the stereo eyepiece 80 the beam deflection unit 23 deflects the expanded laser beam 15 vertical to its propagation direction accordingly the laser focus can be directed to different points in the cornea the depth of focus can be varied by displacing the focusing optics 23 along the optical axis or by adapting the focal length of the focusing optics circular paths are preferably traveled by the deflecting unit for cutting the circular surface the circle radius is reduced from circular path to circular path and the repetition rate is so adapted that a uniform spot distance is maintained the depth of focus is adapted from circular path to circular path in such a way that the cut follows the curvature of the cornea to perform astigmatic corrections of eyesight cylindrical correction the depth of focus can be moved up and down twice over the course of the circular path so that a lenticle with a cylindrical lens portion is formed for the flap edge the depth of focus is slowly displaced from the base of the flap to the outside of the cornea while the radius remains fixed so that a cylindrical jacket is formed the laser beam must be interrupted on an arc shaped segment of the circles described above in order to leave a hinge at which the prepared flap is held for this purpose laser pulses are simply coupled out of the radiation source 11 the radiation source 11 is a femtosecond radiation source with the parameters described above which is preferably directly diode pumped and therefore simple and reliable the emitted laser beam 15 is preferably expanded to a 1 to 2.