The use of elastic emission machining (EEM) for fabricating optics from low-thermal-expansion glass for extreme ultraviolet (EUV) lithography is examined. EUV optics require figure accuracy and surface roughness of 0.1 nm root mean square (rms) or better. EEM using a rotating-sphere head is demonstrated to achieve this level of surface smoothness after a certain depth of removal dependent on the material being processed. In tests of continuous machining for 12 h, no increase in surface roughness is observed, demonstrating the high temporal stability of this noncontact processing method. EEM using a rotating-sphere head is thus confirmed to have sufficient figuring and smoothing capability for the fabrication of EUV optics. (c) 2007 American Vacuum Society.