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For the first time, to the best of our knowledge, we have experimentally determined all of the components of the piezo-optic tensor for monoclinic crystals. This has been implemented on a specific example of triglycine sulfate crystals. Based on the results obtained, the complete elasto-optic tensor has been calculated. Acousto-optic figures of merit (AOFMs) have been estimated for the case of acousto-optic interaction occurring in the principal planes of the optical indicatrix ellipsoid and for geometries in which the highest elasto-optic coefficients are involved as effective parameters. It has been found that the highest AOFM value is equal to 6.8×10−15 s3/kg for the case of isotropic acousto-optic interaction with quasi-longitudinal acoustic waves in the principal planes. This AOFM is higher than the corresponding values typical for canonic acousto-optic materials, which are transparent in the deep ultraviolet spectral range.