Reverse optimization reconstruction of aspheric figure error in a non-null interferometer.

Aspheric non-null testing, as an alternative to the traditional null testing, achieves more flexible measurements. However, figure-error reconstruction in non-null tests has always been difficult due to the presence of retrace error. A novel method with reverse optimization is proposed for aspheric figure-error reconstruction in a non-null interferometer. It is a generalized and effective approach based on system modeling and polynomial fitting. An optimization function is set with polynomial coefficients of the desired figure error as variables and those of the detected experimental wavefront as optimization targets. Through the reverse optimization process with iterative ray tracing, the optimal solutions can be extracted and the desired figure error is reconstructed with a simple fitting procedure. Numerical simulations verifying the high accuracy of the proposed method are presented with error considerations. A set of experiments has also been carried out to demonstrate the validity and repeatability of this method.