Final Report Summary - PHARAOH (Detection of exo-Planets via High-Accuracy Radial-velocity spectrographic measurements with Adaptive Optics enHancement) The objective of the PHARAOH project is to assess the complementarity of adaptive-optics with high-resolution spectrographs in future ground-based optical/near-infrared telescopes to mitigate radial-velocity errors intrinsic to incomplete/inhomogeneous illumination of the spectrograph. To that end the PHARAOH project was structured into three work-packages:WP1: Adaptive-optics modelling and simulationsWP2: Impact of adaptive-optics on an E-ELT high-resolution, high-stability spectrographWP3: Coordination of instrumentation-directed activitiesWe have conducted studies with 1 PhD, 1 MSc and 3 internships on subjects related to adaptive-optics wave-front reconstruction and high-sensitivity wave-front sensing. This allowed us to contribute to a free-access, open use software package available to the community. With it we developed a non-linear iterative minimisation code to optimise the beam-shape of the adaptive-optics corrected PSF at the focal plane of the E-ELT. Statistical results show that deformable-mirror generated residuals include focus and astigmatism modes, that are either generated by AO itself during normal use or due to opto-mechanical constraints have little impact in broadening the PSF. This seems to exclude this option and thus we have next provided an analytical solution for a PSF modulated with circular tip/tilt which effectively broadens the AO-corrected PSF in a user-controlled manner. However it requires the modulation to operate at a higher frame-rate than the AO short-exposure. Whether this modulation can be introduced with the pre-focal deformable mirrors or needs a dedicated proprietary AO system ahead of the spectrograph is on-going work.For propagation of the electric field in fibres we contacted the Dept of Physics and Astronomy from Univ. of Porto. A simulation code that could provide us with light scrambling estimates in the near and far field of optical fibres needed be integrated. We have proposed a research topic for an internship but could find no student to develop it. The analytical developments mentioned allowed us to use them into a parallel application: direct imaging of extra-solar planets. We have developed an anti-aliasing Wiener filter reconstruction to mitigate residual errors after AO correction in high-contrast instruments and develop analytical models of high-sensitivity wave-front sensors for both improved correction and improved sky-coverage.As part of the general activities and expertise in high-angular resolution we have contributed to the Raven technical and scientific demonstrator. We had a two-weeks visit from Kate Jackson and participated in the 2 observing runs of the instrument at Subaru telescope in Hawaii.