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Chapter 7:
Ray Spot Diagrams
Abstract
7.1 Introduction In Chapters 2â6, we have determined the primary wave aberrations of simple optical imaging systems. In this chapter, we use the relationship between the wave and ray aberrations given in Section 1.2 to determine the ray distribution for a point object, called the ray spot diagrams, in the Gaussian image plane. For each primary aberration, we determine the extent or the size of the image spot in terms of its peak value and the focal ratio of the image forming light cone. In the case of spherical aberration and astigmatism, we consider ray distributions in defocused image planes as well and determine the plane in which the spot size is minimum. These minimum-size spots are referred to as the circles of least confusion and represent the best aberrated images based on geometrical optics. In lens design, one often tries to minimize the radius of gyration of the spot rather than its radius. However, we will see in Chapter 8 that, in reality, which is based on diffraction of light at the exit pupil of the system, an image distribution is not given by the corresponding ray spot diagrams. For example, the aberration-free image of a point object is a point according to geometrical optics, but its diffraction image for a circular pupil consists of a bright spot surrounded by concentric dark and bright rings. However, certain features of the aberrated images of the two types are common. 7.2 Wave and Ray Aberrations Consider an optical system consisting of a series of rotationally symmetric coaxial refracting and/or reflecting surfaces imaging a point object. We have discussed in Chapter 1 that the primary aberration function representing the wave aberration at its exit pupil can be written W(r,Î¸;h â² )=a s r 4 +a c h â² r 3 cosÎ¸+a a h â²2 r 2 cos 2 Î¸+a d h â²2 r 2 +a l h â²3 rcosÎ¸, where (r,Î¸) are the polar coordinates of a point in the plane of the exit pupil, h â² is the height of the Gaussian image point, and a s , a c , a a , a d , and a t represent the coefficients of spherical aberration, coma, astigmatism, field curvature, and distortion, respectively. The angle Î¸ is equal to zero or Ï for points lying in the tangential or meridional plane (i.e., the plane containing the optical axis and the point object and, therefore, its Gaussian image). The chief ray, which, by definition, passes through the center of the exit pupil, always lies in this plane. The plane normal to the tangential plane but containing the chief ray is called the sagittal plane. As the chief ray bends when it is refracted or reflected by a surface, so does the sagittal plane.