Huygens Principle, and Polarization after reflection of a perfect metallic surface in a vacuum

Up front, I should be clear I am NOT asking about polarization effects which are induced by partial reflection/refraction involving materials such as air and water and their indexes of refraction. For this question, please assume I mean an ideal reflector in a vacuum. This is not a question about Brewster’s angle, Snell’s law, or similar.

I’m trying to model the antenna patterns off of a reflector (assume a parabolic dish for now) where the incoming plane wave is not in the ideal direction for the parabola, and/or the receiving feed horn is not at the ideal focal point.

Huygens Principle says I can treat every incoming wave as though it re-radiates spherically from the point of reflections. Then by summing (integrating over the whole reflector) the complex phasors at my point of reception, I can get the combined response. Performing this numerically and sampling across the reflector, I can get a reasonable gain and phase response for the beam pattern.

However, Huygens Principle doesn’t seem to say much of anything about the polarization of the re-radiated points. So, my question is: Considering just a single ray with a linear polarization, reflecting off of one tiny patch of the surface, how is the polarization rotated as it is received at an arbitrary point?

I assume a valid answer should show the same properties as ideal reflection for when the angle of incidence does equal the angle of reflection. For instance, vertical linear polarization remains vertical, horizontal stays horizontal, left circular polarization becomes right circular, and vice versa.