In a free viewpoint video system, the scene is captured by a number of cameras and it would be desirable to optimize the configuration of cameras, such as their location or orientation, to improve the rendering quality. This paper introduces a mathematical representation of the multi-camera geometry, called the correspondence field (CF), which can be used to quantify the suitability of a camera configuration for a given arrangement of objects in the scene. The correspondence field describes the spatial topology of the intersecting rays of cameras, arranged as a number of layers or surfaces in the field of view of cameras. The paper derives the topology of CF for certain camera arrangements and analyzes the impact of changes in camera location or orientation on this topology. It demonstrates that CF can be used to find the optimum camera configuration for a given objective. It also presents simulation results of this method using our light field simulator.