Image Processing Reference

In-Depth Information

Image Stabilization

5

Figure 1.3
Comparison of long- and short-exposure images illustrating the effect of

beam wander.

motion can be complicated. However, a strong correlation often exists with the

wind direction at a particularly dominant layer of the atmosphere located at a spe-

cific height above the earth's surface.

1.5 Image Jitter

A plane wave entering a telescope or lens system is focused to a point of light at the

focal plane. When the beam is larger than the entrance aperture of the optical sys-

tem, the image at the focal plane is defined by the shape of the aperture and is the

Fourier transform of the aperture (Hecht 2002). In many optical systems, the aper-

ture is circular and the plane wave image is thus transformed into an Airy function

whose central disc is proportional to the ratio of the wavelength to the diameter of

the aperture:

λ

θ

=

244

.

(radians)

(1.1)

D

SF

==

θ

244

.

λ

f

(meters),

#

is the wavelength,
D
is the aperture diameter,
F

is the focal length,
f
#
is the focal ratio and
S
is the diameter of the central disc. Fig-

ure 1.4 shows the form of the Airy function.

Compared to the size of a telescope aperture, the wavelength of visible light is

very small, between 0.4 and 0.75

where

θ

is the angular resolution,

λ

m. Equation 1.1 shows that the size of the Airy

disc is proportional to the wavelength of light used and scaled by 2.44 times the

f
-ratio. For optical telescopes, the
f
-ratio is typically between
f
/2 and
f
/40, resulting

in a physical diameter between approximately 5 and 100 wavelengths for the Airy

µ