Multi-Aperture Telecentric Lenses Exhibit Varying Magnification for Objects Lens at Different Distances from the Lens
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space. Most imaging systems with conventional Multi-aperture telecentric lenses exhibit varying magnification for objects lens at different distances from the lens. This causes several problems for machine vision and other Bo Wu applications. (i) Objects closer to the lens appear Lei Ye to be larger than those farther from the lens; The Hong Kong Polytechnic University, China for example, in an image of a cylindrical pipe the top and bottom crown edges appear to be concentric even though the two circles are A multi-aperture telecentric lens is a single perfectly identical. (ii) Object shapes vary with telecentric lens with multiple aperture stops their distance from the center of the field of that enable it to capture multidirectional parallel view (FOV); for example, circles near the center light rays. Unlike conventional optical systems in of the FOV appear to be egg-shaped when photogrammetry or computer vision, which use moved toward the periphery. (iii) Some features a pair of stereo cameras for three-dimensional or objects may be hidden by objects closer to (3-D) reconstruction, a multi-aperture telecen- the lens. In contrast, a telecentric lens removes tric lens uses image(s) obtained from the light these perspective or parallax errors to produce rays separated by different aperture stops for 3-D an orthographic projection that provides the reconstruction. A multi-aperture telecentric lens same magnification at all distances. Pioneered by is ideal for use in a variety of machine vision Moore (1973), telecentric lenses have been pur- applications, such as noncontact measurement sued by researchers in various settings (Watanabe and inspection systems, 3-D reconstruction of and Nayar 1996; Bai and Sadoulet 2007). In close-range targets, and intelligent vision systems particular, telecentric lenses are commonly used in robotic equipment. in machine vision applications, where software The telecentric lens is discussed here firstly. analysis is simplified and more accurate due to Detailed configurations of the multi-aperture the reduction of parallax. Imaging systems with telecentric lens are then discussed. Key aspects of telecentric lenses have made it possible to reach using a multi-aperture telecentric lens for 3-D dimensional measurement accuracies that can reconstruction – including its geometric model be better than those generated by contact and and an evaluation of the potential accuracy – are laser-based methods (Djidel et al. 2006). then presented. There are three types of telecentric lens. The first is an object-space telecentric lens, in which Telecentric lens the aperture stop is placed at the front focal plane of the lens, resulting in an entrance pupil loca- tion at infinity. A shift in the object plane does A telecentric lens is a compound lens used in not affect image magnification. Such lenses are an imaging system to make objects appear to be used in machine vision systems because image the same size independent of their location in magnification is independent of the objects’ The International Encyclopedia of Geography. Edited by Douglas Richardson, Noel Castree, Michael F. Goodchild, Audrey Kobayashi, Weidong Liu, and Richard A. Marston. © 2017 John Wiley & Sons, Ltd. Published 2017 by John Wiley & Sons, Ltd. DOI: 10.1002/9781118786352.wbieg0106 MULTI-APERTURE TELECENTRIC LENS o Figure 1 An idealized double telecentric lens. distance or position in the field of view. The stop placed at the common focal plane of the second is an image-space telecentric lens, in front and rear elements such that it only passes which the aperture stop is placed at the rear the light rays that are parallel to the optical axis. focal plane of the lens, resulting in an exit pupil In summary, telecentric lenses have the fol- location at infinity. A shift in the image plane lowing advantages over conventional lenses: (i) does not affect image magnification. Such lenses constant magnification independent of shift in are used in image sensors that do not tolerate a object and/or image planes; (ii) low distortion, wide range of angles of incidence. The third is normally in the range of 0.1% for high-quality a double telecentric lens, in which the aperture telecentric lenses; (iii) reduction or elimination stop is placed at the common focal plane, result- of perspective error; (iv) increased image resolu- ing in both the entrance and exit pupils being tion; and (v) uniform image plane illumination. located at infinity. Shifting either the image However, they also have several disadvantages. or object planes does not affect magnification First, more optical elements are used than in given that double-telecentric systems are afocal. conventional lens systems due to the complex Double telecentric lenses have magnification design. Second, large aperture optical elements that is more precisely constant than those that in the region of telecentricity are required to are only object-space telecentric because the provide a nonvignetted FOV. The large aperture intersection position of the principal ray on and more optical elements lead to increases the detector does not change, which allows for in the cost and weight of the imaging system. the precise measurement of objects regardless Third, traditional telecentric lenses use fixed of their positions. Figure 1 illustrates an ide- focal lengths, which result in fixed FOVs. An alized double telecentric lens with two thin investigation of varying FOVs requires the use positive-powered elements, with the aperture of several fixed magnification lenses. Zinter 2 MULTI-APERTURE TELECENTRIC LENS and Sanson (2001) presented an endeavor to view between apertures. Image disparities from develop a telecentric zoom lens for this type of multiple perspectives in the focal plane facilitated task. Finally, it is not possible to obtain depth the derivation of 3-D information. To take information from the telecentric images due to advantage of the orthographic projection of the the orthographic projection of the telecentric telecentric lens and the image disparities from lens. Despite the disadvantages inherent in the multiple, multi-aperture telecentric lenses have telecentric lens design due to its increased com- been investigated for use in 3-D reconstruction plexity, the numerous benefits make telecentric in recent years (Kim and Kanade 2011). lenses a popular choice in a variety of applica- A multi-aperture telecentric lens has mul- tions. The last drawback evokes the development tiple aperture stops rather than one, as in a of a multi-aperture telecentric lens. conventional telecentric lens. Figure 2 illustrates an idealized multi-aperture telecentric lens. There are two aperture stops O and O′ on Multi-aperture telecentric lens the focal plane, of which O is located at the focal point of the lens and the other O′ is at a In applications such as machine vision, the 2-D distance from the focal point. The aperture stop information and the 3-D depth information from O selectively passes light rays that are parallel to the scene must be extracted simultaneously.Stereo the optical axis because O is located at the focal vision using multiple cameras is the conventional point of the lens and only passes the rays. The ′ approach to infer depth information based on aperture stop O selectively passes light rays that are parallel to each other but not parallel to the parallax from multiple perspectives, which has ′ a long history in the fields of photogrammetry optical axis. Assuming O is an infinitely small aperture stop, the light rays selected by O′ are and computer vision. In recent years, a vari- ′ ety of techniques, such as motion parallax and parallel to the vector from the lens center to O depth-from-focus, have been implemented in (blue dashed line in Figure 2). 3-D imaging systems. However, these systems In a conventional stereo vision system, as illus- are relatively expensive and require complex trated in Figure 3, two cameras are used to form stereo images and the depth information of any camera calibration and geometric processing. As object in the scene can be derived from the dis- mentioned, the telecentric lens has the desirable parity of the same object imaged on the stereo property of orthographic projection, which images. From Figure 3, for an object point P, its makes it easier to measure or compare an object’s disparity is: physical length independently from its depth in relation to the camera. However, it is not possible f d = x1 + x2 = B (1) to obtain depth information from the image, as Z there is no foreshortening effect in telecentric where f is the focal length of the camera, B is images. The multiple aperture technique has been the baseline between the stereo cameras, and Z used in imaging systems to provide 3-D informa- is the depth of point P. In equation 1, both B tion. For example, Fife, Gamal, and Wong (2006) and f are fixed, and thus the disparity d is linearly presented an image sensor comprising an array proportional to the inverse of the depth. of apertures each with its own local integrated In a simplified multi-aperture telecentric optics and pixel array. A lens focused the image lens system (1× magnification), as illustrated in above the sensor, creating overlapping fields of Figure 4, the distance between the two aperture 3 MULTI-APERTURE TELECENTRIC LENS ( ) stops is B, which can be considered the baseline Z d = 4 − B (2) between the two aperture stops. The focal length f of the lens is f. The image plane is located at a distance f from the focal plane. A spatial auxiliary In equation 2, both the baseline length, B,and coordinate system is used with its origin at focal length, f, are fixed; thus the disparity, d, the center of the image plane. Its z-axis aligns is linearly proportional to the depth, Z,ofthe object point.