Candidate structures for nanocrystal and other specimens are obtained based on a specimen complex spectrum that is determined as a Fourier transform of a phase-contrast electron micrograph. The specimen can also be assessed based on an amplitude portion of the complex spectrum using a lattice-fringe fingerprint. In some examples, the specimen complex spectrum is compensated based on an electron microscope transfer function, a specimen tilt, or based on other crystallographic compensation. Amplitude or phase portions of the compensated complex spectrum can be compared with reference structures stored in one or more reference structure databases.