Investigation of prediction and control methods for the dynamic tool influence function of millimeter-scale ion beam
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In the fabrication of short-wavelength optical components, critical mid-spatial-frequency (MSF) errors in the 0.1-1 mm-1 band are a major barrier to achieving picometer-level surface figure accuracy. Ion beam figuring (IBF) with a millimeter-scale beam spot is suitable for correcting errors in this frequency range. However, for a narrow beam with a full width at half maximum (FWHM) smaller than 2 mm, there is an obvious inconsistency between the static and dynamic tool influence functions (TIF), giving rise to a time-variant tool influence function (TV-TIF). This seriously limits the convergence of MSF errors correction. In this work, the influence of TV-TIF in millimeter-scale-beam IBF is analyzed by coupling the energy deposition distribution with the evolution of surface topography, and the analysis is verified experimentally. A broadening function is introduced to establish a convolution relationship between the static and dynamic TIFs. Based on the equivalent global TIF and the convergence rates in different spatial-frequency bands, a parameter inversion method for the dynamic TIF is proposed. Simulation and experimental results show that the deviation between the inverted TIF parameters and the true values is less than 10%. Experiments were carried out on a home-built IBF platform using a fused silica planar mirror. The root-mean-square (RMS) surface error was reduced from 1.479 nm to 0.228 nm. These results confirm the accuracy of the proposed dynamic TIF prediction method and the effectiveness of the TV-TIF compensation method for suppressing critical MSF errors and supporting picometer-level surface fabrication.
