FR3140439A1 - Ultrasound imaging method by multidimensional Fourier transform using two separate multi-element transducers - Google Patents

Abstract

The invention relates to a method of ultrasonic imaging of an object having two opposite faces, from a pair of multi-element transducers comprising a transmission transducer with L elements and a reception transducer with N elements, each placed on the same side or on two opposite sides of the object to be imaged. The invention makes it possible to facilitate real-time imaging of any shape and orientation defects in solid structures. For this, the algorithm described in application WO 2020/128344A1 is modified by adding a step of taking into account the distance between the two transducers in writing the spectrum of the image as a function of the spectrum of the signals received. We add the coordinates of the center of the receiver which are then distinct from that of the transmitter. The expression of the cylindrical wave (or spherical in 3D) must then take into account this difference between positions of the transmitting multi-element transducer and the receiving multi-element transducer. Figure 3

Description

Ultrasound imaging method by multidimensional Fourier transform using two separate multi-element transducers

The invention relates to the field of ultrasonic imaging using multi-element ultrasonic transducers, applied to non-destructive ultrasonic testing of objects.

A multi-dimensional Fourier transform ultrasound imaging method uses two separate multi-element transducers to enable the imaging of certain types of defects in a solid structure.

The invention generally applies to the detection and imaging of defects of the porosity, crack, inclusion or other type in a solid structure corresponding to a part or an object to be imaged which can be made up of different materials (metal, concrete, composite…) and which has at least one flat surface on which two multi-element transducers can be positioned.

Manufacturing or fatigue defects can appear in industrial components, particularly metallic ones. These defects can take any orientation or depth, it is therefore necessary to have an ultrasound imaging method capable of detecting them with a good signal-to-noise ratio, and which is compatible with real-time imaging. In particular, defects such as thin cracks located approximately halfway through the thickness of thick parts can be particularly difficult to detect with a single sensor. An objective is therefore to propose a rapid imaging method capable of detecting defects presenting an unfavorable orientation.

There are mainly two types of imaging methods in non-destructive testing by ultrasound which can be separated into so-called 'pulse-echo' methods on the one hand and so-called 'pitch-catch' methods on the other hand.

A pulse-echo control method is a method in which the same translator (single or multi-element) is used as transmitter and receiver of ultrasonic waves. The oldest 'pulse-echo' methods consisted of using the signals recorded by a single-element translator (capable of both emitting and receiving ultrasound) in a multitude of control positions. The imaging rate was then limited by the speed of movement of the translator, and the performance limited by the shape of the emitted beam. This technique was followed by a method using a multi-element translator (that is to say comprising a set of elements capable of emitting or receiving ultrasonic waves) whose excitation of the different elements at well-chosen instants made it possible to modulate the shape of the ultrasound beam (and therefore the depth inspected); coupled with mechanical movement of the translator, this technique suffered from the same cadence limitations (and impossibility of real-time imaging).

In 2005 (Holmes et al, ‘Post-processing of the full matrix of ultrasonic transmit–receive array data for non-destructive evaluation’, NDT&E Int) an imaging method with a single position of the multi-element translator was proposed; it consists of transmitting successively with each of the channels of the translator, recording the signals separately on each receiving channel and finally applying a reconstruction algorithm on these signals in the time domain called TFM (Total Focusing Method). The rate, which is higher, still remains limited when a large number of elements are used for the inspection.

Improvements to the TFM algorithm were subsequently proposed in order to accelerate its speed and improve the signal-to-noise ratio of the images. Among them, we note plane wave imaging, which consists of using all the elements of the transducer simultaneously in emission, with excitation moments on each channel well calculated to lead to the generation of a wave ultrasound planes in the medium at a desired angle. The signals are then recorded on each reception channel before applying a reconstruction algorithm to the signals in the time domain (see for example: “Plane Wave Imaging for ultrasonic non-destructive testing: Generalization to multimodal imaging”, L. Lejeune et al, Ultrasonics 2016). If the signal acquisition time is then reduced, the imaging rate remains limited by the algorithmic complexity.

Finally another area of improvement has been studied in the literature consisting of reducing this algorithmic complexity by carrying out post-processing of the signals received in the frequency domain instead of the time domain (see for example “2-D and 3-D Reconstruction Algorithms in the Fourier Domain for Plane-Wave Imaging in Nondestructive Testing”, L. Merabet et al, IEEE-TUFFC 2019 as well as patent application FR3090965A1). This made it possible to perform real-time imaging with a transducer comprising a large number of elements (particularly for imaging in a volume).

The so-called “pitch-catch” inspection methods, for their part, are based on the use of two separate sensors, one used to emit ultrasonic waves, the other to receive them. One of the advantages of this device is the ability to detect defects close to the surface of a structure, in particular defects such as cracks oriented perpendicular to the surface of the structure, via the diffraction echo on the ends of the structure. the latter (they advantageously replace pulse-echo methods for shallow defects, the latter suffering from a blind zone close to the surface); they are also called ‘TOFD’ (time of flight diffraction) methods.

The TOFD configuration has also been proposed in combination with multi-element transducers (see for example “TOFD Inspection with Phased Arrays”, C BRILLON et al, 17th WCNDT, 2008; or patent application EP2605009A1) to produce an image of the environment without moving mechanically the transducers. Defects at various depths are then imaged, with a reconstruction algorithm based on the signals received in the time domain.

Finally, in addition to the 'TOFD' configuration, control solutions using sensors positioned on either side of a structure with parallel faces also exist (see for example engineering techniques; M Castaings, ' SIMULATION OF NON-DESTRUCTIVE TESTING BY ULTRASOUND', Cofrend 2008; detection of defects by shading phenomenon of the transmitted field (see for example M. Nieto et al, 6th International Symposium on NDT in Aerospace, 2014 “TTU Phased Array: Quality and Productivity”).

The methods presented previously based on the post-processing in the time domain of the signals recorded by a multi-element transducer (whether in “pulse-echo” or “pitch catch” mode) suffer from a higher algorithmic complexity than the methods presented previously. imaging in the frequency domain, which results in a lower imaging rate.

Furthermore, imaging with a single multi-element sensor (whether in frequency or time) does not make it possible to detect all types of defects taking any orientation. Existing methods offer either so-called 'direct mode' detection (i.e. without bouncing of the ultrasonic beam on the bottom of the part), or detection in post-bounce mode. In direct mode, the ultrasonic response of a crack-type defect with an orientation close to normal to the surface will be very weak (only a diffraction echo on the end of the defect can be detected, but its amplitude can be very low in case of fine opening of the crack). In post-bounce mode, geometrically it is not always possible to measure specular echo for defects at mid-thickness with a single sensor, as illustrated in the figure. which shows two examples of imaging a part P from a single phased array transducer TR.

In the figure on the left, the specular echo reflected on the defect at the bottom of room D returns to the TR sensor. On the other hand, in the figure on the right, the defect D being at the heart of the part P (and the opening (i.e. lateral dimension) of the sensor TR being limited by the combination of admissible inspection frequency and the number of elements of the maximum admissible transducer), the specular echo on the fault D does not return to the TR sensor.

The documents “2-D and 3-D Reconstruction Algorithms in the Fourier Domain for Plane-Wave Imaging in Nondestructive Testing”, L. Merabet et al, IEEE-TUFFC 2019 and WO 2020/128344A1 describe a transform ultrasound imaging method multidimensional Fourier based on a single multi-element transducer.

• Réaliser une transformée de Fourier de la matrice des signaux reçus M(t,xi) à la fois selon l’axe du temps t et selon chacun des axes xi du capteur multi-éléments (1≤i≤N, avec N=1 si le capteur est linéaire et N=2 si le capteur est matriciel)
• Considérer un modèle simplifié de la propagation des ondes dans le milieu, sous forme d’onde plane en émission jusqu’à un diffuseur, puis onde cylindrique (cas d’une image 2D avec un transducteur linéaire) ou sphérique (cas d’une image 3D avec un transducteur matriciel) depuis le diffuseur jusqu’au récepteur
• Ecrire le spectre de l’image en fonction du spectre des signaux reçus calculés à l’étape 1
• En déduire l’image du milieu par transformée de Fourier inverse.

From an emission of plane waves by the transducer, the signals received on each of the channels of this same transducer are post-processed in the frequency-wavenumber domain. The algorithm then consists of:

• Carry out a Fourier transform of the matrix of received signals M(t,xi) both along the time axis t and along each of the axes xi of the multi-element sensor (1≤i≤N, with N=1 if the sensor is linear and N=2 if the sensor is matrix)
• Consider a simplified model of the propagation of waves in the medium, in the form of a plane wave in emission up to a diffuser, then a cylindrical wave (case of a 2D image with a linear transducer) or spherical (case of an image 3D with a matrix transducer) from the broadcaster to the receiver
• Write the spectrum of the image based on the spectrum of the received signals calculated in step 1
• Deduce the image of the middle by inverse Fourier transform.

The algorithmic complexity is then reduced compared to that of a reconstruction of the same signals in the time domain, allowing a significant gain in imaging rate.

This solution does not, however, make it possible to respond to the present technical problem because a single multi-element transducer is considered here and the algorithm is not compatible as it stands with the use of a transmitter transducer physically distinct from a transducer receiver.

Thus, no existing method makes it possible to image all types of defects regardless of their orientation.

The invention proposes an improvement to the method described in patent application WO 2020/128344A1 in order to adapt it to two separate multi-element transducers operating respectively in transmission and reception.

The invention thus makes it possible to facilitate real-time imaging of any shape and orientation defects in solid structures. For this, the algorithm described in application WO 2020/128344A1 is modified by adding a step of taking into account the distance between the two transducers in writing the spectrum of the image as a function of the spectrum of the signals received. We add the coordinates of the center of the receiver which are then distinct from that of the transmitter. The expression of the cylindrical wave (or spherical in 3D) must then take into account this difference between positions of the transmitting multi-element transducer and the receiving multi-element transducer.

• Commander le transducteur d’émission pour générer M émissions successives d’ondes ultrasonores,
• Commander le transducteur de réception pour recevoir simultanément et pendant une durée prédéterminée, pour chaque émission, N signaux temporels de mesure correspondant à des échos dus à des rétro-diffusions de l’émission considérée dans l’objet,
• Echantillonner temporellement chaque signal temporel de mesure en N_téchantillons successifs,
• Déterminer M matrices MR_m, 1≤m≤M, de signaux temporels ultrasonores de taille NxN_t, chaque coefficient MR_m(u_i,t_j) de chaque matrice MR_mreprésentant le t_j-ième échantillon temporel du signal de mesure reçu par le u_i-ième élément du transducteur de réception dû à la m-ième émission,
• Appliquer une transformation de Fourier multi-dimensionnelle en lignes et colonnes à chaque matrice MR_mpour obtenir M matrices spectrales FTMR_m, 1≤m≤M,
• Convertir chaque matrice spectrale FTMR_mpour obtenir M images spectrales FTI_mdans un espace de nombres d’ondes spatiaux, cette conversion comportant l’application d’une relation de transformation matricielle des M matrices FTMR_men les M images spectrales FTI_met l’application d’une transformation à l’aide d’un système d’équations de changement de repère, cette conversion comportant la prise en compte d’un facteur correctif dépendant de la position relative du transducteur de réception par rapport au transducteur d’émission,
• Combiner les M images spectrales FTI_met appliquer une transformation de Fourier multidimensionnelle inverse en lignes et colonnes à l’image spectrale résultante FTI pour obtenir une première image ultrasonore I de visualisation de l’objet.

The subject of the invention is a method for ultrasonic imaging of an object having two opposite faces, from a pair of multi-element transducers comprising a transmission transducer with L elements and a reception transducer with N elements, each placed on the same face or on two opposite faces of the object to be imaged, the method comprising the steps of:

• Control the emission transducer to generate M successive emissions of ultrasonic waves,
• Control the reception transducer to receive simultaneously and for a predetermined duration, for each transmission, N temporal measurement signals corresponding to echoes due to backscattering of the emission considered in the object,
• Temporally sample each temporal measurement signal in N _t successive samples,
• Determine M matrices MR _m , 1≤m≤M, of ultrasonic temporal signals of size NxN _t , each coefficient MR _m (u _i ,t _j ) of each matrix MR _m representing the t _j -th temporal sample of the measurement signal received by the u _i -th element of the reception transducer due to the m-th emission,
• Apply a multi-dimensional Fourier transform in rows and columns to each matrix MR _m to obtain M spectral matrices FTMR _m , 1≤m≤M,
• Convert each FTMR spectral matrix _m to obtain M FTI spectral images _m in a space of spatial wavenumbers, this conversion comprising the application of a matrix transformation relation of the M FTMR matrices _m into the M FTI spectral images _m and l application of a transformation using a system of reference change equations, this conversion comprising the taking into account of a corrective factor depending on the relative position of the reception transducer with respect to the transmission transducer ,
• Combine the M FTI spectral images _m and apply an inverse multidimensional Fourier transform in rows and columns to the resulting FTI spectral image to obtain a first ultrasound image I for viewing the object.

According to a particular aspect of the invention, the multi-element transducers are matrix and during the conversion of each spectral matrix FTMR _m into each spectral image FTI _m , the matrix transformation relation takes the following form:

where k _u , k _v and k _t are the wave numbers, respectively spatial in two respective dimensions and temporal, representative of the rows and columns of each FTMR spectral matrix _m , is the pulsation of the ultrasonic waves and c their propagation speed, k _x , k _y and k _z are the spatial wave numbers representative of the rows and columns of each FTI spectral image _m and corresponding to a reference (x,y,z ) whose origin is the first element of the emission transducer, the plane (x,y) corresponds to one of the faces of the object and the z axis being perpendicular to this face of the object, is an amplitude coefficient dependent on the pulsation of the ultrasonic wave, d _x , d _y and h are the respective coordinates along the x, y and z axes of the reception transducer in said reference frame, at least one of the values of d _x , d _y or h being not zero.

According to a particular aspect of the invention, during the conversion of each spectral matrix FTMR _m into each spectral image FTI _m , the reference change equations take the following form:

Or And are incident angles which define the direction of propagation of the plane wave emitted by an element of the emission transducer

According to a particular aspect of the invention, the multi-element transducers (TR_E, TR_R) are linear and during the conversion of each spectral matrix FTMR _m into each spectral image FTI _m , the matrix transformation relation takes the following form:

where k _u and kt are the wave numbers, respectively spatial and temporal, representative of the rows and columns of each FTMR spectral matrix _m is the pulsation of the ultrasonic waves and c their propagation speed, k _x and k _z are the spatial wave numbers representative of the rows and columns of each FTI spectral image _m and corresponding to a reference point (x, z) whose origin is the first element of the emission transducer, the x axis being parallel to one of the faces of the object and the z axis being perpendicular to this face of the object, is an amplitude coefficient dependent on the pulsation of the ultrasonic wave, d and h are the respective coordinates along the x and z axes of the reception transducer in said reference frame, at least one of the values of d or h being non-zero.

According to a particular aspect of the invention, during the conversion of each spectral matrix FTMR _m into each spectral image FTI _m , the reference change equations take the following form:

Or is an incident angle which defines the direction of propagation of the plane wave emitted by an element of the emission transducer.

According to a particular aspect of the invention, in which the elements of the emission transducer (TR_E) are controlled for M successive emissions of plane ultrasonic waves of emission angles , successively different in M emission zones.

According to a particular aspect of the invention, the respective central operating frequencies of the transmission (TR_E) and reception (TR_R) transducers are different.

• Commander le transducteur d’émission pour recevoir simultanément et pendant une durée prédéterminée, pour chaque émission, N’ signaux temporels de mesure correspondant à des échos dus à des rétro-diffusions de l’émission considérée dans l’objet,
• Echantillonner temporellement chaque signal temporel de mesure en N’_téchantillons successifs,
• Déterminer M’ matrices MR’_m, 1≤m≤M’, de signaux temporels ultrasonores de taille N’xN’_t, chaque coefficient MR’_m(u_i,t_j) de chaque matrice MR’_mreprésentant le t_j-ième échantillon temporel du signal de mesure reçu par le u_i-ième élément du transducteur d’émission dû à la m-ième émission,
• Appliquer une transformation de Fourier multi-dimensionnelle en lignes et colonnes à chaque matrice MR’_mpour obtenir M’ matrices spectrales FTMR’_m, 1≤m≤M’,
• Convertir chaque matrice spectrale FTMR’_mpour obtenir M’ images spectrales FTI’_mdans un espace de nombres d’ondes spatiaux, cette conversion comportant l’application d’une relation de transformation matricielle des M’ matrices FTMR’_men les M’ images spectrales FTI’_met l’application d’une transformation à l’aide d’un système d’équations de changement de repère,
• Combiner les M’ images spectrales FTI’_met appliquer une transformation de Fourier multidimensionnelle inverse en lignes et colonnes à l’image spectrale résultante FTI’ pour obtenir une seconde image ultrasonore I’ de visualisation de l’objet,
• Fusionner la première image ultrasonore I avec la seconde image ultrasonore I’ pour obtenir une image ultrasonore finale I_f.

In an alternative embodiment, the method according to the invention further comprises the following steps:

• Control the transmission transducer to receive simultaneously and for a predetermined duration, for each emission, N' temporal measurement signals corresponding to echoes due to backscattering of the emission considered in the object,
• Temporally sample each temporal measurement signal in N' _t successive samples,
• Determine M' matrices MR' _m , 1≤m≤M', of ultrasonic temporal signals of size N'xN' _t , each coefficient MR' _m (u _i ,t _j ) of each matrix MR' _m representing the t _j - ith time sample of the measurement signal received by the u _i -th element of the transmission transducer due to the m-th emission,
• Apply a multi-dimensional Fourier transform in rows and columns to each matrix MR' _m to obtain M' spectral matrices FTMR' _m , 1≤m≤M',
• Convert each spectral matrix FTMR' _m to obtain M' spectral images FTI' _m in a space of spatial wavenumbers, this conversion comprising the application of a matrix transformation relation of the M' matrices FTMR' _m into the M'FTI' _m spectral images and the application of a transformation using a system of reference change equations,
• Combine the M' spectral images FTI' _m and apply an inverse multidimensional Fourier transformation in rows and columns to the resulting spectral image FTI' to obtain a second ultrasound image I' for viewing the object,
• Merge the first ultrasound image I with the second ultrasound image I' to obtain a final ultrasound image I _f .

In a variant embodiment, the method according to the invention comprises displaying the first ultrasound image I or the final ultrasound image I _f by means of computer-aided design software.

The subject of the invention is a computer program downloadable from a communications network and/or recorded on a computer-readable medium and/or executable by a processor, characterized in that it comprises instructions for executing the steps of an imaging method according to the invention, when said program is executed on a computer.

• une sonde comprenant un couple de transducteurs multi-éléments comprenant un transducteur d’émission à L éléments et un transducteur de réception à N éléments et destinés à être placés chacun sur la même face ou sur deux faces opposées de l’objet à imager,
• des moyens de commande des L éléments du transducteur d’émission pour M émissions successives d’ondes ultrasonores,
• des moyens de commande des N éléments du transducteur de réception pour recevoir simultanément et pendant une durée prédéterminée, pour chaque émission, N signaux temporels de mesure correspondant à des échos dus à des rétro-diffusions de l’émission considérée dans l’objet,
• et un processeur de reconstitution d’une image ultrasonore de visualisation de l’objet, configuré pour exécuter les étapes de la méthode selon l’invention

The subject of the invention is an ultrasonic probing device, for ultrasonic probing of an object, comprising:

• a probe comprising a pair of multi-element transducers comprising a transmission transducer with L elements and a reception transducer with N elements and each intended to be placed on the same face or on two opposite faces of the object to be imaged,
• means for controlling the L elements of the emission transducer for M successive emissions of ultrasonic waves,
• means for controlling the N elements of the reception transducer to receive simultaneously and for a predetermined duration, for each transmission, N temporal measurement signals corresponding to echoes due to back-scattering of the emission considered in the object,
• and a processor for reconstituting an ultrasound image for displaying the object, configured to execute the steps of the method according to the invention

According to a particular aspect of the invention, the multi-element transducers are linear or matrix.

The invention also relates to an assembly comprising an ultrasonic probing device according to the invention and an object to be imaged, the emission transducer and the reception transducer being positioned on the same face of the object or on two faces opposites of the object.

Other characteristics and advantages of the present invention will appear better on reading the description which follows in relation to the following appended drawings.

represents a diagram of an ultrasound imaging device according to the prior art,

represents a diagram of an ultrasound imaging device according to a first embodiment of the invention,

represents a flowchart of the steps of implementing an ultrasound imaging method according to one embodiment of the invention,

represents an illustrative diagram of the implementation of the ultrasound imaging method according to the invention by means of the device of the ,

represents a diagram of an ultrasound imaging device according to a second embodiment of the invention,

represents an illustrative diagram of the implementation of the imaging method according to the invention by means of the device of the ,

represents an example of an ultrasound image obtained using the imaging device according to the second embodiment,

represents a particular implementation of the ultrasound imaging device according to the second embodiment of the invention for imaging a certain type of defects.

The invention aims to carry out ultrasonic imaging of a solid part, for example with the aim of non-destructive testing of the part, by means of two multi-element ultrasonic transducers, one operating in emission and the other other in reception.

The number of elements of each transducer can be different, the inter-element distance is constant for the same transducer but can be different between the two transducers.

There illustrates a first embodiment of the invention for which the two transducers TR_E, TR_R are positioned on the same flat surface on one side of the part P to be imaged.

The TR_E transmission and TR_R reception transducers each comprise an ultrasonic probe having a housing in which a number of ultrasonic elements arranged in a network are arranged linearly or matrixly. Each transducer can be made by a piezoelectric sensor, a micro-machined sensor or an electromagnetic acoustic transducer (EMAT) or any other element making it possible to emit and receive ultrasonic waves.

The part P to be imaged is for example a mechanical part that we wish to examine by non-destructive testing. The part P can be immersed in a liquid, such as water and the ultrasonic probe is then kept at a distance from the part P so that the water separates them. But the probe can also be in direct contact with part P.

The ultrasonic elements of the TR_E emission transducer are designed to individually emit ultrasonic waves towards the part P in response to control signals. The ultrasonic waves emitted correspond to a plane wave which is then created in the part P in a given direction...

The ultrasonic elements of the receiving transducer TR_R are designed to detect echoes of the ultrasonic waves reflecting or back-scattering on and in the part P and to provide measurement signals corresponding to these echoes.

Each TR_E, TR_R transducer further comprises an electronic circuit for controlling the ultrasonic elements (in transmission) and processing the measurement signals (in reception).

The electronic circuit has for example a central processing unit and a memory in which is recorded a computer program configured to implement the processing necessary for the emission of ultrasonic waves on the one hand and the processing of the measurements in reception of on the other hand in order to generate an image of the part P.

There illustrates on a flowchart the steps of implementing an ultrasound imaging method according to one embodiment of the invention.

The first step 301 consists of activating the ultrasonic elements of the emission transducer TR_E in order to emit at least one plane wave in a direction given by an emission angle. In a variant, several plane waves are emitted successively with different emission angles as shown schematically on the .

A plane ultrasonic wave having a given emission angle can be obtained by applying delay laws recorded in memory, for example in a delay law base, to the ultrasonic elements of the emission transducer TR_E. Each delay law defines delays to be applied to the different elements of the emission transducer so as to generate a plane ultrasonic wave at a desired emission angle. Different delay laws can be provided for different emission angles.

By varying the emission angles, it is thus possible to image a zone contained in the union of all the successive emission zones corresponding to each emission angle.

In step 302, the reception transducer TR_R is activated to receive, for each plane wave emission, simultaneously by the N ultrasonic elements and for a predetermined acquisition duration, N temporal measurement signals, measuring in particular echoes due to backscattering of each emission considered in the room P. In particular, these echoes can come from a defect D in the room, for example a crack type defect.

On reception of the signals resulting from each of the M successive emissions, the set S of the NxM temporal measurement signals received by the N ultrasonic elements of the transducer TR_R is returned by the probe to the central processing unit. In a manner known per se, these time signals are sampled and digitized into Nt successive samples before being submitted for processing by the computer program.

In step 303, we construct M matrices MRm, 1≤m≤M, of ultrasonic temporal signals of size NxNt, qualified as matrices of responses to plane waves. Each coefficient MRm(ui,tj) of each matrix MRm representing the tj-th time sample of the measurement signal received by the ui-th element of the reception transducer TR_R in response to the m-th transmission.

Optionally, a temporal filtering step is carried out on each MRm matrix, this filtering aimed at removing any information found at flight times excluded from the zone of interest in the object P.

In step 304, each matrix MRm is transformed into a matrix FTMRm of frequency signals by two-dimensional Fourier transform in rows and columns, advantageously by discrete two-dimensional Fourier transform and, even more advantageously, by two-dimensional calculation of FFT (from the English “Fast Fourier Transform”) if the numbers N and Nt of rows and columns of each matrix MRm allow it, that is to say if they correspond to powers of 2. We thus obtain M spectral matrices FTMRm, 1 ≤m≤M, whose coefficients FTMRm(kui, ωj) are spectral values taken as functions of discrete values kui, 1≤i≤N, of a spatial wavenumber ku (relating to the relative arrangements of the elements of the transducer reception) and discrete values ωj, 1≤j≤Nt, of a pulse ω (relative to the sampling instants).

The pulsation ω depends on the frequency and the wave number k _t through the following relationships:

, with c the propagation speed of the waves considered and f their frequency. The FTMRm spectral matrices can be expressed indifferently as a function of the pulsation ω or the wave number k _t , the transition from one to the other expression being carried out by means of a change of reference.

In step 305, each FTMR spectral matrix _m is then converted into an FTI spectral image _m in a space of spatial wave numbers respectively relating to the abscissa and ordinate axes of the final image that we wish to obtain. We thus obtain M spectral images FTI _m , 1≤m≤M, of size N _x xN _z and of coefficients FTI _m (kx _i ,kz _j ) where the kx _i , 1≤i≤N _x , are discrete values d 'a spatial wave number kx relative to the chosen abscissa axis (for example parallel to that of the transducers) and where the kz _j , 1≤j≤N _z , are discrete values of a spatial wave number kz relative to the chosen ordinate axis (for example perpendicular to that of the transducers). This conversion comprises the application of a matrix transformation relation of the M FTMR matrices _m into the M spectral images FTI _m and the application of a transformation using a system of reference change equations. More precisely, the matrix transformation gives values for the spectral images at points (kx' _i ,kz' _j ), 1≤i≤N and 1≤j≤N _t , which do not correspond to the discrete values (kx _i , kz _j ) chosen but depend on the system of reference change equations which links the values of the wave numbers kx and kz to the values of the wave numbers ku and pulsation ω or the wave number kt. The desired FTI coefficients _m (kx _i ,kz _j ), with 1≤i≤N _x and 1≤j≤N _z , can nevertheless be easily found by interpolation of the FTI _m values (kx' _i ,kz' _j ) obtained by matrix transformation, using the system of reference change equations which makes it possible to know the positioning of the points (kx' _i ,kz' _j ), 1≤i≤N and 1≤j≤N _t .

Optionally, when several plane waves have been emitted in different directions, a step of combining the M spectral images FTI _m into a single resulting spectral image FTI with coefficients FTI(kx _i ,kz _j ), 1≤i≤N _x and 1≤ j≤N _z is achieved. In a simple and rapid embodiment, the FTI spectral image can result from a sum at each pixel (kx _i , kz _j ) of the M FTI spectral images _m .

In step 306, the spectral image FTI is transformed into an ultrasound image I for displaying the object P by two-dimensional inverse Fourier transform in rows and columns, advantageously by inverse discrete Fourier transform, and, even more advantageously, by two-dimensional calculation of IFFT (from the English “Inverse Fast Fourier Transform”) if the numbers N _x and N _z of rows and columns of the resulting FTI spectral image allow it, that is to say if they correspond to powers of 2. The ultrasound image I displaying the object P is of size N _x xN _z and of pixel values I(x _i ,z _j ).

Optionally, it is also possible to combine the ultrasound images obtained for different directions of plane waves emitted after application of the inverse Fourier transform instead of combining the spectral images.

There illustrates an example of application of the invention according to the first embodiment of the invention.

In this example, the transducers TR_E and TR_R are linear, that is to say that the ultrasonic elements are arranged along a line and they are a distance d apart, separated on the same plane. The imaging device is thus capable of performing 2D imaging of the part.

A plane wave is emitted by the transmission transducer TR_E with a direction θ. On the , we have schematically represented the LR delay laws applied to the different ultrasonic elements to generate the plane wave.

We fix a reference R whose origin is the first element EL_1_E of the emission transducer TR_E, the x axis is parallel to the surface of the part P on which the transducers are arranged and the z axis is perpendicular to this surface .

The measured field by the element U of the receiving transducer TR_R following the emission of a pulsating plane wave (and therefore wave number kt = /c, with c the speed of propagation of the wave in the medium) according to the direction by the transmitter transducer TR_E and reflected on the point of coordinates (x,z) in the frame R linked to the transmitter transducer, is written in the following form, after application of a Fourier transformation according to the time variable:

r is the vector of coordinates of the calculation point, and U is the vector of coordinates of the current element of the receiving transducer TR_R, Or is the wave number ( /c) at the central transmission frequency (and x is the unit vector carried by the x axis, z the unit vector carried by the z axis). It is then necessary to take into account the fact that the centers of the transmitter and receiver transducers are distinct; to do this, arbitrarily, we express U and r in the frame linked to the transmitting transducer (we can indifferently express the coordinates in the frame linked to the receiving transducer). In the particular case of the example described in , U = (u+d,0) (u is the scalar variable defining the horizontal position of the receiver element in the frame linked to the receiver) and r = (x,z). d is the distance between the two transducers.

In equation (1.1), the function (Hankel function of order 0 and second kind) describes the “return” propagation of a cylindrical wave between the receiving transducer TR_R and the image point . Function is written in the following form:

By injecting equation (1.2) into (1.1), the spectrum is then written:

By applying a Fourier transform according to the variable u, the spectrum is written:

where F is the spectrum of the ultrasound image f(x,z) of the part to be imaged.

We can deduce :

The image is then obtained by calculating the inverse Fourier transform:

The equations above reveal a term in the equation for converting the spectrum of the measured field into a spectral image. This term is linked to the distance d between the transmitting and receiving transducers.

By applying this principle to the method according to the invention, we obtain the following matrix transformation relationship between the M matrices FTMRm and the M spectral images FTIm (step 305):

More precisely, according to the previous discrete notations, for all m, 1≤m≤M, we obtain:

We further obtain the following system of general reference change equations, which links the values of the wave numbers k _x and k _z to the values of the wave numbers k _u and kt:

More concretely, according to the previous discrete notations, for all m, 1≤m≤M, this gives:

In a variant embodiment, this step is followed by an interpolation step as described in patent application WO 2020/128344A1 in order to define kx'i and kz'j on a regular grid and therefore be compatible with algorithms discrete Fourier transform more or less fast. This can consist of any known type of interpolation (nearest neighbor, linear, cubic, spline etc).

According to a variant of the first embodiment, the transducers TR_R and TR_E are matrix, that is to say they each comprise a matrix of ultrasonic elements. An advantage to using matrix sensors is that they allow 3D imaging and not simply 2D.

In this case, it is no longer necessary to consider a 2D plan reference (x,z) but a 3D reference (x,y,z) with for example the plane (x,y) corresponding to the plane in which the two matrix transducers are arranged .

We then note dx the distance between the two transducers along the x axis and dy the distance between the two transducers along the y axis.

The plane wave emitted by the emission transducer is then defined by two angles (instead of just one for the 2D case) which define a direction of propagation in the frame (x,y,z).

The direction of the plane wave is thus given by the vector .

An element of the reception transducer TR_R is also defined in the 3D coordinate system by the coordinates )=( ), where (u,v) are the respective distances along the x,y axes of an element of the reception transducer relative to the first element of this transducer.

Similar to the 2D case developed above, the spectrum of the measured field by the element ) of the receiving transducer TR_R following the emission of a pulsating plane wave depending on direction by the issuer is written in the following form:

Here, the function describes the “return” propagation of a spherical wave between the receiving transducer TR_R and the image point . Function is written in the following form:

By injecting equation (1.4) into (1.3), the spectrum is then written:

with

By applying a Fourier transform according to the variables u and v, the spectrum is then written:

where F is the spectrum of the 3D image f(x,y,z).

Thus, we obtain the following conversion and change of reference equations:

The image (x,y,z) is obtained by calculating the trilinear inverse Fourier transform:

The term is linked to the relative position of the receiving transducer relative to the transmitting transducer.

By applying the above principle to the method according to the invention, and similarly to the 2D case, we obtain the following matrix transformation relationship between the M matrices FTMRm and the M spectral images FTIm (step 305):

More precisely, according to the previous discrete notations, for all m, 1≤m≤M, we obtain:

We further obtain the following system of general reference change equations, which links the values of the wave numbers kx, ky and kz to the values of the wave numbers ku, kv and kt:

We now describe a second embodiment of the invention, illustrated by the , for which the transmission and reception transducers are positioned on two opposite parallel faces of the part P to be imaged.

In the example of the , the reception transducer TR_R is placed on the opposite face of the part in relation to the emission transducer TR_E. In other words, the reception transducer TR_R is at a distance h from the transmission transducer along the z axis of the mark, h being the depth of the room P. But the reception transducer can also be positioned at a non-zero distance from the emission transducer along the x axis as is also illustrated in .

There schematizes another embodiment for which the two transducers are placed opposite each other and the distance between the two transducers along the x axis is zero.

The ultrasound imaging method described in remains applicable identically for this second embodiment. A difference must be taken into account, however, in the corrective factor which depends on the relative positioning of the two transducers in the equation for converting the spectrum of the measured field into a spectral image.

Indeed, in this second embodiment, the expression of the spectrum of the field received by an ultrasonic element U=(u,h) of the reception transducer following the emission of a pulsating plane wave depending on direction by the transmitting transducer is always written:

However, this time, in the Cartesian coordinate system (x,z) centered on the first element of the transmitting transducer, the function is written in the following form:

(2.2)

By injecting equation (2.2) into (2.1), the spectrum is then written:

By applying a Fourier transform according to the variable u, the spectrum is then written:

We can deduce :

A sign - appears in the expression of which reflects the fact that the cylindrical wave from the calculation point r to the receiver propagates in the positive direction of the z axis.

The same calculation steps are then applied: possible average of for all angles of plane waves emitted, then an inverse two-dimensional Fourier transform is carried out to go back to the image f(x,z).

Thus, in the case of application of the and for 2D imaging, we obtain the following matrix transformation relationship between the M matrices FTMRm and the M spectral images FTIm (step 305):

We further obtain the following system of general reference change equations, which links the values of the wave numbers kx and kz to the values of the wave numbers ku and kt:

There shows an ultrasound image I obtained using a device according to the second embodiment for which 6 plane waves are emitted by a linear transducer TR_E in different directions. The plane waves interact with crack-type defects D located at the heart of the part P. The positioning configuration of the transducers TR_E, TR_R facing each side of the part (as represented in Figure ) is optimal for the detection of specular echoes on defects such as fine cracks contained in a plane perpendicular to the entry surfaces of the part and whose depth is close to mid-thickness (we see on the that the defect located closest to mid-thickness leads to a specular echo of higher amplitude on the ultrasound image shown on the right). This type of defect is in fact particularly difficult to detect with a single sensor since only the echoes created by diffraction on the ends of the defect can possibly be detected, but are of very low amplitude. In particular, in components made of coarse-grained steel for which the structure generates noise on the images, the amplitude of the diffraction echoes can be drowned in this noise.

In the case where, in the frame linked to the transmitting transducer, the receiving transducer has both non-zero coordinates on the z axis and on the x axis, then the expression of the spectrum of the wave field measured on a element u of the reception transducer becomes:

And we obtain the following conversion and change of reference equations:

Thus, we obtain the following more general matrix transformation relation between the M matrices FTMRm and the M spectral images FTIm (step 305):

This variant is of particular interest for defects such as fine cracks contained in a plane perpendicular to the entry surfaces of the part, and which would not be located at mid-thickness. Specular echoes are then more easily detected when the transmitter and receiver are offset along the x axis. An example of this type of configuration is shown in with a reception transducer TR_R offset from the transmission transducer TR_E along the x axis and a fault D located closer to the reception transducer than to the transmission transducer.

In the case of 3D imaging using matrix transducers, the conversion and reference change equations are obtained in a similar way. We finally obtain the following matrix transformation relation:

Thus, in general and as described in support of the various examples cited above, the device according to the invention comprises two transducers acting respectively in transmission and reception which can be linear or matrix in order to produce 2D or 3D imaging. and which can be placed on the same plane on the same side of the part to be imaged or on two opposite parallel faces of the part to be imaged. In the latter case, the two transducers can be opposite each other or offset along the axis parallel to the planes of the transducers.

In all scenarios, the method according to the invention comprises a step 305 of conversion between the M matrices FTMRm and the M spectral images FTIm which is based on a matrix transformation relation which takes into account a coefficient reflecting the relative position of the receiving transducer relative to the transmitting transducer.

According to an alternative embodiment, the method described in this document can be combined with that described in the Applicant's patent application WO 2020/128344A1 in the following manner. During each series of plane wave emissions carried out by the transmitting transducer TR_E, the elementary signals measured both on the receiving transducer TR_R and on the transmitting transducer TR_E are recorded. The imaging method described in the aforementioned patent application is applied to the signals measured by the transmitting transducer TR_E and the method according to the present invention is applied to the signals measured by the receiving transducer TR_R.

Then, the ultrasound images obtained via the two methods are merged using any known fusion method, for example an average of the pixels of the two images.

• Le transducteur d’émission TR_E est commandé pour recevoir simultanément et pendant une durée prédéterminée, pour chaque émission, N’ signaux temporels de mesure correspondant à des échos dus à des rétro-diffusions de l’émission considérée dans l’objet,
• chaque signal temporel de mesure est échantillonné temporellement en N’_téchantillons successifs,
• On détermine ensuite M’ matrices MR’_m, 1≤m≤M’, de signaux temporels ultrasonores de taille N’xN’_t, chaque coefficient MR’_m(u_i,t_j) de chaque matrice MR’_mreprésentant le t_j-ième échantillon temporel du signal de mesure reçu par le u_i-ième élément du transducteur d’émission dû à la m-ième émission,
• On applique ensuite une transformation de Fourier multi-dimensionnelle en lignes et colonnes à chaque matrice MR’_mpour obtenir M’ matrices spectrales FTMR’_m, 1≤m≤M’,
• On converti ensuite chaque matrice spectrale FTMR’_mpour obtenir M’ images spectrales FTI’_mdans un espace de nombres d’ondes spatiaux, cette conversion comportant l’application d’une relation de transformation matricielle des M’ matrices FTMR’_men les M’ images spectrales FTI’_met l’application d’une transformation à l’aide d’un système d’équations de changement de repère, les équations de transformation étant données par (dans le cas 2D) :

In other words, in this alternative embodiment, the following processing operations are carried out by the transmission transducer TR_E in parallel with the reception transducer TR_R:

• The transmission transducer TR_E is controlled to receive simultaneously and for a predetermined duration, for each emission, N' temporal measurement signals corresponding to echoes due to backscattering of the emission considered in the object,
• each temporal measurement signal is sampled temporally in _N't successive samples,
• We then determine M' matrices MR' _m , 1≤m≤M', of ultrasonic temporal signals of size N'xN' _t , each coefficient MR' _m (u _i ,t _j ) of each matrix MR' _m representing the t _j -th time sample of the measurement signal received by the u _i -th element of the transmission transducer due to the m-th transmission,
• We then apply a multi-dimensional Fourier transformation in rows and columns to each matrix MR' _m to obtain M' spectral matrices FTMR' _m , 1≤m≤M',
• Each spectral matrix FTMR' _m is then converted to obtain M' spectral images FTI' _m in a space of spatial wave numbers, this conversion comprising the application of a matrix transformation relation of the M' matrices FTMR' _m into them. M' spectral images FTI' _m and the application of a transformation using a system of reference change equations, the transformation equations being given by (in the 2D case):

• Then we combine the M' spectral images FTI' _m and we apply an inverse multidimensional Fourier transformation in rows and columns to the resulting spectral image FTI' to obtain a second ultrasound image I' for displaying the object,
• Finally, the first ultrasound image I obtained by the receiver transducer is merged with the second ultrasound image I' obtained by the transmitter transducer to obtain a final ultrasound image I _f .

An advantage to the simultaneous operation of the two transducers in reception to generate two ultrasound images of the same part is that this makes it possible to improve the precision of the final image for a limited complexity of implementation, the processing necessary for the two images which can be carried out in parallel from the measurements received simultaneously by the two transducers TR_E, TR_R.

The ultrasound image obtained using the invention can be displayed on an interface using 2D or 3D computer-aided design software.

In a variant embodiment, the receiver transducer can have a central operating frequency different from the central operating frequency of the transmitter transducer, this makes it possible in particular to carry out frequency harmonic imaging. In other words, in this case, the receiver transducer receives measurement signals at harmonic frequencies of the central operating frequency of the transmitter transducer.

Each transducer can be positioned directly against one side of the part to be controlled or can be separated from the part by a height of water.

The invention has the notable advantage of allowing better imaging of thin-thickness crack-type defects located at mid-thickness of thick parts.

Claims (13)

Ultrasound imaging method of an object having two opposite faces, using a pair of multi-element transducers comprising a transmission transducer (TR_E) with L elements and a reception transducer (TR_R) with N elements, placed each on the same face or on two opposite faces of the object to be imaged, the method comprising the steps of:

• Control (301) the emission transducer (TR_E) to generate M successive emissions of ultrasonic waves,
• Control (302) the reception transducer (TR_R) to receive simultaneously and for a predetermined duration, for each transmission, N temporal measurement signals corresponding to echoes due to backscattering of the emission considered in the object,
• Temporally sample each temporal measurement signal in N _t successive samples,
• Determine (303) M matrices MR _m , 1≤m≤M, of ultrasonic temporal signals of size NxN _t , each coefficient MR _m (u _i ,t _j ) of each matrix MR _m representing the t _j -th temporal sample of the signal measurement received by the u _i -th element of the reception transducer due to the m-th transmission,
• Apply (304) a multi-dimensional Fourier transformation in rows and columns to each MR matrix _m to obtain M spectral matrices FTMR _m , 1≤m≤M,
• Convert (305) each FTMR spectral matrix _m to obtain M FTI spectral images _m in a space of spatial wavenumbers, this conversion comprising the application of a matrix transformation relation of the M FTMR matrices _m into the M FTI spectral images _m and the application of a transformation using a system of reference change equations, this conversion comprising the taking into account of a corrective factor depending on the relative position of the reception transducer (TR_R) by relative to the emission transducer (TR_E),
• Combine the M FTI spectral images _m and apply an inverse multidimensional Fourier transform (306) in rows and columns to the resulting FTI spectral image to obtain a first ultrasound image I for viewing the object.

Ultrasound imaging method according to claim 1 in which, the multi-element transducers (TR_E, TR_R) are matrix and during the conversion of each spectral matrix FTMR _m into each spectral image FTI _m , the matrix transformation relation takes the form next :

where k _u , k _v and k _t are the wave numbers, respectively spatial in two respective dimensions and temporal, representative of the rows and columns of each FTMR spectral matrix _m , is the pulsation of the ultrasonic waves and c their propagation speed, k _x , k _y and k _z are the spatial wave numbers representative of the rows and columns of each FTI spectral image _m and corresponding to a reference (x,y,z ) whose origin is the first element of the emission transducer, the plane (x,y) corresponds to one of the faces of the object and the z axis being perpendicular to this face of the object, is an amplitude coefficient dependent on the pulsation of the ultrasonic wave, d _x , d _y and h are the respective coordinates along the x, y and z axes of the reception transducer in said reference frame, at least one of the values of d _x , d _y or h being not zero. Ultrasound imaging method according to claim 2 in which, during the conversion of each FTMR spectral matrix _m into each FTI spectral image _m , the reference change equations take the following form:

Or And are incident angles which define the direction of propagation of the plane wave emitted by an element of the emission transducer Ultrasound imaging method according to claim 1 in which, the multi-element transducers (TR_E, TR_R) are linear and during the conversion of each FTMR spectral matrix _m into each FTI spectral image _m , the matrix transformation relation takes the form next :

where k _u and kt are the wave numbers, respectively spatial and temporal, representative of the rows and columns of each FTMR spectral matrix _m is the pulsation of the ultrasonic waves and c their propagation speed, k _x and k _z are the spatial wave numbers representative of the rows and columns of each FTI spectral image _m and corresponding to a reference point (x, z) whose origin is the first element of the emission transducer, the x axis being parallel to one of the faces of the object and the z axis being perpendicular to this face of the object, is an amplitude coefficient dependent on the pulsation of the ultrasonic wave, d and h are the respective coordinates along the x and z axes of the reception transducer in said reference frame, at least one of the values of d or h being non-zero. Ultrasound imaging method according to claim 4 in which, during the conversion of each FTMR spectral matrix _m into each FTI spectral image _m , the reference change equations take the following form:

Or is an incident angle which defines the direction of propagation of the plane wave emitted by an element of the emission transducer. Ultrasound imaging method according to any one of the preceding claims, in which the elements of the emission transducer (TR_E) are controlled for M successive emissions of plane ultrasonic waves of emission angles , successively different in M emission zones. Ultrasound imaging method according to any one of the preceding claims in which the respective central operating frequencies of the transmission (TR_E) and reception (TR_R) transducers are different. Ultrasound imaging method according to any one of the preceding claims further comprising the following steps:

• Control the transmission transducer (TR_E) to receive simultaneously and for a predetermined duration, for each emission, N' temporal measurement signals corresponding to echoes due to backscattering of the emission considered in the object,
• Temporally sample each temporal measurement signal in N' _t successive samples,
• Determine M' matrices MR' _m , 1≤m≤M', of ultrasonic temporal signals of size N'xN' _t , each coefficient MR' _m (u _i ,t _j ) of each matrix MR' _m representing the t _j - ith time sample of the measurement signal received by the u _i -th element of the transmission transducer due to the m-th emission,
• Apply a multi-dimensional Fourier transform in rows and columns to each matrix MR' _m to obtain M' spectral matrices FTMR' _m , 1≤m≤M',
• Convert each spectral matrix FTMR' _m to obtain M' spectral images FTI' _m in a space of spatial wavenumbers, this conversion comprising the application of a matrix transformation relation of the M' matrices FTMR' _m into the M'FTI' _m spectral images and the application of a transformation using a system of reference change equations,
• Combine the M' spectral images FTI' _m and apply an inverse multidimensional Fourier transformation in rows and columns to the resulting spectral image FTI' to obtain a second ultrasound image I' for viewing the object,
• Merge the first ultrasound image I with the second ultrasound image I' to obtain a final ultrasound image I _f .

An ultrasound imaging method according to any one of the preceding claims comprising displaying the first ultrasound image I or the final ultrasound image I _f by means of computer-aided design software. Computer program downloadable from a communications network and/or recorded on a computer-readable medium and/or executable by a processor, characterized in that it comprises instructions for executing the steps of an imaging process according to any one of claims 1 to 9, when said program is executed on a computer. Ultrasonic probing device, for ultrasonic probing of an object (P), comprising:

• a probe comprising a pair of multi-element transducers comprising a transmission transducer (TR_E) with L elements and a reception transducer (TR_R) with N elements and intended to be each placed on the same face or on two opposite faces of the 'object to be imaged (P),
• means for controlling the L elements of the emission transducer (TR_E) for M successive emissions of ultrasonic waves,
• means for controlling the N elements of the reception transducer (TR_R) to receive simultaneously and for a predetermined duration, for each transmission, N temporal measurement signals corresponding to echoes due to backscattering of the transmission considered in the object,
• and a processor for reconstituting an ultrasound image for displaying the object, configured to execute the steps of the method according to any one of claims 1 to 9.

Ultrasonic sounding device according to claim 11 in which the multi-element transducers (TR_E, TR_R) are linear or matrix. Assembly comprising an ultrasonic probing device according to any one of claims 11 to 12 and an object to be imaged, the emission transducer and the reception transducer being positioned on the same face of the object or on two opposite faces of the object.