This paper explores the mathematical and algorithmic properties of two sample-based microtexture models: random phase noise (RPN ) and asymptotic discrete spot noise (ADSN ). These models permit to synthesize random phase textures. They arguably derive from linearized versions of two early Julesz texture discrimination theories. The ensuing mathematical analysis shows that, contrarily to some statements in the literature, RPN and ADSN are different stochastic processes. Nevertheless, numerous experiments also suggest that the textures obtained by these algorithms from identical samples are perceptually similar. The relevance of this study is enhanced by three technical contributions to micro-texture synthesis from samples. A solution is proposed to three obstacles that prevented the use of RPN or ADSN to emulate micro-textures. First, RPN and ADSN algorithms are adapted to color images. Second, a preprocessing is proposed to avoid artifacts due to the non-periodicity of real-world te...