Geometrical Theory of Third-Order Aberrations
In Section 1.4 we used the Hamiltonian formulation to trace rays in some rotationally symmetric optical systems. They were derived under the paraxial approximation, i.e., the rays forming the image were assumed to lie infinitesimally close to the axis and to make infinitesimally small angles with it. It was found that the images of point objects were perfect, i.e., all rays starting from a given object point were found to intersect at one point, which is the image point. Such an image is called an ideal image. In general, rays that make large angles with the z axis or travel at large distances from the z axis do not intersect at one point. This phenomenon is known as aberration. In this chapter we will use the Hamiltonian formulation as developed by Luneberg (1964) to derive explicit expressions for aberrations in rotationally symmetric systems.
KeywordsObject Plane Spherical Aberration Chromatic Aberration Thin Lens Exit Pupil
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