174 



DIELECTRIC. CONSTANT. ABSORPTION AND SC.\TTERING 



values of p, the cross section reduces to the first term 

 ol' this series, which, when the dielectric absorption 

 is negligible, reduces to the Eayleigh scattering cross 

 section. Table 12 includes the results of the numer- 

 ical computations and Figures 1-3 and 16 are their 

 graphical representation. 



The knowledge of the total cross section and scat- 

 tering cross section allows the computation of the 

 alisolute proliabilitiestj^ for the waves to be scattered 

 in any direction or to be absorbed internally by spher- 

 ical water drops. The scattering probabilities are 

 given in Table 13. The probabilities for internal ab- 

 sorption are complementary to these, i.e., they are 

 equal to (1 — u^). It is thus seen that, with the 

 exception of the shortest waves and the biggest rain- 

 drops, the probability of the waves being absorbed in- 

 ternally, the absorbed wave energy heating the drops, 

 is much larger than the probability of their being 

 scattered in any direction. 



In Section 10.1.8 the differential scattering cross 

 section in a chosen direction is first derived rapidly and 

 then is given explicitly so as to show clearly the con- 

 tributions of the induced electric dipole, electric quad- 

 rupole, magnetic dipole, and tlieir interference terms. 

 Attention is here called to the already well-known 

 fact that in the optical spectrum region dissymmetry 

 appears in the angular distribution of the scattered 

 radiation. That is to say, the larger the parameter p 

 or the nearer the <li'op diameter to the wavelength, the 

 greater the power scattered in the direction of the 

 propagation in comparison with that scattered back- 

 ward or at 180° to the direction of propagation. 



The back-scattering cross section or radar cross 

 section of water drops is given in the form of a series 

 in ascending powers of the parameter p. Table 11 

 contains the results of numerical computations of 

 these radar cross sections for water drops in the diam- 

 eter range 0.05 to 0.-55 cm and wavelength range 3 

 to 100 cm. 



The radar cross section allows the determination 

 of a radar attenuation constant. The radar absorp- 

 tion coefficient, or the double of the attenuation con- 

 stant, is the fraction of the incident power scattered 

 backward by a layer of unit thickness of the echoing 

 medium. Table 15 contains the numerical values of 

 this radar absorption coefficient in different rains of 

 known drop size distribution, and Figure 17 is its 

 graphical representation. Table 10 is a somewhat 

 modified form of Table 15, in so far as it gives in 

 decibels the fraction of the incident power scattered 



backward by a 1-km layer of different rains. The 

 theoretically predicted back scattering seems to be 

 in fair agreement with the rather few experimental 

 data on the power received in radar observations of 

 rains or rain clouds. 



In conclusion it may be stated that, in view of the 

 scarcity of meteorological data and the irregularities 

 inherent in meteorological phenomena, the theory 

 provides a satisfactory picture of the propagation of 

 microwaves through a variety of precipitation forms 

 present in the atmosphere. 



i"2 K-BAND ABSORPTION — 



EXPERIMENTAL- 



Our knowledge of the attenuation of K-band radia- 

 tion in the normal atmosphere is based upon the 

 theory outlined by Van Vleck and upon a number of 

 experiments, some of which were i;ndertaken to ob- 

 tain data needed in the theory, others of which were 

 attempts to measure directly absorption by the at- 

 mosphere. 



The width of the rotational lines of water vapor in 

 the infrared has recently been measured in work at 

 the University of Michigan. The width of the oxygen 

 lines responsible for the strong absorption at 0.5 cm 

 and the rather small effect at K band are inferred 

 from experiments at the Kadiation Laboratory. The 

 aljsorption in oxygen was measvired directly at sev- 

 eral wavelengths in the neighborhood of 0.5 to 0.6 

 cm. The gas was contained in a w^ave guide about 6 ni 

 long. This guide could be evacuated and then filled 

 with gas to any desired pressure between zero and 

 roughly 1,000 mm Hg. The radiation was obtained 

 as the second harmonic generated in a crystal rectifier 

 fed by a K-band oscillator. The source was amplitude 

 modulated at audio frequency, and the signal was 

 detected by a second crystal at the far end of the 

 wave-guide path. The attenuation in the gas was de- 

 termined by comparing the signal received with the 

 guide evacuated to that received with gas present in 

 the guide. The absorption of pure oxygen, at various 

 pi'essures, as well as that of controlled mixtures of 

 oxygen and other gases, was measured. The results 

 confirm the predictions of the theory in a very con- 

 vincing manner and suggest a value of the line width 

 lying between 0.05 and 0.03 cm"^. 



Direct measurements of atmospheric absorption 

 at K band have been made by a group at the Radia- 



"By E. M. Purcell, Radiation Laboratory, MIT. 



