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Optical engineering, which addresses modeling, design, fabrication, and testing of optical systems, is often associated with imaging systems and the design of lenses. Thus, classical optical engineering is largely based on a ray-optical representation of electromagnetic fields and the modeling of their propagation by geometrical optics, i.e., ray tracing. This geometrical theory of field propagation is obtained from general electromagnetic wave theory at the short-wavelength limit, as illustrated in Chapter 3 of Ref. 1. It serves well the propagation of smoothly modulated fields that are are typically of concern in the modeling of imaging systems and illumination systems. As soon as the truncation of fields by apertures (see Sect. 8.8 in Ref. 1 and Refs. 2,3) or other high-frequency field modulations become important in an application, wave-optical propagation techniques must be applied. Strong modulations may be inherent in the field we wish to obtain; consider for instance the generation of a top-hat profile laser beam. Such modulations may be introduced by strong aberrations (see Chapter 9, Ref. 1), or by the use of microstructured elements. Independently of the reason, geometrical optics modeling starts to fail. Often the use of geometrical optics for modeling the propagation of fields is directly associated with a ray-bundle representation of the field, which the optical designer can employ to evaluate the quality of an imaging system by investigating spot diagrams in or near the image plane. The representation of fields by rays is indeed a basic characteristic for modeling in conventional optical engineering. If the geometrical optics propagation model starts to fail, we need to give up the ray-optical field representation as well. It should be noted, however, that a wave-optical field representation in combination with a geometrical optics propagation model can give very reasonable results, as we will see in Sect. 18.5.
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