A simulation study is presented that evaluates the performance of Hartmann wave-front sensors with measurements obtained with the Fried geometry and the Hutchin geometry. Performance is defined in terms of the Strehl ratio achieved when the estimate of the complex field obtained from reconstruction is used to correct the distorted wave front presented to the wave-front sensor. A series of evaluations is performed to identify the strengths and the weaknesses of Hartmann sensors used in each of the two geometries in the two-dimensional space of the Fried parameter r0 and the Rytov parameter. We found that the performance of Hartmann sensors degrades severely when the Rytov number exceeds 0.2 and the ratio l/r0 exceeds 1/4 (where l is the subaperture side length) because of the presence of branch points in the phase function and the effect of amplitude scintillation on the measurement values produced by the Hartmann sensor.
Concerning the problem of transmitting a laser beam from one telescope to another telescope through a turbulent medium, it is established that using an adaptive optical system on both telescopes to precompensate an outgoing laser beam based on the aberrations measured on the received laser beam leads to an iteration that maximizes the transmission (neglecting attenuation losses) of laser power between the telescopes. Simulation results are presented demonstrating the effectiveness of this technique when the telescopes are equipped with either phase-only or full-wave compensation systems. Simulation results are shown that indicate that for a uniform distribution of the strength of turbulence, 95% transmission of laser power is attained when both telescopes can achieve full-wave compensation provided that the aperture diameter D of the two telescopes is greater than twice the Fresnel length square root of lambdaL, where A is the wavelength of propagation and L is the distance between the two telescopes.
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