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Chapter 3:
Optical Aberrations
Abstract
3.1 INTRODUCTION Given the radii of curvature of the surfaces of an imaging system and the refractive indices of the media surrounding them, the position and the size of the Gaussian image of an object can be determined by using the equations given in Chapter 1. By determining the position and the size of its entrance and exit pupils, the irradiance distribution of the image of an object with a certain radiance distribution can be calculated, as discussed in Chapter 2. However, the quality of the image, which depends on the aberrations of the system, was not discussed. In this chapter, the concepts of wave and ray aberrations are introduced and a relationship between them is derived. The wave aberrations for a certain point object represent the optical deviations of its wavefront at the exit pupil from being spherical. If the wave aberrations are zero, i.e., if the wavefront is spherical, then all the rays converge to its center of curvature and a perfect point image is obtained. The aberrations of a system lead to an imperfect image. The ray aberrations represent the displacement of the rays from the center of curvature in an image plane passing through it. Although the ray aberrations of a system for a certain point object can be obtained by tracing the rays through the system and up to the image plane, they can also be obtained from the wave aberrations. However, the distribution of rays in an image plane does not represent the true picture of an image, since it does not take into account the diffraction of the wavefront at the exit pupil. Since the wave aberrations play a fundamental role in determining the image quality, their knowledge is essential. It is also noteworthy that the wave aberrations of a multielement system are additive, i.e., the wave aberration of a ray for the entire system is equal to the sum of its wave aberrations for each of the elements. This is not true of the ray aberrations; the aberration of a ray in the final image plane can not be obtained by adding its values in the image planes for the elements. Of course, the contribution of an element to the ray aberration in the final image plane can be obtained from its contribution, for example, to the primary wave aberrations of the ray according to the equations derived in Chapter 4. A defocus wave aberration is introduced when the image is observed in an image plane other than the one in which the center of curvature lies. It is also introduced if one or more imaging elements of the system are displaced along its optical axis. We derive a relationship between the longitudinal defocus of an image and the defocus aberration resulting from it. Similarly, when an imaging element is slightly tilted or displaced perpendicular to the axis, a wavefront tilt is introduced. We show how the wavefront tilt is related to the wavefront tilt aberration. Next, the possible aberrations of an imaging system that is rotationally symmetric about its optical axis are discussed.