Image Processing Reference
In-Depth Information
Effects of Turbulence on a Wavefront
15
Figure 2.4
Formation of a plane wave from a distant source. A plane wave shows no
structure and so the source is unresolved when imaged. (Earth image courtesy of
NASA, Astronomy Picture of the Day.)
The physical interpretation of the terms in the exponent are that the until of
time refers to the frequency effects,
x
term to the distance, and the
refers to the
phase of the light. In the case of two rays that emerge from a single source, such as a
laser, the phase and frequency terms are the same, but the rays can traverse different
paths. Because of this path difference, the two rays, though of the same frequency
and initial phase, are delayed and the wavefront distorted. This delay and corre-
sponding shift in the wavefront is the important component of wavefront propaga-
tion.
Returning to the discussion from Chapter 1, light emitted from a distant star can
be considered as coming from a perfectly spherical source. At a given instant near
the star, the light emitted at the same moment travels the same distance and so is in
phase. These spheres of constant phase are referred to as a wavefront. This is shown
pictorially in Fig. 2.4.
As the waves move out from the star, the curvatures lessen until on the scale of
a telescope they are essentially flat. If this flat wavefront intersects something that
has a varying index of refraction, then various points in the wavefront experience
different optical paths and become out of phase with other wavefront elements. The
result is the final wavefront, deviating in shape from the original flat wavefront.
Also, this final wavefront shows that an overall tilt has appeared in the wavefront.
There is no reason to believe that the optical disturbances passing through the
atmosphere would be static. The wavefront and its angle to the direction of propa-
gation vary with time.
ϕ
