An improvement of the crystal quality of opal films self-assembled from polymer spheres in a moving meniscus using the agitation by white noise acoustic vibrations is demonstrated. A tenfold higher ordering of a hexagonal sphere packing in the (111) plane is achieved. This crystallization method, the mechanism of which is described in terms of the stochastic resonance, is a contrast to the widely used approach based on maintaining equilibrium conditions during the crystallization process. The precise quantification of the incremental lattice order improvement as a function of acoustic noise intensity is achieved by calculating the probability of finding an opposite partner for each sphere in the lattice. This method is examined against conventional and established techniques such as Fourier transforms and translational and bond-orientational correlation functions, and its advantages are demonstrated. Rotational symmetry analysis of diffraction resonances in measured and calculated optical transmission spectra as a function of the azimuth lattice orientation are carried out to confirm that the surface ordering translates into the bulk ordering of high index crystal planes, which are most sensitive to disorder.