Turbulence characterization with a Shack-Hartmann wavefront sensor

Abstract

In the field of optical atmospheric propagation, knowledge of optical-turbulence strength and other key statistical parameters is crucial for performance prediction and system design. Hartmann-sensor data can be used to reliably estimate the essential parameters characterizing optical turbulence, including the Fried coherence length (r0), the Greenwood frequency (fG, a measure of the temporal turbulence bandwidth due to wind or beam slewing), and the inner scale of turbulence (`0). The earliest approaches for estimating r0 were based on modulationtransfer-function (MTF) measurements.1 This requires accurate calibration and stability of the system MTF, which is often problematic. Astronomers have used differential motion (DIMM: differential image-motion monitor) and scintillation to measure ‘seeing’ conditions.2 (In astronomy, seeing refers to the blurring of images caused by moving air cells in the Earth’s atmosphere.) Others have used the slope-structure function estimated from a Hartmann wavefront sensor, principally for r0 estimation.3 It is well known that r 5=3 0 is proportional to the variances of quantities related to the optical phase. For example, one could estimate r0 from the variance of the focus mode in aberration, the tilt, or the total phase. In general, a quite general form for an r0 estimator is