SLODAR

SLODAR, or Slope Detection And Ranging, is a technique used in astronomical adaptive optics to determine the vertical distribution of atmospheric turbulence. It uses a Shack-Hartmann wavefront sensor to measure the slopes of incoming wavefronts from two stars that are close on the sky. By computing the cross-covariance of the measured slopes for pairs of subapertures across the pupil, and exploiting the geometric parallax between the lines of sight, the method resolves turbulence strength as a function of altitude, Cn^2(h), in discrete layers.

The basic idea is that turbulence at a given altitude h introduces correlated tilt patterns in the wavefronts of the two stars that are spatially offset by h times the angular separation between the stars. The observed slope cross-covariances form a set of equations relating the unknown Cn^2(h) at a set of altitudes to measured covariances; solving this inverse problem yields the vertical turbulence profile. The technique often assumes the frozen-flow hypothesis and a Kolmogorov spectrum.

SLODAR is used to characterize atmospheric conditions for adaptive optics, particularly for tomographic and multi-conjugate AO systems, and to monitor seeing at observatories. Typical implementations use natural double stars; variants employ laser guide stars to extend altitude reach, though LGS introduce complications such as cone effect and focus anisoplanatism.

Limitations include dependence on suitable star separations and brightness, finite altitude range and resolution set by telescope aperture and WFS sampling, and sensitivity to noise and calibration errors.