4-3] EFFECT OF POLARIZATION ON REFLECTION 179 



in terms of the wavelength. Fig. 4-2 shows a plot of a' I a versus i?/X for 

 various values of 2Z,/A. 



4-3 EFFECT OF POLARIZATION ON REFLECTION 



Although the majority of radars utilize linear polarization, for certain 

 purposes other polarizations are found to be advantageous. The use of 

 circular polarization, for example, reduces rain clutter considerably. Since 

 any state of polarization may be described in terms of two orthogonal 

 polarizations (for example, horizontal and vertical, or right-hand and left- 

 hand circular), we may denote an arbitrarily polarized incident wave by 

 the matrix 



(f:) 



Er = (V] (4-16) 



in which the orthogonal components £i, E2 are complex quantities, or 

 phasors. 



The radar area of a target depends on the polarization of the incident 

 wave. A long thin (in comparison to X) wire is a good example, since its 

 reflection is very small when the incident field is linearly polarized at right 

 angles to the wire axis, and maximum when parallel to the axis. It is 

 evident, therefore, that the radar area and radar length are dependent on 

 the polarization of the incident field. 



For targets of complex shape, the total field strength incident at a given 

 point of the target is the resultant of the primary field from the radar and 

 the reradiated fields from other parts of the target. Especially in the case 

 of targets of large size which are in part inclined to the wave front, some 

 of the latter fields have a component of polarization orthogonal to that of 

 the primary field. For targets of symmetrical shape (as viewed from the 

 radar) this cross-polarized component balances out in back-scattering, but 

 otherwise it usually does not. Hence, in general, the back-scattered field 

 has a different polarization from the incident field. The coupling between 

 the incident and scattered polarizations depends on the incident polariza- 

 tion itself. As a result, the radar length is a tensor quantity, which may be 

 written in matrix form as 



in which each of the components /n, etc. is a phasor. For example, if the 

 1-polarization is horizontal and 2-polarization is vertical, /n represents the 

 radar length of the horizontally polarized echo from a horizontally polarized 

 radar, /12 is the radar length of the horizontally polarized echo from a verti- 

 cally polarized radar, etc. The reflected field-at-unit-distance is then given 

 by 



