Image Processing Reference
Effects of Turbulence on a Wavefront
Figure 2.12 The effect of image jitter on the intensity of the light at the receiver. The
curves from top to bottom are for σ p values of 0, 0.5 and 1 radian rms for D= 1m and λ
= 1 µm.
where I 0 , is the original intensity, T is the optical transmission,
p is the rms wave-
front error in radians,
σ α is the rms jitter in radians, D is the aperture diameter, and
is the wavelength.
Using Eq. 2.5, the intensity change caused by the effects of image jitter and
high-order aberrations is shown in Fig. 2.12.
The effects of beam wander and image jitter become significant when deter-
mining the sensitivity of detectors or the power needed to transmit information.
Aberrations in a wavefront have a direct effect on the quality of an image. In the
case of a flat wavefront focused onto a screen from a lens, an aberration-free wave-
front produces a high-quality Airy pattern. This pattern is characterized as shown in
The effect of small aberrations in the wavefront lowers the height of the central
peak of the Airy pattern. With large amounts of aberration in the system, the peak is
lost altogether and the light smears out completely. The ratio of the amount of light in
the peak to the maximum amount of light in the peak is referred to as the Strehl ratio.
The Strehl ratio is a fundamental metric for evaluating the amount of aberration
in the image plane. A Strehl ratio of 0.8 corresponds to a Rayleigh limit of 1, or a