The transfer function associated with the Knox–Thompson speckle imaging technique is investigated. Numerical model transfer functions using log-normal statistics for perturbations of the complex wave front, the near-field approximation, and a Kolmogorov spectrum for atmospheric turbulence statistics are presented. Simple approximations for the transfer function are discussed. As with the transfer function of Labeyrie’s speckle interferometry technique, the portion beyond the seeing limit can be represented as the transfer function of an unaberrated telescope times a seeing-dependent constant. An additional factor depends on the frequency shift of the Knox – Thompson cross spectra. The influence of the frequency shift on the reconstructed phase error is discussed for simple reconstruction problems.