What is a disoriented double bounce?

One of the first scattering mechanism studied in polarimetry is the “double bounce”. It is everywhere, as soon as the ground is horizontal, and an object has a vertical axis.
One of the first canonical targets studied in polarimetry that implies “double-bounce” is the dihedral, such as that formed by a horizontal face (the ground) and a vertical face (the wall). But it is not said that this situation is actually rare, because it implies that the wall has a direction parallel to the axis of the trajectory.

If an incident wave hits such a vertical wall, its response is strong, because whatever the angle of incidence, two successive specular reflections will always return in the same direction as the backscatter. If we assume that the object is metallic, then the corresponding Sinclair polarimetric matrix is:

In real life, objects are rarely metallic. In fact, as soon as there is a reflection coefficient on a dielectric surface, a dysmetry is introduced between the polarimetric channels, which varies with the angle of incidence.

But here, we are more interested in what happens when the double bounce is said to be “disoriented”.
But what angle of “disorientation” are we talking about?

• Most often, we think of the azimuthal axis. That is, the angle between the edge of the dihedral and the direction of the satellite’s trajectory axis. Because most of the time, there is no reason for these two axes to be parallel.

• We can also think of the slope of the ground, and thus the elevation of the edge of the dihedral.

In these two cases, the effect of these rotations are not similar to a rotation around the axis of the incident wave, which would result in a rotation on the Sinclair matrix, but does not change the overall geometry of acquisition: it still involves two specular bounces!

A rotation around the line of sight does not change the symmetry of the acquisition configuration

Unfortunately, in the first two cases, it is not simple at all to model the response of this object, because it necessarily involves scattering phenomena: that is to say that we can no longer consider smooth surfaces that respond only in the specular direction. At least one “bounce” will imply a dysmetry between the directions of scattering, and thus a diffusion mechanism on one of the surfaces.

Effect of azimuthal rotation : the “disoriented double bounce”. Case with specular mechanism on the ground

Effect of a slope: rotation of a dihedral along the ground range axis. Case with specular mechanism on the wall.

These two phenomena, inclusion of a slope in the double rebound, and disorientation of the dihedral, are equivalent only when the properties of the two surfaces (roughness and permittivity of the ground and the wall) are the same.

To model this kind of phenomena, it is necessary to leave geometrical optics -which simply describes the wave as a light ray- and to use scattering models by rough surfaces. These are the same tools that will allow us to better model bistatic situations, where the transmitter and the receiver are no longer in the same place, and where the reflection symmetries are also broken.

Bottom line:
● A disoriented double bounce is most often the phenomenon that occurs between a vertical wall and a horizontal ground, when the wall is not parallel to the azimuth direction

● The equivalent polarimetric matrix is not equivalent to a rotation of the Sinclair matrix of the “well oriented” case.

● Generally, all the physical phenomena involved are modified. Diffusion is often implied. To properly model the signal, it is necessary to know the dielectric permittivity and possibly the roughness of surfaces. At high frequencies (X-band), the details predominate.

Tyler, S., Dupuis, X., Guinvarc’h, R., & Thirion-Lefevre, L. (2022, July). A First Test on Permittivty Inversion of a Double Bounce in a SAR Image. In IGARSS 2022–2022 IEEE International Geoscience and Remote Sensing Symposium (pp. 5668–5671). IEEE.

Guinvarc’h, R., & Thirion-Lefevre, L. (2017). Cross-polarization amplitudes of obliquely orientated buildings with application to urban areas. IEEE Geoscience and Remote Sensing Letters, 14(11), 1913–1917.

Thirion-Lefevre, L., Guinvarc’h, R., & Colin-Koeniguer, E. (2020). The combined effect of orientation angle and material on PolSAR images of urban areas. Remote Sensing, 12(10), 1632.

Thirion-Lefevre, L., & Guinvarc’h, R. (2022, July). Polarimetry and Permittivity in SAR Remote Sensing. In IGARSS 2022–2022 IEEE International Geoscience and Remote Sensing Symposium (pp. 4419–4422). IEEE.