The unexpected features of square-law nonlinearity inherent in the non-collinear three-phonon acousto-optical interaction controlled by elastic waves of finite amplitude in birefringent crystals with linear acoustic attenuation are distinguished and investigated. They lead to breakthrough applications of strongly nonlinear three-phonon interaction to linear optical spectrum analysis with ~100% efficiency and qualitatively improved resolution. Principally new physical degree of freedom, unique for this nonlinear phenomenon, is revealed and characterized. The indispensable theoretical developments and proof-of-principle acousto-optical experiments with specially designed wide-aperture tellurium dioxide cell are presented. The obtained experimental results confirm the elaborated approaches promising potentially the highest possible spectral resolution that one can expect in principle from acousto-optical technique within optical spectrum analysis.