Astronomy Principles and Practice Fourth Edition.pdf

318 Astronomical optical measurements
Intensity
Diffraction
pattern
I A
Seeing
disk
I S
Distance through image
Figure 19.8. The seeing disc of a star is superposed in the theoretical diffraction pattern in the image plane. The
ratio of the peak intensities, I S /I A is referred to as the Strehl index.
Airy disc, I A . The ratio, S = I S /I A ,isreferredtoastheStrehl index and it is not uncommon for it to
be no greater than a few per cent.
For the small telescope, the entering wavefronts are essentially plain but arriving at the aperture
with a range of tilts relative to the optic axis. Each plain section provides an image—the diffraction
image produced by the telescope—which is sharp. Its position in the focal plane, however, depends on
the tilt angle. As the orientation of the deformations in the successive wavefronts change, so does the
position of the sharp image. This is illustrated in figure 19.7(b).
When a larger telescope is used, an image is formed which is the resultant of many simultaneous
corrugations in the accepted wavefront. Each deformation produces a displacement of the sharp image
with the result that their combination is a blurred-out patch. It should be obvious that if a photograph
is taken of a star using a small telescope, the dancing of the sharp image during the exposure will result
in a blurred image, the effect being the equivalent of a visual inspection of the star image provided by
a larger telescope.
With the introduction of CCD detectors with quantum efficiencies ∼100 times higher than the
photographic plate, it is possible to record frames of bright objects with sufficiently short exposure
times such that the wavefront disturbances at the end of the exposure maintain correlation with
those at the beginning. The time scales for this condition are of the order of 5–50 ms. Under this
circumstance, each frame provides a record with distortions corresponding to particular patterns of
wavefront disturbances. The images are recorded with ‘frozen’ seeing with some pictures being
of better quality than others, the sharpest occurring when the whole wavefront over the aperture is
essentially plain.
Any imaging system relies on the principle of the application of phase delays of differing degree
across the surface of the accepted wavefronts (see section 16.4). Following manufacture, the curvatures
of the final optical surfaces should follow contours according to the design specification with local
departures which are no greater than about λ/8. This can be translated into phase departures by
remembering that λ ≡ 2π. Acceptable manufacturing phase errors over the surface may be of the
order of 2π/8 ≈ 0·75 rad.
Atmospheric turbulence is constantly introducing additional phase delays and advances over the
telescope aperture. If these are small, i.e. some fraction of a radian, little or no deterioration of the
image would be noticed. They are, however, usually larger than this with a very apparent blurring of
the image. As the phase structures are constantly changing, over short time intervals there may be
occasions when their effect is small and an ‘instantaneous’ sharp image is produced. According to the
theory of atmospheric turbulence, the probability of having phase variations less than 1 radian over the