A system for processing a portion in a processing volume of a transparent material by application of focused radiation including a device for generating and an optical system for focusing radiation, with a device for changing the position of the focus of the radiation and a control device. This system performs a slow scanning movement of the focus and an independent fast scanning movement of the focus which section can be moved by the slow scanning movement in the entire processing volume in an arbitrary direction as well as by a system into which a scan pattern is encoded, with scanning movement including at least one lateral base component in the x- and/or y-direction, which is superimposed by components with synchronous change-of-direction-movements in the z-direction and in x-direction and/or y-direction. The invention also includes corresponding methods, a control program product and a planning unit.
