The reflection and transmission coefficients for walls and surfaces in the environment can be determined once the angle of incidence, and the polarization of the incident field with respect to the surface are known. In order to calculate the horizontally and vertically polarized fields, it is assumed that the point of reflection is far enough from the source of the field for the field to be treated as a plane wave, and thus the electric and magnetic fields are perpendicular to the direction of propagation.
Using the surface normal, , the angle of grazing
incidence,
, is given as
where ,
is a vector in the
direction of propagation, and
denotes a vector dot product.
The direction of the horizontally polarized component of the incident
field is given by
where denotes the vector cross product. Likewise, the
direction of the vertically polarized component of the incident field
is given by
From these, the components of the incident electric field are computed as
where is the component of the electric field,
,
that is horizontally polarized with respect to the surface, and
is the vertically polarized component. The reflected field can then
be expressed as
where is in the direction of the vertically polarized component
of the reflected field, given by
Once the reflected field has been determined, it is used as the field for incident waves on further reflecting surfaces, diffracting edges, or on the receiver. The process of determining the electric field that is diffracted by an edge is similar in form where the vertically and horizontally polarized components of the incident electric field are determined, modified by the diffraction process, and recombined to form the diffracted field. The effects of wave expansion from the point source (free-space loss) are incorporated into the received field at the end of the calculation as only the amplitude of the field components are affected by this process. A correction factor is introduced when diffraction is incorporated in the propagation mechanism due to the additional expansion process that is introduced by a diffracting edge.