The device has a control program that determines the dependency of the position of the apex of the cornea (12) on properties of the pupil in the eye (10) to be treated and computes the position of the ablation center for the refractive surgery from this dependency by means of the properties of the pupil measured. Independent claims are also included for the following: (A) a control program for an inventive device (B) and a method of producing a control program. EP1985269A1