ِAngular distribution of a scattered field

[Ahmed123]

SA
I study the reflection from a rough surface and get the field as the attached figure
my question
can I use the field distribution to get the angular distribution of the scattered field and how can I project the field to plane waves?

 

[tech99]

I think that the surface behaviour is specular at low grazing angles, and ceases to behave as rough. This angle is determined by the Rayleigh Roughness criterion. RMS height of hills < lambda/(8 x cos Theta). The angle Theta is the angle of incidence.
A useful article here:-
https://www.google.com/url?sa=t&rct...g_Models.pdf&usg=AOvVaw1iTBDzREw0-7qx7aD_oMdK

 

[tech99]

Re your last question, for a given reflected ray, the wave vibrates at right angles to the direction of travel.