Figure 1: Schematic illustration of the use of mesospheric sodium as a beacon for adaptive optics.
Adaptive optics employing the sodium guide star puts puts special power and spectral requirements on the drive laser used to excite the sodium atoms: the power must be sufficiently great that a substantial number of sodium atoms in the mesosphere, of which there are typically only a few thousand per cm3, are excited, and to accomplish this efficiently the spectrum of the laser radiation should cover a substantial portion of the effective Doppler width (about 3 GHz). In order to realize a guide star approximating a point source, moreover, the laser must have good beam quality as characterized, for instance, by a Strehl ratio.
Several groups are actively pursuing the goal of closed-loop atmospheric compensation with the sodium guide star. During the past year we have collaborated with researchers at the Air Force Starfire Optical Range, with the purpose of evaluating various possible laser systems to be mounted on their 3 1/2-m telescope under construction. Together with a wavefront sensor and an electronically controlled deformable mirror, this system is expected to provide high- quality ground-based imaging. Our work involves a full density-matrix treatment of the 24 states of the sodium D2 line, including Doppler broadening and polarization, temporal, spectral, and spatial characteristics of the laser. Propagation through the turbulent atmosphere is treated statistically under the assumption that the turbulence is well described by the Kolmogorov theory; the latter provides us with an analytical expression for refractive-index correlations in a way well known in the theory of propagation in turbulent media.
Of particular interest to the Starfire group has been the variation of photon return signals with
the peak intensity and spectrum of the laser pulse train. (In the scheme under consideration
the field from the laser is phase-modulated in order to produce a frequency spectrum
covering a large portion of the sodium absorption profile.) Figure 2 shows a comparison
between our simulations and the one set of experimental data points available to us at the
present time. The simulations involve an adjustable parameter, namely the column density of
mesospheric sodium, and in Figure 2 we assume the value 5 x 109 cm-2, which is believed, on
the basis of other studies, to be typical for the site and time at which the data were taken. We
are presently extending these simulations in order to suggest an optimal laser pulse format for
the Starfire system.
Figure 2: Predicted (circles) photon returns (number per cm2 per ms) compared to curve fit through measured data points (solid curve).