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Showing papers on "Total internal reflection published in 1992"


Journal ArticleDOI
TL;DR: It is reported that small particles with diameters of 1-27 microm have moved in the evanescent fields produced by a laser beam.
Abstract: We report that small particles with diameters of 1–27 μm have moved in the evanescent fields produced by a laser beam. The evanescent field in the experiment was produced in the near field of the surface of a high-refractive-index sapphire prism illuminated by a 1.06-μm YAG laser beam with an incident angle larger than the critical angle. Both polystyrene latex spheres and glass spheres bounced and ran along the surface of the prism when the laser beam was on. The maximum running speed obtained was approximately 20 μm/s. A micrograph of the running particles is shown with plots of the measured velocity versus the incident angle of the laser beam. Applications of this phenomenon are also discussed.

355 citations


Patent
08 May 1992
TL;DR: In this paper, a multifiber optical connector plug is proposed to realize low reflection and low insertion loss without using the refractive index matching material, which can be formed by a pair of such connectors with spring member for pressing the multifiber optic connector plugs toward each other in the axial direction and guide pins for aligning the optical connector plugs.
Abstract: A multifiber optical connector plug capable of realizing low reflection and low insertion loss, without using the refractive index matching material. The multifiber optical connector plug includes a connector plug member made of a plastic material, having a connecting facet on which endfaces of the optical fibers to be connected with other optical fibers are arranged in a transverse direction between the guide pin insertion holes, with the endfaces of the optical fibers projecting out of the connecting facet, the connecting facet being inclined with respect to an axial direction along optical axes of the optical fibers by an angle which is larger than a total reflection critical angle of light beams transmitted through the optical fibers. The connecting facet may have a flat surface shape or a convex ellipsoidal surface shape. A multifiber optical connector can be formed by a pair of such multifiber optical connector plugs with spring member for pressing the multifiber optical connector plugs toward each other in the axial direction and guide pins for aligning the multifiber optical connector plugs.

196 citations


Journal ArticleDOI
TL;DR: In this article, the reflection and transmission characteristics of the slab are related to the complex band structure of the photon field associated with the given crystallographic plane of the corresponding infinite crystal, which is introduced in the manner of the low-energy electron diffraction theory.
Abstract: The authors consider periodic structures made of spheres embedded in a host material with a different dielectric function. They show how to calculate the reflection and transmission of electromagnetic waves by a slab of the material parallel to a given crystallographic plane. The method of calculation is based on a doubling-layer scheme which obtains the reflection and transmission matrix elements for the multilayer from those of a single layer. The reflection and transmission characteristics of the slab are related to the complex band structure of the photon field associated with the given crystallographic plane of the corresponding infinite crystal, which is introduced in the manner of the low-energy electron diffraction theory. They present numerical results which demonstrate the applicability of the method to real systems of current interest and point out some interesting physics which arose from their calculations. They show in particular that the nondegenerate bands of the photon field at the centre of the surface Brillouin zone do not couple to the incident radiation, leading to total reflection at normal incidence.

179 citations


Journal ArticleDOI
TL;DR: A new method of angle measurement that is based on the internal-reflection effect at an air-glass boundary that has the advantage of a simple sensor design for applications ranging from a wide measurement range to extremely high resolution.
Abstract: We describe a new method of angle measurement that is based on the internal-reflection effect at an air-glass boundary. The method uses a differential detection scheme to largely reduce the inherent nonlinearity of the reflectance versus the angle of incidence in internal reflection. With nonlinearity reduced, the displacement of the angle of incidence can be determined accurately by measuring the reflectance. The resolution and measurement range are determined by the initial angle of incidence, the polarization state of the light, and the number of reflections. Compared with interferometers and autocollimators, this method has the advantage of a simple sensor design for applications ranging from a wide measurement range to extremely high resolution. Other advantages are compact size, simple structure, and low cost. A theoretical analysis of the method and some experimental results of a prototype sensor are presented. The possible applications of the method are also discussed.

140 citations


Journal ArticleDOI
TL;DR: The differential experimental method uses the high sensitivity of the eigenstates of a quasi-isotropic laser to small perturbations to measure an intracavity Goos-Hanchen effect for angles of incidence both below and above the critical angle.
Abstract: The Goos-H\"anchen longitudinal shift at total reflection of an optical Gaussian beam is experimentally investigated for only one reflection. The differential experimental method uses the high sensitivity of the eigenstates of a quasi-isotropic laser to small perturbations to measure an intracavity Goos-H\"anchen effect for angles of incidence both below and above the critical angle. The measurements are in good agreement with our calculations of the longitudinal shift for Gaussian laser beams.

139 citations


Journal ArticleDOI
TL;DR: In this article, the scattering and diffraction of plane SV waves underground, circular, cylindrical cavities at various depths in an elastic half space is studied, where the cavities, studied here, are at depths of two to five cavity radii measured from the surface to the center of the cavity.

136 citations


Journal ArticleDOI
TL;DR: In this article, a macroscopic approach is proposed to calculate the intensity detected by a small spherical tip above a regular glass lattice illuminated in total internal reflection, and the model is based on the macroscopy approach for calculating the images obtained in scanning tunneling optical microscopy.
Abstract: A theoretical model for calculating the images obtained in scanning-tunneling optical microscopy is proposed. We calculate the intensity detected by a small spherical tip above a regular glass lattice illuminated in total internal reflection. The model is based on a macroscopic approach. We show that the resolution is limited neither by the wavelength nor by the decay length of the evanescent wave but that it is determined by the tip–sample distance and by the signal-to-noise ratio. We also discuss the quality of the images. In general, the intensity profile does not reproduce the sample profile. We analyzed two kinds of filtering that can deform the true profile. We also show that for a small sample period a strong signal is obtained only in TM polarization.

136 citations


Journal ArticleDOI
TL;DR: In this paper, a quantitative theory of the nonspecular scattering of x rays from multilayer structures having rough interfaces is presented, and the results are valid for arbitrary polarization and angles of incidence (measured from the normal) less than the critical angle for total external reflection.
Abstract: A quantitative theory of the nonspecular scattering of x rays from multilayer structures having rough interfaces is presented. The results are valid for arbitrary polarization and angles of incidence (measured from the normal) less than the critical angle for total external reflection. A structural model is adopted wherein each interface is assumed to be described by a surface having statistically random roughness with a well‐behaved power spectrum. In addition, the model accounts for arbitrary correlation of the roughness between different interfaces. Calculations are presented for a variety of roughness configurations to investigate the dependence of the nonspecular scattering on the fundamental structural parameters. In particular, it is shown that the scattering from correlated roughness exhibits characteristic resonance behavior (quasi‐Bragg diffraction).

125 citations


Journal ArticleDOI
30 Oct 1992-Science
TL;DR: In this article, an x-ray resonance effect in an organic thin film on an xray reflecting mirror is reported, which is the result of interference between reflected and refracted x-rays at the air-organic thin film interface and occurs at incident angles slightly above the critical angle of the film.
Abstract: An x-ray resonance effect in an organic thin film on an x-ray reflecting mirror is reported. The resonance effect is the result of interference between reflected and refracted x-rays at the air-organic thin film interface and occurs at incident angles slightly above the critical angle of the film. In excellent agreement with theory, the primary resonant x-ray electric field that is confined in the organic thin film is approximately 20 times as intense as the electric field of the incident beam when measured at a position close to the center of the film. Resonance-enhanced x-rays can be used to characterize the internal structure of Langmuir-Blodgett thin film membranes. This effect may also find use in x-ray-based thin film devices and in the structural analysis of adlayers and surfaces that have thus far proved difficult, if not impossible, to study because of sensitivity limitations.

98 citations


Patent
03 Dec 1992
TL;DR: In this article, a reflective type liquid crystal display device excelling in uniformity and capable of making a bright display is presented, where collimators for limiting the incident angle θ to the upper surface of the light from the lamps are disposed between the light guide plate and lamps.
Abstract: A reflective type liquid crystal display device excelling in uniformity and capable of making a bright display is presented. At the front side of the liquid crystal display element, that is, at the observer side, a light guide plate is disposed, and a pair of lamps are disposed at the outer side of the confronting side surfaces of the light guide plate. Collimators for limiting the incident angle θ to the upper surface of the light from the lamps are disposed between the light guide plate and lamps. That is, by the collimators, the incident angle θ to the upper surface is defined so that the incident light may be totally reflected, and that the reflected light may not be totally reflected by the lower surface 61b. As a result, the light from the lamps will not reach the observer directly, and a uniform illumination of the liquid crystal display element may be realized. Besides, at the observer side of the liquid crystal display element, a light guide plate forming protrusions is disposed, and a pair of lamps are disposed at the outer side of the confronting side surfaces of the light guide plate. Furthermore, between the light guide plate and lamps, collimators for limiting the incident angle θ of the light from the lamps into the upper surface are disposed. Accordingly, the light from the lamps does not reach the observer directly, and the light entering the protrusions formed on the light guide plate is emitted to the liquid crystal display element side. Thus, a uniform illumination into the liquid crystal display element is realized.

96 citations


Journal ArticleDOI
TL;DR: The attenuated total internal reflection modulator (ATRM) as discussed by the authors is a light modulator based on coupling a light beam to a surface plasmon wave, and its fabrication is compatible with GaAs integrated circuit technology.
Abstract: The modulation efficiency and bandwidth limitations of a new type of light modulator, the attenuated total internal reflection modulator (ATRM), are described. The ATRM is based on coupling a light beam to a surface plasmon wave, and its fabrication is compatible with GaAs integrated circuit technology. We demonstrate modulation to 22 GHz (the extrapolated 1.5 dB optical modulation bandwidth is 26 GHz) and show that devices with high modulation index can be built using existing materials.

Journal ArticleDOI
TL;DR: Boundary-value computations are presented that reveal that the feedback responsible for the observed lasing modes is associated with total internal reflection at the liquidsilica interface.
Abstract: We describe the observation of laser emission at wavelengths corresponding to whispering-gallery modes from a highly refractive dye-doped solvent flowing in a normally illuminated silica capillary fiber. The cylindrical whispering-gallery-mode laser described here differs from the well-known spherical droplet laser in that it has an internal refractive index discontinuity. Boundary-value computations are presented that reveal that the feedback responsible for the observed lasing modes is associated with total internal reflection at the liquid–silica interface. No laser peaks are observed when the refractive index of the solvent is less than that of the silica.

Patent
08 Apr 1992
TL;DR: In this paper, low angle V-grooves are provided in the target surfaces of optoelectronic or photovoltaic devices such as solar cells and photodetectors to increase the efficiency by promoting total internal reflection of light reflected from the target surface at the interface of the coverglass and the external environment.
Abstract: Low angle V-grooves are provided in the target surfaces of optoelectronic or photovoltaic devices such as solar cells and photodetectors. The low angle V-grooves increase the efficiency of the devices by promoting total internal reflection of light reflected from the target surface at the interface of the coverglass and the external environment.


Journal ArticleDOI
TL;DR: A miniature fused-silica monolithic optical ring resonator in which the Gaussian mode is confined by total internal reflection, which has applications in linear and nonlinear optics.
Abstract: We have characterized a miniature fused-silica monolithic optical ring resonator in which the Gaussian mode is confined by total internal reflection. Laser light is coupled into and out of the resonator by frustrating one of the total internal reflections by means of a prism. The resonator can be overcoupled and undercoupled by varying the resonator–prism distance. The minimum measured resonator linewidth was less than 3 MHz. This type of broadband, stable, low-loss resonator has applications in linear and nonlinear optics.

Proceedings ArticleDOI
TL;DR: In this article, a high energy telescope design is presented which combines grazing incidence geometry with Bragg reflection in a graded d-spacing multilayer coating to obtain significant sensitivity up to 6O keV.
Abstract: A high energy telescope design is presented which combines grazing incidence geometry with Bragg reflection in a graded d-spacing multilayer coating to obtain significant sensitivity up to --6O keV. The concept utilizes total reflection and first order Bragg reflection in a graded d-spacing multilayer structure in a way that higher energies are reflected from the deepest layers in the stack. The specific design presented in this paper is based on Ni/C and Mo/C structures with dspacings ranging from 25A to 100 A. X-ray reflectivity data obtained with Cu Kc1 (8. 05 keV) are presented from the first graded d-spacing structures of this kind.

Journal ArticleDOI
TL;DR: In this paper, the scattering of linearly polarized electromagnetic waves incident from a dielectric from a rough surface separating the dielectrics from a vacuum is studied by using the extinction theorem.
Abstract: The scattering of linearly polarized electromagnetic waves incident from a dielectric from a rough surface separating the dielectric from a vacuum is studied by using the extinction theorem. The angular distributions of the ensemble average of intensity of the reflected and transmitted fields are calculated numerically for several values of the angle of incidence, the surface statistical parameters, and the dielectric permittivity. To determine the effect of the corrugation on the transmitted evanescent waves, we also obtain the angular spectrum of the transmitted field as a function of the momentum parallel to the surface in the nonradiative zone. The total mean reflected and transmitted energies (reflectance and transmittance), as well as their incoherent parts in the case of slight corrugations, are derived by integrating the angular intensity distribution over the angle of observation. This permits the analysis of the influence of the corrugation and of the phenomenon of total internal reflection within two different systems of surface correlation length T namely, for T larger and smaller than the wavelength. In particular, enhanced backscattering and forward transmission are predicted for surfaces with both T and the rms deviation greater σ than the wavelength of the incident light.

Journal ArticleDOI
TL;DR: In this paper, the form functions of an aluminum cylindrical shell immersed in water have been calculated by the direct summation of the Rayleigh series at angles between α=0° and α=35°.
Abstract: Acoustic scattering from an isotropic elastic hollow cylindrical shell of infinite length excited by an obliquely incident plane acoustic wave is investigated. The form functions of an aluminum cylindrical shell immersed in water have been calculated by the direct summation of the Rayleigh series. Computations are made at angles (with the normal to the cylinder axis) between α=0° and α=35°. The results of the theoretical calculation are in good agreement with the results of experiments. The experimental results have shown in a frequency range of k1a=0 –20 that the resonances are related to three wave families: the circumferential wave (l=2) detected for angles smaller than the ‘‘angle of longitudinal wave in thin rods’’ (αl), the guided wave (p=1) detected for angles smaller than the second critical angle (αT), and the Scholte–Stoneley wave (l=0). The evolution of the resonance frequencies is followed for different angles and one can note experimentally, that at an angle superior to the Rayleigh critical ...

Patent
30 Jul 1992
TL;DR: In this paper, a light-guiding device consisting of an interference pattern which acts as a diffraction grating to diffract and reflect the light, incident from the light-incident surface, in a predetermined direction is proposed.
Abstract: A light-guiding device having a light-incident surface and a light-outgoing surface for guiding light incident from the light-incident surface from the light-outgoing surface toward a light-receiving surface of a photodetector for generating an electric signal corresponding to a quantity of the received light. The device comprises a hologram layer having an interference pattern which acts as a diffraction grating to diffract and reflect the light, incident from the light-incident surface, in a predetermined direction. The hologram layer is interposed between first and second total reflection layers. The first total reflection layer has a first total reflection surface disposed in opposed relation to one of the longitudinal surfaces of the hologram layer so that the light diffracted and reflected by the hologram layer is incident on the first total reflection surface at a predetermined angle larger than the critical angle so as to be total-reflected thereon, and the second total reflection layer has a second total reflection surface disposed in opposed relation to the other longitudinal surface of the hologram layer so that the incident light passing through the hologram layer is incident on the second total reflection surface at a predetermined angle greater than the critical angle so as to be total-reflected thereon. This arrangement improves the light-receiving performance concurrently with reducing the thickness of the device.

Journal ArticleDOI
TL;DR: The differential reflection of left and right circularly polarized light from a naturally chiral liquid was enhanced and quantitatively measured under conditions of total reflection, making the first observation of molecular optical activity by coherent light scattering.
Abstract: The differential reflection of left and right circularly polarized light from a naturally chiral liquid was enhanced and quantitatively measured under conditions of total reflection. In accord with recent predictions, the observed signal at the critical angle was some 3 orders of magnitude larger than the intrinsic chiral parameters (~10−7). This is to our knowledge the first observation of molecular optical activity by coherent light scattering.

Journal ArticleDOI
TL;DR: Total reflection X-ray fluorescence spectrometry (TXRF) uses an ingenious excitation technique for energy-dispersive Xray spectral analysis as mentioned in this paper, where a sample is placed on an optically flat carrier and irradiated at a grazing incidence (an angle of only a few minutes) so that the carrier totally reflects the primary beam.
Abstract: Total reflection X-ray fluorescence spectrometry (TXRF) uses an ingenious excitation technique for energy-dispersive X-ray spectral analysis. A minute amount of sample is placed on an optically flat carrier and irradiated at a grazing incidence (an angle of only a few minutes) so that the carrier totally reflects the primary beam. The method is particularly suitable for micro-, trace and surface layer analysis. Microanalysis can be performed because <1 µg of a solid sample or <10 µl of a solution are required. Trace analyses are based on detection limits at the picogramme level and can be applied to aqueous solutions (1 pg ml–1), acids (10 pg ml–1), biological materials (10 ng ml–1) and ultra-pure metals (10 ng g–1) after matrix separation. A simple and reliable quantification can be carried out by the addition of an internal standard element. Surface and thin-film analyses are applied to semiconductor wafer materials. Contaminations at 1 × 1010 atoms cm–2 can be detected and even nanometre thick layers can be investigated by non-destructive depth profiling. For this latter purpose, the angle of incidence is continuously varied in the range of total reflection and an angle-dependent intensity profile is recorded.

Journal ArticleDOI
TL;DR: Substrate wave propagation and Bragg diffraction by multiplexed holographic gratings have been used to demonstrate a new 1-to-30 fanout optical interconnect having an overall diffraction efficiency of 87.8% and individual channel efficiency of 3.0 +/- 0.8%.
Abstract: Substrate wave propagation and Bragg diffraction by multiplexed holographic gratings have been used to demonstrate a new 1-to-30 fanout optical interconnect having an overall diffraction efficiency of 87.8% at 514.5 nm and an individual channel efficiency of approximately 3.0 +/- 0.8%. The device configuration utilizes the large multiplexing capability of dichromated gelatin polymer films and substrate total internal reflection to realize large channel fanouts within the plane of a soda-lime glass substrate. A simplified theoretical formulation is presented to treat the corresponding three-dimensional holographic diffraction problem in the Bragg regime for slanted phase gratings. Results are compared with experimentally measured quantities for singly exposed phase gratings in different polarization conditions and incident angle orientations. The limitations of using multiplexed holograms in multiplanar substrate interconnection applications are also discussed.

Journal ArticleDOI
TL;DR: In this paper, a self-consistent method was developed to analyze the influence of incident light beam polarization on an image shape recently recorded from scanning tunneling optical devices, and the electromagnetic coupling between the object and a nanometer-size detector was described from a dynamic matrix including all dipolar correlations inside the system.
Abstract: A whole self-consistent method is developed in order to analyze the influence of incident light beam polarization on an image shape recently recorded from scanning tunneling optical devices. The electromagnetic coupling between the object and a nanometer-size detector is described from a dynamic matrix, including all dipolar correlations inside the system. This matrix, expressed in terms of field propagators, permits us to analyze the physical mechanisms responsible for the conversion of evanescent waves into homogeneous propagating modes inside the detector. The numerical results are compared with those obtained for layered metallic or dielectric nanoparticles deposited upon a glass substrate. The shape and the contrast of the images are both sensitive to the field polarization and to the external frequency in the case of metallic objects. Moreover, as was observed in experimental studies, the p-polarized mode seems to give better contrast in the images.

Journal ArticleDOI
TL;DR: In this paper, a grating of a periodicity of 417 nm and a thickness of 5 nm have been imaged both in TM and TE modes, and the difference of behavior of the field versus the polarization of the incident light has been shown.
Abstract: The scanning tunneling optical microscope (SNOM, STOM, PSTM, etc.) is the equivalent of the electron scanning tunneling microscope in the electromagnetic domain. Although it was born at the same time, its actual development is more recent. Here, some new results obtained with the version working in total reflection (STOM/PSTM) are reported. A grating of a periodicity of 417 nm and a thickness of 5 nm have been imaged both in TM and TE modes. It is first noted that the optical image is well resolved. Furthermore, the difference of behavior of the field versus the polarization of the incident light has been shown. More precisely, the TM mode seems to be highly sensitive to small index and topography variations due to surface contaminants. Such effects are generally not imaged by atomic force microscopy working in attractive mode, because they affect the surface topography slightly. The SNOM could be thus a very powerful tool for detecting pollutants over the surface of objects like glasses, lenses, gratings...

Journal ArticleDOI
TL;DR: In this paper, an evanescent field optical microscope (EFOM) is presented which employs frustrated total internal reflection o n a localized scale by scanning a dielectric tip in close proximity to a sample surface.

Patent
05 Aug 1992
TL;DR: In this article, an optically diffuse reflective layer is disposed over the upper and lower scintillator body sections to reflect light photons generated within the scintilator body to be reflected from the sidewalls toward the cap, or reflected directly to the optically transmissive window.
Abstract: A radiation detection device includes a scintillator having an upper scintillator body section and a lower scintillator body section. The upper section forms an arcuate-shaped cap through which the incident radiation enters the scintillator, and the lower section has sidewalls disposed at a selected taper angle with respect to the longitudinal axis of the scintillator body and an optically transmissive window disposed opposite the cap of the upper section such that optical photons can pass from the scintillator to a photodetector coupled to the window. An optically-diffuse reflective layer is disposed over the sidewalls and the cap. The sidewalls typically have a positive taper angle, being closer to one another near the optically transmissive window and farther from one another near the cap. The arcuate shape of the cap typically conforms to the arc of a circle centered on the optically transmissive window. The selected taper angle of the sidewalls and the radius of the arc of the cap are chosen to cause light photons generated within the scintillator body to be reflected from the sidewalls toward the cap and reflected from the cap towards the optically transmissive window (or reflected directly to the optically transmissive window for sidewalls having a negative taper angle) such that the photons are focussed on the window and strike the window at an angle greater than the critical angle for the scintillator-to-photodetector interface.

Journal ArticleDOI
TL;DR: In this article, numerical simulations of total reflection X-ray photoelectron spectroscopy (TRXPS) are presented, which is an even more powerful tool for the study of surface chemistry and physics than ordinary Xray photo electrophysiology.

Journal ArticleDOI
01 Oct 1992-EPL
TL;DR: In this paper, a high-resolution study of x-ray scattering from a laterally structured surface is reported, showing that total external reflection displays a distinct dip in the reflectivity for incident angles, and around a Bragg peak a system of truncation rods is found.
Abstract: A high-resolution study of x-ray scattering from a laterally structured surface is reported. Total external reflection displays a distinct dip in the reflectivity for incident angles < c (critical angle) and around a Bragg peak a system of truncation rods is found. Generalized Fresnel equations in conjunction with a kinematical theory provide a quantitative explanation of both findings. The method is well suited for characterising modulations on a mesoscopic length scale.

Patent
25 Nov 1992
TL;DR: In this paper, a flexible transducer for use in a photon tunneling microscope apparatus is described, which consists of an optically transmissive body having a totally internally reflecting (TIR) surface therein and a second surface plano-parallel to the TIR surface.
Abstract: A flexible transducer for use in a photon tunneling microscope apparatus, the transducer comprising an optically transmissive body having a totally internally reflecting (TIR) surface therein and a second surface plano-parallel to the TIR surface when the TIR surface and the second surface are in an unstressed state, the second surface comprising a combination light energy entrance surface and light energy exit surface, the TIR surface being oriented such that light energy introduced at the second surface within the critical angle normally is reflected totally from the interior of the TIR surface to the second surface. A light pattern of variable intensity emerges from the second surface as a result of frustration of total internal reflection at the TIR surface occuring as the TIR surface is brought sufficiently proximate a sample surface. The flexible transducer and the TIR surface thereof are arranged and adapted to be brought into optical contact with, and to conform to, varied macrophotography configurations of the sample surface. The disclosure further relates to methods for making and using the flexible transducer.

Journal ArticleDOI
TL;DR: In this article, the linear, inviscid reflection of a straight-crested surface wave from a vertical wall is determined on the hypothesis that the contact angle of the meniscus vanishes.
Abstract: The linear, inviscid reflection of a straight-crested surface wave from a vertical wall is determined on the hypothesis that the contact angle of the meniscus vanishes. The reflection coefficient is a function of the parameter γ ≡ k0l, where k0 is the wavenumber of the incident wave and l is the capillary length, and is approximated by R = exp (−4iγ2) for a gravity–capillary wave for which γ [Lt ] 1. The solution of this reflection problem is used to obtain matched-asymptotic approximations for standing waves in channels and circular cylinders. The meniscus-induced, fractional reduction of the frequency of the dominant mode in a deep circular cylinder is 0.77 γ2 (which exceeds the increase of ½γ2 associated with the capillary energy of the free surface). This decrement is within 2 mHz of the value inferred from the measurements of Cocciaro et al. (1991) after allowing for the reduction in frequency induced by the viscous boundary layers at the walls, but there are residual uncertainties (in this comparison) associated with the wetting process at the moving contact line and possible surface contamination.