Genetic algorithm for solution of the inverse problem in high-resolution X-ray reflectometry

Sutyrin, A. G.; Prokhorov, D. Yu.

doi:10.1134/s1063774506040055

Cited by 4 publications

(11 citation statements)

References 10 publications

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“…Nevot & Croce, 1980;Bushuev & Sutyrin, 2000;Sutyrin & Prokhorov, 2006). The derivation of the modified Parratt recurrent relationships will be sketched (cf.…”

Section: Theoretical Background the Modified Parratt Recurrent Relatmentioning

confidence: 99%

“…Over the last 20 years there has been substantial success using the high-resolution X-ray reflectometry (HRXR) technique coupled appropriately with theoretical model assumptions (see, e.g., Cowley & Ryan, 1987;Sinha et al, 1988;Holy et al, 1999;Asadchikov et al, 1999;Bushuev & Sutyrin, 2000;Bushuev et al, 2002;Lomov et al, 2005;Sutyrin & Prokhorov, 2006;Baake et al, 2006;Bridou et al, 2006;Lemoine et al, 2006;Hodroj et al, 2006). At present, the most promising method for solving the MLS problem is to decode the one-dimensional HRXR scan data jR ðexÞ 0 ðÞj 2 that result from grazing X-ray specular scattering by an MLS (see Fig.…”

Section: Introductionmentioning

confidence: 99%

“…The fundamental theoretical model of grazing X-ray specular scattering by an MLS was developed by Parratt (1954) and is based on sequential Fresnel reflections by each plane layer of the MLS. This theoretical model has been fruitful in retrieving MLS parameters using the HRXR method in a number of works (Bushuev & Sutyrin, 2000;Bushuev et al, 2002;Sutyrin & Prokhorov, 2006). Together they describe the influence of surface and interface roughness on the X-ray specular scattering.…”

Section: Introductionmentioning

confidence: 99%

“…The Levenberg-Marquardt algorithm (Eadie et al, 1971;Gill et al, 1981; see also Sutyrin & Prokhorov, 2006) is of great interest in that it represents the direct fusion of the Newton algorithm and a gradient-direction-type algorithm to optimize the iterative procedure itself. Nevertheless, although diverse iterative numerical methods work more or less well and are frequently used, their application to the determination of MLS parameters has not been explored in any detail and needs to be developed further (Sutyrin & Prokhorov, 2006; see also Golberg, 1989). There is virtue in iterative methods that are based upon the minimization of the HRXR error functional F{P} as a function of the parameters {P} in a least-square fashion.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic Newton–gradient-direction-type algorithm for multilayer structure determination using grazing X-ray specular scattering: numerical simulation and analysis

Chukhovskii

2008

Acta Cryst Sect A

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A new dynamic iterative algorithm code for retrieving macroscopic multilayer structure parameters (the layer thickness and complex refraction index for each layer, the surface roughness and the interface roughness between the layers) from specular scattering angular scan data is proposed. The use of conventional direct methods, particularly the well known Newton algorithm and gradient-direction-type algorithm operating dynamically to minimize the error functional in a least-squares fashion, is explored. Such an approach works well and seems to be effective in solving the inverse problem in the high-resolution X-ray reflectometry (HRXR) method. In order to demonstrate some features of the proposed iterative algorithm, numerical calculations for retrieving three-layer structure parameters are carried out using simulated HRXR angular scan data. The calculations indicate clearly that the dynamic iterative algorithm is convergent and capable of yielding the true solution. It is important that the performance coefficient for successful iterative cycles for the absolute minimization of the HRXR error functional is quite high even if the initial values of the search parameters are chosen rather far from the true values. It is particularly noteworthy that the relative number of successful iterative cycles is of the order of 90-40% when only moderately accurate initial parameter values, varying by +/-10-40% from the true values, are presumed.

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“…Nevot & Croce, 1980;Bushuev & Sutyrin, 2000;Sutyrin & Prokhorov, 2006). The derivation of the modified Parratt recurrent relationships will be sketched (cf.…”

Section: Theoretical Background the Modified Parratt Recurrent Relatmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Dynamic Newton–gradient-direction-type algorithm for multilayer structure determination using grazing X-ray specular scattering: numerical simulation and analysis

Chukhovskii

2008

Acta Cryst Sect A

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“…Over the last 20 years the scattering of short-wavelength radiation from rough surfaces and/or interfaces has been the object of a number of works [see, for example, Sinha et al (1988), Holy et al (1999), Bushuev et al (2002), Nosik (2002), Lazzari (2002), Lomov et al (2005), Sutyrin & Prokhorov (2006), Bridou et al (2006), Hodroj et al (2006), Schmidbauer et al (2008), Zozulya et al (2008) and Chukhovskii (2009); also the pioneering works of Yoneda (1963), Nevot & Croce (1980) and Petrashen' et al (1983)].…”

Section: Introductionmentioning

confidence: 99%

X-ray specular scattering from statistically rough surfaces: a novel theoretical approach based on the Green function formalism

Chukhovskii

Polyakov

2010

Acta Cryst Sect A

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The Green function formalism is applied to the problem of grazing-incidence small-angle X-ray scattering from statistically rough surfaces. Kirchhoff's integral equation is used to describe the X-ray wavefield propagation through a single rough surface separating vacuum and medium. Taking into account multiple diffuse X-ray scattering effects, the reflection R(coh)(θ) and transmission T(coh)(θ) coefficients of the specular wave are obtained using the Gaussian statistical model of rough surfaces in terms of the two-point height-height correlation function. In the limiting cases when the correlation length xi is equal to zero or infinity, analytical formulae for the reflection R(coh)(θ) and transmission T(coh)(θ) coefficients of the specular wave are obtained. It is important that in the case xi --> infinity they coincide with the corresponding reflection R(DW)(θ) and transmission T(DW)(θ) coefficients related to the conventional Debye-Waller approximation for describing the grazing X-ray scattering from a rough surface. In the case of finite values of correlation length \xi the reflection |R(coh)(θ)|(2) and transmission |T(coh)(θ)|(2) scans are numerically calculated.

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BornAgain: software for simulating and fitting grazing-incidence small-angle scattering

et al. 2020

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BornAgain is a free and open-source multi-platform software framework for simulating and fitting X-ray and neutron reflectometry, off-specular scattering, and grazing-incidence small-angle scattering (GISAS). This paper concentrates on GISAS. Support for reflectometry and off-specular scattering has been added more recently, is still under intense development and will be described in a later publication. BornAgain supports neutron polarization and magnetic scattering. Users can define sample and instrument models through Python scripting. A large subset of the functionality is also available through a graphical user interface. This paper describes the software in terms of the realized nonfunctional and functional requirements. The web site https://www. bornagainproject.org/ provides further documentation.

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Genetic algorithm for solution of the inverse problem in high-resolution X-ray reflectometry

Cited by 4 publications

References 10 publications

Dynamic Newton–gradient-direction-type algorithm for multilayer structure determination using grazing X-ray specular scattering: numerical simulation and analysis

Dynamic Newton–gradient-direction-type algorithm for multilayer structure determination using grazing X-ray specular scattering: numerical simulation and analysis

X-ray specular scattering from statistically rough surfaces: a novel theoretical approach based on the Green function formalism

BornAgain: software for simulating and fitting grazing-incidence small-angle scattering

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