# A Spatial 4-DOF Laser Collimation Measurement System
## 1 Introduction
Based on the principle of grating spectroscopy, the laser grating method achieves multi-degrees-of-freedom measurement by obtaining the different pieces of information carried by each separate beam of light. [PERSON] et al. propose a 6-DOF measurement method using a single optical encoder unit and discuss uncertainty estimations in terms of error sources [9], but the system is complex and costly. Compared with the Dalian University of Technology, [PERSON] developed an interferometric method based on the machine tool table five-degrees-of-freedom geometric error measurement system. Halo is a four-quadrant detector QD. My system uses three CMOS; the impact on the CMOS image surface of the spot changes to dissolve the straightness of the moving end of the angular change to improve the measurement of the range, the X-direction range of \(\pm 2.0\) mm, Y-direction range of \(\pm 1.6\) mm, X-direction pitch angle range of \(\pm 1.9^{\circ}\), and Y-direction yaw angle range of \(\pm 1.4^{\circ}\). The range of X-direction is \(\pm 2.0\) mm, the Y-direction range is \(\pm 1.6\) mm, the X-direction pitch angle range is \(\pm 1.9^{\circ}\), and the Y-direction yaw angle range is \(\pm 1.4^{\circ}\). Compared with [PERSON]. [PERSON] et al., who proposed a laser net straightness interferometer for the simultaneous measurement of six-degrees-of-freedom motion errors, my system has a simpler structure and the laser collimation method is less affected by different environments, such as high temperatures. The method also adapts better to low altitudes, vacuum, and other conditions. The cost of my system is lower compared to the six-degrees-of-freedom measurement method using a single optical encoder unit proposed by [PERSON] et al. The reason that a multi-DOF measurement system is developed in this paper is that it is necessary to measure multiple DOFs simultaneously in real time in order to adjust the DOF of the optical load in high space and solve the defocusing phenomenon. Therefore, it is necessary to develop a multi-DOF measurement system. Six-degrees-of-freedom systems contain some principle problems: a set of systems are required to measure six degrees of freedom at the same time, and the \(Z\)-axis requires the interference method to be used, while the \(Z\)-axis roll angle measurement requires a high-precision method; these problems should be further studied [23; 24; 25]. The actual measurements of six degrees of freedom can be made using two systems: one system placed as shown in the figure and the other with the laser output light perpendicular to the YOZ plane of the optical load. The measurement principle of the optical system developed in this paper uses the optical collimation method. The principle of the optical collimation method is that the laser has directivity and the exit angle is approximately \(0^{\circ}\), which can be regarded as parallel light. When reflecting from a plane, parallel light changes slightly when the plane is moved in a certain direction of freedom. The principle of laser optical collimation range and angle measurement can be used to calculate the value of displacement or the angle according to the slight change in the displacement of parallel light and the relationship between displacement and distance or angle. Section 2 of the article describes the basic principle of the optical path structure and separately describes the ranging optical path, angle measurement optical path, optical isolator's basic principle, and the measurement results of the optical path diagram principle crosstalk analysis. Section 3 of the article continues the error analysis to the CMOS installation error, using the homogeneous transformation matrix method for the analysis. In Section 4, the system is built according to the schematic diagram of the optical path, the change in the small degree of freedom of the mobile terminal is simulated, the system is measured, and the calibration test and stability test are carried out.