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Chapter 9:
Spot Sizes and Diagrams
In Chapter 4 we developed paraxial ray-tracing equations to determine the Gaussian imaging properties of a system, vignetting of rays, size of imaging elements and apertures, and obscurations in mirror systems. In the paraxial approximation, all rays from a point object that are transmitted by the system pass through the Gaussian image point. However, when the rays are traced according the exact laws of geometrical optics, they generally intersect in the vicinity of the Gaussian image point. The ray distribution on an observation surface, as depicted by the intersection points, is called the spot diagram, and its extent is called the spot size. In this chapter, we discuss the distribution of rays in the image of a point object aberrated by a primary aberration. The density of rays over an observation surface is called the geometrical point-spread function. We define its centroid and sigma value, and calculate them for primary aberrations, without explicitly calculating the ray density distribution [1]. In the case of spherical aberration and astigmatism, the ray distribution and spot size are also considered in image planes other than the Gaussian, thereby introducing the concept of aberration balancing. In the early stages of the design of an optical imaging system, one often considers its transverse ray aberrations in an image plane for a set of rays lying along a certain line in the plane of the exit pupil and passing through its center. Such a set of rays is called a ray fan. We illustrate the wave and ray aberrations for ray fans along the x and y axes. Also discussed are the balanced aberrations for the minimum spot sigma in terms of Zernike circle polynomials. Aberration tolerances, including the depth of focus, and a golden rule of optical design are discussed. The characteristics of the ray spots and tolerance for primary aberrations are summarized in the last section.
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