# A Spatial 4-DOF Laser Collimation Measurement System
## 1 Introduction  
Spatial freedom refers to the change in straightness in the XYZ triaxial direction of an object and the change in the XYZ triaxial angle direction. Detecting the precision of spatial freedom has always been an important subject in the field of industry and aviation. Errors in machine tools in the industrial field directly affect the machining accuracy of the machine tools. The positioning and motion accuracy can be improved by measuring and compensating for machine errors in real time. In the field of industrial robots, it is necessary to detect the position of the robot, provide feedback, and control its movement. The degree of freedom of the optical electron microscope needs to be tested in real time, so it can be adjusted. In the field of aviation, with the continuous development of satellite technology in China, indicators such as the detection range, resolution, and stability of optical remote sensing satellites are increasing [1, 2]. Due to the very complex carrying and operating environment of space loads, they are mainly subjected to space thermal deformation (STD) caused by the changes in solar incidence angle during launch. After these influences, the geometric positioning of the high orbit will gradually change. By affecting the relative pose between the primary mirror and the sub-mirror of the optical load, while causing the optical load to defocus, the resolution and other parameters of the optical load will be affected, and the final positioning accuracy of the camera will be affected [3, 4, 5, 6, 7]. Recently, a method was proposed where the freedom from the star sensor to the star is known and the freedom from the star to the ground is known, and only the freedom from the starsensor to the optical load needs to be measured, as the freedom from the optical load to the ground can be obtained by solving this. Therefore, it is necessary to develop a system for measuring the freedom of optical load in space. The number of degrees of freedom in a measurement can be divided into contact and non-contact types. In most scenarios in the industrial and aviation fields, where direct contact with the measured object is not possible, non-contact measurement is preferred. The current mainstream non-contact measurement method, used domestically and abroad, is to use a laser as the measurement medium. The current mainstream laser measurement methods are the interference method, diffraction method, and collimation method. Laser interferometry has a measurement range from micrometers to meters or larger, with a measurement accuracy at the nanometer level, and its advantages include medium economic efficiency and general environmental requirements. Its advantage is its high precision, but its disadvantage is its high sensitivity to the environment, including environmental factors such as temperature, vibration, and air flow [8; 9; 10; 11]. The advantage of using diffraction-precision microns are that they can be used for high-resolution image analysis, and are suitable for high-resolution image analysis and for observing fine structures, while their disadvantages are that they is highly demanding on the optical system and limited by the diffraction limit [12; 13; 14; 15]. The accuracy of the collimation method is at the micron level, and its advantages are that it is simple and easy to use, has low equipment maintenance costs and a fast measurement speed, and can provide measurements over a large range. The disadvantages are affected by the stability of the light source. In summary, after comprehensively considering the accuracy and environmental economy, the optical collimation method was selected [16; 17; 18; 19]. This is shown in Table 1.  
[PERSON] of Dalian University of Technology developed a 5-DOF geometric error measurement system for machine tool tables based on interferometry, which is used to determine the error correction accuracy of machine tool errors in the range \(\pm 1\)