Rough surface inverse scattering within the Rytov approximation

Schatzberg, Alon; Devaney, Anthony J.

doi:10.1364/josaa.10.000942

Cited by 30 publications

(15 citation statements)

References 11 publications

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“…Besides constituting a good starting point for the testing of our inverse solvers, the problem of reconstruction and synthesis of periodically modulated interfaces (crystal lattices, diraction gratings, etc), is indeed one of the highest interest in modern optics. We refer the reader to the works [4,15,16,17,19] for examples of application, and to [1,10,11,13,20,21,22,23,24,25,26], for alternative n umerical solutions to inverse problems within this context. Uniqueness for the problem of reconstruction of periodic structures from far{eld data corresponding to a nite numberof incident plane waves at distinct wavelengths was recently established in [12].…”

Section: Introductionmentioning

confidence: 99%

A high-order perturbation approach to profile reconstruction: I. Perfectly conducting gratings

Reitich¹

1999

Inverse Problems

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A new method for the reconstruction of two-dimensional periodic structures from scattered far-eld data is presented. The approach is based on the recently developed \Methods of Variation of Boundaries" (MVB) for the solution of forward scattering problems. Here, the inverse problem is formulated as that of minimization of an appropriate nonlinear least-squares cost functional. The analytic continuation ideas inherent to MVB are then advanced to enable a global line search at each step of a proposed conjugate gradients algorithm. Through a numberofnumerical examples it is demonstrated that such globalization may be necessary to overcome the nonconvexity of the cost which, in turn, is shown to persist even when the global minimizer is known to be unique.

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Section: Introductionmentioning

confidence: 99%

A high-order perturbation approach to profile reconstruction: I. Perfectly conducting gratings

Reitich¹

1999

Inverse Problems

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“…The well-posedness for general nonperiodic rough surfaces is given in [22]. Scattering and imaging of shallow corrugations have been treated by assuming the Kirchhoff approximation [7], the Rytov approximation [4], or the Born approximation [23]. Instead our approach is based on the Rayleigh hypothesis, which is discussed below.…”

Section: Radiation Condition and Rayleigh Hypothesismentioning

confidence: 99%

“…Rough surface scattering is of fundamental interest in optics, radiowave propagation, and acoustics [1][2][3][4][5][6][7][8] and forms the basis of near-field imaging, which is the operation principle behind such instruments as scanning near-field optical microscopy [9][10][11][12] and near-field acoustic microscopy [13]. Nearfield imaging is a microscopic technique that breaks the diffraction limit by exploiting the properties of evanescent waves.…”

Section: Introductionmentioning

confidence: 99%

Compressive imaging of subwavelength structures: periodic rough surfaces

Fannjiang

Tseng

2012

J. Opt. Soc. Am. A

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A compressed sensing scheme for near-field imaging of corrugations of relative sparse Fourier components is proposed. The scheme employs random sparse measurement of near field to recover the angular spectrum of the scattered field. Surprisingly, it can be shown heuristically and numerically that under the Rayleigh hypothesis the angular spectrum is compressible and amenable to compressed sensing techniques. Iteration schemes are developed for recovering the surface profile from the angular spectrum. The proposed nonlinear least squares in the Fourier basis produces accurate reconstructions even when the Rayleigh hypothesis is known to be false.

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“…5,6 The theory of surface nonradiating sources developed here can probably be extended to apply to surface structures that do not scatter incident radiation and hence can be expected to play an important role in the inverse surface scattering problem. 15 Another potential application of nonradiating surface sources occurs in applications where it is desired to radiate a field by using a surface source having only a singlet or doublet component but not both. An example of this occurs in experimental time reversal, 13 where the singlet and doublet components of a surface source are prespecified but the physical transducers used to radiate the field correspond to a singlet or doublet source.…”

Section: Summary and Potential Applicationsmentioning

confidence: 99%

Nonradiating surface sources

Devaney

2004

J. Opt. Soc. Am. A

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The class of three-dimensional (3D) nonradiating sources to the inhomogeneous Helmholtz equation is generalized to include nonradiating surface sources that are localized on closed or infinite surfaces sigma and that generate no radiation throughout one of the two space regions whose common boundary is sigma. The class of non-radiating surface sources is shown to be identical to the class of so-called secondary surface sources that are generated from boundary values of a field radiated by a 3D source. In particular, it is proven that any secondary surface source radiating into the interior (exterior) of sigma is a nonradiating surface source relative to the exterior (interior) of sigma, and vice versa. Examples of nonradiating surface sources are included, and a discussion is given of possible applications of such sources.

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Rough surface inverse scattering within the Rytov approximation

Cited by 30 publications

References 11 publications

A high-order perturbation approach to profile reconstruction: I. Perfectly conducting gratings

A high-order perturbation approach to profile reconstruction: I. Perfectly conducting gratings

Compressive imaging of subwavelength structures: periodic rough surfaces

Nonradiating surface sources

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