Form error evaluation of ultra-precision freeform surfaces using genetic algorithm joint with sequential quadratic programming

Ultra-precision freeform surfaces have gained more and more applications in optical systems. To meet the required performance, they need to be manufactured with an extremely high form of accuracy. Meanwhile, there is still a lack of standard or definitive method to evaluate their form accuracy. In this paper, a Genetic Algorithm (GA) joint with Sequential Quadratic Programming (SQP) was developed for their form error evaluation. The GA was used to solve the Algebraic Distance (AD) based initial matching. Then SQP, based on the Orthogonal Distance (OD), is adopted to finely adjust the measured data correspondingly with the designed model and to achieve a unified evaluation result. From the evaluation results, it can be seen that this proposed method can robustly obtain the form error when the measured surfaces have different initial poses. The accuracy can reach far less than 1 nm which is sufficient for evaluating the ultra-precision freeform surface.