Image Processing Reference
Figure 1.4 Cross section and a 3D plot (inset) of a normalized Airy function.
disc. In the case of large telescopes, it can be difficult to prevent the Airy disc from
moving several microns or more because of mechanical vibrations or wind buffet-
ing the optical system. The motion of the Airy disc in the image plane results in a
blurry image. This undesired motion or vibration is often referred to as jitter and
contributes to the blurring of the image.
Blur resulting from image motion can be easily seen using a camera that takes
long as well as short exposures. In a short exposure, an imaging array located at the
focal plane shows a spot that has the characteristics identified in Eq. 1.1; however,
it is displaced in its position on the array. A long-exposure image records the mo-
tion of the spot that occurs during the exposure time as if there is a much larger illu-
minated region, showing a disc that is broadened significantly. This long-exposure
shape is no longer recognizable as an Airy function and has a shape that is often
approximated by a Gaussian function.
Image dancing or jitter can be minimized by measuring the motion and adjust-
ing the optical path so that the image remains fixed in the focal plane—that is, the
image is stabilized. Image stabilization is also important when the image is not dif-
fraction limited. A plane wave passing through a turbulent medium does not remain
a plane wave, but becomes distorted shaped somewhat like a potato chip. When im-