**SAN JOSÉ STATE UNIVERSITY**

ECONOMICS DEPARTMENT

*Thayer Watkins*

**Remote Sensing with Radar**
### The Layover Phenomenon in Radar Images

A radar image, which is based upon the slant distance of objects from
the radar transmitter, has a special problem concerning objects of different
heights as well as different distances. Taller objects may appear closer
than shorter objects with the same horizontal locations. The diagram
below illustrates the effect. Note however, that radar images are not
in color but only show shades of gray.
For objects with steep slopes the situation is similar to the case of a
vertical object which was shown above.

If the slope of the object is sufficiently low the radar image
is laid out front to back and there is foreshortening as seen below.

The matter of whether the radar images of objects have layover or foreshortening
depends upon a relationship between slope angle of the object and the
angle of the line between the radar emitter and the object. Since this latter
angle would vary with the point on an extended object being considered it might
seem that the condition for determining the nature of the radar image
from the angles would be complicated. Actually
the geometric condition that determines whether there is layover or foreshortening
in quite simple. Consider the radar emitter as a point and consider a straight
line that passes along the slope of the object. From the point a line can
be drawn that is perpendicular to the slope line. If the point of intersection
of the perpendicular with the slope line is above the object then there will
be layover. If the point of intersection is below the object there will be
foreshortening. The two situations are depicted below.

There is the third case in which the point of intersection of the
perpendicular with the slope line occurs within the object. In this case
the part of the object above the point of intersection is foreshortened and
the part below is laid over. But the images of the object which are equal
distances from the point of intersection map into the same point in the
radar image. Since the intensities of the points add the image of the object
would appear extra bright and because the image of the object would be
severly foreshortened the image of the object would be virtually a bright
point.

Having considered the simplest of objects above it is now appropriate to
consider more complex objects, such as a cone-shaped mountain. The diagram
below shows the case of sufficiently steep mountain such that the image is
laid over in the radar image. The representation of the image is rather
crude but it shows generally the layover effect. The diagram also does not
show the radar shadow of the mountain.

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