Profile measurement using standing wave trapping

Mild to steep standing waves of the fundamental mode are generated in a narrow rectangular cylinder undergoing vertical oscillation with forcing frequencies of 3.15 Hz to 3.34 Hz. A precise, non-intrusive optical wave profile measurement system is used along with a wave probe to accurately quantify the spatial and temporal surface elevations. These standing waves are also simulated by a two-dimensional spectral Cauchy integral code. Experiments show that contact-line effects increase the viscous natural frequency and alter the neutral stability curves. Hence, as expected, the addition of the wetting agent Photo Flo significantly changes the stability curve and the hysteresis in the response diagram. Experimentally, we find strong modulations in the wave amplitude for some forcing frequencies higher than 3.30 Hz. Reducing contact-line effects by Photo-Flo addition suppresses these modulations. Perturbation analysis predicts that some of this modulation is caused by noise in the forcing signal through ‘sideband resonance’, i.e. the introduction of small sideband forcing can generate large modulations of the Faraday waves. The analysis is verified by our numerical simulations and physical experiments. Finally, we observe experimentally a new form of steep standing wave with a large symmetric double-peaked crest, while simulation of the same forcing condition results in a sharper crest than seen previously. Both standing wave forms appear at a finite wave steepness far smaller than the maximum steepness for the classical standing wave and a surface tension far smaller than that for a Wilton ripple. In both physical and numerical experiments, a stronger second harmonic (in time) and temporal asymmetry in the wave forms suggest a 1:2 resonance due to a non-conventional quartet interaction. Increasing wave steepness leads to a new form of breaking standing waves in physical experiments.

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Eels Under Standing Wave Conditions

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100054911 ◽

1982 ◽

Vol 40 ◽

pp. 492-495

Author(s):

O.L. Krivanek ◽

J. TaftØ

Keyword(s):

Standing Wave ◽

Wave Conditions ◽

Set Up ◽

A Site ◽

Complex Crystal

It is well known that a standing electron wavefield can be set up in a crystal such that its intensity peaks at the atomic sites or between the sites or in the case of more complex crystal, at one or another type of a site. The effect is usually referred to as channelling but this term is not entirely appropriate; by analogy with the more established particle channelling, electrons would have to be described as channelling either through the channels or through the channel walls, depending on the diffraction conditions.

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Voltage and Orientation Dependence of Characteristic X-Ray Production in Thin Crystals

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100118941 ◽

1985 ◽

Vol 43 ◽

pp. 414-415

Author(s):

G. Thomas ◽

K. M. Krishnan ◽

Y. Yokota ◽

H. Hashimoto

Keyword(s):

Standing Wave ◽

Incident Beam ◽

Orientation Dependence ◽

Incident Plane Wave ◽

Crystalline Materials ◽

X Ray ◽

Incident Plane ◽

Crystal Unit Cell ◽

Beam Orientation ◽

Acceleration Voltage

For crystalline materials, an incident plane wave of electrons under conditions of strong dynamical scattering sets up a standing wave within the crystal. The intensity modulations of this standing wave within the crystal unit cell are a function of the incident beam orientation and the acceleration voltage. As the scattering events (such as inner shell excitations) that lead to characteristic x-ray production are highly localized, the x-ray intensities in turn, are strongly determined by the orientation and the acceleration voltage. For a given acceleration voltage or wavelength of the incident wave, it has been shown that this orientation dependence of the characteristic x-ray emission, termed the “Borrmann effect”, can also be used as a probe for determining specific site occupations of elemental additions in single crystals.

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3-D optical transfer in excitation field synthesis microscopes

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100136696 ◽

1995 ◽

Vol 53 ◽

pp. 64-65

Author(s):

Vijay Krishnamurthi ◽

Brent Bailey ◽

Frederick Lanni

Keyword(s):

Standing Wave ◽

Spatial Information ◽

3D Structure ◽

Complete Recovery ◽

Weighting Factor ◽

Optical Transfer Function ◽

Excitation Field ◽

Optical Transfer ◽

Set Up ◽

Focus Plane

Excitation field synthesis (EFS) refers to the use of an interference optical system in a direct-imaging microscope to improve 3D resolution by axially-selective excitation of fluorescence within a specimen. The excitation field can be thought of as a weighting factor for the point-spread function (PSF) of the microscope, so that the optical transfer function (OTF) gets expanded by convolution with the Fourier transform of the field intensity. The simplest EFS system is the standing-wave fluorescence microscope, in which an axially-periodic excitation field is set up through the specimen by interference of a pair of collimated, coherent, s-polarized beams that enter the specimen from opposite sides at matching angles. In this case, spatial information about the object is recovered in the central OTF passband, plus two symmetric, axially-shifted sidebands. Gaps between these bands represent "lost" information about the 3D structure of the object. Because the sideband shift is equal to the spatial frequency of the standing-wave (SW) field, more complete recovery of information is possible by superposition of fields having different periods. When all of the fields have an antinode at a common plane (set to be coincident with the in-focus plane), the "synthesized" field is peaked in a narrow infocus zone.

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