It is well documented that nonlinear optical systems can exhibit chaotic behavior. This behavior even appears in air when the light intensity is large enough. Chaotic behavior is well characterized by statistical means, because of sensitivity to initial conditions. Beam quality, ๐ 2 or the beam propagation parameter, is a key propagation parameter that is dependent on the spatial distribution of the optical field and deviations the medium makes from homogeneity or linearity. In order to better understand beam quality statistics for random fields in a nonlinear medium, an experimental system has been developed, and undergone initial testing. A Boston Micromachines Multi-DM 140 12x12 rectangular deformable mirror (DM) is used to induce phase screens on a 532nm visible beam, which then enters a lens-based beam profiling unit. Using computer controls and data pipelines, thousands of phase screened beams can be measured for beam quality automatically. Experimental testing shows stability of beam quality measurement across thousands of trials, and beam ensembles with long (of order beam size) coherence lengths to be feasible. Upon refinement of DM modeling with the insertion of a nonlinear medium the system can be made to test statistical models of nonlinear optics.