Aggregation of nanodispersed particles plays an essential role in the technology of colloidal systems. In this work the formation of clusters composed of long-living gas nanobubbles in electrolyte aqueous solutions has been studied experimentally by combining three distinct but complementary laser techniques: dynamic light scattering (DLS), laser phase microscopy, and polarimetric scatterometry. We propose a mathematical approach to modeling the structure of spherical particle clusters that is based on the solution of inverse problem of optical wave scattering with allowance for cluster-cluster aggregation. In this way we found the characteristic size of nanobubbles and fractal properties of their clusters in aqueous solutions of NaCl. The described method can be applied to the exploration of clustering in a wide class of disperse systems of spherical particles.