Results of experiments with the laser guide star adaptive optics system on the 3-meter Shane telescope at Lick Observatory have demonstrated a factor of 4 performance improvement over previous results. Stellar images recorded at a wavelength of 2 micrometers were corrected to over 40 percent of the theoretical diffraction-limited peak intensity. For the previous two years, this sodium-layer laser guide star system has corrected stellar images at this wavelength to approximately 10 percent of the theoretical peak intensity limit. After a campaign to improve the beam quality of the laser system, and to improve calibration accuracy and stability of the adaptive optics system using new techniques for phase retrieval and phase-shifting diffraction interferometry, the system performance has been substantially increased. The next step will be to use the Lick system for astronomical science observations, and to demonstrate this level of performance with the new system being installed on the 10-meter Keck II telescope.

This paper describes the effects of Laser Guide Star spot elongation and Rayleigh scattering on wavefront sensing performances. An analytical model of Rayleigh scattering and a numerical model of laser plume generation at the altitude of the atmospheric sodium layer were developed. These models, integrated into a general Adaptive Optics (AO) simulation, provide information about the non-uniform centroid measurement accuracy on the sensor sub-apertures. The effects of laser power, laser type, laser launching position, sensor sampling and sensor field of view on the AO loop performances are analyzed and discussed.

The performance of a sodium laser guide star adaptive optics system depends crucially on the characteristics of the laser guide star in the sodium layer. System performance is quite sensitive to sodium layer spot radiance, that is, return per unit steradian on the sky, hence we have been working to improve projected beam quality via improvements to the laser and changes to the launched beam format. The laser amplifier was reconfigured to a 'bounce-beam' geometry, which considerably improves wavefront quality and allows a larger round instead of square launch beam aperture. The smaller beacon makes it easier to block the unwanted Rayleigh light and improves the accuracy of Hartmann sensor wavefront measurements in the AO system. We present measurements of the beam quality and of the resulting sodium beacon and compare to similar measurements from last year.

We will present a system to perform closed-loop optical tests of the 64 cm diameter, 336 actuator adaptive secondary made at the Steward Observatory Mirror Laboratory. Testing will include Shack-Hartmann wavefront sensing and modal correction of static and dynamic aberrated wavefronts. The test optical system is designed so that experiments can be made with both the focal plane instrument and secondary installed in their normal configuration at the MMT, or with the same 9 m spacing in a laboratory test tower. The convex secondary will be illuminated at normal incidence through two 70 cm diameter lenses mounted just below. The artificial, aberrated star is projected from near the wavefront sensor in the Cassegrain focus assembly. Computer generated holograms correct for spherical aberration in the really optics at the test wavelengths of 0.594 and 1.5 micrometers . Atmospheric turbulence is reproduced by two spinning transmission plates imprinted with Kolmogorov turbulence. The Shimmulator will give us the opportunity to test fully the adaptive optics system before installation at the new MMT, hence saving much precious telescope time.

We present the first results of test performed on a reduced size adaptive secondary prototype named P36. The full size unit, named MMT336, is ready to be assembled and it is planned to install it at the 6.5m conversion of the Multiple Mirror Telescope by the end of this year. The design of the final unit consists of: a convex thin deformable mirror whose figure is controlled by 336 electro-magnetic force actuators, a thick reference shell and a third aluminum shell used for actuator support and cooling. The force actuator response function is adjusted using both open and closed loop compensation to obtain an equivalent position actuator thanks to nearly co-located capacitive position sensors. The digital real-time control and the unit monitoring is done using custom-made electronics based on DSPs. The preliminary dynamical test aimed at identifying the P36 mirror response function to obtain a proper dynamics compensation were successful. In fact two main results have been obtained: 1) an accurate identification of the feedforward matrix used to control the mirror 2) settling time of approximately 0.5 ms, well within the specifications. We also complement these lab results with results obtained from simulations of the full size mirror dynamics.

We have designed a new type of curved deformable mirror with 3000 actuators. It will be used at the 6.5 m MMT telescope in an adaptive optics system to correct the wavefront on a scale of 12 cm, for diffraction limited images in visible light and for high contrast imaging with a coronagraph in the near IR. The mirror's 51 cm diameter glass faceplate, 400 microns thick, will be actuated by tubular piezoceramic actuators on 8 mm centers. The mirror is made concave so it can be used in a simple, compact optical relay with no need for large collimator or camera elements. A prototype deformable mirror with 300 elements that test the support and assembly techniques is being built for lab test and will be tested in a closed loop adaptive optics system at the Steward Observatory.

Behavior of micromachined membrane deformable mirrors under continuous laser load has been investigated experimentally and theoretically. It was shown that load-induced variation of the membrane temperature and mechanical tension result in addition thermal deformation of the deformable mirror figure. Modeling the membrane tension and thermal deformation as functions of beam diameter, optical power and mirror design parameters, we found that the thermal resistance of the mirror substrate is critical for high- power operation. According to our estimations an optically- designed membrane mirror with 99.8 percent reflectivity can be safely loaded with up to 500W of optical power in a 10mm- diameter beam. This model was compared with experimental data obtained for micro-machined membrane deformable mirrors with five different types of reflective coatings loaded with up to 70W beam with power density of up to 20W/mm². We also demonstrated operation of a multilayer membrane mirror in a stable resonator of a diode-pumped YAG:Nd laser with output power of up to 4.5W.

Design of a wavefront sensing system for an adaptive optical system requires knowledge of the spatial content of the aberrations to be sensed. Rules of thumb using quantities such as the number of actuators across the diameter of a deformable mirror are often used, but these may not work well for system with irregular actuator configurations or significant inter-actuator coupling. A novel approach using Fourier transform analysis of a matrix decomposition of the deformable mirror influence function matrix is presented. This approach allows the calculation of the spatial content of the aberrations corrected by a deformable mirror with an arbitrary actuator configuration and the design of a wavefront sensor to support that deformable mirror.

The optimal track loop controller in an adaptive optics system is a function of the steering mirror dynamics, the temporal statistics of the input disturbance signal, measurement noise, and the sensor gain. The atmospheric input statistics and the sensor gain of a quadrant detector are slowly time-varying on a scale of minutes. If all parameters are known a prior, the analytical optimal controller is found by augmenting the dynamics of the input disturbance spectra and solving an H₂ optimization problem. Near optimal control is achieved by augmenting the mount jitter dynamics and a first order approximation of the atmosphere dynamics and finding the LQG/LTR controller. The optimal bandwidth to compensate for time-varying atmospheric disturbance and noise levels is found by optimizing the loop gain. Recursive least squares is used to estimate the sensor gain and optimize the bandwidth in real time. The only measurements necessary for optimization are the residual track errors from a high frame rate, low noise quad cell algorithm and from a low frame rate dense ccd array using a centroid algorithm. Provided the temporal variations in the sensor gain are slow, closed loop robust stability is guaranteed by constraining the optimization algorithm via projection. Simulation results are presented which verify that the constrained optimal controller is achieved under a variety of conditions.

Tactical airborne electro-optical systems are severely constrained by weight, volume, power, and cost. Micro- electrical-mechanical adaptive optics provide a solution that addresses the engineering realities without compromising spatial and temporal compensation requirements. Through modeling and analysis, we determined that substantial benefits could be gained for laser designators, ladar, countermeasures, and missile seekers. The developments potential exists for improving seeker imagery resolution 20 percent, extending countermeasures keep-out range by a factor of 5, doubling the range for ladar detection and identification, and compensating for supersonic and hypersonic aircraft boundary layers. Innovative concepts are required for atmospheric pat hand boundary layer compensation. We have developed design that perform these tasks using high speed scene-based wavefront sensing, IR aerosol laser guide stars, and extended-object wavefront beacons. We have developed a number of adaptive optics system configurations that met the spatial resolution requirements and we have determined that sensing and signal processing requirements can be met. With the help of micromachined deformable mirrors and sensor, we will be able to integrate the systems into existing airborne pods and missiles as well as next generation electro-optical systems.

This paper describes an extended-image tracking technique based on the maximum likelihood estimation. The target image is assumed to have a known profile covering more than one element of a focal plane detector array. It is assumed that the relative position between the imager and the target is changing with time and the received target image has each of its pixels disturbed by an independent additive white Gaussian nose. When a rotation-invariant movement between imager and target is considered, the maximum likelihood based image tracking technique described in this paper is a closed-loop structure capable of providing iterative update of the movement estimate by calculating the loop feedback signals from a weighted correlation between the currently received target image and the previously estimated reference image in the transform domain. The movement estimate is then used to direct the imager to closely follow the moving target. This image tracking technique has many potential applications, including free-space optical communications and astronomy where accurate and stabilized optical pointing is essential.

The possibility of designing and running an AO system working in the visible for observations with a large diameter telescope is still under debate due to the large number of sub-pupils required to properly sample the incoming WaveFront. On the other hand, the situation is much more relaxed in the IR, where r₀ is much larger, and several systems are forthcoming or already in operation. Morossi et al. proposed to support IR AO system with on-line multi-aperture selection devices. They showed that the image quality of a ground-based telescope in the visual could be improved by means of pupil segmentation and on-line multi- sub-aperture selection notwithstanding the large D/r₀ ratio.

Power spectra function was used usually to describe the time domain characteristic of atmosphere disturbed wavefront. Power spectra reject function, which defines as the ratio of the power spectra function of the close-loop compensated wavefront to the open-loop disturbed wavefront, was used to describe the control effect of an adaptive optical system. In this paper the control effect of the Zernike wavefront modals for an adaptive optical system using direct-gradient wavefront reconstruction algorithm was analyzed by using the power spectra reject function of Zernike model coefficients. The dynamic models of Zernike modal compensation for the direct-gradient algorithm were established. The power spectra reject functions were calculated from the theoretic model and compared with those gotten from experimental data. It is shown that there is coupling between some Zernike modals while using the direct-gradient algorithm. Although the control bandwidth was affected slightly, the power spectra reject function of the coupled Zernike modals become worse at low frequency range, this causes the wavefront compensation effect descended to some degree.

Mellin transform techniques are applied to develop power series formulas to efficiently evaluate covariances for zernike representations of turbulence-induced phase distortions along a pair of ray paths through the atmosphere from one or several sources at finite or infinite range. The formulas also apply when the phase distortions are temporally filtered by a closed loop adaptive optics system. The power series formulas are developed using an automated computer logic algorithm designed to solve multiple contour integrals in multiple complex planes resulting from the application of Mellin transform techniques. Results are presented for the von Karman turbulence spectrum with a finite outer scale. Amplitude scintillation effects are neglected. The Taylor hypothesis is assumed to model the temporal behavior of the turbulence using either a fixed or random wind profile. The resulting formulas are weighted integrals of the refractive index structure constant C_n²(z), where the weighting functions are power series in from one to six indices depending on the beacons used and the choices made regarding the atmospheric turbulence spectrum and the direction of the wind.

A 21-element adaptive optics system installed at the 2.16m telescope of Beijing Astronomical Observatory has been in operation. It is made up of a pair of shearing interferometer (SI), a 21-element deformable mirror, a fast steering mirror, a digital wavefront processor, a precise tracking subsystem and a PtSi IR CCD camera. In this paper the performance of the system will be briefly introduced. Its observation results in IR K band and in visible band are reported. For the system, 0.25 arcsec resolution has been achieved in IR K band, which approaches the diffraction limit of the 2.16m aperture. In visible band, 0.13arcsec resolution has been also achieved. For the star of magnitude 9.^m2, the compensation of the system is still effective. The error rejection bandwidth of the system can be adjusted in the range from 5Hz to 40Hz according to the beacon magnitude and the strength of the atmospheric turbulence.

We discuss the design of the laser guide star system to be implemented with ALTAIR, the Gemini North adaptive optics system. We give an overview of the sodium physics in order to understand why some lasers are more efficient than others to produce bright artificial stars. We present some simulation results which set the laser output power requirement when launching a perfect beam to the sky. Preliminary designs for the beam transfer optics, the laser launch telescope and the safety systems are also presented.

A laboratory adaptive optics system has been built for testing the wave front sensor hardware and software for the new Multiple Mirror Telescope adaptive optics system. The system will also allow different wave front reconstruction and prediction schemes to be examined. The laboratory system contains a silicon micromachined adaptive mirror with 37 electro-static actuators as well as a novel approach for generating atmospheric turbulence. The design and initial testing of the system are presented.

High resolution spectroscopy experiments with visible adaptive optics (AO) telescopes at Starfire Optical Range and Mt. Wilson have demonstrated that spectral resolution can be routinely improved by a factor of approximately 10 over the seeing-limited case with no extra light losses at visible wavelengths. With large CCDs now available, a very wide wavelength range can be covered in a single exposure.

Adaptive optics (AO) coupled to laser guide star systems is crucial to future ground based astronomical observations. It allows correction of image distortion caused by the Earth's turbulent atmosphere, over a hugely larger fraction of the sky than achieved by using only natural stars. Yet there are still very few such systems producing any sort of scientific results. ALFA, now offered on a shared risk basis as a user- instrument at Calar Alto Observatory in Spain, is continuing to improve its performance during closed loop operation on both natural and laser guide stars. The ability to close the loop on the LGS through thin cirrus cloud has the potential to increase the number of nights previously considered suitable for the laser by a factor of about two. In particular, science observations carried out on such a night are described. As part of the TMR network for Laser Guide Stars at Large Telescopes we are studying the distribution of atoms in the mesospheric sodium layer and its evolution over time. Additionally, a new experiment to provide an on- line monitor of the mesospheric sodium layer has been proposed and the results of a simulation are presented. This study will be of importance to large telescopes with laser stars at good astronomical sites where accurate statistics of the sodium layer are required, both for optimal scheduling of observations and for keeping the wavefront sensor focused on the LGS.

We present the requirements, design, and resulting new layout for the laser guide star/natural guide star adaptive optics (AO) system on the 3-meter Shane telescope at Lick Observatory. This layout transforms our engineering prototype into a stable, reliable, maintainable end-user- oriented system, suitable for use as a facility instrument. Important new features include convenient calibration using proven phase-shifting diffraction interferometer or phase- diversity techniques; a new scatter rejection in LGS mode and better guide-star selection NGS mode; high-sensitivity, wide-field acquisition camera; and significant improvements in adjustment motorization and optomechanical stability.

We demonstrate the recovery, without a priori object knowledge, of the unknown object and point spread functions (PSFs) from multiframe focal-plane data. By modeling the object Fourier spectrum as an unprejudiced linear combination of the cross-spectra of the measurements and the PSFs, we significantly reduce the number of degrees-of- freedom for the blind deconvolution problem.

The adaptive optical system for the Starfire Optical Range 3.5-meter telescope includes a SHack-Hartmann wavefront sensor (WFS) with 30 by 30 subapertures and a continuous facesheet deformable mirror (DM) with 31 by 31 actuators within the telescope aperture. Time histories of turbulence- induced phase distortions have been estimated from WFS gradient measurements and DM actuator commands acquired simulators with the adaptive optics loop closed. The statistics of these phase distortion profiles have been characterized in terms of spatial structure functions, Zernike coefficient statistics, and temporal power spectral densities. The results obtained are in good agreement with predictions based upon Kolmogorov theory.

We present a technique that can be used to quantify the frozen flow hypothesis with data from wavefront sensors such as those found in adaptive optics systems. The method is first tested with simulated data. Analyzing data from the 1.5-m and 3.5-m telescopes at the Starfire Optical Range, we then find that the frozen flow hypothesis is an accurate description of the temporal development of atmospheric turbulence on time scales on the order of 1-10 milliseconds, but that significant deviations from the frozen flow behavior are found for longer time scales.

A phase-shifting diffraction interferometer (PSDI) has been integrated into an adaptive optics (AO) system developed by LLNL for use on the three meter Shane telescope at Lick Observatory. The interferometer is an all fiber optic design, which is extremely compact. It is useful for calibrating the control sensors, measuring the aberrations of the entire AO optical train, and measuring the influence functions of the individual actuators on the deformable mirror. The PSDI is particularly well suited for this application because it measures converging, quasi-spherical wavefronts, such as are produced by an AO imaging system. Thus, a PSDI can be used to measure the aberrations of the entire AO system, in-situ and without errors introduced by auxiliary optics. This provides an extremely accurate measurement of the optical properties of the AO system.

An optical instrument for measuring the thickness of a thin gap or transparent film is presented. It will be used to calibrate the adaptive secondary mirror under development for the Steward Observatory 6.5 m Multiple Mirror Telescope. Capacitative sensors in the mirror assembly measure dynamically the thickness of the nominally 50 micrometers air gap between the deformable mirror and a glass reference body. The miniature interferometer has been developed to accurately determine the gap thickness so that the capacitive sensor may be calibrated. Interference fringes are produced by illuminating an air gap, which is between two reflective surfaces, with monochromatic plane waves and observing the reflected light. Intensity variations are measured as the wavelength of illumination is varied over an octave. The film thickness is determined by correlating the observed fringes with those modeled for different gaps. Absolute measurement to an accuracy of a small fraction of a wavelength is possible.

The influence function matrix of an adaptive optical system defines the mapping between commands to the deformable mirror actuators and the outputs of the wavefront sensor. The condition number of that matrix can be used to quantify the controllability and observability of the system. This condition number is a function of both deformable mirror parameters and wavefront sensor parameters. Its dependence on the grating period and the subaperture size for a shearing interferometer wavefront sensor is examined through simulation studies and useful design guidelines are developed.

Any adaptive optics system must be calibrated with respect to internal aberrations in order for it to properly correct the starlight before it enters the science camera. Typical internal calibration consists of using a point source stimulus at the input to the AO system and recording the wavefront at the output. Two methods for such calibration have been implemented on the adaptive optics system at Lick Observatory. The first technique, Phase Diversity, consists of taking out of focus images with the science camera and using an iterative algorithm to estimate the system wavefront. A second technique sues a newly installed instrument, the Phase-Shifting Diffraction Interferometer, which has the promise of providing very high accuracy wavefront measurements. During observing campaigns in 1998, both of these methods were used for initial calibrations. In this paper we present results and compare the two methods in regard to accuracy and their practical aspects.

This paper describes the construction and testing of the Shack-Hartmann wavefront sensor camera for the new MMT adaptive optics system. Construction and use of the sensor is greatly simplified by having the 12 X 12 lenslet array permanently glued to the detector array, obviating the need for any further realignment. The detector is a frame transfer CCD made by EEV with 80 by 80 pixels, each 24 microns square, and 4 output amplifiers operated simultaneously. 3 by 3 pixel binning is used to create in effect an array of quad-cells, each centered on a spot formed by a lenslet. Centration of the lenslet images is measured to have an accuracy of 1 micrometers rms. The maximum frame rate in the binned mode is 625 Hz, when the rms noise is 4.5-5 electrons. In use at the telescope, the guide star entering the wavefront sensor passes through a 2.4 arcsec squares field stop matched to the quall-cell size, and each lenslet samples a 54 cm square segment of the atmospherically aberrated wavefront to form a guide star image at a plate scale of 60 micrometers /arcsec. Charge diffusion between adjacent detector pixels is small: the signal modulation in 0.7 arcsec seeing is reduced by only 10 percent compared to an ideal quad-cell with perfectly sharp boundaries.

This paper gives a general overview of the application of focal plane masks to adaptive optical wavefront sensing systems, and shows how they are related to several wavefront sensor used in optical shop testing. The results of several numerical simulation of a wavefront sensor based on a phase contrast type focal plane mask are then presented. In the last section, we outline a proposal for a wavefront sensor based on a dark ground type focal plane mask. This method can be used in conjunction with fiber based optical interferometers to yield an adaptive optics system which does not need to take corrected light from the observation path for use in the analysis of the aberrations. Only aberrated light is taken from the observation path and sent to the wavefront sensor, thus creating a very economical wavefront sensor.

Adaptive optics has been successfully used in astronomy to obtain near diffraction limited images. It also can be used to improve the laser beam quality. In this paper, a test that a He-Ne laser was used to simulate an annular beam and was cleaned up by the 61 elements adaptive optical system is reported. The results show that the beam quality is improved.

For non-Kolmogorov turbulence, phase structure function, residual phase structure function and long-exposure modulation transfer function (MTF) of low-order correction adaptive optical system are deduced by introducing generalized phase spatial spectrum. The analysis shows long- exposure MTF is as functions of (Beta) , which is the power- law exponent of phase power spectrum, and (rho) ₀, which indicates the strength of atmospheric turbulence. Numerical results of long-exposure MTF, Strehl ratio and FWHM for different (Beta) and (rho) ₀ are presented under the following conditions respectively: (1) the wavefront disturbance is not correcte,d namely open-loop; (2) the wavefront tilts are corrected; (3) one order and two order modes are corrected.

Feedback control theory offers several useful tools for analysis of adaptive optics systems. The basic tools of single-input-single-output analysis are applied to design first order and optimal filters for a specific loop bandwidth or gain margin as a function of latency and sample rate. Optimizing filter loop band-width as a function of temporal disturbance and noise statistics is addressed with respect to the internal model principles. Latency, due to camera readout and processing time, is shown to be the primary design driver for optical AO system performance. The effects of wavefront sensor saturation are discussed and simulation and experimental results are presented.

PASS-2 is an experiment designed to perform photometry of the polychromatic laser guide star. The tilt of an atmospherically distorted wave front coming from an astronomical object cannot be determined with a monochromatic laser guide star. If it is possible to produce a laser guide star that emits light at different wavelengths, however, the tilt can be determined from the measurable differences between the tilts at the different wavelengths. This is the concept of the polychromatic laser guide star. The PASS-2 experiment is a step towards an implementation of an adaptive optics system that uses a polychromatic laser guide star for the wave front tilt measurement. The goal of the experiment is to validate the feasibility of a polychromatic laser guide star adaptive optics system and to determine the laser parameters that produce the optimal return flux from the polychromatic laser guide star. To this end, the return flux from the polychromatic laser guide star at 330 and 589.6 nm will be measured as a function of laser parameters, atmospheric conditions, and the density of the mesospheric sodium layer.

We present the results of a compete set of static and dynamic runs of the FEA model of the MMT adaptive secondary. The thin mirror is the most delicate component of the MMT adaptive secondary unit, as it provides the deformable optical surface able to correct the incoming wavefront. The static performances are evaluated as a function of the various load cases arising form gravitational loads and from the forces deriving from the magnetic interactions between actuators. In addition, computations were performed to assess the dynamic response to the high bandwidth, adaptive correcting force.s In both cases, the performances of the adaptive mirror design are able to accommodate the severe specifications.

In adaptive optical system, the configuration of the sub- apertures of wave-front sensor and deformable mirror actuators will affect the wave-front correcting ability and stability of the system. For annular profile laser beam, six kinds of annular configurations with sub-apertures of wave- front sensor arranged around the annular and a square configuration with square sub-apertures of wave-front sensor are simulated. These configurations are compared each other in the wave-front correcting ability and stability. The optimum configuration for annular beam is selected.

The probability distribution function for the mixing scatter ratio is derived and used to model variations in total backscatter coefficient and extinction profiles in the visible and the near IR. The profiles, based on 25 years of lower stratospheric aerosol measurements, are used to estimate signal-to-noise ratio, laser-pulse energy, and wavefront measurement error with respect to backscatter strength, guidestar pulse length and altitude, and read noise. The results show that for a given wavefront error, (1) visible guidestars require less pulse energy for aerosol concentrations near background where molecular backscatter dominates, and (2) for high aerosol loading following a major volcanic event, a NIR guidestar requires a lower pulse energy than for visible wavelength sensing.

The diffraction-limited spatial cut-off frequency D/(lambda) of a telescope aperture is not an absolute limit to imaging resolution, and various methods exist to obtain spatial information at frequencies much higher than D/(lambda) under specialized circumstances. In particular, spectrally dissimilar objects can be discerned at separations far smaller than the Airy radius, by exploiting both the spatial and spectral information available. This general method is applied in differential speckle interferometry and chromatic position difference imaging. We describe proposed experiments, using the University of Durham's ELECTRA adaptive optics instrument, to perform a variant of chromatic position different imaging at IR wavelengths, but incorporating the very large resolution gain provided by AO image correction. This method, related in principle to differential speckle interferometry, involves measuring the shift of image centroid with wavelength across a spectrally dispersed image. The implementation of this experiment on ELECTRA requires only a simple modification to the standard ELECTRA optical configuration. The optical arrangement is described, and examples of astronomical applications are presented.

The ALFA-Laser of the MPE/MPIA adaptive optic system utilizes a 4W cw-laser for the creation of a sodium layer guide star. The artificial star serves as a reference source for the adaptive optics system installed at the Calar Alto observatory in souther Spain. Several distortion sources are affecting the laser beam and result in a laser guide star spot size too large on which to lock the adaptive optics loop properly. Therefore a number of analysis tools have been installed just before the laser beam expander and measurements of the beam quality have been performed. In this contribution we present parts of the experimental setup and results of these measurements. In addition we report on experimental studies of the guide star brightness when exciting the sodium layer with different polarization states of the laser radiation. A surprisingly large gain in response flux, when using circular polarization, has been measured. The complicated behavior of the polarization state with telescope position, due to phase changes at the beam relay mirrors, makes a control loop necessary to keep the projected beam optimal.

In the framework of the European Training and Mobility of Researchers program, a network named 'Laser Guide Star for 8-m Class Telescopes' has been funded. One task of this network consists in developing a numerical simulator devoted to laser guide star adaptive optics systems for astronomy. The principal aim of this simulator is to support investigations about laser guide star problems like cone effect and tip-tilt indetermination. In order to allow all kinds of solutions to these problems, the simulator structure was built as versatile as possible. This software package includes several modules that allow atmospheric perturbations simulation, geometrical wavefront sensing and reconstruction, points-spread function calculation, time filtering, etc. The paper describes the version 1.0 of this simulator called LA³OS², together with an example of application.

We have experimentally demonstrated for the first time a method for sensing wavefront tilt with a laser guide star (LGS). The tilt components of wavefronts were measured synchronously from the LGS using a telescope with 0.75 m effective aperture and from Polaris using a 1.5 m telescope. The Rayleigh guide star was formed at the altitude of 6 km and at a corresponding range of 10.5 km by projecting a focused beam at Polaris from the full aperture at the 1.5 m telescope. Both telescope mounts were unpowered and bottled down in place allowing us to substantially reduce the telescope vibration. The maximum value of the measured cross-correlation coefficient between the tilt for Polaris and the LGS is 0.71. The variations of the measured cross- correlation coefficient in the range from 0.22 to 0.71 are caused by turbulence at altitudes above 6 km, which was not sampled by the laser beacon, but affected the tilt for Polaris. It is also caused by the cone effect for turbulence below 6 km, residual mount jitter of the telescopes, and variations of the S/N. The experimental results support our concept of sensing atmospheric tilt by observing a LGS with an auxiliary telescope and indicate that this method is a possible solution for the tip-tilt problem.

We report preliminary results of wavefront tilt measurements for the star Polaris at the Starfire Optical Range 3.5 m telescope at Kirtland AFB in Albuquerque, NM. We measured full aperture gradient tilt by using five pupil masks representing aperture diameters from 0.1m to 3.5m. Two optical configurations were exploited. In the first configuration, five images of Polaris were recorded simultaneously on one camera frame. The telescope was operated in its normal sidereal pointing mode. In the second configuration, pupil masks were changed sequentially. Additional measurements were collected with the telescope bolted to attempt to mitigate the effects of mont jitter. The coordinate system of the tilt measurement was rotated so that the cross-correlation coefficient between X- and Y-axis tilt components is equal to zero. Several interesting results were obtained. We observed anisotropy of the statistics of wavefront tilt. The observed one-axis tilt variances are unequal and the horizontal tilt variance is consistently greater than the vertical one. We believe these effects dare due to anisotropy of the large evidence of the effects of non-Kolmogorov turbulence on wavefront tilt. The measured tilt variance vs. aperture diameter curve has a knee beyond which the tilt variance no longer decreases for larger diameters. In the low and high frequency range the tilt power spectra obey the f^-2/3 and f^-11/3 power law, respectively. The tilt temporal correlation scale for the 3.5m aperture is on the order of 0.4 sec.