Thin Phase Screen Research Articles

Anisotropic ionospheric scintillation in weak scattering regime

Transionospheric radio signals might undergo random modulations of their amplitude and phase caused by scattering on irregular structures in the ionosphere. These scintillation phenomena are highly anisotropic, depend on local geomagnetic field configuaration and on the relative position of the signal receiver and scattering irregularity. We derive analytical expressions of anisotropic amplitude and phase scintillation indices using the model of a thin random phase screen. These results extend the classical derivations of [C. Rino, Radio Sci. 14, 1135 (1979)] to a larger domain of applicability including very slant propagation links of the radio wave signals. The derived generalization is based on the assumption that the ionospheric scattering layer has a spherical symmetry as opposed to the original Rino’s assumption of a plan-parallel ionospheric layer. The derived scintillation indices have the simpler analytical form, determine the regions of enhanced scintillation by taking into account the finite curvature of the Earth and of the ionospheric shell, and are divergence-free for large zenith angles of propagation links. For the illustration we discuss the geometric enhancement of scintillation for communication links via a geostationary beacon satellite over the equator.

Wave optics simulations of plane-wave propagation in non-Kolmogorov turbulence

We derive limits for wave optics simulations of plane wave propagation in non-Kolmogorov turbulence using the split-step method and thin phase screens. These limits are used to inform two simulation campaigns where the relationship between volume turbulence strength and normalized intensity variance for various non-Kolmogorov power-laws. We find that simulations of smaller power laws are limited turbulence strengths with Rytov numbers of 7 when the simulation side-length sampling rate is 8192. Under these same conditions it is possible to simulate volume turbulence strength out to Rytov numbers of 12 for Kolmogorov power-laws and higher. We show that the peak scintillation and Rytov number where peak scintillation occur increases monotonically with power-law. Also, that if turbulence strength is fixed, the relationship between scintillation index and power-law depends on the operating regime. In weak turbulence the relationship is negative, and it is positive in stronger turbulence. This work also emphasizes the importance of properly scaling turbulence strength with comparing results with different power-laws and the influence and importance of defining inner and outer scales in these simulations.

Average irradiance with boresight pointing errors for flat-topped beam under atmospheric turbulence

Flat-topped beams offer a promising solution to mitigate turbulence-induced spreading in free space optical communication (FSOC). Although average irradiance is fundamental to the performance of flat-topped beam-based FSOC, the impacts of FSOC boresight pointing errors on average irradiance have rarely been discussed in prior works. Herein, we establish a general closed-form expression of the average irradiance with boresight pointing errors for flat-topped beam-based FSOC. This theoretical expression has been verified through thin-phase screen. The results show that unequal standard variance and nonzero mean boresight pointing errors change the shape and central position of the average irradiance. Furthermore, the general closed-form expression of the average receiving power with boresight pointing errors is further deduced and verified. The boresight pointing errors induce an additional loss of the average received power. This work provides general closed-form expressions to analyze and design the link of flat-topped beam-based mobile FSOC in atmospheric turbulence.

Lensing from small-scale travelling ionospheric disturbances observed using LOFAR

Observations made using the LOw-Frequency ARray (LOFAR) between 10:15 and 11:48 UT on the 15th of September 2018 over a bandwidth of approximately 25–65 MHz contain discrete pseudo-periodic features of ionospheric origin. These features occur within a period of approximately 10 min and collectively last roughly an hour. They are strongly frequency dependent, broadening significantly in time towards the lower frequencies, and show an overlaid pattern of diffraction fringes. By modelling the ionosphere as a thin phase screen containing a wave-like disturbance, we are able to replicate the observations, suggesting that they are associated with small-scale travelling ionospheric disturbances (TIDs). This modelling indicates that the features observed here require a compact radio source at a low elevation and that the TID or TIDs in question have a wavelength <~30 km. Several features suggest the presence of deviations from an idealised sinusoidal wave form. These results demonstrate LOFAR’s capability to identify and characterise small-scale ionospheric structures.

Statistical properties of a return wave generated from an arbitrary rough target in atmospheric turbulence by a partially coherent beam with radial polarization

The interaction of a radially polarized partially coherent beam with an arbitrary rough target embedded in a bi-static LIDAR system in the presence of atmospheric turbulence was illustrated. The target could modelled as a combination of a Goodman-like thin random phase screen and a Gaussian lens. Within the framework of paraxial approximation, the analytical formulas for the cross-spectral density matrix elements of the beam at the source plane, at the target plane, just after the target and at the receiver plane were derived. It was found that the statistical properties of the return wave were dependent not only upon the transverse correlation width of the target, but also on the turbulence. In addition, it was possible to predict the target type by measuring the spectrum and polarization properties of the return beam in the receiver plane.

Intensity fluctuations in ground-to-satellite laser beam transmission induced by atmospheric turbulence: reconsideration of strong fluctuation.

This paper reports beam wave intensity fluctuations in uplink (ground-to-satellite) laser beam transmission caused by atmospheric turbulence. Intensity fluctuation in the strong region was apparently induced by uplink measurement in previous experiments. Statistical values of the uplink fluctuation were estimated by numerical calculation using moment equation analysis with thin phase screen approximation. The beam profile of the uplink, the scintillation index, and the covariance of the uplink intensity fluctuation were calculated using models of the refractive index structure constant. The generation of strong intensity variation was explained as the result of a speckle pattern on the receiving plane at the satellite produced by atmospheric turbulence when scanned along with trajectory of the satellite.

Computation of Brightness Temperature of Sea-foam Modelled as Sequences of Thin Phase Screens using Matlab

Sea surface temperature of the ocean is a significant climate parameter. Satellites provide data for analysing and monitoring the sea surface temperature (SST). Satellite remote sensing provide thermal data in a short duration over large area. Temperature measurement by remote sensing is dependent on the principle that most objects emit electromagnetic (EM) radiation corresponding to temperature, wavelength and emissivity of the objects. Brightness temperatures are detected by thermal sensors, however, brightness temperature coincides with the real temperature of objects if they are black bodies. In this paper, we estimated the effective dielectric constant of sea foam layer which is a very important parameter in investigating ocean brightness temperature. This was done at WindSat frequencies and using a discretization method to evaluate the dielectric constant of a random distribution of air-bubbles discretized into slices of sea foam layer. For efficient evaluation of scattering by foam covered sea surface and measurement of brightness temperature in milli-Kelvin, we develop a discrete based physical model of sea foam which provides accurate estimate of the complex effective dielectric constant of sea foam. The foam covered sea foam layer is modelled as sequences of thin phase screens ( slices ofsea foam layer) with equal depth . Each layer comprised of random distribution of bubbles that follows a log-normal distribution pattern with geometrical and optical properties such as foam layer thickness, foam void fraction, foam volume fraction, sea surface temperature and sea surface salinity. Results of sea surface emissivity and brightness temperature as a function of polarization, angle of incidence, WindSat frequencies and thickness of sea foam are presented.

A Thin Phase Screen Model for Surface Plasmon Polaritons

We develop a thin phase screen model for the transmission of a surface plasmon polariton through a curved boundary between two different co-planar metal surfaces. The result is illustrated by applying it to the determination of the intensity distribution of the electric field of a surface plasmon polariton that has been transmitted through a quadratic (parabolic) boundary, through a cubic boundary, and through a periodic boundary.

Modulation transfer function of the imaging probe using an 8.8 mm-long and 125 µm-thick graded- index short multimode fiber

We measured the modulation transfer function (MTF) of a short multimode fiber (SMMF) probe and proposed the optical model including the thin random phase screen (TRPS) to explain degradations of imaging characteristics. SMMF is a graded index multimode fiber for optical communication. That length is 8.8mm and the diameter of core is 50µm. With the wavelength of 780nm, for spatial frequencies from128lp/mm to 228lp/mm MTFs were measured at 0.179–0.062 in reflection images and these contrasts were 19% to contrasts without TRPS. With parameters of σϕ of 1.5rad and W of 2–3.5µm calculated results almost correspond to measured ones. Dependences of contrasts on wavelength were also measured. With the spatial frequency of 200lp/mm, at the wavelength of 0.8µm the contrast decreased to 17% due to TRPS and at that of 0.5µm the contrast decreased to 6%. Measured dependences of contrasts on wavelength with the spatial frequency of 228 lp/mm approximately correspond to calculation results with 200lp/mm. These basic characteristics are useful to design the imaging optics by means of SMMF.

Imaging characteristics of an 8.8 mm long and 125 μm thick graded-index short multimode fiber probe.

We demonstrated the feasibility of an ultrathin imaging probe with a 50-μm core diameter, a 125 μm total diameter, and an 8.8 mm length, which is a typical graded-index multimode fiber for optical communications. We used an ABCD matrix to analyze the imaging conditions and magnification, which corresponded closely to the measured results. The lateral resolution was calculated at 1.2 μm with a wavelength of 730 nm, which reflects the image test pattern where a period of 4.38 μm was measured with a wavelength of 730 nm. In the numerical aperture of the objective lens, we experimentally evaluated the tradeoff between the magnification and the coupling efficiency. At four wavelengths of 540 nm, 632 nm, 730 nm, and 852 nm, the contrast and signal intensity versus the wavelength were investigated to show that the contrast at 632 and 730 nm is relatively high. By using a thin random phase screen model, we explained that as the wavelength decreases the greater the decrease in the optical transfer function at higher spatial frequencies. Using a 635 nm LED light source, we imaged the surfaces of chicken tendons in contact and the surface roughness was visible.

FREQUENCY-DEPENDENT DISPERSION MEASURES AND IMPLICATIONS FOR PULSAR TIMING

ABSTRACT The dispersion measure (DM), the column density of free electrons to a pulsar, is shown to be frequency dependent because of multipath scattering from small-scale electron-density fluctuations. DMs vary between propagation paths whose transverse extent varies strongly with frequency, yielding arrival times that deviate from the high-frequency scaling expected for a cold, uniform, unmagnetized plasma (1/frequency2). Scaling laws for thin phase screens are verified with simulations; extended media are also analyzed. The rms DM difference across an octave band near 1.5 GHz is ∼ 4 × 10−5 pc cm−3 for pulsars at ∼1 kpc distance. The corresponding arrival-time variations are a few to hundreds of nanoseconds for DM ≲ 30 pc cm−3 but increase rapidly to microseconds or more for larger DMs and wider frequency ranges. Chromatic DMs introduce correlated noise into timing residuals with a power spectrum of “low pass” form. The correlation time is roughly the geometric mean of the refraction times for the highest and lowest radio frequencies used, ranging from days to years, depending on the pulsar. We discuss implications for methodologies that use large frequency separations or wide bandwidth receivers for timing measurements. Chromatic DMs are partially mitigable by including an additional chromatic term in arrival time models. Without mitigation, an additional term in the noise model for pulsar timing is implied. In combination with measurement errors from radiometer noise, an arbitrarily large increase in total frequency range (or bandwidth) will yield diminishing benefits and may be detrimental to overall timing precision.

TwofoldPTsymmetry in doubly exponential optical lattices

We introduce a family of non-Hermitian optical potentials that are given in terms of double-exponential periodic functions. The center of $\mathcal{PT}$ symmetry is not around zero and the potential satisfies a shifted $\mathcal{PT}\text{-symmetry}$ relation at two distinct locations. Motivated by wave transmission through thin phase screens and gratings, we examine these refractive index modulations from the perspective of optical lattices that are homogeneous along the propagation direction. The diffraction dynamics, abrupt phase transitions in the eigenvalue spectrum, and exceptional points in the band structure are examined in detail. In addition, the nonlinear properties of wave propagation in Kerr nonlinearity media are studied. In particular, coherent structures such as lattice solitons are numerically identified by applying the spectral renormalization method. The spatial symmetries of such lattice solitons follow the shifted $\mathcal{PT}\text{-symmetric}$ relations. Furthermore, such lattice solitons have a power threshold and their linear and nonlinear stabilities are critically dependent on their spatial symmetry point.

Temporal power spectrum of irradiance fluctuations for a Gaussian-beam wave propagating through non-Kolmogorov turbulence.

In the past decades, both the increasing experimental evidence and some results of theoretical investigation on non-Kolmogorov turbulence have been reported. This has prompted the study of optical propagation in non-Kolmogorov atmospheric turbulence. In this paper, based on the thin phase screen model and a non-Kolmogorov power spectrum which owns a generalized power law instead of standard Kolmogorov power law value 11/3 and a generalized amplitude factor instead of constant value 0.033, the temporal power spectrum of irradiance fluctuations for a Gaussian-beam wave is derived in the weak fluctuation regime for a horizontal path. The analytic expressions are obtained and then used to analyze the influence of spectral power law variations on the temporal power spectrum of irradiance fluctuations.

Rytov variance equivalence through extended atmospheric turbulence and an arbitrary thickness phase screen in non-Kolmogorov turbulence

An arbitrary thickness phase screen model can describe scintillation index for Gaussian beam propagating through a phase screen more accurate than thin phase screen model. To describing actual scintillation index for Gaussian beam propagating through an extended medium using a phase screen in weak non-Kolmogorov turbulence, the scintillation index and Rytov variance for arbitrary thickness phase screen model are derived. Specially, the ratio of the Rytov variances for a phase screen and extended random media is found under the assumption of equivalence in scintillation index of the two cases. The theoretical results show that the normalized Rytov variance varies with the power law of the turbulence spectrum, the relative thickness of the phase screen, the position of the phase screen, the transmitter beam parameters and the radial position at output plane. The influences of these variables are also simulated. These results will be applied to simulation of adaptive optics and laser communication.

Energy conservation: a third constraint on the turbulent point spread function

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.

Analysis of Wave Front Fluctuations in Strong Turbulence Using Thin Phase Screen Approximation

Analysis of Wave Front Fluctuations in Strong Turbulence Using Thin Phase Screen Approximation

Mathematic model analysis of Gaussian beam propagation through an arbitrary thickness random phase screen

In order to research the statistical properties of Gaussian beam propagation through an arbitrary thickness random phase screen for adaptive optics and laser communication application in the laboratory, we establish mathematic models of statistical quantities, which are based on the Rytov method and the thin phase screen model, involved in the propagation process. And the analytic results are developed for an arbitrary thickness phase screen based on the Kolmogorov power spectrum. The comparison between the arbitrary thickness phase screen and the thin phase screen shows that it is more suitable for our results to describe the generalized case, especially the scintillation index.

Assessment of the use of a diffuser in propagation-based x-ray phase contrast imaging

A rotating random-phase-screen diffuser is sometimes employed on synchrotron x-ray imaging beamlines to ameliorate field-of-view inhomogeneities due to electron-beam instabilities and beamline optics phase artifacts. The ideal result is a broader, more uniformly illuminated beam intensity for cleaner coherent x-ray images. The spinning diffuser may be modeled as an ensemble of transversely random thin phase screens, with the resulting set of intensity maps over the detector plane being incoherently averaged over the ensemble. Whilst the coherence width associated with the source is unaffected by the diffuser, the magnitude of the complex degree of second-order coherence may be significantly reduced [K. S. Morgan, S. C. Irvine, Y. Suzuki, K. Uesugi, A. Takeuchi, D. M. Paganin, and K. K. W. Siu, Opt. Commun. 283, 216 (2010)]. Through use of a computational model and experimental data obtained on x-ray beamline BL20XU at SPring-8, Japan, we investigate the effects of such a diffuser on the quality of Fresnel diffraction fringes in propagation-based x-ray phase contrast imaging. We show that careful choice of diffuser characteristics such as thickness and fiber size, together with appropriate placement of the diffuser, can result in the ideal scenario of negligible reduction in fringe contrast whilst the desired diffusing properties are retained.

Distortion of waves with profile discontinuities in the medium with a periodic transverse inhomogeneity distribution

For the purpose of describing the joint influence of nonlinear effects and refractive inhomogeneities on the evolution of intense acoustic waves, a model of the medium the local velocity of sound of which is periodic in the transverse direction and decreases in the propagation direction, which generalizes the known models of the layered medium and of the infinitesimally thin phase screen, is proposed. An exact solution is found for the wave with arbitrary initial conditions: time profile and transverse profile. The spatial wave structure in the inhomogeneous medium is calculated; it is shown that narrow high-amplitude regions are formed and the rate of nonlinear effect accumulation changes. It is shown that the amplitude of the wave at long distances from the source may differ little from its initial value due to compensation for the effects of nonlinear attenuation and of focusing by inhomogeneities. Possibilities of amplification of intense waves depending on the proportion between parameters of the wave and those of the inhomogeneous medium are studied.

Theory and simulation of ionospheric effects on synthetic aperture radar

Space-based synthetic aperture radar (SAR) necessarily involves imaging through the ionosphere. At low frequencies (VHF, UHF and L-band) the ionosphere will degrade the SAR image. Previous work has shown that the amount of image degradation strongly depends on the integrated strength of ionospheric turbulence, CkL. The focusing, sidelobes and integrated sidelobe ratio all depend on CkL in a manner that can be directly predicted by a simple analytic theory, which is reviewed and extended to cover any synthetic aperture length. Simulations of the ionosphere, using a thin phase screen parabolic equation approach, are performed under different ionospheric conditions for a number of possible SAR systems and the results compared with the analytic theory. It is concluded that, provided that the scattering is weak, the theory represents a good predictor of SAR performance, even at UHF. The known statistics of CkL can therefore be used to predict the performance of any trans-ionospheric SAR without performing a simulation.