A General Stress Patterning Method for Manufacturing Ultra-Precise Free-Form Deformation in Thin-Substrates

A device includes a substrate and a stressed layer disposed on a first surface of the substrate. The stressed layer includes: a first set of patterns having a predetermined geometry, size, and arrangement selected to control an equibiaxial stress field of the stressed layer, wherein the equibiaxial stress field varies in magnitude over the first surface of the substrate, and a second set of patterns etched into the first set of patterns and the substrate, the second set of patterns comprising a plurality of substantially parallel lines arranged to control at least a uniaxial stress field of the stressed layer, wherein the uniaxial stress field varies in magnitude over the first surface of the substrate.