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Analysis of aiming performance limitation for an optical system in atmospheric turbulence

In an optical system that is transmitting a laser beam through the atmosphere by phase compensation with adaptive optics, the aiming performance depends on the method of wavefront tilt detection, which can be divided into Zernike tilt detection and gradient tilt detection. A unified formulation for both methods is obtained to calculate the residual tilt angle jitter and tilt correction factor, which are defined as the evaluation indexes of the aiming performance. A parameter L0 called the equivalent atmospheric coherence length is expressed as an integral over the structure constant profile of the refraction index and is modulated by a modulation function that is determined by the ratio of the offset distance to the aperture. As a result, the tilt correction factor can be represented as (r0/L0)5/6, where r0 is the atmospheric coherence length. Simulations illustrate that the aiming performance of an optical system based on gradient tilt detection is better than that of Zernike tilt detection under identical conditions. For the two types of system, the aiming performance will be decreased as the ratio of the offset distance to the aperture increases and the atmospheric conditions worsen.