Inverse scattering for near-field microscopy

Carney, P. Scott; Schotland, John C.

doi:10.1063/1.1320844

Cited by 71 publications

(75 citation statements)

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“…Means to interpret NSOM images have been developed, 8,9 including the solution of a three-dimensional near-field inverse scattering problem. [10][11][12][13][14][15][16][17][18] The resulting methods are known as near-field optical tomography ͑NFOT͒. NFOT experiments require the acquisition of multiple complete NSOM data sets for varying directions of illumination or observation of the field.…”

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confidence: 99%

Nanoscale optical tomography using volume-scanning near-field microscopy

Sun

Schotland

Hillenbrand

et al. 2009

Applied Physics Letters

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Nanoscale optical tomography using volume-scanning near-field microscopy

Sun

Schotland

Hillenbrand

et al. 2009

Applied Physics Letters

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“…It was recently demonstrated that when both the phase and amplitude of the optical near field are available, the near-field ISP may be solved, and an inversion formula was presented in [19]. Validation of the results was demonstrated by numerical simulation.…”

Section: Introductionmentioning

confidence: 97%

Near-Field Scanning Optical Tomography: A Nondestructive Method for Three-Dimensional Nanoscale Imaging

Sun

Carney

Schotland

2006

IEEE J. Select. Topics Quantum Electron.

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We present the theoretical foundation for near-field scanning optical tomography, a method for threedimensional optical imaging with subwavelength resolution. An analysis of the forward problem for both scalar and vector optical fields is described. This is followed by the construction of the pseudoinverse solution to the linearized inverse scattering problem. The results are illustrated by numerical simulations. KeywordsImaging, inverse problems, inverse scattering, microscopy, near-field optics, scanning probe microscopy, tomography This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This journal article is available at ScholarlyCommons: http://repository.upenn.edu/be_papers/82 Abstract-We present the theoretical foundation for near-field scanning optical tomography, a method for three-dimensional optical imaging with subwavelength resolution. An analysis of the forward problem for both scalar and vector optical fields is described. This is followed by the construction of the pseudoinverse solution to the linearized inverse scattering problem. The results are illustrated by numerical simulations.

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“…The linearized inverse problem has the solution = K ␣ + ⌽ ␣ , where K ␣ + denotes the pseudoinverse of K ␣ which has been obtained elsewhere. 2,6 To derive the solution to the nonlinear ISP, we act on Eq. ͑2͒ with K + and thereby obtain ͑6͒ where ˜͑ 1͒ = K ␣ + ⌽ ␣ .…”

Section: ͑3͒mentioning

confidence: 99%

“…This inverse scattering problem ͑ISP͒ has been studied within the accuracy of the single-scattering or first Born approximation. 6 The question of existence and uniqueness of solutions has been addressed, and computationally efficient inversion formulas are known. 2 The purpose of this letter is to extend these results to account for the effects of multiple scattering.…”

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confidence: 99%

“…5 Near-field tomography ͑NFT͒ is a recently proposed computed imaging modality for three-dimensional optical imaging with subwavelength resolution. 2,[6][7][8] NFT is nondestructive and achieves nanoscale resolution by combining the experimental methods of near-field optics with the mathematical tools of inverse scattering theory. The diffraction limit to resolution is overcome by exploiting the ability of evanescent waves to carry information on subwavelength scales.…”

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Nonlinear inverse scattering and three-dimensional near-field optical imaging

Panasyuk

Markel

Carney

et al. 2006

Applied Physics Letters

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The nonlinear inverse scattering problem for electromagnetic fields with evanescent components is considered. A solution to this problem is obtained in the form of a functional series expansion. The first term in the expansion corresponds to the pseudoinverse solution to the linearized inverse problem. The higher order terms represent nonlinear corrections to this result. Applications to the problem of three-dimensional optical imaging with subwavelength resolution are described and illustrated with numerical simulations.

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Inverse scattering for near-field microscopy

Abstract: We derive the analytic singular value decomposition of the linearized scattering operator for scalar waves. This representation leads to a robust inversion formula for the inverse scattering problem in the near zone. Applications to near-field optics are described.

Cited by 71 publications

References 14 publications

Nanoscale optical tomography using volume-scanning near-field microscopy

Nanoscale optical tomography using volume-scanning near-field microscopy

Near-Field Scanning Optical Tomography: A Nondestructive Method for Three-Dimensional Nanoscale Imaging

Nonlinear inverse scattering and three-dimensional near-field optical imaging

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