An ion-beam microcontouring process is developed and implemented for figuring millimeter scale optics. Ion figuring is a noncontact machining technique in which a beam of high-energy ions is directed toward a target substrate to remove material in a predetermined and controlled fashion. Owing to this noncontact mode of material removal, problems associated with tool wear and edge effects, which are common in conventional machining processes, are avoided. Ion-beam figuring is presented as an alternative for the final figuring of small (<1-mm) optical components. The depth of the material removed by an ion beam is a convolution between the ion-beam shape and an ion-beam dwell function, defined over a two-dimensional area of interest. Therefore determination of the beam dwell function from a desired material removal map and a known steady beam shape is a deconvolution process. A wavelet-based algorithm has been developed to model the deconvolution process in which the desired removal contours and ion-beam shapes are synthesized numerically as wavelet expansions. We then mathematically combined these expansions to compute the dwell function or the tool path for controlling the figuring process. Various models have been developed to test the stability of the algorithm and to understand the critical parameters of the figuring process. The figuring system primarily consists of a duo-plasmatron ion source that ionizes argon to generate a focused (～200-μm FWHM) ion beam. This beam is rastered over the removal surface with a perpendicular set of electrostatic plates controlled by a computer guidance system. Experimental confirmation of ion figuring is demonstrated by machining a one-dimensional sinusoidal depth profile in a prepolished silicon substrate. This profile was figured to within a rms error of 25 nm in one iteration.
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