Backscatter Coefficient Measurements Research Articles

Simulation of ultrasound backscatter coefficient measurement using the finite element method

Ultrasound backscatter coefficient (BSC) measurement is a method for assessing tissue morphology that can inform on pathologies such as cancer. The BSC measurement is, however, limited by the accuracy with which the investigator can normalise their results to account for frequency dependent effects of diffraction and attenuation whilst performing such measurements. We propose a simulation-based approach to investigate the potential sources of error in assessing the BSC. Presented is a tool for the 2D Finite Element (FE) simulation mimicking a BSC measurement using the planar reflector substitution method in reduced dimensionality. The results of this are verified against new derivations of BSC equations also in reduced dimensionality. These new derivations allow computation of BSC estimates based on the scattering from a 2D scattering area, a line reference reflector and a theoretical value for the BSC of a 2D distribution of scatterers. This 2D model was designed to generate lightweight simulations that allow rapid investigation of the factors associated with BSC measurement, allowing the investigator to generate large data sets in relatively short time scales. Under the conditions for an incoherent scattering medium, the simulations produced BSC estimates within 6% of the theoretical value calculated from the simulation domain, a result reproduced across a range of source f-numbers. This value of error compares well to both estimated errors from other simulation based approaches and to physical experiments. The mathematical and simulation models described here provide a theoretical and experimental framework for continued investigation into factors affecting the accuracy of BSC measurements.

Efficient grain size evaluation based on single direction measurement of ultrasonic backscattering coefficient

<sec>GH4742 nickel-based superalloy exhibits excellent mechanical properties, and grain size is a key factor affecting its performance. A physical model-based ultrasonic backscattering method makes grain size measurement accurate and efficient. Nevertheless, it is constrained by complex models or multiple measurements taken from various beam angles. As a result, a backscattering coefficient method that requires only a single measurement for grain size evaluation is proposed. In contrast to the existing methods, the proposed method solely focuses on the backscattering coefficient component of the backscattering signal. It effectively eliminates the influence of unrelated factors, such as the measurement system and the acoustic field, through the utilization of reference signals.</sec><sec>The independent scattering model is employed to derive the backscattering coefficient, which solely pertains to the material itself. The relationship between grain size and backscattering coefficient is described by using a spatial correlation function. To consider the irrelevant factors, an experimental measurement method is developed by using the reference signals. Through numerical calculation and analysis, it has been observed that the backscattering coefficient is closely related to the frequency. When the product of the wavenumber and the grain size is significantly greater than 1 (<inline-formula><tex-math id="M1">\begin{document}$ ka\gg 1 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231959_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231959_M1.png"/></alternatives></inline-formula>), a Stochastic scattering limit is reached. Conversely, when <inline-formula><tex-math id="M2">\begin{document}$ ka\ll 1 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231959_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20231959_M2.png"/></alternatives></inline-formula>, a Rayleigh scattering limit is observed. Furthermore, the backscattering coefficient is directly proportional to the grain size. As a general trend, larger grain sizes result in higher backscattering coefficient.</sec><sec>Three sets of GH4742 specimens with different grain sizes are prepared for phased array ultrasound experiments. It can be observed that the experimental backscattering coefficients, root mean square (RMS) values, and the amplitude trend of time domain signal are consistent. To perform grain size inversion, the backscattering coefficients in the effective bandwidth range of the probe are selected. By utilizing the least-square method, the theoretical backscattering coefficient is employed to fit the curves of the experimental backscattering coefficients. The evaluation results are compared with those obtained by metallographic analysis. The results show that the grain sizes obtained by the proposed method have a maximum relative error of –22.7% and a minimum relative error of –3.7%.</sec>

Uncertainty Analysis of Particle Backscattering Coefficient Measurement for Multiple Highly Turbid Water Areas in Ocean Color Remote Sensing

Uncertainty Analysis of Particle Backscattering Coefficient Measurement for Multiple Highly Turbid Water Areas in Ocean Color Remote Sensing

High-frequency Quantitative Ultrasound Imaging of Human Rotator Cuff Muscles: Assessment of Repeatability and Reproducibility.

This study evaluated the repeatability and reproducibility of using high-frequency quantitative ultrasound (QUS) measurement of backscatter coefficient (BSC), grayscale analysis, and gray-level co-occurrence matrix (GLCM) textural analysis, to characterize human rotator cuff muscles. The effects of varying scanner settings across two different operators and two US systems were investigated in a healthy volunteer with normal rotator cuff muscles and a patient with chronic massive rotator cuff injury and substantial muscle degeneration. The results suggest that BSC is a promising method for assessing rotator cuff muscles in both control and pathological subjects, even when operators were free to adjust system settings (depth, level of focus, and time-gain compensation). Measurements were repeatable and reproducible across the different operators and ultrasound imaging platforms. In contrast, grayscale and GLCM analyses were found to be less reliable in this setting, with significant measurement variability. Overall, the repeatability and reproducibility measurements of BSC indicate its potential as a diagnostic tool for rotator cuff muscle evaluation.

Neural Network-Based Wind Measurements in Rainy Conditions Using the HY-2A Scatterometer

Wind measurement using spaceborne scatterometers has been used for various scientific and operational purposes. However, the major problem of such measurements is contamination by rain. To improve the wind measurement using the HY-2A scatterometer under rainy conditions, a neural network-based model was established in this study. The model is almost autonomous in that it only needs the backscatter coefficient measurement data and the observation geometry information from the HY-2A scatterometer itself. The model can distinguish between rain-contaminated wind pixels and rain-free wind pixels and significantly improve the accuracy of wind speed measurements using HY-2A scatterometer alone. TAO data and linearly calibrated ECMWF data were used in the study to validate the neural network-inverted wind speed. Under no rain conditions, the RMS of the neural network-inverted wind speed and TAO wind speed was 1.06 m/s, with a deviation of −0.21 m/s, which is a small difference from the standard method inverted wind speed. Under rain conditions, the RMS and deviation were 1.94 m/s and 0.66 m/s, respectively, which were better than the statistical results of the conventional maximum likelihood estimation method. The validated results using linearly calibrated data also indicate that the neural network-inverted wind speed is closer to the validation data under rain conditions.

An explicit formulation for the retrieval of the overlap function in an elastic and Raman aerosol lidar

Abstract. We derive an explicit (i.e., non-iterative) formula for the retrieval of the overlap function in an aerosol lidar with both elastic and Raman N2 and/or O2 channels used for independent measurements of aerosol backscatter and extinction coefficients. The formula requires only the measured, range-corrected elastic and the corresponding Raman signals, plus an assumed lidar ratio. We assess the influence of the lidar ratio error in the overlap function retrieval and present retrieval examples.

Simulation of a tissue backscatter coefficient measurement experiment using the finite element method

Ultrasound has been shown to be an effective imaging modality for investigating tissue health. For example, the backscatter coefficient (BSC) has been shown to be a biomarker of tumour response to therapy but is limited in its application clinically due to the difficulty of accurately acquiring attenuation and diffraction corrections. To assess the variability in BSC assessment, we present a finite element tool simulating a singleelement planar reflector substitution method estimate of the BSC of a set of simulated phantoms. BSC estimates were computed with errors <5% of the theoretical value for a range of source apertures and over a set of phantoms with varying scatterer number densities to within 10%. In addition, the firstorder amplitude envelope statistics of backscattered waves were shown to be commensurate with Rayleigh scattering models. These results indicate that the tool is accurate in its replication of soft tissue-like scattering, suggesting that it could be an opportune testing ground for investigating sources of variability in BSC measurements and the testing of algorithms and hypotheses for interrogating the scattering behaviour of soft tissues.

Investigation of the planar reflector substitution method using the finite element method

The backscatter coefficient (BSC) has been shown to be an indicator of tissue state in assessing tumour response to therapy, but it is limited in its clinical applicability by the difficulty in acquiring the appropriate reference spectrum. The accuracy of a BSC estimate made by the substitution method is influenced by the quality of the reference spectrum, which normalises the measurement to the source’s diffraction field and spectral characteristics. Among the reference objects employed for normalisation, a planar reflector has been popular. With the sample region at the focus of a focused source or the last axial maximum of an unfocused source, the reflector has been placed either at this depth or half this depth by different authors. This work explores the effect of planar reflector positioning on BSC estimation. FE models were constructed to simulate BSC measurements of virtual phantoms with various sources, and the estimates compared to scattering theory. The results indicate that unfocused sources provide more accurate BSC estimates when the reflector is placed at half the distance to the last axial maximum (d), while focused sources provide better estimates with the planar reflector at the focal plane, and that focal-plane reflector positioning is preferable for source radii-of-curvature ≤ d.

A Comparison of the Barrick and Backscatter Ionogram Methods of Calculating Sea Surface Backscatter Coefficients

An understanding of land and sea surface backscatter coefficients at high frequencies (HF) is required to accurately assess ionospheric propagation conditions for over-the-horizon radar. In this paper, two methods of calculating sea surface backscatter coefficients are compared. The first method is a theoretical method developed by Barrick in 1972, which treats the sea as a slightly rough surface defined by a wave height spectrum and uses a perturbation approach. The second method compares the difference between observed and modelled backscatter ionograms in which all other losses are accounted for to obtain a measurement of the sea surface backscatter coefficient. Similar trends and values for the sea surface backscatter coefficients from each method were found despite the many models and assumptions required for both these methods. However, it was noted that there was a larger range of values for the sea surface backscatter coefficients when the Barrick method was used.

Contactless Antenna Gain Pattern Estimation From Backscattering Coefficient Measurement Performed Within a Reverberation Chamber

This communication presents the antenna gain pattern estimation from backscattering coefficient measurement performed within a reverberation chamber (RC). The antenna backscattering coefficient is measured for two load conditions, namely, an open circuit (OC) and a 50 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Omega $ </tex-math></inline-formula> load, enabling to distinguish the radiation and structural modes from the total backscattered field. This approach is applied to the measurement of the gain pattern of a Vivaldi antenna at 6.5 GHz and compared with a conventional transmission-type measurement within an anechoic chamber (AC). The main lobe of the radiation pattern is in good agreement between both measurements. The difference between maximal gains, retrieved after a reference measurement using a metallic plate, is equal to 0.04 dB. A second validation is performed using a log-periodic antenna at 3.5 GHz, showing less than 0.76 dB difference over the measured angular range. To the best of our knowledge, this is the first time that a contactless gain pattern measurement is performed and validated within an RC.

Impact of Vertical Profiles of Aerosols on the Photolysis Rates in the Lower Troposphere from the Synergy of Photometer and Ceilometer Measurements in Raciborz, Poland, for the Period 2015–2020

The effect of the aerosol vertical distribution on photolysis frequencies of O3 and NO2 is studied. Aerosol measurements in Raciborz (50.08° N, 18.19° E), Poland, made using the CIMEL Sun photometer and collocated CHM-15k “Nimbus” ceilometer are analyzed for the period 2015–2020. Vertical profiles of the aerosol extinction are derived from the Generalized Retrieval of Atmosphere and Surface Properties (GRASP) algorithm combining the ceilometer measurements of the aerosol backscattering coefficient with the collocated CIMEL measurements of the columnar characteristics of aerosols. The photolysis frequencies are calculated at the three levels in the lower troposphere (the surface and 0.5 and 2 km above the surface) using a radiative transfer model, Tropospheric Ultraviolet and Visible (TUV), for various settings of aerosol optical properties in the model input. The importance of the aerosol vertical distribution on photolysis frequencies is inferred by analyzing statistics of the differences between the output of the model, including the extinction profile from the GRASP algorithm, and the default TUV model (based on columnar aerosol characteristics by the CIMEL Sun photometer and Elterman’s extinction profile). For model levels above the surface, standard deviation, 2.5th percentile, 97.5th percentile, and the extremes, calculated from relative differences between these input settings, are comparable with the pertaining statistical values for the input pair providing changes of photolysis frequencies only due to the variability of the columnar aerosol characteristics. This indicates that the vertical properties of aerosols affect the distribution of the photolysis frequencies in the lower troposphere on a similar scale to that due to variations in columnar aerosol characteristics.

Investigation of the Anisotropic Patterns in the Altimeter Backscatter Measurements Over Ocean Wave Surfaces

This article attempts to analyze the influence of the anisotropic effects of the ocean wave surface on SAR altimetry backscatter coefficient (Sigma-0) measurements, which has not been intensively addressed in publications. Data of Sentinel-3A, Cryosat-2, and Jason-3 altimeters allocated by the WW3 numeric wave model were analyzed, and the patterns of Sigma-0 with respect to the wave direction were acquired under ∼2 m significant wave height. The ocean waves were classified into six categories, among which the moderate swell and short win-wave cases were analyzed intensively. Swell-dominated ocean surface shows less randomness than the wind-wave-dominated ocean surface. Clear and significant sinusoid trends are found in the Sigma-0 and SSB patterns of both operational modes (SAR mode and PLRM mode) of the Sentinel-3A altimeter for the moderate swell case, indicating the sensitivity of Sigma-0 and SSB measurements to the anisotropic features of the altimeter measurements. The anisotropic pattern in the Sentinel-3A PLRM Sigma-0 is somewhat counterintuitive, but the analysis of Jason-3 altimeter data would show similar results. Additionally, by comparing the anisotropic patterns of two orthogonally polarized SAR altimeters (Sentinel-3A and Cryosat-2), we could draw the conclusion that the Sigma-0 measurements are not sensitive to the polarization mode. As for the SSHA patterns, no clear sinusoid could be identified for the moderate swell. A possible explanation is that the SSB pattern may be overwhelmed in the complicated factors that can influence the SSHA pattern.

A novel retrieval algorithm of multi-longitudinal-mode high-spectral- resolution lidar based on complex degree of coherence and the analyses of absolute errors

Multi-longitudinal-mode (MLM) high-spectral-resolution lidar (HSRL) selects an optical interferometer with the periodic transmittance function as the spectral discriminator to separate aerosol Mie scattering signals and molecular Rayleigh scattering signals excited by the MLM pulsed lasers, such as Mach-Zehnder interferometer, Michelson interferometer, Fabry-Perot etalon and so on. In this paper, we deduce a novel algorithm for retrieving aerosol backscattering coefficient, optical depth, and aerosol extinction coefficient in the application of the MLM HSRL, in which the lidar returns should be considered as a quasi-monochromatic light. Under such a condition, the effective transmittance of Mach-Zehnder interferometer is a function of the complex degree of coherence, which plays an important role in the retrieval algorithms of aerosol optical properties. The retrieval algorithms of aerosol backscattering coefficient, optical depth and aerosol extinction coefficient based on the complex degree of coherence are presented in detail and their correctness is verified by the system simulation using an experimental Mie-Rayleigh lidar returns. Meanwhile, the absolute errors of the measurements of aerosol backscattering coefficient and optical depth are analyzed from the systematic errors and random errors. The simulation results show that the presence of aerosol layers or cloud layer deteriorates considerably the accuracy of the retrieved aerosol backscattering coefficient and optical depth, and the total absolute error of aerosol backscattering coefficient is ignored, as well as the total absolute error of optical depth can be controlled within 0.4 in the majority of the lidar data when the relative error of δ is within 20%. Both measurement examples and continuous observations from the constructed MLM HSRL have proven that the MLM HSRL has the capability in the application of fine detection of aerosol optical properties.

SCATSAT-1 backscattering coefficient over distinct land surfaces and its dependence on soil moisture and vegetation dynamics

ABSTRACT The objective of this study is to examine the potential of SCATSAT-1 data for estimating the soil moisture and vegetation over the continental regions by evaluating the variabilities in backscattering coefficients measured over different land surface types. The SCATSAT-1 is Ku-band wind Scatterometer, which provides backscattering coefficient measurements over the globe in HH and VV polarization at fixed incidence angles. Variabilities in the backscatter coefficients over different land surfaces, mainly over four different geo-climatological regions of India, are studied based on 3 years of SCATSAT-1 dataset in conjunction with other collocated measurements. The SCATSAT-1 backscattering coefficient provides the quantitative measure of the seasonality over a region due to unique distribution of soil moisture and vegetation characteristics of that region. The variabilities in soil moisture and vegetation in these regions are compared and applicability of change detection method for estimating the soil moisture over these regions has been analysed. Based on regression analysis on SMOS measured soil moisture and SCATSAT-1 measured backscattering coefficient, a relationship has been established for the soil moisture estimation from the SCATSAT-1 backscattering coefficient.

Study of Low Terahertz Radar Signal Backscattering for Surface Identification

This study explores the scattering of signals within the mm and low Terahertz frequency range, represented by frequencies 79 GHz, 150 GHz, 300 GHz, and 670 GHz, from surfaces with different roughness, to demonstrate advantages of low THz radar for surface discrimination for automotive sensing. The responses of four test surfaces of different roughness were measured and their normalized radar cross sections were estimated as a function of grazing angle and polarization. The Fraunhofer criterion was used as a guideline for determining the type of backscattering (specular and diffuse). The proposed experimental technique provides high accuracy of backscattering coefficient measurement depending on the frequency of the signal, polarization, and grazing angle. An empirical scattering model was used to provide a reference. To compare theoretical and experimental results of the signal scattering on test surfaces, the permittivity of sandpaper has been measured using time-domain spectroscopy. It was shown that the empirical methods for diffuse radar signal scattering developed for lower radar frequencies can be extended for the low THz range with sufficient accuracy. The results obtained will provide reference information for creating remote surface identification systems for automotive use, which will be of particular advantage in surface classification, object classification, and path determination in autonomous automotive vehicle operation.

Simple method to extend the range of ECO-BB for waters with high backscattering coefficient.

The ECO-BB (Sea Bird Scientific) is a popular instrument used by water optics researchers to measure the backscattering coefficient of waters in the visible to near-infrared wavelengths. The ECO-BB is calibrated by default for oceanic waters where the backscattering coefficient is typically low. In inland and coastal waters however, there is a tendency for the ECO-BB to reach saturation due to the high number of suspended particles. In the paper, a simple method is presented to extend the range of the ECO-BB instrument in such waters using a nephelometric turbidimeter. The method was first tested on powdered calcium carbonate in pure freshwater, followed by collected water samples from the Singapore Straits and the Lupar River in Sarawak. All three tests confirm the correlation between the ECO-BB and turbidimeter and show that the turbidimeter is a good proxy for backscattering coefficient measurements in turbid waters.

Development of a 355-nm high-spectral-resolution lidar using a scanning Michelson interferometer for aerosol profile measurement.

A simple 355-nm high-spectral-resolution lidar (HSRL) is developed for continuous observation of aerosol profiles. A scanning Michelson interferometer is used to separate the Rayleigh and Mie scattering components. The interferometer is periodically scanned in the range of one fringe. Interference contrast, which contains aerosol backscatter information, is estimated at each height through fitting analysis of the scan data. The interference contrast and fringe position are calibrated with the reference signals taken from the transmitted laser. Furthermore, the 1-day continuous measurement of aerosol backscatter and extinction coefficients is demonstrated. Comparison with a nighttime Raman lidar indicates a good performance of the scanning method.

Experimental investigation of acoustic backscattered field from a medium with random and aligned fibers

Some soft tissues, such as skeletal muscles, have fiber-like structures that make them anisotropic. Acoustic backscattering from such tissues or media has been of interest to many scientists in biomedical fields because it complicates interpretation of imaging data. Backscatter coefficient measurements show diagnostic promise for this purpose both in vitro and in vivo. Many parameters, e.g., effective scatterer diameter or average scattering strength, can be estimated with acoustic backscatter measurements. In the present work, we experimentally study the backscatter coefficient of a medium with aligned or random fibers and estimate the effect of fiber orientation upon the backscattered field and the estimated scatterer diameter. Using an experimental approach, we explore the relationship between the backscatter coefficient of a medium with multiple fibers and with a single fiber. In addition, we investigate the effect of the spatial Fourier transform of the fiber distribution in the medium with its frequency dependence of backscatter coefficients. The experimental results show that backscatter coefficients of a medium with random fibers can be modeled by the product of number density of fibers, backscatter coefficients of the same single fiber, and the spatial Fourier transform of the fiber distribution.Some soft tissues, such as skeletal muscles, have fiber-like structures that make them anisotropic. Acoustic backscattering from such tissues or media has been of interest to many scientists in biomedical fields because it complicates interpretation of imaging data. Backscatter coefficient measurements show diagnostic promise for this purpose both in vitro and in vivo. Many parameters, e.g., effective scatterer diameter or average scattering strength, can be estimated with acoustic backscatter measurements. In the present work, we experimentally study the backscatter coefficient of a medium with aligned or random fibers and estimate the effect of fiber orientation upon the backscattered field and the estimated scatterer diameter. Using an experimental approach, we explore the relationship between the backscatter coefficient of a medium with multiple fibers and with a single fiber. In addition, we investigate the effect of the spatial Fourier transform of the fiber distribution in the medium with its frequ...

Optical characterization of marine phytoplankton assemblages within surface waters of the western Arctic Ocean.

An extensive data set of measurements within the Chukchi and Beaufort Seas is used to characterize the optical properties of seawater associated with different phytoplankton communities. Hierarchical cluster analysis of diagnostic pigment concentrations partitioned stations into four distinct surface phytoplankton communities based on taxonomic composition and average cell size. Concurrent optical measurements of spectral absorption and backscattering coefficients and remote‐sensing reflectance were used to characterize the magnitudes and spectral shapes of seawater optical properties associated with each phytoplankton assemblage. The results demonstrate measurable differences among communities in the average spectral shapes of the phytoplankton absorption coefficient. Similar or smaller differences were also observed in the spectral shapes of nonphytoplankton absorption coefficients and the particulate backscattering coefficient. Phytoplankton on average, however, contributed only 25% or less to the total absorption coefficient of seawater. Our analyses indicate that the interplay between the magnitudes and relative contributions of all optically significant constituents generally dampens any influence of varying phytoplankton absorption spectral shapes on the total absorption coefficient, yet there is still a marked discrimination observed in the spectral shape of the ratio of the total backscattering to total absorption coefficient and remote‐sensing reflectance among the phytoplankton assemblages. These spectral variations arise mainly from differences in the bio‐optical environment in which specific communities were found, as opposed to differences in the spectral shapes of phytoplankton optical properties per se. These results suggest potential approaches for the development of algorithms to assess phytoplankton community composition from measurements of seawater optical properties in western Arctic waters.

Calibration of an airborne oceanographic lidar using ocean backscattering measurements from space.

We used satellite measurements of the optical backscattering coefficient to calibrate the signal from an airborne oceanographic lidar. This technique provided the radiometric calibration for the lidar signal and a local estimate of the ratio of the particulate backscattering coefficient, bbp, to the volume scattering function at the scattering angle of 180°, βp(180). Results using an ordinary regression, a reduced major axis regression, and a least squares bisector suggest that either of the latter two provided a better result than an ordinary regression. The statistical errors in the two recommended regressions, the difference in calibrations factors between them, and the difference between these and a laboratory calibration were all less than 5%.