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 Chapters 2, 3, and 4. 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 5. However, the quality of the image, which depends on the aberrations of the system, was not discussed. In Gaussian optics, all of the object rays from a certain point object transmitted by a system pass through the Gaussian image point. The imaging system converts the spherical wavefront diverging from the point object into a spherical wavefront converging to the Gaussian image point. In reality, however, when the rays are traced according to the exact laws of geometrical optics, they generally do not converge to an image point.
In this chapter, the wave and transverse ray aberrations are discussed, 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. The wave aberrations are zero if the wavefront is spherical, in which case all of the rays converge to its center of curvature, and a perfect point image is obtained. The ray aberrations represent the displacement of the rays from the Gaussian image point.
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