Twyman effect in thin curved optics: effects of variable thickness and curvature

Grinding or finishing of thin curved optics introduces surface-localized stresses that may result in bending deformations, thus affecting optical performance (Twyman effect). The Twyman effect depends on local thickness of the optic as well as its curvature. We use numerical and analytical techniques to assess the effects of these variables for shallow and deeply curved axisymmetric optics. A useful metric of comparison, valid for shallow optics, is the deformation of a similar flat optic (window). This comparison is inadequate for more curved optics, which demonstrate a smaller deformation that is now localized in a boundary layer near the optic-free edge. The effects of thickness variation are also presented. Normal deflection and slope for a positive optic (thickness at the center greater than the tip) are well approximated by a constant thickness optic. This is not the case for a negative optic, where deformations near the apex are more pronounced, thus extending significant deformations through the full optic aperture.