Characterization of atmospheric turbulence using wavefront slope measurements

Abstract

Turbulence has long been recognized as one of the most significant factors limiting the performance of optical systems operating in the presence of atmosphere. Atmospheric turbulence over vertical paths has been well characterized, both theoretically and experimentally. Much less is known about turbulence over long, horizontal paths. Perturbations of the wavefront phase can be measured using a Hartmann wavefront sensor (H-WFS). These measurements can be used to characterize atmospheric turbulence directly. Theoretical expressions for the slope structure function of the H-WFS measurements are derived and evaluated using numerical quadrature. By concentrating on the slope structure function, we avoid the phase reconstruction step and use the slope measurements in a more direct fashion. The theoretical slope structure function is compared to estimated slope structure functions computed from H-WFS measurements collected in a series of experiments conducted by researchers at the U.S. Air Force's Phillips Laboratory. These experiments involved H-WFS measurements over high altitude (airborne) horizontal paths 20 - 200 km in length.