Evaluation of r(o) for Propagation Down Through the Atmosphere

The concept of the quantity r(o) as a length that measures the effect of atmospheric turbulence on optical systems that are wavefront distortion sensitive is briefly reviewed. It is pointed out that no precise set of data on r(o) for propagation down through the atmosphere has been published. Using astronomical seeing data obtained by Hoag and by Meinel it is shown how statistics for r(o) can be derived, at least for observatory quality sites. We find that the two sets of data are in very good agreement and conclude that r(o) is variable from night to night and distributed according to a log-normal distribution. For 0.55-microm light and zenith propagation, the median value of r(o), is 0.114 m and changes by a factor of 1.36 for occurrences one standard deviation from the median.