Methods for correcting tilt anisoplanatism in laser-guide-star-based multiconjugate adaptive optics

Abstract

Multiconjugate adaptive optics (MCAO) is a technique for correcting turbulence-induced phase distortions in three dimensions instead of two, thereby greatly expanding the corrected field of view of an adaptive optics system. This is accomplished with use of multiple deformable mirrors conjugate to distinct ranges in the atmosphere, with actuator commands computed from wave-front sensor (WFS) measurements from multiple guide stars. Laser guide stars (LGSs) must be used (at least for the forseeable future) to achieve a useful degree of sky coverage in an astronomical MCAO system. Much as a single LGS cannot be used to measure overall wave-front tilt, a constellation of multiple LGSs at a common range cannot detect tilt anisoplanatism. This error alone will significantly degrade the performance of a MCAO system based on a single tilt-only natural guide star (NGS) and multiple tilt-removed LGSs at a common altitude. We present a heuristic, low-order model for the principal source of tilt anisoplanatism that suggests four possible approaches to eliminating this defect in LGS MCAO: (i) tip/tilt measurements from multiple NGS, (ii) a solution to the LGS tilt uncertainty problem, (iii) additional higher-order WFS measurements from a single NGS, or (iv) higher-order WFS measurements from both sodium and Rayleigh LGSs at different ranges. Sample numerical results for one particular MCAO system configuration indicate that approach (ii), if feasible, would provide the highest degree of tilt anisoplanatism compensation. Approaches (i) and (iv) also provide very useful levels of performance and do not require unrealistically low levels of WFS measurement noise. For a representative set of parameters for an 8-m telescope, the additional laser power required for approach (iv) is on the order of 2 W per Rayleigh LGS.

MCAO for the E-ELT: preliminary design overview of the MAORY module

“…The NGs are needed to recover the low order modes tomography which is affected by the Tip-Tilt indetermination of the laser beacons [6]. A dichroic beam splitter reflects the light of wavelengths longer than 600nm, which is used by scientific instruments, while it transmits shorter wavelengths light which is used by the LGS Wavefront Sensor (WS).…”

Simulation model based approach for long exposure atmospheric point spread function reconstruction for laser guide star multiconjugate adaptive optics

“…The LGS loop runs a tomographic minimum variance wavefront reconstruction algorithm at 800 Hz from measurements from six high-order LGS Shack-Hartmann WFSs (each of order 60 × 60). The NGS loop runs a classical least-squares reconstruction matrix, R NGS , at low frame rate (generally around 90 Hz), controlling five modes, defined as global TT and three TTA modes distributed on the system's two DMs, from the combined measurements from a tip/tilt/focus/ astigmatism (TTFA) NGS WFS (i.e., an order 2 × 2 Shack-Hartmann WFS) and two additional fullaperture TT NGS Shack-Hartmann WFSs [15]. The TTFA NGS WFS is required in order to disentangle the atmospheric and mesospheric sodium layer focus errors.…”

“…For LGS MCAO, multiple low-order NGS WFSs are required to correct low-order tomographic nullmodes invisible to the high-order LGS WFSs but producing absolute and differential magnification on the science focal plane [15], commonly referred to as tip/ tilt anisoplanatism (TTA). More importantly, the effects of angular and focal anisoplanatism are very different from what they are for LGS GLAO and SCAO: the PSF is much more uniform across an extended FoV (characterized by the generalized isoplanatic angle [16]) and the TTR SR of a point source at infinity (science target) is actually larger than that of a point source in the same direction but at finiterange (the LGS of the multi-LGS constellation pointing to the science target), since the deformable mirror (DM) fitting step is optimized for the science target at infinity, not for the finite range LGSs.…”

“…Important features to note are that the science TTR to LGS SF ratio [i.e., the extrapolation filter described in Eq. (15)] is smaller than unity (i.e., the LGS SR is smaller than the science TTR SR), insensitive the seeing variations (i.e., the filter is robust against seeing modeling errors), but sensitive to LGS WFS signal level (opposite behaviors of the science TTR and LGS SF make the filter sensitive to this type of modeling error). In contrast to SF ratios, OTF ratios are sensitive to seeing variations.…”

Towards the phase A review of MAORY, the multi-conjugate adaptive optics module for the E-ELT

“…To solve the LGS tip-tilt indetermination problem, also 3 Natural Guide Stars (NGS) are used (Ellerbroek & Rigaut [9]): as a baseline two of them are used to measure tip-tilt only, while the third, positioned on the brightest star found on the search FoV, is used to measure tip-tilt and focus, in order to provide a reference for the rapidly variable focus term in the LGS signals, due to the Sodium layer instability. The 3 NGS are searched on a wide FoV ∼ 2.6 arcmin and are observed in the near IR (H band), in order to take advantage of the spot shrinking ensured by the high-order correction driven by the LGS WFS, allowing the use of faint NGS that translate into a high sky coverage.…”