## Turbulence

The underlying cause of the speckles seen in high magnification, short exposure images is atmospheric turbulence. Coulman4 wrote an excellent distillation of atmospheric turbulence and how it applies to astronomy. To simplify for the binary star astronomer, atmospheric turbulence can be thought of as many pockets of air of subtly different temperature moving across the column of air defined by the telescope aperture, and in the direction of the object. In a time averaged sense, most seeing conditions (an observer's working measurement of turbulence) can be described by two numbers: r0, a measurement of the diameter of the typical pocket of air passing in front of the telescope aperture; and t0, a measurement of how long a typical pocket of air "influences" the wavefront getting into the telescope. The value of r0 has a wavelength dependence:

Typical values of r0 (at 550 nm) and t0 are 10 cm and 15 milliseconds, respectively.

In practical terms, one might hear of the seeing being "1.6 arcseconds". This is actually a measurement of the "seeing disk", the diameter at the full-width half maximum (FWHM) of a Gaussian (equations of the form exp(-x2) representation of the stellar intensity. To translate this into a value of r0, ten Brummelaar5 calculates:

seeing y

where X is the wavelength, D the objective diameter of the optical system, and 0seeing the FWHM diameter (in radians) of the seeing disk. So, 1.6'' seeing, as viewed at 550 nm through a 50 cm telescope, translates to r0 of about 5 cm.

Measuring r0 requires determinations of inter-ferometric visibilities at different exposure times and extrapolating back to the exposure time of 0. Determining object visibilities is a bit beyond the scope of this chapter, so suffice it to say that for the speckle astronomer, r0 determination is a more qualitative exercise. When the highly magnified image of the object meanders "slowly" along its random path, the conditions are said to be those of "slow seeing". If the object appears more animated in its travels, conditions are described as "fast seeing". How r0 affects the design and operation of an astrometric speckle system is described by Mason.6 