Abstract: Apparatus comprising a tool (2) for forming an aspherical surface on a material (14), and a support for supporting the material (12) for rotation about an axis, the arrangement being such that the tool (2) is restricted to movement with respect to the material (14) in two substantially linear axes transverse to each other. The apparatus may be a high-performance machine comprising a measuring arrangement (18) mounted so as to extend substantially across the surface of the material (14) and serving to measure the distance between the tool (2) and a referencing region (32) of the measuring arrangement (18) which can be in the form of a symmetrical metrology device (18), the metrology device being structurally unloaded. The apparatus is substantially symmetrical in two substantially vertical planes substantially perpendicular to and intersecting each other.