Atmospheric characterization in the presence of strong additive measurement noise

Abstract

The phase structure function and the phase-slope structure function have been used to characterize atmospheric-turbulence parameters—parameters that are important in the performance evaluation and ultimately in the design of adaptive optics systems for astronomical imaging applications and for laser beam propagations. We have extended the method to account for the effects of strong beam-path-induced aberrations and additive measurement noise. A stable noise-suppressant algorithm is devised in which the estimation is done sequentially: first the atmospheric-turbulence parameters are estimated independently, and then the noise-variance parameter is estimated. The developed theory is applied to the Shack–Hartmann wave-front-sensor data collected in the recently completed Airborne Laser Extended Atmospheric Characterization Experiment for very-long-horizontal-path (between 60 and 100 km) laser beam propagations. The estimated r0 values are in general agreement with the values obtained from the high-bandwidth scintillometer analysis on data taken in the same experiment. In addition, if the atmospheric turbulence spectrum can be described by a simple power law, then the data reduction with use of the developed estimation equations, which allow arbitrary atmospheric-turbulence power-law values, indicates that deviation from Kolmogorov turbulence is negligible.