Study on the performances of dwell time algorithms in ion beam figuring

Dwell time calculation is one of the most important process in a highly deterministic computer-controlled Ion Beam Figuring (IBF) process. It is modeled as a deconvolution process between the desired removal map and the beam removal function, which is an ill-posed inverse problem. A good dwell time solution should fulfill four requirements: 1) it must be non-negative; 2) it should closely duplicate the shape of the desired removal map; 3) the total dwell time is expected to be as short as possible; 4) the calculation time is reasonable. Dwell time algorithms, such as Fourier transform-based algorithm, matrix-based algorithm, and Bayesian-based algorithm, have been proposed and applied to IBF. However, their performances were never clearly examined and described accordingly. In this research, we provide a quantitative study on the performances of these dwell time algorithms based on the aforementioned four requirements.