非球面的非零位检测较其零位检测而言具有更强的通用性，但非零位检测偏离了零位条件，所产生的回程误差给被测非球面的面形重构带来一定困难。针对非球面非零位检测中回程误差的校正与面形重构问题，提出了基于检测系统理论建模的非球面面形逆向求解技术。该方法对实际检测系统进行理论建模，设置被测面面形为变量，以实际检测到的波前作为目标函数，通过拟合优化得到的结果进而重构出被测面面形。对逆向优化重构技术进行了仿真验证、实际检测和误差分析，实际测量口径为101.0 mm的凹抛物面反射镜，检测结果与标准零位法测得结果一致，峰谷值和均方根值误差分别优于λ/20和λ/50。

Aspheric nonnull testing methods can achieve more flexible measurement of aspheres than the null testing ones. However, due to the violation of the null condition, retrace error exists and data reduction is difficult for this reason. In order to solve this problem, a reverse optimization data reduction approach based on theoretical simulation of the testing system is proposed. Simulation system is set according to the experimental apparatus. Surface figure errors are variables during the optimization procedure while the experimental wavefront is set to be the objective function. Aspheric surface figure error can be then reconstructed by fitting the solutions obtained from the optimization process. Simulation verification, experiment and error analysis are considered for this method. An experiment for testing a concave paraboloidal mirror with 101.0 mm clear aperture is taken. The result is very similar to that of null test (autocollimation method) with the peak-to-valley value and root-mean-square value errors less than λ/20 and λ/50, respectively.