In the simulation below, a collimated beam of plane waves travel from left to right. Red is a positive wave amplitude, blue is a negative wave amplitude and black is no wave amplitude. Two point scatterers are placed in the beam. These scatterers emit circular waves with the wavelength of the incident beam. The phase of the scattered waves is coherent with the incident beam. The scatterer emits a wave peak when a wave peak in the incident beam arrives.

If both of the scattering strengths F₁ and F₁ are set to zero, there are no scattered waves. If the scattering strength of only one scatterer is set to zero and the other scatterer is moved to the edge of the collimated beam, you can see the circular waves being emitted coherently with the incident beam.

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F1 =  [cm3/2] F2 =  [cm3/2] x1 =  [cm] x2 =  [cm] y1 =  [cm] y2 =  [cm] λ =  [cm]

In some directions the scattered waves add constructively and in other directions the scattered waves add destructively. For waves in two dimensions, the amplitude of the scattered waves is,