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Two beam surface fluctuation specular reflection spectroscopy
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View: Figures


Image of FIG. 1.
FIG. 1.

Schematic representation of a one beam and two beam SFSRS experiment. For both experiments the component of surface of the probed wavevectors k depends on the positioning of the spots on the detector with respect to the plane of incidence. For isotropic samples configurations (a) and (b) are nearly equivalent. In configuration (c) a component parallel to the incident plane (and perpendicular to r) is correlated by the cross power spectrum. In configuration (d) a component perpendicular to the plane of incidence is correlated.

Image of FIG. 2.
FIG. 2.

Schematic showing key optical components of the two beam set-up in the perpendicular (⊥) configuration.

Image of FIG. 3.
FIG. 3.

The raw experimental cross power spectra at r ∼ 0 (rough light upper lines – red online) and r ∼ 5R (rough light lower lines – light blue online) with spline (smooth thick black line) for n-hexadecane samples in parallel and perpendicular configurations. A subset of the splined experimental data (thin black lines) shows the general behaviour of the cross power spectral density in these two configurations. Typical raw experimental power spectra are also shown in two cases (rough dark upper lines – dark blue online).

Image of FIG. 4.
FIG. 4.

Experimental (solid lines) and model (dashed lines) S 12(ω) n-hexadecane data showing variation with r at four frequencies.

Image of FIG. 5.
FIG. 5.

Model (a) and experimental (b) P(ω, k) for rhodorsil 47v20 silicon oil.

Image of FIG. 6.
FIG. 6.

P(ω, k) calculated by inversion of experimental data (solid lines) and using the expression given in the literature (Ref. 16) (dashed lines) for the (a) silicon oil and (b) hexadecane and samples at four frequencies.

Image of FIG. 7.
FIG. 7.

Experimental P(ω, k) for rhodorsil (dashed lines) with a comparison to a fit to a model parameterized by surface tension, viscosity and density (solid lines).

Image of FIG. 8.
FIG. 8.

Measured one beam S(ω) and two beam S 12(ω, r) for suspensions of 350 nm diameter latex spheres in water, at concentrations 0.01 to 0.1 wt. % (measured extinction coefficients (Ref. 17) γ = 90 to 1100 m−1) demonstrating S 12(f, r) insensitivity to bulk turbidity.

Image of FIG. 9.
FIG. 9.

Comparison of P(ω, k) evaluated by direct calculation (solid black line) and by model inversion for n-hexadecane at ω/(2π) = 1000 Hz in various conditions illustrating artifacts: (a) for variable Δd and fixed r max and (b) for variable r max and fixed Δr.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Two beam surface fluctuation specular reflection spectroscopy