A control apparatus for controlling a thickness of a substrate, such as a glass ribbon. The control apparatus comprises a laser assembly and a shielding assembly. The laser assembly generates an elongated laser beam traveling in a propagation direction along an optical path. The shielding assembly comprises at least one shield selectively disposed in the optical path. The shield is configured to decrease an optical intensity of a region of the elongated laser beam. The shielding assembly is configured to change an intensity profile of the elongated laser beam from an initial intensity profile to a targeted intensity profile. A desired targeted intensity profile can be dictated by an arrangement of the shield(s) relative to the optical path, and can be selected to affect a temperature change at portions of the substrate determined to benefit from a reduction in thickness.