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.

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A wave optics simulation has been used to compare the perfonnance of adaptive optics systems in the presence of near field and distributed turbulence. For a given total turbulence strength (integrated C2 or collimated r& the Greenwood frequency (due to a moving target) and the log-amplitude variance will be larger and the isoplanatic patch size will be smaller with distributed turbulence. The larger log-amplitude variance will degrade a phase-only adaptive optics system both because of the uncorrectable amplitude variations and because the scintillations will cause errors in the wavefront sensor and reconstructor. JilNTRODUOIONMost adaptive optics systems have been designed to correct atmospheric turbulence between the ground and space. For these systems the turbulence is concentrated near the adaptive optics system. For horizontal paths the turbulence is distributed along the path. This leads to significant differences in the performance of adaptive optics systems.Many of these differences can be quantified by the turbulence parameters such as the coherence length1 (r&, the isoplanatic patch size2 (O&, the log-amplitude variance3 (a2), the Greenwood frequency4(fg), and the tilt frequency5 (ft). r0 is the effective aperture size in the presence of turbulence. 0 ' the "maximum" angle allowed between the beacon and the aimpoint. fg is the required closed loop control bandwidth for a system with an infinite aperture. (The required bandwidth for a finite sized aperture is smaller.) f is the bandwidth required for control of the gradient tilt. The formulas for these parameters and the corresponding scaling laws for estimating adaptive optics system performance are: r0 = . 185 [Jz Cn2(z) (1-z/zt)513 dz I2]3'5 2 k(d/r&513 0 = .0581 [JAz Cn2(z) z513 dz I x2f3'5 a2 (9/9)5/3 a2 4.78 'Az C2(z) (z-z2/zt)516 dz I 7I6 fg = 2.31 [Jz v(z) C2(z) dz I 2]3"5 a2 (g3db)513 = .331 [JAz v2(z) Cn2(z) dz / 2]"2 m116where Cn2(z) is the turbulence strength, zt is the range to the target, k is the fitting factor (typically around .27), d is the actuator spacing, 3db is the closed loop control bandwidth, a2 is the residual phase variance in radians squared, v(z) is the transverse wind velocity, 9 is the angle between the beacon and target, D is the beam diameter, and a0 is the standard deviation of the gradient or G-tilt. The formulas 0-8194-1413-7/94/$600 SP!E Vol. 2120 Laser Beam Propagation and Control (1994)! 87 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/27/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx