A plurality of waveguide display substrates, each waveguide display substrate having a cylindrical portion having a diameter and a planar surface, a curved portion opposite the planar surface defining a nonlinear change in thickness across the substrate and having a maximum height D with respect to the cylindrical portion, and a wedge portion between the cylindrical portion and the curved portion defining a linear change in thickness across the substrate and having a maximum height W with respect to the cylindrical portion. A target maximum height Dt of the curved portion is 10−7 to 10−6 times the diameter, D is between about 70% and about 130% of Dt, and W is less than about 30% of Dt.