On photometric aspects of catadioptric cameras

Several imaging systems called catadioptric cameras have been developed that use a combination of lenses and mirrors to obtain wide fields of view. Geometric aspects of them have been well studied so far. This paper focuses on photometric aspects of the catadioptric cameras. We discuss how geometric distortion of images of the catadioptric cameras resulting from the curvedness of the mirror affects the image irradiance. We show that the image irradiance is determined only by natures of the lenses comprising the cameras and it is independent of the shape of the mirrors. This is because an increase in a solid angle of space per a single image pixel is canceled out by a decrease in an apparent solid angle of the lens aperture viewed from a scene point via the mirror. Thus, the image irradiance of catadioptric cameras is not affected by geometric distortion due to the mirror curvedness. This is contrast to cameras with ordinary lenses alone, especially ones with fisheye lenses, in which the image irradiance is actually affected by image distortion. Theoretical results as well as results of numerical simulations are presented.