independently machined and mounted together in a precision assembly to form a single optical element for example in a cylindrical geometry the inner surface can be turned to form a section of a concave ellipse and the outer cylindrical surface can be used to register the segment against a precision mount an ellipsoid can have the property that all rays emanating from one focus are returned after a single reflection from an inner ellipsoidal surface to a second focus in some embodiments the inner reflective surface of each segment can be machined to a specific ellipsoidal form such that when two or more segments are assembled a continuous ellipsoidal focusing element can be obtained the precision with which the axis of the inner reflecting surface and that of the outer surface coincide can define the optical alignment of multiple segments in some embodiments the inner reflective surfaces of the individually fabricated segments can be conical in shape conical shapes can advantageously allow for more efficient and or effective polishing of the surface any desired shape for the inner surface of the optical element can advantageously be approximated as a series of conical segments for example if the desired shape for the inner surface is an ellipsoid then conical segments can be formed where the average slope of the conical segments is made to approximate the slope of the desired ellipsoid the accuracy of the approximation can be increased by decreasing the width of the segments in general one or more segments.