Iterative wavelet-transform-based surface decomposition algorithm for multi-tool fabrication in computer-controlled optical surfacing

As demand for high-precision optical mirrors in astronomy increases, combined fabrication using multiple polishing tool sizes has been adopted widely. To address remaining limitations in computational and fabrication efficiency, this paper proposes an iterative wavelet-transform-based surface decomposition algorithm (IWTSD) and an associated multi-tool fabrication strategy. IWTSD applies the two-dimensional dual-tree complex wavelet transform (2D-DTCWT) with iterative refinement to decompose a target surface into two or more scale-separated, non-negative component surfaces. Specific surface extension operation with an optimized factor is used to adapt IWTSD for non-rectangular apertures. This decomposition reduces both computational cost and total polishing dwell time compared with similar methods. Simulations demonstrate that IWTSD-based multi-tool fabrication achieves comparable surface error convergence using only 2/3 of the dwell time required by other multi-tool fabrication based on alternative surface decomposition algorithms, and yields a residual RMS about 1/3 that of single-tool fabrication. Experimental polishing of a 1150 mm off-axis aspheric mirror showed that overall RMS decreased from 0.655 <i>λ</i> to 0.21 <i>λ</i>, and residuals at each scale were substantially reduced. These results demonstrate that the proposed method can improve fabrication efficiency for large-aperture optical mirrors with low computational cost.