Theoretical Resolution Angles for Point and Line Test Objects in the Presence of a Luminous Background

A theoretical study has been made of the diffraction patterns for a circular aperture for point and line test objects in the presence of a luminous background. The study involves the superposition of the diffraction pattern elements of the test object and the image of the luminous background. From this superposition it is possible to relate the contrast of the image of the test object to the angle subtended by the test object elements and their apparent contrast at the entrance pupil of the optical system under consideration. This relation has been found useful in studying the resolving power of optical systems. For example, it is possible to determine the contrast of the image of a test object at the limit of resolution under a wide variety of conditions. It is also possible to determine the loss in resolution caused by a given reduction in image contrast regardless of the cause.