Compact spatial phase-shifting quadrature detection for nanometer displacement measurement

Conventional phase-shifting detection system enables compact quadrature signal acquisition; however, it suffers from severe sensitivity to angular perturbations induced by spatial positional shifts of non-collinear beams. Here, we present a robust spatial phase-shifting interference detection method using spatial interference fringes and a dual-detector configuration arranged along the fringe normal direction. A physical model for quadrature signal acquisition is established, in which the robustness is quantitatively characterized by the ratio of the projected fringe periods along the detector axis before and after angular perturbation. The analysis demonstrates that under a specific homologous angular perturbation of 0.005°, the relative deviation of the longitudinal fringe interference geometric configuration is 3 × 107 times that of the optimized transverse fringe interference geometric configuration. The optimized transverse fringe interference geometric configuration can maintain the ratio at a level extremely close to 1, thereby ensuring stable phase matching and signal orthogonality. The proposed method is applied to a grating interferometer and validated through simulations and experiments. The optimized system achieves a maximum residual error of 21.29 nm and a maximum standard deviation of 12.71 nm over a 300 µm measurement range, demonstrating enhanced robustness and suitability for compact grating interferometric displacement measurement system.