[1] [1] Guan J, Kchert P, Weichert C, et al. A high performance one-dimensional homodyne encoder and the proof of principle of a novel two-dimensional homodyne encoder[J]. Precision Engineering, 2013, 37(4): 865-870.

[2] [2] Zhou Shaolin, Yang Yong, Chen Wangfu, et al. Dual-grating-based nanometer measurement[J]. Acta Optica Sinica, 2009, 29(3): 702-706.

[3] [3] Xia Haojie, Fei Yetai, Fan Guangzhao, et al. 2D nano-displacement measurement with diffraction grating[J]. Nanotechnology and Precision Engineering, 2007, 5(4): 311-314.

[4] [4] Peng Donglin, Fu Min, Zhu Ge, et al. Study on a novel linear displacement sensor based on the orthogonal modulating light intensity[J]. Acta Optica Sinica, 2014, 34(12): 1212007.

[5] [5] Kimura A, Gao W, Arai Y, et al. Design and construction of a two-degree-of-freedom linear encoder for nanometric measurement of stage position and straightness[J]. Precision Engineering, 2010, 34(1): 145-155.

[6] [6] Liu C H, Cheng C H. Development of a grating based multi-degree-of-freedom laser linear encoder using diffracted light[J]. Sensors and Actuators A, 2012, 181(7): 87-93.

[7] [7] Wang Xueying. Research of high-precision displacement measurement system based on the principle of diffraction and interference[D]. Harbin: Harbin Institute of Technology, 2014: 54.

[8] [8] Chu Xingchun, Lü Haibao, Zhao Shanghong. Wide-range grating interferometer with nanometer resolution[J]. Opto-Electronic Engineering, 2008, 35(1): 55-59.

[9] [9] Yang Dongxing, Yan Shuhua, Du Liebo, et al. Design of a miniature single-grating displacement measuring system with nanometer resolution[J]. Infrared and Laser Engineering, 2013, 42(4): 1020-1025.

[10] [10] Qiao Dong. Study on the measurement technology of high precision absolute linear encoder[D]. Changchun: Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, 2015: 131-132.

[11] [11] Qiao Dong, Xu Zhijun, Wu Hongsheng, et al. A method for compensating interpolation error of absolute linear encoder[J]. Acta Optica Sinica, 2015, 35(1): 0112008.

[12] [12] Xia Haojie. Research on precise 2-D plane grating measurement system and key technology[D]. Hefei: Hefei University of Technology, 2006: 83-100.

[13] [13] Hong Xin, Zhang Defen, Jiang Chengzhi, et al. Study of laser-Doppler displacement-measuring technique by polarization phase-shifting and grating produced frequency beat[J]. Chinese J Lasers, 1998, 25(5): 432-436.

[14] [14] Du Jun, Qu Yanchen, Zhao Weijiang, et al. Measuring error of phase modulation laser Doppler shift measuring method[J]. Acta Optica Sinica, 2014, 34(7): 0712001.

[15] [15] Yu Qifeng, Lu Hongwei, Liu Xiaolin. Precision measurement and motion measurement based on the images[M]. Beijing: Science Press, 2002: 56-60.

[16] [16] Fei Yetai. Accuracy theory and data analyses[M]. Beijing: China Machine Press, 2010: 5-6.