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# Polarization signatures

## Polarization signatures

(OP)
Hi,

I'm studying the PolSAR basics and came across the polarization signatures (co-pol and cross-pol). There is a case of a sphere or trihedral corner reflectors (odd-bounce) described for example here: http://pages.csam.montclair.edu/~chopping/rs/CCRS/chapter3/chapter3_8_e.html.

I do not understand why the power of the co-polarized signature has maximum values for linear polarizations (ellipticity=0) since "The wave is backscattered with the same polarization, except for a change of sign of the ellipticity (or in the case of linear polarization, a change of the phase angle between Eh and Ev of 180o)". If I understand right one reflection of linearly polarized wave should cause a phase shift of 180 degrees between Eh and Ev, which results in ortogonal polarization (except the case of V and H polarizations).

What am I missing here?

### RE: Polarization signatures

These forums do not allow 'student' questions, but reading between the lines I see a 'Mining' professional asking about what might be a Remote Sensing question. So I'll assume you're a professional asking a professional question.

...

If you stand in front of a mirror (assuming an approximately 'normal' [90°] reflection), do you see an image of yourself standing, or lying down? That's pretty much all you need to understand to see why linear polarization reflects ('normal') as same-orientation (H or V) linear polarization.

Note also the basic physics/logic laws of symmetry. If geometrical symmetry is preserved then there'd be nothing for Nature to choose turning left from turning right. If Nature can't choose one over the other, then (generally) She doesn't go there.

For the CP case, hold up a clock in the mirror. Notice that it's backwards. So each reflection reverses the sense of CP (LHCP<>RHCP). Double reflection gets you back where you started. Odd number leaves it reversed.

Whatever logic you used to decide that linear reflections are returned with orthogonal orientation, that logic is wrong.

I'm being careful to specify 'normal' [approximately 90°] reflections. There can be some odd things happening at shallow angles. The topic of Remote Sensing gets into those sort of details. I'm only addressing the simple case.

### RE: Polarization signatures

If you think only of electrons as physical objects that move. Polarization is the direction of their motion.

One note on circular polarization, there are two definitions in the US, FCC vs. IEEE, which are exact opposites. So if someone asks you to make Right Hand or Left Hand circular polarization, RHCP or LHCP, then ask them whether it's IEEE description or not. You will likely confuse them since not many know this. GPS is IEEE defined and most broadcast radio and TV stations are FCC defined.

### RE: Polarization signatures

(OP)
VE1BLL, Higgler - thanks for your replies.

I understand that the polarization does not change to the orthogonal after the reflection. It is only the matter of the point from which we are looking. In case of BSA convention (like standing in front of the mirror) we observe the received polarization as orthogonal (in case of linear polarizations with orientation different than 0 (H), 90 (V) or 180 (H) degrees), while in fact it is the same polarization as the incident one, but the "mirror" effect makes it look like orthogonal.

Let me know if I'm on the right track.

PS. If so, then in BSA case, the co-polarization for linear non-vertical, non-horizontal polarization would be the "ortogonal" one (meaning that the polarization of the wave did not change, but the direction of propagation changed).

### RE: Polarization signatures

Circular Polarization does change orientation from most surfaces when bouncing off a flat surface. Only a low angle bounce off a flat dielectric surface (e.g. air to ground bounce) does circular polarization not change orientation due to snells law. Low angle no change, higher angle yes change, depends on soils dielectric value and angle of incidence.
So RHCP transmitted out usually (99%) gets LHCP received (cross pole)  from a flat surface.

for a flat surface, reflected V can't change to H, and vice versa, but use a slanted wire (slant 45) to reflect energy and your transmitted V splits to receive equal parts V and H  pole.

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