A theoretical study shows that gravitational wave diffraction can probe extended mass distributions, much as charged-particle scattering reveals the structure of atomic nuclei. The authors derive, at first order in the lens potential, a relation between the central diffractive image contribution in a gravitationally lensed gravitational waveform and the Fourier transform of the projected lens density. For finite-mass lenses, this contribution takes the form of a point-mass Born amplitude multiplied by a normalized mass form factor, analogous to the one appearing in nuclear scattering.

The key to the method is that the frequency of waves emitted by a merging compact binary evolves during coalescence, so the signal samples the form factor across different spatial scales. That structure is imprinted in the interference pattern with the primary image. The authors quantify the observational reach using full numerical wave-optics calculations, applying them to extended dark matter objects, primordial black holes dressed by dark matter halos, and superradiance clouds of ultralight bosons around black holes.

The results indicate that five years of observation with next-generation gravitational wave detectors would be enough to distinguish extended lenses from point masses, reaching dark matter fractions of order 10⁻⁵. It would also be possible to separate halo-dressed primordial black holes from matched bare black holes, with sensitivity to primordial black hole dark matter fractions down to order 10⁻⁶. For sufficiently close source-lens configurations, scalar superradiance clouds would leave distinguishable diffraction signatures for boson masses of roughly 10⁻¹⁷ to 10⁻¹² eV.

The proposed framework offers a way to characterize both extended dark matter and the astrophysical environment of compact objects, opening a new observational window beyond the geometric lensing approximation.