Area projections of fisheye photographic lenses

Abstract Fisheye photographic lenses project a hemispherical object region onto a circle on the image plane and thus often are used for measurement of plant leaf cover and shading of plant stands. In general, for these lenses, object regions of equal solid angle do not result in images of equal area. Instead, the area of a projected region varies significantly as a function of the angle between the optical axis of the lens and the center of the object region. This study demonstrates that very small amounts of radial lens distortion produce relatively large changes in projected areas on the image plane and describes the projection of image regions for several commonly available fisheye lenses.