  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.
