This Letter reports on new methods and a consistent model for voltage tunable optical transmission gratings. Elastomeric gratings were molded from holographically written surface relief gratings in an azobenzene sol-gel material. These were placed on top of a transparent electroactive elastomeric substrate. Two different electro-active substrate elastomers were employed, with a large range of prestretches. A novel finite-deformation theory was found to match the device response excellently, without fitting parameters. The results clearly show that the grating underwent pure-shear deformation, and more surprisingly, that the mechanical properties of the electro-active substrate did not affect device actuation.