## 1 Introduction  
Laser trackers are renowned for their exceptional precision, flexibility, rapid detecting speed, and expansive range capabilities [1]. As a result, they are widely employed in large-scale measurement fields, including aircraft assembly and the aerospace industry [2, 3], robot calibration [4], geometric error verification of the CMM and machine tools [5, 6], high-energy physics alignments [7], the railway industry [8], and other fields [9, 10, 11]. Laser trackers are an innovative type of large-size space measuring instrument that combine several advanced technologies, including fast tracking, laser interference ranging, precision goniometry, optoelectronic detection, and precision manufacturing. In addition to measuring the three-dimensional coordinates and attitude of stationary targets in space, the instrument can also track and measure moving targets in space [12]. Currently, the laser tracker mainly has two primary mechanical constructions. The first structure is to install a tracking mirror in the head of the tracker [13, 14]. The laser beam from the laser is emitted from the bottom of the tracker. It is reflected by the tracking mirror pointing at the target ball and then returned to the tracker head. The other structure is to install a laser in the head of the tracker. The beam from the laser is directly emitted from the tracker head to the reflective target sphere [14; 15; 16]. This paper focuses on the second approach. Laser trackers have three axes: a transit axis, a standing axis, and a laser optical axis, all of which should be orthogonal to one another. As a result of parts manufacturing, optical machine structure installation, and adjustment, the axis system will produce offset, tilt, eccentricity, and other errors that will cause the laser tracker measurement to be inaccurate. Therefore, it is necessary to compensate for these misalignment errors to improve the measurement accuracy of the laser tracker. Different approaches were performed to measure misalignment errors, such as the two-face system and length measurement tests [17; 18; 19]. Both tests are performed to analyze the performance of the laser tracker. [PERSON] et al. [20; 21] proposed error models of the laser tracker and used the two-face and length measurement tests to identify the sensitivity of geometric errors. It is difficult to identify individual geometric errors in these performance tests, and the measurement process is complex. Some studies [22; 23; 24] establish kinematic error models and use the nonlinear optimization method to identify the exact values of the geometric error parameters at one time. Compared to performance tests, the calibration process mentioned above takes less time. However, the above models are complex and have a large number of error parameters. In [25], two test rods were assembled on the transit axis as a reference, and the authors used a micrometer to measure the transit tilt and offset error. The test rod is a cylindrical rod that is coaxially assembled on the end of the transit axis to extend the hidden transit axis. However, the measurement accuracy is easily influenced by the operator, and the adjustment process of the coaxiality error of test rods installation costs much time. [PERSON] [26] and [PERSON] [27] used a laser diode mounted on a transit axis; the PSD was used to obtain the laser trajectory to fit the error. However, the authors did not consider the laser diode and the PSD installation eccentricity error. To address the problem that existing calibration processes are complex and that existing calibration methods have limited precision, we propose a fast and novel method to identify the transit tilt and offset errors in a laser tracker. It is highly efficient, accurate, and simple to use without adjustment. The measurement system consists of two test rods and a telecentric measurement system. Firstly, the two test rods are coaxially assembled on the end of the transit axis to extend the central axis of the transit axis.