# Calibration Method of Orthogonally Splitting Imaging Pose Sensor Based on General Imaging Model
## 1 Introduction  
With the development of advanced industrial equipment intelligence and digitalization, the demand for accurate pose measurement, which can measure a wide range of space targets, is increasing. The visual pose measurement has the advantages of non-contact, simplicity, stability, and moderate accuracy. It is widely used in aerospace, machine building, robot navigation and other fields. At present, the visual sensors used in the visual pose measurement system include the area array CCD and the line array CCD. Compared with the area array CCD, the line array CCD has higher resolution and faster speed in vision measurement. But the line array CCD can only obtain a one-dimensional image, so multiple line array CCDs are combined to realize the spatial measurement of the target [1; 2; 3]. However, the target must be in the public view of all line array CCDs; the measurement range is thus limited in a small range. In order to satisfy the measurement requirements of a wide range, high precision and fast speed, the orthogonally splitting imaging pose sensor based on linearray CCD is designed. The new sensor is composed of a special optical imaging system and dual line array CCDs to simulate monocular measurement with an area array CCD. Compared with binocular or trinocular vision measurements, the new sensor can solve the problems of small measurement range, and has higher resolution to improve the accuracy of measurement.  
The optical system of the pose sensor is composed of two parts: the imaging system and the beam splitting system. Responsible for imaging a target point as a two-dimensional image, the imaging system is composed of an aperture and spherical mirror group as an objective lens with a large field of view. The beam splitting system is responsible for dividing the two dimensional image into two one-dimensional images, which are received by the line array CCD in the corresponding direction. It is composed of a beam splitting prism and two cylindrical mirror groups.  
Owing to the special optical imaging structure, for the optical system of the orthogonally splitting imaging pose sensor, there exists various types of distortion, such as the radial distortion caused by wide field of view, one-way error caused by cylindrical lens, and linear and non-linear error caused by assemble technology. These distortions will affect the geometry relationship between the target and its image, and the ideal model of pinhole imaging model cannot properly describe the actual optical imaging relationship. Normally calibration method based on pinhole imaging model ignores tangential distortion and takes radial distortion into consideration. The main calibration methods including Tsai two-step [4], Weng [5], and Zhang [6] requires at least two images corresponding to the target in the world coordinates. But problems do exist with these approaches. Pupil aberration and assembly error still exist. [PERSON] [7; 8] proposed a rotational symmetry model to solve the problem of pupil aberration, but they could not solve the problem of assembly error.  
With the above mentioned analysis, this paper proposes a calibration method based on a general imaging model [9; 10; 11; 12] to calibrate the orthogonally splitting imaging pose sensor. General imaging model is a black box model. It describes the mapping relation between the incoming light and the pixel without considering distortion. Thus the model can apply to any optical imaging system. This paper adopts continuous vector-valued functions to express the mapping relation solved by radial basis function interpolation. And adaptively selected control points are selected by Kmeans clustering method to improve fitting accuracy. The calibration method requires only one image corresponding to the target in the world coordinates.