Quasi-absolute surface figure test with two orthogonal transverse spatial shifts

A new zonal wavefront reconstruction algorithm with pixel-level spatial resolution and high accuracy is proposed, which is able to reconstruct the original wavefront of general aperture shape from only two difference wavefronts measured at two orthogonal shear directions with shear amounts equaling arbitrary moderate integral multiples of the sample interval. Based on this algorithm, a quasi-absolute surface figure test method is presented, which requires only two additional translational measurements with shifts of arbitrary moderate integral multiples of sample interval along x and y directions besides the original position measurement. Optical schemes of the proposed method for testing flat, spherical and cylindrical surfaces are investigated, and special considerations and challenges for calibrating spheres and cylinders are also briefly formulated theoretically. Thorough errors analysis is formulated for obtaining high accuracy test result. Simulations and experiments on a flat surface are conducted to validate the proposed algorithm and method. Compared with existing absolute test methods with Pseudo-Shear Interferometry (PSI) technique, the presented method has advantages, like, less number of measurements, arbitrary moderate shear amounts and the high signal-to-noise ratio it can reach.