Millimeter-scale error correction with the frequency-adaptive dwell time optimization in spot-sized ion beam figuring

In optical fabrication, millimeter-scale errors, particularly from 1 mm to 10 mm, can be effectively corrected using spot-sized ion beam figuring (IBF), which enables the tool influence function (TIF) size to be reduced to the millimeter or submillimeter level. However, when the error scale approaches the TIF size, the precision of dwell time calculation is limited, necessitating the increased additional material removal (AMR) to achieve accurate correction, at the cost of extended machining times. To address this trade-off, this study proposes the frequency-adaptive dwell time optimization method that leverages linear time-invariant (LTI) systems and transfer functions (TF) to pre-compensate material removal, enhancing both precision and efficiency. The comprehensive simulations demonstrate its distinctive advantages over traditional AMR optimization, particularly when higher-spatial-frequency errors predominate. In experimental validation, the shell-type structure was used to generate errors with spatial wavelengths from 2.6 mm to 11.2 mm. After correction using the TIF with the full width at half maximum (FWHM) of 2 mm, the root-mean-square (RMS) value of error was successfully reduced from 5.68 nm to 0.73 nm, confirming its feasibility and effectiveness.