Backscattering Matrix Research Articles

Improved Clutter Suppression Algorithm for Atmospheric Target Detection Using Polarimetric Doppler Radar

When using dual-orthogonal frequency modulation continuous wave (FMCW) polarimetric radar, the polarimetric range-Doppler spectra of the atmospheric targets are contaminated by noise, clutter, and artificial signals that disturb the analysis of atmospheric target parameters, such as reflectivity, mean Doppler velocity, and Doppler width. This paper describes an improved clutter suppression method that is able to detect most atmospheric targets while suppressing clutter, noise, and artificial signals as well as possible. By using logical decisions that are based on the spectral linear depolarization ratios (SLDRs), a binary mask matrix is constructed, and the characteristics of this original mask matrix are improved via mathematical morphology methods. To suppress clutter, noise, and artificial signals and retain atmospheric targets, we multiply the range-Doppler spectra by the improved mask matrix. The raw atmospheric data are acquired using the Polarimetric Agile Radar S- And X-band (PARSAX) radar, which is able to measure the backscattering matrix of atmospheric targets in one sweep. After calibration, the range-Doppler polarimetric spectra are processed using the proposed clutter suppression method, and the atmospheric targets are successfully detected. Compared with the unprocessed data and the data processed by noise clipping and double SLDR filtering, the data processed by the proposed method show improvement in the ability to determine the atmospheric targets in the range-Doppler spectrogram, the reflectivity, the mean Doppler velocity, and the Doppler width.

Bias Correction and Doppler Measurement for Polarimetric Phased-Array Radar

This paper discusses ways to avoid and/or mitigate biases in polarimetric variables inherent to agile-beam planar phased-array radars. Two bias-avoiding schemes produce unbiased estimates of the polarimetric backscattering covariance matrix which are then combined into bias-free polarimetric variables. One concerns full polarimetric measurements and calls for adjusting the amplitudes and phases of the array elements so that the transmitted field equals that generated by a mechanically steered polarimetric weather radar antenna; this is followed by an additional adjustment of the received fields. The second scheme is also applicable to full polarimetric measurements but involves adjustments only of the received fields. Crucial to both schemes is decoupling of the Doppler effects from the terms of the covariance matrix. It is a significant part of the bias issue that had not been previously addressed. A scheme to reduce bias applicable to nondepolarizing media (i.e., diagonal backscattering matrix) is also addressed; it calls for multiplication of the fields received by each dipole as opposed to a combination of multiplication and addition required for full correction. The schemes are applied to the alternate transmission and simultaneous reception polarimetric mode and the simultaneous transmission and simultaneous reception mode.

Transformation of the light backscattering matrices from crystal clouds during a variation of the zenith sensing angle

Problems concerning the interpretation of the results of crystal cloud investigations by laser sensing are considered. The parameters characterizing the orientation of cloud particles are determined using backscattering matrix elements. It is shown how these parameters are related to the probability density of the particle distribution over the spatial orientation angles. The trends in the change of the backscattering matrices at variations of the zenith angle of a sensing path inclination are shown by the example of a monodisperse ensemble of ice particles.

NUMERICAL SIMULATION ON SEARCHING THE OPTIMUM SOURCE-DEPTH DISTRIBUTION FOR REVERBERATION INVERSION BY SIMULATED ANNEALING

To extract the intrinsic bottom back-scattering information from the reverberation data in shallow water has been a challenge topic for long time. It is shown that the modal back-scattering matrix (MBSM) is the intrinsic description of the bottom scattering.1 The optimum source-depth distribution for inverting MBSM from the reverberation data has been discussed with a Pekeris waveguide.2 In the present work, we extend the procedure to the general case of non-Pekeris waveguide by using the simulated annealing (SA) approach. Numerical simulated examples on searching the optimum source-depth distribution for MBSM inversion are presented. It is shown that: (1) the SA is an effective approach for searching the optimum source-depth distribution for MBSM inversion (2) the MBSM inverted from the optimal source-depth distribution has the strong stability against noise.

Study on target characteristic polarization state in co-polarized channel for the coherent case

The target characteristic polarization state in the co-polarized channel for the coherent case was studied in greater detail, with emphasis on the analysis of the characteristic polarization states variable with the target parameters. The Sinclair backscatter matrix was diagonalized under the change of polarization basis via a unitary transformation matrix. Then the diagonal matrix was parameterized by four parameters viz. matrix amplitude, absolute phase, amplitude ratio and phase difference. The behavior of the characteristic polarization states with the varieties of target parameters was discussed together with the power density plot. The characteristic polarization states were displayed on the Poincare sphere and six conclusions were obtained, which provide theoretic support for decreasing the computational complexity of target characteristic polarization state, or anticipating its position in the power density plot. Several simple target cases were considered for validating these conclusions.

Forest cover type classification at Mt. Asama using ALOS fully Polarimetric PALSAR data, in Nagano prefecture, central Japan

PALSAR (Phased Array L-band Synthetic Aperture Radar) was installed on the Japanese ALOS (Advanced Land Observing Satellite) that was launched on 24 January 2006. This is the first satellite regularly operated with fully polarimetric SAR in the world, and is considered useful for monitoring forest and biomass, as well as topography and land use. Forest cover types and stand volume classifications were produced for Mt. Asama using unsupervised and supervised classifications from the backscatter matrix using polarimetric PALSAR data. The Mt. Asama region was selected for study because of its gentle geographic features and large number of representative Japanese larch (Larix kaempferi), red pine (Pinus densifolia), and sub-alpine conifer (Abies mariesii and Tsuga diversifolia) forests. The unsupervised classification data allowed the forest region to be distinguished from fields, rice fields, pastures, residential areas, roads, and bare ground. We also produced forest cover type and volume classification images using a supervised classifier with GIS and field data, with a classification accuracy of 11.0-56.5%. The accuracy of highest volume classes was 301-450 m3/ha (56.5%) and 451-800 m3/ha (49.6%). This may have been because the influence of geographic features such as slope azimuth and ridges were larger than that of forest cover types. Therefore, polarimetric PALSAR data are suitable for monitoring deforestation and detecting changes in forest cover types in a homogenous, large forested region without complex mountainous geographic features.

A Shallow-Water Reverberation Model Based on Perturbation Theory

A shallow-water reverberation model is developed based on Bass perturbation theory. The key component for shallow-water reverberation modeling, the modal backscattering matrix (MBSM), has been investigated and the explicit analytic expressions of the MBSM both for the scattering due to interface roughness and due to sediment volume inhomogeneities are derived. For rough interface scattering, it is shown that the angular dependence and the frequency dependence of the MBSM can be separated: the angular dependence is given by sin <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> (? <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> P/2)sin <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> (? <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> P/2), where ? <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> is the modal grazing angle and P is a bottom parameter related to the bottom reflection phase shift, and the frequency dependence is given by k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4-n</sup> , where n depends on the power spectrum of the roughness, for instance, n = 3 for Goff-Jordan spectrum. The difference between the scattering due to sediment volume inhomogeneities and the scattering due to rough interface is that there is an extra factor contributed by the vertical correlation and the exponential attenuation of the modal function weighting on the vertical direction in the sediment medium. This extra factor has some important impacts: (1) there will be, in general, a coupled angular-frequency behavior, (2) the angular pattern will decrease more rapidly at small grazing angle area, and (3) the angular pattern is no longer separable. It is shown that only for a ?thin? layer (or low frequency), the scattering due to volume inhomogeneities will have a similar behavior as the scattering due to rough interface. The significant feature of the angular pattern for both kinds of scattering is a marked departure from Lambert's law at small grazing angle area. The explicit analytic expression of the MBSM, and the differences between the two kinds of bottom scattering, given in this paper, provide the opportunity for a comprehensive model-data comparison and a better understanding of the scattering mechanism.

Spectral properties of the backscattering matrix in random scattering media

We investigate, both experimentally and theoretically, the spectral properties of the backscattering operator in random media. The experimental set up consists in an array of 64 programmable ultrasonic transducers placed in front of a random scattering medium. The impulse responses between each couple of transducers are measured and form the interelement matrix.The evolution of the singular values with time and frequency is computed by means of a short‐time Fourier analysis. Our aim is to compare the mean distribution of the singular values with the predictions of Random Matrix Theory (RMT). Two kinds of random media have been investigated: a highly scattering medium in which multiple scattering predominates and a weakly scattering medium. In both cases, residual correlations that may exist between matrix elements are shown to be a key parameter. The mean distribution of singular values exhibits, surprisingly, very different behaviors in the single and multiple scattering regimes. The agreement between experimental results and RMT predictions is found to be very good in both cases. The results are applied to the detection of a target embedded in a random scattering medium with the DORT method.

The optimum source depth distribution for reverberation inversion in a shallow-water waveguide

An approach for extracting the modal backscattering matrix from reverberation data in shallow water was proposed recently (Shang, Gao, and Tang, 2002). The kernel matrix of the inversion is constructed using the square of the modal functions. The singularity of this matrix (or the stability of the inversion) is the crucial issue to be considered. In this paper, we discuss this issue analytically for a Pekeris waveguide with the limited mode number M. The method that we used for singularity analysis is to calculate the maximum value of the determinant of this kernel matrix. We found that there is an optimum source depth distribution corresponding to the maximum value of the determinant of the kernel matrix. That means that, by choosing the optimum source depth distribution, we can get the most stable inversion. The conclusion is that, under a quite tolerant condition, the matrix is not singular, and the backscattering matrix can be inverted.

Relationship Between Integrated Bottom Scattering Strength and Modal Backscattering Matrix

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The integrated bottom scattering strength (ISS) and the modal backscattering matrix (MBSM) have been used to describe the bottom backscattering in shallow-water reverberation modeling, and both can be extracted from the reverberation data. The relationship between the ISS and the MBSM based on the same reverberation data in shallow water is discussed. It is shown that the ISS is an angular weighting average of the MBSM in mode space. The weighting factors are range–depth–frequency-dependent and also depend on the sound-speed profile (SSP) in the water column. Thus, the ISS has a complex variation. This complexity of the ISS causes it to be so variable that it provides little basic understanding of the scattering. Numerical examples are conducted to show this complexity. </para>

Principal Component Analysis (PCA) in the Context of Radar Polarimetry

Statistical and computational techniques for revealing the internal structure that underlies the set of random correlated data exists in a great variety at present; and target decomposition theorems, either in the coherent or incoherent formulation, are well established. In spite of this fact a rather innovative and new concept is presented in this contribution. In turn the Principal Component Analysis (PCA) is considered to possibly add value to existing approaches, and it allows for an interpretation of polarimetric synthetic aperture radar measurements using variables obtained via linear transformation. Starting with the Sinclair backscatter matrix S which will be further transformed into the so called target feature vector by stacking column elements of S and generating the covariance matrices averaged over a certain pixel array, we show, how the Sinclair backscatter matrix is decomposed into the sum of a maximum of four 2 x 2 elementary point scatter matrices which are weighted by the principal components, whereas the variances of these components agree with the eigenvalues of the covariance matrix. This mathematical development defines a decomposition which expresses scattering mechanism from distributed targets in terms of scattering matrices via an incoherent step.

Characteristics of bottom-roughness backscattering matrix in mode space

The bottom backscattering matrix of a normal-mode reverberation model describes the coupling relationship between the incident normal mode and scattering normal mode in the shallow-water waveguide. The numerical analysis of the bottom roughness backscattering matrix and the result of backscattering matrix inversion from experimental data were presented from mode space. The results show that: (1) at a close distance, the value of the backscattering matrix elements inclines toward high modes. The matrix is similar to a 2D high-pass filter; (2) at a middle distance, the value of the backscattering matrix elements inclines toward middle modes. The matrix is similar to a 2D bandpass filter; (3) at a far distance, the value of the backscattering matrix elements inclines toward low modes. The matrix is similar to a 2D low-pass filter. This phenomenon is caused by mode attenuation in the shallow-water waveguide. [Work supported by the NSFC.]

NUMERICAL SIMULATION OF EXTRACTING MODAL BACK-SCATTERING MATRIX FROM REVERBERATION IN SHALLOW-WATER WAVEGUIDE

Modal back-scattering matrix is the key component for reverberation predicting and also important for understanding the mechanism of bottom back-scattering. To extract the modal back-scattering matrix from reverberation data is a challening topic. So far, inversion of modal back-scattering matrix from reverberation data is based on some a priori assumptions. A new method for extracting modal back-scattering matrix from reverberation data in shallow-water waveguide is proposed recently [Shang et al., 2002]. In this paper numerical simulation of extracting the modal back-scattering matrix has been performed, it is shown that the inversion by changing the source depth works very well for lower frequency. Alternatively, the inversion by using the reverberation data at different ranges is proposed and it is shown that this approach is suitable on certain conditions.

Algorithms for Estimating the Complete Group of Polarization Invariants of the Scattering Matrix (SM) Based on Measuring All SM Elements

The procedure for estimating polarization invariants of the backscattering matrix in horizontal-vertical basis is considered for radar observation of arbitrary nonreciprocal objects. Two polarization invariants are added to the well-known six Huynen-Euler invariants. These new invariants (nonreciprocity angle and difference in absolute phases of the symmetric and antisymmetric parts of the scattering matrix) describe the nonreciprocal properties of the object itself. With the simultaneous measurement of all eight quadratures of the scattering matrix elements, the closed-form expressions for calculating the eight polarization invariants are given. The derived expressions are the starting point for complete estimation of the polarization properties of arbitrary radar objects with a nonsymmetric scattering matrix. The given approach can be used to study various polarization effects in remote radar sensing of artificial and natural objects, and also to simulate polarization measurement processes and estimation errors caused by the measurements of scattering matrix elements at different instants.

Studies of the Polarimetric Covariance Matrix. Part II: Modeling and Polarization Errors

Abstract A polarimetric radar covariance matrix model is described to study the behavior of the co-to-cross covariances in precipitation. The 2 × 2 propagation matrix with attenuation, differential attenuation, and differential phase is coupled to the backscatter matrix leading to a propagation-modified covariance matrix model. System polarization errors are included in this model as well. This model is used to study the behavior of the magnitude and phase of the co-to-cross covariances and the linear depolarization ratio (LDR) in rainfall. It is shown that the model predictions are consistent with data collected with the Colorado State University (CSU)–University of Chicago–Illinois State Water Survey (CHILL) radar in intense rainfall. A method is also given for estimating the system polarization errors from covariance matrix data collected in intense rainfall.

Numerical simulation on the extraction of modal back-scattering matrix from reverberation data for high frequency cases

The modal back-scattering matrix can be extracted from reverberation data. For high frequency cases the ‘window smoothed’ processing has been proposed by E. C. Shang, T. F. Gao and D. J. Tang (2002) to extract the ‘window averaged’ back-scattering matrix. It is pointed out in this paper that in order to inverse the ‘window averaged’ back-scattering matrix by changing the source depth data we have to assume that the matrix is not related to the source depth, and the numerical simulation on the question has been conducted.

Development of a ground-based radar for scattering measurements

A ground-based C-band scatterometer system has been constructed at the Multimedia University, Malaysia. This is an inexpensive FM-CW radar that was efficiently constructed from a combination of commercially available components and in-house fabricated circuitry. The system has full polarimetric capability for determining the complete backscattering matrix of a natural target. It will be used to conduct in-situ backscatter measurements on Earth terrain, such as vegetation fields, forests, and soil surfaces. This paper presents the system design and the evaluation results of the scatterometer system. The system was tested at a football field. A metal sphere was used as the calibration target. The backscattering matrices of an 8 trihedral corner reflector and of a 4 /spl times/ 8 dihedral corner reflector were measured. The dihedral was rotated at different angles to provide different sets of polarimetric data. The results were compared with the theoretical values to verify the effectiveness of the calibration technique. The external calibration and internal calibration procedures, as well as the approach used in measuring the relative phase response, are discussed.

Extraction of modal backscattering matrix from reverberation data in shallow-water waveguide. Part I. Theory

Extracting the bottom backscattering information from reverberation data in shallow-water waveguide is an attractive but difficult issue. In previous works, some a priori assumption (for instance, the Lambert’s Law, or the separability of the backscattering matrix) has been made in order to solve this problem. In this paper, new approaches are proposed. The modal backscattering matrix can be extracted directly from reverberation data without any a priori assumption on scattering coefficient. The backscattering information inversion is based on the following three components: (1) mode-filtering at the receiving vertical array, (2) changing the point source depth to obtain different incident mode excitation, and (3) using mode stripping in the waveguide as an additional mode filter. For lower frequency the linear inversion is presented, and for higher frequency the sequential inversion with angle interval smoothing is proposed. [Work supported by ONR.]

Depolarization of light backscattered by randomly oriented nonspherical particles

We derive theoretically and validate numerically general relationships for the elements of the backscattering matrix and for the linear, delta(L), and circular, delta(C), backscattering depolarization ratios for nonspherical particles in random orientation. For the practically important case of randomly oriented particles with a plane of symmetry or particles and their mirror particles occurring in equal numbers and in random orientation, delta(C) = 2delta(L)/(1 - delta(L)). Extensive T-matrix computations for randomly oriented spheroids demonstrate that, although both delta(L) and delta(C) are indicators of particle nonsphericity, they cannot be considered a universal measure of the departure of particle shape from that of a sphere and have no simple dependence on particle size and refractive index.

Enhanced backscattering of polarized light from discrete random media: calculations in exactly the backscattering direction

Enhanced backscattering of polarized light by disordered media composed of independently scattering particles of arbitrary size and shape is studied theoretically. Rigorous relations between the cyclical and the ladder parts of the backscattering matrix in exactly the backscattering direction are derived for three commonly used representations of polarization, and the corresponding polarization backscattering enhancement factors are introduced. The ladder part of the Stokes-backscattering matrix is calculated by solving Chandrasekhar’s vector radiative transfer equation [ Radiative Transfer ( Clarendon, London, 1950)]. The general properties of the enhancement factors are studied, and the results of numerical computations are reported for finite and semi-infinite homogeneous slabs composed of spherical and randomly oriented nonspherical particles. It is shown that the enhancement factors depend strongly on the direction of light incidence, the optical thickness of the medium, the true absorption, and the particle size and shape.