Motivated by recent experiments on intensity correlations of the waves transmitted through disordered media, we demonstrate that the speckle pattern from disordered photonic crystal with incomplete band-gap represents a sensitive tool for determination the stop-band width. We establish the quantitative relation between this width and the angualar anisotropy of the intensity correlation function.PACS numbers: 42.25. Dd, 42.70.Qs Introduction. A wave propagating in a random medium undergoes multiple scattering and forms a complicated intensity pattern, commonly referred to as a specle pattern. It is described in statistical terms, with the help of probability distributions and correlation functions. The intensity correlation function, δI(r)δI(r ′ ) , where δI(r) is the deviation from the averaged intensity at point r, contains a short range term [1], C 1 (r, r ′ ), which oscillates on a scale of the wave length and exponentially decays beyond the mean free path, l. It also contains small long-range terms [2][3][4], which become dominant for |r − r ′ | ≫ l. Although the theory of speckle patterns was developed some time ago, it is only recently that the first experimental measurements of the spatial correlator C 1 (r, r ′ ) were reported both for microwaves [5] and optical waves [6,7]. These experiments were carried out for isotropic disordered media; macroscopic isotropy was also assumed in the existing theories. In this isotropic situation comparison with the theory has enabled the authors [6] to infer the effective refractive index, which is the only relevant parameter of the medium in the absence of disorder.The main message of this paper is that, in a medium with underlying spatial structure, the pattern of intensity correlations exhibits a vastly richer behavior as compared to the isotropic case. Moreover, additional features in C 1 (r, r ′ ) carry quantitavive information about this structure. As an example, we consider a disordered incompletebandgap photonic crystal and demonstrate how the band-structure parameters can be extracted from the angular anisotropy of the correlator C 1 .Superficially, it may seem that a wave with frequency ω, arriving from a distant source, after having been scattered by many random inhomogeneities, will lose all information about the crystal band-structure. Our point, though, is that C 1 (r, r ′ ) is essentially a local object: It is determined by scattering events in the vicinity of the points r, r ′ , and it is not sensitive to the "prehistory", i.e., scattering events experienced by the wave before arrival to the point r. In other words, C 1 (r, r ′ ) can serve as a "microscop" for observation of the local interference picture (on a scale smaller than l), thus, revealing the band-structure of the inherent photonic crystal. Such a microscop is particularly well suited for determination of the band-structure of realistic photonic crystals, since it is not affected by the long-range disorder. On the other hand, long-range disorder is a generic feature of realisitic crystals,...