Image Processing Reference
the atmosphere before it is imaged. Earth's atmosphere is optically active; that is,
the atmosphere interacts with the wavefront, most often to the detriment of the
It is somewhat ironic that, having traveled many millions of miles through
space, the wavefront shape becomes distorted in the last few hundred kilometers
before the light arrives on the surface of the earth. The result for a telescope is poor
image quality because the wavefront shape changes as it travels from the top of the
atmosphere to earth's surface. For astronomical imaging, the atmosphere acts as an
aberrator, degrading the image quality. However, it is not yet clear why the reverse—
that is, looking down on the planet—does not have the same problem.
The density, temperature, and pressure of the atmosphere vary with the height
above the earth, resulting in a changing index of refraction with height. As such,
light passing through the atmosphere is affected differently at different heights be-
cause of these changes in the atmospheric index of refraction. The thicker atmo-
sphere near the earth's surface causes a greater effect on the light passing through it
than does the atmosphere higher up.
Satellites typically orbit well outside the atmosphere to avoid atmospheric drag.
For comparison, the International Space Station orbit is between 340 and 360 km,
with the main portion of the atmosphere being below 100 km.When looking down
through the atmosphere from the space station, the aberrating effect of the atmo-
sphere is significantly closer to the earth's surface than to the observer. Ground-
based astronomical telescopes, having the aberrating effect of the atmosphere lo-
cated closer to them than to the object being observed, are in an opposite situation.
Understanding the effect of the position of the aberrator, or the agent that in-
duces distortions in the beam of light, relative to the optical receiver is the key to
understanding the physical properties of the distortion.
A simple example will help to explain the concept. If one places a piece of clear
plastic tape on top of an image, the effect of the tape is negligible and the underlying
image is clearly visible. However, positioning the tape above the image, closer to the
eye, causes the same image to be distorted almost to the point of unrecognizability.
Plastic tape is a large aberrator compared to the atmosphere, but it illustrates the effect
of the aberrator position. The example also illustrates why the effects of the atmosphere
are so deleterious when one looks up from the ground through it, but are negligible
from a satellite looking down to the ground (the “tape,” in this case, being on the im-
age). The next chapter explores the structure of the atmosphere in more detail.
1.3 Wavefronts and Optical Systems
A plane wave entering a telescope or a lens is transformed into a spot of light on the
image side. A plane wavefront is characteristic of an unresolved image, so contains
no information about the source. Thus, in the focal plane of the optic, the shape of
the image is the Fourier transform of the aperture shape (Goodman 1968).
A wavefront passing through the atmosphere is changed by local variations in
the index of refraction. As a result, when an aberrated wavefront enters the aperture