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14. Slant range / ground range

Slant range / ground range The figure shows two types of radar data display:
- slant range image, in which distances are measured between the antenna and the target
- ground range image, in which distances are measured between the platform ground track and the target, and placed in the correct position on the chosen reference plane

Slant range data is the natural result of radar range measurements. Transformation to ground range requires correction at each data point for local terrain slope and elevation.
Geneva, Switzerland This figure illustrates an example of SAR data using a Seasat scene of Geneva (Switzerland). The slant range image is displayed on the left of the screen, while the ground range image is on the right side.
The geometric distortions present on a radar image can be divided into:
- Range distortions: Radar measures slant ranges but, for an image to represent correctly the surface, it must be ground range corrected
- Elevation distortions: this occurs in those cases where points have an elevation different from the mean terrain elevation

15. Optical vs. microwave image geometry

Geometries The figure presents a comparison between respective geometries of radar image and oblique aerial photos.
The reason for the major differences between the two image's geometry is that an optical sensor measures viewing angles, while a microwave imagers determines distances.

16. Foreshortening

Image geometry

Image geometry
The most striking feature in SAR images is the "strange" geometry in range direction. This effect is caused by the SAR imaging principle: measuring signal travel time and not angles as optical systems do.

The time delay between the radar echoes received from two different points determines their distance in the image. Let us consider the mountain as sketched in the figure. Points A, B and C are equally spaced when vertically projected on the ground (as it is done in conventional cartography).

However, the distance between A'' and B'' is considerably shorter compared to B'' - C'', because the top of the mountain is relatively close to the SAR sensor.

Foreshortening is a dominant effect in SAR images of mountainous areas. Especially in the case of steep-looking spaceborne sensors, the across-track slant-range differences between two points located on foreslopes of mountains are smaller than they would be in flat areas.
This effect results in an across-track compression of the radiometric information backscattered from foreslope areas (see example of ERS image to the left) which may be compensated during the geocoding process if a terrain model is available.
Foreshortening is obvious in mountaineous areas (top left corner), where the mountains seem to "lean" towards the sensor.
It is worth noting that shortening effects are still present on ellipsoid corrected data.

17. Layover


If, in the case of a very steep slope, targets in the valley have a larger slant range than related mountain tops, then the foreslope is "reversed" in the slant range image.
This phenomenon is called layover: the ordering of surface elements on the radar image is the reverse of the ordering on the ground. Generally, these layover zones, facing radar illumination, appear as bright features on the image due to the low incidence angle.
Ambiguity occurs between targets hit in the valley and in the foreland of the mountain, in case they have the same slant-range distance. For steep incidence angles this might also include targets on the backslope.
Geocoding can not resolve the ambiguities due to the representation of several points on the ground by one single point on the image; these zones also appear bright on the geocoded image.
These images were acquired over a mountainous zone close to the city of Udine (I), by ERS-1 and Landsat-5 respectively.
The effect of layover is visible in the whole SAR image, in particular on the two mountains that are on the right of the lake. The height of the upper one (San Simeone) is about 1000 m above the valley bottom (1220 msl), while the height of the lower one (Brancot) is 1015 msl.