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 have been well studied. This paper focuses on photometric aspects of catadioptric cameras. We discuss how geometric distortion of images of catadioptric cameras resulting from curvature of the mirror affects image irradiance. We show that image irradiance is determined only by the nature of lenses comprising the cameras and is independent of mirror shape. This is because an increase in the solid angle of space per single image pixel is canceled out by a decrease in the apparent solid angle of the lens aperture viewed from a scene point via the mirror. Thus, image irradiance of catadioptric cameras is not affected by geometric distortion due to mirror curvature. This is in contrast to cameras with ordinary lenses alone, especially fisheye lenses, in which image irradiance is actually affected by image distortion. Theoretical results as well as results of numerical simulations are presented.