Fig. 1. Grating interferometer. (a) Homodyne grating interferometer^[7]; (b) heterodyne grating interferometer^[8]

Fig. 2. Principle of straightness interferometry. (a) Two-dimensional grating interferometry^[29]; (b) Wollaston prism interferometry^[30-31]

Fig. 3. Measurement of roll angle by interferometry. (a) Heterodyne interferometry based on wave plate^[49]; (b) light intensity method based on wave plate^[50]

Fig. 4. Measurement of roll angle based on diffraction grating. (a) Double grating interferometry^[61]; (b) grating double beam method^[63]

Fig. 5. Multi-degree-of-freedom error measurement system based on one-dimensional grating. (a) 6DOF error measurement system based on divergent light source^[71]; (b) 5DOF error measurement system^[73]

Fig. 6. Multi-degree-of-freedom error measurement system based on two-dimensional grating. (a) 6DOF measurement system based on reflective grating^[81]; (b) 6DOFmeasurement system based on transmission grating^[83]

Fig. 7. Multi-degree-of-freedom measurement system based on three cube-corner prisms. (a) Measurement system based on three cube-corner prisms^[86]; (b) XM-60 6DOF error measurement system^[87]

Fig. 8. Multi-degree-of-freedom measurement system based on two cube-corner prisms. (a) Femtosecond laser dispersion interferometer^[90]; (b) 6DOF measurement system based on two cube-corner prisms^[91]

Fig. 9. Error measurement system based on single cone 6DOF^[93]

Fig. 10. Multi-degree-of-freedom measurement system based on a cube-corner prism. (a) 3DOF measurement system based on dual optical comb interference^[96]; (b) schematic of dual-comb ranging system^[98]; (c) time-domain characteristic of dual-comb system^[98]; (d) principle of dual-comb combined ranging method^[98]

Fig. 11. API XD Laser 6DOF error measurement system. (a) Photo of XD Laser system^[99]; (b) optical path diagram of XD Laser system^[99]

Fig. 12. Multi-degree-of-freedom measurement system based on right angle prism. (a) 6DOF measurement system based on right angle prism^[107]; (b) 5DOF measurement system based on right angle prisms^[112]

Fig. 13. X-Y platform 6DOF simultaneous measurement system^[113]

Fig. 14. Collimated beam based multi-degree-of-freedom measurement system^[114-116]

Fig. 15. Simultaneous measurement system of 6DOF error based on conical hexaprism^[117]

Fig. 16. Multi-parameter simultaneous measurement system of NC machine tool.(a) Single linear axis 6DOF error measurement system^[126]; (b) 21 errors measurement system for 3 linear^[129]; (c) simultaneous measurement of rotation axis 6DOF error^[130]; (d) linear axis and rotation axis 6DOF error measurement scheme^[131]