Ray optics can give you a good physical feel for radiation and spur design ideas, but we need to question the accuracy of their use. Ray optics or geometric optics (GO) methods come from the design of lens and optical reflectors where the wavelength is very short compared to the size of the object being analyzed, whereas we may be interested in analyzing or designing an antenna on a structure only a few wavelengths in size. Below we show that GO is essentially correct over most of the radiation sphere and that by using elements of the geometric theory of diffraction [GTD (UTD)], the pattern prediction can be improved. In this case improvement means that we will increase the area of the radiation pattern that becomes more accurate. You will discover that it takes an increasing amount of effort to improve small areas of the pattern prediction, and at some point you should decide that it fails to give enough improvement to justify the work. Your real design purpose is to determine antenna dimensions that produce the desired antenna response. Of course, as the expense of the antenna increases, your customer may demand better predictions of the final result, and then the cost of a better analysis is justified. You need to accept a new approach. Even though a part of the pattern prediction shows errors, obvious discontinuities, it only means that the pattern is inaccurate in directions near them and that over most of the radiation sphere the prediction is essentially correct.

Discussion of this method begins with simple examples given in two-dimensional space that introduce the ideas behind GO and GTD. These examples can ignore the details of rotation of polarization directions because the waves are either polarized with the electric field normal to the page or located in the plane of the page. We consider radiation blockage by objects, the reflection of rays by the objects, and the diffraction of rays around edges that fills in the pattern in the shadow regions and across the boundary of the last reflected ray.

After the discussion of simple examples, the key points of GTD will be given for use in three-dimensional problems. This involves the rotation of coordinate systems so that ray polarizations line up with planes of incidence for reflections, with edges for diffraction and curvature directions on curved surfaces that shed rays around the object into the shadow. You will need to investigate the references if you want to develop your own routines, but this discussion will introduce you to the topic and give you an appreciation of the method so that you can use available computer programs and understand their limitations.

GO uses ray methods to approximate electromagnetics. It is exact only in the limit of zero wavelength (infinite frequency), but we gain useful insight from it at any frequency. It will not give good results close to physical boundaries; but when we include the GTD, the results are accurate down to one-wavelength sizes and are useful at λ/4 sizes. GO gives us physical insight when we deal with reflectors. We must consider three aspects to use GO fully: (1) ray reflections, (2) polarization, and (3) amplitude variations along the ray path and through reflections.