# Design and Analysis of High-Accuracy Telecentric Surface Reconstruction System Based on Line Laser
## 1 Introduction  
Due to the significant advance in optical electronic technology, micro-electronic technology and industrial manufacturing, non-contact measurement technology based on triangulation with cameras has come to the foreground [1]. Compared with other measured technology, non-contact measurement based on triangulation with cameras is commercial and fast when there is not a strict requirement for accuracy. The perspective effect and lens distortion of conventional lenses affect the accuracy severely in close-range measurement [2]. However, the application of telecentric lenses further elevates the accuracy for non-contact measurement with cameras, especially for the 3D metrology in a microscopic scale, since telecentric lenses provide the orthographic projection and possess the characteristics of low distortion, constant magnification and amplified depth of field [3, 4, 5]. As it is different from conventional lenses for telecentric lenses in imaging models and calibration methods, the research about non-contact measurement with telecentric lenses has become one of the hotspots in this field recently [6, 7]. Analogously, telecentric non-contact measurement technology can also be divided into active and passive techniques. Passive techniques do not rely on an external light source while active techniques are quite the contrary. Among passive techniques, telecentric stereo vision is on the forefront [8, 9, 10]. Compared with passive techniques, active techniques are highly applied for better performance in accuracy. The light sources employed in active techniques mainly contain structured light and laser light [11]. For the techniques of structured light, it is the combination of the projector and camera. There has been research which employs the projector with a conventional lens and the camera with a telecentric lens, respectively, and also the projector and camera both staffed with telecentric lens [12]. Moreover, the light system of binocular cameras with telecentric lenses is studied [13; 14]. The techniques of structured light need to project several structured light images to measure a narrow invariant region. Meanwhile, the techniques of laser light, also called laser scanner techniques, generally require a single camera, a laser generator and a platform [15]. The measured range of laser scanner techniques is determined by the platform employed, among which a 1D displacement platform is frequently utilized in industrial inspection [16], while other types of platforms are used for 3D reconstruction and other applications [17; 18]. The adoption of telecentric lens has become the tendency to improve the accuracy for techniques of laser light. In order to realize the high-accuracy measurement with the techniques of laser light with telecentric lenses, there are three main challenges. The first challenge is the unmeasured region caused by the principle of triangulation. The technique is essentially based on the intersection of the optical line and laser plane, which leads to a systematic error when the surface of the measured object is abrupt enough [19]. The intersection angle forms an unmeasured region due to occlusion where depth changes significantly. The second challenge is that the calibration method for conventional lenses is not suitable for telecentric lenses due to their different projection model [20]. Moreover, the recovery of the depth information for telecentric lens is not direct, and the problem also affects the system structure calibration for the system with telecentric lenses. The last challenge is the laser stripe extraction. The laser stripe in image is expected to be an ideal line without width. Nevertheless, it is too wide to be used for positioning directly in practice, so a sub-pixel laser stripe extraction method is essential and it can directly affect the measured accuracy [16].