Abstract
In this paper, we describe Fourier-based wave-front sensors (WFSs) as linear integral operators, characterized by their kernel. In the first part, we derive the dependency of this quantity with respect to the WFS’s optical parameters: pupil geometry, filtering mask, and tip/tilt modulation. In the second part, we focus the study on the special case of convolutional kernels. The assumptions required to be in such a regime are described. We then show that these convolutional kernels allow to drastically simplify the WFS model by summarizing its behavior in a concise and comprehensive quantity called the WFS impulse response. We explain in particular how it allows to compute the sensor’s sensitivity with respect to spatial frequencies. Such an approach therefore provides a fast diagnostic tool to compare and optimize Fourier-based WFSs. In the third part, we develop the impact of the residual phases on the sensor’s impulse response, and show that the convolutional model remains valid. Finally, a section dedicated to the pyramid WFS concludes this work and illustrates how the slope maps are easily handled by the convolutional model.

Abstract
Atmospheric profiling is a requirement for controlling wide-field adaptive optics (AO) instruments, analysing the AO performance with respect to the observing conditions and predicting the point spread function (PSF) spatial variations. We present PEPITO, a new concept for profiling atmospheric turbulence from post facto tip-tilt (TT) corrected shortexposure images. PEPITO utilizes the anisokinetism effect in the images between several stars separated from a reference star, and then produces the profile estimation using a model-fitting methodology, by fitting to the long-exposure TT-corrected PSF. PEPITO has a high sensitivity to bothC2 n(h) and L0(h) by relying on the full telescope aperture and a large field of view(FOV). It then obtains a high vertical resolution (1-400 m) configurable by the camera pixel scale, taking advantage of fast statistical convergence (of the order of tens of seconds). With only a short-exposure capable large format detector and a numerical complexity independent of the telescope diameter, PEPITO perfectly suits accurate profiling for night optical turbulence site characterization or AO instruments operations. We demonstrate, in simulation, that the C2 n(h) and L0(h) can be estimated to better than 1 per cent accuracy, from fitted PSFs of magnitude V = 11 on a D = 0.5m telescope with a 10 arcmin FOV.

Abstract
In order to enhance the scientific exploitation of adaptive optics (AO)-assisted observations, we investigate a novel hybrid concept to improve the parametric estimation of point spread function (PSF) called PSF Reconstruction and Identification for Multiple-source characterization Enhancement (PRIME). PRIME uses both focal and pupil-plane measurements to estimate jointly the model parameters related to the atmosphere [Cn2(h), seeing] and the AO system (e.g. optical gains and residual low-order errors). Photometry and astrometry are provided as by-products. The parametric model in use is flexible enough to be scaled with field location and wavelength, making it a proper choice for optimized on-axis and off-axis data-reduction across the spectrum. Here, we present the methodology and validate PRIME on engineering and binary Keck II telescope NIRC2 images. We also present applications of PSF model parameters retrieval using PRIME: (i) calibrate the PSF model for observations void of stars on the acquired images, i.e. optimize the PSF reconstruction process, (ii) update the AO error breakdown mutually constrained by the telemetry and the images in order to speculate on the origin of the missing error terms and evaluate their magnitude, and (iii) measure photometry and astrometry with an application to the triple system Gl569 images.

Abstract
Wavefront sensors (WFSs) encode phase information of an incoming wavefront into an intensity pattern that can be measured on a camera. Several kinds of WFSs are used in astronomical adaptive optics. Among them, Fourier-based WFSs perform a filtering operation on the wavefront in the focal plane. The most well-known example of a WFS of this kind is the Zernike WFS. The pyramid WFS also belongs to this class. Based on this same principle, WFSs can be proposed, such as the n-faced pyramid (which ultimately becomes an axicon) or the flattened pyramid, depending on whether the image formation is incoherent or coherent. To test such concepts, the LAM/ONERA on-sky pyramid sensor (LOOPS) adaptive optics testbed hosted at the Laboratoire d'Astrophysique de Marseille has been upgraded by adding a spatial light modulator (SLM). This device, placed in a focal plane produces high-definition phase masks that mimic otherwise bulk optic devices. We first present the optical design and upgrades made to the experimental setup of the LOOPS bench. Then, we focus on the generation of the phase masks with the SLM and the implications of having such a device in a focal plane. Finally, we present the first closed-loop results in either static or dynamic mode with different WFS applied on the SLM.

Abstract
For extremely large telescopes, adaptive optics will be required to correct the Earth’s turbulent atmosphere. The performance of tomographic adaptive optics is strongly dependent on the vertical distribution (profile) of this turbulence. An important way in which this manifests is the tomographic error, arising from imperfect measurement and reconstruction of the turbulent phase at altitude. Conventionally, a small number of reference profiles are used to obtain this error in simulation; however these profiles are not constructed to be representative in terms of tomographic error. It is therefore unknown whether these simulations are providing realistic performance estimates. Here, we employ analytical adaptive optics simulation that drastically reduces computation times to compute tomographic error for 10 691 measurements of the turbulence profile gathered by the Stereo-SCIDAR instrument at ESO Paranal. We assess for the first time the impact of the profile on tomographic error in a statistical manner. We find, in agreement with previous work, that the tomographic error is most directly linked with the distribution of turbulence into discrete, stratified layers. Reference profiles are found to provide mostly higher tomographic error than expected, which we attribute to the fact that these profiles are primarily composed of averages of many measurements resulting in unrealistic, continuous distributions of turbulence. We propose that a representative profile should be defined with respect to a particular system, and that as such simulations with a large statistical sample of profiles must be an important step in the design process.

Abstract
We present the status and plans for the Keck All sky Precision Adaptive optics (KAPA) program. KAPA includes four key science programs, an upgrade to the Keck I laser guide star (LGS) adaptive optics (AO) facility to improve image quality and sky coverage, AO telemetry based point spread function (PSF) estimates for all science exposures, and an educational component focused on broadening the participation of women and underrepresented groups in instrumentation. For the purpose of this conference we will focus on the AO facility upgrade which includes implementation of a new laser, wavefront sensor and real-time controller to support laser tomography, the laser tomography system itself, and modifications to an existing near-infrared tip-tilt sensor to support multiple natural guide star (NGS) and focus measurements.