Tilt angular anisoplanatism and a full-aperture tilt-measurement technique with a laser guide star

A method is presented for sensing atmospheric wave-front tilt from a laser guide star (LGS) by observing a laser beacon with auxiliary telescopes. The analysis is performed with a LGS scatter model and Zernike polynomial expansion of wave-front distortions. It is shown that integration of the LGS image over its angular extent and the position of the auxiliary telescope in an array reduce the tilt sensing error associated with the contribution from the downward path. This allows us to single out only the wave-front tilt of the transmitted beam on the uplink path that corresponds to the tilt for the scientific object. The tilt angular correlation is analyzed in the atmosphere with a finite turbulence outer scale. The tilt correlation angle depends on the angular size of the telescope and the outer scale of turbulence. The tilt sensing error increases with the auxiliary telescope diameter, suggesting that an auxiliary telescope must be small. The Strehl ratio associated with the contribution from the downward path is in the range from 0.1 to 0.9 when the relative telescope diameter D/r(0) varies from 4 to 93 and the turbulence outer scale is in the 10-150-m range. Tilt correction increases the Strehl ratio compared with the uncorrected image for all the system parameters and seeing conditions considered. The method discussed gives a higher performance than the conventional technique, which uses an off-axis natural guide star. A scheme for measuring tilt with a beam projected from a small aperture is described. This scheme allows us to avoid phosphorescence of the main optical train for a sodium LGS.