Abstract

In this work the bandwidth requirements for compensation of the turbulence-induced tilt associated with a ground based telescope used for astronomical observation are studied in detail, Kilmogorov statistics and the Taylor hypothesis are used to develop expressions for the G-tilt and Z-tilt power spectra in the presence of wind. A closed loop servo with a transfer function of the form, H(f) = (1 + if/f_3dB)^-1 is applied to these disturbances and the one axis one sigma jitter σ_θ is computed. The analysis illustrates that σ_θ = (λ/D)(f_T/f_3dB), where λ is the wavelength, D is the telescope diameter, f_3dB is the servo bandwidth, and f_T is the fundamental tracking frequency for atmospheric turbulence-induced tilt compensation. As a consequence, a servo bandwidth equal to f_T results in a one-axis one-sigma jitter equal to the diffraction angle, λ/D. For G-tilt the fundamental tracking frequency is given by $f_{\text{T}}=0.331D^{-1/6}{\lambda }^{-1}{(\sec \psi )}^{1/2}{\left[{\displaystyle \int d}h{C}_n^2(h)V^2(h)\right]}^{1/2}$ where ψ is the zenith angle, $C_n^2(\cdot )$ is the refractive-index structure constant, and V(·) is the wind velocity profile.

© 1991 Optical Society of America