It can be seen by inspection, that the field at the plane, z units away from the plane, consists of the unperturbed field distribution reduced in amplitude by plus an infinite sum of "paired echos” or replicas of the unperturbed field distribution laterally displaced by . For a typical set of parameters, radians, and z = 200 km, the lowest order echo is displaced by: respectively. Thus to lowest order in cp, the intensity distribution is: with where is the unperturbed field distribution on the plane. If the , which is the radiation field of an untruncated Gaussian aperture distribution, then the intensity distribution:
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