We propose a novel omnidirectional structured light system comprising a fisheye camera and a catadioptric projector, enabling dense 3D reconstruction. In addition, we present a streamlined calibration procedure that calibrates the entire procedure using only a planar checkerboard and demonstrates robust convergence and a high success rate even under unfavorable parameter initialization. Experimental results validate the proposed method, achieving reprojection errors of 0.43 pixels for the camera and 0.63 pixels for the projector. Furthermore, the practical utility of the system is confirmed through successful dense 3D reconstructions. The source code is available at: https://github.com/GotoIlsan/Omnidirectional-Structured-Light-System.