On the normalization of scintillation autocovariance for generalized SCIDAR

The Generalized SCIDAR (Scintillation Detection and Ranging) technique consists in the computation of the mean autocorrelation of double-star scintillation images taken on a virtual plane located a few kilo-meters below the telescope pupil. This autocorrelation is normalized by the autocorrelation of the mean image. Johnston et al. in 2002 pointed out that this normalization leads to an inexact estimate of the optical-turbulence strength C(2)(N). Those authors restricted their analysis to turbulence at ground level. Here we generalize that study by calculating analytically the error induced by that normalization, for a turbulent layer at any altitude. An exact expression is given for any telescope-pupil shape and an approximate simple formula is provided for a full circular pupil. We show that the effect of the inexact normalization is to overestimate the C(2)(N) values. The error is larger for higher turbulent layers, smaller telescopes, longer distances of the analysis plane from the pupil, wider double-star separations, and larger differences of stellar magnitudes. Depending on the observational parameters and the turbulence altitude, the relative error can take values from zero up to a factor of 4, in which case the real C(2)(N) value is only 0.2 times the erroneous one. Our results can be applied to correct the C(2)(N) profiles that have been measured using the Generalized SCIDAR technique.

Applying SLODAR to measure aberrations in the eye

As a proof of concept we apply a technique called SLODAR as implemented in astronomy to the human eye. The technique uses single exposures of angularly separated "stars" on a Hartmann-Shack sensor to determine a profile of aberration strength localised in altitude in astronomy, or path length into the eye in our application. We report on the success of this process with both model and real human eyes. There are similarities and significant differences between the astronomy and vision applications.

Wind profiling based on the optical beam intensity statistics in a turbulent atmosphere

Reconstruction of the wind profile from the statistics of intensity fluctuations of an optical beam propagating in a turbulent atmosphere is considered. The equations for the spatiotemporal correlation function and the spectrum of weak intensity fluctuations of a Gaussian beam are obtained. The algorithms of wind profile retrieval from the spatiotemporal intensity spectrum are described and the results of end-to-end computer experiments on wind profiling based on the developed algorithms are presented. It is shown that the developed algorithms allow retrieval of the wind profile from the turbulent optical beam intensity fluctuations with acceptable accuracy in many practically feasible laser measurements set up in the atmosphere.

Atmosphere-like turbulence generation with surface-etched phase-screens

We built and characterized an optical system that emulates the optical characteristics of an 8m-class telescope like the Very Large Telescope. The system contains rotating glass phase-screens to generate realistic atmosphere-like optical turbulence, as needed for testing multiconjugate adaptive optics systems. In this paper we present an investigation of the statistical properties of two phase-screens etched on glass-plate surfaces, obtained from Silios Technologies. Those etched screens are highly transmissive (above 85%) from 0.45 to 2.5 microm. From direct imaging, their Fried parameter r0 values (0.43+/-0.04 microm and 0.81+/-0.03 microm, respectively, at 0.633 microm) agree with the expectation to within 10%. This is also confirmed by a comparison of measured and expected Zernike coefficient variances. Overall, we find that those screens are quite reproducible, allowing sub-millimetre r0 values, which were difficult to achieve in the past. We conclude that the telescope emulator and phase-screens form a powerful atmospheric turbulence generator allowing systematic testing of different kinds of AO instrumentation.

Implementation of fast-Fourier-transform-based simulations of extra-large atmospheric phase and scintillation screens

Fast-Fourier-transform-based simulations of single-layer atmospheric von Kármán phase screens and Kolmogorov scintillation screens up to hundreds of meters in size were implemented and tested for applications with percent range accuracy. The tests included the expected and the observed structure and pupil variance functions; for the phase, the tests also included the Fried turbulence parameter r0 measured by the seeing and by a simulated differential image motion monitor. The standard compensations used to correct the undersampling at low spatial frequencies were improved, and those needed for the high spatial frequencies were determined analytically. The limiting ratios of the screen sampling step to r0 and of the screen size to the pupil aperture were estimated by means of the simulated data. Sample results are shown that demonstrate the performances of the simulations for single-layer Kolmogorov and von Kármán phase screens up to 200 m in size and for Kolmogorov scintillation screens for pupils up to 50 m of aperture.

Horizontal scintillation detection and ranging Cn2(z) estimation

The strength of optical turbulence, Cn2(z), 2-3 m above ground level, was measured as a function of distance along a 1.23-km path by the simultaneous capture of the scintillation from two infrared laser sources. The data collected differ in a number of important aspects from the normal vertical scintillation detection and ranging (SCIDAR) data in astronomy. The SCIDAR inversion method for the horizontal path problem is outlined and demonstrated on experimental data collected from three field trials.

Generalized scintillation detection and ranging results obtained by use of a modified inversion technique

The measurement of the strength of atmospheric optical turbulence by use of a modified generalized SCIDAR (scintillation detection and ranging) inversion technique is outlined and demonstrated. This new method for normalizing and inverting scintillation covariances incorporates the geometry specific to generalized SCIDAR. Examples of profiles from two astronomical observation sites are presented.

Analysis of modes and behavior of a multiconjugate adaptive optics system

We study the so-called three-dimensional mapping of turbulence, a method solving the cone effect (or focus anisoplanatism) by using multiple laser guide stars (LGSs). This method also permits a widening of the corrected field of view much beyond the isoplanatic field. Multiple deformable mirrors, conjugated to planes at chosen altitudes among the turbulent layers, are used to correct in real time the wave fronts measured from the LGSs. We construct an interaction matrix describing the multiconjugate adaptive optics system and analyze the eigenmodes of the system. We show that the global tilt mode is singular because it cannot be localized in altitude, so that it must be corrected only once at any altitude. Furthermore, when the tilt from the LGS cannot be measured, the singularity of the global tilt yields the delocalization of particular forms of defocus and astigmatism. This imposes the use of a single natural guide star located anywhere in the corrected field to measure these modes. We show as an example that the cone effect can be corrected with a Strehl of 0.8 with four LGSs (tilt ignored) on an 8-m telescope in the visible when a single laser star provides a Strehl of 0.1. The maximum field of view of 100 arc sec in diameter can be reconstructed with an on-axis Strehl ratio of 30%. We also show that the measurement of the height of the layers can be done with current techniques and that additional layers, not accounted for, do not significantly degrade the performance in the configuration that we model.

Application of an exclusively binarized correlation-calculation method to wind velocity measurement by use of stellar scintillation patterns

An exclusively binarized method for the correlation calculation of image processing is presented with application to velocity measurements. The exclusively binarized correlation-calculation method is capable of determining the peak position of the correlation even with a small number of random-pattern images. Because the velocity is deduced from the movement of the correlation-peak position within a time interval, the method is suitable for the velocity measurement of random patterns. The method is applied to the measurement of the upper-atmospheric wind velocity by use of stellar scintillation patterns.

Temporal coherence of individual turbulent patterns in atmospheric seeing

We used a variation of the generalized scidar (scintillation detection and ranging) technique to examine the temporal coherence of turbulent patterns at different altitudes in the atmosphere above Palomar Observatory. This enables us to test the validity of a frozen turbulence hypothesis in the local reference frame of the moving atmosphere. The data set analyzed here contains three turbulent patterns, each at a different altitude, which remain internally coherent over time scales of 0.28-0.41 s. This measurement is significant, because it is made on a 5-m aperture, allowing moving patterns to be tracked over time scales longer than their own lifetimes.

Modeling scintillation from an aperiodic Kolmogorov phase screen

We propose a technique for the accurate modeling and simulation of scintillation patterns that are due to Kolmogorov statistics without assuming periodic boundary conditions. We show how the more physically justifiable assumption of smoothness results in a propagation kernel of finite extent. This allows the phase screen dimensions for an accurate simulation to be determined, and truncation can then be used to eliminate the unwanted spectral leakage and diffraction effects usually inherent in the use of finite apertures. A detailed outline of the proposed technique and comparison of simulations with analytic results are presented.