First of all a new method

namely aspheric gradient method

is presented to determine actuator arrangements for shaping aspheric surface

and the theoretical analysis and two calculating formulas of this method are described. Secondly

based on an example of off-axis ultra-thin large-aperture spherical mirror

the initial solution of actuator arrangements is given by the aspheric gradient method

and the finite element analysis and the surface errors for shaping aspheric surface are accomplished. Thirdly

the optimizations of actuator arrangement are done. Finally

three methods of actuator arrangements

namely aspheric gradient

square and circular methods are compared using finite element analysis. The results show that the initial solution based on average value of aspheric gradient is most alike with the final solution

and it is in accord with the relation that the greater the aspheric gradient the greater the surface density of actuator arrangements. Meantime

the optimization can also further reduce the number of actuators and further improve the form errors. The aspheric gradient method has more advantages than the square and annulus methods

which makes it suitable for incorporation in the field of the shaping aspheric surface to determine the initial solution of actuator arrangements.