Probability Density Function Of Intensity Research Articles

PROBABILITY CHARACTERISTICS OF CONCENTRATION FLUCTUATIONS IN PLUME DISPERSAL

The probability characteristics of the concentration fluctuation in pollutant plume dispersion in a neutral stratified atmospheric boundary layer were investigated experimentally in a wind tunnel experiment. It was examined using a tracer gas without buoyancy, which emitted from a fixed point in the ground surface. The diffusion fields in the boundary layer were examined using an isolated building model. Instantaneous concentration fluctuations were measured along the mean plume centerline at various downwind distances from the source at different heights with the frequency of 1KHz. Probabililistic analysis was performed on the concentration fluctuation, and results were presented for probability density functions (PDF) of mean concentration, fluctuation intensity and crosswind mean-plume dispersion. Furthermore, the effects of turbulence intensity on the statistical nature of concentration fluctuations were presented and discussed. Probability density functions of the concentration fluctuation data have shown a significant nonGaussian behavior. The lognormal distribution appeared to be the best fit to the shape of actual probability density functions of fluctuating concentration measured in the boundary layer wind flows in a wind tunnel. The plume dispersion PDF near the source was observed shorter than that those far from the source.

Speckle with a finite number of steps

The statistical properties of classical, fully developed speckle must be modified when the speckle is generated by a random walk with a finite number of steps. It is shown that for such speckle, the standard negative-exponential probability density function for speckle intensity often overestimates the probability that the intensity exceeds a given threshold. In addition, while any linear transformation of the fields in a classical speckle pattern does not change the intensity statistics, the same is not true for finite-step speckle. The implications of these facts in certain applications are discussed.

Experimental verification of optical backhaul links for high‐altitude platform networks: Atmospheric turbulence and downlink availability

AbstractOptical backhaul downlinks from high‐altitude platforms (HAPs) are investigated. An experiment demonstrated the advantages of optical links: a small and lightweight terminal with low power consumption was launched to the stratosphere and data transmitted down to a ground station at a rate of 1.25 Gbit/s. Owing to the chosen system parameters and the high budget margin, disturbing turbulence effects did not decrease the link performance.The scientific aspect of the experiment was to study turbulence effects in order to design future systems with higher transmission performance. On the day of the experiment, measured scintillation and wavefront distortions were minimal in the morning. The best atmospheric conditions were observed about 3 h after sunrise with a peak of the atmospheric coherence length r0 at 16 cm. An r0 of 4 cm was measured as the worst case before sunrise and later during the day. This trend could also be observed for power‐ ($ {\sigma _P^2} $) and intensity scintillation index ($ {\sigma _I^2} $). The latter $ {\sigma _I^2} $ changed from 0.28 (best case) to 1.12. For small $ {\sigma _I^2} $, a lognormal intensity probability density function was measured.Apart from the robust intensity modulation scheme with direct detection which was used for the trial, future improved systems could benefit from a coherent transmission scheme. According to the r0 measurements and further simulations on heterodyne efficiency it turned out that the aperture size can be decreased from 40 to 10 cm without any significant change in the link margin.Future stratospheric optical links between HAPs or links from platforms to satellites will not suffer from cloud blockage but it remains an issue for up/downlinks to a ground station. This can be mitigated by ground‐station diversity. Four optical ground stations in the southern part of Europe can lead to an availability of over 98%. The separation distance of the ground stations is about 900 km with a negligible correlation of cloud cover. A change of wavelength from the employed 1.55 to a wavelength around 11‐µm with minimum cloud attenuation would increase the link availability for thin clouds. Copyright © 2007 John Wiley & Sons, Ltd.

An atlas-based fuzzy connectedness method for automatic tissue classification in brain MRI

Abstract A framework incorporating a subject-registered atlas into the fuzzy connectedness (FC) method is proposed for the automatic tissue classification of 3D images of brain MRI. The pre-labeled atlas is first registered onto the subject to provide an initial approximate segmentation. The initial segmentation is used to estimate the intensity histograms of gray matter. Based on the estimated intensity histograms, multiple seed voxels are assigned to each tissue automatically. The normalized intensity histograms are utilized in the FC method as the intensity probability density function (PDF) directly. Relative fuzzy connectedness technique is adopted in the final classification of gray matter and white matter. Experimental results based on the 20 data sets from IBSR are included, as well as comparisons of the performance of our method with that of other published methods. This method is fully automatic and operator-independent. Therefore, it is expected to find wide applications, such as 3D visualizati...

System performance using different types of in-line optical regenerators

We analytically compare the system performance of various types of in-line optical regenerators in long distance amplified links. The evolution of the probability density function (pdf) of the optical signal intensity is evaluated, and bit error ratio (BER) is estimated numerically. Critical issues of common solutions are found.

Macrospatial Correlation Model of Seismic Ground Motions

It is very important to estimate a macrospatial correlation of seismic ground motion intensities for earthquake damage predictions, building portfolio analyses etc., whereby damage in different locations has to be taken into account simultaneously. This study focuses on spatial correlation of the residual value between an observed and a predicted ground motion intensity, which is estimated by an empirical mean attenuation relationship. The residual value is modeled in such a way that the joint probability density function (PDF) of seismic ground-motion intensity can be characterized by the spatial correlation model as well as an empirical mean attenuation relationship, assuming that it constitutes a homogeneous two-dimensional stochastic field. Using the dense observation data of earthquakes that occurred in Japan and Taiwan in recent years, the macrospatial correlation model is proposed and the assumption of homogeneity is verified in this paper.

Planar Fluorescence Imaging of a Supersonic Axisymmetric Base Flow with Mass Bleed

Acetone planar laser-induced fluorescence (PLIF) was used to study the supersonic flow over an axisymmetric base with mass bleed. Detailed side-view and global end-view images were obtained in the recirculation regions, shear layer, and trailing wake. For the three bleed rates studied, the instantaneous behavior of the flowfield deviated substantially from the expected mean flow, especially for bleed rates below the optimal case. Large pockets of unmixed bleed fluid dominated the flowfield for the low and intermediate bleed rates, even in the trailing wake, highlighting the unsteady nature of the flowfield. The power-on condition for the high-bleed-rate case was the most temporally stable flowfield, due to the high momentum of the bleed jet. A multiplateau stirring effect was prevalent for all cases, consistent with previous compressible shear layer findings, and the effect increased with increasing bleed rate and distance downstream. Probability density functions (PDFs) of PLIF intensity indicated a similar mixing character between the low and intermediate bleed rates in the near wake and for all bleed rate cases in the trailing wake. The multiplateau stirring effect and unmixed bleed fluid pockets were represented well in the mixing PDFs.

Analysis of multipath scintillations from long range acoustic transmissions on the New England continental slope and shelf

Observations of intensity fluctuations for broadband, 400-Hz multipath arrivals observed during the 1996 New England shelfbreak PRIMER study are described. Acoustic signals were generated by two bottom-mounted sources located on the continental slope in roughly 290-m water depth and were received on a 52-m-long vertical-line-array (VLA) located in 93-m water depth. Propagation ranges were 42.2 and 59.6 km. The bathymetry, oceanography, and bottom geology of the PRIMER site are described. Acoustic observables of point intensity, peak intensity, and integrated energy over the VLA are treated in terms of the scintillation index, log-intensity variance, and intensity probability density functions (PDFs). Variability of the observables are decomposed into high and low frequency components with time scales less than and greater than 2 h, to facilitate correlation to ocean processes at different timescales. Parabolic equation numerical simulations using a quasi-random undular tidal bore model are able to reproduce many of the observed intensity fluctuation to within a factor of 2, and they allow investigation of scintillation behavior as a function of range.

Measurements of intensity scintillations and probability density functions of retroreflected broadband 980-nm laser light in atmospheric turbulence

Intensity scintillation variances and intensity probability density functions (PDFs) were experimentally measured for broadband (2 nm), 980-nm laser light reflected by two or more corner cube retroreflectors as a function of retroreflector lateral spacing over a short (75 m) atmospheric optical path. The PDFs transitioned from broad double-peaked beta-shaped densities to lognormal as the retroreflector spacing was increased to exceed the optical field's lateral coherence length. Specific spacing for a given average atmospheric structural C n 2 eliminated interference between the light beams returned by the retroreflectors.

Monte Carlo simulation of irradiance distribution on the retina after refractive surgery.

Generation of random wavefronts for ocular wave aberration statistics across the population has been used for various analyses. We propose a more accurate simulation procedure. This simulation technique is not intended to be a perfect representation of an eye, but instead is a tool for those applications where a correct distribution of aberrations across a population is necessary. Our technique consists of the generation of coefficients of the wavefront expansion into Zernike modes. The simulation makes use of the variance of every mode measured on a large population by using compact and reliable wavefront sensors. The simulation procedure was verified by reproducing two statistical functions that characterize eye behavior. This tool can be used to predict the performance of sensing techniques and to evaluate the consequences of customized ophthalmic elements and refractive surgery. It may also be useful for deriving both first and second order photon statistics of the point-spread function on the human retina (a key parameter in certain visual perception models). A new tool for analysis of customized refractive surgery is presented and the evolution of the light intensity probability density function on the retina with compensation attained after customized correction of the eye's aberrations is analyzed.

The optical near-field speckles and their first order statistics on the basis of the integral equations of electromagnetic field

From Helmholtz equation of the harmonic electromagnetic waves, the integral equations of the light field at the medium boundaries are obtained by use of the Green's theorem and are discretized into linear equation set with the values of the light field and its derivative as the unknowns. On solving the linear equation set, we realize the rigorous computations of the light fields at the boundaries. Then the intensities of the light waves scattered by the random self-affine fractal surfaces in the optical near-field are calculated, and the propagation characteristics, the evolutions of the contrast and the intensity probability density function of the near-field speckles are studied in detail. The near-field speckles are much different from the conventional speckles in the diffraction regions and in the imaging systems. There are obvious local fluctuations in the intensity distributions of the near-field speckles and such fluctuations disappear after propagating a distance of one wavelength from the medium surfaces. For the random surfaces with smaller lateral correlation lengths, the speckle contrasts approach the saturation values and the speckle fields approach Gaussian distribution within the near-field, while for the random surfaces with larger lateral correlation lengths, such evolutions become comparatively slow.

First- and second-order statistics of optical near fields.

The statistical properties of the intensity in close proximity to highly scattering, randomly inhomogeneous media are investigated. Whereas the intensity probability density function obeys the same law irrespective of the distance z from the interface, the second-order intensity correlation length changes for distances smaller than the wavelength. Contrary to predictions of the conventional coherence theory, the corresponding field correlation length can be smaller than the wavelength of light.

Ray dynamics in a long-range acoustic propagation experiment.

A ray-based wave-field description is employed in the interpretation of broadband basin-scale acoustic propagation measurements obtained during the Acoustic Thermometry of Ocean Climate program's 1994 Acoustic Engineering Test. Acoustic observables of interest are wavefront time spread, probability density function (PDF) of intensity, vertical extension of acoustic energy in the reception finale, and the transition region between temporally resolved and unresolved wavefronts. Ray-based numerical simulation results that include both mesoscale and internal-wave-induced sound-speed perturbations are shown to be consistent with measurements of all the aforementioned observables, even though the underlying ray trajectories are predominantly chaotic, that is, exponentially sensitive to initial and environmental conditions. Much of the analysis exploits results that relate to the subject of ray chaos; these results follow from the Hamiltonian structure of the ray equations. Further, it is shown that the collection of the many eigenrays that form one of the resolved arrivals is nonlocal, both spatially and as a function of launch angle, which places severe restrictions on theories that are based on a perturbation expansion about a background ray.

Impact of speckle on laser range-gated shortwave infrared imaging system target identification performance

The U.S. Army and the U.S. Air Force are investigating laser range-gated shortwave IR (LRG-SWIR) imaging systems for use in target identification. When coupled to an electron-bombarded CCD, the imaging system can obtain high-resolution images at long ranges. Speckle, an image artifact inherent in laser-illuminated imaging systems, results from interference patterns caused by the coherent illumination. Laser speckle degrades target identification performance but can be reduced by averaging successive LRG-SWIR images. This research is a first attempt at quantifying target identification performance degradation associated with laser speckle. The research begins with a laboratory experiment to verify a speckle model that includes power spectral density and intensity probability density functions. An LRG-SWIR sensor simulation is developed that includes coherent illumination resulting in speckle target images. A field demonstration is performed to verify the fidelity of the simulation. The simulation is then applied to the U.S. Army Night Vision and Electronic Sensors Directorate (NVESD) target identification set with various levels of image averaging and blur. Observer performance results are analyzed in terms of target identification probability and the effects of various levels of blur and speckle are characterized.

Recent results from basin-scale ocean acoustic wave propagation: Implications for the general theory of the approach to saturation

Long-range ocean acoustics as a problem in wave propagation through random media is unique in several ways. First the propagation takes place in the ocean sound channel (a waveguide), and second, a primary source of sound speed fluctuations are the anisotropic and inhomogeneous ocean internal waves (not turbulence). Recent observations of 75 Hz, broadband transmissions over several thousand kilometers have revealed fascinating results on the approach to saturation. Two distinct propagation regimes are observed in the same pulse: a fully saturated regime characterized by Rayleigh statistics, and an unsaturated regime in which the probability density function for intensity is nearly log-normal. The transition between these two regimes is extremely rapid. The saturated region of the pulse is composed of acoustic energy traveling near the waveguide axis, while the unsaturated region is composed of acoustic energy strongly refracted by the waveguide. This fact suggests a fundamental stabilizing influence by the waveguide. Application of path-integral theory, which was successful in describing shorter-range ocean experiments, cannot describe these two regimes. Recent efforts using semiclassical and ray chaos theory have led to new insights into the observational results and to the failure of the path-integral theory, yet a complete theoretical description remains elusive.

The effects of turbulent intermittency on scattering and estimates for the degree of saturation

Turbulent fluctuations in atmospheric wind and temperature fields are observed to be erratic in time; strong activity is typically interspersed with periods of relative calm. This property, referred to as turbulent intermittency, has an observable effect on the statistics of scattered acoustic signals. For fully saturated scattering, large intensity deviations about the mean result in a divergence from log-normal intensity probability density functions (pdfs) typically used to describe such statistics. Previous studies have developed the theory to predict the intensity pdf’s that account for both turbulent intermittency and the degree of saturation [Norris et al., J. Acoust. Soc. Am. 109, 1871–1880 (2001); Wilson et al., J. Acoust. Soc. Am. 99, 3393–3400 (1996)]. The new formulation with intermittency is compared to the generalized gamma pdf previously proposed for propagation in random media. It is also compared to data collected over a 140 m line-of-sight path at 110 to 525 Hz. Experimental characterization of the pdf parameters relating to intermittency and signal saturation is attempted with partial success. Strength/diffraction parameters and complex signal moments are computed to further define the scattering effects as a function of frequency and help identify limitations in the theory.

Computational ghost imaging study based on incoherent light from blackbody radiation

In recent years, ghost imaging has made important progress in the field of remote sensing imaging. In order to promote the application of solar ghost imaging in this field, this paper studies the computational ghost imaging based on the incoherent light of blackbody radiation. Firstly, according to the intensity probability density function of blackbody radiation, the expression of contrast-to-noise ratio (RCN) describing the quality of computational ghost imaging is obtained, and then the random speckle pattern simulating blackbody radiation is generated by computer with the idea of slice sampling, finally, a digital light projector is used to modulate and generate the random modulated light that simulates the blackbody radiation light source, and this light source is used to realize the computational ghost image of the reflective object in the experiment. The “ghost image” of the object under different measurement frame numbers is reconstructed, and the contrast-to-noise ratio describing the imaging quality is measured. The results show that the image quality is relatively good when the average intensity (gray) of the randomly modulated speckle is about 160. On the other hand, the contrast-to-noise ratio of the image gradually increases from 0.8795 to 1.241, 1.516, 1.755, 2.100 and 2.371 as the number of measurement frames increases from 2,000 to 4,000, 6,000, 8,000, 12,000 and 20,000, respectively. The experimental results are basically consistent with the theoretical analysis. The results are of great significance for the application of ghost imaging with incoherent light, such as sunlight, which is approximately regarded as blackbody radiation, in the field of remote imaging.

Further analysis of intensity fluctuations from a 3252-km acoustic propagation experiment in the eastern North Pacific Ocean

In the Acoustic Thermometry of Ocean Climate (ATOC) program’s Acoustic Engineering Test (AET), broadband 75-Hz center frequency transmissions were recorded on a 700-m-long vertical array, 3252 km distant from a midwater source suspended from R/P FLIP. The transmissions occurred over a 6-day period. Previously reported results from the AET using 12.7-min averaged data by Colosi et al. [J. Acoust. Soc. Am. 105(6), 3202–3218 (1999)], hereafter referred to as Colosi99) revealed surprisingly weak acoustic scattering for early arriving identifiable wavefronts. Colosi99 found pulse time spreads on the order of 0–5 ms and the probability density function (PDF) of peak intensity was close to log normal. In this paper these results are confirmed using 1.8-min averaged data. It is also shown that scintillation index (SI) is a strong function of position along the pulse with the smallest values occurring at the peak and larger values occurring at the tails. Intensity PDFs of identifiable wavefronts are reanalyzed in terms of both peak intensity and integrated pulse energy (IE) where the integration is over ±50 ms from the wavefront peaks. While SI for the IE are somewhat smaller than for the peak intensity, the PDFs are both very closely log normal. Regarding multipathing along the wavefronts, it is found that on average there are 1.7 peaks per wavefront segment per hydrophone and the intensity PDF of all multipath peaks is log normal. The combined observation of weak scattering and multipathing is a novel result. A reanalysis of the scintillations in the AET transmission finale where no wavefronts are evident is presented. Colosi99 analyzed the finale in terms of peak scintillations and found a near log-normal intensity PDF. Reprocessing the full field without limiting data to intensity peaks and accounting for mean intensity nonstationarity yields an intensity PDF which is much closer to the exponential distribution associated with full saturation; these results show that the finale region can be expected to behave much like Gaussian random noise.

Theoretical analysis of the measurement precision in particle image velocimetry

An analytical expression for the error in the sub-pixel displacement is derived. The expression relates the error to the second- and fourth-order moments of the intensity probability density function, which can both be expressed in terms of the source density. Scaling relations for the error as a function of the particle-image diameter are determined by means of the Cramer–Rao lower bound, for both constant image density and constant source density. The analytical expression is evaluated for the error as a function of the sub-pixel displacement, the particle-image diameter, and the image density, and the results are validated against results from Monte-Carlo simulations. It is demonstrated that results obtained from synthetic PIV images that do not represent the correct image intensity probability density function systematically underestimate the displacement measurement error.

Bistatic scattering: A new way to improve sonar detection capabilities?

In the field of seabed sonar imagery, it is necessary to establish local scattering models to improve the performances of the detection or recognition algorithms. In this paper, we present the Probability Density Function (PDF) of the acoustic intensity scattered by a natural profile as a function of the bistatic angle. To do this we have developed a 1-D bistatic scattering model called NEWS (Numerical Estimation for Waves Scattering) that incorporates physical phenomenons like multiple reflections, shadow and the reflection coefficient of the profile. Moreover, NEWS takes into account acquisition parameters like sensors characteristics and their positions in relation to the center of the illuminated area. Gaussian spectra for the profile height fluctuation are considered. Five hundred profiles are generated. For each profile NEWS’s algorithm gives the angular distribution of the scattered field in amplitude and in phase for all geometries and as a function of incident and scattered wave. The acoustic intensity is then treated as a random variable, and histograms are established. The PDF of the scattered intensity is compared to the K, Weibull and lognormal distributions and we examine the statistical informations providing by bistatic sonar.