A Novel Calibration Method for Object Plane Tilt Angle Measurement in Microscope System

A novel calibration method is proposed to measure object plane tilt angle in microscope system with small-depth-field. The proposed method is constructed by a space model about calibration board and the surface of image. Only a rotating disk, a goniometer and a calibration board with some features are needed, the tilt angle between the object plane and image plane and their geometric relationship can be estimated by the space model. Compared with some classical calibration methods with expensive equipment, the proposed method is easy to be implemented with relative cheap equipments. Moreover, it has been proved that the proposed method is quite efficient through experimental verification. It can also contribute to three dimensional applications in computer vision of microsystems. Introduction With the rapid development of microscopic technologies, precise measurement and high accuracy machining had stepped into the process of industrial applications, such as steel for hot working, assembly of precision electronic components or precision instruments, lens calibration, and so on [1, 2]. However, due to the small-depth-field of optical microscope amplification characteristic, the precise observation is greatly restricted under microscope. Such as defocusing caused by object plane tilt in microscope system may influence the assembly of auxiliary measuring device. In terms of precise medical observation, people adjust working distance to observe object multi-facetedly by rotating object stage of microscope system. However, it is usually inefficient and dissatisfactory in the industrial precision instrument operation. Hence, object plane and image plane in the microscope system should be precisely calibrated by extracting and matching features in image accurately. The camera calibration operation is very important for subsequent dealing with tiny objects such as precise measurement, calibration, three dimensional (3D) reconstruction [3]. Calibration problem had been studied by Hekilla [4], Tsai [5], Zhang [6] etc., and some conclusions had been made, for example monocular convex lens plain surface calibration [7], and it is believed that with three directional rotations, almost all internal and external parameters of camera can be calibrated with chessboard calibration. However, for digital optic microscope, Tsai’s method does not consider the nonlinear distortion of lens and must get the scale factor, so that its accuracy may not be guaranteed. Zhang’s method has to limit the object plane rotation angle from 15 to 45 degree. The unsatisfactory results also exist in Ravn’s method. Due to the limitation on small-depthfield and small field of view in optical microscope system, the precision of the above calibration methods will be more or less influenced [8]. In the existing cognitive, there is a paradox, the images easy to be matched may normally be hard to be calibrated; on the other hand, the abundant characteristics of calibration source normally cannot be applied to be matched directly. No matter in the optimization of photogrammetry [9], or mold measuring to build better optical platform [10], there are such a phenomenon. For high precision 3D reconstruction after matching, tiny deviation is often fatal. The difficulty in calibration is how to find the exact matching sets for data analysis. Some matching algorithms had been proposed [11, 12]. In this paper, on the basis of exact matching, with the spatial geometric relationships, a tilt angle measuring method is proposed for object plane rectification in microscope system. International Conference on Intelligent Systems Research and Mechatronics Engineering (ISRME 2015) © 2015. The authors Published by Atlantis Press 654 Object plane tilt in optical stereoscopic microscope This paper aims to such a test platform with optical stereoscopic microscope that the object is with a small-depth-field, which can be seen from previous works [13]. The experimental platform uses a stereo microscope of ZOOM460N, as shown in Fig. 1(a). In the figure, “A” is a dual camera with independent light path, “B” is the rotating disk with the rotatory accuracy of 1 degree manual adjusted, and “C” is the angle control platform. The lights of observed object first go through a large lens, then go into the two separate light path, go across the objective lens, and then the lights are captured on both sides of the relative camera. The used cameras are 902B Watec of Japanese Company, directly connect the interface to the eyepiece of stereomicroscope. Each frame is obtained by the camera with the size of 704×576. Besides, the accuracy of angle control system is 0.0025 degrees with the precision stepper motor adjusted. That is to say each of 400 steps makes angle control system rotate at one degree. Test sets are divided into 5 degree values, which can be adjusted from 0 to 4 degrees. Figure 1. Experimental platform According to the properties of microscope system, the camera imaging model can be got. However, the object plane tilt exists more or less, but in microscope system, parallelity between image plane and object plane is significant to the subsequent processing. Hence, it is necessary to estimate the angle between the image plane and object plane. This paper intends to get the correct angle between the image plane and object plane, so as to solve the problem of local blurring caused by angular deviation of the two planes. New calibration method for measuring object plane tilt angle In most cases, camera calibration can be described by using radial and tangential distortion model, and the object surface can be fitted by different calibration methods. It is known that calibration error and accuracy of calibration model have a great influence on subsequent matching and 3D reconstruction. Based on good matching of feature points for plane rectification, the proposed method can be used in monocular as well as binocular microscope system. Moreover, monocular rectification can be used to deduce binocular polar plane rectification. A. Geometric model building In this paper, a rotating disk is used to simulate the actual situation. The rotating disk can provide a feature constraint, through which the feature of points and finally the tilted object plane can be got. The calibration model is usually based on the following two accepted assumptions [14]: • The model is a pin-hole model which allows us to consider the focus point as a real mathematical coordinate point; • The acquisition system is reliable. Fig. 2 represents the relationships between the image plane and object plane. Theory is if the object is at a distance, one can assume the light rays will arrive perpendicularly to the plane of the lens, and thus converge at the focal point. In Fig. 2, the upper part denotes the image plane, while the lower part is the object plane which may tilt in microscope system (presuppose that object is as a particle in object plane). Fig. 2(a) shows the ideal relationship between the image plane and object plane, in which the two planes are parallel with each other. The imaging model in Fig. 2(b) is the actual slant imaging, which is used to calculate the tilt angle of the two planes. By calculating the