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In this section, we will derive the far‐field EM scattering from a perfectly conducting object. This formulation is closely parallel with the derivations that can be found in References (Chu et al. 1991; Bhalla and Ling 1993). The geometry of the problem is assumed to be as shown in Figure 2.2 where a PEC object is illuminated by a plane wave with exp(jωt) time dependence and incident wave vector of The incident electric and magnetic wave fields are given by

(2.1)

and

(2.2)

where E_o and give the magnitude and the polarization direction of the incident electric field. According to the physical optics (PO) theory (Balanis 1989), the current induced on the surface of the object is given by the following well‐known formula:

Figure 2.2 Electromagnetic scattering from a perfectly conducting object.

(2.3)

Here, is the outward unit vector of the illuminated object's surface. The vector r^′ is defined from the origin to any point on the illuminated surface (S_lit) of the object. The scattered electric field at the far‐field region along the observation vector of r is given by

(2.4)

where is the wavenumber vector in the scattering direction. Putting Eq. 2.3 into 2.4 will yield the scattered field equation in terms of the incident electric field as

(2.5)

This is the scattered electric field in the far field using the PO approximation. As will be explored in Chapter 4, this formula will constitute a basis for the derivation of inverse synthetic aperture radar (ISAR) imaging algorithm.