On the flexure of telescope secondary mirrors

The theory of elasticity is applied to the determination of the flexure of telescope secondary mirrors in the field of gravity. With respect to the basic configuration defined by a mirror of essentially constant thickness, we consider the thickness profile to be a free parameter. As a first approach to the problem, we study four thickness configurations supported by their central zone, and having the same total mass. The sharp edge lenticula configuration leads to Euler-Gauss hypergeometrical functions. The quasi-conical configuration is that which gives ideal rigidity since its own deformations, purely parabolic, do not result in any image quality degradation. The configuration permitting one to aspherize the mirror by the dioptric elasticity method also represents a considerable gain in rigidity compared to the basic configuration.