Abstract
This paper introduces the science software of HARMONI. The Instrument Numerical Model simulates the instrument from the optical point of view and provides synthetic exposures simulating detector readouts from data-cubes containing astrophysical scenes. The Data Reduction Software converts raw-data frames into a fully calibrated, scientifically usable data cube. We present the functionalities and the preliminary design of this software, describe some of the methods and algorithms used and highlight the challenges that we will have to face.

Abstract
HARMONI is the E-ELT's first light visible and near-infrared integral field spectrograph. It will provide four different spatial scales, ranging from coarse spaxels of 60 × 30 mas best suited for seeing limited observations, to 4 mas spaxels that Nyquist sample the diffraction limited point spread function of the E-ELT at near-infrared wavelengths. Each spaxel scale may be combined with eleven spectral settings, that provide a range of spectral resolving powers (R ~3500, 7500 and 20000) and instantaneous wavelength coverage spanning the 0.5 - 2.4 µm wavelength range of the instrument. In autumn 2015, the HARMONI project started the Preliminary Design Phase, following signature of the contract to design, build, test and commission the instrument, signed between the European Southern Observatory and the UK Science and Technology Facilities Council. Crucially, the contract also includes the preliminary design of the HARMONI Laser Tomographic Adaptive Optics system. The instrument's technical specifications were finalized in the period leading up to contract signature. In this paper, we report on the first activity carried out during preliminary design, defining the baseline architecture for the system, and the trade-off studies leading up to the choice of baseline.

Abstract
HARMONI is a visible and near-infrared integral field spectrograph designed to be a first-light instrument on the European extremely large telescope. It will use both single-conjugate and laser tomographic adaptive optics to fully exploit high-performance and sky coverage. Using a fast AO modelling toolbox, we simulate anisoplanatism effects on the point spread function of the single-conjugate adaptive optics of HARMONI. We investigate the degradation of the correction performance with respect to the off-Axis distance in terms of Strehl ratio and ensquared energy. In addition, we analyse what impact the natural guide source magnitude, AO sampling frequency and number of sub-Apertures have on performance. We show, in addition to the expected PSF degradation with the field direction, that the PSF retains a coherent core even at large off-Axis distances. We demonstrated the large performance improvement of fine tuning the sampling frequency for dimer natural guide stars and an improvement of approx. 50% in SR can be reached above the nominal case. We show that using a smaller AO system with only 20x20 sub-Apertures it is possible to further increase performance and maintain equivalent performance even for large off-Axis angles.

Abstract
CANARY is an open-loop tomographic adaptive optics (AO) demonstrator that was designed for use at the 4.2m William Herschel Telescope (WHT) in La Palma. Gearing up to extensive statistical studies of high redshifted galaxies surveyed with Multi-Object Spectrographs (MOS), the demonstrator CANARY has been designed to tackle technical challenges related to open-loop Adaptive-Optics (AO) control with mixed Natural Guide Star (NGS) and Laser Guide Star (LGS) tomography. We have developed a Point Spread Function (PSF)-Reconstruction algorithm dedicated to MOAO systems using system telemetry to estimate the PSF potentially anywhere in the observed field, a prerequisite to deconvolve AO-corrected science observations in Integral Field Spectroscopy (IFS). Additionally the ability to accurately reconstruct the PSF is the materialization of the broad and fine-detailed understanding of the residual error contributors, both atmospheric and opto-mechanical. In this paper we compare the classical PSF-r approach from Véran (1) that we take as reference on-Axis using the truth-sensor telemetry to one tailored to atmospheric tomography by handling the off-Axis data only. We've post-processed over 450 on-sky CANARY data sets with which we observe 92% and 88% of correlation on respectively the reconstructed Strehl Ratio (SR)/Full Width at Half Maximum (FWHM) compared to the sky values. The reference method achieves 95% and 92.5% exploiting directly the measurements of the residual phase from the Canary Truth Sensor (TS).

Abstract
Estimating the outer scale profile, L0(h) in the context of current very large and future extremely large telescopes is crucial, as it impacts the on-line estimation of turbulence parameters (Cn2(h), r0, ?0 and t0) and the performance of Wide Field Adaptive Optics (WFAO) systems. We describe an on-line technique that estimates L0(h) using AO loop data available at the facility instruments. It constructs the cross-correlation functions of the slopes of two or more wavefront sensors, which are fitted to linear combinations of theoretical responses for individual layers with different altitudes and outer scale values. We analyze some restrictions found in the estimation process, which are general to any measurement technique. The insensitivity of the instrument to large values of outer scale is one of them, as the telescope becomes blind to outer scales larger than its diameter. Another problem is the contradiction between the length of data and the stationarity assumption of the turbulence (turbulence parameters may change during the data acquisition time). Our method effectively deals with problems such as noise estimation, asymmetric correlation functions and wavefront propagation effects. It is shown that the latter cannot be neglected in high resolution AO systems or strong turbulence at high altitudes. The method is applied to the Gemini South MCAO system (GeMS) that comprises five wavefront sensors and two DMs. Statistical values of L0(h) at Cerro Pachón from data acquired with GeMS during three years are shown, where some interesting resemblance to other independent results in the literature are shown.

Abstract
Sky-coverage in laser-Assisted AO observations largely depends on the system's capability to guide on the faintest natural guide-stars possible. Here we give an up-To-date status of our natural guide-star processing tailored to the European-ELT's visible and near-infrared (0.47 to 2.45 µm) integral field spectrograph-Harmoni. We tour the processing of both the isoplanatic and anisoplanatic tilt modes using the spatio-Angular approach whereby the wavefront is estimated directly in the pupil plane avoiding a cumbersome explicit layered estimation on the 35-layer profiles we're currently using. Taking the case of Harmoni, we cover the choice of wave-front sensors, the number and field location of guide-stars, the optimised algorithms to beat down angular anisoplanatism and the performance obtained with different temporal controllers under split high-order/low-order tomography or joint tomography. We consider both atmospheric and far greater telescope wind buffeting disturbances. In addition we provide the sky-coverage estimates thus obtained.