DEVICE AND METHOD FOR NON-DESTRUCTIVE TESTING OF A TEST PERSON USING ULTRASOUND ACCORDING TO DGS METHOD

Description

[0001] The subject matter of the present invention is a device and a method for the non-destructive testing of a test object by means of ultrasound, the device, or the method, being configured for characterizing flaws or discontinuities in the material of a test object in accordance with the DGS method. In particular, the device, or the method, is provided for characterizing a flaw or a discontinuity in the test object material that are located within the near field of an ultrasonic transducer used for generating the ultrasound.

[0002] US 2013 / 0291640 A1 discloses an ultrasonic inspection system to scan for discontinuities in thick solid objects. Discontinuity size and position is correlated with an equivalent reflector size by the DGS method. US 5 511 425 A discloses a flaw detector incorporating DGS. US 2011 / 016979 A1 discloses non destructive testing. CERTO et al: "DGS curve evaluation applied to ultrasonic phased array testing", (NON-DESTRUCTIVE TESTING AND CONDITION MONITORING), BRITISH INSTITUTE OF NON-DESTR. TEST., NORTHAMPTON, gb, vol.52, no. 4, 1 April 2010, pages 192-194 discloses a phased array for ultrasonic testing of an object by applying DGS curve evaluation; in order to avoid the overestimation of a defect detected in the near-field region, said region is re-examined using fewer active elements in order to reposition the defect in the far-field of the inspection probe.

[0003] The so-called DGS method (DGS = distance, gain, size) was developed in Europe in the late fifties of the 20th century. It is a method for the quantitative assessment of flaws or discontinuities in the material of a test object and is based on a comparison of the echo indication stemming from a flaw or a discontinuity with the amplitude of a reference reflector irradiated with sound in a defined manner. In practical use, a circular disk reflector is used which is perpendicularly irradiated with sound. Within the context of the DGS method, a detected flaw or a detected discontinuity is thus quantitatively characterized by means of a comparison with the size of a circular disk reflector that supplies a flaw indication with an equivalent echo amplitude. The size of such a circular disk reflector is referred to as the "equivalent reflector size" (ERS) of the flaw / discontinuity to be characterized. Theoretically, other reference reflectors, e.g. cross bores, can be used in the work. However, this is unusual.

[0004] Even if the flaw sizes / ERS values determined by means of the DGS method are comparable only under strict conditions with the actual flaw size or the size of a discontinuity, as it can be determined by destructive testing, for example, it was nevertheless introduced into a variety of testing standards, such as the European testing standard EN 583-2:2001.

[0005] If one considers the sound field generated by a, for example, circular plane ultrasonic transducer, one finds that a plurality of consecutive maxima of the sound pressure form along the acoustic axis adjacent to the ultrasonic transducer surface. The distance of the last sound pressure maximum on the acoustic axis from the ultrasonic transducer is referred to as the near-field length N, the sound field between the ultrasonic transducer and the near-field length is referred to as the near field, and the adjacent sound field as the far field. In the context of theoretical considerations and practical tests, it was found that the echo amplitude in the far field of a circular disk reflector irradiated with sound perpendicularly characteristically decreases with a rising distance between the ultrasonic transducer and the circular disk reflector. If, for a given, for example circular, ultrasonic transducer with a given transducer diameter and transmission frequency, the curve of the echo amplitude of the respective gain factor f, which is required to bring the echo indication of the circular disk reflector to the level of a reference echo, is plotted for a plurality of circular disk reflectors of different diameters as a function of the distance between the circular disk reflector and the ultrasonic transducer, a host of curves is obtained which is referred to as DGS diagrams. Such a DGS diagram, which has been taken from DEN 583:2-2001, is shown in Figure 1 by way of example. In practice, it was found that experimentally determined echo amplitudes on circular disk reflectors follow the theoretically predicted curves with good accuracy in the DGS diagram, provided the distance between the ultrasonic transducer and the circular disk reflector is at least 70% of the near-field length N of the ultrasonic transducer used for ultrasound generation. Consequently, the above-mentioned European testing standard EN 583-2:2001 also prescribes that in the context of the DGS method, the aforementioned condition is mandatorily required to be observed. In practice, this means that it is obligatory that test probes with a small near-field length must be used for testing near-surface regions. However, this constitutes a limitation with regard to the transmission frequency of the test probe used or of the dimensions of the ultrasonic transducer used in the test probe for ultrasound generation. Depending on the testing task to be solved, they can be disadvantageous because, for example, different ultrasound frequencies experience different levels of sound attenuation in the material of the test object to be inspected. Moreover, the geometric dimensions of the ultrasonic transducer used for ultrasound generation determine both the divergence of the sound field generated and the maximum obtainable sound pressures.

[0006] As a result, a plurality of different ultrasonic test probes with different transmission frequencies and transducer dimensions generally have to be kept in store for a comprehensive ultrasonic testing of a test object.

[0007] It is therefore the object of the invention to propose a device and a method that avoid the aforementioned drawbacks. In particular, the device, or the method, is supposed to be suitable for the non-destructive testing of a test object by means of ultrasound, the device being configured for characterizing flaws or discontinuities in the material of the test object in accordance with the DGS method, which are located in the near field of an ultrasonic transducer used for generating the ultrasound.

[0008] This object is achieved by a device according to claim 1 and by a method according to claim 8. The subclaims following the independent claims constitute advantageous developments of the invention.

[0009] A device according to the invention comprises an ultrasonic test probe with an ultrasonic transducer for generating and coupling an ultrasonic field into the test object and, if necessary, for recording resulting echo signals from the test object. Preferably, the technique used is the pulse echo technique, i.e. the echo signals are recorded at the coupling location. In this technique, one and the same test probe is generally used both for generating and coupling the ultrasonic pulses into the test object as well as for recording the echo signals, i.e. of the ultrasonic pulses reflected in the test object. In principle, however, transsonification can also be used in the operation, i.e. separate test probes are used for generating and coupling the ultrasonic pulses into the test object as well as for recording the echo signals, i.e. the signals that have passed through the test object and were reflected in the process on a flaw or discontinuity. In that case, the device would comprise a second ultrasound-receiving test probe configured in a manner comparable to the first ultrasound transmitting test probe and adapted to receive the echo signals from the test object.

[0010] Furthermore, the device comprises a control unit for controlling the ultrasound transmitting test probe in such a way that the latter generates ultrasonic pulses with a certain bandwidth B. Furthermore, the device comprises a receiving unit for recording echo signals by means of the ultrasonic test probe from the test object, wherein in this case, if necessary, a receiving test probe with preferably identical ultrasonic properties can be used, which is formed separate from the transmitting test probe. Finally, the device comprises an evaluation unit connected to the receiving unit. The evaluation unit is configured for processing the echo signals from the test object recorded by the receiving unit.

[0011] According to the invention, the evaluation unit is now configured to determine, from echo signals recorded from the test object and caused by flaws or discontinuities in the test object material, an equivalent reflector size ERS of the echo-generating flaw or the echo-generating discontinuity in accordance with the DGS method. In this case, the basis of the determination of the equivalent reflector size is a DGS diagram that depends on the bandwidth B of the insonified ultrasonic pulses.

[0012] The bandwidth-dependent DGS diagram to be used according to the invention, which includes the course of the echo amplitude of a circular disk reflector or of an equivalent size as a function of the distance between the ultrasonic transducer and the circular disk reflector for a plurality of circular disk reflectors of different diameters, can in this case both be experimentally determined prior to the measurement, as well as be based on theoretical considerations. In particular, a method will be outlined below with which the course of the echo amplitude of an equivalent size of a circular disk reflector can be calculated as a function of the distance between the reflector and the transducer. Within the context of the present invention, "DGS diagram" is supposed to denote both the above-mentioned host of curves, which includes a plurality of curves for the echo amplitudes or an equivalent size of circular disk reflectors of different diameters as a function of their distance from the transmitting transducer, and a suitable mathematical representation of such a host of curves, for example in the form of an analytic function that comprises the diameter of the circular disk reflector as a parameter. Such a mathematical representation may also consist of a table into which the results of a numerical calculation of the course of the echo amplitude as a function of the distance between the transmitting transducer and the circular disk reflector have been entered for a plurality of different reflector diameters.

[0013] In a particularly preferred embodiment of the device according to the invention, the device according to the invention, and thus generally the entirety consisting of the ultrasonic test probe and the control unit, is configured to generate a sound field that is rotationally symmetric in the test object. Corresponding, in particular obliquely insonifying, ultrasonic test probes are known from WO 2010 / 130819 A1 by the applicant. From this application, in particular, the manner is apparent in which manner a single-part transmitting transducer of an obliquely insonifying ultrasonic test probe has to be designed in order to generate a sound field that is rotationally symmetric in the test object. For most testing tasks using the pulse echo technique, an oblique insonification is desirable or even required. Within the context of the present invention, a sound field that is rotationally symmetric in the test object permits a simplified calculation of the material-specific or transmitting transducer-specific DGS diagram. It is also clear from WO 2010 / 130819 A1 that it is possible to generate a sound field that is rotationally symmetric in the test object also by means of phased array technique. For this purpose, selected transducers of a two-dimensional plane array, for example, are controlled by individually controllable transducer in a phase-accurate manner. In that case, the control unit is to be configured to be suitable for this purpose. Both options mentioned herein for generating a sound field that is rotationally symmetric in the test object are part of the subject matter of the present invention.

[0014] Within the context of intensive theoretical analyses and practical tests, it was also found that the use of pulsed sound results in differences in the DGS diagram depending on the polarization of the ultrasonic pulse in the test object. In a preferred embodiment, the DGS diagram provided in the device according to the invention takes into account the polarization of the testing pulses in the test object material. However, it was also found that in many cases of practical application, the differences in the DGS diagrams for the different polarization directions are so slight that they practically cannot be resolved any more experimentally. Therefore, in a simplified embodiment, a uniform DGS diagram can be used for both polarization directions.

[0015] In another preferred embodiment, the control unit of the device according to the invention is configured, in order to determine the equivalent reflector size of a detected flaw or detected discontinuity, to carry out a method during which the echo amplitude of a reference reflector is recorded on a test body. In the process, the reference reflector is situated at the distance d ref from the test probe. As a rule, the back-face echo of a test body with a circular-arc shaped back face is used (so-called test body No. 1). In that case, the so-called amplitude correction, which allows for the fact that the reflecting surface is not plane, but curved, and thus has a focusing or defocusing effect, has to be taken into account in the determination of the echo height of the back-face echo. However, it is also conceivable that alternative reference reflectors are used, e.g. the bottom of a circular bore. Using the echo amplitude thus determined, the theoretical DGS curve specific to the reference reflector, that is, usually the back-face echo curve, can be shifted in the DGS diagram in the y-direction in such a way that the detected reference echo comes to lie on the shifted DGS curve.

[0016] In order to determine the ERS value of a detected flaw or a detected discontinuity situated at a certain distance d Fehler from the test probe, the gain factor G ref is determined which must be adjusted in order to adjust the echo amplitude of the reference echo to a certain value, typically 80%, of the maximum indication height.

[0017] In the next step, the gain factor G Fehler is determined, which is required to adjust the echo amplitude of the flaw to the same value as the reference echo, that is, e.g. 80% of the indication height. Then, the difference ΔG of the two gain values is plotted into the DGS diagram, at the position of the reference echo d ref , in the y-direction downwards, that is, ΔG = G Fehler - G ref . In the next step, the difference Δd of the distances d ref and d Fehler is plotted towards the left in the x-direction, i.e. Δd = d ref - d Fehler . Then, the resulting end point lies on the DGS curve of the circular disk reflector that would generate an echo signal of the same height. This method is schematically illustrated in Fig. 2.

[0018] By identifying the DGS curve characterized by the diameter D of the circular disk reflector, on which the end point as described above comes to lie, the ERS value of the detected flaw is then determined. On the one hand, this may take place by selecting the DGS curve stored in the evaluation unit that has the smallest deviation in the y-direction from the determined end point. However, this may also take place by a suitable interpolation between the DGS curves stored in the evaluation unit. If the general DGS curve for the selected type of reference reflector is provided in the evaluation unit in the form of a function that depends on the characteristic size of the selected reference reflector, e.g. on the diameter D of a circular disk reflector, the characteristic size of the reference reflector can be determined with this by calculation.

[0019] Within the context of the present invention, this functionality can advantageously be applied to the automatic determination of the equivalent reflector size ERS of a flaw or discontinuity located in the near field of the test probe used for the ultrasound inspection. The automatic determination of the parameter P results in an increased reproducibility and objectivity of the test result.

[0020] It was also found in the context of the theoretical or practical testing of the present invention that the DGS diagram of a given transmitting transducer in a given material not only takes a particularly simple form if the sound field coupled into the test object by the transmitting transducer is rotationally symmetric in the test object, but if, in addition, the condition is satisfied that the dimensions of the ultrasonic transmitting transducer are large compared with the diameter of a circular disk reflector whose distance-dependent echo signal is to be calculated. As can be gathered from WO 2010 / 130819 A1 by the applicant, a rotationally symmetric sound field can be generated in the test object in the case of an oblique insonification if the transmitting transducer has an approximately elliptic shape. In the context of the present invention, the diameter D of the transmitting transducer can in such a case be assumed to be the diameter of a circular transmitting transducer of the same surface area.

[0021] This assumption has been found in practice to be sustainable, which is presumably due to the fact that the sound power of ultrasonic transducers with a different shape, but otherwise identical surface area, is identical. The theoretically calculated echo signal has deviates slightly from experimentally determined values, in particular in the case in which the thus defined "diameter" of the elliptical transmitting transducer is at least twice as large as the diameter of the circular disk reflector under consideration. Depending on the correct geometry and the transmission frequency of the transmitting transducer used, a more restrictive criterion can also be required, for example, that the characteristic dimensions of the transmitting transducer have to be four times or, particularly preferably, eight times as large as the diameter of the circular disk reflector under consideration.

[0022] In another preferred embodiment of the present invention, the device according to the invention is configured in such a way that the included evaluation unit is configured to generate an indication for a human operator if the ratio between the equivalent reflector size ERS determined from a flaw indication in a suitable manner, for example within the context of a fitting routine, to typical dimensions of the transmitting transducer used exceeds a preset threshold.

[0023] The method according to the invention is based on the non-destructive testing of a test object by means of ultrasound. It serves for characterizing such flaws or discontinuities in the material of the test object by means of the DGS method which are located in the near field of an ultrasonic transducer used for generating the ultrasound. In this case, the method comprises the following method steps: coupling ultrasonic pulses with a certain bandwidth B into the test object, recording echo signals from the test object which are correlated with a flaw or discontinuity, determining an equivalent reflector size ERS of a flaw or discontinuity causing the recorded echo signals from received echo signals based on a DGS diagram, which was determined taking into consideration the bandwidth B of the insonified ultrasonic pulses.

[0024] Preferably, the technique used is the pulse echo technique, i.e. the echo signals are recorded at the coupling location. In this technique, one and the same test probe is generally used both for generating and coupling the ultrasonic pulses into the test object as well as for recording the echo signals, i.e. of the ultrasonic pulses reflected in the test object. In principle, however, transsonification can also be used in the operation, i.e. separate test probes are used for generating and coupling the ultrasonic pulses into the test object as well as for recording the echo signals, i.e. the signals that have passed through the test object and were reflected in the process on a flaw or discontinuity.

[0025] The present invention for the first time makes it possible to characterize flaws by means of the DGS method which are located in the near field of the transmitting transducer used. This simplifies the application of the DGS method considerably, because the number of ultrasonic test probes required for a testing task is significantly reduced. If the DGS method is used in accordance with the prior art, reproducible results can only be obtained in the far field of the transmitting transducer. If an echo indication suggests that the flaw / discontinuity is located within the near field of the transmitting transducer, then one has to switch to a test probe with a transmitting transducer having a shorter near-field length. On the one hand, this increases the technical expenditure but also extends the testing time. Furthermore, a change of test probe inevitably also constitutes a source of testing inaccuracies.

[0026] In a preferred embodiment of the method, the ultrasonic pulses generate a sound field that is rotationally symmetric in the test object. This is advantageous particularly if the ultrasonic pulses used for testing are insonified obliquely into the test object, which is advantageous or even an absolute requirement for many testing tasks. It should be noted that both the ultrasonic test probe used for transmitting and the ultrasonic test probe used for receiving may comprise only a single ultrasonic transducer that generally determines the properties of the ultrasonic field generated / recorded by the test probe, i.e. propagation direction, diameter and opening angle or beam shape. However, it is also possible to generate an ultrasonic field by means of a transmitting test probe or to record it by means of a receiving test probe that comprises a plurality of ultrasonic transducers that can be individually controlled in a phase-accurate manner, e.g. in the form of a segmented, large-surface ultrasonic transducer. Through the phase-accurate control of the individual ultrasonic transducers, such a "phased array" permits a far-ranging beam control, i.e. a specific setting of the orientation of the propagation direction, diameter and opening angle or the beam shape in general of the generated or recorded ultrasonic field. This technique, which is also known as "phased array" technique, can be used advantageously within the context of the present invention.

[0027] In a preferred embodiment of the method according to the invention, the DGS diagram is determined taking into account the polarization P (longitudinal vs. transversal) of the insonified ultrasonic pulses. This results in another increase of the accuracy or reproducibility of the flaw size determination by means of the device according to the invention or the method according to the invention.

[0028] The reproducibility of the flaw size determination can also be improved by using, in the context of the method, a DGS diagram in the form of a function containing the diameter DKSR of a circular disk reflector as a parameter p. In order to determine the equivalent reflector size ERS of a detected flaw / discontinuity, the above-described method is carried out.

[0029] It should be noted that the device according to the invention and the method according to the invention are, in particular, suitable for characterizing flaws or discontinuities in the material of the test object in accordance with the DGS method, which are located in the near field of an ultrasonic transducer used for generating the ultrasound. However, the device and method are also suitable for characterizing flaws or discontinuities in the material of the test object in accordance with the DGS method, which satisfy the distance criterion of the European testing standard EN 583-2:2001 cited in the introduction.

[0030] This also applies to the features of the following exemplary embodiment, from which further features and advantages of the device according to the invention and the method according to the invention become apparent. The exemplary embodiment serves for illustrating the invention to a person skilled in the art and is therefore to be understood as an example, and not to be limiting. It refers to the Figures, which show the following: Fig. 1: a DGS diagram for continuous sound according to the prior art (taken from EN 583:2-2001), Fig. 2: an exemplary DGS diagram for illustrating the method for determining the equivalent reflector size of a flaw, Fig. 3: an exemplary embodiment of a device according to the invention, Fig. 4: the geometry of the sound field at the end of the near field, Fig. 5: the ultrasonic pulse, used with an envelope, Fig. 6: the spectrum of the ultrasonic pulse used, Fig. 7: a graphical representation of a plurality of test measurements to which a DGS diagram according to the prior art was adapted, and Fig. 8: a graphical representation of the plurality of test measurements from Fig. 7 to which a bandwidth-dependent DGS diagram according to the present invention was adapted.

[0031] Figure 3 shows an exemplary embodiment of a testing device 1 according to the invention for the non-destructive testing of a test object 100 by means of ultrasound. The testing device 1 is configured for characterizing flaws or discontinuities 99 in the material of the test object 100 in accordance with the DGS method, which can be located, in particular, in the near field of an ultrasonic transducer 14 used for generating the ultrasound. The testing device 1 comprises an ultrasonic test probe 10 with a single-part ultrasonic transducer 12 for generating and coupling an ultrasonic field into the test object 100 and for recording resulting echo signals from the test object 100. The test probe 10 is configured for an oblique insonification into the test object 100. To this end, the ultrasonic transducer 12 is disposed on a wedge-shaped leading body 14.

[0032] Furthermore, the testing device 1 comprises a control unit 20 for controlling the ultrasonic test probe 10, so that the latter generates a sequence of ultrasonic pulses with a certain transmission frequency f, which is typically between 1 and 5 MHz and within a bandwidth typically between 20 and 40%. The pulse sequence frequency typically lies in the range of a few kHz. The control unit 20 is connected to the test probe 10 and in particular to the ultrasonic transducer 12 thereof.

[0033] Furthermore, a receiving unit 30 is provided for recording echo signals by means of the ultrasonic test probe 10. The receiving unit 30 is also connected to the test probe 10 and in particular to the ultrasonic transducer 12 thereof.

[0034] Finally, an evaluation unit 40 connected both to the control unit 20 and to the receiving unit 30 is provided, which is configured for processing the echo signals from the material of the test object 100 recorded by the ultrasonic transducer 12 of the test probe 10. The evaluation unit 40 is connected to a display device 42 in the form of an LCD or an OLED, on which the amplitude of the received echo signals, for example, can be displayed in a time-resolved manner (A scan). A representation of the gain factor f, which is required to bring the maximum echo signal of a flaw / discontinuity 100 to the echo height of a reference reflector (e.g. back-face echo) spaced equally distant from the transmitting transducer, is equivalent to the representation of the echo amplitude. A DGS diagram taken from EN 583:2-2001 is shown in Fig. 1 by way of example.

[0035] In order to determine the equivalent reflector size of a detected flaw or detected discontinuity, the device 1 is configured to carry out a method during which the echo amplitude of a reference reflector is recorded on a test body. In the process, the reference reflector is situated at the distance d ref from the test probe. As a rule, the back-face echo of a test body with a circular-arc shaped back face is used (so-called test body No. 1).

[0036] In order to determine the ERS value of a detected flaw or a detected discontinuity situated at a certain distance d Fehler from the test probe, the gain factor G ref is determined which must be adjusted in order to adjust the echo amplitude of the reference echo to a certain value, typically 80%, of the maximum indication height.

[0037] In the next step, the gain factor G Fehler is determined, which is required to adjust the echo amplitude of the flaw to the same value as the reference echo, that is, e.g. 80% of the indication height. Then, the difference ΔG of the two gain values is plotted into the DGS diagram, at the position of the reference echo d ref , in the y-direction downwards, that is, ΔG = G Fehler - G ref . In the next step, the difference Δd of the distances d ref and d Fehler is plotted towards the left in the x-direction, i.e. Δd = d ref - d Fehler . Then, the resulting end point lies on the DGS curve of the circular disk reflector that would generate an echo signal of the same height. This method is schematically illustrated in Fig. 2.

[0038] By identifying the DGS curve characterized by the diameter D of the circular disk reflector, on which the end point as described above comes to lie, the ERS value of the detected flaw is then determined. On the one hand, this may take place by selecting the DGS curve stored in the evaluation unit that has the smallest deviation in the y-direction from the determined end point. However, this may also take place by a suitable interpolation between the DGS curves stored in the evaluation unit. If the general DGS curve for the selected type of reference reflector is provided in the evaluation unit in the form of a function that depends on the characteristic size of the selected reference reflector, e.g. on the diameter D of a circular disk reflector, the characteristic size of the reference reflector can be determined with this by calculation. In this case, the device can be implemented in the control unit 20, the evaluation unit 40 or even in a higher-level control unit which is part of the device 1.

[0039] The control unit 20, the receiving unit 30 as well as the evaluation unit 40 including the display device 42 are accommodated in a common ultrasound control device 50, which is connected via a communication line 60 to the test probe 10.

[0040] In an alternative embodiment, the control unit 20, the receiving unit 30 and the evaluation unit 40 can be integrated separately or jointly and partially or completely into the test probe 10.

[0041] The ultrasonic test probe 10 is configured according to WO 2010 / 130819 A1, so that it generates a sound field that is rotationally symmetric to the acoustic axis in the test object 100. For this purpose, an only approximately circular and non-planar ultrasonic transducer is generally required, whose "diameter" is hereinafter designated D. A size was already specified in the introductory part which, within the context of the invention, can be considered equivalent to the "diameter" D of such an only approximately circular ultrasonic transducer 12. Reference is made thereto.

[0042] The evaluation unit 40 is configured for determining an equivalent reflector size ERS of the flaw or discontinuity 99 from received echo signals based on a DGS diagram determined theoretically or experimentally taking into consideration the bandwidth B of the insonified ultrasonic pulses and the geometric dimensions of the substantially circular ultrasonic transducer 12. For this purpose, the DGS diagram is stored in the evaluation unit 40 as an analytic function F containing the diameter D KSR of a circular disk reflector as a parameter p. Alternatively, the function F can also be stored in a numerical form for a plurality of different parameters p.

[0043] In order to provide the user of the device with a numerical value for the equivalent reflector size ERS of the detected flaw / discontinuity 99 which reproducibly characterizes the flaw / discontinuity 99, the evaluation unit 40 is configured to determine, from the determined gain factor for an indication height of, for example, 80%, the parameter p, i.e. the diameter D of an equivalent circular disk reflector, by calculation from the function F. This diameter constitutes the equivalent reflector size of the flaw / discontinuity 99 according to the DGS method. As a result, the user obtains from this adaptation a reproducible value for the equivalent reflector size ERS of the detected flaw / discontinuity 99, which can be entered into a record.

[0044] Furthermore, the evaluation unit 40 is configured to generate an indication for a human operator in the form of an acoustic alarm signal and a visual error indication in the form of a color-coded message display panel 42, if the ratio of the "diameter" D defined above to the equivalent reflector size ERS determined from a flaw indication drops below a predetermined threshold.

[0045] The value 1 / 2 has proved to be a suitable maximum threshold. A higher measuring accuracy or an improved reproducibility are obtained if the threshold is selected to be lower, e.g. 1 / 4 or even 1 / 8. If the evaluation unit 40 generates such an indication, the measured ERS value should be ignored by the operator. Alternatively, the evaluation unit 40 is configured in such a way that such an ERS value is automatically discarded.

[0046] A possible approach for theoretically determining the sound pressure on the acoustic axis for pulsed sound is based on considerations regarding the sound pressure of a circular transmitting transducer with the diameter D for continuous sound. The sound pressure p A (z,t) at the distance z from the transducer at the time t is in this case calculated using the following formula: p A z t = ωZ ∫ S 1 r cos ωt − kr dS wherein: ω: angular frequency Z: acoustic impedance k: wave number S: surface area of the circular transducer and r = z 2 + a 2 und k = 2 π λ dS ≈ a da dφ

[0047] It thus follows: p A z t = 2 ωZ ∫ a = 0 D 2 ∫ φ = 0 2 π a a 2 + z 2 cos ωt − k a 2 + z 2 da dφ

[0048] First, the integration over φ is carried out: p A z t = 4 πωZ ∫ a = 0 D 2 a a 2 + z 2 cos ωt − k a 2 + z 2 da

[0049] This integral equation can be solved algebraically: p A z t = − 2 πcZ sin ωt − k D 2 2 + z 2 − sin ωt − kz with the sound velocity c.

[0050] Using the trigonometric addition theorems, this term can be simplified: sin x − sin y = 2 cos x + y 2 sin x − y 2 p A z t = − 4 πcZ cos 2 ωt − k D 2 2 + z 2 − kz 2 sin k D 2 2 + z 2 − z 2 = − 4 πcZ cos 2 ωt − k D 2 2 + z 2 − kz 2 sin π λ D 2 2 + z 2 − z

[0051] Only the time-independent extremes p max (z) of the sound pressure p A (z,t) are of interest here. Therefore, only the extreme values are used for the cosine term and the absolute value of the sine term is considered: p max z = 4 πcZ sin π λ D 2 2 + z 2 − z

[0052] The distance from the transducer to the last sound pressure maximum on the acoustic axis is referred to as near-field length N. The extremes can be derived from the argument of the sine term in equation (9). Generally, the sine function has its extremes at: 2 n + 1 2 π mit n ∈ ℕ 0

[0053] Therefore, the following term has to be examined: π λ D 2 2 + z 2 − z = 2 n + 1 2 π mit n ∈ ℕ 0 ⇒ 2 D 2 2 + z 2 = 2 n + 1 λ + 2 z

[0054] Squaring the equation and solving it for z yields: z = D 2 − 2 n + 1 2 λ 2 4 2 n + 1 λ

[0055] Thus, z is at a maximum when the term behind the minus sign in the numerator and the denominator are as small as possible, i.e. for n=0. Thus, z max = N applies. N = D 2 − λ 2 4 λ

[0056] The following correlation can be derived from Figure 4: Application of the Pythagorean theorem to the right-angled triangle formed of half the transducer diameter D / 2, the near-field length N and the marginal ray r in order to calculate the length of the marginal ray r up to the end of the near field yields: r 2 = N 2 + D 2 2 ⇒ r 2 = D 2 − λ 2 4 λ 2 + D 2 2 ⇒ r 2 = D 2 + λ 2 2 16 λ 2 ⇒ r = D 2 + λ 2 4 λ ⇒ r = D 2 − λ 2 4 λ + λ 2 ⇒ r = N + λ 2

[0057] That means that the difference of travel between the central ray and the marginal ray at the end of the near field is exactly λ / 2 in the case of continuous sound. Due to the fact that usually, D >> λ, the following approximation for the near-field length N is frequently used in practice instead of equation (13): N ≈ D 2 4 λ

[0058] For an exemplary calculation for pulsed sound, a Gaussian curve with a central frequency of 4 MHz, as shown in Fig. 5, is selected as an envelope for the cosine function. The approximation by a Gaussian curve is justified in most cases in practice; the central frequency is selected to be typical. The pulse used is shown in Figure 6 and has a bandwidth of 30%, which is selected by way of example.

[0059] With this pulse, the sound pressure on the acoustic axis is calculated with the following exemplary, but typical values. c = 5.92 km / s (sound velocity in the test object) D = 20 mm (transducer diameter) f = 4 MHz (central frequency of the ultrasonic pulse)

[0060] The result of the calculation is shown in Figure 7. The maximum of this sound pressure curve is at 85.4 mm. If, however, the near-field length is calculated using formula (13), the result is 67.2 mm. The result of a calculation using the simplified formula (15) is 67.6 mm. Obviously, the near-field length depends on the bandwidth of the pulse used, as can also be seen from Table 1, in which the dependency of the near-field length on the bandwidth of the ultrasonic pulse is listed for constant transducer dimensions D and the central frequency f. Table 1: Near-field length as a function of the bandwidthBandwidthNear-field length20 %78.1 mm30 %85.4 mm40 %91.7 mm50 %97.2 mm

[0061] For calculating the sound pressure on the acoustic axis for pulsed sound, the integral (5) that applies for continuous sound was modified as follows: p A z t = 4 πωZ ∫ a = 0 D 2 e A z − z 2 + a 2 2 a a 2 + z 2 cos ωt − k a 2 + z 2 da

[0062] The selected Gaussian curve moves together with the sound. Thus, a model of the pulse can be generated. This equation can only be solved numerically. The factor A is used to set the bandwidth. Again, the trigonometric addition theorems are used for solving the integral. Thus, the above integral can be divided into two integrals: p A z t = 4 πωZ cos ωt ∫ a = 0 D 2 e A z − z 2 + a 2 2 a a 2 + z 2 cos k a 2 + z 2 da ︸ x 1 + 4 πωZ sin ωt ∫ a = 0 D 2 e A z − z 2 + a 2 2 a a 2 + z 2 sin k a 2 + z 2 da ︸ x 2

[0063] This yields, as a solution of p(z,t), a term of the form: F = x 1 cos ωt + x 2 sin ωt

[0064] The values of B and φ can be determined from the following equation: x 1 cos ωt + x 2 sin ωt = B sin ωt + φ ⇒ x 1 cos ωt + x 2 sin ωt = B sin ωt cos φ + B cos ωt sin φ

[0065] By comparison, it follows from the last equation: x 1 = B sin φ x 2 = B cos φ

[0066] Therefore, the following continues to apply: 1 x 1 2 sin 2 φ = 1 x 2 2 1 − sin 2 φ sin 2 φ = x 1 2 x 1 2 + x 2 2 sin φ = ± x 1 x 1 2 + x 2 2 B z = ± x 1 2 + x 2 2

[0067] Thus, the sound pressure p A on the acoustic axis can be given, for any depth and for any point in time t, as: p A z t = B z sin ωt + φ

[0068] Since only the maximum sound pressure p Amax is of interest here, this is obtained from: p Amax = B z

[0069] The curve for the back-face echo p rwe (z,t) is obtained if the fact is taken into account that ultrasound is totally reflected on the back face and returns to the transducer. However, the sound has now traveled the distance 2z (where z: distance to the back face). Therefore, equation (16) has to be adapted accordingly (z is replaced by 2z): p rwe z t = 4 πωZ ∫ a = 0 D 2 e A 2 z − 4 z 2 + a 2 2 a a 2 + 4 z 2 cos ωt − k a 2 + 4 z 2 da

[0070] This constitutes the equation for the back-face echo, which usually has to be solved numerically.

[0071] In order to calculate the ERS curves p ksr (z,t), it is presumed that the circular disk reflector oscillates over the entire surface with the calculated sound pressure p(z,t) on the acoustic axis at the distance z. Only the distances (shortest travel time) between the transducer and the circular disk reflector were considered. The received sound pressure is then obtained from the double integral over the circular disk surface area as a transmitter and over the transducer surface area as a receiver. In this case, the fact that the sound pressure of the circular disk reflector must be calculated for the distance from z to 2z (return travel of the sound) must be taken into account. This does not apply to the term for the distance, because the sound pressure for the way there p A (z) is already included in the calculation. Dispensing with proportionality factors, the following integral is then to be calculated, again using the addition theorems: p ksr z t = p A z ∫ x = 0 D 2 ∫ y = 0 D KSR 2 e A 2 z − 4 z 2 + x 2 2 x y x 2 + 4 z 2 cos ωt − k x 2 + 4 z 2 dx dy where D: transducer diameter D KSR : diameter of the circular disk reflector p A (z): maximum sound pressure on the acoustic axis at the distance z

[0072] After the, if necessary numerical, calculation of this integral for all desired ERS curves, in which various proportionality factors were suppressed for simplification, the calculated curves must yet be shifted to the correct distance from the back-face echo curve. For example, the considerations on pages 102 and 103 of the book by Krautkrämer, Werkstoffprüfung mit Ultraschall, fifth completely revised edition, can be used for calculating the necessary shifts. These considerations only relate to the far field, so that they can also be used for pulsed sound.

[0073] As a result, a plurality of ERS curves is obtained which are specific to the transmitting transducer used, because they depend on the geometric dimensions D of the transmitting transducer, the transmission frequency f and on the bandwidth B of the generated pulses. Together with the back-face echo curve, which was also calculated, they form the transmitting transducer-specific DGS diagram for pulsed sound, which also applies in the near field, and can therefore form the basis for a reproducible determination of the equivalent reflector size ERS of a flaw / discontinuity 99, even if that lies in the near field of the ultrasonic transmitting transducer used. In the far field, the DGS diagram for pulsed sound then asymptotically approaches the DGS diagram for continuous sound used in the prior art, c.g. in the testing standard EN 583-2:2001.

[0074] During the validation of the ERS curves thus calculated, it was found that significant deviations are obtained if the size of the circular disk reflector becomes comparable to the size of the transmitting transducer. Presumably, this is connected with the assumption that the circular disk reflector oscillates over its entire surface with the same sound amplitude having a validity which is limited to large equivalent reflector sizes ERS. In order to obtain reproducible experimental results, it has proved in practice to make sense to pay attention to the criterion that the experimentally determined equivalent reflector size is no greater than half of the diameter D of the transmitting transducer, wherein, for the diameter of the generally approximately circular transmitting transducer, use is made, for example, of the above-defined size (diameter of a circular ultrasonic transducer of the same surface area).

[0075] The effect on the near field of the DGS diagram determined for pulsed sound is apparent from Figures 7 and 8. Fig. 7 shows a graphical representation of a plurality of experimentally obtained gain values according to the DGS method, which were obtained in test measurements on circular disk reflectors (blind holes Ø 3 mm with different depths in a testing body). A DGS diagram according to the prior art, i.e. a DGS diagram according to EN 583-2:2001, was adapted to these experimentally obtained values. The pronounced deviations between the theoretical curve pattern and the measured values in the near field of the test probe are clearly recognizable. RW in this case denotes the back-face echo, ERS the echo of a circular disk reflector with a diameter of 3.1 mm.

[0076] In contrast, Figure 8 shows a graphical representation of the plurality of test measurements from Fig. 7 to which a bandwidth-dependent DGS diagram according to the present invention was adapted. Here, the result is also a diameter of the examined circular disk reflector of 3.1 mm. However, the echo curve for an equivalent reflector with 3.1 mm shows a good correspondence with the experimentally obtained values also within the near field of the test probe used. This implies that, using echo amplitudes of a flaw / discontinuity 99 located in the near field of the test probe, its ERS value can also be determined with good accuracy and reproducibility.Reference numerals

[0077] 1Testing device 10Test probe 12Ultrasonic transducer 14Leading body 20Control unit 30Receiving unit 40Evaluation unit 42Display device 44Message display panel 50Ultrasound control device 60Communication line 99Flaw, discontinuity 100Test object

Claims

1. A device (1) for the non-destructive testing of a test object (100) by means of ultrasound, the device (1) being configured for characterizing flaws or discontinuities (99) in material of the test object (100) in accordance with a DGS, i.e. distance-gain-size, method, which are located in the near field of an ultrasonic transducer (12) used for generating the ultrasound, wherein the device (1) comprises the following: a. an ultrasonic test probe (10) with an ultrasonic transducer (12) for generating and coupling an ultrasonic field into the test object (100), b. a control unit (20) for controlling the ultrasonic test probe (10) in such a way that the latter generates ultrasonic pulses with a certain bandwidth B, c. a receiving unit (30) for recording echo signals by means of the ultrasonic test probe, and d. an evaluation unit (40), which is connected to the receiving unit (30) and configured for processing the recorded echo signals, e. wherein the evaluation unit (40) is configured for determining an equivalent reflector size ERS of the flaw or discontinuity (99), from received echo signals, based on a bandwidth-dependent DGS diagram determined dependent on the geometric dimensions D of the transmitting transducer (12), the transmission frequency F and the bandwidth B of the insonified ultrasonic pulses together with a calculated back-face echo curve, characterized in that the back-face echo curve and ERS curves are calculated according to the following: theoretically determining the sound pressure on the acoustic axis for pulsed sound based on considerations regarding the sound pressure of a circular transmitting transducer with the diameter D for continuous sound, the sound pressure pA(z,t) at the distance z from the transducer at the time t being calculated using the following formula: p A z t = ωZ ∫ S 1 r cos ωt − kr dS wherein: ω: angular frequency Z: acoustic impedance k: wave number S: surface area of the circular transducer and r = z 2 + a 2 und k = 2 π λ dS ≈ a da dφ it thus follows: p A z t = 2 ωZ ∫ a = 0 D 2 ∫ φ = 0 2 π a a 2 + z 2 cos ωt − k a 2 + z 2 da dφ first, the integration over φ is carried out: p A z t = 4 πωZ ∫ a = 0 D 2 a a 2 + z 2 cos ωt − k a 2 + z 2 da this integral equation is solved algebraically: p A z t = − 2 πcZ sin ωt − k D 2 2 + z 2 − sin ωt − kz with the sound velocity c; using the trigonometric addition theorems, this term is simplified: sin x − sin y = 2 cos x + y 2 sin x − y 2 p A z t = − 4 πcZ cos 2 ωt − k D 2 2 + z 2 − kz 2 sin k D 2 2 + z 2 − z 2 = − 4 πcZ cos 2 ωt − k D 2 2 + z 2 − kz 2 sin π λ D 2 2 + z 2 − z only the time-independent extremes pmax(z) of the sound pressure pA(z,t) are of interest here, therefore, only the extreme values are used for the cosine term and the absolute value of the sine term is considered: p max z = 4 π cZ sin π λ D 2 2 + z 2 − z the distance from the transducer to the last sound pressure maximum on the acoustic axis is referred to as near-field length N; the extremes are derived from the argument of the sine term in equation (9); the sine function has its extremes at: 2 n + 1 2 π mit n ∈ ℕ 0 therefore, the following term is examined: π λ D 2 2 + z 2 − z = 2 n + 1 2 π mit n ∈ ℕ 0 ⇒ 2 D 2 2 + z 2 = 2 n + 1 λ + 2 z squaring the equation and solving it for z yields: z = D 2 − 2 n + 1 2 λ 2 4 2 n + 1 λ thus, z is at a maximum when the term behind the minus sign in the numerator and the denominator are as small as possible, i.e. for n=0, thus, zmax = N applies; N = D 2 − λ 2 4 λ the Pythagorean theorem is appled to the right-angled triangle formed of half the transducer diameter D / 2, the near-field length N and the marginal ray r in order to calculate the length of the marginal ray r up to the end of the near field yields: r 2 = N 2 + D 2 2 ⇒ r 2 = D 2 − λ 2 4 λ 2 + D 2 2 ⇒ r 2 = D 2 + λ 2 2 16 λ 2 ⇒ r = D 2 + λ 2 4 λ ⇒ r = D 2 − λ 2 4 λ + λ 2 ⇒ r = N + λ 2 that means that the difference of travel between the central ray and the marginal ray at the end of the near field is exactly λ / 2 in the case of continuous sound; due to the fact that usually, D >> λ, the following approximation for the near-field length N is useable instead of equation (13): N ≈ D 2 4 λ for calculating the sound pressure on the acoustic axis for pulsed sound, the integral (5) that applies for continuous sound is modified as follows: p A z t = 4 πωZ ∫ a = 0 D 2 e A z − z 2 + a 2 2 a a 2 + z 2 cos ωt − k a 2 + z 2 da the selected Gaussian curve moves together with the sound, thus, a model of the pulse is generated, this equation being solved numerically, the factor A is used to set the bandwidth, again, the trigonometric addition theorems being used for solving the integral, thus, the above integral is divided into two integrals: p A z t = 4 πωZ cos ωt ∫ a = 0 D 2 e A z − z 2 + a 2 2 a a 2 + z 2 cos k a 2 + z 2 da ︸ x 1 + 4 πωZ sin ωt ∫ a = 0 D 2 e A z − z 2 + a 2 2 a a 2 + z 2 sin k a 2 + z 2 da ︸ x 2 this yields, as a solution of p(z,t), a term of the form: F = x 1 cos ωt + x 2 sin ωt the values of B and φ are determined from the following equation: x 1 cos ωt + x 2 sin ωt = B sin ωt + φ ⇒ x 1 cos ωt + x 2 sin ωt = B sin ωt cos φ + B cos ωt sin φ by comparison, it follows from the last equation: x 1 = B sin φ x 2 = B cos φ therefore, the following continues to apply: 1 x 1 2 sin 2 φ = 1 x 2 2 1 − sin 2 φ sin 2 φ = x 1 2 x 1 2 + x 2 2 sin φ = ± x 1 x 1 2 + x 2 2 B z = ± x 1 2 + x 2 2 thus, the sound pressure pA on the acoustic axis can be given, for any depth and for any point in time t, as: p A z t = B z sin ωt + φ since only the maximum sound pressure pAmax is of interest here, this is obtained from: p Amax = B z the curve for the back-face echo prwe(z,t) is obtained as the fact is taken into account that ultrasound is totally reflected on the back face and returns to the transducer, however, the sound has now traveled the distance 2z, therefore, equation (16) is adapted accordingly so that z is replaced by 2z: p rwe z t = 4 πωZ ∫ a = 0 D 2 e A 2 z − 4 z 2 + a 2 2 a a 2 + 4 z 2 cos ωt − k a 2 + 4 z 2 da this constitutes the equation for the back-face echo; in order to calculate the ERS curves pksr(z,t), it is presumed that the circular disk reflector oscillates over the entire surface with the calculated sound pressure p(z,t) on the acoustic axis at the distance z, only the distances with shortest travel time between the transducer and the circular disk reflector are considered, the received sound pressure is then obtained from the double integral over the circular disk surface area as a transmitter and over the transducer surface area as a receiver, in this case, the fact that the sound pressure of the circular disk reflector must be calculated for the distance from z to 2z i.e. return travel of the sound must be taken into account, this does not apply to the term for the distance, because the sound pressure for the way there pA(z) is already included in the calculation, dispensing with proportionality factors, the following integral is then calculated, again using the addition theorems: p ksr z t = p A z ∫ x = 0 D 2 ∫ y = 0 D KSR 2 e A 2 z − 4 z 2 + x 2 2 x y x 2 + 4 z 2 cos ωt − k x 2 + 4 z 2 dx dy where DKSR: diameter of the circular disk reflector pA(z): maximum sound pressure on the acoustic axis at the distance z after the calculation of this integral for all desired ERS curves, in which various proportionality factors were suppressed for simplification, the calculated curves are shifted to the correct distance from the back-face echo curve; these considerations only relate to the far field, so that they can also be used for pulsed sound, as a result, a plurality of ERS curves is obtained which are specific to the transmitting transducer used, because they depend on the geometric dimensions D of the transmitting transducer, the transmission frequency f and on the bandwidth B of the generated pulses, together with the back-face echo curve, which was also calculated, they form the transmitting transducer-specific DGS diagram for pulsed sound, which also applies in the near field, and therefore forms the basis for a reproducible determination of the equivalent reflector size ERS of a flaw / discontinuity (99), even if that lies in the near field of the ultrasonic transmitting transducer used.

2. The device (1) according to claim 1, wherein the device (1), in particular the test probe (10), is configured to generate a sound field that is rotationally symmetric in the test object.

3. The device (1) according to claim 1 or 2, wherein the test probe (10) is configured for oblique insonification into the test object (100).

4. The device (1) according to any of claims 1, 2 or 3, wherein the DGS diagram is determined dependent on the polarization P of the insonified ultrasonic pulses.

5. The device (1) according to any preceding claim, wherein the DGS diagram is stored in the evaluation unit (40) as a function F containing the diameter DKSR of a circular disk reflector as a parameter (p).

6. The device (1) according to any preceding claim, wherein the evaluation unit (40) is configured to generate an indication for a human operator if the ratio of the diameter D to the equivalent reflector size ERS determined from a flaw indication drops below a predetermined threshold,7. The device (1) according to claim 6, wherein the threshold is greater than 1 / 8, preferably greater than 1 / 4, and particularly preferably greater than or equal to 1 / 2.

8. A method for the non-destructive testing of a test object (100) by means of ultrasound, the method serving for characterizing flaws or discontinuities (99) in material of the test object (100) in accordance with a DGS, i.e. distance-gain-size, method, which are located in the near field of an ultrasonic transducer (12) used for generating the ultrasound, wherein the method comprises the following method steps: a. coupling ultrasonic pulses with a certain bandwidth B into the test object (100), b. recording echo signals from the test object (100), c. determining an equivalent reflector size ERS of a flaw or discontinuity (99) causing the recorded echo signals, from received echo signals, based on a bandwidth-dependent DGS diagram determined dependent on the geometric dimensions D of the transmitting transducer (12), the transmission frequency F and the bandwidth B of the insonified ultrasonic pulses together with a calculated back-face echo curve, characterized in that the back-face echo curve and ERS curves are calculated according to the following: theoretically determining the sound pressure on the acoustic axis for pulsed sound based on considerations regarding the sound pressure of a circular transmitting transducer with the diameter D for continuous sound, the sound pressure pA(z,t) at the distance z from the transducer at the time t being calculated using the following formula: p A z t = ωZ ∫ S 1 r cos ωt − kr dS wherein: ω: angular frequency Z: acoustic impedance k: wave number S: surface area of the circular transducer and r = z 2 + a 2 und k = 2 π λ dS ≈ a da dφ it thus follows: p A z t = 2 ωZ ∫ a = 0 D 2 ∫ φ = 0 2 π a a 2 + z 2 cos ωt − k a 2 + z 2 da dφ first, the integration over φ is carried out: p A z t = 4 πωZ ∫ a = 0 D 2 a a 2 + z 2 cos ωt − k a 2 + z 2 da this integral equation is solved algebraically: p A z t = − 2 πcZ sin ωt − k D 2 2 + z 2 − sin ωt − kz with the sound velocity c; using the trigonometric addition theorems, this term is simplified: sin x − sin y = 2 cos x + y 2 sin x − y 2 p A z t = − 4 πcZ cos 2 ωt − k D 2 2 + z 2 − kz 2 sin k D 2 2 + z 2 − z 2 = − 4 πcZ cos 2 ωt − k D 2 2 + z 2 − kz 2 sin π λ D 2 2 + z 2 − z only the time-independent extremes pmax(z) of the sound pressure pA(z,t) are of interest here, therefore, only the extreme values are used for the cosine term and the absolute value of the sine term is considered: p max z = 4 πcZ sin π λ D 2 2 + z 2 − z the distance from the transducer to the last sound pressure maximum on the acoustic axis is referred to as near-field length N; the extremes are derived from the argument of the sine term in equation (9); the sine function has its extremes at: 2 n + 1 2 π mit n ∈ ℕ 0 therefore, the following term is examined: π λ D 2 2 + z 2 − z = 2 n + 1 2 π mit n ∈ ℕ 0 ⇒ 2 D 2 2 + z 2 = 2 n + 1 λ + 2 z squaring the equation and solving it for z yields: z = D 2 − 2 n + 1 2 λ 2 4 2 n + 1 λ thus, z is at a maximum when the term behind the minus sign in the numerator and the denominator are as small as possible, i.e. for n=0, thus, Zmax = N applies: N = D 2 − λ 2 4 λ the Pythagorean theorem is appled to the right-angled triangle formed of half the transducer diameter D / 2, the near-field length N and the marginal ray r in order to calculate the length of the marginal ray r up to the end of the near field yields: r 2 = N 2 + D 2 2 ⇒ r 2 = D 2 − λ 2 4 λ 2 + D 2 2 ⇒ r 2 = D 2 + λ 2 2 16 λ 2 ⇒ r = D 2 + λ 2 4 λ ⇒ r = D 2 − λ 2 4 λ + λ 2 ⇒ r = N + λ 2 that means that the difference of travel between the central ray and the marginal ray at the end of the near field is exactly λ / 2 in the case of continuous sound; due to the fact that usually, D >> λ, the following approximation for the near-field length N is useable instead of equation (13): N ≈ D 2 4 λ for calculating the sound pressure on the acoustic axis for pulsed sound, the integral (5) that applies for continuous sound is modified as follows: p A z t = 4 πωZ ∫ a = 0 D 2 e A z − z 2 + a 2 2 a a 2 + z 2 cos ωt − k a 2 + z 2 da the selected Gaussian curve moves together with the sound, thus, a model of the pulse is generated, this equation being solved numerically, the factor A is used to set the bandwidth, again, the trigonometric addition theorems being used for solving the integral, thus, the above integral is divided into two integrals: p A z t = 4 πωZ cos ωt ∫ a = 0 D 2 e A z − z 2 + a 2 2 a a 2 + z 2 cos k a 2 + z 2 da ︸ x 1 + 4 πωZ sin ωt ∫ a = 0 D 2 e A z − z 2 + a 2 2 a a 2 + z 2 sin k a 2 + z 2 da ︸ x 2 this yields, as a solution of p(z,t), a term of the form: F = x 1 cos ωt + x 2 sin ωt the values of B and φ are determined from the following equation: x 1 cos ωt + x 2 sin ωt = B sin ωt + φ ⇒ x 1 cos ωt + x 2 sin ωt = B sin ωt cos φ + B cos ωt sin φ by comparison, it follows from the last equation: x 1 = B sin φ x 2 = B cos φ therefore, the following continues to apply: 1 x 1 2 sin 2 φ = 1 x 2 2 1 − sin 2 φ sin 2 φ = x 1 2 x 1 2 + x 2 2 sin φ = ± x 1 x 1 2 + x 2 2 B z = ± x 1 2 + x 2 2 thus, the sound pressure pA on the acoustic axis can be given, for any depth and for any point in time t, as: p A z t = B z sin ωt + φ since only the maximum sound pressure pAmax is of interest here, this is obtained from: p Amax = B z the curve for the back-face echo prwe(z,t) is obtained as the fact is taken into account that ultrasound is totally reflected on the back face and returns to the transducer, however, the sound has now traveled the distance 2z, therefore, equation (16) is adapted accordingly z is replaced by 2z: p rwe z t = 4 πωZ ∫ a = 0 D 2 e A 2 z − 4 z 2 + a 2 2 a a 2 + 4 z 2 cos ωt − k a 2 + 4 z 2 da this constitutes the equation for the back-face echo; in order to calculate the ERS curves pksr(z,t), it is presumed that the circular disk reflector oscillates over the entire surface with the calculated sound pressure p(z,t) on the acoustic axis at the distance z, only the distances (shortest travel time) between the transducer and the circular disk reflector are considered, the received sound pressure is then obtained from the double integral over the circular disk surface area as a transmitter and over the transducer surface area as a receiver, in this case, the fact that the sound pressure of the circular disk reflector must be calculated for the distance from z to 2z i.e. travel of the sound must be taken into account, this does not apply to the term for the distance, because the sound pressure for the way there pA(z) is already included in the calculation, dispensing with proportionality factors, the following integral is then calculated, again using the addition theorems: p ksr z t = p A z ∫ x = 0 D 2 ∫ y = 0 D KSR 2 e A 2 z − 4 z 2 + z 2 2 x y x 2 + 4 z 2 cos ωt − k x 2 + 4 z 2 dx dy where DKSR: diameter of the circular disk reflector pA(z): maximum sound pressure on the acoustic axis at the distance z after the calculation of this integral for all desired ERS curves, in which various proportionality factors were suppressed for simplification, the calculated curves are shifted to the correct distance from the back-face echo curve; these considerations only relate to the far field, so that they can also be used for pulsed sound, as a result, a plurality of ERS curves is obtained which are specific to the transmitting transducer used, because they depend on the geometric dimensions D of the transmitting transducer, the transmission frequency f and on the bandwidth B of the generated pulses, together with the back-face echo curve, which was also calculated, they form the transmitting transducer-specific DGS diagram for pulsed sound, which also applies in the near field, and therefore forms the basis for a reproducible determination of the equivalent reflector size ERS of a flaw / discontinuity (99), even if that lies in the near field of the ultrasonic transmitting transducer used.

9. The method according to claim 8, wherein the ultrasonic pulses generate a sound field that is rotationally symmetric in the test object (100).

10. The method according to claim 8 or 9, wherein the ultrasonic pulses are insonified obliquely into the test object (100).

11. The method according to any of claims 8 to 10, wherein the DGS diagram is determined dependent on the polarization P of the insonified ultrasonic pulses.

12. The method according to any of claims 8 to 11, wherein a DGS diagram in the form of a function is used which contains the diameter DKSR of a circular disk reflector as a parameter (p).

13. The method according to claim 12, wherein a fitting of the function F with respect to the parameter p to experimentally determined echo values of the flaw / discontinuity (99) is carried out to determine the equivalent reflector size ERS of a detected flaw / discontinuity (99).

14. The method according to any of claims 8 to 13, wherein an indication for a human operator is generated if the ratio of the diameter D to the equivalent reflector size ERS determined from a flaw indication drops below a predetermined threshold.