Image Processing Reference
The performance of an image-stabilization system is commonly evaluated by mea-
suring the difference or residual error between the corrected and the true wavefront.
The residual error is a combination of the errors introduced by the individual com-
ponents that make up the complete system. In evaluating the performance of an im-
age-stabilization system, it is convenient to assume that each of the individual com-
ponent errors is random and uncorrelated, so that they can be combined as a simple
summation. This is not precisely correct; however, it is common to treat them this
way to avoid the additional complications from correlation.
The tool most commonly used to evaluate the system performance is the Strehl
ratio, first used by K. Strehl in 1895. The Strehl ratio measures the height of the
Airy function compared to its ideal height. This is a very sensitive measure of the
performance of the optical system, because even small changes cause a degradation
of the Strehl ratio. For comparison, an optical system operating at the Rayleigh
limit will have a Strehl ratio of 0.8 (Smith 2000).
This chapter provides an introduction to image structure, the Strehl ratio, and
how it applies to image stabilization and comparison of system performance.
6.2 Image Structure
An image of a star in the focal plane of a large telescope is blurred from its ideal dif-
fraction-limited form because of the refractive variations of the atmosphere. How-
ever, if a longer wavelength is used, the aperture diameter is reduced (stopped
down), or the exposure time reduced, wavefront smoothes out, and the spot size in
the focal plane is reduced. When very short exposures are used, the diffraction-lim-
ited spot can often be seen. If several short-exposure images are recorded in se-
quence, the diffraction-limited spot can be seen moving within the extent of a
long-exposure image. This is illustrated in Fig. 6.1.
The scale of the turbulence, Fried's parameter ( r 0 ), must be on the same order in
size as the telescope aperture ( D ) for the shape of the spot to be near diffraction lim-
ited. If the ratio D/r 0 is near 1, then the image blurring is dominated by image motion;
but as this ratio increases, the blurring is due to higher-order terms. This effect is il-
lustrated in Fig. 6.2, which shows the various components of image motion.