Abstract
An ultraprecise aspherical mirror, which is difficult to fabricate by conventional mechanical machining, is required for optics, particularly in the field of coherent hard X-rays or extreme-ultraviolet lithography. In this review, we introduce new fabrication methods of elastic emission machining (EEM) and plasma chemical vaporization machining (PCVM). They are noncontact machining methods using chemical reactions and enable ultraprecise numerically controlled figuring by dwell time control. We also introduce ultraprecise aspheric ellipsoid mirrors for focusing hard X-rays fabricated using PCVM and EEM with a new figure testing method, were found to achieve nearly diffraction-limited focusing performance.