Chapter 10 

 SCATTERING AND ABSORPTION OF MICROWAVES 



The object of the present chapter is to summarize 

 the status of absorption and scattering of micro- 

 waves by different solid obstacles, by liquid water 

 or ice particles floating or falling in the atmosphere 

 like those present in clouds, fog, rain, hail, and snow. 

 The absorption of microwaves by the atmospheric 

 gases as well as the aforementioned meteorological 

 elements will also be summarized here. 



The following grouping of the material included 

 suggests itself naturally: absorption and radar cross 

 section ; targets (planes, ships) ; absorption and scat- 

 tering by rain, hail, snow, clouds, and fog; and 

 absorption by the atmospheric gases, oxygen, and 

 water vapor. 



101 ABSORPTION AND RADAR 



CROSS SECTION 



Any object irradiated by electromagnetic waves 

 will in general remove energy from the incident 

 beam both by absorption and by scattering. The 

 absorbed energy is transformed into heat in the 

 body, while the scattered energy appears in the form 

 of radiation propagated generally in every direction 

 around the scatterer as the source. 



Let us call P a the power removed from the beam 

 through the internal absorption of the object. Its 

 absorption cross section is defined by 



A-^ 



(1) 



where W t is the power density in the incident beam, 

 that is, the power passing a unit cross-sectional area. 

 Similarly, if P s is the total power removed from 

 the beam through scattering in every direction, then 

 the scattering cross section associated with this 

 object is 



s = wr (2) 



The value of S gives information about the total 

 scattered energy, but this is not directly useful in 

 radar work because one is interested only in that 

 fraction of the total scattered power which travels 

 in the direction of the receiver. One wants then a 



parameter involving the scattered power per unit 

 area W r at the radar receiver instead of the total. 

 If the target is an isotropic scatterer, 



P. 



Wr 



iwd' 2 



(3) 



d being the distance from the target to the receiver. 

 The scattering cross section can thus be written as 



S 



W 



(4) 



For targets other than isotropic scatterers, however, 

 this procedure fails since one cannot say that the 

 power per unit area at the radar is PJi-n-d 2 . Never- 

 theless, it is useful to define a parameter, 



A 12 ^ 



(5) 



which is called the radar cross section in analogy 

 with the scattering cross section jS of an isotropic 

 scatterer. This cross section cr may be thought of 

 as the scattering cross section which the target in 

 question would have if it scattered as much energy 

 in all directions as it actually does scatter in the 

 direction of the radar receiver. For an isotropic 

 scatterer a = S, but in general it does not. 



It can be shown 3, that the ratio of the received 

 power P 2 to the output power Pi is given by 



P 2 _ n n a 



K ~ Gl(j2 4rf 



3AW 



Sird) Ap 



(6) 



The gains (?i, G% and path factor A p are defined in 

 Volume 3, Chapter 2, and X is the wavelength of the 

 radiation used. (See also Volume 3, Chapter 9.) This 

 formula can be used for the determination of <r. Or 

 if cr is known, it may serve to calculate the possible 

 range. (It may be noted here that sometimes aA\ 

 is called radar cross section.) Also, a characteristic 

 length L, sometimes called the scattering coefficient, 

 is occasionally defined in relation to cr by 



a = 4irL 2 . (7) 



For simple targets a may be calculated. Table 1 

 contains a few calculated radar cross sections. 



a See Volume 3 of the Summary Technical Report of the 

 Committee on Propagation. 



82 



