Laser guide star simulations for 8-m class telescopes
Contents
1. theoretica position m Figure 2 Example of a Kolmogorov Zernike phase screen together with the associated theoretical straight line and simulated crossed line structure functions together with the associated structure function that shows a very good agreement between theory and simulation 1000 phase stripes of dimension 1024x512px corresponding to 32mx16m were used for this test with Lo 20 m and ro 1 m 4 2 Zernike polynomials method When the Zernike polynomials method is used the phase screens are generated as the sum of the first N jmaz 1 Zernike polynomials Z 4 6 Imaz plr Z 9 3 j 2 where r and are the polar coordinates on the pupil of radius R The piston term j 1 is not considered because the point spread function PSF is not depending on it For each phase screen realization an independent set of the 375 376 pixel magnification hna hya h2 hna hya hy hya hya ho Figure 3 Principle of the 3 layers downward propagation algorithm involving the light scattering back from a sodium LGS coefficients c is obtained with the correct statistics stated by the N x N covariance matrix Cj ajaj Only a small portion of the matrix has non zero elements so the sparse matrix algorithms are used to allocate less memory and increase the code speed To obtain a good behavior of the phase screens at high spatial fre2. Proc of SPIE Vol 3353 Adaptive Optical System Technologies ed D Bonaccini R K Tyson Jun 1998 Copyright SPIE Laser guide star simulations for 8 m class telescopes F Delplancke M Carbillet N Hubin S Esposito F Rigaut E Marchetti A Riccardi Viard R Ragazzoni M Le Louarn and L Fini ESO Karl Schwarzschild Str 2 85748 Garching bei Muenchen Germany Osservatorio Astrofisico di Arcetri L go E Fermi 5 50125 Firenze Italy Centro Galileo Galilei Calle Alvarez de Abreu 70 38700 Santa Cruz de La Palma Spain 4Qsservatorio Astronomico di Padova vicolo dell Osservatorio 5 35122 Padova Italy ABSTRACT We describe in this paper the development of a simulation tool for modeling any kind of adaptive optic system with laser guide star within the framework of the European network Laser Guide Star for 8 m Class Telescopes This is intended to support investigations about laser guide stars problems like cone effect and tip tilt determination The different kind of software modules to be developed are listed and the libraries already distributed among the network are described phase screen generation with fast Fourier transform and Zernike methods downward propagation for natural and laser guide stars wavefront sensing and reconstruction with Shack Hartmann and curvature sensor of various geometries The future studies for solving the cone effect are also presented Keywords adaptive opt
3. Poisson equation with the Neumann boundary conditions has to be solved for the direct reconstruction gt 16 10 SYSTEM PERFORMANCES DATA DISPLAY AND I O Several modules have been developed in order to display the incident wavefront the sensor image s the sensor signals the reconstructed wavefront and the wavefront structure function They can be plugged simply after the modules giving the corresponding data and displaying the images at the requested positions with the requested sizes as demonstrated in Fig 6 and Fig 7 The other modules will be developed as a function of the needs of the other module libraries 11 WORK IN DEVELOPMENT FUTURE WORK A major difficulty with LGS is the cone effect which is due to the slight difference between the conical propagation path of the laser beam and the cylindrical path of the stellar beam In order to correct the cone effect multiple LGS systems can be used Different methods with multiple LGS have been studied either using 2 D reconstruction stitching and merging methods or 3 D reconstruction tomography methods 19 29 The difference between stitching and merging is the fact that the subapertures measure the wavefront from all LGSs in the merging method whereas in the stitching method each subaperture senses only one spot and the boundaries of adjacent spots as illustrated in Fig 8 Sasiela and Tyler have described these methods but did not provide detailed algorithms to perfo
4. cone effect with multispot LGS Rayleigh scattering LGS spot elongation Na layer saturation effects tip tilt solving via polychromatic LGS and perspective methods There is still a lot of work to be done but our goal is at term to provide the scientific community with a powerful flexible versatile and easy to use software package for AO LGS simulations ACKNOWLEDGMENTS The authors gratefully acknowledge the financial support of the European Community through the Training and Mobility of Researchers program network under contract number ERBFMRX CT96 0094 381 382 10 11 13 l4 15 16 17 18 19 20 REFERENCES M L Louarn R Foy N Hubin and M Tallon Laser guide star for 3 5 and 8 m telescopes performances and astrophysical implications MNRAS 295 pp 756 763 1998 M L Louarn N Hubin R Foy and M Tallon Sky coverage and psf shape with lgs ao on 8 m telescopes in Adaptive Optical System Technologies D Bonaccini and R K Tyson eds Proc SPIE March 1998 pp paper 3353 99 1998 M Tallon and R Foy Adaptative telescope with laser probe isoplanatism and cone effect Astron Astrophys 235 pp 549 557 1990 F Rigaut and E Gendron Laser guide star in adaptive optics the tilt determination problem Astron Astrophys 261 pp 677 684 1992 F Roddier The effects of atmospherical turbulence in optical astronomy Progress in Optics 1
5. geometry Figure 7 Example of the results obtained with the modeling of a curvature wavefront sensor 3 rings with 1 4 and 8 subapertures of equal area extra focal distance 30cm scanning with 5 sampling points in the extra focal plane noise implemented point like NGS of magnitude 5 From left to right the WFS geometry map the incident wavefront pure defocus two symmetrical intra and extra focal images and the image of the CWFS signals 379 380 8 1 Centroid Estimator Each subaperture image is extracted from the image given by the Shack Hartmann wavefront sensing module The position in camera pixels of its centroid is computed and then the centroid position coming from the calibration measurements is subtracted in order to give the real decentering due to the wavefront aberrations If the subaperture does not receive enough flux its signals is set at a reference zero value The centroid position can then be converted in real wavefront slopes with the appropriate factor It is required only when one wants to reconstruct the wavefront in closed loop the centroids can be used directly So this operation is placed outside of this module An example of the results that can be obtained is given in Fig 6 8 2 Curvature and Slope Estimator for the CWFS This module takes the image cube coming out of the curvature wavefront sensing module adds the intra focal images on one side and the extra focal images on the other side
6. profile The three directions of the winds are fixed see Fig 3 Two cases are taken into account at the same time the sodium LGS one and the NGS one In the NGS case the layers phase screens are simply added in order to obtain the resulting propagated phase perturbations at the telescope pupil In the sodium LGS case one has to take into account the altitude hy of the sodium layer scattering the LGS with respect to the turbulent layers ones h This results in a pixel magnification by a factor pee for the phase screens before their adding The output is a number of pupil screens following the kind of temporal evolution chosen for each Guide Star see Fig 4 which parameters are the type Natural or Laser the off axis angle and the position angle Jp omcennenanenisttnatnen se iesnettettett etn SONA TT CONN GSR bs ODO ORE 5 0 t GAUDE NGS on axis LGS on axis Figure 4 Example of propagated screens vs time evolution The evolving screens are computed for two different cases corresponding to an on axis NGS and on axis sodium LGS The evolution time is here 0 1s 6 WAVEFRONT SENSOR GEOMETRY The wavefront sensing WFS geometry definition has been separated from the wavefront sensing modules because any kind of sensor geometry square radial etc can be used with any kind of sensor curvature Shack Hartmann etc The classical associations Shack Hartmann square or curvature radial are not always requ
7. 9 pp 283 375 1981 R G Lane A Glindeman and J C Dainty Simulation of a kolmogorov phase screen Waves in Random Media 2 pp 209 224 1992 N Roddier Atmospheric wavefront simulation using zernike polynomials Opt Eng 29 pp 1174 1180 1990 W H Press B P Flannery 5 A Teukolsky and W T Vetterling Numerical Recipes in C Cambridge University Press Cambridge 1986 R Noll Zernike polynomials and atmospheric turbulence J Opt Soc Am 66 pp 207 211 1976 W Magnus F Oberhettinger and R P Soni Formulas and Theorems for the Special Functions of Mathematical Physics Springer Verlag Berlin 1966 M Born and E Wolf Principles of Optics Pergamon New York 1985 D L Fried Least square fitting a wavefront distorsion estimate to an array of phase difference measurements J Ont Soc Am 67 pp 370 375 1977 W H Southwell Wavefront estimation from wavefront slope measurements J Opt Soc Am 70 pp 998 1006 1980 R K Tyson Principle of Adaptive Optics 2nd edition Academic Press Boston 1993 F Roddier Curvature sensing and compensation a new concept in adaptive optics Appl Opt 27 pp 1223 1225 1988 F Roddier Wavefront sensing and irradiance transport equation Appi Opt 29 pp 1402 1403 1990 R J Sasiela Wavefront correction by one or more synthetic beacons J Opt Sec Am A 11 pp 379 393 1994 G A Ty
8. Guide Star for 8 m Class Telescopes was started in Europe in January 1997 This European Commission program and the network are described in Sect 2 One of the tasks of this network is to create a large software library for AO simulations in order to give a useful toolbox for research on the LGS problems and on optimal use of photons The exact aims of this simulation tool and the description of its contents can be found in Sect 3 A complete software package able to model any standard AO system should be delivered for the end of 1998 Then new softwares modeling advanced structures or new concepts will be progressively added to the package Up to now a certain number of routines have been developed related to Other author information Send correspondence to F D F D E mail fdelplan eso org M C E mail marcel arcetri astro it 372 e Phase screen generation using either a fast Fourier transform FFT method with sub harmonics adding SHA or Zernike polynomials see Sect 4 Downward propagation using geometric optics and applied to any number of NGS and LGS see Sect 5 Wavefront sensor geometry defining square radial hexagonal or user defined geometries see Sect 6 Wavefront sensing modeling either a Shack Hartmann or a curvature sensor see Sect 7 Wavefront sensor signal computation evaluating the slopes and or curvatures of the wavefront see Sect 8 Wavefront reconstruction giving the phase of the recon
9. The intra and extra focal are computed by integrating the image intensity under each subaperture The photon noise is then added if requested by the user Finally the differential signal is computed using the following equation Sintra Sestra 5 S 1 e G Sola G Sintra or Sestra L where Sintra and Seztra are the intra and extra focal signals on the considered subaperture G is the gain of running average and Soga is the denominator of Eq 5 at the previous iteration If G is set to 1 one finds back the usual curvature sensing equation for the differential signal The signals obtained during the calibration process have then to be subtracted from the measured values If a subaperture does not receive any photon the signal is set to zero An example of the results that can be obtained is given in Fig 7 9 WAVEFRONT RECONSTRUCTION For the wavefront reconstruction we have the choice between the direct zonal reconstruction from the slopes or and the curvatures and the reconstruction through modes which allows to filter them The latter requires to choose a set of modes Zernike Karhunen Loeve or mirror modes Zonal reconstruction can be implemented directly and depends only on the geometry on which one wants to reconstruct 2 4 Up to now the zonal reconstruction based on Fried geometry with a least square algorithm has been implemented but the modal methods will be developed as soon as possible For the curvature sensing the
10. ds are available at the moment a FFT SHA based one and a Zernike polynomials based one but we plan to incorporate also a Karhunen Loeve and a fractal based methods 4 1 FFT SHA method The implemented FFT SHA method allows to generate phase screens y x y assuming either a Kolmogorov or a von K rm n spectrum vz Vy from which calculate the modulus of A v vy the Fourier transform of y z y Assuming the near field approximation and small phase perturbation gt the Kolmogorov spectrum is given by 11 By Ve Vy 0 0228 r7 v2 TaS 1 where ro is the Fried parameter Within the framework of the classical FFT based technique a Kolmogorov phase screen is obtained by taking the inverse FFT of vz Vy which modulus is obtained by using Eq 1 and which phase is random uniformly distributed The obtained phase screens suffer however from the lack of spatial frequencies vz vy 373 374 Table 1 List of the proposed module libraries with their types parameters purposes and methods for the user interface modules the adaptive optics modules and the utility modules Module Library Method Purpose Parameters Guide object definition Types NGS extended LGS Parameters size spectral type magnitude offset altitude Telescope and common optics Parameters diameter focal ratio central obscuration Sensor geometry Types square radial hexagonal custom Phase screen generation T
11. en in Fig 5 This module can handle the case of a vibrating membrane where the extra focal domain is scanned sinusoidally But one cannot take an infinite number of extra focal images Thus the user has to discretize the scanning domain into a number n of sampling points where the images will be computed Usually about 10 sampling points within one period give a good approximation of reality For the extra focal plane i the defocus is a quadratic function of the distance L given by f l i r Li r f sia 4 where l is the distance of the extra or intra focal plane the closest to the focus f is the focal length of the telescope and common optics and is the WFS wavelength For each point the pure defocus wavefront is computed and convolved with the wavefront to be analyzed This defocused phase screen is imaged again on the sensor lenslet array The intensity of this image is computed convolved with the possible extended reference or calibration object normalized and converted into the corresponding number of photons The sky background is added It is considered to be equally distributed on all the subapertures The obtained images for each extra focal distance are stored in an image cube the output of this routine 8 WAVEFRONT SENSOR SIGNAL COMPUTATION The WFS signal computation modules have to convert the wavefront sensor images into the numerical signals representing some of the wavefront characteristics For instance from
12. he rebining in order to have an integer number of sampling points per physical pixel of the camera 7 WAVEFRONT SENSING The wavefront sensing modules firstly take the wavefront corrected by the deformable mirror secondly add the possible static aberrations of the common optics and finally compute the image s coming out of the wavefront sensor In the case of the Shack Hartmann it gives one image composed of the images of each sub aperture rebined according to the pixel size of the WFS camera In the case of the curvature sensor it gives a set of extra focal images 7 1 Shack Hartmann Wavefront Sensor A scheme of the SHWFS principle is given in Fig 5 From the wavefront incident on the pupil the program extracts the parts arriving on each subaperture and computes the images made by these ones Then it takes their intensity and in case of extended reference object or calibration source e g an optical fiber convolves it with the image of this object It applies the sky background noise except with the fiber calibration source and rebins the sampling points to the camera pixels The result is normalized and converted in number of photons Finally the photon and read out noises are applied if required A threshold can also be applied if asked by the user All the subaperture images are gathered in a general wavefront sensing image which is the output of this module 7 2 Curvature Wavefront Sensor A scheme of the CWFS principle is giv
13. ics laser guide star atmospheric perturbations wavefront sensing cone effect atmospheric tomography 1 INTRODUCTION For large telescopes 8 m class the use and performances of adaptive optics AO are limited by the sky coverage i e the lack of bright enough natural stars to be used as reference sources An AO system for large telescopes thus requires the generation of artificial reference sources Up to now the only viable proposed solution is the laser guide star LGS Two types of LGS can be used one using the Rayleigh scattering in the lower atmosphere up to 20km altitude of a laser beam the other using the excitation of sodium atoms in the mesosphere Na layer at 90km altitude Both solutions are inducing other problems linked among others to the finite altitude of the artificial star cone effect and to the impossibility to measure the tilt as on a natural guide star NGS In order to efficiently implement LGS on AO systems the investigation of the solutions to those problems requires powerful and versatile simulation codes Another topic that must also be investigated in AO is the optimal use of the photons coming to the telescope by the study of innovative wavefront sensing techniques The best use of photons would allow to increase the limiting magnitude of NGS AO and thus to increase the sky coverage or to reduce the necessary laser power A Training and Mobility of Researchers Network devoted to the study of Laser
14. ilt of the incoming wavefront the cone effect due to the parallax between the sodium LGS at 90km and the program object the implementation effects on observations at the telescope and at other telescopes on the site the specification of the lasers and of their operation mode as well as the in depth analysis of the astrophysical requirements Each of these problems is approached as follows A theoretical analysis of the problem is performed based on a common simulation code Then when appropriate experiments at lab and onto the sky are built operated and analyzed The ultimate goal of the program is to deliver specifications of the LGS as optimal as possible The tasks are dispatched between five workpackages WP The first one investigates the scientific programs which can ultimately be done with LGS on 8m telescopes accounting for the technical con straints i e tilt correction and field The aim of the second WP is to produce a code for simulating the ensemble atmosphere telescope AO LGS to model different AO systems or LGSs This is the object of the present paper The third WP takes care of operational issues Safety and light pollution studies must be concluded before operating a LGS Laser type and configuration laser operation and maintenance and astronomical operation issues are currently investigated The fourth WP studies advanced wavefront sensing for tilt measurement field increase and better use of photons The fifth WP g
15. ired It could be useful to make other associations or to use other kinds of sensor geometry and to compare their respective performances related to noise propagation sensitivity redundancy etc Three main classical geometries are implemented square radial and hexagonal not yet developed A custom geometry can also be given by the user The parameters of those geometries are described below These modules compute the geometrical parameters needed for the wavefront sensing modules from the physical parameters entered by the user Their outputs must be compatible with the Shack Hartmann and with the curvature modules The input parameters common to all the geometries are the size of the simulation in sampling points corresponding to the size of the phase screens to be analyzed the size of the pupil in meters and in sampling points the size of the wavefront sensor in sampling points which can be smaller or bigger than the pupil but smaller than the simulation size and the wavelength at which the wavefront sensing is operated 6 1 Squared Geometry The user gives as particular inputs the linear number of subapertures under the pupil and the subaperture size in arcsec The program adjusts the number of sampling points in order to have it integer under each subaperture determines which sub apertures are active i e receive a large enough number of photons computes their positions and makes an image of the sensor Moreover if it is ass
16. ives experimental feedback to the precedent theoretical studies by using AO and LGS on real telescopes by measuring seeing vertical distributions by making experiments with polychromatic guide stars More details can be found on the Web site http www obs univ lyonl fr tmr lgs We shall now describe in more details the second workpackage 3 SIMULATION PACKAGE DEVELOPMENT 3 1 Aims of the Software Package The general aim of our work is to develop a complete software library of any possible element of an AO LGS system This library will at first include known classical elements like Shack Hartmann or curvature wavefront sensors Later on it will also incorporate software modeling new elements and advanced complex phenomena like the different solutions proposed for the cone effect Thus the structure of the software library should allow the largest versatility to the user in order to test any combination of elements to search for optimal configurations to model any partial or end to end complex system and to adapt easily to newly developed software In order to satisfy this requirement the basic elements of the software library should be as atomic as possible representing an elementary process of the system the deformable mirror the tip tilt mirror the wavefront sensor the reconstructor etc The atomic element must keep a physical meaning They have also to be compatible to each other so that they can be plugged together to f
17. ler Merging a new method for tomography through random media J Opt Soc Am A 1 pp 409 424 1994 A J Jankevics and A Wirth Wide field of view adaptive optics in Active and Adaptive Optical Components M E Ealey ed Proc SPIE 1543 pp 438 448 1991 J M Beckers Increasing the size of the anisoplanatic patch with multiconjugate adaptive optics in Very Large Telescopes and Their Instrumentation M H Ulrich ed Proc ESO conference March 1988 pp 693 703 1988
18. ns calibration source System modes Mirror Zernike or Karhunen Loeve modes Mode gain determination Methods analytical numerical Transfer function Of the global system or of part of it lower than the inverse of the necessarily finite dimension of the simulated array To compensate from this effect the technique of SHA proposed by Lane et al 6 which consists in generating additional random frequencies and add their effects to the already sampled frequencies has been chosen In the case of a von K rm n spectrum 4l a8 1 5 Sp Vz Vy 0 0228 r3 3 4 u z 2 0 the same procedure is applied allowing to reach large values of the desired wavefront outer scale L anyway if Lo is already sampled by the FFT no SHA is needed Figure 1 shows an example of phase screen actually a phase stripe useful for temporal evolution e g in the framework of the downward propagation module of Sect 5 generated using this method and a von K rm n modulus structure function von Karman _ _ 25 cS as 3 20 Simulation theoretico poritdseriaebarriitiviinl 0 PES OO ee Se ee o 2 4 position m Figure 1 Example of a von K rm n FFT phase stripe together with the associated theoretical straight line and simulated doted line structure functions structure function Kolmogorov Sa es a A a A sor rore simulation D 40r
19. ociated with a Shack Hartmann wavefront sensor some rebining process is needed in order that an integer number of sampling points corresponds to one physical pixel of the camera The module prepares the parameters for this operation This adjustment is not needed in case of a curvature sensor where the intensity over the full subaperture is detected as a whole An example of the sensor image is given in Fig 6 6 2 Radial Geometry Here the user can give the data on two ways Either he is giving only the number of rings and the number of subapertures for each ring and the program helps him to build a radial sensor with subaperture of equal surfaces 377 378 standard configuration Or the user gives in an ASCII file all the parameters needed to construct the sensor the inner and outer diameters of each ring the number of subapertures for each ring and the angular orientation of the first subaperture of each ring relative to a reference direction An example of such a radial sensor is given in Fig 7 The program computes the position of each active subaperture and the image of the active sensor 6 3 Custom Geometry The user can also introduce any kind of sensor geometry by giving the map of the sensor an image where one places zeros out of the sensor and pupil and a number corresponding to each subaperture under this one The program then computes the positions of each subaperture and for the Shack Hartmann prepares the parameters of t
20. orm larger structures Moreover the general structure of the software library should allow to use parallel processing for time consuming simulations Software will be written in IDL language within a Unix Linux environment SPARC or PC 230 MHz with at least 128 Mb of RAM The input parameters of the AO system will be provided by the user either interactively through the user interface or in a dedicated file The output data will be available in FITS format for eventual post processing with other astronomical software A full extensive technical documentation and user manual will also be provided 3 2 Software Library Structure The software library will be made of modules and macros that will be linked together by the user interface The modules correspond to the atomic elements and must be stand alone routines i e not requiring to use other non standard IDL routines They have to be under an immediately executable format in order to spare processing time The module size has been chosen in order to increase flexibility and possibility of unusual uses allowing research work The outputs of the modules should be the data which can be interesting to display or to store for future analysis e g the sensor image or the incident wavefront We foresee three different types of modules according to their purposes AO modules which implement computational algorithms User Interface modules used to implement user interfaces and Utility modules
21. quencies jmaz must be large enough to take into account polynomials with a number of oscillations over the pupil diameter comparable to the chosen sampling usually at least 2 or 3 px per ro In these conditions jmaz can be as large as a few thousands in the visible for 8 m class telescopes The usual definition formula for the Zernike radial component is not effective to compute polynomials with 7 gt 1030 when double precision arithmetic is used To overcome this problem we developed an algorithm based on an alternate definition for Z p 8 involving the recurrence definition of the Jacobi polynomials and the relationship between the Zernike and the Jacobi polynomials Figure 2 shows an example of phase screen generated using this last method The structure function computed from 400 phase screens 256x256 px i e 8mx8m with fmar 4186 and ro 1m is here again in very good agreement with the theoretical one Kolmogorov here In both cases the output is a number of phase screens or stripes suitable for the rest of the simulation modules 5 DOWNWARD PROPAGATION The downward propagation module is aimed to propagate the phase through up to three turbulent layers of the atmosphere down to the telescope pupil To each of these layers is affected a phase screen previously generated as described in Sect 4 1 together with an altitude h with i 1 2 3 a wind speed v and a relative weight determined with respect to the integrated C2
22. rm the wavefront reconstruction The tomographic method permits to reconstruct the phase corrugations of each turbulent layer using matrix inversion methods Tallon and Foy Jankewicks et alt have explained possible 3 D reconstructions Figure 8 Principle schemes of the stitching merging and tomography methods for solving the cone effect These 3 D reconstruction methods are based on the fact that generally in astronomical sites turbulence is concentrated in a few 2 to 5 thin turbulent layers Assuming that one knows the height and number of these layers for example by using SCIDAR techniques one can by solving a set of linear equations reconstruct the phase aberrations in each of these layers Multiple deformable mirrors can then be used to correct each layer separately in their optically conjugated planes This allows one to solve the cone effect and also to increase dramatically the corrected AO field of view A simulation of this method has been realized and the results are being analyzed Several inversion methods are being investigated The geometry of the laser spots and their number are also being investigated A laboratory experiment realized at Centre de Recherches Astronomiques de Lyon has also been made in order to simulate real measurements and to check the validity of computer simulations This experiment includes phase screens to simulate atmospheric turbulence and an array of micro lenses to measure
23. structed screen see Sect 9 Data display I O and performance estimation see Sect 10 Finally our future work about cone effect is introduced see Sect 11 and conclusions are drawn on the other future applications of our software package see Sect 12 2 THE LASER GUIDE STAR FOR 8 M CLASS TELESCOPES TMR NETWORK Within its Fourth Framework program the European Community wants to promote the formation of young re searchers in sciences and engineering via its Training and Mobility of Researchers TMR program A full de scription of the TMR program its purposes its actions can be found on the European Community Web site at http www cordis 1u Our LGS network groups the following research teams Centre de Recherches Astronomiques de Lyon Observatoire de Lyon France coordinator European Southern Observatory Instituto de Astrofisica de Canarias Spain Os servatorio Astrofisico di Arcetri Italy Imperial College of London United Kingdom Max Planck Institute fuer Extraterrestrische Physik Germany and National University of Ireland Galway The LGS network aims at co ordinating the efforts in Europe to produce a comprehensive set of theoretical and experimental studies which are necessary to implement the LGS on the 8 m telescopes VLT Gemini LBT and ORM in which European countries are implied Several problems have to be addressed before the LGS implementation They concern the correction for image wandering the t
24. the Shack Hartmann image one can calculate the centroid positions of the subpupil images From the curvature images one can calculate the classical differential signal under each subaperture which is linked to the curvatures and slopes of the wavefront But other methods could be used like the global wavefront reconstruction using the full image characteristics and not only the first or second order terms or like the asymmetric algorithm for the curvature sensor which allows to retrieve the shape of the extended object Presently only the slope estimator for the SHWFS centroiding and the classical symmetric algorithm for the CWFS are implemented They are described here below telescope _ intrafocal wavefront plane wavefront K membrane mirror slope measurement ae sensor scanning displacement of centroid Figure 5 Principle scheme of the Shack Hartmann wavefront sensor under one of the subapertures at left and of the curvature wavefront sensor with a vibrating membrane at right Figure 6 Example of the results obtained with the modeling of a Shack Hartmann wavefront sensor 7x7 subaper tures of 2 18 arcsec pixel size 0 136 arcsec read out noise 10 e rms point like NGS of magnitude 3 From left to right the WFS geometry map the incident wavefront Kolmogorov phase screen the SHWFS image the corresponding slopes represented as facets and arrows and the reconstructed wavefront zonal Fried
25. the produced phase aberrations Results of this experiment are also being analyzed 12 CONCLUSIONS In this paper have been presented the aims the results and the future works of the European network Laser Guide Star for 8 m Class Telescopes in the field of developing a software package in order to modelize any type of AO system simple or complex end to end or partial with or without LGS At first the package will cover all the AO sub systems whose theory has already been developed Then new modules will be added as a function of the advanced researches made in the network The first basic package will be completed by the end of 1998 Up to now the developed modules include phase screen generation with FFT and SHA or with Zernike poly nomials downward propagation geometrical optics for any number of LGS and NGS wavefront sensor geometry definition square radial hexagonal or custom wavefront sensing Shack Hartmann or curvature wavefront es timation centroiding or curvature and slopes wavefront reconstruction zonal with Fried geometry several data display I O and performance estimations These routines have been described in more details with their assumptions parameters methods inputs and outputs The future software investigations will concern advanced wavefront sensors for a better use of photons advanced modal control advanced reconstruction methods flexible time and modal filtering for tip tilt and higher orders
26. used for I O and other housekeeping tasks The list of the proposed modules ordered as a function of their purposes is given in Table 1 The modules can be associated together to make larger structures that we call macros From the implementation point of view a macro is a single program in the classical sense built up with the use of modules Most of them will be made by the user by means of the user interface but some of them will also be provided directly to the user mainly for initialization and calibration purposes The list of the proposed macros is given in Table 2 Tn order to allow the implementation of easy to use end to end simulation applications a number of modules will be implemented which can be used by developers to create interactive interfaces to macro parameters and data with built in knowledge of the structure of the application and of required data and parameters This seems to be a necessary condition to allow unexperienced users to manage a simulation experiment without the need to cope with the internal structure of the simulation program itself Such modules will manage the data input from users and perform all the required checks on data consistency to guarantee at least to some extent that the following run can be actually performed 4 PHASE SCREEN GENERATION The phase screen generation module is aimed to generate phase screens corrupted by the atmospheric turbulence for the whole LGS AO simulation package Two metho
27. ypes Kolmogorov von Karman Methods FFT SHA Zernike Karhunen Loeve fractal Downward propagation Methods geometrical Fresnel polychromatic Upward propagation LGS Methods Fresnel speckle Wavefront sensing Types Shack Hartmann curvature Tip tilt sensing Separate or not Wavefront estimation Methods centroids curvatures global wavefront reconstruction Influence functions Methods analytical numerical Wavefront reconstruction Methods interaction matrix neural network Modal filtering Time filtering On tip tilt sensing or higher order wavefront sensing Methods Proportional Integrator Derivator predictor Hysteresis Linked to the mirror deformations Tip tilt mirror Separate or not Deformable mirror Types piezostack bimorph with various boundary conditions Laser tools Parameters power Rayleigh scattering Na layer structure saturation Data display Wavefronts images mirror shapes curves Data I O Types FITS HDF Performance evaluation __ Structure function variance analysis PSD Table 2 List of the proposed macro libraries with their methods purposes or parameters Macro Library Method Purpose Parameters Interaction matrix Methods zonal modal Command matrix Methods least square maximum likelihood optimal estimation WFS initialization Parameters geometrical parameters of the WFS WFS calibration Gives the reference measurements from static aberratio
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