Optimization of wavefront reconstruction accuracy for conjugate shift differential absolute testing

The conjugate shift differential method, based on Fourier transforms, is critical for surface error testing of high-precision optical elements. However, this common approach is also prone to periodic spectrum loss. As such, this paper proposes conjugate double shift differential (CDSD) absolute testing, which can effectively compensate for spectrum loss and achieve accurate wavefront reconstructions. Spectrum loss in the single shift differential method is analyzed through a study of the Fourier reconstruction process. A calculation model for the proposed CDSD method is then established and constraint conditions for shift quantities are provided by analyzing double shear effects observed in transverse shear interference. Finally, the reconstruction accuracies of various spectrum compensation methods are compared. Results showed that spectrum loss became more evident with increasing shift amounts. However, the CDSD method produced the smallest measurement error compared with conventional direct zero filling and adjacent point averaging, suggesting our approach could effectively improve absolute shape measurement accuracy for planar optical elements.