Study of weighted space deconvolution algorithm in computer controlled optical surfacing formation

Abstract

Theoretical and experimental research on the deconvolution algorithm of dwell time in the technology of computer controlled optical surfacing (CCOS) formation is made to get an ultra-smooth surface of space optical element. Based on the Preston equation, the convolution model of CCOS is deduced. Considering the morbidity problem of deconvolution algorithm and the actual situation of CCOS technology, the weighting spatial deconvolution algorithm is presented based on the non-periodic matrix model, which avoids solving morbidity resulting from the noise induced by measurement error. The discrete convolution equation is solved using conjugate gradient iterative method and the workload of iterative calculation in spatial domain is reduced effectively. Considering the edge effect of convolution algorithm, the method adopts a marginal factor to control the edge precision and attains a good effect. The simulated processing test shows that the convergence ratio of processed surface shape error reaches 80%. This algorithm is further verified through an experiment on a numerical control bonnet polishing machine, and an ultra-smooth glass surface with the root-mean-square (RMS) error of 0.0088 \mum is achieved. The simulation and experimental results indicate that this algorithm is steady, convergent, and precise, and it can satisfy the solving requirement of actual dwell time.