Dwell time algorithm in ion beam figuring

To get a high-precision optical surface, the deconvolved process of dwell time was transferred to a matrix equation in which the damped factor and the extra removal amount were introduced to expand the freedom of solution. A path weight factor and a surface error weight factor were used to take the scanning path and the initial surface error into account. Combined with the Gerchberg bandlimited extrapolation algorithm for initial surface error map extension, a high-precision final surface could be obtained within a factual aperture. Two surface error maps were calculated to $\text{rms}=0.1\mathrm{nm}$ from $\text{rms}=130.23\mathrm{nm}$ and to $\text{rms}=0.08\mathrm{nm}$ from $\text{rms}=282.74\mathrm{nm}$. The simulations show that a perfect dwell time solution could be obtained by the revised matrix equation and initial surface error map extension with the help of the least squares QR (LSQR) algorithm.