The analysis of the optical elements and optical systems discussed in chapter 5 were based on the paraxial approximation. Moreover, in all the considerations we did not limit the transversal extent of the optical system. It was an implicit assumption that the systems were infinite in their transversal dimensions. Obviously, an infinite optical element, such as a spherical lens, is not only physically impossible, but it is also in strong contradiction to the paraxial approximation. As a consequence, all our previous results must be modified to take into account the physical and technical limitations. Nevertheless, we must emphasize that the results obtained with the indicated nonphysical assumptions can still serve as a good first order approximation. They also provide a good insight into the physical processes involved. The modifications considered in this chapter are necessary refinements to assess more exactly the actual characteristics of a real system.
In chapter 5 we derived several optical transformations, the most important of which are the Fourier transformation and imaging. To derive these processes we evaluated the transfer function of a lens by using the paraxial approximation. The finite value of the terms and factors ignored within the approximations used introduces various distortions on the ideal transformations that were derived. These distortions are called lens aberrations. Lens aberrations limit the performance of optical systems and one of the main tasks of an optical design engineer is to find ways that correct or compensate these aberrations. The basic procedures involve modifications of the spherical lens surfaces, the combination of several lenses, each with different corrections, to replace a single lens, and the placements of apertures in well selected positions. Indeed, sophisticated computer design programs are available commercially and some of them can also be downloaded from the computer networks to optimize these design parameters.
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