Wavefronts

Simulations of that kind result in a wide variety of A-scans and wavefront snapshots. The first screening of this material reveals, that the simulations in which the transducer is coupling partly to the V-butt weld and partly to the steel exhibit quite a number of pulses in the A-scans because the coupling at the interface of the weld results — due to the anisotropic behavior of the weld — in a complicated splitting of the transmitted wavefront. The different parts of the splitted wavefront are reflected and diffracted by the backwall, the interface, and — if present — by the notch and, therefore, many small signals are received by the transducer, which can only be separated and interpreted with great difficultie.s. 

Only the simulations in which the transducer is coupling either to the V-butt weld or to the surrounding steel can be analyzed in a simple and intuitive way, which means that the different pulses in the A-scan signals can be related uniquely to the reflection or diffraction of the wavefront at the weld, the backwall, and/or the notch. 

The following observations are discussed in detail and supported by EFIT wavefront snapshots ... 

The diffraction of the incident 45°-S V -transducer-pulse at the interface between the isotropic steel and the anisotropic weld may result in two transmitted qSV-wavefronts, a particular phenomenon to be explained with pertinent slowness diagrams. 

Second corner reflection The first corner reflection appears as usual when the transducer is coupled to the probe at a certain distance from the V-butt weld. The second corner reflection appears if the transducer is positioned well above the V-hutt weld. If the weld is made of isotropic material the wavefront will miss (pass) the notch without causing any reflection or diffraction (see Fig. 3(a)) for this particular transducer position. In the anisotropic case, the direction of the phase velocity vector will differ from the 45° direction in the isotropic case. Moreover, the direction of the group velocity vector will no longer be the same as the direction of the phase velocity vector (see Fig. 3(b), 3(c)). This can be explained by comparing the corresponding slowness and group velocity diagrams. 

Figure 3 Snapshots of the shear wavefronts for different types of weld material to show the direction of the wave unit vector k (a phase velocity unit vector Cp ) and the group velocity unit vector...

Notch tip With perpendicular grain orientation no notch tips are detected. The snapshots (see Fig. 7 second and third snapshot from top on the right) show that in the direction to the receiver there is a gap in the reflected / diffracted quasi shear wavefront. In contrast, the notch tips can be detected within the herringbone structure. 

The divergence factor (DF) introduced by the asymptotic expansion, accounts for the deformation of the refracted wavefront (initially spherical in the coupling medium). It ensures, under the GO approximation, the energy conservation of a ray-pencil propagating... 

We first supposed that the field radiated into the piece by the transducer is known, thanks to the Champ-Sons model. Then, the main approximation used consists in making far field assumptions in the beam defect interaction area. In the case of a focused transducer we assume that the incident wavefronts on the defect are plane. This is equivalent to say that the defect is located in or near the transducer focal area and that a defect located outside this zone does not cause a significant echo. In the case of planar contact transducer, the incident wavefronts on the defect are assumed to be spherical The incident field on the defect is therefore approximated by the product of a spatial function gfp,0,z)describing the amplitude distribution in the beam and a time-delayed waveform < ) ft) representing the plane or spherical propagation in the beam. The incident field on the defect can therefore be approximated for ... 

Therefore, we may say that head wave is the excited shear wave when longitudinal wave is spreading along boundaries. This is the head wave which we often call. In Fig.3 the wavefront of head wave is indicated by AB. The biggest circular arc AC in Fig.3 is the wavefront of longitudinal wave. The small arrow beside the circular line indicates the direction of displacement after the wavefront arrives and the written character 8 nearby indicates its... 

After a photoelastic experiment it is not easy to see the wavefront of head wave. 

This is because on one hand, heav wave is weaker and on the other hand, photoelastic testing method is unfavorable for observing the sound field of axial symmetry. The sound field (see Fig.4) excited by strip ciystal in solid is observed with photoelastic testing method. The wavefront of head wave can be see in Fig.4, which is a circumstantial evidence of wavefront of head wave excited just by point-shape crystal. We can calculate... 

Fig. 4 The visible wavefront of head wave in the sonnd field of square crystal...

The smallest unit (packet) of electromagnetic energy (a photon) is related to frequency by the formula, E = hv, in which E is the energy and h is Planck s constant. Alternatively, the relation can be written, E = hc/A,. Frequency (v) is a number with units of cycles per second (cps, the number of times a wavefront passes a given point in unit time, sec ) and is given the name Hertz (Hz), Planck s constant is a fundamental number, measured in J sec or erg-sec. 

Figure 1 Bragg diffraction. A reflected neutron wavefront (D, Dj) making an angle 6 wKh planes of atoms will show constructive interference (a Bragg peak maxima) whan the difference in path length between Df and (2CT) equals an integral number of wavelengths X. From the construction, XB = d sin 6.

The spirals are composed of active wavefronts propagating over regions of quiescent sites. Simple singularities around which long-wavelength spirals form include... 

Lorentz-Invariance on a Lattice One of the most obvious shortcomings of a CA-based microphysics has to do with the lack of conventional symmetries. A lattice, by definition, has preferred directions and so is structurally anisotropic. How can we hope to generate symmetries where none fundamentally exist A strong hint comes from our discussion of lattice gases in chapter 9, where we saw that symmetries that do not exist on the microscopic lattice level often emerge on the macroscopic dyneimical level. For example, an appropriate set of microscopic LG rules can spawn circular wavefronts on anisotropic lattices. 

Furthermore, under certain conditions (e.g. local unidirectional block) it is possible that the activation wavefront is delayed and encounters areas already repolarized. This may result in a circulating wave-front (= reentrant circuit reentrant arrhythmia), from which centrifugal activation waves originate and elicit life-threatening ventricular fibrillation. 

In astronomy, we are interested in the optical effects of the turbulence. A wave with complex amplitude U(x) = exp[ irefractive index, resulting in a random phase structure by the time it reaches the telescope pupil. If the turbulence is weak enough, the effect of the aberrations can be approximated by summing their phase along a path (the weak phase screen approximation), then the covariance of the complex amplitude at the telescope can be shown to be... 

Imaging is considered to be diffraction-limited for S > 0.8— the Marechal criterion. (This corresponds to a wavefront error of A/14.) The Strehl ratio decreases rapidly with increasing wavelength since ro oc A /. ... 

Figure d. Wavefront eiror generated by a surface error of amplitude h. 

The first example is the 4-m class William Herschel telescope, at la Pakna, whose optical specifications, drafted by D. Brown, were expressed in terms of allowable wavefront error as a function of spatial frequencies matching those of atmospheric turbulence. 

Last but not least, two epoch-marking technologies have been successfully implemented in 1989 and 1994 active optics, with the 3.5 m ESO New Technology Telescope (NTT), and segmentation, with the 10 m Keck. In the former, real-time adjustments of the primary mirror support forces and of the alignment of the secondary mirror guarantee consistent, optimal performance, and allow relaxation of opto-mechanical fabrication tolerances. These adjustments being derived from wavefront analysis of off-axis stellar sources located outside the scientihc held of view, imply minimal operational overheads at the beneht of reliable, substantial performance improvement... 

In general a surface or wavefront z(p, 0) can be expanded in functions that span the space. As an example one can expand in cylindrical polynomials ... 

The design of the Owl 100-m telescope relies extensively on proven fabrication technologies, in particular on mass- or serial-production schemes, and incorporates several distinct wavefront control loops. The overall characteristics of the current design are listed in Table 1. 

Control Multi-stage, distributed wavefront control phasing, pre-setting, field stabilization, focusing, fine centering, dual conjugates active optics, adaptive optics... 

Low number of surfaces (6) for the complete range of wavefront control functions field stabilization, active focusing and centering, actively deformable surfaces, dual conjugates adaptive optics ... 

The OWL concept is built on the VLT experience, with extensive wavefront control capability. The number of degrees of freedom is however substantially larger, as shown in Tab. 2. 

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