Slope Detection and Ranging (SLODAR) is a technique for the measurement of the vertical profile of atmospheric optical turbulence strength. Its main applications are astronomical site characterization and real-time optimization of imaging with adaptive optical correction. The turbulence profile is recovered from the cross-covariance of the slope of the optical phase aberration for a double star source, measured at the telescope with a wavefront sensor (WFS). Here, we determine the theoretical response of a SLODAR system based on a Shack–Hartmann WFS to a thin turbulent layer at a given altitude, and also as a function of the spatial power spectral index of the optical phase aberrations. Recovery of the turbulence profile via fitting of these theoretical response functions is explored. The limiting resolution in altitude of the instrument and the statistical uncertainty of the measured profiles are discussed. We examine the measurement of the total integrated turbulence strength (the seeing) from the WFS data and, by subtraction, the fractional contribution from all turbulence above the maximum altitude for direct sensing of the instrument. We take into account the effects of noise in the measurement of wavefront slopes from centroids and the form of the spatial structure function of the atmospheric optical aberrations.

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Determination of the profile of atmospheric optical turbulence strength from SLODAR data

A pyramid wavefront sensor with no dynamic modulation

Using five independent analytic and Monte Carlo simulation codes, we have studied the performance of wide-field ground-layer adaptive optics (GLAO), which can use a single, relatively low order deformable mirror to correct the wave-front errors from the lowest altitude turbulence. GLAO concentrates more light from a point source in a smaller area on the science detector, but unlike with traditional adaptive optics, images do not become diffraction-limited. Rather, the GLAO point-spread function (PSF) has the same functional form as a seeing-limited PSF and can be characterized by familiar performance metrics such as full width at half-maximum (FWHM). The FWHM of a GLAO PSF is reduced by 01 or more for optical and near-infrared wavelengths over different atmospheric conditions. For the Cerro Pachon atmospheric model, this correction is even greater when the image quality is poorest, which effectively eliminates "bad seeing" nights; the best seeing-limited image quality, available only 20% of the time, can be achieved 60%–80% of the time with GLAO. This concentration of energy in the PSF will reduce required exposure times and improve the efficiency of an observatory up to 30%–40%. These performance gains are relatively insensitive to a number of trade-offs, including the exact field of view of a wide-field GLAO system, the conjugate altitude and actuator density of the deformable mirror, and the number and configuration of the guide stars.

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Performance Modeling of a Wide-Field Ground-Layer Adaptive Optics System

Several wide-field-of-view adaptive optics (WFAO) concepts such as multi-conjugate AO (MCAO), multi-object AO (MOAO), and ground-layer AO (GLAO) are currently being studied for the next generation of Extremely Large Telescopes (ELTs). All these concepts will use atmospheric tomography to reconstruct the turbulent-phase volume. In this paper, we explore different reconstruction algorithms and their fundamental limitations, conducting this analysis in the Fourier domain. This approach allows us to derive simple analytical formulations for the different configurations and brings a comprehensive view of WFAO limitations. We then investigate model and statistical errors and their effect on the phase reconstruction. Finally, we show some examples of different WFAO systems and their expected performance on a 42 m telescope case.

Tomographic reconstruction for wide-field adaptive optics systems: Fourier domain analysis and fundamental limitations

The performance of modal Multi-Conjugate Adaptive Optics systems correcting a nite number of Zernike modes is studied using a second-order statistical analysis. Both natural and laser guide stars (GS) are considered. An optimized command matrix is computed from the covariances of atmospheric signals and noise, to minimize the residual phase variance averaged over the eld of view. An ecient way to calculate atmospheric covariances of Zernike modes and their projections is found. The modal covariance code is shown to reproduce the known results on anisoplanatism and the cone eect with single GS. It is then used to study the error of wave-front estimation from several o-axis GSs (tomography). With increasing radius of the GS constellation , the tomographic error increases quadratically at small , then linearly at larger when incomplete overlap of GS beams in the upper atmospheric layers provides the major contribution to this error, especially on low-order modes. It is demonstrated that the quality of turbulence correction with two deformable mirrors is practically independent of the conjugation altitude of the second mirror, as long as the command matrix is optimized for each conguration.

/pdf/optimized-modal-tomography-in-adaptive-optics-3gidktvwo1.pdf

Optimized modal tomography in adaptive optics

In the context of multiconjugate adaptive optics, the optimum linear estimation of a wave-front phase for a target object using the phases of several surrounding natural guide stars (NGS’s) is studied. A Wiener-filter-type estimator is constructed. The minimum residual wave-front-phase (tomographic) error depends on the turbulence vertical profile, and for typical profiles it is almost insensitive to the presence of strong layers, contrary to current belief. Tomographic error is characterized by a new parameter δK, equivalent profile thickness, which depends on the NGS number K (typically δ5=0.5 km). The angular radius of the NGS configuration must not exceed r0/δK. Exact profile knowledge is not required. When the optimized filters are constructed from some model profile, the loss of the field size is within 10% with respect to exact profile knowledge. Moreover, a method to measure turbulence profile using wave-front-sensor data is outlined. Noise propagation in the restoration algorithm is significant, but not dramatic. Noise increases with increasing size of NGS constellation. Practically, guide stars for tomography should be at least as bright as those for classical adaptive optics.

http://www.ctio.noao.edu/~atokovin/papers/JOSAA_18_774.pdf

Limiting precision of tomographic phase estimation

In this paper, we study the performance of an adaptive optics system with 4 laser guide stars (LGS) and a natural guide star (NGS), and compare it to the system with 1 LGS, both installed on an 8-m telescope. Focus anisoplanatism is obtained with a numerical simulation. The typical errors of NGS wavefront are computed with analytical formulae. The entire system is studied to obtain its performance in terms of achievable Strehl ratio. This 4-LGS method allows to push adaptive optics system towards the visible part of the spectrum without tomographic reconstruction of 3D atmospheric perturbation. The cone effect is two times smaller with 4-LGS than with 1-LGS, allowing to reach almost a Strehl ratio of 0.5 at 500 nm. Considering the NGS errors and the focus anisoplanatism, the Strehl ratio (SR) can reach 0.45 at 1.25 micrometer under good seeing (GS) conditions with the Nasmyth Adaptive Optics System (14 X 14 sub-pupils wavefront sensor) at the Very Large Telescope.© (2000) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

/pdf/adaptive-optics-with-four-laser-guide-stars-cone-effect-2qq36hsmky.pdf

Elise Viard

Papers

Limiting precision of tomographic phase estimation

Optimized modal tomography in adaptive optics

Adaptive optics with four laser guide stars: cone effect correction on large telescopes