Image Stabilization - Introduction to Image Stabilization - page 5

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