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In the previous chapter, application of paraxial raytracing enabled reducing multi-element systems to a compact description in terms of the cardinal points and the entrance and exit pupils. As long as the elements of the optical system are rotationally symmetric and aligned with regard to a common optical axis, these techniques can be used to represent even the most complex systems. In effect, the reduction to cardinal points and pupils can replace the optical system with a "black box," where only the properties of the principal planes, nodal points, focal points, and pupil locations and sizes are known. Knowledge of these properties enables the location of the image plane to be found for a given object. This plane, the Gaussian imaging plane, is conjugate to the object plane. Furthermore, the entrance pupil serves as a port into the black box. Any light coming from the object that makes it into the entrance pupil will get mapped to the exit pupil (assuming no vignetting and no reflection losses of the surfaces) and emerge to contribute to the final image. For an ideal optical system, a point on the object would be mapped to a point on the image plane predicted by the Gaussian imaging equation. Furthermore, the transverse position of the image point would be determined by transverse position of the object point multiplied by the magnification of the optical system. In actual optical systems, this mapping process is not perfect. To understand how the mapping process deviates from the ideal case and to determine the implications of these imperfections of the imaging process, a wavefront picture of optical imaging must be examined.
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