Abstract

Applications for concave mirrors that are off axis portions of surfaces of revolution are increasing due to continued improvements in fabrication techniques and an accompanying reduction in cost. For imaging applications, it is desirable to know the effect that object position has on the resulting image position and quality and how these image characteristics depend on the surface geometry. We have addressed these topics for the specific case of an ellipsoid of revolution. We analyze the imaging properties of the ellipsoid by considering that a point source is located at an arbitrary position in the vicinity of one focus. The point source is modeled as emitting a cone of rays symmetrically distributed about a specified direction. The intersection of this diverging cone with the ellipsoidal mirror defines the region of the ellipsoid that images the point source. Ray aberrations are evaluated by considering the transverse ray intercepts at a target plane that is oriented normal to the converging cone of rays. Wave aberrations are determined in the traditional manner by considering the optical path difference between the convergent wavefront and a spherical reference wave centered at the paraxial image location. We will show how aberrations vary as different portions of the ellipsoid are involved in the imaging process and also illustrate the effect on the geometrical image produced by a tilt of the target plane.

© 1993 Optical Society of America