Inclusion in water - single element - 5 MHz probe

 

Probe parameters

The CIVA entry signal parameters for the 5 MHz probe have been determined in the same way as the 2.25 MHz probe.

The central frequency is the one given by the manufacturer:

• Central frequency = 5 MHz

The bandwidth and the phase are determined by adjustments of temporal shapes of measured and with COMPLETE_SOV simulated echoes of the Ø2 mm SDH located at 8 mm depth in the stell calibration block. The reference echo has been measured for a water path of 29 mm (Figure 35).

The entry signal bandwidth and phase also obtained are:

• Bandwidth =65%
• Phase = 290°

The attenuation in water has been taken into account, L waves attenuation coefficient values in water at the frequency 5 MHz entered in CIVA is:

• coeff_Attenuation = 0.005 dB/mm

This value from the literature has been validated by comparison with experimental and simulation results of the Ø2 mm SDH located at 8 mm depth echo obtained varying the water path.

The SOV and COMPLETE_SOV computations with consideration of the attenuation of 0.005 dB/mm at 5 MHz is in very good agreement with measures (Figure 36).

 

The reference in amplitude for the experiment/CIVA comparisons is the amplitude af the L0° specular echo of the Ø2 mm SDH located at 8 mm depth inspected at a water path of 29 mm (Figure 35). As the with SOV and COMPLETE_SOV simulated amplitudes of this echo are similar (Figure 37), the same value in point has been used as reference for both models.

 

Figures 38 and 39 show the field emitted by the probe in water after a CIVA beam computation. 

The maximal amplitude emitted by the probe on its axis is at a distance of 33.7 mm. The focal spot width at -3 dB is 1.9 mm at this distance (Figure 38). 

The Ø4 et 6 mm inclusions are also much greater than the focal spot (Figure 39). They are represented at the same scale of the cartography scale in order to show their dimensions relatively to the focal spot.

In the table below are recalled CIVA restrictions for inclusions echoes with the 5 MHz probe. Those restrictions have been suppressed in the framework of this study in a development version in order to calculate the echoes of the 4 inclusions with the 3 SOV, COMPLETE_SOV and SPECULAR models. In the commercial version of CIVA, configurations corresponding to the "no" boxes in the Table 7 cannot be calculated due to these bridles.

5MHZ	Ø 1mm	Ø 2mm	Ø 4mm	Ø 6mm
SOV	yes	no	no	no
COMPLETE_SOV	yes	no	no	no
SPECULAR	no	yes	yes	yes

 

experimental results

The experimental amplitude/distance echodynamic curves obtained for the 4 inclusions are presented on the Figure 40. On the top, the amplitudes are relative to a reference echo amplitudes (SDH); on the bottom, the amplitudes are normalized. It can be noted that:

• the maximal amplitude of the echoes increases by 5 to 6 dB when the inclusion diameter is doubled. An increae of 2.5 dB is measured between the  Ø4 et 6 mm inclusions. 
• the « d_max » distance at which the echo amplitude is maximal has been recorded on the amplitude/distance curves. It depends quite not on the inclusion diameter: d_max  varies from almost 32 mm to 34 mm (see following table).
• outside « d_max », the decreasing slope do not depend on the inclusion diameter.

The XY experimental curves obtained for the 4 inclusions at the experimental focal distances are presented on the Figure 4 (normalized amplitudes). The focal spot width do not depend on the inclusion diameter.

The shape of the specular echoes of   Ø1 to 6 mm inclusions located at the focal spot of 33.5 mm or in far fiels at 60 mm from the probe do not depend on the inclusions diameter (Figure 42). The echo arriving after the first contribution is even more far from the first echo than the inclusion diameter is great.

 

 

MEaSURE/CIVA comparisons

• Amplitude/distance curves

The comparisons of experimental and with  SOV-COMPLETE, SOV and SPECULAR models simulated amplitude/distance curves are presented Figure 43 ( Ø1 mm and  Ø2 mm inclusions) and Figure 44 (Ø4 mm and  Ø6 mm inclusions). 

 

 

The d_max  distance at which the amplitude/distance amplitude is maximal is indicated in the Table 8 for the measure and the 3 CIVA models.

Distance “D” of amp max (mm)	Simulated beam	Inclusion Ø1mm	Inclusion Ø2mm	Inclusion Ø4mm	Inclusion Ø6mm
	33.5
Measure		33.5	34	32.5	32
SOV		34	33	32.5	31.5
COMPLETE_SOV_BEAM		29	28.5	30.5	26.5
SPECULAR		28.5	28	28	28

Discrepancies between d_{maxEXPERIMENTAL}  and  d_maxCIVA  are indicated in the Table 9.

Δdistance of amp max ΔDsim/exp (mm)	Inclusion Ø1mm	Inclusion Ø2mm	Inclusion Ø4mm	Inclusion Ø6mm
SOV	+0.5	-1	0	-0.5
COMPLETE_SOV_BEAM	-4.5	-5.5	-2	-5.5
SPECULAR	-5.5	-6	-4.5	-4

• SOV Model : at small probe/inclusion distances, SOV predictions are not in agreement with the measure (particularly at distances smaller than d_max) and point out a SOV predictions instability. 

The « d_{max_SOV} » distance is very close to  d_{max_experimental}  for all inclusions.

d_{max_SOV}  depends on the inclusion diameter and varie by 31.5 to 34 mm (Table 8).  Discrepancies between d_{max_SOV}  and d_{max_experimental} are smaller than 1 mm (Table 9).

At great probe/inclusion distances, SOV model predictions are in agreement with the measure for the Ø1 mm and  Ø2 mm inclusions. They are not in agreement for the Ø4 mm and  Ø6 mm inclusions (overestimation reaching 2 dB for the Ø6 mm inclusion).

 

• COMPLETE_SOV model : small probe/inclusion distances, COMPLETE_SOV predictions are not in agreement with the measure: COMPLETE_SOV overestimates the amplitudes around d_max  for all inclusions (from 2 to 3 dB). 

The « d_{max_COMPLETE_SOV} » distance is far from d_{max_experimental}  for all inclusions. 

d_{max_COMPLETE_SOV}  depends on the inclusion diameter and varies by 26.5 to 30.5 mm (Table 8). The differences between d_{max_COMPLETE_SOV} and d_{max_experimental} are important: COMPLETE_SOV overestimates d_max of 2 to 5.5mm (Table 9).

At great probe/inclusion distances, simulations are close to the one obtained with the SOV model at great distances. Consequently, they are far from the measure for the Ø4 mm and  Ø6 mm inclusions (overestimation reaching 2 dB for the Ø6 mm inclusion). 

 

• SPECULAR model : it gives results close to COMPLETE_SOV model results, exceept for the Ø4 mm and  Ø6 mm inclusions amplitudes in far field which are well predicted by SPECULAR while COMPLETE_SOV overestimates them. 

The « d_{max_SPECULAR} » distance is far from d_{max_experimental}  for all inclusions.

d_{max_SPECULAR}  does not depend on the inclusions diameter and is 28 mm (Table 8).

Discrepancies between d_{max_ SPECULAR} and d_{max_experimental} are important: SPECULAR overestimates d_max from 4 to 6 mm (Table 9).

 

Those measure/simulations comparisons point out: 

• at small probe/inclusion distances, COMPLETE_SOV results are better than SOV results because COMPLETE_SOV eliminates some not valid approximations in the probe far field. However, as SOV results, they show important discrepancies with the measure. No error has been found and those observed discrepancies in far field have to be analyzed. It can be explained in part by the probe description and by the all models common hypothesis which considers that a probe surface vibration is « piston mode » like.   
• The SPECULAR model prediction are good for the Ø4 mm and  Ø6 mm inclusions echoes while both other models overestimate the amplitudes relatively to the measure. It is important to note that those SOV and COMPLETE_SOV bad predictions for the Ø4 mm and  Ø6 mm inclusions echoes validates the restriction that allows only SPECULAR model for both inclusions. 
• the bad predictions for  d_max  for COMPLETE_SOV and SPECULAR models  (discrepancies reaching 6 mm).

An example of experimental and with SOV, COMPLETE_SOV and SPECULAR simulated A-scans of inclusions echoes are represented on the Figures 45 and 46 for different distances between probe and inclusion. 

 

 

The specular echo is well predicted by the 3 models. The SOV and COMPLETE_SOV models also predict quite well the contribution coming after this echo when the probe/inclusion distance is great enough so that it is temporally separated from the specular echo. SPECULAR model does not simulate this contribution.

 

• Cartographies in the XY plane at the focal distance

The  « XY » experimental echodynamic curves extracted at the probe/inclusion distance of 34 mm (experimenal focal distance) are close to the one simulated with the 3 models almost 2 mm around their maximum (Figure 47). Beyond, the 3 models tends to under estimate the inclusions echoes amplitudes when they move away from the probe axis. 

Warning : those curves are normalized in ampitude (max amplitude = 0 dB) in order to compare the focal widths.

 

The focal spot width at -6 dB does almost not depend on the inclusion diameter, it is 2 mm according to the measure, value close to the one predicted by the 3 CIVA models.

Experimental  and  simulated (with SOV, COMPLETE_SOV and SPECULAR) A-scans of the 4 inclusions echoes are represented below. The inclusions are located at the experimental distance on the probe axis (A-scans at the left hand side of each figure) and at different increments (A-scans in the middle and at the right hand side). 

Those comparisons show that the 3 models predict similar echoes close to the measure exceept for the Ø6 mm inclusion and for the 6 mm shift (Figure 49, right hand side). COMPLETE_SOV and SPECULAR predictions are different from SOV predictions and are closer to the measure. This illustrates the contribution of the COMPLETE_SOV model relatively to SOV when the inclusion is shifted from the probe axis and that the «plane wave» approximation is not valid anymore.

The comparisons of the experimental and with  SPECULAR and KIRCHHOFF models simulated amplitude/distance curves (Figure 50) show a good agreement for the great water paths  (> 70 mm). Both models overestimate the amplitudes by less than 2 dB. For smaller water paths, the overestimation does not exceed 3 dB. 

As the amplitudes, the measured and simulated (with SPECULAR and KIRCHHOFF) A-scans are slightly different at the small water paths but become very close at great water paths (Figure 51).

Measured and simulated (with SPECULAR) A-scans have been represented on the Figure 52 in order to point out the good prediction of the phase evolution of the infinite plane echo when the probe/plane distance increases. It can also be seen on thoses figures that the A-scans predicted by the SPECULAR model have a lower frequency than the experimental A-scans.

 

Central frequency (fc) and bandwidth (BW) at -6 dB have been compared:

• measured and with SPECULAR and KIRCHHOFF spectra of the infinite plane placed at 33 mm (focal distance), 100 mm and 200 mm (far field) from the probe. Results are gathered in the Table 10.
•  measured and with SOV, COMPLETE_SOV and SPECULAR  Ø1 mm et Ø4 mm inclusions situated on the probe axis at 33.5 mm, 100 mm and 200 mm. The  Ø1 mm inclusion results are reported in Table 11.

Infinite plane
Distance probe/plane	33mm		100mm		200mm
	fc (MHz)	BW (MHz)	fc (MHz)	BW (MHz)	fc (MHz)	BW (MHz)
Measure	4.7	3.3	5	3.5	4.9	3.3
SPECULAR	4	3.1	4.3	3.2	4.3	3.2
KIRCHHOFF	4.9	3.2	4.9	3.2	4.8	2.9

 

Inclusion Ø4mm
Distance probe/inclusion	33mm		100mm		200mm
	fc (MHz)	BW (MHz)	fc (MHz)	BW (MHz)	fc (MHz)	BW (MHz)
Measure	4.5	2.8	5	3.25	4.9	3.2
SOV	4.9	3.1	4.9	3.3	4.8	3.2
SOV-COMPLETE-BEAM	4	2.7	4.8	3.2	4.7	3.2
SPECULAR	3.9	2.8	4.4	3.2	4.3	3.1

 

Regarding the central frequency, those comparisons show that:

• For the infinite plane: an underestimation at the central frequency of the infinite plane echoes spectra with SPECULAR model, while KIRCHHOFF model correctly predicts those frequencies.
• For the inclusions:
  • the central frequencies of SOV and COMPLETE_SOV models are the same at great distances. They generally are underestimated relatively to the experiment (max -0.5 MHz for the Ø1 mm non restricted inclusion in CIVA). On the other hand, at the focal distance 33 mm, COMPLETE_SOV predicts central frequencies lower than SOV (that can be seen on A-scans obtained with both models, figure 53) and that deviate from the measure.  
  • an underestimation of the central frequency of inclusions echoes spectra with SPECULAR model (as for the infinite plane)

Regarding the bandwith:

• the echoes bandwith slightly varies around 3 MHz with the reflector and the distance from the probe is well predicted by all models. 

 

We evaluated the effect of a variation of 0.25MHz (5% of the center frequency "fc" equal to 5 MHz used in previous simulations) on the results of simulations.

To understand this effect on the echoes of the inclusions and the infinite plane, the good agreement experiment / simulation for the reference echo (SDHØ2mm at 8mm depth inspected with a water height of 19mm) for the 3 frequencies ( 4.75MHz, 5MHz and 5.25MHz) has been verified. Indeed, it is essential to allow the comparison measurement / simulation for other reflectors.

Figure 54 shows that the reference A-scan echoes simulated at three frequencies are in accordance with the measurement (Figure 54).

 

 

The amplitude/distance curves simulated with SOV, COMPLETE_SOV and SPECULAR for the 3 frequencies have been plotted. Figure 55 shows the results for the Ø6mm inclusion. The reference for each curve amplitudes corresponds to the amplitude of the SDH echo at the same frequency.

 

We noticed that the central frequency variation leads to a variation of the amplitudes of the inclusions around the maximal amplitude (2dB max.) and leads to a variation of the probe/inclusion distance ( around 2 mm) where is measured the maximal amplitude. These variations can be considered as simulation uncertainties linked to the uncertainty on the value of the central frequency of the entry signal. 

 

For steel inclusions, at short distances probe / inclusion, all three models show results different from the experiments. Although COMPLETE_SOV makes fewer approximations than SOV in the near field, this is not enough to predict good amplitudes for inclusions located at small distances. Moreover discrepancies between measurement and COMPLETE_SOV for the maximum of the amplitude curves / distance position is very important. At large probe/inclusion distances,SOV and COMPLETE_SOV results are identical. They are consistent with the measurement for inclusions of 1 and 2 mm diameter but disagree for inclusions of Ø4m and Ø6mm which justifies the bridle currently present in CIVA (which allows for calculation of these inclusion echoes only the model SPECULAR). The center frequency spectrum of the inclusions echoes and of the infinite plane is generally underestimated by COMPLETE_SOV and SPECULAR models. The differences observed in this study are being analyzed.