End-to-end model for the Polychromatic Laser Guide Star project (ELP-OA)

In order to optimize parameters for the ELP-OA project, we have developped an end-to-end model from the laser emission to the computation of the tip-tilt Strehl ratio. ELP-OA aims at measuring the wavefront tip-tilt from the laser guide star alone, without any natural source. It relies on 2-photon excitation of mesospheric sodium, achieved by two laser chains (at 569nm and 589nm) delivering 34W average power each. The modeled twin laser beam is launched with a three aperture interferometer that produces an interferometric pattern in the mesosphere after the passage through a Kolmogorov phase screen. The backscattered flux is computed with an optical Bloch equations code [1]. The result of this excitation is an emission at different wavelengths. The wavelengths retained are 330nm, 569nm and 589nm. An image of this polychromatic LGS (PLGS) is computed, as it will be observed at the 1.52m telescope at the Observatoire de Haute-Provence (OHP), through a Kolmogorov phase screen again. Then we simulate the adaptive optics device (adapted from ONERA’s BOA AO) at the telescope except for tip-tilt. Air refraction index variations due to atmospheric turbulence create a dispersion between 330nm and 569nm, and the tip-tilt value is derived from this dispersion. This dispersion between 330nm and 569nm is measured using a correlation method and a sub-pixel interpolation. The calculation of the relative position between two simultaneous images at 330nm and 569nm gives a position error, from which the Strehl ratio for tip-tilt is deduced. At this time, we have got Strehl ratios up to approximatively 35% at 550nm, for tilt corrected r0 = 10cm and a projector baseline of 70cm