Method for characterizing the porosity of a plate by high-resolution ultrasonic scanning

Abstract

A method for characterizing the porosity of an aluminum alloy plate, comprising: applying a probe to the plate; activating an emitting transducer of the probe so that said transducer emits an incident ultrasonic wave towards the plate; detecting, by a sensing transducer of the probe, a detection signal representative of an ultrasonic wave reflected by the plate under the effect of the incident wave; repeating steps a) to c) by moving the emitting transducer and the emitting transducer along mesh points on the surface; from the detection signals detected at each step c), characterizing the porosity of the plate; the method being characterized in that at each step b), the acoustic wave is focused to a focal depth between 4 mm and 12 mm. Figure 1B.

Description

Title of the invention: Method for characterizing the porosity of a plate by high-resolution ultrasonic scanning. Technical field

[0001] The technical field of the invention is the characterization of the porosity of a metal plate, in particular an aluminum plate. EARLIER ART

[0002] Porosity is a criterion taken into account during the quality control of a metal plate intended for particular applications, for example aeronautics or construction.

[0003] Currently, porosity characterization is performed by applying a dye to the plate and forming an image of it. This technique is designated by the acronym DPI (Dye Penetrant Inspection Technique). Using such a technique requires the preparation of a plate whose dye-exposed surface is sufficiently smooth to allow for obtaining a usable image. This necessitates specific preparation involving mechanical and / or chemical polishing. Such preparation is time-consuming, especially since it must be carried out carefully so as not to damage the pores opening onto the dye-exposed surface. Furthermore, interpretation requires an experienced operator: the characterization result can be operator-dependent.High levels of dispersion were observed following inspection of the same plate by different operators. Another limitation is the inability to characterize closed pores that do not open onto the dye-receiving face.

[0004] Ultrasonic acoustic scanning is an attractive alternative. This technique is described in the publication by Mas Fanny et al., “Development of new laboratory-scale tests to optimize industrial thermo-mechanical processing of thick plate products: Application to AlCuLi alloys,” Proceedings of the 16th International Aluminium Alloys Conference 2018. It is a non-destructive technique, requiring no specific preparation, faster to implement, and offering good repeatability of measurements. Furthermore, acoustic scanning can be easily automated. It is therefore a less expensive and simpler method to implement.

[0005] Within the same plate, the shape and size of the pores are variable. Determining only the number of pores per unit area may be insufficient to characterize porosity. Indeed, other parameters must be taken into account, For example, size or shape. The inventors developed a method for characterizing a plate using ultrasound, allowing them to characterize porosity by taking into account various parameters. This results in a more refined characterization of porosity than a simple determination of pore density. Description of the invention

[0006] A first object of the invention is a method for characterizing the porosity of an aluminum alloy plate, delimited by a surface, the method comprising the steps: a. application of a probe facing the plate, the probe comprising at least one transducer configured to emit an ultrasonic wave incident towards the plate and / or to detect an ultrasonic wave reflected in the plate; b. activation of a transducer of the probe, called the emission transducer, so that the emission transducer emits an incident ultrasonic wave towards the plate; c. detection, by a transducer of the probe, called a detection transducer, of a detection signal representative of an ultrasonic wave reflected by the plate under the effect of the incident wave; d. repetition of steps a) to c) by moving the emitting transducer and the emitting transducer along the surface of the plate, according to a mesh defining several mesh points; e. from the detection signals detected at each step c), characterization of the porosity of the plate;

[0007] The process being characterized in that: - at each step b), the acoustic wave is focused, according to a focusing depth below the surface of the plate, so as to converge to a focusing depth, below the surface, and diverge from the focusing depth; - The depth of focus is between 4 mm and 12 mm.

[0008] Applying the probe to the plate does not imply that the plate is in contact with the probe. Generally, a layer of water extends between the probe and the plate.

[0009] The transmitting transducer and the detecting transducer can form a single transducer.

[0010] According to one possibility, step e) comprises: - ei) taking into account a minimum amplitude; - e-ii) selection of detection signals whose amplitude is greater than the minimum amplitude; - e-iü) determination of the presence of a defect when at least one detection signal, corresponding to a point of the mesh, is selected during sub-step e-ii).

[0011] Substep e-iii) may include a determination of the presence of a defect when at least two detection signals, corresponding to two adjacent mesh points, are selected during substep e-ii).

[0012] The process may include: - e-iv) calculation of a porosity density indicator, corresponding to a number of defects determined per unit area, at different points of the mesh; - ev) possibly determination of an overall porosity density indicator of the plate as a function of the porosity density indicators calculated during substep e-iv).

[0013] The process may include: - e-vi) taking into account a reference number, greater than 2; - e-vii) determination of the presence of a type 1 critical defect when the detection signals corresponding to a number of adjacent mesh points, greater than or equal to the reference number, are selected during substep e-ii); - e-viii) determination of a type 1 critical porosity indicator as a function of the number of type 1 critical defects resulting from sub-step e-vii).

[0014] Step e) may include: - e-ix) taking into account a critical amplitude; - ex) selection of detection signals whose amplitude is greater than the critical amplitude; - e-xi) determination of the presence of a critical defect of type 2 when at least one detection signal corresponding to a point of the mesh is selected during substep ex); - e-xii) determination of a type 2 critical porosity indicator as a function of the number of type 2 critical defects resulting from sub-step e-xi).

[0015] The substep e-xi) may include a determination of the presence of a type 2 critical defect when at least two detection signals, corresponding to two adjacent mesh points, are selected during the substep ex).

[0016] The method may include determining the conformity of the part based on: - porosity density indicators resulting from substep e-iv) or from the overall porosity density indicator resulting from substep ev); - and / or the type 1 critical porosity indicator resulting from substep e-viii); - and / or the type 2 critical porosity indicator resulting from substep e-xii).

[0017] The critical amplitude, taken into account during step e-ix) is generally greater than the minimum amplitude taken into account during step ei).

[0018] The diameter of the transducer can be between 100 pm and 500 pm.

[0019] The frequency of the incident wave can be between 10 MHz and 20 MHz.

[0020] The depth of focus can be between 4 and 8 mm, and preferably between 5 and 7 mm.

[0021] The mesh is preferably two-dimensional.

[0022] Another object of the invention is an ultrasonic probe, comprising at least one transducer, configured to emit an ultrasonic wave focused towards an object and / or to detect an ultrasonic wave reflected by the object, the probe being connected to a processing unit, the processing unit being configured to implement: • steps ei) to e-iv) or ei) to ev) of the process according to the first object of the invention; • and / or steps e-vi) to e-viii) of a process according to the first object of the invention; • and / or steps e-ix) to e-xii) of a process according to the first object of the invention.

[0023] The invention will be better understood upon reading the description of the exemplary embodiments presented later in this description, in connection with the figures listed below. FIGURES

[0024] Fig. 1A schematically represents an ultrasonic acoustic transducer emitting an acoustic wave in water.

[0025] Fig. 1B shows the transducer positioned opposite a plate to be controlled, with a layer of water remaining between the plate and the transducer.

[0026] Figure 2 schematically illustrates the main steps in implementing a process for characterizing the porosity of a plate.

[0027] Fig. 3 represents a performance of defect detection by the process described in relation to Fig. 2.

[0028] Fig. 4 combines figures 4A, 4B, and 4C. Figure 4A shows a spatial distribution of the intensity of reflected waves in a plane parallel to the thickness of a plate. Figure 4B shows a type 2 critical defect. Figure 4C shows a type 1 critical defect.

[0029] Fig. 5 shows a spatial distribution of the intensity of reflected waves in a plane parallel to the thickness of a plate.

[0030] [Fig.6] is identical to [Fig.5]. A unit area of ​​1 inch x 1 inch has been identified.

[0031] The [Fig.7] shows an identification of critical defects of type 1 and type 2 on the spatial distribution of the [Fig.5].

[0032] Figures 8A and 8B are a comparison between a prior art method (DPI) ([Fig.8A]) and the method of the object of the invention ([Fig.8B]) in terms of dispersion of measurements. PRESENTATION OF SPECIFIC IMPLEMENTATION METHODS

[0033] Figure 1A represents an ultrasonic probe 1, intended for inspecting an object, for example a metallic part such as an aluminum plate. This could, for example, be a plate made of a 2XXX or 7XXX type alloy. The ultrasonic probe includes a transducer 2, configured to emit and receive an ultrasonic acoustic wave. In this example, the transducer acts as both a transmitting and receiving transducer. Alternatively, the probe includes separate transmitting and receiving transducers.

[0034] The transducer 2 is a spherically focused transducer, which is a preferred embodiment. It is configured to focus the acoustic wave at a focal distance from the emitting transducer. In [Fig. 1A], the spherically focused transducer is shown immersed in water 6. The acoustic wave is focused at a point, at a focal distance Fo from the transducer 2. The focal length Fo can, for example, be 50 mm. This is a focal length in water.

[0035] Other types of focusing are conceivable, for example cylindrical focusing, according to which the acoustic wave is focused along a line.

[0036] In [Fig. IB], the transducer is shown immersed in water 6 and extending to a distance d = 25 mm from an aluminum alloy plate 10 to be inspected. Due to the differences in acoustic properties between water and the aluminum alloy, the acoustic wave is focused at a focal depth F of 6 mm below the surface S delimiting the plate 10. At the focal depth F, the spatial extent of the ultrasonic wave emitted by the transducer is minimal. Preferably, the focal depth below the surface of the plate is between 4 and 12 mm, and more preferably between 4 and 8 mm, and even more preferably between 5 and 7 mm. Around the focal depth, the acoustic beam forms a focused zone 4, which extends over a width of approximately 2 mm parallel to the thickness of the The plate is positioned parallel to a Z-axis perpendicular to the plate's surface. The acoustic wave converges to the focal zone and then diverges beyond it. The focal zone is defined as a layer extending on either side of the focal length, within which the beam is considered sufficiently focused. Regardless of the transducer used, the distance between the transducer and the plate in the water is arranged to achieve the previously described depth of focus.

[0037] The transducer is, for example, a piezoelectric material pellet with a diameter D of 0.5 inch and emitting an acoustic wave at a frequency of 15 MHz. Generally, the frequency of the emitted acoustic wave is preferably between 10 MHz and 20 MHz.

[0038] When the part has a defect 11, or another interface, a portion of the incident acoustic wave is reflected, forming a reflected acoustic wave. The reflected acoustic wave is detected by the transducer. The characteristics of the reflected wave, in particular the time of flight between the emission of the incident wave and the detection of the reflected wave, make it possible to locate, in depth, the defect or, more generally, the interface that gave rise to the formation of the reflected wave. The intensity of the reflected wave can also be used to characterize the defect, as described below.

[0039] As previously stated, a quality indicator of aluminium plates is a level of porosity, the latter being subject to specifications.

[0040] The first few millimeters below surface S constitute a dead zone 13, which is difficult to characterize using an ultrasonic modality. This dead zone is conducive to the formation of spurious echoes that interfere with the interpretation of the measured signal. Therefore, it is considered suboptimal for the focused zone 4 of the ultrasonic wave to be less than 4 or 5 mm from the surface S of the plate. Advantageously, the depth of focus extends between 4 and 8 mm from the surface S of the plate, and preferably between 5 mm and 7 mm from the surface S. The depth of focus is advantageously determined to be as close as possible to the dead zone, so as to limit the attenuation of the ultrasonic beam within the plate, between the dead zone and the focused zone 4.

[0041] The diameter of the ultrasonic beam, at the focal distance F, is preferably between 100 pm and 500 pm. The diameter of the ultrasonic beam defines the minimum size of a defect to be characterized. By "minimum," we mean here a hollow inclusion 11, forming the porosity. Using a smaller diameter reduces the minimum size of a defect to be characterized. The diameter of the ultrasonic beam determines the thickness of the focused zone 4: a diameter between 100 pm and 500 pm allows us to obtain a focused zone thickness of approximately 2 mm.

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[0049] If the focal length is chosen to be 6 mm, this allows the detection of defects in a focused area 4 extending between 5 and 7 mm below the surface S. A shorter beam diameter reduces the thickness of the focal area: this reduces the number of defects that can be detected. Generally speaking, the frequency of the ultrasonic wave is between 10 MHz and 20 MHz. The transducer is moved along mesh points defined by a spatial mesh, preferably two-dimensional and regular, established on the surface S. The step between two adjacent mesh points is determined as a function of the beam radius in the focusing zone. For example, it could be the radius multiplied by 2. This allows sufficient overlap between two adjacent measurements. In addition to a With an appropriate focal zone thickness, a beam size between 100 pm and 500 pm allows for a reasonable number of mesh points. This achieves a compromise between accuracy (minimum defect size to be observed) and measurement speed, i.e., the transducer's scanning time across all mesh points. The transducer 2 is connected to a processing unit 5, programmed to receive the transducer's detection signal and perform processing operations to establish porosity indicators as described below. The processing unit is, for example, a microprocessor connected to a memory containing instructions for implementing these processing operations. The processing unit is configured to select the detection signals detected within a predefined time gate, corresponding to the focused area, i.e., on the order of 1 mm on either side of the depth of focus. Figure 2 illustrates the main steps of a process for characterizing the porosity of a plate. In step 100, the transducer is positioned facing the surface S of the plate, with a layer of water interposed between the plate and the transducer. In step 110, the transducer is scanned to cover the various points of the mesh. Each point of the mesh corresponds to a measurement point. The detection signals from the transducer are transmitted to the processing unit 5, which determines the intensity of the reflected wave at each mesh point. The processing unit 5 is also programmed to implement the steps described below. In step 120, the measurements are interpreted to determine the presence of a defect at each mesh point. Measurement parameters are associated with each mesh point, for example, the signal amplitude. detected, which translates the amplitude of the reflected acoustic wave. A spatial distribution of the reflected wave intensity at each measurement point can thus be obtained. Such a spatial distribution is illustrated in Figures 4A, 5, 6, and 7.

[0050] During step 130, a minimum amplitude of the detection signal is taken into account. The minimum amplitude can be predefined, for example, during a calibration phase. Calibration consists of establishing the minimum amplitude using a representative part of the part being examined, and containing defects of known dimensions. In [Fig. 2], calibration corresponds to phase 90. For example, calibration consists of determining a nominal amplitude, corresponding to a nominal defect of known dimensions. The minimum amplitude is then determined as a function of the nominal amplitude. It could, for example, be 20% of the nominal amplitude.

[0051] According to one possibility, the minimum amplitude is established from a statistical distribution of the amplitudes of the detected signals: it may, for example, be a fractile, for example the 20% fractile or an amplitude greater than a certain percentage of the maximum amplitude of the detection signals detected during the calibration phase.

[0052] During a step 131, detection signals are selected whose amplitude is greater than the minimum amplitude taken into account during step 130.

[0053] During a step 132, when at least one detection signal or at least two detection signals, respectively obtained on at least one mesh point or at least two adjacent mesh points, have an amplitude greater than the minimum amplitude, the presence of a defect is established at said mesh points.

[0054] In step 133, a porosity density indicator is established, corresponding to the number of defects identified in step 132 for a predetermined area, for example, 1 inch by 1 inch. The porosity density indicator can be established in different contiguous areas of the plate. The porosity density indicator constitutes a first quality criterion for the plate. An overall porosity density indicator can be established for the entire plate: this is, for example, the maximum porosity indicator measured in different areas or an average of porosity indicators obtained in different areas of the plate.

[0055] In step 140, a predetermined reference number is taken into account. The reference number may, for example, be 16. Among the defects identified in step 132, those extending along a number of adjacent mesh points greater than or equal to the reference number are selected. These defects correspond to type 1 critical defects. This corresponds to detection signals measured on at least 16 adjacent mesh points, the intensity of which exceeds the minimum amplitude considered in step 130. A critical defect of type 1 thus corresponds to a defect extending continuously over at least 16 adjacent mesh points. Spatially extensive defects are addressed here.

[0056] In step 141, a type 1 critical porosity indicator is established, corresponding to the number of type 1 critical defects identified in step 140 for a predetermined area, for example, 1 inch by 1 inch. The type 1 critical porosity indicator can be established in different contiguous areas of the plate. The type 1 critical porosity indicator constitutes a second plate quality criterion.

[0057] During step 150, a critical amplitude, representative of the presence of a critical defect, is taken into account. The critical amplitude can be predefined during the calibration phase 90. Calibration consists of establishing the critical amplitude from a representative part of the part being examined, and containing defects whose dimensions are known and considered critical. The critical amplitude is then determined as a function of the nominal amplitude described previously. For example, it could be 80% of the nominal amplitude.

[0058] According to one possibility, the critical amplitude is established from a statistical distribution of the amplitudes of the detected signals: it may, for example, be a fractile, for example the 80% fractile or an amplitude greater than a certain percentage, for example 80%, of the maximum amplitude of the detection signals detected during the calibration phase.

[0059] During a step 151, among the detection signals, those whose amplitude is greater than the critical amplitude are selected.

[0060] During step 152, when at least one detection signal obtained at a measurement point of a defect has an amplitude greater than the critical amplitude, the presence of a type 2 critical defect is established at said measurement points. According to one possibility, a type 2 critical defect corresponds to two detection signals, obtained respectively at two adjacent measurement points, having an amplitude greater than the critical amplitude.

[0061] In step 153, a type 2 critical porosity indicator is established, corresponding to the number of defects identified in step 152 for a predetermined area, for example, 1 inch by 1 inch. The type 2 critical porosity indicator can be established in different contiguous areas of the plate. A type 2 critical defect thus corresponds to a particularly echogenic defect under the effect of a sudden change in acoustic impedance. The type 2 critical porosity indicator constitutes a third quality criterion for the plate.

[0062] During step 160, a conformity level of the part is determined, based on at least one of the previously defined indicators: - Porosity density indicator resulting from step 133 or overall porosity density indicator; - Critical porosity indicator type 1 resulting from step 141; - Type 2 critical porosity indicator resulting from step 153.

[0063] The level of compliance can combine these indicators. It can also be a vector, where each term corresponds to one of the indicators listed above.

[0064] The level of conformity can then be compared to a previously established reference conformity level, which defines the acceptable values ​​for each indicator. Based on the comparison, part 10 is declared compliant or non-compliant. The comparison is not necessarily performed by the processing unit. It can be performed by an operator.

[0065] According to one possibility, the conformity level can allow the part to be assigned to a specific use among various existing uses, each use being associated with an acceptance standard. Several conformity levels can be defined, each corresponding to a specific use. The part is then directed to the use for which it meets the required conformity level.

[0066] According to one variant, the process involves determining only one or two criteria from among the three previously defined criteria. In other words, the process may not involve determining the three porosity criteria defined in steps 133, 141, and 153, respectively.

[0067] A test was carried out according to the following experimental parameters: - Transducer: Diameter 0.5 inches - frequency 15 MHz - underwater focal length of 2 inches. - Water path (water thickness, or water column): 25.2 mm; - Notch between each measurement: 0.28 mm; - Tested part: sample of a 7040 type aluminum alloy plate after rolling; - Time gate fixed so as to analyze signals reflected from a depth between 5 mm and 7 mm.

[0068] The sample examined was analyzed by a reference method, X-ray tomography, to obtain a three-dimensional characterization of the pores. The spatial resolution of the reference method is 30 pm. It was found that 95% of the pores detected by tomography were also detected by ultrasonic testing. Figure 3 shows the number of pores detected as a function of depth.

[0069] The x-axis represents the depth within the plate. The y-axis quantifies the correct detection of a pore: the value is 1 when a pore is detected (true positive) and 0 when a pore is not detected even though it is detected by the reference method (false negative). The ratio of correctly detected pores is 95%.

[0070] Figure 4A shows a cross-sectional view of the plate in an XZ plane parallel to the plate thickness, where Z corresponds to the plate thickness. This represents a spatial distribution of the intensity of detection signals in the cross-sectional plane. Each point corresponds to a pore. The pores are identified in the area corresponding to a plate thickness between 5 mm and 7 mm. Figure 4B is a detail of a type 2 critical pore: an intense reflected signal on at least two adjacent points (i.e., 2 image pixels). Figure 4C is a detail of a type 1 critical pore: a spatially extended pore, on at least 16 adjacent points (i.e., 16 image pixels). The gray level corresponds to the intensity of the reflected signal.

[0071] Fig. 5 shows an example of characterization of another plate which has been degraded in such a way as to increase porosity.

[0072] Figure 6 shows the plate pictured in Figure 5. In Figure 6, a frame has been drawn outlining a unit area of ​​1 inch by 1 inch. There are 43 defects in the unit area. This corresponds to the porosity density indicator defined in connection with step 133.

[0073] Figure 7 shows another example of the characterization of the plate pictured in Figure 5. In Figure 7, critical type 1 and critical type 2 defects are highlighted. There are 21 critical type 1 defects and 37 critical type 2 defects.

[0074] Comparative tests were carried out on a sample A and a sample B made of aluminum alloy. Each sample was characterized several times by ultrasound and by DPI at 6 different depths. For each sample, the standard deviation of the measurements was determined.

[0075] Figure 8A is a graphical representation of the intervals (intervalplot) of measurements performed on samples A and B by DPI. In each figure, the y-axis corresponds to the maximum number of defects identified on a 1-inch by 1-inch area. A 95% confidence interval is also shown. Figure 8B is a similar representation considering measurements performed by ultrasound. It can be observed that the measurements are less dispersed using the ultrasonic testing method. On each plate, the number of defects detected by ultrasonic testing is greater than the number of defects detected by DPI. This is because the ultrasonic testing method addresses a volume extending on either side of the depth of focus, unlike the DPI method, which addresses a surface.

[0076] The invention can be implemented for the inspection of metal parts, particularly plates, to verify their conformity with acceptability specifications. In addition to rapid and non-invasive implementation, the invention allows to establish categories of defects, for example critical defects of type 1 and critical defects of type 2, which is not permitted by the prior art DPI method.

Claims

1. Demands Method for characterizing the porosity of an aluminum alloy plate, delimited by a surface, the method comprising the following steps: a. application of a probe (1) facing the plate (10), the probe comprising at least one transducer (2) configured to emit an ultrasonic wave incident towards the plate and to detect an ultrasonic wave reflected in the plate; b. activation of a transducer of the probe, called the emission transducer (2), so that the emission transducer emits an incident ultrasonic wave towards the plate; c. detection, by a transducer of the probe, called the detection transducer (2), of a detection signal representative of an ultrasonic wave reflected by the plate under the effect of the incident wave; d. repetition of steps a) to c) by moving the emitting transducer (2) and the detecting transducer (2) along the surface of the plate, according to a mesh defining several mesh points; e. from the detection signals detected at each step c), characterization of the porosity of the plate (10); - at each step b), the acoustic wave is focused (4), according to a depth of focus below the surface of the plate, so as to converge to a depth of focus, below the surface, and diverge from the depth of focus; - The focusing depth is between 4 mm and 12 mm - in which the transmitting transducer and the detecting transducer form a single transducer, the process being characterized in that: and in which step e) comprises: - ei) consideration of a minimum amplitude; - e-ii) selection of detection signals whose amplitude is greater than the minimum amplitude; - e-iii) determination of the presence of a defect (11) when at least one detection signal, corresponding to a point on the mesh, is selected during substep e-ii), and in which substep e-iii) includes a determination of the presence of a defect when at least two detection signals, corresponding to two adjacent mesh points, are selected during substep e-ii). - e-iv) at different points on the mesh, calculation of a porosity density indicator, corresponding to a number of defects determined per unit area; - ev) optionally determination of an overall porosity density indicator of the plate as a function of the porosity density indicators calculated during substep e-iv).

2. A method according to claim 1, comprising: - e-vi) taking into account a reference number, greater than 2; - e-vii) determining the presence of a type 1 critical defect when the detection signals corresponding to a number of adjacent mesh points, greater than or equal to the reference number, are selected during substep e-ii); - e-viii) determining a type 1 critical porosity indicator as a function of the number of type 1 critical defects resulting from substep e-vii).

3. A method according to any one of the preceding claims, wherein step e) comprises: - e-ix) consideration of a critical amplitude; - ex) selection of detection signals whose amplitude is greater than the critical amplitude; - e-xi) determination of the presence of a type 2 critical defect when at least one detection signal corresponding to a point of the mesh is selected during substep ex); - e-xii) determination of a type 2 critical porosity indicator as a function of the number of type 2 critical defects resulting from substep e-xi).

4. A method according to claim 3, wherein substep e-xi) comprises a determination of the presence of a type 2 critical defect when at least two detection signals, corresponding to two adjacent mesh points, are selected during substep ex).

5. A method according to claims 1 and 2 and (3 or 4), comprising determining the conformity of the part based on: - the porosity density indicators resulting from substep e-iv) or the overall porosity density indicator resulting from substep ev); - and / or the type 1 critical porosity indicator resulting from substep e-viii); - and / or the type 2 critical porosity indicator resulting from substep e-xii).

6. A method according to any one of claims 3 or 4, wherein the critical amplitude, taken into account in step e-ix) is greater than the minimum amplitude taken into account in step e-

7. IJ- Method according to any one of the preceding claims, wherein the diameter of the transducer is between 100 pm and 500 pm.

8. A method according to any one of the preceding claims, wherein the frequency of the incident wave is between 10 MHz and 20 MHz.

9. A method according to any one of the preceding claims, wherein the depth of focus is between 4 and 8 mm, and more preferably between 5 and 7 mm.

10. A method according to any one of the preceding claims, wherein the mesh is two-dimensional.

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