John C. Lambropoulis
The Twyman effect refers to the fact that, when a thin optical plate has one side ground, the plate bends with the ground side becoming convex, i.e. as if the ground side is in a residual compressive stress. Such deformation often shows up as “power” on form measurements of the other (usually polished) plate surface. For thin flat optics, Twyman effects become important at aspect ratios of 1:25 or thinner. In this case, the optic bends throughout its surface with a constant curvature, i.e. bending extends over the whole surface. Here we discuss Twyman effects for mildly or highly curved thin axisymmetric optics such as cylinders, spheres, and shallow lenses or mirrors. We also outline extensions to more complex geometries, such as ogives. We show that the deformation in thin curved optics is significantly different from flat plates: In curved optics, deformation consists of a simple stretching contribution, valid over the largest portion of the optic, plus a complex, spatially-dependent bending contribution in a boundary layer, valid near the free edges of the optic.