl groups drives the latter process, whereas at elevated temperatures S ( ω ) reflects the classical methyl group reorientation. Ultimately, S ( ω ) visualizes and quantifies variations in the electron spins couplings and thus reports on the underlying spin dynamics as a powerful decoherence descriptor.

Regularized dynamical decoupling noise spectroscopy – a decoherence descriptor for radicals in glassy matrices