Reverse optimization reconstruction method in non-null aspheric interferometry

Aspheric non-null test achieves more flexible measurements than the null test. However, the precision calibration for retrace error has always been difficult. A reverse optimization reconstruction (ROR) method is proposed for the retrace error calibration as well as the aspheric figure error extraction based on system modeling. An optimization function is set up with system model, in which the wavefront data from experiment is inserted as the optimization objective while the figure error under test in the model as the optimization variable. The optimization is executed by the reverse ray tracing in the system model until the test wavefront in the model is consistent with the one in experiment. At this point, the surface figure error in the model is considered to be consistent with the one in experiment. With the Zernike fitting, the aspheric surface figure error is then reconstructed in the form of Zernike polynomials. Numerical simulations verifying the high accuracy of the ROR method are presented with error considerations. A set of experiments are carried out to demonstrate the validity and repeatability of ROR method. Compared with the results of Zygo interferometer (null test), the measurement error by the ROR method achieves better than 1/10λ.