• Current Optics and Photonics
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• v.1 no.4
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• pp.336-343
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• 2017

A wide field-of-view (FOV) image contains more visual information than a conventional image. This study proposes a new type of hyperbolic mirror for wide FOV image acquisition. The proposed mirror consists of a hyperbolic cylindrical section and a bowl-shaped hyperbolic omnidirectional section. Using an imaging system with this mirror, it is possible to achieve a $213.8^{\circ}$ horizontal and a $126.94^{\circ}$ vertical maximum FOV. Parameters of each section of the mirror are designed to be continuous at the junction of the two parts, and the resultant image is seamless. The image-acquisition model is obtained using ray-tracing optics. To rectify the geometrical distortion of the original image due to the mirror, an image-restoration algorithm based on conformal projection is presented in this study. The performance of the proposed imaging system with the hyperbolic mirror and its image-restoration algorithm are verified by experiments.

• The Journal of Korea Robotics Society
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• v.10 no.3
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• pp.146-153
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• 2015

In order to contain as much information as possible in a single image, a wide FOV(Field-Of-View) imaging system is required. The catadioptric imaging system with hyperbolic cylinder mirror can acquire over 180 degree horizontal FOV realtime panorama image by using a conventional camera. Because the hyperbolic cylinder mirror has a curved surface in horizontal axis, the original image acquired from the imaging system has the geometrical distortion, which requires the image processing algorithm for reconstruction. In this paper, the image reconstruction algorithms for two cases are studied: (1) to obtain an image with uniform angular resolution and (2) to obtain horizontally rectilinear image. The image acquisition model of the hyperbolic cylinder mirror imaging system is analyzed by the geometrical optics and the image reconstruction algorithms are proposed based on the image acquisition model. To show the validity of the proposed algorithms, experiments are carried out and presented in this paper. The experimental results show that the reconstructed images have a uniform angular resolution and a rectilinear form in horizontal axis, which are natural to human.

• Korean Journal of Optics and Photonics
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• v.12 no.5
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• pp.352-355
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• 2001

A null lens is designed for testing the hyperbolic mirror which is the first mirror of the off-axis three mirror anastigmat(TMA) designed as a high resolution camera for remote sensing. To choose a better null lens system for the hyperbolic surface under test, both autostigmatic and mixed type null lenses are designed and analysed for sensitivity with respect to change of each surface parameter such as the radius of curvature and the thickness.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.16 no.3
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• pp.2117-2122
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• 2015

Wide FOV(Field-of-View) is required to contain much more visual information in a single image. The wide FOV imaging system has many industrial applications such as surveillance, security, tele-conference, and mobile robots. In order to obtain a wide FOV panorama image, an imaging system with hyperbolic cylinder mirror is proposed in this paper. Because the horizontal FOV is more important than the vertical FOV in general, a hyperbolic cylinder mirror is designed in this paper, that has a hyperbolic curve in the horizontal surface and is the same as a planar mirror in the vertical axis. Imaging model of the proposed imaging system is presented by ray tracing method and the hyperbolic cylinder mirror is implemented. The imaging performance of wide FOV is verified by experiments in this paper. This imaging system is cost-effective and is possible to acquire a wide panorama image having 210 degree horizontal FOV in real-time without an extra image processing.

• Current Optics and Photonics
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• v.3 no.4
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• pp.329-335
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• 2019

Wide FOV imaging systems are important for acquiring rich visual information. A conventional catadioptric imaging system deploys a camera in front of a curved mirror to acquire a wide FOV image. This is a cumbersome setup and causes unnecessary occlusions in the acquired image. In order to reduce both the burden of the camera deployment and the occlusions in the images, this study uses a secondary planar mirror in the catadioptric imaging system. A compact design of the catadioptric imaging system and a condition for the position of the secondary planar mirror to satisfy the central imaging are presented. The image acquisition model of the catadioptric imaging system with a secondary planar mirror is discussed based on the principles of geometric optics in this study. As a backward mapping, the acquired image is restored to a distortion-free image in the experiments.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1259-1267
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• 2014

In this paper we show that any chain transitive set of a diffeomorphism on a compact $C^{\infty}$-manifold which is $C^1$-stably limit shadowable is hyperbolic. Moreover, it is proved that a locally maximal chain transitive set of a $C^1$-generic diffeomorphism is hyperbolic if and only if it is limit shadowable.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.5 s.236
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• pp.726-733
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• 2005

A spherical surface referenced Shack-Hartmann method is studied for inspecting machining accuracy of large concave mirror This method is so strong to the vibration environment for using as an on-machine inspection system during polishing process of large optics comparing with the interferometry. The measuring uncertainty of the system is shown as less than p-v 150 m. On-machine measured surface profile data with this method is used for feed back control of the polishing time or depth to improve the surface profile accuracy of large concave mirror. Also, the spherical surface referenced Shack-Hartmann method is useful for measuring aspheric such as parabolic or hyperbolic surface profile, comparing that the interferomehy needs a special null lens, which is to be a reference and difficult to fabricate.

• Korean Journal of Optics and Photonics
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• v.17 no.5
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• pp.412-419
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• 2006

We design and fabricate an autostigmatic null lens system assembled in a fixed tube mount in order to evaluate the shape of an aluminum hyperbolic mirror with the diameter of 300 mm and the f-number of 1.98, which is fabricated by a high precision aspherical DTM (diamond turning machine). Also, we evaluate the degree of shape of the aspherical mirror by this autostigmatic null lens testing method. The autostigmatic null lens system assembling in a fixed tube mount has several advantages of light weight, good mechanical stability, etc. The permissible fabricating limits of null lenses and a mount are determined by considering various tolerances to assure the measurement reliability.

• Journal of Institute of Control, Robotics and Systems
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• v.18 no.5
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• pp.479-486
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• 2012

In this paper, a ranging system is proposed that is able to measure 360 degree omnidirectional distances to environment objects. The ranging system is based on the structured light imaging system with catadioptric omnidirectional mirror. In order to make the ranging system robust against environmental illumination, efficient structured light image processing algorithms are developed; sequential integration of difference images with modulated structured light and radial search based on Bresenham line drawing algorithm. A dedicated FPGA image processor is developed to speed up the overall image processing. Also the distance equation is derived in the omnidirectional imaging system with a hyperbolic mirror. It is expected that the omnidirectional ranging system is useful for mapping and localization of mobile robot. Experiments are carried out to verify the performance of the proposed ranging system.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.16 no.6
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• pp.4108-4114
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• 2015

An image acquisition by using an optical mirror is called as a catadioptric method. The catadioptric imaging method is generally used for acquisition of 360-degree all directional visual information in an image. An exemplar omnidirectional optical mirror is the bowl-shaped hyperbolic mirror. In this paper, a single camera omnidirectional stereo imaging method is studied with an additional concave lens. It is possible to obtain 3 dimensional coordinates of environmental objects from the omnidirectional stereo image by matching the stereo image having different view points. The omnidirectional stereo imaging system in this paper is cost-effective and relatively easy for correspondence matching because of consistent camera intrinsic parameters in the stereo image. The parameters of the imaging system are extracted through 3-step calibration and the performance for 3-dimensional coordinates reconstruction is verified through experiments in this paper. Measurable range of the proposed imaging system is also presented by depth-resolution analysis.