The profile of atmospheric turbulence strength along a laser propagation or imaging path is thought to significantly influence performance. We use wave optics simulation to evaluate performance under random variations of turbulence profiles along a 50-km propagation path. Performance is given by power in the bucket (PIB) strehl in a (lambda) /D bucket. For a point source and under the conditions we investigated, we conclude that, in addition to the Rytov parameter, knowledge of r₀ can significantly improve performance prediction.

The Rytov parameter is a common name given to the log- amplitude variance predicted by an approximate solution to Maxwell's equations for propagation through media with random index of refraction (Rytov theory). Empirical evidence suggests that the Rytov parameter is a non- observable in many practical experiments where the variance of irradiance saturates, an effect not predicted by the standard theory. Nevertheless, the Rytov parameter is useful as an indicator of integrated turbulence strength for extended propagation and thus a desirable experimental quantity to estimate. In this work, we propose an optical configuration and related analysis techniques that provide a practical method for determining the Rytov parameter when scintillometry-based methods fail. This method employs differential-tilt measurements, resulting in a measurable quantity which is proportional to the Rytov parameter and for which Rytov theory is a good approximation. The differential-tilt technique is also insensitive to gimbal motion and additive noise. We illustrate that this method provides approximately 5% relative error in determining the Rytov parameter and may be used to characterize atmospheric turbulence well beyond the limits of conventional scintillometry.

Limited samples of the turbulence structure in the tropopause suggest that conventional models for atmospheric turbulence may not apply through this portion of the atmosphere. This paper discusses the instrumentation requirements, design and calibration of a balloon borne sensor suite designed to accurately measure the distribution and spectral spatial character of the index of refraction fluctuations through the tropopause. The basis for the data system is a 16 bit dynamic range, high data rate sample and hold instrumentation package. Calibration and characterization of the constant current anemometers used in the measurements show them to have a frequency response greater than 170 Hz at the -3 Db point and sufficient resolution to measure a C_n² of 1 x 10^-19 cm^-2/3. A novel technique was developed that integrates the over 20 signals into two time correlated telemetry streams. The entire system has been assembled for a flight in the late summer of 2000.

We describe the current status of the ELP-OA project in which we try to demonstrate in practice that it is possible to measure the tilt of a wave front using only a polychromatic laser guide star and no natural guide star. The first phase of ELP-OA, consisting of feasibility experiments, has recently been completed successfully. This paper provides an overview over the results of this first phase and over the continuation of the ELP-OA project.

Phase retrieval is a non-linear technique to recover the phase in the Fourier domain using intensity measurements at the image plane and additional constraints. We describe a method to solve the phase retrieval problem using linear iterations near the solution, a technique that gives both physical insight into phase retrieval and numerical results. When phase retrieval is done on data from subdivided apertures, there is a loss of information about the relative piston terms of the subapertures and this error has been quantified. We find that there is a smaller wavefront error when estimating the phase form a full aperture than from a subdivided aperture. However, using a combination of intensity measurements from a full and a subdivided aperture gives a much better performance. The error in estimating the wavefront also increases with increasing turbulence levels.

We propose an optimal approach for the phase reconstruction in a large Field Of View (FOV) for Multiconjugate Adaptive Optics (MCAO). This optimal approach is based on a Minimal Mean Square Error (MMSE) estimator that minimizes the mean residual phase variance in the FOV of interest. It accounts for the C_n² profile in order to optimally estimate the correction wavefront to be applied to each DM. This optimal approach also accounts for the fact that the number of DM will always be smaller than the number of turbulent layers since the C_n² profile is a continuous function of the altitude h. Links between this optimal approach and a tomographic reconstruction of the turbulence volume are established. In particular, it is shown that the optimal approach consist in a full tomographic reconstruction of the turbulence volume followed by a projection on the deformable mirrors accounting for the considered FOV of interest. The case where the turbulent layers are assumed to match the mirror positions (model- approximation approach), which might be a crude approximation, is also considered for comparison. This model-approximation approach will rely on the notion of equivalent turbulent layers. A comparison between the optimal and model-approximation approach is proposed. It is shown that the optimal approach provides very good performance even with small number of DM's (typically one of two). Accurate results are obtained, on simulation for a 4- m telescope on a 150 x 150 arcseconds FOV only using 3 guide stars and 2 DM.

This article presents an analysis of scintillation effects after propagation through atmospheric turbulence. It uses an expansion of the log-amplitude on the Zernike modes in the weak perturbation regime. An analytical evaluation of the error introduced by scintillation on wavefront slope measurements is then derived. For a typical profile corresponding to astronomical conditions, scintillation introduces a wavefront measurement error whose standard deviation is of the order of (lambda) /20 in the visible.

The problem of optimally pointing a laser beam is commonly referred to as the tracking problem. Accurately pointing the beam in the presence of scintillated atmospheric conditions is difficult. The objective here is to understand the limitations of how well we can point a laser beam to a target point under long path, scintillated conditions. We investigate performance for both the case of tilt-only compensation and tilt compensation used in conjunction with higher order compensation. For the scintillated conditions considered here we find that only when we considered higher order compensation in conjunction with tracking do we see benefit from tracking. This leads us to claim that the tracking problem is difficult, if not impossible, to decouple form the high order compensation problem for the scintillated conditions considered in this work.

The effects of non-uniform wind on the arrival angle temporal power spectrum of the spherical wave are numerically calculated and analyzed by using analytical formulae in Rytov approximation. The finite outer and inner scale is also included in the formulae by using modified Von-Karman spectrum of the turbulence. The results show that the non-uniform wind velocity through the propagation path will induce much change in line shape of the power spectrum. There are three scaling regions in arrival angle power spectrum of a spherical wave from Rayleigh star, which are proportional to f^2/3, f^5/3, f^10/3 (or f^11/3), respectively. In some conditions (small averaged wind velocity, relative larger random wind in horizontal propagation path near the ground), the power spectrum of spherical-wave is approximately proportional to f^-8/3 in much wider frequency region, rather than f^-11/3 as in uniform wind condition.

This paper has established the models calculating aero-optic effect of the hypersonic flying vehicle, and using a new turbulence hypothesis model, which is on base of Johnson- King & k-(epsilon) equation. Then the calculating program was designed. In the last part, the calculating result was discussed.

The point spread function (PSF) of an adaptive optics system evolves in the Field Of View (FOV). This variation strongly limits the conventional deconvolution methods for the processing of wide FOV images. A theoretical expression of this PSF variation is derived. This expression is both validated on simulations and experimental data. It is then applied to the a posteriori processing of stellar fields. Using the available prior information about the object (point-like sources), this technique allows the restoration of the star parameters (positions and intensities) with a precision much better than the conventional methods, in a FOV much larger than the isoplanatic field.

This paper deals with the restoration of the shape of an object observed with a high-resolution infrared imaging device, through atmospheric turbulence. The propagation path is quite long (a few tenth kilometer) and the image is thus disturbed. A sequence of short-exposure images of the interesting object is recorded. We can see that the object shape fluctuates randomly during the sequence, but that its edges remain sharp, thanks to the very short exposure time. A bayesian analysis of the Fourier descriptors associated to the edges shows that the optimal shape is the one corresponding to the mean Fourier descriptors. We thus propose two ways to estimate this shape. The first one consists in matching point-to-point each pair of successive edges in the sequence and take the average position of each point. The second one consists in applying an active contour (a snake) on the images. This contour evolves with the object shape during the sequence. From the set of positions of its nodes, we can calculate quite easily the optimal shape.

Space-variant blur occurs when imaging through volume turbulence over sufficiently large fields of view. Space- variant effects are particularly severe in horizontal-path imaging, slant-path (air-to-ground or ground-to-air) geometries, and ground-based imaging of low-elevation satellites or astronomical objects. In these geometries, the isoplanatic angle can be comparable to or even smaller than the diffraction-limited resolution angle. Clearly, space-invariant methods used in conjunction with mosaicing will fail in this regime. Our approach to this problem has been to generalize the method of Phase-diverse Speckle (PDS) by using a physically motivated distributed phase-screen model to accomplish both pre- and post-detection correction. Previously reported simulation results have demonstrated the reconstruction of near diffraction-limited imagery using imagery which was severely degraded by space-variant blur. In this paper, we present a novel adaptation of the space- variant PDS scheme for use as a beacon-less wavefront sensor in a multi-conjugate AO system when imaging extended scenes. We then present results of simulation experiments demonstrating that this multi-conjugate AO-compensation scheme is very effective in improving the quality and resolution of collected imagery.

Atmospheric turbulence adversely affects imaging systems by causing a random distribution of the index of refraction of the air through which the light must propagate. The resulting image degradation can seriously undermine the effectiveness of the sensor. In many astronomical systems, which typically have a very narrow field of view, the entire image can be modeled by the convolution of the object with a single point spread function (PSF), and as a result of the narrow field of view, adaptive optical systems can be highly effective in correcting astronomical images. In the case of tactical infrared sensors the field of view is generally much larger than the isoplanatic angle, and the image cannot be modeled by a single point spread function convolved with the scene. Hence, adaptive optical solutions to wide angle infrared imaging over horizontal paths would be difficult, if not impossible, and post-detection processing of the images is required to mitigate turbulence effects. The overall effect of turbulence within a given isoplanatic path is not as strong as in the astronomical imaging case due to shorter paths and longer wavelengths. Tilt and low order turbulence modes dominate the aberration experienced within individual isoplanatic patches, greatly simplifying image reconstruction problems. In this paper we describe an algorithm for processing video sequences capable of partially correcting these turbulence effects. The algorithm is based on block matching algorithms used in video compression. Simulation results show that this algorithm reduces the squared error of the imagery, and subjectively better images are obtained.

The Multispectral Thermal Imager (MTI) is a satellite system developed by the DoE. It has 10 spectral bands in the reflectance domain and 5 in the thermal IR. It is pointable and, at nadir, provides 5m IFOV in four visible and short near IR bands and 20m IFOV at longer wavelengths. Several of the bands in the reflectance domain were designed to enable quantitative compensation for aerosol effects and water vapor (daytime). These include 3 bands in and adjacent to the 940nm water vapor feature, a band at 1380nm for cirrus cloud detection and a SWIR band with small atmospheric effects. The concepts and development of these techniques have been described in detail at previous SPIE conferences and in journals. This paper describes the adaptation of these algorithms to the MTI automated processing pipeline (standardized level 2 products) for retrieval of aerosol optical depth (and subsequent compensation of reflectance bands for calibration to reflectance) and the atmospheric water vapor content (thermal IR compensation). Input data sources and flow are described. Validation results are presented. Pre-launch validation was performed using images from the NASA AVIRIS hyperspectral imaging sensor flown in the stratosphere on NASA ER-2 aircraft compared to ground based sun photometer and radiosonde measurements from different sources. These data sets span a range of environmental conditions.

Statistical variations in the size, position, shape and orientation of hexagonal ice crystals in a 3D volume complicates the modeling of image transfer through cirrus clouds. These variations will give rise to fluctuations in image quality as measured by the MTF of a single realization of a cloud/receiver combination. Computing the average MTF from several realizations of the cloud/receiver combination, allowing for a different cloud composition on every realization can alleviate these fluctuations. In this paper, we present the result of the multiple MTF for clouds of different optical depths, distinguishing the separate contributions of scattered as well as unscattered light. Finally, we apply the MTF thus generated to create images of objects as seen through the cloud.

Recent studies pointed out the correlation existing between the differential attenuation measurements, made using frequencies falling around the 22.235 GHz absorption line of water vapor, and the shape of the water vapor profiles. Such evidence induced us to develop a deterministically based profile retrieval procedure that exploits several differential attenuation measurements made at several frequencies around 22.235 GHz. In this paper, after having described the aforementioned deterministic procedure, a transmission system is proposed to obtain the differential attenuation measurements for a quasi-vertical satellite- Earth multifrequency link. Such transmission system is based on a sinusoidal amplitude modulation and a feasibility study about the minimum exploitable signal-to-noise ratio was considered as well. Both the retrieval procedure and the results of the feasibility study on the transmission system are then tested through simulations of multifrequency attenuation measurements. Such simulations are based on an atmospheric propagation model (MPM: Millimeter-wave Propagation Model) and on real radiosonde data providing profiles of temperature, pressure, and water vapor concentration.

On a basis of a Monte Carlo simulation model, the atmospheric aerosol contributions to laser beam widening for a horizontal propagation path at various elevations is estimated and compared with beam widening caused by turbulence. It is shown that the beam widening caused by atmospheric aerosols is significant, often even more significant than that caused by turbulence.

The Self-Calibrating H₂O and O₃ Nighttime Environmental Remote Sensor (SCHOONERS) is a compact, integrated UV-IR imaging spectrograph and imager. The instrument has a 25 cm diameter aperture and employs a two- axis gimbaled telescope to provide acquisition and tracking of the star. It also uses a two-axis high-precision vernier mirror to correct for spacecraft jitter and maintain the star within the field-of-view. The imaging spectrograph, covering a spectral range between 300 and 900 nm, measures the varying absorption of starlight as a star sets through the nighttime Earth's atmosphere to determine vertical profiles of atmospheric constituents. The relative star position measured by the co-aligned imager not only provides position feedback to the acting tracking loop of the vernier mirror, but also measures the star refraction angle for determining the atmospheric density and temperature profiles. The SCHOONERS scanning platform and its high- precision tracking mirrors provide 44 microradian azimuth pointing stability and 60 microrad altitude tracking accuracy (3(sigma) ). Its built-in image tracking and motion compensation mechanism, coupled with its small size and limited spacecraft resources required, makes it suitable for deployment on existing and future commercial spacecraft platforms as an instrument-of-opportunity after the year 2002. A laboratory facility has been developed to demonstrate the instrument performance, especially its capability to acquire and track a setting, refracting, and scintillating star, to compensate for various degrees of platform jitter, and to provide the pointing knowledge accuracy required for the determination of atmospheric density and temperature. Hardware includes an accurately moving variable intensity point source to simulate the star and motion stages to generate jitter at the instrument. Software simulates the stellar refraction, attenuation, and scintillation for a full end-to-end test of the instrument.

Conventional beam control techniques are often divided into two categories. Tracking control addresses the stabilization of the beam on a target, whereas higher-order control addresses the broadening of the beam due to atmospheric aberrations. For scenarios where strong turbulence is distributed throughout the entire propagation path, the effectiveness of conventional beam control techniques is greatly reduced over less-stressing scenarios. In this case, the effect on objective measures of beam compensation performance is not equally distributed between tracking and higher-order control. In this study, we have developed an analytic framework in which to quantify the efficiency of each type of control with respect to standard compensation performance metrics. This analysis highlights that the performance of each type of control must be assessed relative to the other. Using wave-optics simulation along with out analytic framework, we quantify the efficiency of a centroid tracker and an adaptive optics system using standard least-squares reconstruction with a point-source beacon for atmospheric Rytov parameter values of 0.1 < R < 1.0. We find that R<0.4, both tracking and higher-order control contribute equally to the observed performance degradation. For R>0.5, however, conventional higher-order control is the principal source of compensation performance degradation.