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We propose a general method of designing phase-shifting algorithms for grating lateral shearing interferometry. The algorithms compensate for the zeroth-order effect error and phase-shifting error in varying degrees. We derive a general expression of the phase-shifting algorithm in grating lateral shearing interferometer and introduce the corresponding design method. Based on the expression and method, four phase-shifting algorithms are designed with different phase-shifting errors to obtain high measurement accuracy. A new 13-frame phase-shifting algorithm is designed and simulated with a large zeroth-order effect. Simulation results verify the general expression and the corresponding design method.

Based on the analysis of existing guiding mechanisms, a novel 2-DOF compound compliant parallel guiding mechanism (2-DCCPGM) is proposed in this paper, which has compact structure, long motion range and negligible parasitic displacements. The relationship between the guiding displacements and the driving forces have been obtained from the pseudo-rigid-body (PRB) model of 2-DCCPGM. And the dynamic analysis is taken as well. Some design criteria are put forward, based on the analytical results. To analysis the guiding capability and the dynamic performance of 2-DCCPGM, finite element analysis (FEA) has been carried out. And the results of the static FEA simulations confirmed that the 2-DCCPGM barely generates parasitic displacements. A prototype has been manufactured, and experiments have been conducted to validate the performance of the 2-DCCPGM. And from the experimental results, the 2-DCCPGM has been proved to have satisfactory guiding performance. Moreover, the experiment results have also revealed that the machining deviation of the flexure hinges of 2-DCCPGM could cause parasitic displacements and reduce the guiding linearity of the 2-DCCPGM.

The grating lateral shearing interferometer may achieve ultra-high accuracy absolute testing after eliminating the systemic errors from the interferometer itself and the orthogonality problem between two shearing directions. Aiming at the interferometer, we proposed a two-step algorithm for removing the rotationally asymmetric systemic errors from our shearing setup. This rotation method provides a new approach for acquiring the wavefront aberration by choosing the rotation angles with the minimum decentration and to satisfy the immune of systemic errors at the same time. Simulation and experiment verified that it is more propitious to eliminate the systemic errors when it is applied to our shearing setup.