UT - Geometrical Echoes: Models and Experiments


 Two CIVA models will be to be compared between each other and with experiments; the Kirchhoff model and the new specular model.

In the case of the Kirchhoff model, the reflecting surface is discretized in simple surfaces. This model allows edge echoes and specular reflection calculations. However, diffraction echoes are not correctly taken into account. Geometrical echoes are calculated from the reciprocity principle on the specimen surface and backwall. To recap, the reciprocity principle consists of inverting the emitter and receiver role, in order to simplify the problem. The Kirchhoff model relies on a high frequency approximation valid for reflector dimensions greater than the wave length. The accuracy of this model decreases when the observation angle deviates from the specular direction.

In the case of the specular model, the geometrical echo calculation is based on the integration of the acoustic field directly based on the receiver, unlike to Kirchhoff model which uses the reciprocity principle. The field is then separately evaluated for each mode by the pencil method. For regularly reflecting and sufficiently large surfaces, the specular model provides simulation results more accurate than the Kirchhoff model. However, this model is not valid for reflectors smaller than the wavelength and doesn’t take into account diffraction effects on edges or irregularities smaller than the wavelength.


 The echoes measurements have been carried out on isotropic and homogeneous specimens made of ferritic steel. Uncertainties, due to mechanical parameters, due to machined defects on mock-ups and to material homogeneity, have been evaluated with results reproducibility verification of +/- 3 dB (1.5 dB due to the calibrated reflector measurement uncertainty and 1.5 dB due to the measurement uncertainty compared to the reference).

The following table summarizes all measurements, with probe characteristics and calibrations, as well as the type of echo measured and which parameters were varied.


F (MHz) Ø Crystal (mm) Mode Calibration water path (mm) Calibration reflector (Ø in mm) + its depth (mm) BE SE ME Parameters which vary
2 6.35 L(0°to 8°) 20 SDH  Ø2 ,28   X   Water path
L0° 20 SDH  Ø2 ,28     X

N°echo+Water path

2 12.7 L0° 50 SDH  Ø2, 20   X   Water path
2 19 L0° 50 SDH  Ø2, 28   X   Water path
    X N°echo+Water path
5 12.7 L(0° to 10°) 25 ES à 0°   X   Probe tilt/surface
10 linear(32 elts) L(0° to10°) 25 ou 50 ES à 0°   X   Probe tilt/surface
L(-10° to 10°) 25 ou 50 ES à 0° X X   Beam stearing
L0° 25 ou 50 ES à 0° X X   Focalization laws
1 60-focalized L(0° to10°) 290     X   Probe tilt/surface
3,5 matrix(9 elts) L0° 25 ES à 0°   X   Probe tilt/surface
3 linear(64 elts) L(-10° to10°) 25 TFP  Ø6, 150 X X   Beam stearing
L0° 25 TFP  Ø6, 150 X X   Focalization laws
L0° 25 TFP  Ø6, 150     X  

BE : backwall echo, SE : surface echo, ME : multiple echoes.


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