Localizing periodicity in near-field images

We show that Bayesian inference, like that used in statistical mechanics, can guide the systematic construction of Fourier dark-field methods for localizing periodicity in near-field (e.g. scanning-tunneling and electron-phase-contrast) images. For crystals in an aperiodic field, the Fourier coefficient Ze^{i phi} combines with a prior estimate for background amplitude B to predict background phase (beta) values distributed with a probability p(beta - phi | Z,phi,B) inversely proportional to the amplitude P of the signal of interest, when this latter is treated as an unknown translation scaled to B.