182 REFLECTION AND TRANSMISSION OF RADIO WAVES 



complex polarization customarily is 

 resolved into its orthogonal linearly 

 polarized components parallel and 

 perpendicular to the surface, which, 

 in the case of reflection from the 

 Fig. 4-4 Reflection at the Ground. ground, are horizontally and verti- 



cally polarized components, respec- 

 tively. These components can be treated separately and recombined 

 after determining the change in amplitude and phase of each on reflection. 

 The reflection coefficients for horizontal and vertical polarizations are 

 given by the well-known Fresnel equations^ 



sin d - (e - cos^ 0)1/2 



sin e + {e - COS" 0)1/2 

 es'md - (e - cos^^)!/^ 



|p//k-^^^ (4-24) 



Iprk-'*^ (4-25) 



€ sm -f (e - cos20) 1/ 



where 6 = depression angle of the radar (see Fig. 4-4) 



e = complex dielectric constant of the surface. 



The complex dielectric constant e is given in terms of the permittivity and 

 conductivity of the ground k and a by 



6 = --j— = e'-7V' (4-26) 



eo coeo 



where eo = permittivity of free space. 



Values of typical ground constants and reflection coefficients are readily 

 available in the literature. ■'^"^ 



A dependence of the reflection coefficient on frequency enters Equations 

 4-24 and 4-25 through the dependence of e" on frequency. In addition, 

 however, the ground "constants" k and a themselves are functions of 

 frequency, by virtue of the dispersion of water. This dispersion takes place 

 just in the frequency region most used for airborne radar. The resulting 

 dispersion of ground thus depends on its water content. For airborne radar 

 this is particularly important for water surfaces. Figs. 4-5 and 4-6 show the 

 variation of the dielectric properties of pure, fresh, and sea water with 



2See J. A. Stratton, Electromagnetic Theory, Sees. 9.4 and 9.9, McGraw-Hill Book Co., Inc., 

 New York, 1941. 



3F. E. Terman, Radio Engineers' Handbook, pp. 700-709, McGraw-Hill Book Co., Inc., 

 New York, 1943. 



■•C. R. Burrows, "Radio Propagation over Plane Earth-Field Strenirth Curves," Bell System 

 T^f/^. J. 16, 45-75 (1937). 



5R. S. Kirby, J. C. Harman, F. M. Capps, and R. N. Jones, Effective Radio Ground-Conduc- 

 tivity Measurements in the United States, National Bureau of Standards Circular 546. 



