Phase Screen Method Research Articles

A phase screen model for simulating numerically the propagation of a laser beam in rain

The method based on the generalisation of the phase screen method for a continuous random medium is proposed for simulating numerically the propagation of laser radiation in a turbulent atmosphere with precipitation. In the phase screen model for a discrete component of a heterogeneous 'air—rain droplet' medium, the amplitude screen describing the scattering of an optical field by discrete particles of the medium is replaced by an equivalent phase screen with a spectrum of the correlation function of the effective dielectric constant fluctuations that is similar to the spectrum of a discrete scattering component — water droplets in air. The 'turbulent' phase screen is constructed on the basis of the Kolmogorov model, while the 'rain' screen model utilises theexponential distribution of the number of rain drops with respect to their radii as a function of the rain intensity. Theresults of the numerical simulation are compared with the known theoretical estimates for a large-scale discrete scattering medium.

A new phase-screen method for electromagnetic wave propagation in turbulent flows using large-eddy simulation

Use of large-eddy simulation (LES) data in electromagnetic wave propagation modeling is not very common because of the high computational cost involved. A new phase-screen method is proposed to model radio wave propagation, in the atmospheric turbulence, using the resolved scale refractivity obtained from LES. The proposed method offers the same level of accuracy, as the one already existing in the literature, at much cheaper cost.

Multifilamentation of femtosecond laser pulses propagating in turbulent air near the ground

The propagation of femtosecond laser pulses in turbulent air near the ground is analyzed. Confining to a power regime distinctly above the critical power for self-focusing, i.e. P≈100P cr, and concentrating on initial peak intensities around 2.5×1011W/cm2, the onset and early evolution of multiple filaments are addressed. Making use of the turbulence phase-screen method, numerical simulations of the pulse propagation indicate that turbulence fields with spatial scales below 6 mm are able to induce the onset of multifilamentation. An analytical linear plane wave perturbation model of the underlying modulation instability of the pulse front is introduced in support of the computational results. By this means, insight into the amplification of an initial perturbation of the pulse front from the point of view of the spatial frequency domain is given.

Method for super Fresnel resolution in electromagnetic diagnostics of inhomogeneous plasma

The method of electromagnetic diagnostics is suggested, which promises to perform super Fresnel resolution of plasma inhomogeneities, that is resolution, distinguishing details smaller than Fresnel radius. To realize super Fresnel resolution it is suggested to represent the wave field of the source in the form of double weighted Fourier transform (DWFT), deals with Fourier transform simultaneously in coordinates of the sources and in coordinates of receivers. Important property of DWFT is that DWFT transfers into geometrical optics (GO) approximation for smooth inhomogeneous media and becomes equivalent to the Rytov or to small angle Born approximation in the case of weak inhomogeneities. As a result, inverse DWFT allows obtaining linear integral of plasma density both for large scale inhomogeneities, as in GO approximation, and also for inhomogeneities, whose transverse sizes are small as compared with Fresnel radius. DWFT embraces also the results of the phase screen method and allows to take into account phenomenon of micro-multirayness and to describe strong amplitude fluctuations. Using inverse DWFT algorithm, the authors study resolution of systems consisting of discrete sources and receivers. Both analytical estimates and the results of numerical modeling evidence opportunity to observe small scale plasma inhomogeneities with super Fresnel resolution.

2.5D SH Wave Propagation in Heterogeneous Crustal Wave Guides Using the Phase Screen Method

Abstract One-way approximations for regional phases slice the half-space crustal wave guide into a number of slabs perpendicular to the propagation direction; the Moho discontinuity can be easily treated as a perturbation from the crustal background. The advantage of one-way propagation methods is their great saving of computing time and memory compared to full-waveform numerical methods, especially for 3D simulations. In this article, we present general 2.5D SH formulas for the thin-slab method and a generalized screen propagator (GSP) for simulating SH wave propagation in the heterogeneous half-space crustal wave guide. Comparisons of numerical results with a finite-difference (FD) algorithm for a standard flat crustal model show excellent agreement, demonstrating the validity and accuracy of the 2.5DGSP for the half-space problem. We then compare the curves of energy attenuation calculated by the 2D and 2.5D formulas. The comparison shows that the energy attenuation of the 2.5D case is about 1.5–3 times greater than that of the 2D case when the trapped mode is formed. The SH screen propagator is also used to simulate two laterally unvarying (in the y direction) crustal models, showing the path effects on regional wave propagation.

Stochastic realization approach to the efficient simulation of phase screens

The phase screen method is a well-established approach to take into account the effects of atmospheric turbulence in astronomical seeing. This is of key importance in designing adaptive optics for new-generation telescopes, in particular in view of applications such as exoplanet detection or long-exposure spectroscopy. We present an innovative approach to simulate turbulent phase that is based on stochastic realization theory. The method shows appealing properties in terms of both accuracy in reconstructing the structure function and compactness of the representation.

Statistics of caustics in an underwater sound channel

The numerical-analytical phase screen method is used to analyze the statistics of the density of caustics in an underwater sound channel with large-scale random inhomogeneities. Different cases of wave propagation direction with respect to the channel axis are considered, and the influence of the inhomogeneity correlation radius is investigated.

A new cylindrical phase screen method for modeling electromagnetic wave propagation through an inhomogeneous 2‐D atmosphere

In this paper, we investigate the forward modeling of electromagnetic wave propagation through an inhomogeneous, two‐dimensional (2‐D) atmosphere where the transmitter is located at a finite distance from the Earth. A new cylindrical multiple phase‐screen method is developed and both the cylindrical and the traditional planar multiple phase‐screen models are applied to an inhomogeneous atmosphere with a simple refractivity profile. It was found that the two methods yield results that agree very well on the same output cylindrical phase‐screen after the wave was propagated through the atmosphere. Since the cylindrical approach better matches the physical phenomenology of the waves, the phase fronts were found to deviate less over the cylindrical phase‐screens than over the planar screens. Therefore, the cylindrical multiple phase‐screen model requires a smaller number of points to perform the Fast Fourier Transforms (FFT) and Inverse FFT than the planar phase screen model, and thus has a higher efficiency. The cylindrical phase‐screen model can also serve as a new direct and independent check for the traditional planar phase‐screen model.

Mueller-matrix model of an inhomogeneous, linear, birefringent medium: Single scattering case

Using the anisotropic phase-screen method, we derive the generalized Mueller matrix of an inhomogeneous, linear, birefringent medium in the single-scattering case. We show that the Mueller matrix include eight nonzero elements with relations among elements given by m 11= m 22, m 12= m 21, m 33= m 44, and m 34= m 43. Using the derived Mueller-matrix model, we simulate polarization optics for calcite, quartz, and sodium nitrate crystals. At λ=0.63 μm and with small inhomogeneities, the matrix elements are a function of the standard deviation of the crystal thickness, while m 12 shows pronounced sensitivity to the difference of refractive indices. At an observation angle of 0°, inhomogeneous birefringent media behaves as if they are partial polarizers. Matrix elements most sensitive to the inhomogeneity in the UV to near IR wavelengths have been determined.

Estimation of the power scintillation probability density function in free-space optical links by use of multicanonical Monte Carlo sampling

Free-space optics (FSO) can provide cost-effective, high-bandwidth, wireless connections. However, atmospheric turbulence may degrade the performance of FSO links by causing intensity and power scintillations at the receiver. Multicanonical Monte Carlo sampling is used in conjunction with the phase screen method to calculate the statistics, and particularly the probability density function (PDF), of the power fluctuations at an FSO receiver. This allows the efficient calculation of the PDF even for very small values with a limited number of iterations. The obtained PDF can be used to characterize the performance of the system in terms of the error probability.

Estimates of the local parameters of plasma density fluctuations by reflectometry measurements

The question is considered of how to estimate the parameters of local plasma density fluctuations from reflectometry measurements made by probing the plasma with an extraordinary electromagnetic wave. In the geometrical-optics approximation, a formula is derived that relates the fluctuation amplitude of the phase of the reflected signal to the amplitude of local plasma density fluctuations and the range of its applicability is considered. The spectral sensitivity of reflectometry measurements in a reflection region of finite dimensions to poloidal perturbations with wavenumbers k⊥ ⪝ k0 is estimated by the phase-screen method, and the expressions obtained are compared with the results of numerical simulations. Based on the relationships derived, an algorithm is proposed for recovering the amplitude of the local plasma density fluctuations from the fluctuations in the reflected reflectometer signal. The results obtained are compared with the results of the full-wave simulations of the reflection of microwaves from a turbulent plasma. Finally, an example is given of how to recover the data on the amplitude of the local plasma density fluctuations in the T-10 tokamak plasma.

Synthesis of vector wave envelopes in three‐dimensional random elastic media characterized by a Gaussian autocorrelation function based on the Markov approximation: Plane wave case

High‐frequency seismograms of microearthquakes observed at long travel distances have longer apparent durations than the source durations caused by scattering due to lithospheric inhomogeneity. Frequency dependence of the peak delay from the onset and the broadening of seismogram envelope well reflect the spectra of random velocity inhomogeneity. Here we propose a formulation for the envelope synthesis of vector waves in three‐dimensional random elastic media in the case that wavelengths are smaller than the characteristic scale of random inhomogeneity. A stochastic master equation for the two‐frequency mutual coherence function (TFMCF) of potential field is derived on the basis of the Markov approximation, which is a stochastic extension of the phase screen method for solving the parabolic wave equation. From the Fourier transform of TFMCF at a given travel distance, we are able to synthesize the mean square traces of three vector wave components. For the incidence of an impulsive plane P wavelet to random elastic media characterized by a Gaussian autocorrelation function, the mean square envelope of each component at a long travel distance is analytically written by using an elliptic theta function. Each synthesized envelope shows peak delay from the onset and broadening with travel distance increasing; however, the peak delay of the transverse component is larger than that of the longitudinal component. For the same fractional velocity fluctuation, the envelope broadening for S waves is larger than that for P waves.

An asymptotic method of modeling radio occultations

A short-wave asymptotic method of modeling radio signals registered during radio occultation experiments is discussed. The method uses the theory of Fourier integral operators. Use of this method allows for a faster simulation of radio occultation data as compared to the method of multiple phase screens. The method was tested using global fields from analyses of the European Centre for Medium-Range Weather Forecast. The comparison of the asymptotic solution with the multiple phase screen method shows their good agreement. The limits of the applicability of the new method are discussed.

Simulation studies of GPS radio occultation measurements

The atmospheric propagation of GPS signals under multipath conditions and their detection are simulated. Using the multiple phase screen method, C/A‐code modulated L1 signals are propagated through a spherically symmetric refractivity field derived from a high‐resolution radio sonde observation. The propagated signals are tracked by a GPS receiver implemented in software and converted to refractivity profiles by the canonical transform technique and the Abel inversion. Ignoring noise and assuming an ideal receiver tracking behavior, the true refractivity profile is reproduced to better than 0.1% at altitudes above 2 km. The nonideal case is simulated by adding between 14 and 24 dB of Gaussian white noise to the signal and tracking the signal with a receiver operating at 50 and 200 Hz sampling frequency using two different carrier phase detectors. In the upper troposphere and stratosphere the fractional refractivity retrieval error is below 0.3% for 50 Hz sampling and below 0.15% for 200 Hz sampling. In the midtroposphere down to altitudes of about 2 km, phase‐locked loop tracking induces negative fractional refractivity biases on the order of −1 to −2% at 50 Hz sampling frequency. Modifications to the receiver tracking algorithm significantly improve the retrieval results. In particular, replacing the carrier loop's two‐quadrant phase extractor with a four‐quadrant discriminator reduces the refractivity biases by a factor of 5; increasing the sampling frequency from 50 to 200 Hz gains another factor of 2.

Multichannel ATI-SAR with application to the adaptive Doppler filtering of ocean swell waves

Multichannel along track interferometric (MATI) SAR systems are discussed from the point of view of ocean remote sensing. It is shown that the signals scattered by range moving scatterers can be Doppler filtered using a MATI-SAR. Processing techniques are presented, including a phase screen method for the removal of phase errors (including systematic errors and also those resulting from platform motions). A particular radar system (the ESR, enhanced surveillance radar) is described; this has a 3 cm wavelength MATI with two, three or four beams. It is used for investigating and exploiting Doppler effects in ocean radar scattering. It is demonstrated that, by applying adaptive Doppler filtering techniques, the MATI-SAR can significantly increase the imaging sensitivity of ocean features with respect to a conventional SAR. Examples illustrate the use of the ESR MATI-SAR system for imaging ship generated swell waves. Using three beams, the visibility of the wave images is increased by 9.5 dB looking downwind and 5.0 dB looking upwind for horizontal polarisation at grazing angles of 39° and 32°, respectively. Associated Doppler filter responses are shown which show that the scatterers modulated by the swell wave are located in the neighbourhood of the wave crests.

Prestack Depth Migration Method Based on Quasi‐Linear Born Approximation

AbstractIn this paper, a prestack depth migration method based on quasi‐linear Born approximation is carried out in frequency‐wavenumber domain and frequency‐space domain, and is used to process common shot gather data of the Marmousi model. Through comparison with the Split‐Step Fourier migration method, Phase‐Screen migration method and the prestack depth migration method with stable Born approximation, it is apparent that the prestack depth migration method based on quasi‐linear Born approximation produces better migration results with improved handling of lateral velocity variations.

Large fluctuation of wave amplitude produced by small fluctuation of velocity structure

Seismic velocity structure of the real Earth is described by a combination of deterministic large scale structure and small scale fluctuation. When waves propagate in media having the small scale fluctuation, the fluctuation makes the rays bend, introduces focussing and defocusing, and produces fluctuations of wave amplitude. To estimate the size of wave amplitude fluctuation that is caused by velocity fluctuation, the variances of wave amplitudes are evaluated as a function of propagation distance from numerical simulations of scalar wave propagation in 3D random media having Gaussian or exponential autocorrelation functions. The simulations are performed using a phase screen method, which is a numerical procedure for solving the parabolic wave equation. The following conclusions are obtained from the simulations that use two types of incident wave: stationary monochromatic sine wave and transient Ricker wavelet. For velocity fluctuation as small as several percent, the variance of wave amplitude is larger than the square of its average in some cases of high frequency waves. These results show the importance of small error and fine spatial resolution of velocity structure model for proper modeling of wave amplitude. When the fluctuation of the velocity structure is large, the wave amplitude variance increases with the propagation distance until it reaches some peak value after which it decreases with the increase of propagation distance. The variance for the Ricker wavelet incidence is smaller than that for a monochromatic sine wave. Because of the stochastic dispersion due to the small fluctuation of velocity structure, the maximum amplitude decreases with the propagation distance even if there is neither an intrinsic absorption nor back-scattering for the Ricker wavelet incidence.

Modelling complex media: an introduction to the phase-screen method

Traditional ray-tracing methods for seismic modelling become prohibitively difficult to implement for complex media, and are inappropriate to systems where diffraction by sub-wavelength scatterers dominates the seismic response. Direct simulation methods, such as finite-differences, can handle complexity well but are severely restricted by their computational and storage requirements, especially in 3D. The phase-screen method, used for modelling scalar waves in a variety of contexts, promises to overcome both these limitations and was generalized recently to complex-screen or generalized screen method [Wu, R.-S., 1994. Wide-angle elastic wave one-way propagation in heterogeneous media and an elastic wave complex-screen method. J. Geophys. Res. 99 (B1) 751–766; Wild, A.J., Hudson, J.A., 1998. A geometrical approach to the elastic complex-screen. J. Geophys. Res. 103, 707–726] to handle elastic waves. As a “full-wavefield” method, it implicitly accommodates diffracted and converted phases and it is more computationally efficient than 3D finite-difference modelling, because the wavefield is represented at any instant by a 2D plane of values, which are mapped progressively through the 3D volume. In this paper, the basic principles of the phase-screen concept are presented together with an example of the scattered wavefield from a spherical body. The result shows that for a spherical anomaly set in a homogeneous background the reflection from the base has the same apparent polarity as the reflection from the top. This is contrary from what is expected and appears to be a property of spherical bodies. This surprising result is verified by comparison with results from a 3D finite difference code.

Generalization of the phase-screen approximation for the scattering of acoustic waves

With the use of Fourier analysis, we describe the propagation and scattering of acoustic waves in smoothly varying, heterogeneous media. The starting point is the generalized Bremmer coupling series solution — distinguishing multiple up/down scattered constituents — to the wave equation, which requires the introduction of pseudo-differential operators. Then, we introduce a class of approximations to these pseudo-differential operators with the structure of the classical phase-screen method for one-way wave propagation. These approximations induce a fast, iterated, marching algorithm for the evaluation of the Bremmer series. The algorithm consists of multiplications by multiple ‘screen’ functions in the lateral space domain and generalized ‘phase shifts’ in the lateral wave number domain; the shuttling between the two domains is accomplished by the fast Fourier transform. Our scheme extends the use of the classical phase-screen method in the following ways: we consider larger medium variations; we enhance the accuracy for wider scattering angles; we introduce (de)composition operators to incorporate any desired source-or receiver-type with the appropriate radiation characteristics; we include the backscattered field with the aid of the generalized Bremmer coupling series.

Quasi-geometrical optics methods in the theory of wave propagation through a randomly inhomogeneous layer

Some possibilities of using asymptotic methods, such as the Maslov method and the interference-integral method, in problems of wave propagation in randomly inhomogeneous media are considered. It is shown that using the Maslov method and the interference-integral method in a small-angle approximation, and neglecting amplitude fluctuations of partial waves, provides results of heuristic spectral methods that utilize expansions in terms of incoming or outgoing waves. The combined use of these asymptotic methods gives a third heuristic method, a mixed-integral representation obtained earlier by applying the method of two-scale expansions. It is pointed out that results of a mixed-integral representation change to those of the method of smooth disturbances and of the phase-screen method. Unlike the method of two-scale expansions, the proposed approach based on the combined use of asymptotic methods facilitates the process of taking into account the heterogeneity of a background medium.