The authors describe a procedure they believe to be optimum for determining the path of a ray through an atmosphere described by a radially varying refractive index profile on the Earth. The result is exact for patched quadratic profiles inverse problem and is suitable for calculating ray paths in complex profiles. The method also facilitates greatly the inverse problem.

The five distinct regions of on-axis weak scintillation behavior exhibited by Gaussian beam propagation in the turbulent atmosphere are reviewed. One of the regions (D₁) is unique, in that the random irradiance across much of the target plane is non log normal, scintillation predictions derived from the Rytov approximation are inaccurate, and no generally applicable and computationally efficient scintillation theory is currently available. The D₁ region cannot be easily dismissed, since it includes horizontal path focused beams and ground to space collimated beams. A survey of the D₁ region is provided, including physics insight from past publications, the role of the phase screen approximation, and the impact of distributed low order turbulence. An overview of a new approach that yields accurate, computationally efficient scintillation predictions within D₁ is provided.

First-order weak-fluctuation Rytov theory predicts that the longitudinal (on-axis) scintillation component of an untracked focused beam projected along a horizontal path will become significantly smaller as the size of the transmitter aperture increases. At the same time, the radial component near the diffractive edge of the beam is predicted to increase without bound. The results of recent computer simulations are at odds with this behavior, and we believe that this discrepancy is due to the fact that Rytov theory does not correctly account for the effects of beam wander. We present a theoretical structure that accurately describes far-field irradiance fluctuations caused by uncorrected tilt jitter. This new theory is validated by demonstrating excellent agreement between the predicted scintillation index and computer code results for both tracked and untracked beams. For many applications of practical interest, such as free-space optical communications, a good understanding of the time-average Strehl ratio is also essential; simulation results for this parameter are presented and shown to be in good agreement with theory.

A mode coupling approach was studied as a tool to describe the propagation of partially coherent, partially polarized beams in atmospheric turbulence. An approximate expression is derived for the mode power coupling coefficients and some specific cases are studied using numerical methods. Several general results derived from the properties of the coupling coefficients are also presented. Possible applications for sources with tunable polarization distribution characteristics will be discussed.

A method for reducing noise in near-IR laser communications has been proposed that relies upon the dual wavelength output of the He-Xe laser having a high level of noise coherence. However, in transmissions through the atmospheric boundary layer, an additional and significant noise component is added by atmospheric scintillation. These scintillations are mainly limited to frequencies of less than 1 kHz and are correlated in the two laser channels to a degree determined by the channel wavelength separation, the transmission range and the severity of the turbulence regime. To analyze the propagation of waves in random media one normally considers the statistics of the field. In the case of small angle forward scattering, which is the case of interest in laser propagation, field moments higher than the fourth are so difficult to solve that no solutions are known outside of the asymptotic weak and strong approximations. An alternative approach is to conduct numerical experiments in which one generates a realization of the random medium (with the desired statistics) and then calculates the wave field. We have numerically modeled the spatial irradiance intensity as a function of range from a point source under turbulence regimes typical of daytime conditions near the Earth’s surface. Simulations were performed for two closely separated channels in the near-IR (1556.5 and 1558.1 nm). We present the results of these simulations together with the implications for the mitigation of atmospheric scintillation noise by common mode rejection.

There are well known factors which provoke image distortions during the propagation of light in the atmosphere. We used the solution of the linear unsteady 3D Navier - Stokes equations in order to model turbulent fluctuations of the refractive index. Parabolic equation method has been used for the solution of the problem of laser propagation. Density distribution and structure function were determined as well as their temporal evolution. Distortions of the Gaussian beam due to the fluctuations of the refractive index are presented.

With the advent of new developments in tracking, pointing, and compensation of laser beams over the past several years, a requirement has been established for increasing knowledge of optical turbulence along the propagation path. This has stimulated the development of new methodologies to sense the refractive index structure parameter (C_n²) and derived parameters such as the transverse coherence length (r_O), the isoplanatic angle (θ_O), and the Rytov variance (σ_χ²). A historical perspective of these methodologies and instrumentation is presented and both in situ and remote sensing techniques are discussed. Recent designs of r_O meters are shown. Of particular interest is the development of techniques to derive turbulence parameters such as C_n², the eddy dissipation rate (ε), the inner scale (l_O), and the outer scale (L_O). Observational results are discussed using sodar and radar of phenomena generating turbulence including gravity wave activity, jet streams, Kelvin-Helmholtz instabilities, convection, and frontal activity. Both frequency modulated-continuous wave (FMCW) and mesosphere-stratosphere-troposphere (MST) radar are discussed. New techniques and results are shown examining if the turbulent atmosphere is truly Kolmogorov (how often is the structure function represented by the r^2/3 law), stationary, isotropic, and homogeneous. Emerging techniques for sensing turbulence such as optical path profilers and lidar are discussed.

The Naval Research Lab (NRL) is currently operating a lasercom test facility (LCTF) across the Chesaepeake Bay between NRL's Chesapeake Bay Detachment (NRL-CBD) and NRL-Tilghman Island. This lasercom test facility has successfully demonstrated 32 km retro-reflected links at data rates up to 2.5 Gbps. Along with lasercom link studies, atmospheric characterization of the NRL-CBD to Tilghman Island optical path has been investigated. These studies range from passive optical turbulence monitoring based on angle-of-arrival measurements of a spotlight's apparent motion, to intensity and angle-of-arrival measurements of a retro-reflected laser beam. Currently the LCTF is being upgraded from a retro-reflected link to a direct one-way link from NRL-CBD to NRL-Tilghman Island. Initial measurements of atmospheric turbulence effects in this one-way configuration have recently been performed. Results of these past and current atmospheric turbulence studies are presented.

The estimation of the performance of electro-optical systems depends on the accuracy of the atmospheric models being used in the propagation prediction codes. On the basis of a large set of imaging LIDAR measurements a Middle East model of refractive turbulence strength (C_n²) vertical profile has been developed. The model is presented in this work. Implications can be important for optical communication, laser weaponry, imaging through the atmosphere, and adaptive optics.

The results of lidar measurements of aerosol size distribution, volume, and number concentration at different heights in the Mediterranean region (Be'er-Sheva, Israel) and comparison with models (AFGL, MODTRAN) are presented.

There is increasing interest in free space optical communications as an alternative to fibre optics and radio frequency communications, particularly in 'last mile' applications and applications with weight and power restrictions e.g. communications with unmanned aerial vehicles. The potential advantages of free space optical communications include: high bandwidth; no licensing issues; smaller, lighter payloads; low probability of intercept; and immunity from interference/jamming. However, propagation through the atmosphere is subject to atmospheric scintillation noise affecting the signal-to-noise ratio (SNR), effectively reducing the range and bandwidth of the communication link. This scintillation is experienced even over relatively short propagation paths and is caused by small temperature variations in the atmosphere, resulting in index of refraction changes. In this paper we present a technique to correct for atmospheric scintillation noise in free space optical communications and laser remote sensing. It uses common mode rejection to remove co-channel noise, where each channel is transmitted on separate, but closely spaced, wavelengths. The signal-to-noise ratio is significantly increased, thereby increasing the range and/or bandwidth of the link. To date, tests have been conducted with analogue audio and video transmissions. This has been successful, with improvements of up to 12dB in SNR having been demonstrated. This has been limited by the current implementation, which is only at prototype stage -- the ultimate achievable improvement in SNR is anticipated to be significantly higher.

In this paper, we will present information theoretic bounds on the estimated Zernike coefficients for various diversity phase functions. We will show that, in certain cases, defocus diversity may yield higher Cramer-Rao lower bound (CRLB) than some other diversity phase functions. Evaluating the performance of the phase diversity algorithm using simulated images, we find that for an extended scene and defocus diversity, the phase diversity algorithm achieves the CRLB for known objects and approaches the CRLB by about a factor of two for unknown objects.

Free-space optics (FSO) is a technology that uses modulated optical beams to transmit information in a line-of-sight fashion to achieve a high-bandwidth communications link. FSO technology has been investigated for military and civilian “last mile” applications for many years and, more recently, has generated interest for space-based applications. As the use of FSO technology grows, the potential for optical interference that degrades FSO network performance, whether intentional (jamming) or otherwise, becomes a matter of increasing importance. The investigation described in this paper examined the effects of interference upon the operation and performance of a point-to-point FSO link connecting two virtual local area networks. The sources of interference were laser pulses of varying energy, wavelength, and repetition rate produced from a nitrogen-pumped, tunable dye laser. The study evaluated the effect upon FSO link performance of varying the output power of the interfering source for a fixed wavelength, of varying the wavelength of the source for a fixed power, and of varying the pulse repetition rate of the source. The results of the study indicated that FSO link performance was negatively influenced by such interference.

Free-space optics (FSO) is a technology that uses modulated optical lasers to transmit information in a line-of-sight path through the atmosphere. To date, the major focus of FSO research and development has been toward the transmission of digital data, mostly for “last mile” applications. This paper investigates the simultaneous transportation of multiple analog radio frequency (RF) signals over a single FSO link using wavelength division multiplexing (WDM) technology. Experimental measurements of optical peak power and signal-to-noise ratio (SNR) indicate the suitability of FSO links for supporting WDM applications.

Changing the field-of-view of a laser communication system in real-time without mechanical motion could significantly improve signal strength and reduce drop out rates. By incorporating active elements into the optical design, we have designed and demonstrated imaging systems that are capable of variable effective focal lengths with no macroscopic moving parts (i.e. active optical zoom). This technique, in which the active optics serve as variable focal-length lenses, could easily be applied to laser communication systems to improve capability. The key to this concept is to create relatively large changes in the field-of-view of the system with very small changes in the focal lengths of individual elements by leveraging the optical power of conventional optical elements surrounding the active optics. By appropriately designing the optical system, these variable focal-length lenses can provide the flexibility necessary to change the overall system focal length, and therefore field-of-view, that is normally accomplished with mechanical motion in conventional zoom systems.

This paper will describe single and double path laser link measurements over land and sea. The laser system consisted of a CO₂ laser, a pointing and tracking head, a quadrant laser receiver, a 3-5 μm IR-camera, a TV camera and a laser range finder. For the naval scenario the laser system was placed in a building 18 m above water and corner cube targets and a single path receiver were placed on islands at 2.5, 5.5 and 16.5 km. For the land scenario the laser system was placed in a building about 13 meters above ground looking at targets and a single path receiver at 2 km range. Together with the laser registrations, separate instruments such as a scintillometer and a weather station were recording the meteorological parameters. The analysis contains evaluation of temporal and amplitude signal distributions, probability and mean time of fade and tracking performance. Results from single ended and double ended paths will be compared. Different ways of using this database for turbulence simulation and laser system performance predictions also in other wavelength regions will be discussed as well as the impact on applications including laser imaging, free-space laser communications and directed infrared countermeasures.

In May 2004 a joint atmospheric propagation experiment was conducted between the Australian Defence Science and Technology Organisation, the Office of Naval Research and the University of Central Florida. A 45 mm divergent Gaussian beam was propagated along a horizontal 1500 meter path approximately 2 meters above the ground. At the receiver were 3 apertures of diameter 1mm, 5mm, and 13mm. The scintillation was measured at each aperture and compared to scintillation theory, recently developed for all regimes of optical turbulence. Three atmospheric parameters, C_n², l_o and L_o, were inferred from these optical measurements. Simultaneously, a commercial scintillometer, which recorded values for C_n², was set up parallel to the optical path. In this paper, a numerical scheme is used to infer the three atmospheric parameters and comparisons are made with the C_n² readings from the scintillometer.

Mean irradiance data from a field experiment conducted jointly by the Australian Defence Science and Technology Organisation, the Office of Naval Research, and the University of Central Florida is presented. The experiment was conducted in May 2004 in Adelaide, Australia. The propagation path was characterized by conditions of moderate to strong irradiance fluctuations. The data is compared to existing theoretical results and a new theoretical result developed in this paper. The new theoretical result is based on a modified Rytov method that extends the validity of the Rytov method into moderate to strong irradiance fluctuation conditions.

Various experiments have been carried out recently in Middle East (Israel) environments for prediction of aerosol particle concentration and size distribution versus sea-breeze wind speeds and overland ranges. During these experiments aerosol particle concentrations for different overland distances were measured and analyzed. This work proposes a new model for aerosol size distribution prediction up to 50-km distance away from the Mediterranean coast based on an extensive series of measurements. The model introduces coefficients and characteristics of processes of absorption and scattering by aerosol particles in the northern Negev desert areas. Effects of sea breeze wind over different ranges are described by the model proposed in this work using parameters obtained empirically.

The aperture averaging factor is a measurement of the ratio of the atmospheric turbulence-induced irradiance scintillations incident on a receiver with diameter D to those incident on a point receiver. Characterizing the amount of aperture averaging in an optical receiver system will allow for tradeoffs to be made between the error performance of an optical receiver and the size and weight of the receiver. Aperture averaging theory has been extensively developed for optical wave propagation in weak turbulence conditions. A lack of experimental aperture averaging data over a variety of turbulence strengths, test range characteristics, and aperture diameters restricts progress in the development of useable propagation models. Experimental measurements of the aperture averaging factor collected over a test range at the University of Maryland are presented here. The impact of this data on the design of free space optical communication receivers will be discussed.

The Naval Center for Space Technology at the Naval Research Laboratory reports the latest results from the long-range, maritime, free-space lasercom test facility located between Chesapeake Beach, MD and Tilghman Island, MD. The two sections of the facility are separated by 16.2 km of the Chesapeake Bay. Using a new OC-48 receiver developed by NRL’s Optical Science Division with a sensitivity of -33dBm for 10^-9 bit error rate at 2.5 Gbps, we have closed a 32.4 km maritime lasercom link (round trip across the Chesapeake Bay) and performed bit error rate testing while transmitting 1.13 Terabytes of data. Bit error rate testing was also performed at lower data rates when atmospheric conditions were not favorable for high speed (2.5 Gbps), including testing at 150 Mbps through light fog and rain. In addition, we have set up a system for digitizing and transmitting full-color, uncompressed, video along with six audio channels and three RS-232 data channels over the maritime link. The digital link operated at 311 Mbps and could be maintained indefinitely, depending on atmospheric conditions. Several complete videos were transmitted in entirety or in part as well as live video from a handheld camcorder to test the system operation and robustness. The transmitter and receiver were co-located on the western shore of the bay at the NRL Chesapeake Bay Detachment. The data for both the bit error rate testing and the video was transmitted across the bay and returned from an array of retroreflectors located on a tower at Tilghman Island on the eastern shore. The lasercom links were closed with static pointing and with no active atmospheric aberration mitigation such as adaptive optics or fast steering mirrors on the receiver optics.

While the wave structure function has been analytically calculated for a variety of beam types, recent work has begun the exploration of higher-order beams and partially coherent beams. For these waves, no analytic wave structure function has been developed. By extending the well known split step phase screen simulations, we have developed a method of numerically simulating the wave structure function. We present the methods and results of this simulation technique, and describe its applicability to general beams.

Scintillation is one of the most common statistics in the literature of mathematical modeling of laser propagation through random media. One approach to estimating scintillation is through the Rytov approximation, which is limited to weak atmospheric turbulence with the standard Kolmogorov spectrum. Recently, a modification to the Rytov approximation was developed. Through a filter function approach, the new results for scintillation are valid for moderate to strong fluctuations along a horizontal path. To date, expressions governing scintillation for plane, spherical, and Gaussian beam waves has been developed for horizontal propagation paths. For the special cases of plane and spherical waves, expressions have been developed for slant paths. In this paper, an expression governing scintillation of a Gaussian beam along an uplink slant path valid in all regimes of turbulence is presented.

A new type of lidar is under development for measuring profiles of atmospheric optical turbulence. The principle of operation of the lidar is similar to the astronomical seeing instrument known as the Differential Image Motion Monitor, which views natural stars through two or more spatially separated apertures. A series of images is acquired, and the differential motion of the images (which is a measure of the difference in wavefront tilt between the two apertures) is analyzed statistically. The differential image motion variance is then used to find Fried's parameter r₀. The lidar operates in a similar manner except that an artificial star is placed at a set of ranges, by focusing the laser beam and range-gating the imager. Sets of images are acquired at each range, and an inversion algorithm is then used to obtain the strength of optical turbulence as a function of range. In order to evaluate the technique in the field and to provide data for inversion algorithm development, a simplified version of the instrument was developed using a CW laser and a hard target carried to various altitudes by a tethered blimp. Truth data were simultaneously acquired with instruments suspended below the blimp. The tests were carried out on a test range at Eglin AFB in November 2004. Some of the resulting data have been analyzed to find the optimum frame rate for ground-based versions of the lidar instrument. Results are consistent with a theory that predicts a maximum rate for statistically independent samples of about 50 per second, for the instrument dimensions and winds speeds of the Eglin tests.

In optical radar, communication, and energy transfer one frequently encounters the problem of transportating optical radiation energy to an object located in a randomly inhomogeneous medium. The scattering by the refractive index inhomogeneities of such a medium reduces the average intensity in the axial part of light beam and generates fluctuations of the intensity, so that the result is a considerable deterioration of the energy characteristics of systems operating in such media. The amplitude and phase fluctuations of Gaussian beam, propagated through the turbulent atmosphere, are not spatially homogeneous in a transversal beam section. Here we introduce an estimation criterion for beam computed for some different values of aperture/beam diameter ratio. The numerical simulations of beam propagation through the random-inhomogeneous media were performed using modified splitting method. The results of numerical experiments as well as the behavior of proposed criterion are discussed.