FIGURE 13: Telescope's aperture stop is either an opening, or a surface that sets physical boundaries determining the amount of light reaching the image. The image of the aperture stop formed by a system element preceding it in the optical train is entrance pupil, and the image of the aperture stop formed by the element or surface fallowing it in the optical train is exit pupil. The two pupils coincide with the aperture stop - and each other - for a single mirror with the stop at the surface (also, for all practical purposes, for a single lens objective with the stop at the front surface). The two pupils coincide for a stop at the mirror's center of curvature. Rays from the boundaries of the aperture stop coming to the final focus appear as if coming from the boundaries of the exit pupil, and the chief ray CR -the one passing through the center of the aperture stop - appears to be coming from the exit pupil center. These properties make the exit pupil an important element in the aberration calculation, since the cause of wavefront aberrations - optical path difference of in-phase wavefront points with respect to the central point on the chief ray - is directly determined by its position. The above image illustrates a concave mirror with the aperture stop somewhat inside the mirror focus. The mirror images the aperture stop into the exit pupil ExP which appears to be the opening from which the rays converge (exit) toward the image. In two-mirror systems, secondary forms the exit pupil, as its image of the primary mirror, with the image being smaller than the aperture. The two pupils' size ratio is given by pupil magnification m, as ExP=mEnP. Actual size of the exit pupil may be a factor in some calculations. In principle, it is irrelevant, due to the change in the radial coordinate being offset by that in the axial coordinate. Thus, while formally the wavefront is evaluated at the exit pupil, the coordinates used hereafter are, conveniently, those of the aperture stop, whether the two coincide, or not.

FIGURE 14: Basic imaging terms and parameters defined in the 3-dimensional right-hand Cartesian coordinate system. All lengths, as well as indici of reflection and refraction, are positive in the directions of the z, x and y coordinate axes arrows, negative in the opposite direction. The exit pupil ExP from which the wavefront, if perfect, converges to the Gaussian focus GF in the image plane, at the distance equal to the focal length ƒ for axial objects at infinity. The pupil radius d is the unit length for the normalized height in the pupil plane r, ranging from 0 to 1. The pupil angle q ranges from 0 to 2π radians (360 degrees); it is a factor with which optical path difference vary for asymmetrical aberrations. The angle of aberration b is determined by the spatial orientation of the chief ray CR that passes through the pupil center at an inclination angle a - the field angle - in the plane determined by the chief ray and optical axis and defined as tangential plane. Sagittal plane is orthogonal to tangential plane, also containing the chief ray. Point of intersection of the chief ray and focal plane determines the Gaussian image point, and its height h; with the Gaussian focus, it determines the axis of aberration.