1. Apparatus for refractive surgery comprising the following: a laser-beam source ( 34 ), means ( 36 ) for shaping and guiding the laser beam emitted by the laser-beam source, in relation to an eye ( 10 ) to be treated, a camera ( 38 ) for recording the iris and pupil of the eye, a computer ( 40 ), comprising a control program for controlling the said means according to an ablation profile, characterized in that the control program: includes a function of the position of the apex (A) of the cornea ( 12 ) of the eye ( 10 ) in dependence on at least one property of the pupil, during the refractive surgery, records the instantaneous property of the pupil by means of the camera and determines therefrom, by means of the said function, the position of the apex (A) of the cornea, and aligns the ablation profile to the thus determined position of the apex (A) or of a point of the corneal surface having a fixed distance from the apex.