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They can be linked with the incident and scattered amplitude vectors via
: <math>_k\mathbf{a}_{l,m,n} = \frac{1}{2\sqrt{Z_F}}{_k\mathbf{E}}_{l,m,n}+\frac{\sqrt{Z_F}}{2}{_k\mathbf{H}}_{l,m,n}</math>
: <math>_k\mathbf{b}_{l,m,n}=\frac{1}{2\sqrt{Z_F}}{_k\mathbf{E}}_{l,m,n}-\frac{\sqrt{Z_F}}{2}{_k\mathbf{H}}_{l,m,n}</math>
where <math>Z_F = \sqrt{\frac{\mu}{\varepsilon}}</math> is the field impedance, <math>_k\mathbf{a}_{l,m,n}</math> is the vector of the amplitudes of the incident waves to the node, and <math>_k\mathbf{b}_{l,m,n}</math> is the vector of the scattered amplitudes. The relation between the incident and scattered waves is given with the matrix equation
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