Reconstruction of rough-surface profiles with the Kirchhoff approximation

Wombell, R.; DeSanto, John A.

doi:10.1364/josaa.8.001892

Cited by 103 publications

(41 citation statements)

References 14 publications

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“…Such reconstruction will not be exact, because the correlation coefficient between the surface profile and the reflected field phase is less than 1 in absolute magnitude. However, this "qualitative" reconstruction is possible and it is much simpler than previously suggested algorithms, which require measurements of both magnitude and phase of the electric field scattered in all directions from the surface [22]. The measurement techniques for such kind of measurements are already developed for the antenna near-field measurements.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

Numerical Simulations of the Scattered Field Near a Statistically Rough Air-Ground Interface

Yarovoy

Vazouras²,

Fikioris³

et al. 2004

IEEE Trans. Antennas Propagat.

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Abstract-The two-dimensional problem of horizontally polarized wave scattering from an air-ground interface is considered. The diffraction problem is formulated by means of the extinction theorem, leading to a system of two simultaneous surface integral equations. The small-slope approximation has been used to solve this system. This solution was used as a fast forward solver in the Monte Carlo simulations of the scattered field near to the rough interface. Properties of the reflected field have been investigated for a single realization of the rough interface as well as for a statistical ensemble of such interfaces. Special attention has been paid to the phase of the reflected field (in the case of a single realization) and to the variance of the reflected field (in the case of a statistical ensemble), which has direct relation with the surface clutter in ground penetrating radars. A principal possibility to retrieve a surface profile from interferometric measurements of the reflected field near the surface is demonstrated.

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Section: Numerical Results and Discussionmentioning

confidence: 99%

Numerical Simulations of the Scattered Field Near a Statistically Rough Air-Ground Interface

Yarovoy

Vazouras²,

Fikioris³

et al. 2004

IEEE Trans. Antennas Propagat.

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“…(21). Since the phase of the complex exponential changes in the direction defined by k 0 − k r , only regions of the surface where the surface normal is in this direction will contribute to the integral.…”

Section: Theorymentioning

confidence: 99%

“…When light is scattered from the interface between homogenous media, however, it is not necessary to assume the Born approximation and, providing that there is no multiple scattering and the surface is smooth at the optical scale, the process is also linear. A detailed analysis of surface scattering has been presented by Beckmann and Spizzichino [20] and this forms the basis of inverse scattering methods that attempt to deduce surface topography from measurements of the scattered field [21][22][23]. In this case, the surface boundary conditions are assumed and the object can be replaced by an infinitely thin foil-like object, which follows the surface topography and henceforth will be called the "foil model" of the surface.…”

Section: Introductionmentioning

confidence: 99%

Coherence scanning interferometry: linear theory of surface measurement

et al. 2013

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The characterization of imaging methods as three-dimensional (3D) linear filtering operations provides a useful way to compare the 3D performance of optical surface topography measuring instruments, such as coherence scanning interferometry, confocal and structured light microscopy. In this way, the imaging system is defined in terms of the point spread function in the space domain or equivalently by the transfer function in the spatial frequency domain. The derivation of these characteristics usually involves making the Born approximation, which is strictly only applicable to weakly scattering objects; however, for the case of surface scattering, the system is linear if multiple scattering is assumed to be negligible and the Kirchhoff approximation is assumed. A difference between the filter characteristics derived in each case is found. However this paper discusses these differences and explains the equivalence of the two approaches when applied to a weakly scattering object.

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“…The transverse resolution is then easily estimated from the spatial frequency span off that is accessible with the given illumination and detection angles. Note that, in [14], single scattering inversions of 2D surfaces are performed without the paraxial approximation, but with somehow equivalent results: the main and limiting assumption is single scattering.…”

Section: Boundary Integral Formalismmentioning

confidence: 99%

Full wave optical profilometry

et al. 2011

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We show that tomographic diffractive microscopy can be used for profilometry applications with high transverse resolution. We present an iterative reconstruction procedure, based on a rigorous wave scattering model, that permits us to retrieve the profile of rough metallic interfaces from the complex scattered field. The transversal resolution is subwavelength, and can even fall below the classical resolution limit if the profile is rough enough for multiple interactions to occur. Large profiles, with tens of wavelength size, can be investigated.

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Reconstruction of rough-surface profiles with the Kirchhoff approximation

Cited by 103 publications

References 14 publications

Numerical Simulations of the Scattered Field Near a Statistically Rough Air-Ground Interface

Numerical Simulations of the Scattered Field Near a Statistically Rough Air-Ground Interface

Coherence scanning interferometry: linear theory of surface measurement

Full wave optical profilometry

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