Aspherical grads method for calculating best fitting sphere of ultra-thin mirror and finite element analysis

Using the plastic deformation of ultra-thin mirror,the ultra-thin sphere is deformed into asphere by active optics technology,which can avoid the manufacturing problem of large aspheric mirror.Some principles of choosing the best fitting sphere for ultra-thin mirrors are discussed.The reasons to choose aspherical grads as principle are presented.The two spheres which are gotten from aspherical grads method and least square method are analyzed by the finite element method after loading displacements,and the surface errors relative the desired asphere and the maximum stresses are compared.The results show that the best fitting sphere gotten by aspherical grads method has less surface error and stress under same confined condition,same loading position and loading points.