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 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||
|2||12.7||L0°||50||SDH Ø2, 20||X||Water path|
|2||19||L0°||50||SDH Ø2, 28||X||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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