Design optimization of a flexural hinge-based bender for X-ray optics

This paper presents a parameter study and design optimization of a flexural hinge-based bender by use of finite-element modelling and analytical formulation. The relationship between the mirror shape and the driving forces, the so-called bender driving equation, is established. Various parameters are investigated: the material properties, the geometrical parameters, the stress and deformation of the mirror and flexural hinge, the residual slope error of the mirror, and the resolution required for the actuators. Analysis results have been compared with test results for a prototype bender and a silicon mirror (170 × 40 × 10 mm). Both analysis and test results confirm the microradian accuracy of the bent mirror. Finally, a bender design for short-bending-radius applications is also presented.