The statistical fluctuations developed by an optical wave, after passing through atmospheric turbulence, have a non-Gaussian nature. The detected optical intensity appears to have two separate time scales of fluctuations. This paper discusses a plausible physical model for the turbulence scattering of an optical wave that would give rise to a two-time scale fluctuation. The K distribution, H-K distribution and I-K distribution are analyzed as to the possible scattering conditions, by turbulence, these distributions represent.

By building upon the compound field model that leads to the I-K distribution, we develop simple phase distribution models for an optical wave propagating through a turbulent medium that are applicable in weak turbulence regimes. In one case both the absolute phase and phase-difference distributions are closely approximated by the family of one-dimensional K distributions, while in another case the functional form of the phase distribution is that of a simple exponential function.

We report measurements of the spatial coherence properties of light scattered by a turbulent layer - in particular, the dependence of the spatial coherence function of intensity fluctuations on propagation distance is compared with theoretical predictions.

The statistical distribution of experimentally obtained higher oreder moments of optical scintillations probability density is studied. It is shown that this distribution is strongly dependent on the size of the data sample. At reasonable and practical sample sizes the correct estimation of the theoretical value is improbable. In practice, the sample size is limited by the scintillations bandwidth and the length of time in which the turbulence is stationary. At practically available sample sizes the region of the most probable values of the estimated higher order moment is almost independent of the scintillation PDF. The distinction between the candidate PDF's is almost impossible at reasonable sample sizes. These conclusions are derived analitically and demonstrated by simulation techniques.

The statistics of laser scintillation have been studied for many years. The random fluctuations are described by the probability density function (PDF). A rigorous solution for the PDF exists only for weak scattering (log normal PDF) and very strong scattering (negative exponential PDF). Many models for a general PDF have been proposed, and a common method of analysis has been the comparison of the moments of the PDF with experimental data. The accuracy of these experimental estimates for the moments is difficult to determine theoretically. The statistical behavior of these estimates for the moments is determined by simulation of actual experimental procedures assuming various models for the true PDF. Realizations for histograms of digitized data is generated using binomial random deviates. The only parameters required are the total number of statistically independent data samples collected and the average value for each data sample, which depends on the model PDF. Each realization for the histogram generates a realization for the moments. The PDF of these estimates for the moments is approximated by producing a histogram of a large number of such realizations. The PDF of the estimates for the moments then provides reliable confidence intervals. The behavior of the confidence limits is presented for common models for the PDF of laser scintillation.

A transmissometer that operates in the visible/near IR region of the spectrum has been modified to measure beam modulation caused by turbulence along a 300 meter path. The system measures both total transmission and the rms value of the intensity fluctuations and has been designed to allow variation of aperture size and optical wavelength. From these measurements, ai2, a2 and Cn2 are calculated and compared with measurements made with a log-amplitude variance scintillometer. All measurements have been made over a near-ground horizontal path and are compared with the NOAA model that predicts intensity fluctuations based on Cn2, wavelength, and aperture size.

Measurements of the variance of log amplitude, 02, were performed over a 183 m optical path using a NOAA horizontal scintillometer. The otical index of refraction structure constant, Cr21, was measured at several locations along the path using AFGL thermosondes. The theoretical model decribing the relationship between the scintillometer 02 and CA along the path is tested. The comparison is made by numerically integrating CA along the path. This comparison is made for conditions of strong and weak turbulence as well as strong and weak winds. For averages of 10 minutes, the agreement is very good. At shorter time scales of the order of seconds, there is agreement in trend. However, the scintillometer and thermosondederived 02 differ in terms of the magnitude of their fluctuations. The importance of volume ava'aging is discussed when comparing measurements, models and data. The data is then used to consider the stationarity of the ensemble model implicitly used in averaging data. The short term fluctuations in the 02 data are analyzed statistically. These fluctuations in 02 are modeled in terms of a Ylog-normal distribution. The analysis of the spectrum and 4orrelation function of log(02) suggest that quasistationarity may be restricted to time intervals of the order of 10 seconds.

This review describes the present computer codes used to predict atmospheric transmittance. Since these codes are based on modeling of the optical properties of the atmosphere, there is a constant need to validate them in long-path atmospheric transmittance measurements. These measurements and their results will be described here.

A 20 cm-1 resolution band model is presented for the calculation of water vapor molecular transmittance in the spectral region from the near infrared to zero frequency. It was developed for replacing the empirically-obtained, look-up transmission tables presently in LOWTRAN 6. The model consists of an exponential function whose exponent is expressed in terms of atmospheric pressure, temperature and absorber amount, as well as of four defining parameters. Of these parameters, only one is allowed to account for spectral variability over 5 cm^-1 spectral intervals. The model was developed using both FASCODE-generated transmittance data and laboratory measured spectra. The parameters are presented in tabular and graphical form. Comparisons are made between line-by-line calculations, LOWTRAN predictions, and new-model generated transmittance.

A methodology is presented that, for the first time, allows characterization of the atmospheric effects on the propagation of target contrast. The two elements of target contrast are inherent contrast as seen closeup or in the near-field and propagated contrast as produced by the degradation of the inherent target and background radiation in propagating from closeup to engagement range or in the far-field. Atmospheric effects can produce dynamic changes in these two elements. Examples of these changes are presented as well as features or metrics of target contrast which can be used to quantify them. The technology for quantifying changes in target contrast was developed at the U.S. Army Atmospheric Sciences Laboratory, and the equipment is termed the Target Contrast Characterizer (TCC). The basic concept is to simultaneously compare matched images from two imagers--one in the near-field and the other in the far-field--along a common line of sight. For example, if one imager with a 1X lens is used to view a target from 100 m and a second imager is used to view the same target simultaneously with a 10X lens from 1 km, their fields of view will have a common window in the target plane. The ability to compare the images from these two imagers in real-time was made possible by the use of a unique real-time image processing system. This system was developed in the course of an in-house laboratory independent research project of the authors. The application of this real-time image processor to one-to-one comparison of the two matched target scenes allows, for the first time, the separation of the changes in target contrast due to propagation between the near-field and the far-field positions from the changes in the inherent or near-field contrast. In addition, temporal changes of the inherent contrast can be quantified by monitoring the change in the near-field imagery. The TCC already has a wide range of military applications which include assisting the development of aided target recognition systems as well as improved design and performance testing of weapons used to engage enemy targets. The real-time image processing techniques, proof of principle guidelines, and several applications of this technology are detailed.

Attenuation of electromagnetic waves by atmospheric gases is an im-portant consideration in a variety of radar and electro-optical applica-tions. Molecular absorption by strong bands of H₂O and CO₂ defines the atmospheric window regions. The window regions are not totally transparent and feature weak line absorption and continuum absorption. The experimental character of continuum absorption by water vapor in atmospheric window regions at millimeter wavelengths and 10, 4, and 2.2 Am and nitrogen at 4 μm is surveyed. This includes recent measurements at The Johns Hopkins University Applied Physics Laboratory on H₂O at 2.2 μm and the nitrogen collisioninduced band at 4.3 μm. Also, some of the concepts and models used to characterize these phenomena will be reviewed. The search for a unified theory on the water vapor continuum has been elusive, yet the frequency and pressure dependence is consistent with current far-wing theories. The temperature dependence is not totally understood. A model describing the temperature dependence of the nitrogen continuum is emphasized.

A microphysical model is presented which can be used to provide first approximations of vertical extinction profiles for low stratus subclouds. The thermodynamic portion of the model is based on particle growth models by Hanel, drop-size distributions by Duncan and Low, or Shettle and Fenn, bulk phase change thermodynamics, and a mass balance formulation. Complex indices of refraction are estimated using mixture rules by Hanel, and transmission characteristics are determined by using Mie theory. Results obtained for adiabatic and nonadiabatic conditions are presented.

A potential temperature gradient expression for a system composed of air, unsaturated water vapor, and liquid water is presented. Inclusion of the water is shown to provide more accurate results than the more commonly used forms for potential temperature. This expression was also used in conjunction with a damp haze microphysics model to simulate nonadiabatic effects which are also presented. Quantitative comparisons of this more complete expression with those determined from formulations for a system composed of only air and unsaturated water vapor are presented.

Photopic transmittances within and through localized, inhomogeneous dust clouds were estimated by contrast transmittances derived from image processing of video recordings of dust scenes which included optical targets contrasted against the sky or terrain background. Comparison between the estimated contrast transmittances and actual transmittances measured through dust clouds by a transmissometer yielded correlation coefficients of up to 0.933. The contrast transmittances within the dust clouds were estimated from the ratios of contrast between adjacent targets, absolute estimates, and by the use of black and white targets. Comparison between these latter methods yielded correlation coefficients of up to 0.987.

Multispectral countersurveillance systems are designed to alter, disrupt, or disguise the signature of military equipment. Signatures in the spectral regions commonly referred to as ultraviolet, visual, near-infrared, and radar are generated by surface reflections of incident electromagnetic radiation. Camouflage is used in these wavebands to create reflectance patterns similar to those of the natural background with the goal of rendering equipment indistinguishable from natural structures. In contrast, thermal infrared signatures are primarily due to self-emissions rather than reflections of incident radiation. All objects emit electromagnetic radiation; the peak wavelength and intensity of that radiation differ relative to an object's temperature. At ambient temperatures and above, objects emit sufficient electromagnetic radiation in the 8-12 micron wavelength region to be detected by thermal infrared sensorsl. The intensity of thermal infrared energy radiated from equipment surfaces is affected by surface temperature and emissi-vity. Camouflage for infrared signatures is designed to control these conditions and create apparent temperature profiles similar to those of the natural background. The objective of this paper is to discuss the electro-optic properties of surface coatings and their effect in generating and controlling the infrared signatures of tactical equipment.

The current lightweight camouflage screening system (LOSS) used by U.S. military forces consists of a color coated polymer containing radar scattering dipoles (flat stock material) attached to a fish-net type substrate. As a general purpose radar scattering camouflage system, the screen is designed to be reflective enough to reduce the radar return from a covered target, but not so reflective that the screen itself becomes a significant target. The screen is produced to specified transmission parameters. In order to evaluate the effectiveness of the production specifications, screens with different transmission properties were compared using tactical and instrumentation radar systems.

This paper reviews the derivation and validation of a model for beam propagation in aerosol media. The model is a paraxial approximation to the radiative transfer equation. The main feature is the representation of the power flux in the direction normal to the propagation axis by a diffusion process. Coupled partial differential equations are obtained for the forward and backward flux densities. The solutions are compared to beam profile and backscatter measurements performed in laboratory-generated water droplet clouds and to transmittance measurements in falling snow. The effects of optical depth, cloud inhomogeneity, wavelength and receiver field of view are studied. In all cases, the agreement between predictions and experimental data is very good.

By use of a stochastic-analytic approach a scattering theory is presented which describes the spatio-temporal distortion of time dependent laser irradation in a well mixed particulate medium as a series expansion in scattering orders. Although applicable to the general case of arbitrary phase function, the theory is elaborated here for the case of gaussian forward scattering, where it is the generalization of the theory derived by Tam and Zardecki (Optica acta 2b, 659 (1979)) for cw irradation. The individual terms of the series are derived from a general sequence of functions which are independent of the specific parameters of a given case and thus, once computed, can be applied to an arbitrary case of forward scattering.

In this paper we investigate the effect of multiple scattering on the propagation of electromagnetic pulses in a medium containing a random distribution of spherical scatterers. As is well known in multiple scattering theory, interferences or interactions among scatterers are important, and in some cases it is not enough to consider only first order multiple scattering which has been widely used in the study of pulse propagation in random media. As a consequence, the characteristics of scattered pulses, e.g., frequency spectrum, coherence time and coherence bandwidth, can affect the interpretation of the random medium. We examine the scattered field of a narrow band pulse wave by randomly distributed particles and show the importance of multiple scattering on estimating attenuation in the formalism. The magnitudes of the transmitted and returned pulse intensities decrease due to scattering. When a considerable amount of scatterers present in the scattering medium, the attenuation factor needs to be corrected for multiple scattering. In order to see the difference between single and multiple scattering theories on the attenuation of pulse propagation, we present two data sets in quite wide frequency ranges.

The degradation of image quality due to multiple scattering in a turbid medium is analyzed under various conditions of illumination. The emphasis is on the forward-peaked multiple scattering effects, which can adequately be described by the small-angle approximation. In the case of incoherent illumination, the modulation transfer function (MTF) can be given explicitly both in the low- and high-frequency limits. For scattering with smaller degree of anisotropy, the MTF should be computed numerically by considering solutions to the equation of radiative transfer with a line or point source. As the beam power increases, the turbid medium becomes modified by its interactions with the beam, thus affecting the image resolution. In this nonlinear transport regime (flux levels of the order of 106 W/cm2 and higher) the propagation leads actually to beam narrowing. In the context of the imaging problem, an apparent paradoxical situation in which the image of a point source narrows down as the high-energy laser (HEL) beam propagates is discussed.

We have made measurements of the probability density function of irradiance for a laser propagating through atmospheric turbulence. For each measurement, a diverged laser beam was used as the source. The beams were propagated horizontally over flat grassland at a height of 1 to 2 meters. Several path lengths of up to 2.4 km were used. At the receiver, a time series of the irradiance was digitized and recorded for later processing. During each experiment, the cross-path wind velocity, the refractive turbulence structure parameter Cn2, and the inner scale of turbulence 10 were measured optically. These data were recorded along with the irradiance data. To obtain an estimate of the probability density function, we normalized each time series by its mean value and sorted the result into a histogram. At the same time, the second and third moments were calculated. These were used to obtain the parameters of the theoretical density functions that were considered. Two phenomenological density functions have been proposed to describe irradiance fluctuations in the atmosphere. These are the I-K and the lognormally modulated Rician. Each requires two parameters that depend on atmospheric conditions and each can be used under any atmospheric conditions. Both reduce to the widely accepted negative exponential density function in very strong integrated turbulence. Both are numerically tractable. We compare each of these density functions with our measured histograms under a variety of atmospheric conditions.

Using atmospheric modulation transfer function area (MTFA) as a single-valued numerical criterion for image quality propagated through the atmosphere horizontally near the ground, a statistical study of atmospheric imaging data accumulated over a three year period has led to the determination of regression ceofficients with which to quantitatively predict image quality as a function of wavelength, over the 400 - 1000 nm wavelength region, according to weather forecast. Utilization of this procedure is quite simple. One simply plugs in expected values for windspeed, air temperature, and relative humidity in the regression coefficient expression for MTFA. The larger the expected MTFA, the better the expected image quality. Two sets of regression coefficient data have been obtained, one each for desert and non-desert climates, corresponding to summer and winter data here. Preliminary experimentation over a different line-of-sight indicates the accuracy of the prediction is fairly reliable for the summer or desert model.

Atmospheric aerosols, particularly dense, local clouds of smoke, dust and fog, have a variety of extinction, multiple scattering and thermal emission effects on propagation and imaging. This paper presents an approach to simulating realistic aerosol path-radiance effects that are not treated in the usual transmission codes. Depending on illumination and concentration, aerosol clouds may range in appearance from thin translucent wisps to opaque diffuse reflectors or emitters. Typically the clouds are inhomogeneous and have complex, finite geometries. Their radiative transfer properties are therefore particularly difficult to predict. This paper uses a method developed by the U.S. Army Atmospheric Sciences Laboratory to model and investigate the radiative transfer effects of such aerosol clouds under a variety of illumination conditions. The method is applied to show some interesting examples of the contrast and apparent temperature signatures of aerosol clouds themselves, the changes to signatures of partly obscured objects and the effect on received images at the sensor under various illumination conditions.

Multispectral transmissometer systems have been used in a large number of tests to evaluate line-of-sight transmittance through smoke screens. Analysis of the data have shown that for the same spectral band, a wide variation in measured transmittance is possible when different transmissometer systems are used. Since transmittance data is a key factor in interpreting electro-optical system performance, it is important that accurate measurements of potential countermeasures such as smoke screens be obtained. Therefore, a thorough understanding of the factors that can affect transmissometer performance is necessary. In this paper, an analysis is presented of those operational characteristics that can affect multispectral transmissometer performance. An evaluation is performed to identify the most important parameters affecting data quality and to evaluate how these factors can be expected to affect data characteristics. Results are compared with field test data and actual operating systems.

The Electro-Optical Systems Atmospheric Effects Library (EOSAEL) is a comprehensive library of computer codes dealing with atmospheric propagation effects. EOSAEL is a state-of-the-art computer library comprised of fast-running theoretical, semiempirical, and empirical computer programs (called modules) that mathematically describe various aspects of electromagnetic propagation and battlefield environments. The modules are connected through an executive routine, but often are exercised individually. The modules are more engineering oriented than first-principles. The philosophy is to include modules that give reasonably accurate results with the minimum in computer time for conditions that may be expected on the battlefield. EOSAEL models clear air transmission, transmission through natural and man-made obscurants, turbulence, multiple scattering, contrast and contrast transmission, and others. EOSAEL is available to the DoD community and eligible contractors free of charge. An overview of EOSAEL is presented, describing the background philosophy, current capability, and future direction.

A model is presented that describes the behaviour of the sea as an IR-background. The model is based on the Cox-Munk wave slope statistic and the LOWTRAN 6 radiation model. It addresses atmospheric refraction, aerosol absorption and scattering, molecular scattering, emission and absorption. Comparisons with measurements of a calibrated thermal imaging system show good agreements.

Applications involving surveillance, tracking, identification, and modeling of objects on the ocean surface require a knowledge of the visible and infrared radiation incident on that surface. This model allows the user to compute the spectral and band-averaged radiance from the sky for any view angle. The model formulations are based upon an analytic solution of the radiative-transfer equation using an advanced two-stream approximation for the up-welling and downwelling radiation fields. The boundary condition at the lower surface is fulfilled by the use of a diffuse spectral reflectance and a diffuse spectral emissivity. Single and multiple scattering and emission by the maritime aerosols are included by the use of a three-component Navy aerosol model for the boundary layer. The vertical aerosol density profiles are characterized by Fermi-Dirac and exponential distributions with scale heights that are different for each of the three aerosol components. The indices of refraction as well as the sizes of the particulates are functions of the wavelength and the relative humidity. A subroutine in the computerized version of the model explicitly computes the volume attenuation coefficients, the single-scattering albedo, and the single-scattering phase function for use in the sky radiance formulas. The user has the option of implementing any of six standard vertical temperature profiles or he can use his own temperature data. The multiple scattering of the atmospheric and sea-surface thermally emitted radiation is treated in a mathematically exact way by fitting the Planck radiance to a series of exponential functions in optical depth. The model input parameters consist of: current wind speed, 24-hour average wind speed, relative humidity, air mass, ocean temperature, air temperature profile, wavelength, the day of the year, Sun angles, and view angle. Output quantities are: sky radiance and solar irradiance for any wavelength from the visible to 40 micrometers.

Infrared optical properties of the marine boundary layer are basic in the performance of thermal imaging systems, such as forward looking infrared (FLIR) sensors, over the ocean. To aid in evaluating the performance of these sensors, spatial distributions of infrared sky radiance in the 3- 5 μm mid-wavelength infrared (MWIR) and 8 - 12 μm long wavelength infrared (LWIR) spectral bands were measured simultaneously at low elevation angles above the sea surface. Calibrated AGA, Model 780, dual scanning systems functioned as imaging infrared radiometers. Infrared sky radiance and meteorological parameters were recorded concurrently in a series of four data sets during one diurnal cycle starting 15 April 1986 at 1500 Pacific Standard Time (PST) and ending 16 April 1986 at 1730 PST. Radiosondes were released from the deck of the US S POINT LOMA, about 7.6 μm above the ocean, at a range of 5 km due west of the coastal sensor site at Naval Ocean Systems Center, San Diego, CA. Wind speed, direction, sea temperature, and cloud conditions were also recorded on board the ship. Sequential images of radiance distributions provided control data for monitoring the stability or variability of atmospheric conditions throughout the time for radiosonde ascent to about 6 km altitude. Measured IR sky radiance distributions were compared with corresponding clear-sky radiance using the LOWTRAN 6 computer code. Cloud radiance and scattered solar radiation restricted the comparison to elevations close to the optical horizon where aerosol attenuation would be greatest. Infrared aerosol transmittance was inferred from the ratio of measured radiance to calculated clear-sky radiance along the horizon line of sight (LOS). Equivalent temperatures for blackbody radiance at the horizon were either less than or equal to the ambient air temperature near the sea surface, except when the MWIR band included scattered solar radiation; consequently, only the LWIR band could be used to infer aerosol transmittance reliably. Radiance along the optical horizon originated mainly in the lowest 100 m of the atmosphere; therefore, reasonably accurate horizon radiance or transmittance predictions could be made from meteorological data within this low altitude. These results indicate that a LWIR aerosol transmissometer could be developed by computing the ratio of measured horizon sky radiance to calculated clear-sky radiance using local ambient meteorological data.

Earth sensors working on the principle of detection of infrared discontinuity at the horizon are affected by systematic errors due to seasonal changes in radiance. Horizon Crossing Sensors used in spinning satellites, conical scanning or oscillatory types of sensors which find application in three-axis stabilized satellites are generally susceptible to this type of error. The method currently in use involves post-facto corrections by ground based modelling of the radiance which is a function of seasons, latitude and longitude. The latest trend is towards using 'Smart Sensors' with an ability to correct the errors on-board itself. This paper presents an algorithm developed for correcting the systematic error due to radiance changes, on-board the satellite. In this new approach, a relation between systematic errors and radiance gradient between two horizon points is established. The method of sensing the radiance and computing the gradient on-board the spacecraft and a simple correction algorithm which is suitable for implementation by microprocessors have also been derived. Typically, the maximum error due to gradient in radiance is 0.05 degree and it depends upon the type of orbit. The results of the correction algorithm applicable to a typical conical scanning earth sensor for a sun-synchronous, 3 - axis stabilized satellite are included in the paper. The systematic error is reduced to less than 0.01 degree. This is comparable with that from ground based computation which involves the determination of satellite position in orbit and the use of atmospheric models based on large observational data base.

As a prerequisite to the adaptive cancellation of the deleterious effects that the atmosphere can have on image propagation, one needs a propagation model that incorporates as many of the major atmospheric mechanisms as possible that can exist to simultaneously perturb the attendant electro-magnetic wave field. The two principal mechanisms are: 1) scattering due to turbulent fluctuations of the temperature and humidity fields of the atmosphere and 2) scattering and extinction due to atmospheric aerosols and hydrometeors. Collectively, these are taken here to define the turbid atmosphere. Studies have recently been made on wihoc theoretical I and empirical 2, 3 bases where these effects are taken to occur simultaneously on a propagation path but what one ultimately needs is a unified treatment of such situations. There are also other important aspects of the problem that have been hitherto neglected in atmospheric image propagation modelling, viz., the fact that aerosol concentrations along the propagation path are not usually uniformly dispersed along the path and, more importantly, because of prevailing turbulent mixing and motion due to the ever present wind, the concentrations are random functions in the transverse position across the path. This latter aspect can give rise to fluctuating components of the image and spectral contrasts of a target and therefore necessitates a statistical description of these well known imaging parameters as well as the associated optical transfer function. Such statistical fluctuations in the propagating radiation field can, for example, degrade the overall signal-to-noise ratio of an optical device because, in addition to the shot noise which is determined by the average signal level at the imaging device, there is a component that results from the random aerosol scattering mechanism that can, in most cases, dominate over that of turbulence. In the case of the sensitive sensors in use at this time, this noise component may exceed that due to turbulence. What is more important, however, is that if these effects are to be compensated for by a passive adaptive imaging technique (i.e., adaptive image correction without the use of a reference source which is usually a necessity in actual situations) a complete description is needed to use as a priori control information. However, as always, it is desired to strive to keep such a model amenable to analytic solution.

Because turbulent fluctuations in the atmospheric refractive index (n) at wavelength x are related to turbulent fluctuations in the temperature (t) and humidity (q) by n = A(x,P,T,9)t + B(x,P,T,Q)q, it is possible to estimate the refractive index structure parameter C in the atmospheric surface layer from meteorological quantities. I describe two such estimation procedures, one based on the velocity, temperature, and humidity scales u*' t*, and q*, and a second based on the routine meteorological quantities U,, T -Th, and %-Q,. Subscript h here denotes the wind speed (U,), temperature (TO, and humidity (Qh) at rVference height h; subscript s indicates the sUrface value. I tabulate the coefficients A and B as functions of λ, the atmospheric pressure (I)), and the ambient temperature (T) and humidity (Q) in four wavelength regions--visible (including near-infrared), an infrared window, near-millimeter, and radio. A sensitivity analysis of the two estimation procedures demonstrates that the accuracy of the Cn2 estimate is a strong function of the Bowen ratio (Bo), the ratio of sensible to latent heat flux at the surface. At two Bo values within the interval [-10,10], one dependent on λ and the other on enyironmental conditions, the uncertainty in the Cn2 estimate becomes infinite. I focus on C values over snow and sea ice, and my examples are for these surfaces, but the estimation procedures presented can be applied to any geophysical surface that is horizontally homogeneous.

A methodology is presented to characterize propagation through clear air turbulence in the surface boundary layer of the atmosphere, based on readily obtained environmental observables. Obukhov similarity theory is employed to define a consistent set of flux profile relationships, and the Kolmogorov principle of universal equilibrium to estimate a profile for the refractive index structure parameter. This profile serves as input to a propagation model based on weak perturbation theory, allowing estimates of log-amplitude variance, receiver coherence diameter, isoplanatic effective path length, and scintillation averaging length, as well as a variety of subsidiary imaging statistics.

Time series measurements of optical turbulence parameters allow estimation of future values. First, a secular global model is found from the "Clear" database. Then statistical approaches which use past and present data to predict future points are examined. One predictive technique applies the global model plus auto-regression. Comparisons are made with: a.) the global model alone, b.) a polynomial extrapolation, and c.) the assumption that the predicted value equals the present value. The method using auto-regressive linear prediction is the most accurate. This is due to the fact that short-term correlation exists over five to thirty minutes. Sufficient stationarity apparently exits which allows good estimates of one set of prediction coefficients for the entire data base.

This paper presents an approach to modeling effects of atmospheric turbulence in digital images, which allows variation in the atmospheric coherence diameter over the field-of-view. Characteristics of the imaging system are used in deriving a digital filter to represent turbulence, and in evaluating its accuracy. The form of the filter is appropriate for an image/array processor which performs direct convolutions rapidly.

A model of long-exposure image blur due to atmospheric turbulence has been developed using a parallel processor to convolve the input image with the turbulence point spread function (PSF). The model uses two basic dimensionless parameters--the turbulence strength parameter and the sampling factor--to calculate the turbulence-degraded PSF. The turbulence strength parameter is the ratio of the optics diameter to the atmospheric coherence diameter, and the sampling factor is the product of the image pixel spacing (sampling interval) and the cutoff spatial frequency defined by the diffraction-limited incoherent optical transfer function (OTF). The turbulence OTF is computed using the turbulence strength parameter for a given optical system, slant path, and turbulence condition. Then, by taking advantage of the band-limited nature of the incoherent OTF, the turbulence PSF for the imaging system is expressed as a Hankel transform with finite limits and is evaluated numerically. The convolution requires one frame time (1/30 second) for each point in the PSF kernel, thus a 25-point convolution (5 x 5 kernel) of an entire image (512 x 512 pixels) is completed in less than one second.

We discuss the importance of the isoplanatic assumption in conventional imaging and in imaging using intensity interferometry. For conventional imaging, we treat both short- and long-time exposures. In imaging using intensity interferometry, we present a general result, in which isoplanicity is not assumed, and then study the first order non-isoplanatic correction. Explicit calculations are given for the correction under typical atmospheric conditions.

A new technique is described for high resolution imaging through the atmospheric turbulence. As in speckle interferometry, short exposure images are recorded, but in addition the associated wavefronts are measured by a Hartmann-Shack wavefront sensor. The knowledge of the wavefront allows to calculate the instantaneous point spread function. An estimate of the object can be calculated from the correlation of image and point spread function. An experimental set up is described with first laboratory results. It shows the capabilities of the method.

Theoretical and experimental results are compared between two techniques for determining atmospheric "seeing" conditions: (a) a method evaluating the modulation transfer function (MTF) of the atmosphere by measuring the line spread function of a star image, and (b) a method measuring the angle of arrival through two relatively small apertures. Near vertical viewing of single stellar sources is considered in all cases. Values of Fried's parameter, 1.0, derived from simultaneous measurements from the different techniques are presented and comparisons of these data are discussed. Results of measurements of mechanical vibrations of the telescope system are presented and the effect of these vibrations on results obtained by the different techniques are evaluated. Optical arrangements and detectors for the two systems are outlined. The system measuring the line spread function of a stellar image uses a linear CCD while the angle of arrival system employs a 2-D CCD camera.

A new atmospheric turbulence monitor utilizes relative motion between dual images of a single star, formed by two subapertures of a Schmidt-Cassegrain telescope, to calculate Fried's atmospheric seeing parameter, r0. Dual images are formed on a two-dimensional CCD array, and intensity at each pixel location is digitized for calculations by the host computer. Flexibility in frame rate, exposure time, and data processing are incorporated into the system design through extensive use of programmable array logic, state machines, and microcomputer control. The equipment eliminates many problems characteristic of current systems which use one-dimensional detectors and a single image.

A model has been developed for predicting the radiant image of an extended emissive source. The image produced depends on the angular resolution and image size specifications, on the relative positions of the source and the observation system, and on the wavelength or waveband. Several source sizes are provided. The sources in current use represent fires. The radiative transfer equation is used to calculate path radiance based on emission from hot aerosols and gases. Attenuation within the source and between the source and the observation point are taken into account. An averaging technique is used to simulate intensity averaging which occurs when the source size is small compared with the field of view. The first version of the model, which treated only aerosol emission and attenuation, has been incorporated into a program to produce images on a VAX-DeAnza system.

Turbulence parameters are determined from measurements along a 183 m line-of-sight at Palm Bay, Florida and a 300 m path at Sudbury, Massachusetts. A horizontal scintillometer is used to obtain o 2, the variance of log amplitude of the irradiance, and the path-averaged C 2, the atmospheric refractive index structure constant. Thermosondes are also used to obElain Cn₂ at several locations along the optical path. The mean C₂ is determined from three thermosondes and compared to that from the scintillometer. Statistics obtained from processing the 2 sec sampled data over 10 minute periods are presented. Excellent agreement is obtained between the two systems when averaged over 10 minutes. Statistics obtained over shorter periods show a considerable variation in the Cn₂ estimates within the 10 minute period. The range of variation within 10 minute intervals can exceed 50%. Volume averaging, wind speed and direction fluctuations are discussed as possible causes of short time variations in the Cn₂ estimates.

An experiment to collect data on atmospheric turbulence has been conducted on the 107" telescope located at McDonald Observatory in West Texas. Phase and intensity of aberrated starlight have been measured over the aperture of the telescope. Simultaneous measurements of free-atmosphere seeing and local temperature differences have been made to gauge the strength of turbulence within the dome vs. turbulence in the free atmosphere.

Short exposure measurements of the atmospheric lateral coherence length (r₀) are shown to be biased by random apodization at the entrance apertures of a Hartmann r0 measurement device. A model for random apodization cells is mathematically developed and the errors in angle-of-arrival fluctuation measurements and r0 computations are investigated. Compensation for apodization bias is investigated, and some compensating measurement devices are proposed. The influence of instrumental and computational errors on angle-of-arrival fluctuation measurement errors is also discussed.