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.