The Inverse Scattering Problem in Structural Determinations

Ross, G.; Fiddy, Michael A.; Nieto‐Vesperinas, M.

doi:10.1007/978-3-642-81472-3_2

Cited by 21 publications

(7 citation statements)

References 66 publications

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“…In many applications of interest, one cannot justify making assumptions that the incident wavelength is either very small or very large on the scale of the material inhomogeneities. Depending on the frequency range of the incident field and material properties of scattering objects, inverse scattering problems can be divided into two branches: deterministic and stochastic [4]. Problems dealing with the determination of local values such as conductivity and permittivity profiles are deterministic problems.…”

Section: Introductionmentioning

confidence: 99%

Image estimation from scattered field data

Lin

Fiddy

1990

Int J Imaging Syst Tech

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The purpose of this paper is to reappraise the linearizing methods frequently used to solve inverse scattering problems. We describe inversion algorithms based on the Born and the Rytov approximations and the nature of the distortions obtained in the reconstructions when using them. We present extensions of these methods, namely, the distorted-wave Born and the distorted-wave Rytov approximations, which incorporate prior knowledge about part of the scattering structure. A method for inverting scattered field data using these distorted-wave approximations is described, which retains the computational simplicity of the Born and the Rytov techniques. Some examples of their use with simulated and real data are given. A further extension of our distorted-wave formalism, which leads to improvements of the reconstructed image, is suggested. This entails a spectral estimation procedure also based on the incorporation of prior knowledge about the scatterer. This spectral estimation procedure can be useful for interpolation of scattered field data as well as resolution enhancement.

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Section: Introductionmentioning

confidence: 99%

Image estimation from scattered field data

Lin

Fiddy

1990

Int J Imaging Syst Tech

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“…1 -"l Recently a simulated annealing (SA) algorithm was proposed' 2 for phase retrieval from the power spectrum of a real and positive object of finite support, as in the case of astronomical images' 3 -' 8 and in diffractive optics for real objects.' 9 ' 20 This method has been further improved and successfully used in computer simulations of object reconstruction with different signal-to-noise ratios 2 ' and also of photon-limited stellar speckle interferometry. '8 The algorithm is flexible and permits an easy introduction of additional constraints.…”

Section: Introductionmentioning

confidence: 99%

Phase retrieval from experimental far-field intensity data

1990

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We demonstrate the reconstruction of real and positive objects from experimental far-field intensity measurements by means of two phase-retrieval algorithms. Both the iterative Fourier transform and the simulated annealing algorithms are used, and an analysis is made of the advantages and disadvantages of each of these procedures and also of combinations of both methods. The objects tested either were binary or had many gray levels. We worked with data with a considerable amount of experimental noise, and in addition we recognized the importance of taking into account the nonrandom distortions produced by the detecting devices, which can critically bias the results toward erroneous estimates of the objects. Noisy data, however, can create ambiguities in the reconstructions, and hence additional information may be needed to overcome this disadvantage.

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“…Inverse optical problems have been intensively studied for the case of coherent radiation, i.e., in terms of deterministic wave amplitudes [Baltes, 1978[Baltes, , 1980. Comprehensive reviews of the various aspects of the deterministic inverse problems are available [Ferwerda, 1978;Hoenders, 1978;Schrnidt-Weinrnar, 1978;Ross et al, 1980;Boerner, 1980]. Of more recent interest are the corresponding inverse problems for partially coherent sources or stochastic scatterers (such as fluctuating continua, random distributions of discrete scatterers, or rough surfaces) characterized by correlation functions or statistical distributions rather than by deterministic field amplitudes [Ferwerda, 1978;Ross et al, 1980;Baltes et al, 1978;Jakernan and Pusey, 1980;Selloni, 1980;Goulard and Emrnerman, 1980].…”

Section: Introductionmentioning

confidence: 99%

“…(1) The phase reconstruction problem for time and space coherence functions [Baltes, 1980] photons received by a detector from the raw data of photoelectric detection [Selloni, 1980]. (5) Retrieval of statistical features of disordered scattering systems or fluctuating sources from properties of the scattered field [Ross et al, 1980;Zardecki, 1978;Jakernan and Pusey, 1980]. (6) Reconstruction of the photon statistics from a few moments or correlations under given constraints, i.e., the moment problem of quantum optics [Baltes et al, 1979].…”

Section: Introductionmentioning

confidence: 99%