Absolute measurement of optical flat surface shape based on the conjugate differential method.

In this paper the conjugate differential method is proposed to measure the absolute surface shape of the flat mirror using a phase-shifting interferometer. The conjugate differential method is derived from the differential method, which extracts absolute phase differences by introducing the slight transverse shifts of the optic. It employs the measurement schemes making transverse shifts on the orthogonally bilateral symmetry positions. So the measurement procedures have been changed into four-step tests to get the phase difference map instead of three-step tests for the differential method. The precision of the slope approximation is enhanced by reducing couplings between multi-step tests, and the reliability of the measurements can be improved. Several differential wavefront reconstruction methods, such as Fourier transform, Zernike polynomial fitting and Hudgin model method, can be applied to reconstruct the absolute surface shape from the differencing phase maps in four different simulation environment. They were also used to reconstruct the absolute surface shape with the conjugate differential method in the experiment. Our method accords with the classical three-flat test better than the traditional differential method, where the deviation of RMS value between the conjugate differential method and the three-flat test is less than 0.3 nm.