A catadioptric optical system is one that employs both lens and mirror components in the optical path, and can be used to capture a nearly 360° field of view. Such a system had the advantages of processing only one image, and with this image being continuous, not having to deal with discontinuities at the boundaries of view as a ring of conventional cameras would introduce. This paper presents a novel configured catadioptric sensor, a precise omnidirectional stereo vision optical device (OSVOD) based on a common perspective camera coupled with two hyperbolic mirrors. As the hyperbolic mirrors ensure a single viewpoint (SVP) the incident light rays are easily found from the points of the image. In our system the two hyperbolic mirrors, which aligned coaxially and separately, share one focus that coincides with the camera center. So the geometry of our system naturally ensures matched epipolar lines in the two images of the scene. The separation between the two mirrors provides a large baseline and eventually leads to a precise result. The properties mentioned above make the system especially suitable for omnidirectional stereo vision because depth estimation is simple, fast and precise. This proposed system can be used for detecting obstacles by mobile robots, automatic mapping of environments and machine vision where fast and real-time calculations are needed.