## 1 Introduction  
Measurement is a process of obtaining quantifiable information that requires a very high accuracy [1]. Currently, three-dimensional (3D) measurements are widely performed in the design and construction of augmented reality, automated quality verification, restoration of lost computer-aided design data, cultural relic protection, surface deformation tracking, and 3D reconstruction for object recognition [2; 3; 4; 5]. Common 3D measurement approaches can be divided into two categories: contact measurements and non-contact measurements. Normally, the applications of contact measurements are limited by the untouchability of a measured object. In contrast, non-contact measurements exhibit a high flexibility [6]. Among the different non-contact measurement methods, line-structured light 3D measurements are frequently conducted because of their simplicity, high precision, and high measurement speed [7]. A general line-structured light 3D measurement process can be described as follows. (1) A line-structure light beam is emitted by a laser generator. (2) A light plane is projected onto the surface of the measured object. (3) Two-dimensional (2D) image coordinates of the intersection points between the light plane and the object surface are obtained by a camera. (4) The corresponding 3D coordinates of the intersection points are calculated by a developed algorithm. In this technique, proper calibration is of utmost importance because it strongly affects the measurement accuracy and simplicity. Usually, the calibration procedure includes camera calibration and light plane calibration processes. Many research studies on camera calibration have been conducted in the past. [PERSON]'s [8] calibration method based on a planar target is the most widely used approach. To increase its accuracy,various advanced camera calibration techniques have been developed [9, 10]. For example, the form of the calibration board was changed from that of a checkerboard to a circular calibration board because the edge of a characteristic circle contained more information and exhibited a higher positioning accuracy. Moreover, multiple methods for calibrating the light plane were also proposed [11, 12, 13, 14, 15, 16, 17, 18]. [PERSON] [11], [PERSON] [12], and [PERSON] [13] introduced a 3D target to define the light plane calibration points using the cross-ratio invariability principle (CRIP). However, all these three methods were very complex and possessed a low calibration accuracy. [PERSON] [14] proposed an on-site calibration method using a planar target in which light plane calibration points were obtained through repeated target movements. [PERSON] [15] replaced the points with a Pluck matrix; however, the resulting method was complex and required a plane calibration target. [PERSON] [16] utilized a flat board with four balls as a calibration target, while [PERSON] [17] reported a calibration technique based on a one-dimensional (1D) target. The 3D coordinates of a series of intersection points between the light plane and the 1D target were determined from a known distance between select points of the 1D target. The obtained coordinates were fitted to solve the light plane equation. [PERSON] [18] developed a light-structured light vision sensor based on a single ball target. Its calibration process was relatively simple; however, a high-precision ball target was difficult to manufacture. In this study, a new method for the on-site calibration of a line-structured light 3D measurement process based on a single circular target is proposed. The main reason for selecting a circular target as the calibration object is its ease of manufacture. It is almost possible to say that a single circle of known size can be used as a calibration target with our proposed method. First, a line-structured light 3D measurement model is established.