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, List of Figures 1.1 2D representation of the 16 first Zernike Polynomials (a) and decomposition of the turbulence variance on the 400 first Zernike polynomials (b)
, Temporal PSD of the first (a) and 300 th Zernike Polynomial (b), 1994.
, Principle of an Adaptive Optics System
, Linearity curve of a WFS characterized by a sensitivity of 1
, Principle of the Shack Hartmann WFS: the movements of the spots on the detector indicate the presence of local Tip/Tilt at the level of the lenslet array
, SH-WFS measurements corresponding to a non-aberrated wave-front (left) and with aberrations (right), p.27
, Wave Front Error (WFE) as function of the number of photons per subaperture for a PWFS and a, p.28
,
, Illustration of the concept of Fourier Filtering optical System (courtesy of O. Fauvarque, taken from Fauvarque et al. 2017), p.29
, Illustration of the argument of the mask m (a) of a classical Pyramid WFS and corresponding Pyramid Pupils (b) when I P is circular with a central obstruction
, Definition of the PWFS Pupils I i (a) and Quadrants I Q i (b), p.31
, Illustration of the Pyramid Pupils for different modulations, p.32
, Illustration of the PWFS signals corresponding to a Tip (a), a Tilt (b) and a Focus (c) aberration for a modulation of 3?, p.32
, Sensitivity Curves of the PWFS with respect to the KL Modal Basis (see section 1.5.2). The results are given for different modulation radius, p.33
, Linearity curves for different modulation radius for different KL modes (see section 1.5.2)
, Illustration of the impact of residual phase on the push pull measurement of the KL mode 20 (see section 1.5.2) using a Pyramid WFS, p.34
, Illustration of the Optical Gains of the PWFS as a function of the Fried Parameter r 0 . This plot reproduces the results presented in Deo et al
, Illustration of an AO system in the Fried Geometry, p.36
, Image of the DSM indicating the main components of the mirror. Image taken from Biasi et al
, Position of the ASM actuators with respect to the FLAO WFS subapertures, p.38
, Illustration of the Zernike Polynomials (Left) and KL modes (Right) defined for an atmosphere characterized with r 0 = 11cm, p.41
, Chronogram of an AO system characterized by a total of 2 frames delay. T represents the duration of a frame
, Block diagram of a Closed Loop Adaptive System where G(f ) is the open loop transfer function
, Rejection Transfer Function of an AO loop running at 1 kHz for different loop gains. Left: Theoretical, Right: End-to-end simulation, p.43
, 25 (a) Wave-Front Error as a function of the input X-Shift for the different number of modes considered. (b) H-Band PSF (log-scale) versus shift X mis-registration for different numbers of modes controlled in the interaction matrix. The sub-images are 0.5" across, p.46
, Pseudo Synthetic Calibration: Experimental inputs (solid black lines) are injected into the synthetic model (dashed blue lines) to reproduce the registration of the real system. The pseudo-synthetic interaction matrix (dotted red lines) is then regularly updated during the operation tracking the mis-registration parameters
, The Front-bent focus is not displayed in this representation, Optical Layout of the LBT taken from, p.51
, , 2010.
, Band image of the HR8799 multiple planet system using the LMIR-Cam. Image taken from Maire et al
, Adaptive Optics Facility at the UT 4 of the VLT
, Comparison of the observation of the globular cluster NGC 6388 with the instrument MUSE in wide-field mode without Adaptive Optics (Left) and the MUSE narrow field mode (7.5" square) with Adaptive Optics (Right)
, Optical Design of the ELT, p.56, 2018.
, M4 mirror. Taken from
, Variance map of the influence functions of the ASM measured with an interferometer. We can notice the 9 inactive actuators, p.60
, Illustration of the different mis-registration types. The initial DM actuators position is indicated before (black crosses) and after (red crosses) application of the mis-registration, p.61
, Sensitivity in Wave Front Error to the different mis-registrations for a synthetic model of the FLAO system controlling 400 modes, p.62
, Influence Function from the ASM measured with an interferometer showing the overshoot due to the imposed definition of the influence function
, Top-left quarter of an influence function input to the model from an experimental measurement of influence function. It exhibits numerical edge-effects due to the interpolation of the experimental data to apply a rotation to the DM model
, Same influence function after applying an exaggerated anamorphosis of 120 % of the diameter for ?=45 ? (c)
, Each face has an angle of ? = ? 2, Argument of the optical mask m 4 of the perfect Pyramid WFS
, Optical Mask and pupils of the Pyramid WFS Model in presence of an (exaggerated) imperfection
, 68 2.10 Definition of the Pyramid Pupils I i (a) and Pyramid Quadrants I Q i, p.68
, Left: Sum of the four quadrants I 4Q and selection of the valid subapertures m I 4Q (white dots)
, Sum of the four quadrants of the pyramid model compared to the position of m exp I 4Q (white dots) without adjusting ? (b) and after adjusting ? (c)
, Summary of the development of the Pseudo-Synthetic model of the LBT in the simulator. The solid red lines correspond to the experimental inputs and the dashed blue lines to the model components and outputs, p.72
, 16 (a) Residual variance between the experimental and synthetic modal basis for the different mechanical coupling of the influence functions. The values are ordered in decreasing order. (b) Illustration of the cross-matrix B synth T .B exp in the case of 45% mechanical coupling showing that the matrix is well diagonal, Summary of the development of the Pseudo-Synthetic model of the LBT in the simulator
, Each subfigure provides the experimental mode (left), synthetic (center) and residual (right), vol.87
, Comparison of simulated closed loop modal PSD using both interaction matrices, synthetic and experimental. The model was developed using fully synthetic influence functions
, Comparison of 2D slopes maps [S x S y ] for the KL modes 3,10,100 and 400. From Top to bottom: Experimental, Fully Synthetic Model, Synthetic Model with Experimental Influence Functions, p.89
, Closed loop performance using the experimental reconstructor in the simulator and playing around the convergence value of the mis-registration parameters
, Iterative estimation of the scaling parameter ? * and mis-registration parameters ? * from the interaction matrix D ?, p.92
, ? = ? X (b), ? = ? mX (c) and ? = ? mX = ? mY (d) in a 30x30 Cartesian Geometry, Linearity Curves of the identification algorithm for ? = ? rot (a)
, Coupling of the parameters with the rotation. The results are the same for both shifts and for both magnifications. The horizontal black dashed lines give the maximum error that can be accepted
, Coupling of the parameters with the shift X. The algorithm does not exhibit any coupling with the rotation and shift Y parameters. The horizontal black dashed lines give the maximum error that can be accepted (see Figure 2.3)
, Coupling of the parameters with the magnification. The results are the same for both shifts. The horizontal black dashed lines give the maximum error that can be accepted (see Figure 2.3), p.98
, Iterative estimation of large values of mis-registrations updating the meta-sensitivity matrix ? ? * after each estimation of the parameter ? * 99
, Comparison of the estimation of the shift X for interaction matrices impacted by optical gains variations
, Identification of the model mis-registration parameters from reference signals. The estimated interaction matrix can be reduced to only given number of modes
, 2 4 most sensitive modes to a given mis-registration derived from the PCA of ?D ? 0 (? i )
, Sx Sy] corresponding to the 4 most sensitive modes to a given mis-registration derived from the PCA of ?D ? 0 (? i ), WFS measurement, vol.109
, Less sensitive modes to a given mis-registration derived from the PCA of ?D ? 0 (? i )
, Eigen Values distribution of the sensitivity matrices ?D ? 0 (? i ), p.110
, Cumulative variance corresponding to the different mis-registrations. Around 100 modes are required to explain 90% of the variance in all cases, p.110
, Estimation error for a ramp of mis-registration. The results are given for interaction matrices reduced to the 1 st , 10 th , 100 th and 200 th most sensitive modes for each type of mis-registration, p.111
, Sensitivity criteria ? RM S corresponding to various modal basis. The results are given for a rotation of 0.25, 0.75 and 1.25, p.112
, Sensitivity criteria ? RM S corresponding to various modal basis. The results are given for a shift X of 10, 30 and 50 % of a subaperture, p.113
, The results are given for a magnification X of 100.25, 100.75 and 101.25% of the diameter, Sensitivity criteria ? RM S corresponding to various modal basis
, The estimation using 2 (solid blue) and 10 modes PCA (dotted red) is given and can be compared to the estimation using the full interaction matrix (black dashed), Estimation Error for the Rotation (a) and the Shift X (b)
, log scale) when no mode is applied (a) and applying a 10 nm RMS mode corresponding to most sensitive PCA mode to the shift X. Bottom: Residual H-Band PSF (log scale) for the most sensitive PCA modes of the different types of mis-registrations, Top: H Band PSF, p.116
, Band PSF (log scale) and applying different amplitudes for the most sensitive PCA mode to the rotation. Bottom: Corresponding residual H-Band PSF (log scale)
, averaging 20 push/pull measurements for different levels of noise ? and different amplitudes a. The signal corresponds to the PCA mode most sensitive to the shift X, WFS signals, p.119
, Slopes RMS corresponding to the most sensitive PCA mode to the shift X as a function of the number of measurements averaged, p.120
, Illustration of the different modal basis, 30 PCA Modes (a) and 3 PCA Modes (b), used to retrieve the mis-registration parameters, p.120
, This case corresponds to a full interaction interaction matrix (300 KL Modes). The dashed black lines correspond to our specification in terms of accuracy, p.121
, Estimation Error corresponding to a shift X of 20% of a subaperture retrieving 30 PCA Modes on-sky. The dashed black lines correspond to our specification in terms of accuracy
, Estimation Error corresponding to a shift X of 20% of a subaperture retrieving 3 PCA Modes on-sky. The dashed black lines correspond to our specification in terms of accuracy
, Estimation Error corresponding to a shift X of 20% of a subaperture retrieving 3 PCA modes on sky. In the first case (a) we consider the most sensitive modes for each type of mis-registration and in the second case (b), we consider the 100 th PCA modes for each mis-registration. The dashed black lines correspond to our specification in terms of accuracy123
, Estimation corresponding to a shift X using 30 PCA modes. The results are given for different wind speed considering an amplitude a of 10 nm (left) and 20 nm RMS (right) and for different levels of noise (from the top to the bottom)
, Estimation (left) and corresponding Error (right) of a ramp of rotation using 30 PCA modes. The results are given for different level of noise ? and amplitude of push-pull a. In this case, we consider N = 20 measurements for each mode. The dashed black lines correspond to our specification in terms of accuracy
, Estimation (left) and corresponding Error (right) of a ramp of rotation using 3 PCA modes. The results are given for different level of noise ? and amplitude of push-pull a. In this case, we consider N = 20 measurements for each mode. The dashed black lines correspond to our specification in terms of accuracy
, Estimation (left) and corresponding Error (right) of a ramp of shift Y using 30 PCA modes. The results are given for different level of noise ? and amplitude of push-pull a. In this case, we consider N = 20 measurements for each mode. The dashed black lines correspond to our specification in terms of accuracy
, Estimation (left) and corresponding Error (right) of a ramp of shift Y using 3 PCA modes. The results are given for different level of noise ? and amplitude of push-pull a. In this case, we consider N = 20 measurements for each mode. The dashed black lines correspond to our specification in terms of accuracy
, Estimation (left) and corresponding Error (right) of a ramp of shift Y using 30 PCA modes. The results are given for different level of noise ? and amplitude of push-pull a. In this case, we consider N = 20 measurements for each mode. The dashed black lines correspond to our specification in terms of accuracy
, Estimation (left) and corresponding Error (right) of a ramp of shift Y using 3 PCA modes. The results are given for different level of noise ? and amplitude of push-pull a. In this case, we consider N = 20 measurements for each mode. The dashed black lines correspond to our specification in terms of accuracy
, Dynamic estimation of the mis-registration parameters as a function of the time using an amplitude a 20 nm RMS. In this case, we consider N = 20 measurements for each mode. The dashed black lines correspond to our specification in terms of accuracy
, The curves are flat and close to 1 in both cases. The difference between the two curves is due to the different level of residual during the on-sky calibration, Modal gains of a SH-WFS for an r 0 of 15 and 20 cm in the visible
, Relative error with respect to the convergence value for the estimation of a shift Y in a nominal case (slow boiling with low flux), p.140
, Rotation Estimation (a) and Estimation Error (b) as a function of the input rotation for a Frozen Flow of 10 m/s for different levels of noise, p.141
, Shift X Estimation (a) and Estimation Error (b) as a function of the input shift X for a Frozen Flow of 10 m/s for different levels of noise, p.141
, Estimation Error (b) as a function of the input shift Y for a Frozen Flow of 10 m/s for different levels of noise, p.142
, First Estimation of the scaling factor ? as a function of the input misregistration in a Frozen Flow configuration with a wind of 10 m/s for different levels of noise
, Estimation Error of the shift X parameter for a Frozen Flow configuration with a wind of 10 m/s in the X (a) and -X direction (b), p.144
, Definition of the different configurations identified to characterize the estimation of the interaction matrix using telemetry data
, Estimation of the mis-registration parameters as a function of the number of signals used to estimate the interaction matrix from closed loop data in the case of a Frozen Flow turbulence with slow and strong wind for a low and high flux
, Estimation of the mis-registration parameters as a function of the number of signals used to estimate the interaction matrix from closed loop data in the case of a Boiling turbulence with slow and strong wind for a low and high flux
, Interaction matrix signal corresponding to the actuator 100 for a Frozen Flow (a) and a Boiling (b) atmosphere in the case of a slow wind and a low flux
, Interaction matrix signal corresponding to the actuator 100 for a Frozen Flow (a) and a Boiling (b) atmosphere in the case of a fast wind and a low flux
, Interaction matrix signal corresponding to the actuator 100 for a Frozen Flow (a) and a Boiling (b) atmosphere in the case of a slow wind and a high flux
, Interaction matrix signal corresponding to the actuator 100 for a Frozen Flow (a) and a Boiling (b) atmosphere in the case of a fast wind and a high flux
, 1D signal of the estimated interaction matrices signals with no misregistration, corresponding to the actuator 100 for a high flux regime and different configurations of atmosphere (top). 1D signals of noise-free interaction matrices for different shift X (bottom)
, Difference of estimation between an algorithm using a global scaling ? or a different scaling ? X in X and ?
, Estimation Error of the Shift Y as a function of the number of frames considered. The results are given for a Frozen Flow (a) and a Boiling configuration (b) with different wind speeds and levels of noise, p.155
, Wave Front Error (WFE) as a function of the loop gain for a Frozen Flow configuration and a wind of 30 m/s, p.156
, Estimated interaction matrices (slopes X only) in the case of a Frozen Flow of 30 m/s using different loop gains for a high flux (500 Photons per subapertures)
, Shift X estimation in a Frozen Flow configuration with a wind speed of 30 m/s and -30 m/s. We show the estimation for different fluxes (in number of photons per subaperture) as a function of the loop gain, p.158
, Shift X estimation in a Frozen Flow configuration with a wind speed of 5 m/s and 15 m/s. We show the estimation for different fluxes (in number of photons per subaperture) as a function of the loop gain, p.158
, Wave Front Error (WFE) as a function of the wind speed (in subapertures per frames). (b) Shift X Estimation as a function of the wind speed (in subapertures per frames)
, Estimated interaction matrices (slopes X only) for different wind speeds using 20 000 frames
, WFE as a function of the loop gain for a slow (a) and fast Frozen Flow (b). We present the results for different levels of flux, p.162
, Rotation estimation (left) and corresponding estimation error (right) as a function of the input rotation in ? . The results are given for a wind of 5 m/s (top) and 30 m/s (bottom). The dashed lines are the rotation value that corresponds to a shift of 10% of a subaperture for an actuator located on the border of the pupil
, Shift Y estimation (left) and corresponding estimation error (right) as a function of the input shift Y % of a subaperture. The results are given for a slow (top) and fast (bottom) Frozen Flow, corresponding to a wind speed of respectively 5 m/s and 30 m/s
, Shift X estimation (left) and corresponding estimation error (right) as a function of the input shift X % of a subaperture. The results are given for a slow (top) and fast (bottom) Frozen Flow, corresponding to a wind speed of respectively 5 m/s and 30 m/s
, Shift X estimation (left) and corresponding estimation error (right) as a function of the input shift X % of a subaperture. The results are given for a slow (top) and fast (bottom) Boiling, corresponding to a wind speed of respectively 5 m/s and 30 m/s
, Estimation (a) and corresponding error (b) corresponding to a ramp of rotation using a PWFS in a Frozen Flow configuration with a wind speed of 10 m/s in the X direction
, Estimation (a) and corresponding error (b) corresponding to a ramp of shift X using a PWFS in a Frozen Flow configuration with a wind speed of 10 m/s in the X direction
, Estimation (a) and corresponding error (b) corresponding to a ramp of shift Y using a PWFS in a Frozen Flow configuration with a wind speed of 10 m/s in the X direction
, Estimation (a) and corresponding error (b) corresponding to a ramp of rotation using a PWFS in a Frozen Flow configuration with a wind speed of 10 m/s in the X direction. The results are given for a high flux (500 photons per subaperture) and a loop gain of 0, p.170
, Estimation (a) and corresponding error (b) corresponding to a ramp of shitf X using a PWFS in a Frozen Flow configuration with a wind speed of 10 m/s in the X direction. The results are given for a high flux (500 photons per subaperture) and a loop gain of 0, p.170
, Estimation (a) and corresponding error (b) corresponding to a ramp of shift Y using a PWFS in a Frozen Flow configuration with a wind speed of 10 m/s in the X direction. The results are given for a high flux (500 photons per subaperture) and a loop gain of 0, p.171
, Estimation Error of the shift X corresponding to a non mis-registered case with Frozen Flow in the X direction and wind speed of 30 m/s. The cases with gain higher than 1 were diverging, p.172
, Estimation (a) and corresponding error (b) corresponding to a ramp of shift X using a PWFS in a Frozen Flow configuration with a wind speed of 5 and 30 m/s in the X direction. The results are given for a high flux (500 photons per subaperture) and a loop gain of 0.3 and 0.7 with compensation of the OG
, Estimation (a) and corresponding error (b) corresponding to a ramp of shift X using a PWFS in a Boiling configuration with a wind speed of 5 and 30 m/s in the X direction. The results are given for a high flux (500 photons per subaperture) and a loop gain of 0.3 and 0.7 with compensation of the OG
, Impact d'une translation sur les performances de l'OA (WFE = Erreur de Front d'Onde) pour différent nombre de modes KL contrôlés dans le reconstructeur. b) Schéma représentatif de l'ASO Pyramide, p.183
, Principe de l'algorithme itératif d'identification des paramètres de misregistrations ? i à partir d'une matrice de référence expérimentale D ? et de matrices synthétiques D ? *
, Schéma représentatif du développement du modèle Pseudo-Synthétique de FLAO. Les lignes rouges correspondent aux données expérimentales et les lignes pointillées bleues aux données générées par le modèle, p.186
, Densités Spectrales de Puissances modales obtenues avec les reconstructeurs synthétique et expérimental dans le simulateur. (b) DSP modale obtenues avec les reconstructeurs synthétique et expérimental au LBT en simulant une turbulence sur l'ASM
, FEP (en échelle logarithmique) obtenues en simulant une turbulence sur l'ASM dans le cas d'un reconstructeur expérimental (gauche) et synthétique pour 400 modes (centre) et 500 modes (droite)
, 6 4 modes les plus sensibles pour différents types de mis-registrations obtenus grâce à la PCA des matrices de sensibilité, p.189
, Estimation dynamique des mis-registrations en fonction du nombre d'itérations en utilisant 3 modes PCA. A chaque itération, les misregistrations sont modifiées. Le cas présenté correspond à une amplitude de 20 nm RMS et 20 mesures push-pull pour chaque mode. Les lignes noires pointillées correspondent aux niveaux d'erreur maximales pour être dans les spécifications
, FEP en bande H, limitée par la diffraction (a) (échelle logarithmique) et avec une amplitude de 20 nm RMS du mode PCA le plus sensible à la rotation (b). (c) FEP résiduelle (échelle logarithmique), p.191
, Erreur sur l'estimation d'une translation en X pour une atmosphère de type Frozen Flow avec un vent de 10 m/s dans la direction X. Les résultats sont donnés pour un ASO de type Shack-Hartmann dans un régime à bas flux (10 photons par sous-ouverture) et fort flux (500 photons par sous-ouverture)
, Signal en X uniquement) pour différentes valeurs de vent. La matrice d'interaction vraie est donnée dans le coin bas-droite, Matrices d'interaction estimées
, Estimation de la translation en X en fonction du gain de boucle pour une atmosphère de type Frozen Flow avec un vent de 30 m/s dans la direction X. Les résultats sont donnés pour un ASO de type Shack-Hartmann dans un régime à bas flux (10 photons par sous-ouverture) et fort flux (500 photons par sous-ouverture)
, Estimation (a) et Erreur d'estimation (b) d'une translation en X pour une atmosphère de type Frozen Flow avec un vent de 10 m/s dans la direction X. Les résultats sont donnés pour un ASO de type Pyramide dans un régime à bas flux (10 photons par sous-ouverture) et fort flux (500 photons par sous-ouverture)
, Estimation de la translation en X en fonction du gain de boucle pour une atmosphère de type Frozen Flow avec un vent de 30 m/s dans la direction X. Les résultats sont donnés pour un ASO de type Pyramide avec et sans compensation des gains optiques, p.195
, Optical layout of the WFS unit of HOT. The lens L3 is used to focus the light on the top of the Double Pyramid and the lens L4 is in charge of re-imaging the PWFS pupils on the Andor camera detector, p.197
, Distances between the different HOT optical elements
, Courtesy of, A.3 HOT PWFS Pyramid (left) and BMM (right)
, Summary of the development of the Pseudo-Synthetic model of the HOT AO systems in the simulator. The solid red lines correspond to the experimental inputs and the dashed blue lines to the model components and outputs
, The left image corresponds to the interaction matrix experimentally measured with fiber (slopes RMS=0.0955 a.u.) and the right image corresponds to the interaction matrix generated from the synthetic model (slopes RMS=0.1073 a.u.), A.5 Closed-loop pupils of the HOT PWFS simulating the phase screens with the turbulence simulator
, PCA modes corresponding to the rotation for AO systems with different number of subapertures
, PCA modes corresponding to the shift X for AO systems with different number of subapertures
, PCA modes corresponding to the shift Y for AO systems with different number of subapertures
, PCA modes corresponding to the magnification X for AO systems with different number of subapertures
, PCA modes corresponding to the magnification Y for AO systems with different number of subapertures
, 6 1D section of a Gaussian influence function with a mechanical coupling of 45%
, PCA modes corresponding to the rotation for AO systems with different mechanical couplings
, PCA modes corresponding to the shift X for AO systems with different mechanical couplings
, 10 PCA modes corresponding to the magnification X for AO systems with different mechanical couplings
, 11 PCA modes corresponding to the magnification Y for AO systems with different mechanical couplings
, 57 1.2 Comparison of the main different Wave-Front Sensing and Calibration Strategies for the LBT, p.58
, Mis-registration parameters estimation from the new identification algorithm. The values for the shifts are in fraction of a subaperture and the values for the magnifications in percentage of diameter, vol.87
, Definition of the three AO Systems considered to characterized the linearity of the identification algorithm
, Numerical Simulations parameters for the chapter 3, p.105
, Total number of averaged push pull Measurements required to reach convergence (< 1% of a subaperture) for the mis-registration estimation of a shift X in all the conditions of noise investigated (10,100,500 and 1000 photons per subaperture per frame)
, , p.152
, Scaling factors [? X , ? Y ] for a wind speed of 30 m/s, p.153
, Definition of the different configurations identified to characterize the estimation of the interaction matrix using telemetry data
, Summary of the accuracy of the estimated mis-registration parameters in a Frozen Flow configuration with SH, p.175
, Summary of the accuracy of the estimated mis-registration parameters in a Frozen Flow configuration with Pyramid WFS, p.175
, Summary of the accuracy of the estimated mis-registration parameters in a Boiling configuration with SH, p.176
, Summary of the accuracy of the estimated mis-registration parameters in a Boiling configuration with Pyramid WFS, p.176