Echo amplitudes

Composite transducers will replace conventional transducers in applications where the improvement of test sensitivity, signal to noise ratio and axial resolution are mandatory. It must nevertheless also be noted in connection with the broadband feature that though composite probes have a specified nominal frequency, the echo signals allow no echo amplitude... 

All echo amplitudes between -12 dB and + 2 dB, with reference to 50% signal height on the screen, are detected and shown in a color scale display in steps of 2 dB. 

The exact position of reflectors within the weld volume is calculated by means of the known probe position plus weld geometry and transferred to a true-to-scale representation of the weld (top view and side view). Repeated scanning of the same zone only overwrites the stored indications in cases where they reach a higher echo amplitude. The scanning movement of the probe is recorded in the sketch at the top, however, only if the coupling is adequate and the probe is situated within the permissible rotation angle. 

The physics of ultrasound is well known and widely described in many publications. Recording amplitudes from model reflectors at different depths by Dr. Josef Krautkramer in 1959 led to the DGS-diagram Echo amplitudes from disk shaped reflectors of different sizes were... 

The result of a DGS evaluation is the Equivalent Reflector Size (ERS), the diameter of a disk hit perpendicularly at the same distance of the defect, producing an echo amplitude exactly equal to that of the defect. 

With the reference block method the distance law of a model reflector is established experimentally prior to each ultrasonic test. The reference reflectors, mostly bore holes, are drilled into the reference block at different distances, e.g. ASME block. Prior to the test, the reference reflectors are scanned, and their maximised echo amplitudes are marked on the screen of the flaw detector. Finally all amplitude points are connected by a curve. This Distance Amplitude Curve (DAC) serves as the registration level and exactly shows the amplitude-over-distance behaviour" of the reference reflector for the probe in use. Also the individual characteristics of the material are automatically considered. However, this curve may only be applied for defect evaluation, in case the reference block and the test object are made of the same material and have undergone the same heat treatment. As with the DGS-Method, the value of any defect evaluation does not consider the shape and orientation of the defect. The reference block method is safe and easy to apply, and the operator need not to have a deep understanding about the theory of distance laws. 

Changes of instrument gain and/or display range recalculates the curve to maintain the relationship of defect echo amplitudes to the curve. 

Figure 3 Multiple DAC with echo amplitude evaluation and screen compare mode (no defect) on the 12 SVGA colour display of the USLT 2000...

The echo amplitude Ar of a reference reflector depends on the type, size (diameter) d f, and distance Sr,., of the reference reflector, and additionally on a possible attenuation in the reference block and finally the absolute gain setting of the instrument G f. In a combined DAC/DGS evaluation program we define the following ... 

We showed that experimentally recorded DACs and synthetically generated DGS curves are equivalent if the described requirements are fulfilled. Consequently an echo amplitude evaluation program has been developed which combines both techniques in one instrument. The software of the new state-of-the-art Ultrasonic Notebook USLT 2000 allows, apart from many other new possibilities, the combined or exclusive use of the reference block and the DGS method for amplitude evaluation. Even in those situations where DACs cannot be re-... 

As the spins precess in the equatorial plane, they also undergo random relaxation processes that disturb their movement and prevent them from coming together fiilly realigned. The longer the time i between the pulses the more spins lose coherence and consequently the weaker the echo. The decay rate of the two-pulse echo amplitude is described by the phase memory time, which is the time span during which a spin can remember its position in the dephased pattern after the first MW pulse. Tyy is related to the homogeneous linewidth of the individual spin packets and is usually only a few microseconds, even at low temperatures. 

In electron-spin-echo-detected EPR spectroscopy, spectral infomiation may, in principle, be obtained from a Fourier transfomiation of the second half of the echo shape, since it represents the FID of the refocused magnetizations, however, now recorded with much reduced deadtime problems. For the inhomogeneously broadened EPR lines considered here, however, the FID and therefore also the spin echo, show little structure. For this reason, the amplitude of tire echo is used as the main source of infomiation in ESE experiments. Recording the intensity of the two-pulse or tliree-pulse echo amplitude as a function of the external magnetic field defines electron-spm-echo- (ESE-)... 

In electron spin echo relaxation studies, the two-pulse echo amplitude, as a fiinction of tire pulse separation time T, gives a measure of the phase memory relaxation time from which can be extracted if Jj-effects are taken into consideration. Problems may arise from spectral diflfrision due to incomplete excitation of the EPR spectrum. In this case some of the transverse magnetization may leak into adjacent parts of the spectrum that have not been excited by the MW pulses. Spectral diflfrision effects can be suppressed by using the Carr-Purcell-Meiboom-Gill pulse sequence, which is also well known in NMR. The experiment involves using a sequence of n-pulses separated by 2r and can be denoted as [7i/2-(x-7i-T-echo) J. A series of echoes separated by lx is generated and the decay in their amplitudes is characterized by Ty. ... 

The spin echo amplitude M (2x, g )in the presence of a magnetic field gradient of strength g and duration 8 is given, as schematically shown in Fig. 20, by... 

HYSCORE, is a 2D four-pulse ESEEM technique which provides correlation between nuclear frequencies originating from different electron manifolds. The sequence of four microwave pulses is tx/2—x—tx/2—/tx— t2-nl2-x-echo where the echo amplitude is measured as a function of tx and t2 at fixed x. The a-proton anisotropic couplings can be detected by this technique (Konovalova et al. 2001a, Focsan et al. 2008). 

Shortly thereafter came reports of integrated three-pulse photon echoes, especially using the echo peak shift to provide information about spectral diffusion [21, 23]. In one experiment [10, 23] the peak shift shows an intriguing oscillation at short times with a period of about 180 fs, followed by a slower relaxation with a decay time of 1.4 ps. The three-pulse echo amplitude can also be heterodyned, leading to 2DIR experiments [24 26]. The latter experiments provide a wealth of information, and there are several ways to extract the desired spectral diffusion dynamics [149]. 

In the limit of zero gradient, the sequence reduces to the Hahn echo, and it is conventional to expand the echo amplitude as a multiple exponential function of T, and define, the usual transverse relaxation times, T,... 

Fig. 2.3 Oscillation of detected intensity as function of the symmetry reveals the echo amplitude. At least three points must be measured to determine the exact symmetry point and the amplitude. However, a more complete symmetry scan is more robust against external disturbances...

Fig. 4. The CPMG pulse sequence. An echo is formed halfway between two consecutive K pulses. The echo amplitude (or the Fourier transform of the half-echo) provides an evaluation of T2 less affected by translational diffusion than in the simple Hahn sequence. The phase change of k pulses with respect to the initial Jt/2 pulse cancels the effect of (re) pulse imperfections.

Figure 1 The archetypical REDOR pulse sequence. (A) rotor-synchronised S-spin-echo experiment defining the reference echo amplitude Sq the REDOR pulse sequence in (B) with the additional rotor-synchronised /-channel 7i-pulses provides the signal intensity S.

Thus, from a parabolic fit to the REDOR evolution data, the second moment can be evaluated. As mentioned in Section 1, this analysis has to be restricted to the initial part of the evolution curves AS/Sq <0.3, as exemplified in Figure 2. However, the first order approximation entails a systematic imderestimation of M2, as shovm by Bertmer and Eckert. Numerous variations of the original REDOR pulse sequence have been established to adapt the technique to specific needs. To accoimt for pulse imperfections and other experimental errors, Chan and Eckert introduced compensated REDOR. In this approach, an /-channel 7r-pulse in the centre of the pulse sequence cancels the reintroduction of the 7-S dipolar couplings hence the echo amplitudes are solely attenuated by the... 

After a time r, a 180° RF pulse reverses the spin precession. A second gradient pulse of equal duration 8 and magnitude g follows to tag the spins in the same way. If the spins have not changed their position in the sample, the effects of the two applied gradient pulses compensate each other, and aU spins refocus. If the spins have moved due to self-diffusion, the effects of the gradient pulses do not compensate and the echo-amplitude is reduced. The decrease of the amplitude A with the applied gradient is proportional to the movement of the spins and is used to calculate the self-diffusion coefficient. 

Fig. 8. Spin-echo amplitude A(8G)/A(0) vs. x (see Eq. 2) in a poly-isobutylene-benzene solution containing 59 vol. % benzene. Initial decay rate is due to solvent diffusion, slower decay describes polymer diffusion figure shows only the lowest 1/4 of the abscissa domain used in fitting the double exponential (after Ref. 29>, with permission).

The echo amplitude decays with time. This decay is faster than transverse relaxation, since dephasing of nuclei is accelerated by varying local fields at different places in the sample due to inhomogeneity of B0, and since diffusion of nuclei within the sample from one homogeneity range to another may take place. The echo amplitude /l,echo therefore does not decay as a simple exponential. Rather, the decay follows eq. (2.28), the term f(t) accounting for inhomogeneity and diffusion. 

Pulsed-field-gradient NMR (291-292), in which spin echoes are measured in the presence of a time-dependent magnetic field gradient, has been used to determine effective diffusion coefficients, Deff, in beds of zeolite powder. Barrer (35) quotes the expression for the spin-echo amplitude given by Karger (259) in the form ... 

Figure A1.3.4 Semi-log plot of Spin Echo amplitude with changing Hahn Echo experiment interval, x, for an oilseed containing excess moisture (therefore some is free) and oil. Extrapolation of the fitted lines (dashed) to x = 0 gives amplitudes for excess (free) moisture (Aw and oil A0 modified from Schmidt, 1991).

The methodology described in this procedure is limited to systems that do not contain free moisture. In cases when both oil and water signals are refocused after the second pulse (e.g., when free water is present), the spin-echo decay curve can be collected over varying x values. Log of the echo amplitudes versus x can be further analyzed to deconvolute the contribution of various components, in this example water and oil would result in a biexponential decay curve. Extrapolating each decay curve to X 0 gives the signals amplitudes due to the oil and the water fractions (A0 and Aw Fig. A1.3.4). 

The q-space imaging method, which deals with signals only after long diffusion times, discards all information relevant to dynamic aspects of water diffusion and transport, especially the restriction of water transport by membrane and cell wall permeability barriers in cellular tissues. This information is contained in the functional dependence of the pulsed gradient spin echo amplitude S(q,A,x) on the three independent variables q, A, and x (x is the 90-180 degree pulse spacing) [53]. As the tool to explore the q and A dependence of S(q,A,x), generalized diffusion times and their associated fractional populations are introduced and a multiple exponential time series expansion is used to analyze the dependence [53]. 

---