Electron microscopy
Angular/Polar Distribution of X-ray Generation in Electron Microscopy
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Based on theoretical electrodynamics with the interaction of incident electrons on a surface, the angular distribution of generated X-rays can be give in the form of polar equation, [1]
         Angular/Polar Distribution of X-ray Generation in Electron Microscopy ----------------------- [1001]
         θ -- the angle between the directions of emission and acceleration.
          -- the electron acceleration.

Equation 1001 results in a typical dipole characteristic:
         i) a maximum of emission perpendicular at θ = 90° to the dipole.
         ii) a zero emission parallel at θ = 0 and 180° to the dipole.

As shown in Figure 1001, the maximum emission of the x-ray continuum is shifted to smaller angles B because:
         i) the Coulomb field of a moving charge is not exactly radially-symmetric owing to relativistic effects.
         ii) a retardation has to be taken into account due to the finite velocity of wave propagation.

Figure 1001. Polar diagram of the angular distribution of the x-ray continuum generated in Al (left) and Au (right). [1]










[1] Ludwig Reimer, Scanning Electron Microscopy: Physics of Image Formation and Microanalysis, 1998.