Publisher Summary This chapter discusses the effects of atmospheric turbulence in optical astronomy, summarizes the present state of the theory, reviews the experimental checks that have been made, and discusses the implications in the domain of astronomical observations. Diffraction limited resolution has been obtained with large telescopes up to magnitude 13 by means of speckle interferometry. A Michelson interferometer is already working in the visible on a 20 m baseline up to magnitude 4, and many projects are nearing completion. However, such technological progress can be useful only if accurate quantitative measurements prove to be feasible through atmospheric turbulence. In addition, much work remains to be done before achieving a full understanding of atmospheric effects. The relationship between isoplanicity or speckle boiling and the structure of the atmosphere is still not clear.

V The Effects of Atmospheric Turbulence in Optical Astronomy

Vertical profiles of refractivity turbulence structure constant C2n (which is proportional to the radar volume reflectivity) from about 5 to 15 km are measured by the Sunset Radar every 50 seconds. The method of determining such profiles from the radar Doppler spectra is described. The C2n profiles for about an hour are averaged to form (C2n(radar)). The profiles of (C2n(radar)) are quite variable: on the average they decrease by about two orders of magnitude from about 5 to 15 km, and they often change by one order of magnitude from day to day at a given height. A theoretical model is developed that enables the calculation of C2n from routine rawinsonde profiles of wind, temperature, and humidity. This model is based on the assumption that the fluctuations of refractivity that scatter the radio waves are in equilibrium with homogeneous, isotropic, steady-state turbulence in the inertial subrange. An essential and new feature of this model is an estimate of the mean fraction of the radar-observed volume that is turbulent. The resulting profiles of (C2n(model)) agree well with the measured profiles of (C2n(radar)) in general shape, in changes from day to day, and in many details from kilometer to kilometer. This agreement implies that: (1) The vertical profile of C2n can be measured by Doppler radar. (2) The vertical profile of C2n can also be estimated by calculation from routine rawinsonde profiles, using our theoretical model.

Vertical profiles of refractivity turbulence structure constant: Comparison of observations by the Sunset Radar with a new theoretical model

The outer scale of turbulence L0 has been calculated from values of the refractive-index structure coefficient CN2 obtained from spatio-angular correlation measurements of stellar scintillation. It is found that L0 ≤ 5 m for a large range of observations in France, U.S.A., and Chile and that its dependence on altitude Z follows the same general form at all these sites. The prediction of CN2(Z) profiles is shown to be feasible utilizing standard meteorological radiosonde data and this L0(Z) curve. A simple model based on dimensional analysis and a more complicated stochastic model are compared, but the latter appears to have no advantage.

Outer scale of turbulence appropriate to modeling refractive-index structure profiles.

An expression is given for the life-time of stellar speckle as a function of the distribution of wind and turbulence in the Earth's atmosphere. Estimates of this parameter are in agreement with previously published observations and with the results of a laboratory simulation.

https://iopscience.iop.org/article/10.1088/0150-536X/13/5/002/pdf

On the origin of speckle boiling and its effects in stellar speckle interferometry.

Doppler radars measure the refractivity turbulence structure constant Cn2 in a straightforward manner. In this paper we explore the relationship between Cn2 and the intensity of atmospheric turbulence as parameterized by the eddy dissipation rate e. We develop some tentative relations between mean Cn2 and mean e within the framework of inertial range turbulence theory, taking into account the intermittent nature of atmospheric turbulence. These relations permit the estimation of mean e from radar observations alone. The analysis is applied to the determination from Sunset radar data of vertical profiles and time-height contours of mean e.

Use of Doppler radar for the measurement of atmospheric turbulence parameters from the intensity of clear‐air echoes

Astronomical site testing with balloon borne radiosonde: Results about atmospheric turbulence, solar seeing and stellar scintillation.

While site testing for the establishment of a new solar observatory, measurements of the microthermal turbulence as a function of the height were performed over the island of Tenerife (Canary Islands). These measurements were carried out with balloon-borne radiosondes to obtain the vertical profile of the parameters CT2 and Cn2 in order to compute, by means of theory of atmospheric optics, the optical quality of the air mass over the site.

R. Barletti

Papers

Astronomical site testing with balloon borne radiosonde: Results about atmospheric turbulence, solar seeing and stellar scintillation.

A vertical profile of turbulence in the Atlantic air mass measured by balloon‐borne radiosondes