Effects of Turbulence on a Wavefront - Introduction to Image Stabilization - page 17

Effects of Turbulence on a Wavefront 17

size of the turbulent atmospheric cells determine the effect the atmosphere has on
the phase and direction of individual beams. The points of common phase in the
beam denote a wavefront, and on passing through the atmosphere their phases shift.
The wavefront shows more structure and the overall shape is no longer planar. Thus
a wavefront whose outer extent is defined by the aperture of a telescope can have a
very different shape on one side of the aperture compared to the other because of
the changes induced by atmospheric turbulence. Conversely, if the telescope aper-
ture is smaller than the size of the turbulence cells, the effect of atmospheric turbu-
lence is considerably reduced over the aperture.
When analyzing turbulence, an important parameter is the effective size of the
turbulence cells, usually denoted as r 0 or the Fried parameter (Fried 1965), com-
pared to the aperture diameter denoted by D . Thus the ratio D / r 0 (Hardy 1998) is the
crucial relationship in determining whether significant improvements in image
quality will be achieved by compensating image motion. The effect will be signifi-
cant for 1 10. This effect is illustrated in Fig. 2.6.

When the turbulence cells are large compared to the aperture, the effect is to
change the angle of the wavefront to the optical axis of the telescope, and there is

≤ D / r 0 ≤

Figure 2.6 Resolution of an uncompensated telescope as a function of D/r 0 . The plots
are normalized λ /r 0 . Curve A is the diffraction limit; B is the effect of jitter; C and D are
the short- and long-exposure resolutions.