For expanding the measurement range and improvement of accuracy of multi-axes grating encoder, a mathematical model of measurement angle and diffraction spot with QPD was established. We proposed a light spot position calculation method with consideration of both the optimized composite algorithm of laser beam feature of Gaussian distribution and the QPD diagonal algorithm. In this method, we use the piecewise polynomial fitting method to fit and solved the parameters of the traditional Infinite integral algorithm and the Boltzmann function fitting algorithm. Meanwhile, we introduce a weight factor and use the Composite algorithm to compensate the spot position error. Based on the given QPD model and the basic parameters of the laser beam, simulation works are carried out and results show that the maximum error of the spot position can reduce to be an order of 10-6 mm within the 2 mm measurement range using piecewise cubic polynomial fitting, around 10% of the traditional methods.

Heterodyne grating interferometer is widely used in precision positioning due to its high precision and robustness. However, the polarization states of two frequency components in a dual-frequency laser are easy to overlap with each other because of the non-ideality of optical components. It will cause nonlinear error, which limits the measurement precision of the grating interferometer. To improve the frequency aliasing of heterodyne grating interferometer, a polarization adjustment module is proposed to adjust the polarization angle of the dual-frequency laser. The dual frequency system outputs two laser beams with different frequencies separately. The module realizes the polarization adjustment of the two frequency components through two groups of the polarizers and the half-wave plates (HWP). Finally, the polarization directions of two frequency components are orthogonal and combined by the beam splitter (BS). Thus, the nonlinear error caused by frequency aliasing is removed. The polarization adjustment module has the advantages of not changing the direction of the laser propagation and simple structure, which makes it easy to realize integration. It can provide a reference for the solution of frequency aliasing of heterodyne grating interferometer.