During long-term experiments FGAN-FOM measured C_n² values over land with identical scintillometers in two different climates, in moderate climate in mid-Europe and in arid climate. Since C_n² usually changes as a function of time-of-day and of season its influence on electro-optical systems can only be expressed in a statistical way. The cumulative frequencies of occurrence were calculated for a time period of one month for different times of the day. The statistical analysis was applied to calculate the effects of atmospheric turbulence on sensor performance like turbulence MTF, the resolution limit due to turbulence and intensity fluctuation. The calculations were performed for a SWIR sensor (active imaging system) and for typical MWIR and LWIR warning sensors. Turbulence MTF were calculated for a slant path of 5 km from the ground to a height of 100 m for upward and downward looking cases. For horizontal paths at a height of 2 m and 30 m the resolution limits due to turbulence were compared with the corresponding diffraction-limited ones. Calculations of the normalized intensity fluctuations were carried out for two slant propagation paths (zenith angle β = 30° and 80°).

We provide a description of the general meteorological conditions observed during the POLLEX trial, the effects of turbulence on imaging systems, the measurement of the effects of turbulence on a specially constructed image target, and the determination of the refractive index structure parameter using the results from two different scintillometers, from a fast sonic anemometer and hygrometer, and from the bulk meteorology.

We recently developed method for estimating the outer scale of tmospheric turbulence based on the correlation functions of lateral displ cements of thin beams propagating horizont lly over short paths.Here,the method is briefly summerized and comparison between the results of the method obtained by using the von Karman and Hill-Andrews models of turbulence is presented.

In this work we investigate optical distortions caused by the existence of a turbulent shear layer in a beam path. We look at several propagation paths and evaluate the loss of resolution caused by the inhomogeneous layer located at various distances from the transmitter. We use our wave-optics code for atmospheric propagation and implement into it propagation through a shear layer. Thus we are able to calculate a combined beam propagation, either emanating from the optical window or incoming from an outside source. The fluctuations of the index of refraction are calculated using the Wye's model

A main goal of this investigation is to extract local qualitative measurements of elementary turbulence effects on extended image objects from fast image sequences. These local measurements are a prerequisite for the relationship between the local turbulence level versus the degradation of specialized automatic processes and allow the selection of a specific image treatment (e.g. adequate object model) or the tuning (e.g. adaptive turbulence filtering) of an automatic image analysis process (e.g. object tracking). Results of the developed analysis methods on different sequences showing diverse image contents taken in a well known environment (desert test site, indoor experiments, simulation) under various conditions will be presented and discussed with respect to different applications (e.g. local C_N²-estimation).

Renewed interest in the propagation characteristics of a partially coherent beam has led to several recent studies that have extended theoretical developments started in the 1970s and 1980s. In this paper we use a model developed by the authors for single-pass propagation of a partially coherent beam and extend it to the case of a Gaussian-beam wave reflected from a finite rough-surface reflecting target. This model can be modeled as a random phase screen (or diffuser) in front of a smooth finite reflector. The target acts like a deep random phase screen for the case of a fully diffuse surface and becomes a continually weakening phase screen as the target surface become smoother. We present mathematical models for the mutual coherence function (MCF) and the scintillation index of the reflected Gaussian beam wave in the presence of atmospheric turbulence. This analysis includes partial and fully developed speckle from the target. From the normalized MCF, estimates are given for the speckle size in the pupil plane and image plane as a function of transmitted beam wave characteristics, size and roughness of the target, and size of the receiver-collecting lens. Expressions for the scintillation index are valid under weak-to-strong fluctuation conditions and are shown to agree with well-known results in limiting cases of a fully diffuse target and a smooth reflector.

Ray theory plays an important role in determining the propagation properties of high-frequency fields and their statistical measures in complicated random environments. For computations of the statistical measures it is desirable therefore to possess a solution for the high-frequency field propagating along an isolated ray trajectory. In this work a reference wave is applied to obtain an analytic solution of the parabolic wave equation describing propagation along the ray trajectory of the deterministic background medium. The methodology is based on defining a paired field measure as a product of an unknown field propagating in a disturbed medium and the complex conjugate component propagating in a medium without random fluctuations. Once a solution of the equation for the paired field measure is obtained, the solution of the unknown field can be determined in an explicit form by extracting from the paired solution the solution of the deterministic component.

Near the sea surface, strong gradients of temperature and moisture affect the path taken by propagating radiation. Strong gradients in aerosol properties may also be present causing transmittance and radiance to be strongly dependent on the exact path taken by radiation, especially when viewing angles are nearly horizontal. So far, the rapid changes of atmospheric properties with altitude near the surface have been neglected in the calculations of transmittance and path radiance. In this paper, calculations of transmittances under sub- and super-refraction conditions are presented. It is shown that transmittance can vary significantly when accounting for refraction in platform based or limb viewing conditions. Furthermore, calculations of path-radiance in the surface layer, which accounts for the scattering of incident radiation, will be addressed and computational results presented.

A first version of the integrated model EOSTAR (Electro-Optical Signal Transmission and Ranging) to predict the performance of electro-optical (EO) sensor systems in the marine atmospheric surface layer has been developed. The model allows the user to define camera systems, atmospheric conditions and target characteristics, and it uses standard (shipboard) meteorological data to calculate atmospheric effects such as refraction, turbulence, spectrally resolved transmission, path- and background radiation. Alternatively, the user may specify vertical profiles of meteorological parameters and/or profiles of atmospheric refraction, either interactively or in data files with a flexible format. Atmospheric effects can be presented both numerically and graphically as distorted images of synthetically generated targets with spatially distributed emission properties. EOSTAR is a completely mouse-driven PC Windows program with a user-friendly interface and extended help files. Most calculations are performed in real-time, although spectral transmission and background radiation calculations take up to a few seconds for each new meteorological condition. The program can be used in a wide range of applications, e.g., for operational planning and instruction.

The sensitivity of modern infrared sensors, using cooled Focal Plane Arrays (FPA's), allows the detection of small incoming airborne targets at sea as soon as they pop-up over the horizon. Experiments show strong fluctuations of the contrast-irradiance level of target and background at the entrance pupil of the sensor. The characteristics of these fluctuations have an impact on the design of detection- and tracking algorithms of the Infrared Search and Track (IRST) sensors and tracking systems. Several physical phenomena may contribute to the apparent contrast intensity (and thus signal) variations, such as specular sun- or cold sky reflections at the target surface, changes in the aspect angle and height of the target, coherence of the target radiation dependent on its size and range, atmospheric turbulence, wave chopping, diffraction at the wave tops, wave effects on the temperature profile in the atmospheric boundary layer, local droplet clouds produced by breaking waves, detector temporal- and spatial noise and under-sampling and fill-factor effects when the sensor is panning over the scene. The magnitude of each of these effects is estimated and compared to data from measurements. It is in general not simple to determine which effect is dominant in a certain case. The low frequency behaviour of the signal variations suggests that "classical" scintillation is not the major contributor in most cases. It is shown that structure variations in the boundary layer along the path due to waves, may be responsible for most of the low frequency effects.

A critical moment in the detection process of incoming target at sea occurs, when a target just appears above the horizon. The corresponding light rays cross the atmospheric boundary layer, in which the presence of temperature gradients may result in optical distortion effects. This geometric distortion implies propagation effects such as the variation of the angle of arrival of the horizon line, a change in the shape of an extended target, the possible presence of mirages and enhanced or decreased atmospheric transmission or apparent radiant intensity of a point target. This situation is becoming even more complex, when the temperature profile is not constant over the path length, which is likely to be the case in coastal areas with tidal currents. Another effect causing complexity is the presence of surface waves, introducing a vertical motion in the marine boundary layer. All these effects may have an impact on the detection performance of optical and infrared sensors for detection and identification of targets near the horizon. Presently available propagation models are unable to predict accurately the effect of the phenomena on the propagation of surface grazing light beams. A new and accurate ray-tracing model has been developed, allowing quantitative predictions of the various propagation effects for a given profile of the temperature. This model, capable to take into account the dimensions of the target and the receiver aperture, is described in the paper. The ray tracing in the model is based upon the Huygens-Fresnel principle, in contrary to other models, where a layered atmosphere is used. Examples are given of the effect of different temperature profiles and comparisons of predictions are made with data from field measurements.

There is recent interest from the US Department of Defense in free space optical communication networks involving aircraft flying at various altitudes. The optical links between these aircraft may be as long as 100km, and involve communication between network nodes that are moving at sub-sonic speeds. An unresolved issue for links of this kind between pairs of aircraft is the effect of boundary layer turbulence near each aircraft, as well as along the atmospheric path between them. The deployment of optical wireless links in several different scenarios will be described. These include links near to the ground for which the turbulence parameter C_n² varies along the path between transmitter (TX) and receiver (RX), high altitude links between aircraft, and ground to aircraft links. The last two of these may involve boundary layer turbulence near the aircraft node where the turbulence is localized either at the TX or at the RX. Some of the theoretical approaches to examining these situations will be described, as well as an ongoing program of research to examine these situations experimentally. Ways to mitigate the effects of node motion, and scintillation at the RX will be discussed, including the use of non-imaging concentrators at the RX.

Optical wireless networks are emerging as a viable, cost effective technology for rapidly deployable broadband sensor communication infrastructures. The use of directional, narrow beam, optical wireless links provides great promise for secure, extremely high data rate communication between fixed or mobile nodes, very suitable for sensor networks in civil and military contexts. The main challenge is to maintain the quality of such networks, as changing atmospheric and platform conditions critically affect their performance. Topology control is used as the means to achieve survivable optical wireless networking under adverse conditions, based on dynamic and autonomous topology reconfiguration. The topology control process involves tracking and acquisition of nodes, assessment of link-state information, collection and distribution of topology data, and the algorithmic solution of an optimal topology. This paper focuses on the analysis, implementation and evaluation of algorithms and heuristics for selecting the best possible topology in order to optimize a given performance objective while satisfying connectivity constraints. The work done at the physical layer is based on link cost information. A cost measure is defined in terms of bit-error-rate and the heuristics developed seek to form a bi-connected topology which minimizes total network cost. At the network layer a key factor is the traffic matrix, and heuristics were developed in order to minimize congestion, flow-rate or end-to-end delay.

Free space, dynamic, optical wireless communications will require topology control for optimization of network performance. Such networks may need to be configured for bi- or multiple-connectedness, reliability and quality-of-service. Topology control involves the introduction of new links and/or nodes into the network to achieve such performance objectives through autonomous reconfiguration as well as precise pointing, acquisition, tracking, and steering of laser beams. Reconfiguration may be required because of link degradation resulting from obscuration or node loss. As a result, the optical transceivers may need to be re-directed to new or existing nodes within the network and tracked on moving nodes. The redirection of transceivers may require operation over a whole sphere, so that small-angle beam steering techniques cannot be applied. In this context, we are studying the performance of optical wireless links using lightweight, bi-static transceivers mounted on high-performance stepping motor driven stages. These motors provide an angular resolution of 0.00072 degree at up to 80,000 steps per second. This paper focuses on the performance characteristics of these agile transceivers for pointing, acquisition, and tracking (PAT), including the influence of acceleration/deceleration time, motor angular speed, and angular re-adjustment, on latency and packet loss in small free space optical (FSO) wireless test networks.

The possibility of using high-data-rate optical transmitters for satellite communication has generated interest in laser communication systems for ground-to-space and space-to-ground data links. Among the parameters useful to model propagation along a vertical path are the refractive index structure constant C_n² profile and boundary layer turbulent strength. One of the most widely used turbulent models is the Hufnagel-Valley (HV) which depend on vertical wind profile and integrated turbulence along the propagation path. We have developed a statistical studied of the input parameters above Canary Island Observatories using a metereological database to collect the wind profiles and DIMM database to evaluate zero order moment. We are estimated the isoplanatic angle and the down-link scintillation. To check the consistency of the model, we are compared the isoplanatic results with isoplanatic angle measured by SCIDAR campaigns (17 nights along the year). To establish the average turbulence wind speed, we are used an observational correlation finds by Sarazin at other high mountain observatories.

A commercial linear one-dimensional, 1x4096 pixels, zero-twist nematic liquid crystal spatial light modulator (SLM), giving more than 2π phase modulation at λ = 850 nm, was evaluated for beam steering applications. The large ratio (7:1) between the liquid crystal layer thickness and pixel width gives rise to voltage leakage and fringing fields between pixels. Due to the fringing fields the ideal calculated phase patterns cannot be perfectly realized by the device. Losses in high frequency components in the phase patterns were found to limit the maximum deflection angle. The inhomogeneous optical anisotropy of the SLM was determined by modelling of the liquid crystal director distribution within the electrode-pixel structure. The effects of the fringing fields on the amplitude and phase modulation were studied by full vector finite-difference time-domain simulations. It was found that the fringing fields also resulted in coupling into an unwanted polarization mode. Measurements of how this mode coupling affects the beam steering quality were carried out and the results compared with calculated results. A method to compensate for the fringing field effects is discussed and it is shown how the usable steering range of the SLM can be extended to ± 2 degrees.

It was shown that there exist two sources of errors in an adaptive optics system. The first source appears due to limitations induced by the elements of the system such as a Shack Hartmann sensor and deformable mirror. The second associated with the violation of the optical reciprocity principle in algorithm of phase conjugation, namely, with substitute of beacon amplitude distribution by distribution of a Gaussian beam generated by a laser. Absolute correction of turbulent aberration is possible only in case of strict maintenance of a principle, i.e. in case of phase reversal. In the paper the possibility is considered to realize phase reveresal in a linear system and only with the use of phase control of the beam. The system should include two mirrors separated by the vacuum gap of a finite size. Estimations were obtained by correction efficiency on the base of phase conjugation and with the use of two mirror adaptive system.

Earlier research reported a comparison of the wavefronts recorded simultaneously by a Shack-Hartmann and a Distorted Grating Wavefront Sensor (DGWFS). In this paper we present the results of a continuation of this earlier work where we have now closed an adaptive optics loop under simulated propagation conditions using the Advanced Concept Laboratory (ACL) at Lincoln Laboratory. For these measurements only one wavefront sensor controlled the deformable mirror at a time. To make direct comparisons between the sensors we took advantage of the ACL’s ability to exactly replicate a time varying propagation simulation. Time varying and static comparisons of the two sensors controlling the ACL adaptive system under conditions that ranged from a benign path, D/r₀ = 2, to a propagation condition with significant scintillation, D/r₀ =9, will be shown using the corrected far field spot as a measure of performance. The paper includes a description of the DGWFS used for these tests and describes the procedure used to align and calibrate the sensor.

We examine the utility of a wavefront sensor with a variable subaperture size for astronomical adaptive optics. A numerical analysis, based on wavefront variance and Strehl ratio expressions, was used to find the optimal subaperture size and wavefront sensor integration time for several case studies. The results show that a relatively smaller subaperture size can provide improved performance if the atmospheric coherence length r₀ is also small and the source is relatively bright. Similarly, a larger subaperture size can improve performance if r₀ is also large, the source is relatively dim, and the atmospheric temporal variation is relatively slow. These results suggest that a reconfigurable wavefront sensor could have utility for certain situations where conditions vary from nominal values.

Long-baseline optical interferometers have become useful tools for obtaining detailed stellar information and high-resolution images in the astronomy community. Several interferometric systems have been implemented successfully without adaptive optics; however, adaptive optical systems may be needed for a new generation of long-baseline interferometers with large telescopes such as those being developed for the Magdalena Ridge Observatory (MRO). This paper introduces the design trade-offs used to investigate the need for adaptive optics for a long-baseline optical interferometer operating in the turbulent atmosphere. Modeling techniques are combined with analytical equations to study the performance of a long-baseline optical interferometer with and without adaptive optics.

We present FALCON, a concept of new generation multi-objects integral field spectrograph with adaptive optics for the ESO VLT. The goal of FALCON is to combine high angular resolution (0.15 - 0.25 arcsec) and high spectral resolution (R≥5000) in the 0.8-1.8 μm wavelength range across the Nasmyth field (25 arcmin). Instead of compensating the whole field, the correction will be performed locally on each scientific object. This implies to use small miniaturized devices for adaptive optics correction and wavefront sensing. The main scientific objective of FALCON will be extragalactic astronomy. It will therefore have to use atmospheric tomography because the stars required for wavefront sensing will be in most of the cases far outside the isoplanatic patch. We show in this paper that applying adaptive optics correction will provide an important increase in signal to noise ratio, especially for distant galaxies at high redshift.

This note describes a possible Monte Carlo procedure to deal with propagatiaon of optical radiation in a medium containing non-spherical particles, without the limit of isotropic orientation of their axes. It is based on the choice of two polarization states which does not change during the propagation in the turbid medium. An approximate procedure is considered for permitting the use of only two polarization states.

The recently improved ultra-fast aircraft resistance thermometer measures with a time constant of the order 0.1 ms. For an aircraft speed of 100 m/s this time constant corresponds to a spatial resolution of a few centimeters. Measurements made both in the atmosphere and in the low-turbulence wind tunnel at air speed 80 m/s are corrupted with noise of a few kHz frequency. Authors of the thermometer suggest that this noise results from turbulence introduced by vortex shedding from the protective shield. To achieve further improvement of the instrument we have to understand the nature of these aerodynamic disturbances. The present study is carried in two complementary directions. In the first, flow modeling is made with the FEATFLOW 1.2d - a finite element software for the incompressible Navier-Stokes equations. The results of flow simulation are in qualitative agreement with the experiment. In the second, we simulate visualization of the flow using two optical spatial filters: the Foucault filter that gives output intensity signal where bright bias is modulated with 1-D Hilbert transform of an object phase function and modified Zernike phase filter that shifts phase of the spectrum dc term by 0.2π.

High angular resolution observations of the sun are limited by atmospheric turbulence. The MISOLFA seeing monitor (still under construction) is developed to obtain spatial and temporal statistical properties of optical turbulence by analyzing local motions observed on solar edge images. The solar flying shadows used for angle-of-arrival spatio-temporal analysis are observed in the pupil plane image by mean of a rectangular thin slit positioned on the solar edge image. A numerical simulation of the light propagation in both the atmospheric turbulence medium and the MISOLFA optical system is carried out studying the relation of the measured intensity variations in the pupil plane to angle-of-arrival fluctuations in the non-isoplanatic case. First results are presented and discussed.

Atmospheric turbulence is one of the important factors that influence on scene spatial resolution. In order to restore an image with minimum distortions one must know the correlation function for fluctuations of refractive index and the distorting PSF as a result. Grid-generated turbulence is a classic example of homogeneous and isotropic turbulence. Statistical properties of this flow have been investigated experimentally. In our case of grid-generated turbulence the statistical properties are distinct from the Kolmogorov's two-thirds law. Calculations performed on the basis of the linearized three-dimensional unsteady Navier-Stokes equations gave similar results. We modelled laser beam propagation through turbulent atmosphere and obtained numerical data for the distortion of images. The distortion of PSF and the set of resolving functions were found according to the structure function. The problem of compensation of distortions caused by turbulence was solved with the aid of a new local-linear super-resolution method. This method allows to resolve turbulent distortions of PSF at low signal-to-noise ratio.

The experimental study of laser beam propagation in turbulence is relevant to fields such as adaptive optics and optical communications. Turbulence sensing for astronomical purposes requires a convergent laser beam adequately focused on the sodium mesospheric layer. Free Optical communications ground-to-satellite usually are based on divergent laser beams travelling partially through the atmosphere. We present several measurements of the gaussian beam radius for divergent and convergent laser beams propagated in vertical paths. The determinations were carried out at the Teide Observatory (Canary Islands) from the analysis of Rayleigh scattering. The turbulence profile was simultaneously measured with a SCIntillation Detection And Ranging (SCIDAR) instrument. This way, we analyse the influence of the different turbulence layers in the focusing problem through the empirical relation between the beam waist radius and the intensity of the turbulence. We present the experimental set-up, the first results of the experiment and the plans to conduct a statistical study in the future.

Scintillation is increased when laser propagates long distance near horizontally in atmospherics, which limits the ability of conventional adaptive optical system. A theoretical analysis is presented based on extend Huygens-Fresnel theory for Gaussian beam profile. Numerical simulations based on wave optics computer code are given for different atmospheric condition. For given Rytov variance different turbulence strength and propagating distance are considered. Various receiving and projecting apertures are also considered. Rytov variance and propagation Fresnel have more effect on Strehl ratio. The expressions of Strehl ratio versus Rytov variance are obtained from weak to strong scintillation. For given Rytov variance, Strehl ratio with Fresnel number is studied. Large aperture has benefit for correction. The results show that Strehl ratio increases with Fresnel number and saturates to the limit of ideal phase-only correction for given Rytov variance.

It is well known that, a piecewise function can be expanded by an orthogonal set of functions. If the expansion coeficients are suitable for a large number of terms, the reconstruction of function can be achieved with high accuracy. However, for a few of them the reconstruction of the input function, in general, is poor. In this work, we reconstruct discrete image functions using the complex Zernike polynomials. We compare the reconstruction of the input image function in two cases. When the input image is mapped inside or outside an unit circle for several expansion orders. To measure the reconstruction we use the relative error between the input and reconstructed images. Also, we show that the relative error can be reduced if the module of the complex discrete distribution of the reconstruction is squared.

In this work we present an optical-digital system that uses a liquid crystal display (LCD)for the approximate reconstruction of binary images by using the Zernike moments. We use the fact that, each Zernike polynomial can be mapped as an intensity distribution and therefore can be readily displayed with a LCD in an optical incoherent system. On the other hand, the reconstruction of the input image can be obtained from a discrete sum of the data matrices corresponding to the Zernike images weighted by suitable coefficients. These can be numerically computed by using their orthogonality property. The Zernike images acquired by the optical-digital system generate a basis set for the image reconstruction, which depends on both LCD and CCD sensor spatial resolution. The reconstruction is implemented with only thirty six real-valued Zernike moments.

A series of airborne imaging experiments have been conducted on the island of Maui. The imaging platform was a Twin Otter aircraft, which circled ground target sites. The typical platform altitude was 3000 meters, with a slant range to the target of 9000 meters. This experiment was performed during the day using solar illuminated target buildings, and at night with spotlights used to simulate point sources. Imaging system performance predictions were calculated using standard atmospheric turbulence models, and aircraft boundary layer models. Several different measurement approaches were then used to estimate the actual system performance, and make comparisons with the calculations.