Comprehensive analysis of non-diffracting optical waves with two-point binomial coherence function (BCF) is presented. This coherence function consists of two terms, each depending on either separation of points or the central point. We establish the necessary and sufficient conditions for nonnegative definiteness of the BCFs. Spectral analysis, including calculations of the eigenvalues and eigenfunctions, for the general BCF case is presented. We consider two simple BCF examples of and analyzed the conditions leading to the maximum irradiance contrast.