Imaging through volume turbulence gives rise to anisoplanatism (space-variant blur). The effects of volume turbulence on imaging are often modeled through the use of a sequence of phase screens distributed along the optical path. Wallner recently derived a prescription for the optimal functional form and location of multiple phase screens for use in simulating the effects of volume turbulence in infinite-range imaging geometries. We generalized Wallner's method to accommodate the finite range case and to have a more optimal functional form for the phase screens. These methods can also be used for designing a multi-conjugate AO system. Examples of optimal solutions are given for horizontal-path finite-range imaging cases.

Electro-optical sensors on future aircraft and spacecraft will be used for targeting and situational awareness and will be required to have a number of demanding technical characteristics. A key technical challenge to achieving these characteristics is the development of inexpensive, high degree of freedom optical wave front control devices, and the development of effective algorithms for controlling these devices. In this paper we present our research in the development of phase retrieval-based wavefront control algorithms. We have developed wave front control algorithms that allow for dynamic far-field beam steering and shaping, and aberration compensation. Our approach is based on non conventional wave front control achieved by solving a multi- dimensional minimization problem. The minimization problem involves specifying a desired beam shape and using phase- retrieval algorithms to search for an optimal set of wavefront control signals.

In this paper we examine the accuracy with which Zernike coefficients for turbulence-induced wavefront aberrations can be estimated from conventional and Hartmann-sensor images. The performance limit for the estimation of the first 30 Zernike coefficients with a conventional image is shown to be significantly better than the performance limit of an 8 X 8 Hartmann sensor array.

A two deformable mirror concept for correcting scintillation effects in laser beam projection through the turbulence atmosphere has been previously studied. This system uses a deformable mirror and a Fourier transforming mirror to adjust the amplitude of the wave front in the telescope pupil. A second deformable mirror is used to correct the phase of the wave front before it leaves the aperture. The phase applied to the deformable mirror used for controlling the beam amplitude is obtained using a technique based on the Fienup phase retrieval algorithm. In the earlier work pointwise control of the wave front phase was assumed. In this paper we explore the consequences of using realistic finite degree of freedom segmented deformable mirrors to implement the two deformable mirror-based scintillation compensation technique. Our results show that under nearly all conditions of interest single deformable mirror branch point-based phase reconstruction provides equal or superior performance in this laser beam projection paradigm.

In laser beam projection through the atmosphere under conditions where strong scintillation is present, real zeros can appear in the beacon field. Recent advances in phase reconstruction have enabled phase estimation from phase differences in the presence of branch points, or real zeros, in the beacon field. While it is not possible to perfectly fit a physically realizable deformable mirror to the resulting discontinuous phase, the errors in the deformable mirror figure can be minimized based on knowledge of the locations and general shape of the discontinuities. In this paper we review two approaches to reconstructing phase in the presence of branch points, and compare the performance of these approaches to each other and to a conventional least-squares phase reconstructor in a laser beam projection system.

The optical backscatter of the 4W CW laser used to produce a mesospheric sodium-layer laser guide star for the MPE adaptive optics system (ALFA) has been observed from a neighboring 2.2 m telescope. The observations, taken at the Max Planck Observatory in Calar-Alto (Spain), in August 1998, had two aims: study the Na plume (altitude and profile variations) and the Rayleigh cone to achieve Rayleigh scattering measurements. In the framework of the network, `Laser Guide Star for 8 m class telescopes', a program of the European Commission, ESO, MPE and NUI, Galway are collaborating on studying the light pollution due to the MPE ALFA laser.

Phase correction of a plane wave, propagating through a turbulent layer, is considered. The required adaptive corrector element size and the system bandwidth were found by numerical simulation. These requirements were determined to be the same as for weak intensity scintillation approximation. The size of the required segmented mirror element was found to be equal to Fried length r₀ while the tolerable time lag was r₀/V, where V is the wind velocity. However, the local slope sensors become therewith impractical as well as the tip-tilt correction over the corrector subapertures.

A comprehensive model of laser propagation in atmosphere and all portions of an adaptive optics (AO) system for phase compensation is presented and the corresponding computer program is coupled. By using the direct wavefront gradient control method to reconstruct the wavefront phase and utilizing the long-exposure Strehl ratio as the evaluation parameter, the numerical simulation of an AO system in static state with atmospheric propagation of laser beam is carried out. It is found that on certain conditions the phase-screen which describes turbulence in the atmosphere might not be isotropic. The numerical experiments show that the computational results in imaging of lenses by means of the fast Fourier transform (FFT) method agree excellently with those by means of integration method. However, the computer time of FFT method is one order of magnitude less than that of integration method. We present `phase tailoring' of the calculated phase to solve the problem that variance of the calculated residual phase does not correspond to the correction effectiveness of an AO system. It is found for the first time that for a constant delay time of the AO system, when the lateral wind speed exceeds a threshold, the compensation effectiveness of an AO system is better than that of complete phase conjugation. It indicates that a better compensation capability of an AO system does not mean a better correction effectiveness.

For non-Kolmogorov turbulence, the slope structure function and the slope correlation function are used to characterize atmospheric turbulence parameters--(beta) , which is the power-law exponent of the phase power spectrum, and (rho) ₀, which shows the strength of atmospheric turbulence. The slope structure-correlation function, which is related to (rho) ₀ and (beta) , and the slope structure-correlation coefficient, which is only the function of (beta) and independent of (rho) ₀, are developed considering the subaperture size and additive noise. The Shack-Hartmann wavefront sensor data in the recently completed horizontal atmospheric experiments for 1000 m laser beam propagation are utilized to evaluate (beta) and (rho) ₀ according to the developed theory.

This paper is concerned with methods for preprocessing a collection of atmospheric turbulence-degraded short-exposure imagery to improver the resolving power of estimation algorithms. In the first portion of our paper we redefine the method known as frame selection in the context of optimization estimation results. Several measure of image quality are compared against idealized standards demonstrating their relative effectiveness to highly rank the least degraded image frames. In particular, we find the Fisher information measure to be the most noise tolerant and robust frame-selection measure. Results from simulated imaging scenarios demonstrate the improved ability of a multiframe maximum a-posteriori estimator to resolve the passband object distribution as well as to further recover the lost spectral content residing beyond the diffraction limit.

Space-variant blur occurs when imaging through volume turbulence over sufficiently large fields of view. This condition arises in a variety of imaging geometries, including astronomical imaging, horizontal-path imaging, and slant-path (e.g. air-to-ground) imaging. Space-variant effects are particularly severe when much of the optical path is immersed in turbulent media. We present a novel post-processing algorithm based on the technique of phase- diverse speckle (PDS) and a physical model for the space- variant blur. PDS imaging is a combination of phase diversity and speckle imaging which has proven to be an effective post-processing technique for cases with space- invariant blur. We present the details of the algorithm modified to accommodate space-variance and demonstrate its performance with results from both simulation experiments and real-data experiments. The results show that the space- variant PDS algorithm is very effective in cases involving severe space-variant blur, which cause correction techniques based on space-invariant models to fail.

We propose a `Maximum A Posteriori-based' estimation of the turbulent phase in a large field of view (FOV) to overcome the anisoplanatism limitation in adaptive optics. We show that, whatever the true atmospheric profile, a small number of equivalent layers (2 or 3) is required to obtain an accurate restitution of the phase in the whole FOV. The implications on multiconjugate adaptive optics are discussed in terms of number and conjugated heights of the deformable mirrors. The number of guide stars for the wavefront measurements in the field is also discussed: 3 (or even 2) guide stars are sufficient to obtain good performance.

Deconvolution from wavefront sensing is a powerful and low cost high resolution imaging technique designed to compensate for the image degradation due to atmospheric turbulence. It is based on a simultaneous recording of shift exposure images and wavefront sensor (WFS) data. To date, the data processing consists of a sequential estimation of the wavefronts given the WFS data and then of the object given the reconstructed wavefronts and the images. Thus, the information about the wavefronts present in the images if not used for the wavefront estimation. The aim of this communication is to propose and validate a novel method called myopic deconvolution from wavefront sensing. It is a joint estimation of the object of interest and the unknown wavefronts using all data simultaneously in a coherent Bayesian framework. It takes into account the noise in the images and in the wavefront sensor measurements, and the available a priori information on the object to be restored as well as on the wavefronts. As to the object a priori information, an edge-preserving prior is implemented and validated. This method is validated on simulations and on experimental astronomical data.

Most atmospheric correction codes are based in part or in whole on the radiative transfer equation (RTE), which is an integrodifferential equation. It is well known to be an ad hoc equation, which can and has produced incorrect answers. This paper initiates a new way of exploring where the RTE can produce unphysical answers in parameter-ratio ranges of genuine concern. The exploration begins with formulating a new technique for rigorously transforming the scalar RTE, without approximation, into a `pure' partial differential equation (PDE), i.e., one involving only partial derivatives of finite and relative small order. The virtue of this approach is that there are only a small number of analytical and numerical techniques for dealing with integrodifferential equations compared to the vast array of techniques for PDEs. A variety of tools are developed that are more powerful than needed for the particular physical problems to demonstrate the robustness of the technique. An atmosphere is then considered where Rayleigh scattering is dominant and its PDE derived, apparently for the first time. A class of nonlinear integrodifferential equations were also transformed into linear PDEs and solved for a multiplicity of solutions.

We discuss the methodology of interpreting channel 1 and 2 AVHRR radiance data to retrieve tropospheric aerosol properties over the ocean and describe a detailed analysis of the sensitivity of monthly average retrievals to the assumed aerosol models. We use real AVHRR data and accurate numerical techniques for computing single and multiple scattering and spectral absorption of light in the vertically inhomogeneous atmosphere-ocean system. Our analysis shows that two-channel algorithms can provide significantly more accurate retrievals of the aerosol optical thickness than one-channel algorithms and that imperfect cloud screening is the largest source of errors in the retrieved optical thickness. Both underestimating and overestimating aerosol absorption as well as strong variability of the aerosol refractive index may lead to regional and/or seasonal biases in optical thickness retrievals. The Angstrom exponent appears to be the most invariant aerosol size characteristic and should be retrieved along with optical thickness as the second aerosol parameter.

Smoke/obscurant testing requires that 2D cloud extent be extracted from visible and thermal imagery. These data are used alone or in combination with 2D data from other aspects to make 3D calculations of cloud properties, including dimensions, volume, centroid, travel, and uniformity. Determining cloud extent from imagery has historically been a time-consuming manual process. To reduce time and cost associated with smoke/obscurant data processing, automated methods to extract cloud extent from imagery were investigated. The TRACE system described in this paper was developed and implemented at U.S. Army Dugway Proving Ground, UT by the Science and Technology Corporation--Acuity Imaging Incorporated team with Small Business Innovation Research funding. TRACE uses dynamic background subtraction and 3D fast Fourier transform as primary methods to discriminate the smoke/obscurant cloud from the background. TRACE has been designed to run on a PC-based platform using Windows. The PC-Windows environment was chosen for portability, to give TRACE the maximum flexibility in terms of its interaction with peripheral hardware devices such as video capture boards, removable media drives, network cards, and digital video interfaces. Video for Windows provides all of the necessary tools for the development of the video capture utility in TRACE and allows for interchangeability of video capture boards without any software changes. TRACE is designed to take advantage of future upgrades in all aspects of its component hardware. A comparison of cloud extent determined by TRACE with manual method is included in this paper.

The Atmospheric Transmission Large-Area Analysis System (ATLAS) system has been used by the West Desert Test Center (WDTC), Dugway Proving Ground, UT since 1994 to assist in the characterization of aerosol clouds. The ATLAS is a tool for measuring transmittance through aerosol clouds in the far infrared (8 - 14 micrometers ) spectral region. ATLAS is a passive single-ended system employing a thermal imager for data collection and uses the natural background as the reference source. The final ATLAS product is a 2D transmission map of the aerosol cloud as seen by the imager. Historically ATLAS data reduction and map produce has been a lengthy process. This process includes transportation of the infrared video tapes from the field test site to the WDTC Optical Data Laboratory, digitization of infrared tapes, and subsequent image processing of the video frames to produce transmission maps as a function of time. In order to significantly reduce data processing and delivery time, the WDTC and Science and Technology Corporation have developed the Real-Time ATLAS (RT-ATLAS) system. RT-ATLAS is a field- portable system that reduces turn-around time from days to real-time for approximate results and to tens of minutes for final products. This paper describes the physics of the ATLAS technique, the physical RT-ATLAS system, and new enhancements to the ATLAS system. Data examples and analysis are presented and RT-ATLAS strengths and limitations are discussed.

Many properties of the atmosphere affect the quality of images propagating through it by blurring it and reducing its contrast, as well as blur. Use of the standard Wiener filter for correction of atmospheric blur is often not effective because, although aerosol MTF (modulation transfer function) is rather deterministic, turbulence MTF is random. The atmospheric Wiener filter is one method for overcoming turbulence jitter. The recently developed atmospheric Wiener filter, which corrects for turbulence blur, aerosol blur, and path radiance simultaneously, is implemented here in digital restoration of Landsat TM (thematic mapper) imagery over seven wavelength bands of the satellite instrumentation. Turbulence MTF is calculated from meteorological data or estimated if no meteorological data were measured. Aerosol MTF is consistent with optical depth. The product of the two yields atmospheric MTF, which is implemented in the atmospheric Wiener filter. Restoration improves both smallness of size of resolvable detail and contrast. Restorations are quite apparent even under clear weather conditions. Techniques for high resolution restoration involving more versatile filtering techniques, such as Kalman's and adaptive methods, are considered by filter comparison.

The aim of this research is to measure the electromagnetic radiation scattering properties of the atmosphere and to compare the experimental results with a Monte Carlo type model. The radiation scattered by suspended particles, known as aerosols, is the topic of interest. The presence of aerosols between a point source and an observation system causes the formation of a corona around the point source. The intensity of this corona is the Point Spread Function (PSF). A comparison is presented between the measured atmospheric PSF (caused by scattering) and the PSF which is calculated using a Monte Carlo calculation. While in previous studies the maximum path length was 600 meters, in the present research the path length was increased to 2000 meters. The spectral range was extended from the visible to 3.6 micrometers in the infrared. The authors used a collimated black body source for illumination and an IR radiometer as an observation system. The conclusion from the experimental results is that an increase of the beam divergence causes an increase in the scattered light received, as predicted by the model.

The Starfire Optical Range has measured atmospheric scintillation on 1.06 micron laser beams propagated from the ground to retroreflectors on satellites and back to the ground. The primary purpose of this experiment was to examine upward scintillation on laser beams, especially the results of varying the number of beams and their diameters. Separating the energy into beams that sample different portions of the atmosphere reduces the scintillation if the atmospheric turbulence each traverses is independent. How much the beam diameter affects scintillation is determined by diffraction and the size of the Fried parameter.

The measurement sensitivity of CO₂ differential absorption LIDAR (DIAL) can be affected by a number of different processes. Two of these processes are atmospheric optical turbulence and reflective speckle. Atmospheric optical turbulence affects the beam distribution of energy and phase on target. The effects of this phenomenon include beam spreading, beam wander and scintillation which can result in increased shot-to-shot signal noise. In addition, reflective speckle alone has been shown to have a major impact on the sensitivity of CO₂ DIAL. We have previously developed a Huygens-Fresnel wave optics propagation code to separately simulate the effects of these two processes. However, in real DIAL systems it is a combination of these phenomena, the interaction of atmospheric optical turbulence and reflective speckle, that influences the results. In this work, we briefly review a description of our model including the limitations along with a brief summary of previous simulations of individual effects. The performance of our modified code with respect to experimental measurements affected by atmospheric optical turbulence and reflective speckle is examined. The results of computer simulations are directly compared with lidar measurements and show good agreement. In addition, simulation studies have been performed to demonstrate the utility and limitations of our model. Examples presented include assessing the effects for different array sizes on model limitations and effects of varying propagation step sizes on intensity enhancements and intensity probability distributions in the receiver plane.

Infrared scintillation measurements were obtained along a 7 km path over San Diego Bay concurrently with meteorological measurements obtained from a buoy at the midpoint of the path. Bulk estimates of the refractive index structure parameter C_n², were computed from the buoy data and compared with scintillation-derived C_n² values. The bulk C_n² estimates agreed well with the scintillation measurements in unstable conditions. In stable conditions the bulk C_n² estimates were higher than the scintillation data, by up to an order of magnitude on average. This disagreement may be due to the effects of ocean waves in decreasing the vertical temperature and humidity gradients in stable conditions from the assumed Monin-Obukhov similarity theory forms, resulting in bulk C_n² values that are too high. The bulk C_n² estimates decrease rapidly when the absolute air-sea temperature difference approaches small positive values. These predicted decreases in C_n² were not observed in the path-averaged scintillation measurements or in single-point turbulence measurements, demonstrating that bulk models which estimate structure parameters based on mean air-sea differences are not valid when the mean air-sea difference approaches zero. It is believed that obtaining a better understanding of surface wave modification of near- surface atmospheric gradients represents the most promising means toward improving the bulk model.

In this paper we address the problem of estimating vertical profiles of atmospheric water vapor by means of attenuation measurements simultaneously made at different frequencies along a vertical satellite-ground link. The operating frequencies are those around the spectral absorption lines of water vapor at 22.235 GHz, the number of frequencies depending on the required vertical detail. A simulation is presented of such a system, based on a atmospheric propagation model and on radiosonde data providing true profiles of temperature, pressure and water vapor.

In this work, we examine the relevance of an improved model for the microwave brightness temperature over calm ocean to the TOPEX/Poseidon satellite. The model is divided into two sub-models, the atmospheric absorption model and the ocean surface emissivity model. Both models are developed from a comparison via Newthon-Raphson iterative method of ancillary data as required by the radiative transfer equation, with well calibrated radiometer data. Finally, the contribution of both models to the overall error budget for the wet troposphere propagation path delay estimation algorithm is presented. The path delay is used to correct the altimeter sensor on board of the satellite utilized to measure global sea surface topography. The improvement in the accuracy of the path delay is found to be 37% which render more accurate measurements from this satellite mission.

SCIDAR (SCIntillation Detection And Ranging) is a technique for recovering atmospheric C_n² profiles from the scintillation pattern in or near the telescope's entrance pupil plane. The generalized SCIDAR technique allows the measurement of the entire atmospheric C_n² profile. We report on a program of generalized SCIDAR measurements at the Air Force Maui Optical Station (AMOS). We discuss how a short exposure imaging system at AMOS was modified to record SCIDAR data. We also discuss the use of computer simulations of atmospheric propagation to aid in the development of data analysis techniques. Results from the first set of SCIDAR observations are presented.

Laser satellite communication systems are subject to signal fading below a prescribed threshold value owing primarily to optical scintillations associated with the received signal. At large zenith angles between the transmitter and receiver the intensity fluctuations can be much stronger than at small zenith angles, easily exceeding the limitations imposed by weak fluctuation theory. Under such strong conditions the intensity fluctuations cannot be properly modeled by the longitudinal distribution. In this paper we use recently developed expressions for the scintillation index associated with an uplink or downlink path at large zenith angles and calculate the probability of signal fade as a function of threshold below the mean signal level. The analysis presented here is based on both the conventional lognormal model and the gamma-gamma distribution that has recently been proposed for the intensity fluctuations over all conditions of atmospheric turbulence. The gamma-gamma distribution, based on a model that treat intensity fluctuations as a modulation of small-scale scintillations by large-scale scintillations, has two parameters that are naturally linked to the large-scale and small-scale scintillations of the new scintillation model.

Phase differences on a sampled grid in the pupil plane of a coherent imaging system are used in conjunction with a hidden phase approach to estimate images of coherently illuminated objects in the presence of additive Gaussian noise. The imaging system is located in the far-field with respect to the illuminated objects. Conventional least squares and minimum variance image reconstruction approaches are shown to fail because of the presence of point discontinuities in the far-field speckle pattern. Conventional phase reconstruction techniques can not properly sense the phase effects resulting from these point discontinuities or branch points. However, these conventional image reconstruction techniques can be made to work with the addition of a hidden phase term that accounts for the phase effects resulting from the branch points. The hidden phase term is added to the results of both the least squares and minimum variance phase reconstructors and the addition of the hidden phase term is shown to successfully recover the images of several types of extended objects.