Changes

Because we have values for A and <math> A _t </math>, we can almost find <math>A _{recieved} </math>. Unfortunately, we lack values for the new phase-shift term, which is a function of the phase-shifts of <math> \Psi _1 </math> and <math> \Psi _2 </math>. This can be easily expressed as

Because we have values for A and <math> A _t </math>, we can almost find <math>A _{recieved} </math>. Unfortunately, we lack values for the new phase-shift term, which is a function of the phase-shifts of <math> \Psi _1 </math> and <math> \Psi _2 </math>. This can be easily expressed as

<math>\tan { d_f } = \frac{ sin d_1 + sin d_2 }{ cos d_1 + cos d_2 } </math>

<math>\tan { d_f } = \frac{ \sin d_1 + \sin d_2 }{ \cos d_1 + \cos d_2 } </math>

Unfortunately, this term is not simple to calculate. Worse yet, the shape is represented by  

Unfortunately, this term is not simple to calculate. Worse yet, the shape is represented by