An apparatus for refractive ophthalmic surgery by laser radiation including a source of radiation which emits a processing beam a beam path for focusing and scanning. The beam path focuses the processing beam into a cornea of an eye and shifts a position of a focus therein. A beam splitting device generates several foci in the cornea and divides the processing beam into a primary beam and at least one secondary beam. The primary and secondary beams have substantially the same cross section as the processing beam which is incident on the beam splitting device and the beam-splitting device introduces a separation between the primary and secondary beams. The primary and secondary beams expand in the beam path. A contact glass induces a pre-defined geometric boundary surface at the cornea.