outside the surf zone can also be viewed with the antenna at grazing 

 angles; a second mechanism, Bragg scattering , is responsible for the 

 return. In Bragg scattering the ocean waves appear to the microwave 

 radiation as a scattering lattice. Scattered radiation from successive 

 ocean wave crests will reinforce constructively at the radar antenna, if 

 the difference in the path lengths from the radar to each of two wave 

 crests is an integral number of radar wavelengths. Figure 24 illustrates 



Figure 24. 



Water Wove I « 1.5 cm 



Schematic showing Bragg scattering. Wave- 

 length of radar is X r , wavelength of waves 

 is Xu, and degression angle is 6. 



this constructive interference in Bragg scattering where the antenna to 

 scatterer distance is large compared to X w , the ocean wavelength. Let 

 \ r be the radar wavelength and 9 the grazing angle which is small. 

 The difference in the round-trip distance between a signal return from 

 the first crest and that from the second crest is 2x. The condition 

 for constructive reinforcement is then 



nX r = 2x 



n = integer (positive and nonzero) . (5) 



But 



x = Ay cos 9 ; (6) 



thus, the Bragg relationship is 



n\ r = 2Ay cos 6 . (7) 



The strongest return is usually for the first-order Bragg scattering 

 when n equals 1. For most shore-based or ship radars, the grazing 



27 



