Principle of equivalency of the phase difference and off-axis tilt sensing technique with a laser guide star

A full aperture tilt sensing technique which does not require transmitting laser irradiance through the main optical train is described. This technique is based on measurements of differential motion of the images of the two laser guide stars (LGSs) formed in the atmospheric sodium layer by the two parallel collimated laser beams separated at a distance equal to the telescope diameter. It is shown that a one-axis wavefront tilt component might be determined by measuring the LGS's differential motions simultaneously with the main telescope and with an auxiliary telescope. To sense two tilt components, four laser beam and two auxiliary telescopes are needed. A tilt angular anisoplanatism is studied, and parameter of the tilt measurement scheme are estimated.