WAVELENGTH OF A HETEROGENEOUS X-RAY BEAM 



31 



at this point is 1.13. This is the composite absorption coefficient. 

 Referring to Table 1-3 one may observe that the effective wavelength 

 comparable to this mass absorption coefficient of copper is 0.173 A. 



Upon drawing a tangent to the same curve at the 2.0-mm thickness 

 mark it is found that the slope at this point corresponds to a composite 

 absorption coefficient of 0.81 comparable with an effective wavelength 

 of 0.15 A. Note that, as the thickness of the filter increases, the slope 

 decreases, and hence the effective transmitted wavelength decreases; 

 i.e., successive filters harden the transmitted rays. 



10 



6- 



Tungsten target 

 40 kv unfiltered 



0.3 



0.4 0.5 0.6 0.7 



Wavelength in A 



1.0 



Fig. 1-14. A diagrammatic representation of the general radiation emitted from 

 a tungsten target with and without a filter. Note the general hardening of the 

 emission without change in Xn but a pronounced change in X max and loss in intensity 

 of the filtered beam. Compare this with the 30-kv unfiltered beam having about 

 the same area and longer effective wavelength. (After A. W. Hull.) 



This general hardening of filtered x-rays was originally observed by 

 Hull. His spectral distribution curves are shown in Fig. 1-14. Thus 

 if a copper or aluminum filter is placed in the path of the x-radiation 

 the intensity of the filtered radiation is much decreased but the decrease 

 is proportionally greater in the longer-wavelength region owing to the 

 relatively greater absorption of these wavelengths. As a result the 

 effective value of the wavelength is decreased. This is due to the fact 

 that X max is transferred to shorter wavelengths without changing the 

 value of X . For comparison a 30-kv unfiltered emission curve is shown 

 having about the same intensity as the 40-kv filtered radiation, but note 

 that its effective wavelength is much longer. 



