Direct wavefront reconstruction with the cone wavefront sensor using the inverse radon transform.

The cone wavefront sensor consists of a cone (or axicon) placed at the focal plane of the imaging system, from which an annular intensity image is formed. Typically, the wavefront phase is estimated using inversion of an interaction matrix relating the intensity image to different aberration modes. In this paper, we show that the intensity image for the cone wavefront sensor is related to the radon transform of the wavefront phase. A reconstruction method using the inverse radon transform (filtered back-projection) is shown to be able to directly approximate the wavefront phase without the need for an interaction matrix for small wavefront aberrations.

Mitigation of truncation effects in elongated Shack-Hartmann laser guide star wavefront sensor images.

Laser guide star Shack-Hartmann wavefront sensor images on extremely large telescopes (ELT) will be significantly elongated due to the off-axis projection of the laser relative to the subapertures. The finite number of pixels of the wavefront sensor detector means the most elongated images will be truncated, introducing errors in the centroid measurements. In this paper, we propose appending to the truncated wavefront sensor image the most likely missing tails from a high-resolution nontruncated reference image, which can be calculated from all of the low-resolution images. We show, via numerical simulation, that we can improve the centroid estimate for the most elongated subapertures on an ELT in the presence of read and photon noise.

Characterization of near-field ptychography.

Near-field X-ray ptychography has recently been proposed and shown to be able to retrieve a sample's complex-valued transmission function from multiple near-field diffraction images each with a lateral shift of the sample and with a structured (by a diffuser) illumination [Stockmar et al. Sci Rep. 3 (2013)]. In this paper, we undertake the first investigation - via numerical simulation - of the influence of the sampling and step size of the lateral shifts, the diffuser structure size, and the propagation distance on the reconstruction of the sample's transmission function. We find that for a gold Siemens star of thickness 750 nm with typical experimental parameters, for a successful reconstruction - given a theoretical minimum of four required measurements per imaged pixel - at least six diffraction images are required.

Laser guide star wavefront sensing for ground-layer adaptive optics on extremely large telescopes.

We propose ground-layer adaptive optics (GLAO) to improve the seeing on the 42 m European Extremely Large Telescope. Shack-Hartmann wavefront sensors (WFSs) with laser guide stars (LGSs) will experience significant spot elongation due to off-axis observation. This spot elongation influences the design of the laser launch location, laser power, WFS detector, and centroiding algorithm for LGS GLAO on an extremely large telescope. We show, using end-to-end numerical simulations, that with a noise-weighted matrix-vector-multiply reconstructor, the performance in terms of 50% ensquared energy (EE) of the side and central launch of the lasers is equivalent, the matched filter and weighted center of gravity centroiding algorithms are the most promising, and approximately 10×10 undersampled pixels are optimal. Significant improvement in the 50% EE can be observed with a few tens of photons/subaperture/frame, and no significant gain is seen by adding more than 200 photons/subaperture/frame. The LGS GLAO is not particularly sensitive to the sodium profile present in the mesosphere nor to a short-timescale (less than 100 s) evolution of the sodium profile. The performance of LGS GLAO is, however, sensitive to the atmospheric turbulence profile.

Optimal reconstruction for closed-loop ground-layer adaptive optics with elongated spots.

The design of the laser-guide-star-based adaptive optics (AO) systems for the Extremely Large Telescopes requires careful study of the issue of elongated spots produced on Shack-Hartmann wavefront sensors. The importance of a correct modeling of the nonuniformity and correlations of the noise induced by this elongation has already been demonstrated for wavefront reconstruction. We report here on the first (to our knowledge) end-to-end simulations of closed-loop ground-layer AO with laser guide stars with such an improved noise model. The results are compared with the level of performance predicted by a classical noise model for the reconstruction. The performance is studied in terms of ensquared energy and confirms that, thanks to the improved noise model, central or side launching of the lasers does not affect the performance with respect to the laser guide stars' flux. These two launching schemes also perform similarly whatever the atmospheric turbulence strength.

Modeling low order aberrations in laser guide star adaptive optics systems.

When using a laser guide star (LGS) adaptive optics (AO) system, quasi-static aberrations are observed between the measured wavefronts from the LGS wavefront sensor (WFS) and the natural guide star (NGS) WFS. These LGS aberrations, which can be as much as 1200 nm RMS on the Keck II LGS AO system, arise due to the finite height and structure of the sodium layer. The LGS aberrations vary significantly between nights due to the difference in sodium structure. In this paper, we successfully model these LGS aberrations for the Keck II LGS AO system. We use this model to characterize the LGS aberrations as a function of pupil angle, elevation, sodium structure, uplink tip/tilt error, detector field of view, the number of detector pixels, and seeing. We also employ the model to estimate the LGS aberrations for the Palomar LGS AO system, the planned Keck I and the Thirty Meter Telescope (TMT) LGS AO systems. The LGS aberrations increase with increasing telescope diameter, but are reduced by central projection of the laser compared to side projection.

Adaptive optics sky coverage modeling for extremely large telescopes.

A Monte Carlo sky coverage model for laser guide star adaptive optics systems was proposed by Clare and Ellerbroek [J. Opt. Soc. Am. A 23, 418 (2006)]. We refine the model to include (i) natural guide star (NGS) statistics using published star count models, (ii) noise on the NGS measurements, (iii) the effect of telescope wind shake, (iv) a model for how the Strehl and hence NGS wavefront sensor measurement noise varies across the field, (v) the focus error due to imperfectly tracking the range to the sodium layer, (vi) the mechanical bandwidths of the tip-tilt (TT) stage and deformable mirror actuators, and (vii) temporal filtering of the NGS measurements to balance errors due to noise and servo lag. From this model, we are able to generate a TT error budget for the Thirty Meter Telescope facility narrow-field infrared adaptive optics system (NFIRAOS) and perform several design trade studies. With the current NFIRAOS design, the median TT error at the galactic pole with median seeing is calculated to be 65 nm or 1.8 mas rms.

Sky coverage estimates for adaptive optics systems from computations in Zernike space.

A sky coverage model for laser guide star adaptive optics systems is proposed. The atmosphere is considered to consist of a finite number of phase screens, which are defined by Zernike basis polynomials, located at different altitudes. These phase screens are transformed to the aperture plane, where they are converted to laser and natural guide star wavefront sensing measurements. These transformations incorporate the cone effect due to guide stars at finite heights, anisoplanatism due to guide stars off axis with respect to the science object, and adaptive optics systems with multiple guide stars. The wavefront error is calculated tomographically with minimum variance estimators derived from the transformation matrices and the known statistical properties of the atmosphere. This sky coverage model provides fast Monte Carlo simulations over random natural guide star configurations, irrespective of telescope diameter. The Monte Carlo simulations outlined show that inclusion of a finite outer scale for the atmosphere significantly reduces the median wavefront error, that increasing the number of laser guide stars in the asterism reduces the median wavefront error, and that a larger natural guide star patrol field provides a smaller median wavefront error when there is a low star density in the field.

Wave-front sensing from subdivision of the focal plane with a lenslet array.

A wave-front sensing scheme based on placing a lenslet array at the focal plane of the telescope with each lenslet reimaging the aperture is analyzed. This wave-front sensing arrangement is the dual of the Shack-Hartmann sensor, with the wave front partitioned in the focal plane rather than in the aperture plane. This arrangement can be viewed as the generalization of the pyramid sensor and allows direct comparisons of this sensor with the Shack-Hartmann sensor. We show that, as with the Shack-Hartmann sensor, when subdividing in the focal plane, the quality of the wave-front estimate is a trade-off between the quality of the slope measurements over each region in the aperture and the resolution to which the slope measurements are obtained. Open-loop simulation results demonstrate that the performance of the lenslet array at the focal plane is equivalent to that of the Shack-Hartmann sensor when no modulation is applied to the lenslet array. However, when the array is modulated in a manner akin to that of the pyramid sensor, subdivision at the focal plane provides advantages when compared with the Shack-Hartmann sensor.

Phase retrieval from subdivision of the focal plane with a lenslet array.

A phase retrieval algorithm derived from subdivision of the complex field at the focal plane is proposed. This subdivision is achieved with a lenslet array at the focal plane in a manner similar to the pyramid wave-front sensor. The phase retrieval algorithm significantly improves the wave-front estimate that can be attained as a linear combination of the aperture images. This phase retrieval algorithm also avoids the twin-image stagnation problem inherent in phase retrieval and phase retrieval in conjunction with the Shack-Hartmann sensor.