Abstract
In this paper, we describe Fourier-based Wave Front Sensors (WFS) as linear integral operators, characterized by their Kernel. In a first part, we derive the dependency of this quantity with respect to the WFS’s optical parameters: pupil geometry, filtering mask, tip/tilt modulation. In a 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’s model by summarizing its behavior in a concise and comprehensive quantity called the WFS’s Impulse Response. We explain in particular how it allows to compute the sensor’s sensitivity with respect to the spatial frequencies. Such an approach therefore provides a fast diagnostic tool to compare and optimize Fourier-based WFSs. In a 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 slopes maps are easily handled by the convolutional model.

Abstract
We present PRIME (PSF Reconstruction and Identification for Multi-sources characterization Enhancement) as a novel hybrid concept to improve the PSF estimation based on Adaptive optics (AO) control loop data. PRIME uses both focal and pupil plane data to jointly estimate the model parameters, which are both the atmospheric (Cn2 (h), seeing), system (e.g. optical gains, residual low-order errors). 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. We review the methodology and on-sky validations on NIRC2 at Keck II. 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 (iii) measure photometry and astrometry in stellar fields.

Abstract
The Gemini Infrared Multi-Object Spectrograph (GIRMOS) instrument proposes to carry out Multi-Object Adaptive Optics (MOAO) correction on the residual of the Gemini Mutlti-Conjugate AO System (GeMS)corrected wavefronts in either Ground Layer (GLAO) or Multi-Conjugate (MCAO) mode. This work has been undertaken to determine the extent to which the ensquared energy delivered to a GIRMOS IFU can be improved over typical GeMS operation by adding MOAO correction. One of the key advantages of using the MOAO-fed IFUs is the improvement in performance toward the edge of the field, making the full 2’ field of GeMS more available for simultaneous observing. Using the Object Oriented Matlab Adaptive Optics (OOMAO) library1 to simulate the full system under a wide range of configurations and error conditions, we have established the baseline error budget and used the simulation to enable ongoing investigation into the particular control schemes and system errors that arise from using GeMS LGS and NGS WFSs to divide atmospheric correction between up to 3 DMs at different altitude conjugations and optimization directions.

Abstract
We present the status and plans for the Keck All sky Precision Adaptive optics (KAPA) program. The program includes four key science projects, 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. All of these elements have pathfinder relevance for the ELTs. 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.

Abstract
Current designs for all three extremely large telescopes show the overwhelming adoption of the pyramid wavefront sensor (P-WFS) as the WFS of choice for adaptive optics (AO) systems sensing on natural guide stars (NGS) or extended objects. The key advantages of the P-WFS over the Shack-Hartmann are known and are mainly provided by the improved sensitivity (fainter NGS) and reduced sensitivity to spatial aliasing. However, robustness and tolerances of the P-WFS for the ELTs are not currently well understood. In this paper, we present simulation results for the single-conjugate AO mode of HARMONI, a visible and near-infrared integral field spectrograph for the European Extremely Large Telescope. We first explore the wavefront sensing issues related to the telescope itself; namely the island effect (i.e. differential piston) and M1 segments phasing errors. We present mitigation strategies to the island effect and their performance. We then focus on some performance optimisation aspects of the AO design to explore the impact of the RTC latency and the optical gain issues, which will in particular affect the high-contrast mode of HARMONI. Finally, we investigate the influence of the quality of glass pyramid prism itself, and of optical aberrations on the final AO performance. By relaxing the tolerances on the fabrication of the prism, we are able to reduce hardware costs and simplify integration. We show the importance of calibration (i.e. updating the control matrix) to capture any displacement of the telescope pupil and rotation of the support structure for M4. We also show the importance of the number of pixels used for wavefront sensing to relax tolerances of the pyramid prism. Finally, we present a detailed optical design of the pyramid prism, central element of the P-WFS.

Abstract
Gemini Observatory has been awarded from the National Science Foundation a major fund to build a new state-of-the-art Multi Conjugate Adaptive Optics facility for Gemini North on Maunakea called GNAO. The current baseline system will use two lasers each split in two to create an artificial constellation of four laser guide star to measure the distortions caused by the atmosphere. At least two deformable mirror conjugated to 0km and the main altitude layer above Maunakea will be used to correct these distortions. The facility will be designed to feed future instrumentation, initially a near infrared imager and potentially a visiting 4-arm multi object adaptive optics IFU spectrograph.1 In this paper I will present the main characteristics of this exciting facility, its promises and its challenges. I will also present its conceptual design and results of trade studies conducted within the team and the Gemini Adaptive Optics Working Group. The expected first light is for October 2024.