Finite outer scale considerations for beam-steering optimization

Finite turbulence outer scale attenuates turbulence power at low spatial frequencies, providing a finite variance for turbulence-induced phase. The temporal properties of low spatial-frequency aberrations such as tilt are affected directly by finite outer scale turbulence models. When optimal estimation techniques are used in beam-steering applications, the estimator form and its performance are related directly to the correlative properties of tilt and higher-order modes as determined by the value of Lo/D. In this work, we consider the effect of finite turbulence outer scale on the performance of optimal tilt compensation incorporating time-delayed tilt plus higher-order modes. The results indicate that while smaller values of Lo/D provide for higher Strehl ratios after tilt compensation, the Strehl ratio gain obtained through optimal compensation is reduced with decreasing values of Lo/D. For the relative aperture diameter D/r(0) = 5 and using time-delayed tilt plus higher-order modes through Zernike 15, the Strehl ratio gain with time delay upsilon tau/D = 0.5 is approximately 15 for L-0/D = 100. Under the same conditions, the Strehl ratio gain for L-0/D = 2 is approximately 3.