The extension of high quality astronomical observations towards larger apertures, adaptive optics, and infrared wavelengths leads to extrapolation of present knowledge of astronomical "seeing" by means of theoretical models, such as Kolmogorov turbulence conbined with Taylor's "frozen atmosphere" swept past the observer by winds. Observations of path length fluctuations from a star to a two-telescope spatial interferometer at 11-mu-m wavelength, and also measurements of path length fluctuations 3 m above the ground by laser distance interferometers, show substantial deviations from such a model. Intermittent turbulence may be involved and relatively short outer scales are frequently indicated. Path lengths 3 m above the ground show for short times (0.1 s less-than-or-equal-to t less-than-or-equal-to 1 s) that under good seeing conditions fluctuations are approximated by a random walk, with a structure function of time proportional to t rather than t5/3 as expected from the asymptotic approximation of a Kolmogorov-Taylor model for short times. The latter model is somewhat better approximated under poor seeing conditions or for very short times (0.005 s less-than-or-equal-to t less-than-or-equal-to 0.1 s). For longer times (t > 10 s), the structure function is quite variable but generally intermediate between expections for the two models. For excellent seeing, an outer scale of turbulence in the range 5-20 m is often indicated from the measurements made near the ground. Fluctuations in the higher atmosphere, deduced from stellar interferometry, are closer to predictions of a Kolmogorov-Taylor model than are those near the ground. Under excellent seeing conditions, however, fluctuations in the path lengths of stellar radiation frequently increase more slowly than expected for long times (or hence presumably large distances), and sometimes also lead to relatively short outer scales of turbulence (5-20 m) on the basis of a Kolmogorov-Taylor model. These short outer scales are best illustrated by Allan variances, which for the longer times show large variations from the asymptotic approximation to a Kolmogorov-Taylor model which is usually assumed. In general the results indicate that large-aperture telescopes or long baseline interferometry, particularly for IR wavelengths, will often provide better imaging than is expected on the basis of the common assumption that relative fluctuations in path lengths through the atmosphere increase with the 5/3 power of their separation. The results are also favorable for adaptive optics. However, further accumulation of information on fluctuations is needed under a variety of atmospheric conditions typical of astronomical observing in order to more fully characterize performance to be expected of such systems.
