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Fitting a free-form scattering length density profile to reflectivity data using temperature-proportional quenching
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10.1063/1.2403126
/content/aip/journal/jcp/125/24/10.1063/1.2403126
http://aip.metastore.ingenta.com/content/aip/journal/jcp/125/24/10.1063/1.2403126
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Geometry of the model used to describe the experimental system. The beam enters the system through the superstrate with incident wave vector and is reflected at the interface with the variable region. The reflected specular beam leaves the system with wave vector , with a component of . The momentum transfer is calculated as .

Image of FIG. 2.
FIG. 2.

A plot of the temperature parameter (A), the best-fit error (B), and the average error (C) during a typical minimization. The frequent smaller spikes show heating by condition 1 and the large increases of the temperature parameter, indicated by the arrows, demonstrate heating by condition 2.

Image of FIG. 3.
FIG. 3.

Evolution of the scattering length density profile for synthetic profile 3, Eq. (6).

Image of FIG. 4.
FIG. 4.

Upper panels: true SLD profiles (upper curves) and fit SLD profiles (lower curves, with an offset of ) are plotted for A: synthetic profile 1, B: synthetic profile 2, and C: synthetic profile 3. Lower panels: the difference between the true and fit SLD profiles, normalized by the substrate scattering length density.

Image of FIG. 5.
FIG. 5.

Top: Reflectivities (symbols) generated from synthetic profile 1, synthetic profiles 2 and 3. The fits to the data are shown as solid lines. Bottom: Residual fitting error, normalized by the reflectivity, for the fits to synthetic reflectivity data profiles 1–3.

Image of FIG. 6.
FIG. 6.

Top: Experimental x-ray reflectivity data and fit of a single lipid bilayer on quartz in water. Inset panel: the scattering length density profiles obtained using the spline-based model-free fitting algorithm LSQRFL (dashed line) and the Chebyshev-series-based algorithm used in this work (solid line). Bottom: Residual fitting error, normalized by the estimated standard deviation of the measurement error from the fit using the algorithm presented in this work (TPQ) and the algorithm of Ref. 6 (LSQRFL).

Image of FIG. 7.
FIG. 7.

Top: experimental x-ray reflectivity data and fit for cholera toxin in a mixed monolayer on a water subphase. Inset: the scattering length density profiles obtained using the spline-based algorithm LSQRFL (dashed line) and the Chebyshev-series-based algorithm used in this work (solid line). Bottom: Residual fitting error, normalized by the estimated standard deviation of the measurement error from the fit using the algorithm presented in this work (TPQ) and the algorithm of Ref. 6 (LSQRFL).

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/content/aip/journal/jcp/125/24/10.1063/1.2403126
2006-12-27
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Fitting a free-form scattering length density profile to reflectivity data using temperature-proportional quenching
http://aip.metastore.ingenta.com/content/aip/journal/jcp/125/24/10.1063/1.2403126
10.1063/1.2403126
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