Non-linear Compensated Dwell Time for Efficient Fused Silica Surface Figuring Using Inductively Coupled Plasma

Atmospheric plasma etching has been increasingly applied in the fabrication of optical elements for high efficiency and near-zero damage to optical surfaces. However, the non-linearity of material removal rate is inevitable because of the thermal effect of inductively coupled plasma (ICP) etching for fused silica. To apply ICP to figure fused silica surface, the time-varying non-linearity between material removal rate and dwell time is analyzed. An experimental model of removal function is established considering the time-varying non-linearity. According to this model, an algorithm based on nested pulsed iterative method is proposed for calculating and compensating this time-varying non-linearity by varying the dwell time. Simulation results show that this algorithm can calculate and adjust the dwell time accurately and remove surface errors with rapid convergence. Surface figuring experiments were set up on the fused silica planar work-pieces with a size of 100 mm (width) x 100 mm (length) x 10 mm (thickness). With the compensated dwell time, the surface error converges rapidly from 4.556 lambda PV (peak-to-valley) to 0.839 lambda PV within 13.2 min in one iterative figuring. The power spectral density analysis indicates that the spatial frequency errors between 0.01 and 0.04 mm(-1) are smoothed efficiently, and the spatial frequency errors between 0.04 and 0.972 mm(-1) are also corrected. Experimental results demonstrate that the ICP surface figuring can achieve high convergence for surface error reduction using the compensated dwell time. Therefore, the ICP surface figuring can greatly improve surface quality and machining efficiency for fused silica optical elements.