This invention relates to an improvement for applying a layered structure onto a convex surface of a lens. After thermoforming the layered structure, a curvature direction of the layered structure is inverted. The structure is then applied on the lens surface by continuously pushing the structure against the lens surface, starting from a contact point between a convex surface of the structure and the convex surface of the lens. The curvature direction of the layered structure is then inverted again, so that it recovers the curvature direction that resulted from thermoforming. Stresses within the layered structure are then reduced, and the structure can be assembled with the lens without defects.