4-11] SEA RETURN IN A DOPPLER SYSTEM 217 



may vary somewhat from time to time, depending on the condition of 

 the sea surface. 



4-11 SEA RETURN IN A DOPPLER SYSTEM 



The doppler shift due to relative motion of radar and target was discussed 

 in Paragraph 4-4, and the echo frequency due to a transmitted frequency/o 

 was given as 



/=/o + 2F/X (4-66) 



where V is the line-of-sight component of the approach velocity of radar 

 and target. If both radar and target are in motion, then with respect to 

 fixed coordinates V may be divided into two parts, one due to the radar 

 velocity F^, the other to the target velocity Vf Equation 4-66 corre- 

 spondingly may be written as 



/=/o +/.+/.. (4-67) 



If the angle of the target from the ground track of the radar is Xj then the 

 doppler frequency due to the radar motion is 



/. = (2F./X)cosx=/icosx (4-68) 



/i = lVrl\. (4-69) 



If the target is the surface of the sea, then the angle x will vary over the 

 portion of the surface which is illuminated by the radar, owing to the finite 

 width of the antenna beam. Hence there will be induced by the motion of 

 the radar a corresponding band, or spectrum, of doppler frequencies Jr. 

 This may be called an induced doppler spectrum. 



Similarly, if the various portions of the surface are in relative motion, 

 then even if the radar is stationary or the radar beam is so narrow that no 

 appreciable variation in cos x takes place over the illuminated area, a range 

 of doppler frequencies/^ will result from the intrinsic motion of the surface. 

 This may be called the intrinsic doppler spectrum. 



The relative importance of the induced and intrinsic doppler components 

 depends on the relative velocities and the geometry, as well as on the 

 antenna beamwidth. Referring to Fig. 4-40, 



cos X = cos ^0 cos 00 



where 0o is the depression angle and 0o the azimuth angle of the surface 

 target relative to the aircraft motion. 



Hence for a small azimuth deviation ±A(/) from the mean value 0o, we 

 have 



cos X = COS 0o(cos 00 cos A0 ± sin 0o sin A0) 



(4-70) 

 = cos ^o{[l - (A0)V2] cos 00 ± A0 sin0o}. 



