For paraxial propagation of scalar waves classic electromagnetic theory definitions of transverse linear (TLM) and
orbital angular (OAM) momenta of beam waves are simply related to the wave coherence function. This allows the
extension of the TLM and OAM density concepts to the case of partially coherent waves. This is also makes possible to
use the parabolic equations technique to describe TLM and OAM evolution on propagation. We show that both total
TLM and OAM are conserved for the free space propagation, but not for propagation in inhomogeneous medium in
general. Under Markov Approximation (MA), in the presence of the random statistically homogeneous medium the total
TLM and OAM are conserved in average. Based on the MA parabolic equation for the fourth-order coherence function,
we examine for evolution of the total OAM variance. Perturbation solution of this equation shows that the OAM
fluctuations in general grow approximately linearly with the propagation path length. However, this growth appears to
be slower for the beams with rotation-symmetric irradiance.
Traditionally, the partially-polarized light is characterized by the four Stokes parameters. Equivalent description is also
provided by correlation tensor of the optical field. These statistics specify only the second moments of the complex
amplitudes of the narrow-band two-dimensional electric field of the optical wave. Electric field vector of the random
quasi monochromatic wave is a nonstationary oscillating two-dimensional real random variable. We introduce a novel
statistical description of these partially polarized waves: the Period-Averaged Probability Density Function (PA-PDF) of
the field. PA-PDF contains more information on the polarization state of the field than the Stokes vector. In particular, in
addition to the conventional distinction between the polarized and depolarized components of the field PA-PDF allows
to separate the coherent and fluctuating components of the field. We present several model examples of the fields with
identical Stokes vectors and very distinct shapes of PA-PDF. In the simplest case of the nonstationary, oscillating normal
2-D probability distribution of the real electrical field and stationary 4-D probability distribution of the complex
amplitudes, the newly-introduced PA-PDF is determined by 13 parameters that include the first moments and covariance
matrix of the quadrature components of the oscillating vector field.
Theory presented in the companion paper [1] reveals that for paraxial propagation of scalar waves transverse linear momentum (TLM) and orbital angular momentum (OAM) of beam waves are simply related to the wave coherence function, and that the TLM and OAM densities can be measured by a conventional Shack-Hartman sensor, which is typically used for the phase measurements. Here we present the extension of this theory to the case of the OAM fluctuations of a spherical wave intercepted by a finite aperture. We report the OAM measurements derived from the data obtained by the Hartman Turbulence Sensor (HTS) during the field measurement campaign in 2009-10 and data produced by wave optics simulation of the HTS. We examine the statistics of the total OAM intercepted by the wave front sensor aperture and compare it to theoretical results. Modeling data supports the conservation of the mean OAM and relatively slow development of the OAM fluctuations predicted by the theory.
For paraxial propagation of scalar waves classic electromagnetic theory definitions of transverse linear (TLM) and orbital angular (OAM) momenta of beam waves are simply related to the wave coherence function in the coherent wave case. This allows the extension of the TLM and OAM density concepts to the case of partially coherent waves when phase is indeterminate. We introduce a general class of Radial Irradiance-Angular Phase (RI-AP) waves that includes the Laguerre-Gaussian (LG) beams, and similar to LG beams have discrete OAM to power ratio, but have more complex phase shape than simple helices of LG beans. We show on several examples that there no direct connection between the intrinsic OAM and optical vorticity. Namely, neither the presence of the optical vortices is necessary for the intrinsic OAM, nor the presence of the optical vortices warrants the non-zero intrinsic OAM. We examine OAM for two classes of partially-coherent beam waves and show that the common, Schell-type coherence, does not add variety to the TLM and OAM in comparison to coherent waves. However, Twisted Gaussian beam has an intrinsic OAM with per unit power value that can be continuously changed by varying the twist parameters. This analysis suggests an intrinsic OAM creation method based on rotation of tilted Gaussian beam. Using the parabolic propagation equation for the coherence function, we show that both total TLM and OAM are conserved for the free space propagation. We discuss the application of the Shack-Hartman wave front sensor for the OAM measurements.
Statistics of the random phase screens used for the modeling of beam propagation and imaging through the turbulent atmosphere is currently based on the Markov Approximation (MA) for wave propagation. This includes the phase structure functions of individual screens and the use of the statistically-independent screens for the multi-screen splitstep simulation of wave propagation. As the propagation modeling progresses to address the deep turbulence conditions, the increased number of phase screens is required to accurately describe the multiple scattering. This makes the MA a critical limitation, both because phase statistic of the thin turbulent layer does not follow MA, and because the closely space screens cannot be considered as statistically and functionally independent. A recently introduced Sparse-Spectrum (SS) model of statistically homogeneous random fields makes it possible to generate 3-D samples of refractive-index fluctuations with prescribed spectral density at a very reasonable computational cost. This leads to generation of samples of the phase screen sets that are free from the limitations of the MA. We investigated statistics of the individual phase screens and cross-correlations between the pairs of phase screens and found that the thickness Δz of the turbulent layer replaced by the phase screen is a new parameter defining the phase statistics in the non-Markov case. SS-based numerical algorithms for generation of the 3-D samples of the turbulent refractive index, and for the phase screen sets are presented. We also compare the split-step simulation results for the traditional MA and non-Markov screens.
Beam spread and beam wandering are the most perceptible effects of atmospheric turbulence on propagating laser beams. The width of the mean irradiance profile is typically used to characterize the beam spread. This so-called Long- Term (LT) statistic allows for a relatively simple theoretical description. The LT beam size is not a very practical measure of the beam spread because its measurements are sensitive to the movements of the source and detector, and to the large-scale variations of the refractive index that are not associated with turbulence. The Short-Term (ST) beam spread is measured relative to the instantaneous position of the beam center and is free of these drawbacks, but has not been studied as thorough as the LT spread. We use a Markov approximation-based theoretical model for the ST beam irradiance that is valid for the wide range of turbulent conditions. Additional approximations are invoked to allow introduction of the isoplanatic ST Point Spread Function (PSF). Unlike the LT PSF, the ST PSF depends on the overall beam geometry. Adjustments of the initial beam width and focal distance make it possible to increase the contribution of the LT beam spread that is attributed to the beam wander and minimize the ST beam size at the observation plane for any given turbulence level. Analytical calculations of the optimal beam geometry are presented for the simple case of the coherent Gaussian beam, and Kolmogorov turbulence. We present the results of direct numerical simulation of beam wave propagation that confirm the existence of the optimal beam geometry.
A paraxial equation for electromagnetic wave propagation in a random medium is extended to include the depolarization effects in the narrow-angle, forward-scattering setting. A system of two coupled parabolic equations describes propagation of the polarized wave through random medium. In the Cartesian coordinate formulation the coupling term is related to the second mixed derivative of the refractive index. Closed-form parabolic equation for propagation of the coherence tensor is derived under a Markov random process propagation model. The scattering term in this equation includes a rank-four tensor that contains derivatives of the correlation function of the refractive index up to the fourth order. This equation can be also formulated as vector equations for generalized Stokes or lexicographic vectors. In contrast to the scalar case, these equations do not have an analytical solution. For a general partially coherent and partially polarized beam wave, this equation can be reduced to a system of ordinary differential equations allowing a simple numeric solution. For a special case of statistically homogeneous waves an analytical solution exists. In the Stokes vector formulation this solution is described by a range-dependent Mueller matrix. For isotropic random medium this Mueller matrix is diagonal and describes a pure non-uniform depolarizer. Statistics of the random medium is wrapped in a single parameter – depolarization length which is proportional to the fourth derivative of the covariance function at zero. For propagation through atmospheric turbulence estimates based on the perturbation solution support the common knowledge that the depolarization at the optical frequencies is negligible.
Fluctuations in the images of scenes viewed over large distances are the most obvious manifestation of the turbulence effects on the imaging of the incoherent objects. While the average or long-exposure imaging is arguably the most well studied topic of the optical propagation in turbulence, and substantial progress was also made in understanding the average short-exposure imaging, the image scintillations for complex extended scenes are not well understood. We discuss some available results of the image scintillation theory and report on some recent progress. We introduce the concept of the scintillation imaging, when unlike the conventional turbulence imaging techniques the variance of the series of images of the scene is calculated and used to gain information either about the object or about the turbulence on the propagation path. The third constraint in the turbulent PSF [1] plays a critical role in the scintillation imaging making scintillation images insensitive to the constant background and emphasizing the areas with higher local contrast. The bilinear structure of the Object-to-Variance (O2V) maps makes it impossible to use the analogues of the PSF or MTF for scintillation images and precludes development of the general theory of scintillation imaging. We discuss the fundamental properties of the O2V kernel and discuss four examples of scintillation images of simple objects. We present the measurement data where colored scintillation images of the edge were obtained. The variance distributions are normalized using the traditional long-exposure images to remove dependence on the object brightness. In this case scintillations are concentrated near the edge and carry information about the turbulence on the imaging path. The amplitude and width of these variance distributions are sensitive to the turbulence level and can be used as passive scintillometer without the need to deploy the laser source and receiver at both ends of the propagation path. Variance images of the object with sinusoidal brightness distribution consists of the uniform background and doublefrequency sinusoidal oscillations. It has the features consistent with turbulent super-resolution originally described in [2]. Namely, for unresolved object oscillating components disappears while the background persevere.
Monte-Carlo models of the turbulent phase are widely used in the studies of the optical propagation through turbulence atmosphere. However all algorithms, that are currently in use, generate continuous smooth phase samples. Meanwhile, it is well-known that under strong scintillation conditions turbulent phase has singularities, and phase is discontinuous across the branch cuts connecting the singularities. Markov approximation for wave propagation through random inhomogeneous media ^{1, 2} predicts that under the strong scintillation conditions optical field asymptotically has normal distribution ^{3}. We propose to generate the phase samples under strong scintillation conditions by first producing a complex normal random field with a given coherence function, and then recovering the random phase as the argument of this field. This approach allows generation of the two-dimensional discontinuous random phase samples that include phase singularities. Phase simulation algorithm is based on the Sparse Spectrum concept that was introduced in our earlier works, and can be modified to fit any desired shape of the turbulence spectrum. We verify the accuracy of the phase samples statistics by comparison with the theoretical results presented in the companion paper.
Under strong scintillation condition the phase of the optical field propagating through turbulence contains phase singularities. Commonly used statistical description of phase in terms of phase structure function is based on smooth perturbation (Rytov) theory, and does not account for singularities. Markov approximation for wave propagation in turbulence predicts asymptotically normal probability distribution with zero mean for the optical field under strong scintillation conditions, and provides an equation for the coherence function. These allow calculation of all statistics of the field including the amplitude and phase. We derive equations for the single and two-point joint and marginal probabilities distributions of the amplitude and phase, and equation for the phase structure function that are valid for the strong scintillation condition when phase singularities are present.
We introduce a new concept of the Internal Anisotropy (IA) for the homogeneous and isotropic random fields. IA reflects the hidden structures that can exist in the samples of the random field, and are not revealed by the simplest, single and two-point statistical moments. There is presently no established theory of the IA, and no quantitative metrics of IA are available. It is understood, however, that IA cannot be present in any stationary isotropic Gaussian random field, or any single-point transformations of it. We illustrate the IA concept on a simple toy model of two-dimensional random field, and show that IA can affect the third and higher-order multipoint statistical moments. We generate samples of the random irradiance distributions for the plane wave passed through a phase screen with the quasi- Kolmogorov statistics. Visual evaluation suggests the presence of the IA in the irradiance samples. The statistical analysis reveals that the three-point third moment of irradiance exhibit the features consistent with the IA, especially in the focusing conditions. Conditional probabilities of the irradiance gradient components also proved to be sensitive to the IA. We discuss the role of the IA for optimal placement of the multiple receivers of the FSO system using the spatial diversity for fade mitigation.
Recently published Sparse-Spectrum (SS) model of the phase front perturbations by atmospheric turbulence^{1} is based on the trigonometric series with discrete random spectral support. SS model offers substantial computational savings, while preserving the wide range of scales typically associated with turbulence perturbations. We present an improved version of the SS model that accurately reproduces the power-law spectral density of the phase fluctuations in the arbitrary wide spectral band. SS model offers an ample flexibility in the choice of the probability distributions of the components wave vectors. The number of spectral components and the degree of probability distributions overlapping are the primary factors affecting the SS phase statistics. We use the Monte-Carlo model to examine the statistics of the SS phase samples for four basic versions of the SS model. We also present the calculations of the practically important long-exposure Strehl numbers. Non-overlapping SS model with log-uniform partition emerges as the most appropriate for the atmospheric turbulence representation. However, it is possible that the other model types can be used for optical propagation through different turbulent flows, such as air flows around domes and turrets, jets engine plumes, etc.
Monte-Carlo simulation of phase front perturbations by atmospheric turbulence finds numerous applications for design
and modeling of the adaptive optics systems, laser beams propagation simulations, and evaluating the performance of the
various optical systems operating in the open air environment. Accurate generation of two-dimensional random fields of
turbulent phase is complicated by the enormous diversity of scales that can reach five orders in magnitude in each
coordinate. In addition there is a need for generation of the long “ribbons” of turbulent phase that are used to represent
the time evolution of the wave front. This makes it unfeasible to use the standard discrete Fourier transform-based
technique as a basis for the Monte-Carlo simulation algorithm. We propose a novel concept for turbulent phase – the
Sparse Spectrum (SS) random field. The principle assumption of the SS model is that each realization of the random
field has a discrete random spectral support. Statistics of the random amplitudes and wave vectors of the SS model are
arranged to provide the required spectral and correlation properties of the random field. The SS-based Monte-Carlo
model offers substantial reduction of computer costs for simulation of the wide-band random fields and processes, and is
capable of generating long aperiodic phase “ribbons”. We report the results of model trials that determine the number of
sparse components, and the range of wavenumbers that is necessary to accurately reproduce the random field with a
power-law spectrum.
Energy conservation is an essential feature of optical waves propagating through refractive turbulence. It has been known for almost a quarter of a century that energy conservation has an important implication for the fluctuations in the images of the incoherent objects observed through turbulence, namely the image of the uniformly radiating area of an object does not scintillate. As a consequence, the low-contrast parts of an image exhibit weak fluctuation even for very strong turbulence, but scintillations near the sharp edges can be strong even for weak turbulence. The energy conservation property of the turbulent point spread function is essential for modeling turbulent image distortions, both for the development of the image processing techniques and for simulations of turbulent imaging. However, it is regularly overlooked in discussions of turbulent imaging theory and modeling in the current literature. We discuss the relations between energy conservation and anisoplanatism for the most common turbulence imaging models. Our analysis reveals that the only isoplanatic turbulent point spread function (PSF) that is compliant with energy conservation is the thin aperture plane phase screen. This implies that for near-the-ground imaging, and even for astronomical-type imaging under strong turbulence conditions, the turbulent PSF has to be modeled as a random function of four arguments with three functional constraints: non-negative values, finite bandwidth, and energy conservation.
Reciprocity principle for the optical wave propagation in turbulence suggests that scintillations in the focal point of a
coherent optical beam and in the center of the point spread function (PSF) of the imaging system are identical, provided
that the imaging aperture and initial beam irradiance are matched. Rigorous weak and strong scintillation asymptotes of
the scintillation index (SI) in the beam focus indicate that the relatively simple extended Huygens-Fresnel (HF)
approximation is accurate in both asymptotic cases. This motivated us to use the HF approximation for calculation of the
SI in the moderate turbulence case when SI reaches its maximum. The 8 - fold integral representing the SI was
calculated using Mont-Carlo technique. We compare the HF results to the direct numeric wave optics simulation results
and find some discrepancies that can be attributed to the finite grid sampling used in simulation.
In practical situation the exact position of the beam focal point at the end of the long propagation path is rarely available,
but instantaneous, short-term (ST) beam center can be estimated by the beam centroid position. For imaging problems,
the short-exposure (SE) PSF and its scintillation are of great interest. We used the combination of the HF approximation
and available SE imaging model to calculate the short-term SI for the focused beams under weak strong and intermediate
turbulence conditions using the same numeric integration technique as for the Long-Term (LT) case. Calculations show
up to 500% increase in the average irradiance and substantial reduction of scintillation for the SE case.
We use a rigorous Markov approximation-based propagation model to calculate statistical properties of the instantaneous turbulent point spread function (PSF) for weak and strong turbulence conditions. Long-exposure PSF is well-known, and is currently widely used for estimates of optical system performance and simulation of the image distortions caused by turbulence. We discuss some peculiarities of the long-exposure PSF that are related to specifics of propagation in turbulence, which are often overlooked in the literature. Models for the short-exposure PSF have been used since the mid-1960s, and were the subject of some recent publications. We review a recently published model, and present sample calculations of the short-exposure PSF. Based on the available results of the optical propagation theory, we calculate variances of power fluctuations in the instantaneous PSF and the Strehl ratio, and covariance of the total power and the Strehl ratio. Analysis of the calculation results shows that for the most practical situations, the random Strehl ratio is a product of two uncorrelated, random variables-power and axial directivity. This information enables modeling of the instantaneous PSF with random width and height.
Energy conservation is an essential feature of the optical waves propagating through refractive turbulence. It was well
understood for almost 30 years, that energy conservation has a very important consequence for the fluctuations in the
images of the incoherent objects observed through turbulence. Namely the image of the uniformly illuminated areas of
the object does not scintillate. As a consequence the low-contrast parts of the scene exhibit weak fluctuation even for
very strong turbulence, but scintillations near the sharp edges can be strong even for the weak turbulence. Energy
conservation property of the turbulent Point Spread Function (PSF) is essential for modeling of the turbulent image
distortions, both for the development of the image processing techniques and for simulations of the turbulent imaging.
However it is completely neglected in the current literature on the turbulent imaging theory and modeling.
We discuss the relations between the energy conservation and anisoplanatism for the most common turbulence imaging
models. Our analysis reveals that the only isoplanatic authentic turbulent PSF that is compliant with energy conservation
corresponds to the thin aperture plane phase screen model of turbulence. This implies that for the near-the-ground
imaging, and even for the astronomical-type imaging under strong turbulence conditions the turbulent PSF has to be
modeled as a random function of four arguments with certain constraints.
We show some practical ways how the three functional constrains on the turbulent PSF: nonnegative values, finite
bandwidth and energy conservation can be complied with in practical generation of turbulent PSF.
In this review paper we discuss a series of typical mistakes and omissions that are made by engineers and scientists
involved in the theoretical research and modeling of the optical propagation through atmospheric turbulence.
We show how the use of the oversimplified Gaussian spectral model of turbulence delivers the completely erroneous
results for the beam wander. We address a series of common omissions related to calculations of the average beam
intensity: unnecessary use of the approximations when rigorous result is available, invalid application of the RMS beam
size to the turbulence-distorted beams, overlooking the simple theoretical result - average beam intensity is a convolution
with the turbulent Point Spread Function (PSF).
We discuss the meaning and potential dangers of the use of the quadratic structure function for modeling of the turbulent
perturbations. We will also address the issues related to the energy conservation principle and reciprocity that have very
important consequences for the turbulence propagation, but are frequently overlooked in the current literature. We
discuss a series of misconceptions that very common in of the Scintillation Index (SI) calculations. We will clarify the
infamous misunderstanding of the Rytov's approximation: vanishing scintillation at the beam focus, and show the
correct weak and strong scintillation solutions for the SI at the beam focus.
We discuss the flaws of the Fried model of the short-term PSF, and direct to the more accurate PSF model. We will
briefly review the propagation of the polarized optical waves through turbulence and discuss the inadequacy of the
recently published calculations of the electromagnetic beams calculations. We discuss some common errors in
representation of the calculation results for the non-Kolmogorov turbulence.
Arago spot is a small bright spot that is formed in the shadow of the circular obscurer. The coherent nature of the Arago
spot makes it susceptible to the turbulence-induced distortions of the incident wave. We describe the formation of the
Arago spot for the using the narrow-angle Fresnel optics diffraction, and develop a simple equation for the field and
irradiance distributions in the center of the shadow area behind an obscurer. We calculate the average irradiance
distribution, random wander variance and scintillation index of the Arago spot using the Markov approximation for
optical propagation in turbulence. Using the same technique we extend the single obscurer results to the Arago spot
observed in the image of the annular aperture typical for the Cassegrain-type telescopes. The statistics of the Arago spot
distortions can be used for the estimation of the turbulence strength on the propagation path. We suggest an optical
design of a build-in sensor that allows monitoring of the turbulent conditions without interfering with the principal
function of the optical system.
Asymptotic theory of the finite beam scintillations (Charnotskii, WRM, 1994, JOSA A, 2010) provides an exhaustive
description of the dependence of the beam scintillation index on the propagation conditions, beam size and focusing.
However the complexity of the asymptotic configuration makes it difficult to apply these results for the practical
calculations of the scintillation index (SI). We propose an estimation technique and demonstrate some examples of the
calculations of the scintillation index dependence on the propagation path length, initial beam size, wavelength and
turbulence strength for the beam geometries and propagation scenarios that are typical for applications. We suggest
simple analytic bridging approximations that connect the specific asymptotes with the accuracy sufficient for the
engineering estimates. Proposed technique covers propagation of the wide, narrow, collimated and focused beams under
the weak and strong scintillation conditions.
Direct numeric simulation of the beam waves propagation through turbulence expediently complements the
asymptotic theory being most efficient when the governing scales difference is not very large. We performed numerical
simulations of the beam wave propagation through turbulence for conditions that partially overlap with the major
parameter space domains of the asymptotic theory. The results of the numeric simulation are used to confirm the
asymptotic theory and estimate the accuracy of the bridging approximations.
We use a rigorous Markov approximation-based propagation model to calculate statistical properties of the instantaneous
turbulent Point Spread Function (PSF) for the weak and strong turbulence condition. Long-Term PSF is well known and
is currently widely used for the estimates of the optical system performance and simulation of the image distortions
caused by turbulence. We discuss some peculiarities of the Long-Term PSF that are related to the specifics of the
propagation in turbulence, and are often overlooked in the recent literature. Models for the Short-term PSF have been
used since mid-1960's, and were the subject of some recent publications. We review the recently published model and
present sample calculations of the Short-term PSF. We calculate the variances of the power in the instantaneous PSF and
the Strehl ratio at the average PSF center, and correlation between the total power and the Strehl ratio. This information
allows modeling the instantaneous PSF with random width and height. Analysis of the calculation results shows that for
the most practical situations random Strehl ratio is a product of two uncorrelated random variables - power and axial
directivity.
We use the results of the theory of wave propagation in turbulence to analyze the effects of the atmospheric turbulence
on the Free-Space Optical Communication systems under weak and strong scintillation conditions. We found that for the
traditional fiber coupling arrangement statistics of the Power-in-Fiber (PIF) is sensitive to the phase fluctuation at the
collecting aperture, rather than amplitude fluctuation (scintillation). Larger receiving aperture produces stronger PIF
fluctuation. Similar to the scintillation of the sharp focused beams second-order scattering dominates PIF fluctuation for
the weak and strong scintillation conditions. This should have serious effect on the probability distribution of the PIF.
A new coupling arrangement is suggested that alleviates the destructive effect of the phase fluctuation, and allows the
use of large receiving apertures. The trade-off is the decreased coupling efficiency. For our new coupling scheme the PIF
fluctuation is determined by the power flux fluctuation through the collecting aperture. This allows taking advantage of
the scintillation averaging effect to suppress the fading. We review the results of the rigorous Markov-approximation-based
theory of the scintillation averaging that is valid both for a weak and strong scintillation conditions. This technique
reveals several distinct regimes of the power flux fluctuation including the situation where fluctuation is relatively small,
but is not described by the perturbation (Rytov's) theory. We also show how the energy conservation principle inherent
to the wave propagation in the clear air turbulence provides an accelerated rate of the scintillation averaging compare to
the typical averaging estimates.
We analyze some recent publications addressing propagation of the partially coherent polarized beams and beam arrays
in the turbulent atmosphere. We show that the published results are limited to the scalar propagation model, and are not
particular to the beam polarization. Therefore these results are equally relevant for the scalar beam pairs and arrays
discriminated by some parameters such as small frequency shift, time delay or geometry, but not necessary the
polarization. We use the virtual incoherent source model to derive the general form of the mutual coherence function of
the two Schell-type beams. We discuss some physical stochastic models that result in the creation of the Schell-type
beams and beam arrays. New classes of the uniformly, nonuniformly and nonlocally coherent beam pairs emerge
naturally from this analysis. Rigorous, Markov approximation-based, propagation model provides relatively simple
analytic results for the second-order moments of the optical field of the partially-coherent individual beams and beam
pairs. We examine the changes of the beam mutual coherence in the process of the free-space propagation and
propagation through the turbulent atmosphere.
We extend the theory of the on-axis beam scintillations for the
off-axis case beam points for weak and strong
scintillation conditions. Theory is based on the parabolic equation for the beam wave propagation and Markov
approximation for the calculation of the statistical moments of the beam intensity. We use the Feynman path integral
technique and asymptotic analysis to analyze the dependence of the scintillation index on the distance from the beam
axis for collimated beams under weak and strong scintillation conditions. Both strong and weak scintillation cases are
considered. Beam scintillation index naturally separates in the uniform (axial) and inhomogeneous (radial) components
that can be examined separately. Axial component carries most of the diffractive scattering effects whereas the radial
component is mostly related to the pure geometrical perturbation. We examine the contribution of the beam wander to
the scintillation index at the different parts of the beam cross section and show that beam wander alone cannot account
got the expected magnitudes of the scintillation index.
We extend our theory of the on-axis beam scintillations [1] for the case of the propagating on slant turbulent
paths where turbulence is concentrated in a relatively thin layer near the transmitter. Theory is based on the parabolic
equation for the beam wave propagation and Markov approximation for the calculation of the statistical moments of the
beam intensity. Ratio of the turbulence layer thickness to the overall propagation path length adds an extra small
parameter to the asymptotic analysis. However we show that this only causes some changes for the boundaries between
the asymptotic regions established in [1] while preserving their general arrangement.
Using small-angle parabolic approximation and Feynman path-integral technique we derive the exact solution
for optical beam propagation in the low-order turbulence consisting of the optical wedges and lenses distributed along
the propagation path. We present complete solutions for some specific distribution of lenses, and discuss limitations of
LOT as a proxy model for propagation in turbulence.
We present a simple theoretical model for dewarped imaging through a turbulent medium, and calculate the degree of superresolution that can be attained by dewarping of the distorted instantaneous images registered through a turbulent atmosphere. Our estimates show that on 1 km near the ground propagation path spatial frequencies of the dewarped image can exceed the diffraction limit three times with a probability up to 10%.
Tilt-Invariant Approximation is used in the frame of the admittance-operator formalism ft the scattering theory. The result is an explicitly-reciprocal formula for the scattering amplitude which is accurate up to the third order of the perturbation series, and is equivalent to the Kirchoff's approximation in the high-frequency limit.
The theory of short-exposure (SE) imaging and short-term (ST) beam spread is developed based on the Markov
approximation for wave propagation in turbulence and Feymnan path-integral formalism. The theory is not restricted by
the weak scintillation conditions, and takes into account diffraction and geometric properties ofthe beam and imaging
system. We obtain approximations for the ST beam and SE image structure functions, which are free from the drawbacks
ofthe classical SE theory.
The SE case modulation transfer function (MiT) has a two-scale shape with larger scale extending up to the
diffraction cutoff. We show that the imaging system can be optimized to maintain the highest contrast for the given spatial
frequency. The initial beam size and its focusing can be optimized in terms ofthe maximum on-axis intensity and
minimum beam size. These effects have no analogy for the long-term cases.
We discuss the nature and general properties of the effect with regard to the imaging through the turbulent atmosphere. This new effect utilizes the medium inhomogeneities as a part of the optical system to obtain the resolution beyond the diffraction limit. Turbulence superresolution effect relates to the focusing properties of the random medium. We discuss some general properties of image distortions by random refractive medium and present the experimental results revealing important statistical connections between global properties of distorted image and superresolution events. We present the results of the postdetection processing of the short- exposure images which is capable to preserve and accumulate information beyond the diffraction limit.
A short-term beam spread theory developed starting from the path integral representation of the field in random media. The new approximate formula is obtained for average short term intensity distribution. This formula takes into account all geometrical and diffraction beam parameters. Results of average short-term on-axis intensity and beam size calculations are presented. The beam parameters optimization is performed for horizontal and slant paths. The difference between short-exposure and tilt-corrected beam spread and applications of developed theory to adaptive optics problems are discussed.
An approach to short-exposure imaging that takes into account anisoplanatic perturbations of the image is proposed. The short exposure modulation transfer function is formulated using the Marcovian stochastic process approximation. This formula which is free from the drawbacks of Fried's approximations describes the diffraction effects and medium fluctuation distribution along the propagation path.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print format on
SPIE.org.