Optical systems satisfying the approximations introduced in the previous chapter can be treated, as we have seen, by the mathematical framework of Fourier analysis or its shorthand notation, the operator algebra. Therefore, this field is sometimes referred to as Fourier optics. Several books are available on this subject (see, for example, Refs. [10, 14, 31]) as well as a comprehensive selection of articles . In this chapter we employ Fourier optics in its operator description to the analysis of fundamental optical systems.
Most classical optical systems are composed of sections of free space and lenses. As we have seen in section 4.5, mirrors and prisms can be viewed as coordinate rotators and their effect does not need special treatment. A basic building block for optical systems contains a single lens between two sections of free space. Such blocks can be cascaded to construct more complicated optical systems. It will be shown in chapter 12 that, in principle, two lenses are adequate to perform all conventional optical processes. Nevertheless, practical optical instruments contain a large number of lenses to correct for the approximations imposed in our treatment and to overcome technical limitations. So-called nonclassical optical systems and processes will be addressed in later chapters.
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