Objective Aspherical optical elements are widely employed in optical systems due to their large degree of design freedom, and the surface shape accuracy of the elements directly affects the performance of the optical system, but the normal aberration properties result in difficult detection of aspherical surfaces. Annular subaperture stitching interferometry is non-null interferometry for detecting the surface shape of aspherical surfaces, does not need to completely compensate for the normal aberration of aspherical surfaces, but relies on high-precision mechanical motion mechanisms and complex positional error algorithms. Therefore, we propose a method for synchronous annular subaperture interferometry (SASI) to synchronously obtain the interference pattern of two subapertures. Meanwhile, SASI does not need a complex motion mechanism and can increase the dynamic direct detection range of aspherical surfaces by the interferometer to some extent. Furthermore, it can effectively improve the detection speed and reduce the influence of motion error on measurement accuracy. Methods We adopt the theoretical analysis and the combination of simulations and experiments to carry out this research. Firstly, according to the Nyquist sampling theorem, the theory of the SASI method is analyzed to determine the focal distance principle, and the reference unified model is built by coordinate change and Zemax assisted modeling to realize the surface shape reconstruction. Secondly, the measurement of SASI is simulated and verified, the Zemax is adopted to assist in building the measurement system model, and the interference images obtained by the SASI method and interferometer direct detection are simulated respectively. Additionally, the fringe density of the two interference images is compared, and the aspherical surface shape is reconstructed in the simulated measurement experiments to verify the correctness of the SASI method. Finally, we actually measure the aspherical surface and obtain the interference pattern, and the aspherical surface is placed in the best position and measured directly with the interferometer. Furthermore, the interference fringes measured by SASI method are compared with the result of Luphoshcan method, which can further verify the correctness and validity of the SASI. Results and Discussions Our SASI method can accomplish the detection of aspherical surfaces without a complex motion mechanism, and it can also increase the dynamic range of the interferometer for direct detection of aspherical surfaces to a certain extent. Firstly, the SASI theory is analyzed, and a unified model is proposed for reconstructing the surface shape. Secondly, simulation experiments are carried out to detect the surface shape of an asphere with a vertex radius of curvature of 250 mm and an aperture of 80 mm. The simulation results show that the density of interferometric fringe patterns obtained by the SASI is reduced compared with that obtained by the interferometer ( Fig. 4). Meanwhile, by adopting the proposed baseline unified model, the reconstructed surface shape results with the original surface shape of the residual PV of 0.0282 lambda, RMS of 0.0045 lambda are shown in Fig. 6, which initially verifies the validity of the proposed method. Secondly, the aspherical surface with vertex curvature radius of 317 mm and aperture of 90 mm is measured experimentally, and the density of the SASI method is still reduced compared with that of the interferometer directly detecting the same asphere (Fig. 8). Additionally, in Fig. 9 and Table 3, comparison of the reconstructed surface shape with the Luphoshcan result shows that PV is 0.0362 lambda and RMS is 0.0091 lambda of absolute surface error, and the residual deviation of the surface shape is 0.0926 lambda (PV) and 0.0098 lambda (RMS), which further verifies the correctness of the proposed SASI method. Conclusions The proposed SASI method can effectively realize the surface shape detection of aspherical surfaces. On the one hand, the method does not need to move the interferometer or the element to be measured, which utilizes a bifocal lens to form two measurement wavefronts to match different subaperture of the aspherical surface, and then realizes the synchronized annular band subaperture interferometry of the aspherical surface. Finally, this simplifies the measurement device, shortens the measurement time, and reduces the effect of the motion error on the measurement accuracy. On the other hand, this method increases the dynamic range of the interferometer for direct detection of aspherical surfaces to a certain extent. Combined with the aspherical surface example of the SASI method for simulation and measurement experiments to verify the SASI method, the density of interferometric fringe pattern under the detection of the SASI method is significantly reduced. Additionally, the results of the surface reconstruction are consistent with the actual surface results, which further verifies the correctness and validity of the proposed SASI method.
