Phaseless Data Research Articles

Source Modeling Using Phaseless Low-Frequency Near-Field Measurements

Field measurements of both amplitude and phase generally are more complicated and require more expensive equipment than amplitude-only measurements. Phase retrieval from measured phaseless field data is, therefore, of interest for source modeling in dosimetry applications, electromagnetic compatibility investigations, near-field to far-field transformations and antenna diagnostics. We here present a phase-retrieval method that uses an optimization algorithm based on the phase angle gradients of a functional. Numerical test cases have shown that the method is working for different initial phase distributions as well as different placements of the source. The method also works well for a test case with measured 50 Hz magnetic flux density from a transformer. The obtained phase angles on a measurement plane in front of the transformer gave calculated field amplitudes on other measurement planes that agree well with measured field. The ratios between the largest amplitude difference and the largest measured amplitude for the three Cartesian magnetic flux density components, for one of the planes, are for example 6.62%, 9.51% and 6.40%.

COMPARISON BETWEEN TWO PHASE-RETRIEVAL METHODS FOR ELECTROMAGNETIC SOURCE MODELING

Phase-retrieval from measured phaseless field data is of interest for various applications including electromagnetic dosimetry, electromagnetic compatibility investigations, near-field to far-field transformations and antenna diagnostics. In this study two phaseretrieval methods are compared. The first method, the adjoint field method, employs a gradient-based optimization algorithm based on the adjoint fields. The second method, the phase angle gradient method, uses an optimization algorithm based on the phase angle gradients of a functional. The methods are tested with numerical test cases and the phase angle gradient method is found to retrieve the phase with the best accuracy. Moreover it gives results that agree well with correct phase.

Quantitative imaging from diffracted fields intensities: an inversion method and its experimental validation

In many diagnostics and imaging applications intensity only measurements of the diffracted field are available. Hence, it is of interest to develop procedures able to solve the underlying inverse scattering problem under these conditions. In this paper, we introduce an approach in which the geometrical and electromagnetic properties of unknown complex targets are reconstructed from the squared amplitudes of the diffracted fields. The approach relies on some preliminary considerations on the spatial bandwidth of the diffracted intensities which allow one to fix rules to effectively measure the data and on an alternative formulation of the electromagnetic scattering that lowers the ‘degree of non-linearity’ of the relationship among the electric features of the targets and the fields. The proposed procedure is tested against benchmark experimental data in the microwave frequency range and the obtained results confirm the possibility of achieving faithful quantitative images of unknown targets from phaseless data without making approximations in the inverse scattering problem.

A NOVEL LINEAR EM RECONSTRUCTION ALGORITHM WITH PHASELESS DATA

This paper presents a fast and efiective electromagnetic reconstruction algorithm with phaseless data under weak scattering conditions. The proposed algorithm is based on the phaseless data multiplicative regularized contrast sources inversion method (PD- MRCSI). We recast the weak scattering problem as an optimization problem in terms of the undetermined contrast and contrast sources. Using the conjugate gradient iterative method, the problem is solved by alternately updating the contrast sources and the contrast. Additionally, this method can combine with the PD-MRCSI method. Taking advantage of the properties of fast convergence of this algorithm and stable convergence of PD-MRCSI method, the combined technique makes image reconstructions more fast and efiective. Although the method is derived from weak scattering situation, it is also useful for the case which weak scattering approximation is not satisfled. The synthetic numerical reconstruction results, as well as experimental reconstruction results, presented that the proposed method is a very fast and efiective reconstruction algorithm.

Identification of sound-soft 3D obstacles from phaseless data

The inverse problem for time-harmonic acoustic wave scattering to recover a sound-soft obstacle from a given incident field and the far field pattern of the scattered field is considered. We split this problem into two subproblems; first to reconstruct the shape from the modulus of the data and this is followed by employing the full far field pattern in a few measurement points to find the location of the obstacle. We extend a nonlinear integral equation approach for shape reconstruction from the modulus of the far field data [6] to the three-dimensional case. It is known, see [13], that the location of the obstacle cannot be reconstructed from only the modulus of the far field pattern since it is invariant under translations. However, employing the underlying invariance relation and using only few far field measurements in the backscattering direction we propose a novel approach for the localization of the obstacle. The efficient implementation of the method is described and the feasibility of the approach is illustrated by numerical examples.

Inverse scattering from phaseless data in the freespace

In this paper a new approach for microwave imaging of unknown objects embedded in the freespace from phaseless data is presented. Firstly a cost functional is constructed by using the measured amplitude of the total field, which is the norm of the discrepancy between the measured amplitude and the calculated one. Then both the amplitude and phase of the scattered field are retrieved by minimizing the above cost functional. Finally, the geometrical and electrical parameters are reconstructed by using the retrieved scattered field. The phase retrieval process can be achieved in a very short time without adding any burden to the whole inverse scattering problem. The equivalent current density is introduced to reduce the nonlinearity of the inverse problem. The reconstruction of the non-radiating component of the equivalent current density improves the imaging quality. Experimental results are presented for the first time to show the feasibility of inverse scattering from phaseless data. The experimental results also show the validity and stability of the proposed method.

Two-Dimensional Contrast Source Inversion Method With Phaseless Data: TM Case

In this paper, two new approaches are presented for the solution of electromagnetic inverse scattering problems when amplitude-only data are available. The proposed techniques are based on a customized version, which are the so-called contrast source inversion (CSI) and multiplicative regularized CSI (MRCSI) methods. In the proposed approaches, denoted as the phaseless-data (PD)-CSI and the PD-MRCSI, only the term of the cost functional concerning the mismatch between the measured and estimated field data (i.e., the data equation) has been properly redefined. Moreover, the back-projection algorithm has been modified to provide an initial solution ensuring the rapid convergence of the optimization procedures and avoid the reconstruction of false solutions. A set of representative results concerning numerical as well as experimental tests is reported to show the accuracy of the proposed amplitude-only reconstruction approaches.

A multi-frequency MRCSI algorithm with phaseless data

This paper presents a novel multi-frequency multiplicative regularized contrast source inversion (MRCSI) algorithm with phaseless data (PD-MRCSI) for solving a two-dimensional scalar inverse scattering problem. The MRCSI method resolves the inverse scattering problem by minimization of a cost functional which is a linear combination of mismatches in the data equation and the state equation. Through modifying the mismatch in the data equation, we construct a new cost functional which is suitable for the inverse scattering problem with phaseless data. Similar to the MRCSI algorithm, the new cost functional can be minimized by alternatively updating the unknown contrast source and contrast using the so-called Polak–Ribere conjugate gradient method. Numerical results show that the proposed algorithm works effectively and efficiently for solving the inverse scattering problem with phaseless data.

Phaseless Antenna Characterization by Effective Aperture Field and Data Representations

The problem of antenna characterization from phaseless near-field data is addressed by appropriate use of the available information on the Antenna Under Test (AUT) and on the scanning geometry to provide efficient representations for both the unknowns and the data. Such a strategy allows improving the reliability and the accuracy of the proposed characterization algorithm and, at the same time, shortens the overall measurement process. An extensive numerical and experimental analysis, together with a comparison with existing approaches, endorses the algorithm reliability and accuracy and confirms its usefulness for antennas having a general radiating (vector) behavior, i.e., either focusing or non-focusing.

Multifrequency Imaging From Intensity-Only Data Using the Phaseless Data Distorted Rytov Iterative Method

Two multifrequency imaging algorithms are presented for the reconstruction of unknown objects when only the intensity measurement of the total field is available using the phaseless data distorted Rytov iterative method. The first one uses all the frequencies simultaneously to form a matrix equation and only deals with lossless objects. The second one can reconstruct both lossless and lossy objects, in which a low frequency is utilized to guarantee convergence. Then the reconstructed result is used as the initial estimate for a higher frequency. Repeat this process by gradually increasing the working frequency until high imaging quality is achieved. Numerical and experimental results are presented to show the high efficiency of the proposed algorithms.

Polarization Extraction in Planar Near-Field Phaseless Measurements

Near-field measurements typically require both amplitude and phase information to correctly predict the far-field. Unfortunately, there are situations in which the phase data is not available or impractical to obtain. That is why there has been a need for the development of phaseless techniques. Up until now, a number of remarkable solutions to this problem have been proposed by the researcher in different disciplines. Unfortunately, the complete vectorial representation of the field is not investigated in depth. The evaluated cases are usually linearly polarized and only the dominant polarization is investigated while the cross polarized field is usually neglected. This paper addresses the polarization issue in a two-component approach and then proposes a solution to the problem. A searching mechanism, for the incorporation of an appropriate initial guess, is integrated into the well-known, iterative Fourier technique (plane-to-plane) to enhance the algorithm response. Then, using two sets of measured orthogonal information data gathered by two linearly and orthogonally polarized probes, it is shown that with the aid of only a single point amplitude measurement, the polarization characteristics of the antenna can be extracted up to an inherent ambiguity of the right- and left-handedness. In order to have an assessment of the applicability of the proposed method, both linearly and circularly polarized antennas are simulated. Additionally, the method of extracting the polarization from the phaseless data is also verified through a bi-polar near-field measurement.

Tomographic Reconstruction Using the Distorted Rytov Iterative Method With Phaseless Data

Inspired by the successes of the distorted Born iterative method with full data (FD-DBIM) in the electromagnetic inverse scattering problem when the weak scattering approximation breaks down, the distorted Rytov iterative method with phaseless data (PD-DRIM) for the reconstruction of an unknown object embedded in 2-D homogeneous space is proposed when only the intensity data of the total wavefield are available. Similar to FD-DBIM, the PD-DRIM algorithm can also provide the Fre acutechet derivative and the guess solution for the iterative method naturally by updating the Green's function in every iteration step. The validation of the proposed approach is justified by the experimental tests where the scattering data are kindly provided by the Institute Fresnel in Marseille (2005).

Phaseless imaging with experimental data: facts and challenges

Two-dimensional target characterization using inverse profiling approaches with total-field phaseless data is discussed. Two different inversion schemes are compared. In the first one, the intensity-only data are exploited in a minimization scheme, thanks to a proper definition of the cost functional. Specific normalization and starting guess are introduced to avoid the need for global optimization methods. In the second scheme [J. Opt. Soc. Am. A21, 622 (2004)], one exploits the field properties and the theoretical results on the inversion of quadratic operators to derive a two-step solution strategy, wherein the (complex) scattered fields embedded in the available data are retrieved first and then a traditional inverse scattering problem is solved. In both cases, the analytical properties of the fields allow one to properly fix the measurement setup and identify the more convenient strategy to adopt. Also, indications on the number and types of sources and receivers to be used are given. Results from experimental data show the efficiency of these approaches and the tools introduced.

Inversion of Phaseless Total Field Data Using a Two-Step Strategy Based on the Iterative Multiscaling Approach

In this paper, a new approach for the quantitative electromagnetic imaging of unknown scatterers located in free space from amplitude-only measurements of the total field is proposed and discussed. The reconstruction procedure splits the problem into two steps. The method is based on the use of an inverse source algorithm to first complete the scattering data by estimating the distribution of the radiated field in the investigation domain. The object's function profile is then retrieved from the phaseless data via an iterative multiresolution procedure integrated with an effective minimization technique based on the particle swarm algorithm. Numerical examples are provided to assess the effectiveness of the whole two-step strategy in the presence of synthetic noise-corrupted data as well as in dealing with experimental data sets. Comparisons with full-data and "bare" approaches are reported as well

A novel hybrid approach for far-field characterization from near-field amplitude-only measurements on arbitrary scanning surfaces

A novel hybrid procedure is proposed in this paper for far-field reconstruction from phaseless near-field data. A basically interferometric approach is adopted to retrieve the near-field phase from amplitude-only measurements, which are collected by a simple microstrip circuit used in conjunction with two identical probes moving on the scanning surface. A certain number of sets of complex near-field data is obtained, apart from constant phase-shifts to be computed, one for each set. A nonredundant representation based on the introduction of the reduced field is then adopted to evaluate these shifts, with an accurate and fast convergence to the solution. In order to validate the proposed technique, an X-band prototype using two flanged WR-90 waveguides is successfully designed and tested on a cylindrical geometry for a standard pyramidal horn.

Inverse scattering from phaseless measurements of the total field on a closed curve.

A new approach for quantitative electromagnetic imaging of scatterers located in free space from phaseless data is proposed and discussed. The procedure splits the problem into two steps. In the first one, we solve a phase-retrieval problem for the total field, thus estimating the amplitude and phase of the scattered field. Careful analysis of properties and possible representations of both scattered and incident fields allow us to introduce a criterion for an optimal choice of the measurement setup and a successful retrieval. Then the complex permittivity profile is reconstructed in the second step by use of the estimated scattered field. Numerical examples are provided to check the whole chain in the presence of noise-corrupted data.

Far-Field Reconstruction from Phaseless Near-Field Data on a Cylindrical Helix

An efficient procedure is developed for far-field reconstruction from phaseless near-field data on a circular helix. The application of an integrated probe is considered for collecting amplitude data to be used in the near-field phase retrieval. This is performed along the single line given bythe helicoidal curve, thus reducing computation time as compared with planar and plane-polar geometries. Antenna far-field pattern is directlyevaluated from complex near-field helicoidal data by a Fast Fourier Transform based algorithm, so anyintermediate interpolation on a cylindrical surface is avoided. Numerical simulations on arrays of Huyghens sources are presented for assessing the effectiveness of the proposed approach.

Electromagnetic detection of dielectric scatterers using phaseless synthetic and real data and the memetic algorithm

Phaseless data are used to evaluate the application of an electromagnetic inverse-scattering-based procedure for the detection of cylindrical inhomogeneities, which are schematized as multilayer infinite dielectric cylinders with elliptic cross sections. The electromagnetic inverse problem is recast as a global optimization problem and iteratively solved by an efficient memetic algorithm, which combines deterministic and stochastic concepts. Moreover, a recursive analytical procedure is used for the forward-scattering computation. The possibility of localizing and reconstructing the scatterers by using phaseless input data, which would greatly simplify the design of the imaging apparatus, is evaluated both with reference to synthetically produced data and by means of experimental data obtained by a microwave tomograph.

A direct optimization approach for source reconstruction and NF-FF transformation using amplitude-only data

In this paper, we present a direct optimization procedure that utilizes phaseless electric field data over arbitrary shaped surfaces for the reconstruction of an equivalent magnetic current density that represents the radiating structure of an antenna under test. Once the equivalent magnetic current density is determined, the electric field at any point can be calculated. Numerical results (both simulated and experimental) are presented to illustrate the applicability of this approach for nonplanar near-field to far-field (NF-FF) transformation as well as to antenna diagnostics. The results are presented using both theoretical and experimental phaseless data over one and two planes.

Binary-constrained inversion of a buried cylindricalobstacle from complete and phaseless magneticfields

The investigation herein is two-fold: specialization to a homogeneousobstacle of recent work (Lambert M et al 1998 Inverse Problems 14 1265-83) carried on the retrievalof an inhomogeneous cylindrical obstacle buried in a half-space in thetransverse electric (or H) polarization case; extension from the usualcase of complete wavefield data (known amplitude and phase) to the moresevere case of amplitude-only data (absent phase). The developed inversionmethod belongs to the class of modified gradient methods. The fielddistribution (here, the magnetic field) and the distribution of theobstacle parameters (here, the permittivity and conductivity) aresimultaneously sought in a search domain \U0001d49f. This is done by minimizinga two-component objective function, one of which is characterizing thesatisfaction of the wave equations within \U0001d49f, the other thedata fit. But now the electrical parameters of the sought obstacle areprescribed beforehand; this allows one to equate an appropriate complex-valuedcontrast function either to 0 (outside the obstacle) or to a known constant (inside). Two variants of abinary-constrained modified gradient algorithm are developed accordingly,tailored to either complete or phaseless data. Numericalexperimentation illustrates how they behave in a variety of obstacleconfigurations, for both exact and erroneous prescribed contrasts.