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This work presents a novel panoramic stereoscopic system consisting of a fisheye lens camera and a hyperbolic mirror with co-axis installation. From the overlapping field of view captured through the fisheye lens and the reflection of the mirror, position of an object point in 3D Euclidean space can be reconstructed once the system geometry is calibrated. To deal with the non-single viewpoint issue in the catadioptric image, a generic radial distortion model is used to describe the imaging process with a series of viewing cones. The parameters of the viewing cones are estimated using a homography based method with observations of an LCD panel at a few unknown positions. Following this, a closed form solution for 3D reconstruction is used with a non-linear optimization to obtain an optimal calibration. A prototype of the proposed design is constructed. Quantitative experiments are conducted to evaluate the calibration result in terms of 3D reconstruction precision. With the calibration result, we also present potential robotic applications of the proposed system such as 3D environment reconstruction in a 360 degree horizontal field of view.