Method for analysing a medium

Abstract

The present invention relates to a method for analysing a medium that includes: - acquiring (101) echo signals; - calculating (102) a plurality of directional signals from the echo signals; - estimating (103) a set of inter-directional signals for different times of interest (T), based on the plurality of directional signals; and - determining (104) at least one characteristic of the medium as a function of the change over time of the estimated inter-directional signals.

Description

[0001] METHOD FOR ANALYZING A MEDIUM

[0002] FIELD OF THE INVENTION

[0003] The present invention relates to the general technical field of the analysis of a medium by wave propagation, and in particular sound or ultrasonic waves, or electromagnetic waves.

[0004] More specifically, the present invention relates to a method and a device for the analysis of a target object, or of a diffuse medium such as a biological, human or animal tissue.

[0005] In the following, the present invention will be described with reference to medical ultrasound imaging, it being understood that the teachings described herein can be used in other types of applications (non-medical ultrasound, SONAR, RADAR, etc.) using waves whose amplitude, frequency and phase can be controlled or estimated.

[0006] BACKGROUND OF THE INVENTION

[0007] 1. General principle of diffusion

[0008] There are various known solutions for analyzing a medium using the principle of wave diffusion. In order to simplify the discussion, a discrete description is adopted here, although the reality of diffusion is continuous.

[0009] Referring to Figure 1, scattering is a phenomenon by which a wave UE is deflected and redistributed in various directions Ui, l, P, Echi by an interaction with a “scattering object” Obi contained in a medium.

[0010] Analysis solutions generally consist of:

[0011] - emit, using an emitter E, an excitation wave UE into the medium to be analyzed,

[0012] - receive, using a receiver R, echoes Echi, Ech2 following the diffusion of the incident excitation wave UE by one (or more) diffusing object(s) Obi, Ob2 contained in the medium and convert them into reception signals,

[0013] - process the reception signals to extract information about the environment. The reception signals consist of two components:

[0014] - a so-called “simple diffusion” component, and

[0015] - a so-called “multiple diffusion” component.

[0016] More precisely and as previously recalled, the diffusion of the wave induces its deviation and its redistribution in various directions, so that certain parts P of the deviated wave can interact with other diffusing objects Ob2 contained in the medium before being received by the receiver R.

[0017] The parts Echi of the deflected wave that are captured by the receiver R before interacting with other scattering objects Ob2 constitute the simple scattering component.

[0018] The deflected parts Ech2 of the wave that are captured by the receiver R after interacting with several receiving objects Obi, Ob2 constitute the multiple scattering component. Here the description is limited to two scattering objects but is of course generalizable to a larger number of scatterers.

[0019] Traditional analysis solutions for an environment generally use the simple scattering component of reception signals: at each given instant of reception of an echo, the measurement of the time elapsed between the emission of the excitation wave and the reception of the associated simple scattering component is representative of the position of the scattering object.

[0020] However, since the simple scattering component is combined with the multiple scattering component, these traditional analysis solutions are not applicable to media including a large number of scattering objects Obi, Ob2, or if the scatterers present in the medium have a high scattering power.

[0021] 2. Principle of coherent backscattering in the field of optics

[0022] Thus, in highly heterogeneous environments, such as porous environments (bones, lungs, etc.), traditional analysis solutions used to map a region of interest are no longer valid.

[0023] Indeed, the relationship existing between:

[0024] - the time "t" elapsing between the emission (by a transmitter / receiver) of a wave and the reception (by the transmitter / receiver) of a reflected wave, and - the distance "d" between the transmitter / receiver and the diffuser is no longer valid due to the appearance of the multiple diffusion phenomenon.

[0025] This multiple scattering (the main scattering regime in porous media such as the lung) nevertheless contains information characterizing the medium. In particular, if the multiple scattering is sufficiently important (strong scattering, high number of scatterers), it is possible to model the path of a wave in the medium as a random walk itself obeying the properties of scattering, with a scattering constant D, itself linked to the mean free path of scattering L.

[0026] This behavior, identified in optics, gives rise to an echo containing an incoherent scattering component (chaotic multiple scattering background) and a coherent scattering component, concentrated close to the emission location, which gives rise to a phenomenon traditionally called “coherent backscattering cone”.

[0027] In particular, it has been demonstrated in optics that the coherence of the waves is not totally lost thanks to the "coherent backscattering" effect, even in a strongly multi-scattering medium. Indeed, constructive interference between reciprocal paths means that, when an average over several illuminations of the medium is carried out, the backscattered intensity is twice as important in the initial direction of illumination of the medium, than in the other directions (figure 2), which defines a peak (called "coherent backscattering cone" Crc) whose width and evolution over time are related to the transport properties of the medium.

[0028] 3. Adaptation of the principle of coherent backscattering in the field of ultrasound

[0029] These principles, first observed in optics, were then used in the field of ultrasound imaging, notably in documents WO 2020 / 117789 and WO 2019 / 104340.

[0030] Document WO 2020 / 117789 describes a system for detecting lesions and / or anomalies in a heterogeneous environment using ultrasonic waves. This system comprises:

[0031] - an array of ultrasound transducer elements configured to transmit ultrasound signals and to receive backscattered ultrasound signals, and - a processor capable of executing a lesion detection algorithm that processes the backscattered ultrasound signals to: o obtain an inter-element response matrix (IEM), o divide the IEM into a plurality of sub-IEMs corresponding to subsets of the ultrasound transducer elements, and o then perform additional depression detection processing to identify one or more lesions and / or abnormalities.

[0032] Document WO 2019 / 104340 describes a method for measuring micro-architectural properties of a vascular network. The method comprises the steps of:

[0033] - inject an ultrasound contrast agent into a medium,

[0034] - transmitting a plurality of acoustic pulses into the medium using an array of ultrasonic transducers, each respective acoustic pulse being transmitted from one or more elements of the array of ultrasonic transducers,

[0035] - receiving a plurality of backscattered signals with the ultrasonic transducer array in response to each respective acoustic pulse,

[0036] - obtain a response matrix including the backscattered signals

[0037] - extract a coherent or incoherent contribution to the backscattered signals from the response matrix, and

[0038] - quantify a property of the vascular network based on the coherent or incoherent contribution to backscattered signals.

[0039] In WO 2020 / 117789 and WO 2019 / 104340, the ultrasonic transducer array is used in an unconventional manner. Instead of performing conventional beamforming and imaging, the ultrasonic pulses are transmitted by triggering individual elements of the ultrasonic transducer array one by one and receiving the backscattered signals on each element separately. In doing so, an inter-element response matrix is ​​acquired, which can be used to extract the coherent or incoherent contribution to the backscattered signals. For example, in some implementations, the incoherent contribution is extracted.Thus, documents WO 2020 / 117789 and WO 2019 / 104340 propose to adapt the optical theory of "coherent backscattering" to a point approach in the field of ultrasound, i.e. by emitting an ultrasonic wave at a given position (with a single ultrasonic transducer), and receiving a reflected wave at another position (with another single ultrasonic transducer).

[0040] The coherent backscatter cone is then observed when the position of the transducer that emitted the ultrasonic wave (emission point) is close to the position of the transducer that received the ultrasonic wave reflected by the medium (reception point). However, this backscatter cone is so thin that it is most of the time considered to exist only when the emission and reception points are the same.

[0041] The study then focuses on the magnification of an incoherent diffusion halo, whose spatial spreading as a function of time is directly linked to the diffusion constant D.

[0042] 4. Problems associated with existing processes in the field of ultrasound

[0043] The technique described in documents WO 2020 / 117789 and WO 2019 / 104340 consists of:

[0044] - construct an inter-element matrix from ultrasonic emission and reception in the medium, and

[0045] - using this representation to extract a signal comprising a coherent backscattering cone and an incoherent scattering halo has several limitations which significantly degrade its performance in real conditions.

[0046] Especially :

[0047] - the emission and reception points must be in direct contact with the environment studied, and

[0048] - the incoherent nature of the data studied implies a high sensitivity to noise.

[0049] 4.1. Need for direct contact with the environment studied The first limitation (emission and reception points in contact with the environment) poses a problem when the environment is not directly accessible.

[0050] For example, when the medium studied is a human lung, it is not directly accessible since it is protected by the pleura and a layer of subcutaneous tissue.

[0051] It is therefore not possible to position the ultrasonic transducers emitting the ultrasonic wave (emission point) and receiving the reflected ultrasonic wave (reception point) directly in contact with the lung to be studied.

[0052] To overcome this limitation, one solution may be to focus the wave emitted by the transducer directly onto the surface of the lung in order to create a virtual emission point on the surface of the lung to be studied.

[0053] However, this solution requires precise knowledge of the position of the lung in real time, and the ability to obtain sufficiently precise focusing despite the aberrations introduced by crossing the layers of subcutaneous tissue.

[0054] 4.2. Inconsistent nature of the data studied

[0055] The second limitation can also be mitigated by using focusing that concentrates the energy of multiple ultrasonic transducers (of the transducer array) to create a virtual emission point emitting a higher intensity ultrasonic wave.

[0056] However, this focusing only provides a limited energy gain, particularly in the near field, and must be monitored to avoid damaging the surface of the medium which can be particularly fragile (as is the case for the surface of the lung, which particularly absorbs ultrasonic energy and can be inflamed in the event of excessively powerful insonification).

[0057] An aim of the present invention is to propose a method and a device for analyzing a medium making it possible to remedy at least one of the aforementioned drawbacks. BRIEF DESCRIPTION OF THE INVENTION

[0058] To this end, the invention proposes a method for analyzing a diffusing medium, remarkable in that it comprises the following steps:

[0059] - the acquisition, by an acquisition system including a transmitter and a receiver, of signals, in response to the emission of a wave in the medium propagating in a desired emission direction,

[0060] - the calculation, from the acquired signals, of a plurality of directional signals, each directional signal being representative of the evolution over time of a wave reflected by the medium and propagating in a chosen direction of reception, each directional signal being associated with a respective pair of emission and reception directions,

[0061] - estimating a set of inter-directional signals for different times of interest, from the plurality of directional signals, each inter-directional signal being representative of the backscattering of the medium at a respective time of interest, as a function of an angular aperture corresponding to an angle between the direction of emission and the direction of reception,

[0062] - the determination of at least one characteristic of the environment based on a temporal evolution of the estimated inter-directional signals.

[0063] In the context of the present invention, the term “angular aperture” means an angle formed between a direction of emission of a wave and a direction of reception of a wave, in particular a direction of movement of a front of an acoustic wave. In the context of the present invention, the term “mean direction” means a direction corresponding to a bisector between directions of emission and reception of waves. Preferred but non-limiting aspects of the invention are as follows:

[0064] - the estimation step may comprise, for each time of interest considered, the following steps: o selecting a first subgroup of directional signals from the plurality of directional signals, the directional signals of the first subgroup being associated with pairs of transmission and reception directions having an identical first average direction, the first average direction corresponding to a bisector between the transmission and reception directions of each pair, o selecting at least a second subgroup of directional signals from the plurality of directional signals, the directional signals of the second subgroup being associated with pairs of transmission and reception directions having an identical second average direction, the second average direction being different from the first average direction, o calculating, from the directional signals of the first subgroup,a first set of elementary inter-directional signals for different instants around the time of interest, each elementary signal of the first set being representative of the backscattering of the medium at the first average direction and at a respective instant, as a function of the angular aperture, o calculating, from the directional signals of the second subgroup, a second set of elementary inter-directional signals for different instants around the time of interest, each elementary signal of the second set being representative of the backscattering of the medium at the second average direction and at a respective instant, as a function of the angular aperture, o combining the elementary inter-directional signals of the first and second sets in order to obtain the inter-directional signal for the time of interest considered;,

[0065] - each elementary inter-directional signal may be a complex signal obtained by Hilbert transform or demodulation, the combination sub-step consisting of: o extracting the moduli of the elementary inter-directional signals of the first and second sets, and o calculating the average of said moduli in order to obtain the inter-directional signal for the time of interest considered; each elementary inter-directional signal may be a complex signal obtained by Hilbert transform or demodulation, the combination sub-step consisting of: o aligning the elementary inter-directional signals of the first and second sets with each other by multiplying each elementary inter-directional signal by a complex number having an alignment argument to obtain aligned elementary inter-directional signals, o calculating the average of the aligned elementary inter-directional signals in order to obtain the inter-directional signal for the time of interest considered;

[0066] - the alignment argument can be chosen to maximize the energy of the final interdirectional signal for the time of interest considered around the zero angular aperture;

[0067] - the estimation step may comprise, for each time of interest considered, the following steps: o selecting a first subgroup of directional signals from the plurality of directional signals, the directional signals of the first subgroup being associated with pairs of transmission and reception directions having an identical first transmission direction, o selecting at least a second subgroup of directional signals from the plurality of directional signals, the directional signals of the second subgroup being associated with pairs of transmission and reception directions having an identical second transmission direction, the second transmission direction being different from the first transmission direction, o calculating, from the directional signals of the first subgroup, a first set of elementary inter-directional signals for different instants around the time of interest,each elementary signal being representative of the backscattering of the medium at the first direction of emission and at a respective instant, as a function of the angular aperture, o calculating, from the directional signals of the second subgroup, a second set of elementary inter-directional signals for different instants around the time of interest, each elementary signal being representative of the backscattering of the medium at the second direction of emission and at a respective instant, as a function of the angular aperture, o combining the elementary inter-directional signals of the first and second sets in order to obtain the inter-directional signal for the time of interest considered;,

[0068] - each elementary inter-directional signal is a complex signal obtained by Hilbert transform or demodulation, the combination sub-step consisting of: o extracting the moduli of the elementary inter-directional signals from the first and second sets, and o calculating the average of said moduli in order to obtain the inter-directional signal for the time of interest considered;

[0069] - the step of determining at least one characteristic of the environment includes the following sub-steps: o for each estimated inter-directional signal:

[0070] ■ extract a Gaussian component representative of a coherent backscattering cone,

[0071] ■ calculate a width of the Gaussian component, o calculate a reduction factor from the widths calculated for the different times of interest, said factor being representative of the reduction of the widths calculated for the different times of interest, o define a characteristic of the medium from the reduction factor;

[0072] - the transmitter and the receiver may consist of a transducer network, each directional signal being representative of the evolution over time: o of an acoustic wave reflected by the medium and propagating in a desired reception direction, o in response to the emission of an acoustic wave in the medium propagating in a desired emission direction. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Other advantages and characteristics of the method according to the invention will emerge more clearly from the following description of several variant embodiments, given as non-limiting examples, from the attached drawings in which:

[0074] - figure 1 is a schematic representation illustrating the principle of wave diffusion,

[0075] - Figure 2 is a schematic representation of a coherent backscattering cone,

[0076] - Figure 3 is a schematic representation of an ultrasound imaging device including an array of transducers and one (or more) computing unit(s),

[0077] - Figure 4 is a schematic representation of plane and spiral waves emitted by plane and curved transducer arrays,

[0078] - figure 5 is a schematic representation of an analysis method according to the invention,

[0079] - Figure 6 is a schematic representation illustrating the principle of emission of a plane wave from a network of transducers,

[0080] - figures 7a to 7d are schematic representations illustrating the principle of determining an inter-directional matrix,

[0081] - Figure 8 is a schematic representation of several interdirectional matrices K determined for different times t,

[0082] - Figure 9 is a schematic representation illustrating a first example of construction of an inter-directional signal from an inter-directional matrix,

[0083] - Figure 10 is a schematic representation illustrating a second example of forming an inter-directional signal from an inter-directional matrix,

[0084] - Figure 11 is a schematic representation illustrating different subgroups of directional signals selected in an inter-directional matrix,

[0085] - Figure 12 is a schematic representation of sub-steps of the analysis process,

[0086] - Figures 13 to 15 are schematic illustrations of inter-directional signals,

[0087] - Figure 16 is a diagram illustrating the time evolution of a coherent backscattering cone. DETAILED DESCRIPTION OF THE INVENTION

[0088] We will now describe different embodiments of the method and device for analyzing a medium according to the invention with reference to the figures. In these different figures, equivalent elements are designated by the same numerical reference.

[0089] The invention will be described with reference to the field of imaging of the human body by ultrasound. It is obvious to those skilled in the art that the method and device for analyzing a medium according to the invention can be used for other applications, such as SONAR, RADAR applications, or other non-medical applications (seismography, study of materials such as concrete or polycrystalline materials, etc.).

[0090] 1. Presentation

[0091] The method according to the invention allows the analysis of a heterogeneous medium from waves emitted (in the medium) and received (from the medium) according to desired emission and reception directions.

[0092] In the field of ultrasound imaging, transmitting and receiving in directions can be achieved with the analysis device described below with reference to Figure 3, for example by transmitting and receiving plane waves in the medium using the analysis device described below.

[0093] This analysis device is configured to:

[0094] - the acquisition of data which are gathered into an inter-directional signal containing a coherent backscatter cone, and potentially an incoherent background, and

[0095] - the processing of this inter-directional signal in order to determine one (or more) characteristic(s) of the environment.

[0096] It is in particular the study of the coherent backscattering cone contained in this inter-directional signal which makes it possible to determine the characteristic(s) of the medium. In fact, temporal revolution: - of the intensity of the coherent backscattering cone, and

[0097] - the angular opening of the coherent backscattering cone depends on transport characteristics of the medium (such as the diffusion constant D or the mean free path of diffusion).

[0098] The use of plane waves in transmission and reception addresses the first limitation of the technique described in documents WO 2020 / 117789 and WO 2019 / 104340 since a plane wave remains plane when it propagates as long as it does not significantly change medium, and its generation can therefore be done independently of the position of the surface of the medium to be studied.

[0099] The use of plane waves in transmission and reception also partly addresses the second limitation by reducing the risks of degradation of the surface of the medium to be analyzed.

[0100] The coherent cone study (rather than the incoherent halo study proposed in WO 2020 / 117789 and WO 2019 / 104340) allows for reduced noise sensitivity, and opens the possibility of fully in-phase processing (without switching to intensity) which significantly increases the signal-to-noise ratio.

[0101] 2. Device for analyzing an environment

[0102] With reference to Figure 3, an example of a device is illustrated in which the method for analyzing a medium described below can be implemented.

[0103] This device includes:

[0104] - a Ti-T transducer network n for signal acquisition, and

[0105] - a control and processing unit Uc for: o controlling the Ti-T transducer network n and o the processing of signals acquired by the Ti-T transducer network n .

[0106] 2.7. Transducer network

[0107] The Ti-T transducer array n comprises a set of “n” ultrasonic transducers (“n” being an integer greater than or equal to one) arranged linearly. Alternatively, the Ti-T transducers n of the network can be arranged in a curve, or in concentric circles, or in a matrix.

[0108] The Ti-T transducer array n allows the emission of exciting ultrasonic waves towards a medium to be analyzed (organ, biological tissue, etc.), and the reception of acoustic echoes (i.e. ultrasonic waves reflected by the medium to be analyzed).

[0109] Each Ti-T transducer nconsists for example of a rectangular plate of piezoelectric material coated on its front and rear faces with electrodes and covered on the front face with lenses and acoustic impedance matching layers. Such transducers are known to those skilled in the art and will not be described in more detail below.

[0110] In the embodiment illustrated in Figure 3, all Ti-T transducers n of the network are used for both transmission and reception. In other embodiments, separate transducers may be used for transmission and reception.

[0111] 2.2. Control and processing unit

[0112] The control and processing unit Uc is connected to the Ti-T transducer network n .

[0113] It allows you to control Ti-T transducers n of the network, and to process the data acquired by the Ti-T transducersn of the network.

[0114] More specifically, the Uc control and processing unit allows:

[0115] - to order the Ti-T transducers n the emission of ultrasonic waves towards the medium to be analyzed,

[0116] - to order the Ti-T transducers n the reception of echoes reflected by the medium to be analyzed and their conversion into reception signals,

[0117] - to process reception signals.

[0118] The control and processing unit Uc may be composed of one or more distinct physical entities, possibly remote from the Ti-T transducer network n The control and processing unit Uc includes for example:

[0119] - one (or more) controller(s) 11, such as a Smartphone, a personal digital assistant (or “PDA”), or any type of mobile terminal known to those skilled in the art; and - one (or more) calculator(s) 12, such as a computer(s), a microcomputer(s), a workstation(s), and / or other devices known to those skilled in the art including a processor(s), a microcontroller(s), a programmable automaton(s), an application-specific integrated circuit(s), and / or other programmable circuits,

[0120] - one (or more) storage unit(s) 13 comprising one (or more) memory(ies) which may be a ROM / RAM memory, a USB key, a memory of a central server.

[0121] Each element of the control and processing unit can be partially or totally integrated into the probe and / or into a physical entity separate from it (for example controller 11 in the probe, computer 12 and storage unit 13 in a separate entity).

[0122] In addition to storing data associated with the analysis of a medium, the storage unit 13 also makes it possible to store programming code instructions intended to execute the steps of the analysis method described below.

[0123] 3. Analysis process

[0124] 3.1. General information

[0125] One of the advantageous aspects of the analysis method concerns the use of directional waves in transmission and reception, said waves being transmitted and received according to desired directions of interest.

[0126] These directional waves can be plane waves OP as shown in figure

[0127] 4. Alternatively, these directional waves can be Os spiral waves.

[0128] A plane wave OP is a wave whose arrival time of the wavefront at a depth z depends on the lateral position x according to an affine law t(x, z) = a(z) + bx where a depends only on z and b is a constant which depends neither on z nor on x.

[0129] The equivalent of a plane wave OP in a polar frame of reference is called a spiral wave Os. A polar frame of reference is chosen arbitrarily, and the spiral wave Os is defined as the wave whose arrival time of the wavefront at a radius r depends on the angle 0 according to an affine law t(r, 0) = a(r) + b0 where a depends only on r and b is a constant that depends neither on r nor on 0. Those skilled in the art will note that the plane wave OP corresponds to a limiting case of the spiral wave where the origin of the frame moves away to infinity from the probe.

[0130] Directional waves are generated in transmission or reception by the real Ti-T transducer array n by applying to each transducer the delay corresponding to the arrival time of the wavefront at the position of said transducer.

[0131] It is obvious to those skilled in the art that the type of wave is independent of the shape of the transducer array. In particular, a plane transducer array Tn or a curved transducer array Tr2 can be configured to emit a plane wave (using a suitable delay law). The same applies to the cases of spiral or divergent directional waves.

[0132] Regardless of the type of directional waves (i.e. plane, spiral, divergent) used in transmission and reception, the transmission and reception directions can be characterized by transmission and reception angles, these angles being defined as the angle formed by the direction of interest relative to the normal to the transducer array.

[0133] More specifically, in the context of the present invention, the term “emission angle” (respectively “reception angle”) means the angle between:

[0134] - a direction orthogonal (hereinafter referred to as “normal”) to a tangent to the Ti-T transducer array n , And

[0135] - a direction normal to the tangent to the wavefront of the emitted (respectively received) wave thanks to the Ti-T transducer network n , and this, at the moment of emission (respectively reception) of the directional wave.

[0136] 3.2. Process steps

[0137] Referring to Figure 5, the analysis method comprises the following steps:

[0138] - acquisition 101 of a plurality of echo signals in response to the emission of a wave in the propagating medium,

[0139] - calculation 102 of a plurality of directional signals from the acquired echo signals,

[0140] - estimation 103 of a set of inter-directional signals for different times of interest “T”, from the plurality of directional signals, - determination 104 of at least one characteristic of the medium as a function of a temporal evolution of the estimated inter-directional signals.

[0141] Each inter-directional signal is representative of the backscattering of the medium as a function of an angular aperture corresponding to an angle between an emission direction and a reception direction.

[0142] 3.3. Step of acquiring the plurality of directional signals

[0143] Each directional signal is representative of the evolution over time of a reflected wave propagating in a desired reception direction in response to the remission of an incident wave propagating in a desired emission direction. Each directional signal is therefore associated with a respective pair of emission and reception directions different from the pairs of directions of the other directional signals.

[0144] Thus, to acquire the plurality of directional signals:

[0145] - directional emission waves - propagating along different emission directions - are emitted into the medium to be studied using the Ti-T transducer network n , And

[0146] - directional reception waves reflected by the medium to be studied are synthesized from the signals received by the Ti-T transducer network n .

[0147] In the following, the invention will be described with reference to the use of plane directional waves, it being understood that the method can use other types of directional waves such as spiral or diverging waves.

[0148] 3.3.1. Generation of plane emission waves

[0149] To generate a plane emission wave, Ti-T transducers n of the network are activated (in transmission) so that the elementary waves Eh-El n generated by each of the Ti-T transducers n combine to form a plane emission wave having a desired emission direction.

[0150] More precisely, depending on the activation times of the transducers and the amplitude of the excitation voltages applied to the Ti-T transducers n through the control and processing unit Uc it is possible to control the Ti-T transducers n so that they produce elementary ultrasonic waves Eh-Eln combining to form a plane ultrasonic emission wave 14 which propagates through the medium to be analyzed in a desired direction 15 (see figure 6).

[0151] This resulting ultrasonic plane wave 14 can be emitted according to different emission directions (i.e. different directions) by varying the activation times (t, t+At, t+2At, ... t+nAt) of each Ti-T transducer n of the network.

[0152] For example, for the generation of a plane emission wave, all Ti-T transducers n can be activated:

[0153] - simultaneously to obtain a plane emission wave propagating in an emission direction orthogonal to the Ti-T transducer network n , Or

[0154] - successively (according to an activation delay law) to obtain a plane emission wave propagating in an emission direction between -90° and 90° relative to the Ti-T transducer network n .

[0155] In any case, the Ti-T transducers n are all activated to generate the plane wave, that is, the Ti-Tn transducers are all activated in transmission for each reception.

[0156] The reader will appreciate that plane waves are generated by an emission of finite duration. This emission, which can be represented as a function of time or frequency, is characterized by a center frequency as well as a bandwidth.

[0157] 3.3.2. Reception plane wave synthesis

[0158] In the following, we call “reception plane waves” the signals synthesized from the signals received by the Ti-T transducer network. n(delay and summation) representative of waves reflected by the medium and propagating in a chosen direction.

[0159] To synthesize receiving plane waves, one solution may be to simultaneously acquire signals with the Ti-T transducers n .

[0160] Thus, after the emission of a plane emission wave presenting a given emission direction, each transducer is activated in reception to record (acquire and memorize) captured signals representative of the reverberation by the medium of the plane emission wave.

[0161] For each Ti-T transducer n , a captured signal function of time t, {Si(t)}o< isn _i is registered.

[0162] The signals captured by the Ti-T transducers nare then summed according to a time delay law depending on the desired reception angle for the receiving plane wave. For example, to receive a receiving plane wave having a reception angle a from the captured signals {Si^o^^ measured by the Ti-T transducers n , the following summation operation is performed:

[0163] Or :

[0164] - “c” represents the speed of the wave in the medium,

[0165] - “Xi” represents the lateral position of transducer i.

[0166] The processing of the block of captured signals makes it possible to “reorient” the responses recorded by the different Ti-T transducers n to obtain the reception waves at the different desired reception angles. This generates N plane waves in reception from a single transmission.

[0167] 3.3.3. Obtaining directional signals

[0168] The acquisition step allows a plurality of directional signals to be obtained, each directional signal being associated with a respective pair of transmission and reception directions (different from the pairs of the other directional signals of the plurality of directional signals).

[0169] The reader will appreciate that each directional signal is a real signal whose amplitude varies with time. This signal is called an "RF" (for "Radio-Frequency") signal.

[0170] In order to study this signal more easily, its complex representation can be used. This representation, widely known in the fields of wave physics and signal processing, allows the simplification of calculations and the resolution of the wave equation.

[0171] Each directional signal can be found by taking the real part of its complex representation. Furthermore, the complex signal can be characterized by its modulus, representative of the amplitude or envelope of the receiving wave, and by its argument, representative of the phase of the receiving wave.

[0172] To obtain this complex signal from the RF signal, several solutions are possible, such as extracting the analytical signal by Hilbert transform, or demodulating it around the central frequency followed by low-pass filtering. This produces an IQ (in-phase quadrature) signal, which can be modulated or demodulated. This step can be carried out analogically or digitally.

[0173] 3.4. Inter-directional signal set estimation step

[0174] Once the directional signals are acquired, these are used to estimate the set of inter-directional signals for different times of interest “T”.

[0175] To illustrate the implementation of this estimation step, interdirectional matrices will be used in the drawings, it being understood by those skilled in the art that the construction of such interdirectional matrices is not necessary for the estimation of the set of interdirectional signals.

[0176] 3.4.1. Determination of a windowed inter-directional matrix

[0177] Referring to Figure 7a, the principle of constructing a coefficient Kij of a row “i” of a temporally windowed inter-directional matrix K(t) includes the following steps:

[0178] - for Ti-T transducers nof the network, emit a plane wave of emission Oinc having a desired direction of emission (each transducer being activated according to a predetermined activation delay law to generate the plane wave Oincj having the desired direction of emission), - for the Ti-T transducers n of the network, receive a plane wave of reception Orecj having a desired reception direction (obtained by implementing either the first solution or the second solution).

[0179] The received signal obtained varies over time.

[0180] This signal is truncated (windowed) into successive time windows (potentially partially overlapping) - of duration At - each associated with a respective windowed interdirectional matrix.

[0181] For each time window, the corresponding truncated reception signal is multiplied by a windowing function and stored in the coefficient Kij(t) of the associated windowed interdirectional matrix K(t).

[0182] As illustrated in Figures 7b and 7c, the row “ / ” of each windowed interdirectional matrix K(t) is completed by receiving CW, CW receiving plane waves each having a distinct receiving direction from the other receiving plane waves and truncating the receiving signals representative of the CW, CW receiving plane waves into successive time windows.

[0183] These steps are repeated for each row of the matrix K(t).

[0184] More precisely, once all receiving plane waves have been synthesized and truncated for all desired receiving directions, the row "i" of each windowed interdirectional matrix K(t) is determined.

[0185] Referring to Figure 7d, the construction of the “i+1” row of each windowed interangle matrix K(t) can be initiated:

[0186] - by generating a new emission plane wave Oinc,i+i having an emission direction distinct from the emission direction associated with the emission plane wave Oinc used for the previous line “i”,

[0187] - by synthesizing receiving plane waves Ored, etc. having distinct desired receiving directions, and

[0188] - by truncating the reception signals representative of the plane waves of reception Oreci, etc. into successive time windows.

[0189] Thus in each windowed interdirectional matrix K(t):

[0190] - each row “i” is representative of the emission direction of an emitted plane wave, and - each column “j” is representative of a reception direction of a received plane wave.

[0191] In the context of the present invention, the windowed inter-directional matrices K(t) considered can be acquired with transmission and reception directions spaced at a constant pitch. Those skilled in the art will appreciate that the constant pitch condition is not essential in the context of the analysis method according to the invention.

[0192] As illustrated in Figure 8, each directional signal Sd(t) then corresponds to the same coefficient Kij(t) of the windowed inter-directional matrices K(t). This directional signal Sd(t) varies as a function of time.

[0193] 3.4.2. Extraction of each inter-directional signal

[0194] For each time of interest “T” considered, we then construct an interdirectional signal Sid from the values ​​at time “T” of the directional signals Sd.

[0195] Different methods can be implemented for the estimation of an interdirectional signal for a time of interest “T” considered.

[0196] In particular, the estimation of each inter-directional signal Sid can be carried out by selecting directional signals having the same average direction and different angular apertures. For example, Figure 9 illustrates the formation of an inter-directional signal Sid from the values ​​of the selected directional signals (directional signals having a constant average direction and different angular apertures) in an inter-directional matrix K(T) obtained for the time of interest "T" considered.

[0197] Alternatively, the estimation of each inter-directional signal Sid can be carried out by selecting directional signals having the same emission direction and different angular apertures. For example, Figure 10 illustrates the formation of an inter-directional signal Sid from the values ​​of the selected directional signals (directional signals having an identical emission direction and different angular apertures) in an inter-directional matrix K(T) obtained for the time of interest “T” considered. Advantageously, each inter-directional signal (associated with a time of interest “T” considered) can be made more robust by combining it with other inter-directional signals obtained:

[0198] - at different times “t” (i.e. different depths close to those of interest) and

[0199] - at different average directions (see figure 11) or at different emission directions.

[0200] For example and with reference to Figure 12, when each inter-directional signal is made more robust by working on the average directions, the estimation step can include the following sub-steps:

[0201] - selecting 1011 a first subgroup of directional signals from among the plurality of directional signals, the directional signals of the first subgroup being associated with pairs of transmission and reception directions having an identical first average direction (or respectively having an identical first transmission direction),

[0202] - calculate 1013, from the directional signals of the first subgroup, a first set of elementary inter-directional signals (SEI ... Sen) for different instants “t” around the time of interest “T”, each elementary inter-directional signal of the first set being representative of the backscattering of the medium at the first average direction (or respectively at the first emission direction) and at a respective instant “t”, as a function of the angular aperture,

[0203] - selecting 1012 a second subgroup of directional signals from among the plurality of directional signals, the directional signals of the second subgroup being associated with pairs of emission and reception directions having a second average direction identical but different from the first average direction (or respectively having a second identical emission direction, the second emission direction being different from the first emission direction),

[0204] - calculate 1014, from the directional signals of the second subgroup, a second set of elementary inter-directional signals (SET ... Sen) for different instants "t" around the time of interest "T", each elementary inter-directional signal of the second (respectively third, fourth, fifth ... etc.) set being representative of the backscattering of the medium at the second average direction (or respectively at the second emission direction) and at a respective instant "t", as a function of the angular aperture,

[0205] - combine 1015 the different elementary signals selected from the first and second sets in order to obtain the inter-directional signal for the time of interest “T” considered.

[0206] As will be described in more detail below, the combining step may include a combination in time of the elementary signals of the first subgroup on the one hand, and of the second subgroup on the other hand, as well as a combination of the elementary signals of the first and second subgroups.

[0207] Of course, more than two subgroups of directional signals can be used to obtain the inter-directional signal for the time of interest "T" considered. For example, and as illustrated in Figure 11, third P3, fourth P4 and fifth P5 (etc.) subgroups can be selected.

[0208] Thus, the determination of the inter-directional signal (associated with a time of interest "T" considered) by combining the elementary inter-directional signals calculated for the different subgroups of directional signals makes it possible to improve its quality.

[0209] This combination can be done in two different ways:

[0210] - envelope averaging (intensity); or

[0211] - phase averaging.

[0212] 3.4.2.1. Envelope averaging

[0213] In the case of envelope averaging, the envelopes of the interdirectional signals are averaged across time and the mean directions (or emission directions). The resulting interdirectional signal (for the considered time of interest "T") has the shape shown in Figure 13. It includes a Gaussian component representative of the coherent backscattering cone, as described in more detail in section 3.5 below.

[0214] 3.4.2.2. Phase averaging

[0215] In the case of phase averaging, the elementary inter-directional signals are combined in their complex form. Each complex elementary signal can be obtained by Hilbert transform or by demodulation. Each complex elementary signal consists of a "real part" and an "imaginary part":

[0216] - the argument of each complex elementary signal corresponding to the phase of the elementary signal and

[0217] - the modulus of each complex elementary signal corresponding to the amplitude of each elementary signal (this component is used for the envelope averaging described in Section 3.4.2.1).

[0218] In particular, complex modulated or demodulated (IQ) signals are used. Thus, the coherence of a part of the multiple diffusion signals, which are in phase for a given instant and a given average direction, is exploited.

[0219] More precisely, each complex elementary inter-directional signal, when extracted at constant mean direction, presents a coherent backscattering cone whose phase depends on time “t” and the mean direction but not on the angular aperture. The remaining components of this elementary signal (incoherent part and noise) have a phase that can be considered random depending on time, mean direction and angular aperture. To bring out the coherent backscattering cone, it is therefore possible to average the elementary inter-directional signals with their phases. However, since the phase of the coherent backscattering cone depends on the mean angle and time, it is advisable to align the phases of the coherent backscattering cones of the different elementary signals before implementing this averaging. This averaging aims to maximize the energy of the coherent cone obtained (i.e.energy at low angular apertures), and is achieved by multiplying each elementary signal by a complex constant having a so-called alignment phase. This alignment phase is calculated for example:.

[0220] - By solving the problem of maximizing the energy of the coherent cone after averaging, or

[0221] - By measuring (or estimating) the phase of each elementary signal around the zero angular aperture and using the opposite of this phase as the alignment phase.

[0222] The resulting interdirectional signal has the form shown in Figure 14.

[0223] 3.4.2.3. In practice

[0224] For each time of interest "T" considered, the final inter-directional signal is in practice immediately deduced from the directional signals, without going through the construction of inter-directional matrices or groups of elementary signals. We note these directional signals , with :

[0225] - the angle of the emission direction (angle between the normal to the transducer array and the normal to the wavefront of the emitted wave), and

[0226] - fi the angle of the receiving direction (angle between the normal to the transducer array and the normal to the wavefront of the received wave).

[0227] In this case, the angle of the mean direction is defined as 7 = (“+ 3) / 2, e t | a d emi angular aperture is defined as being equal to S = (“- / ^) / 2.

[0228] Each pair of transmitting and receiving directions has a unique corresponding pair of mean direction and angular aperture. Directional signals can be expressed as follows:

[0229] The inter-directional signal is obtained by averaging the directional signals as a function of the average angle 7 and time t (around the time of interest T): Or :

[0230] - M is an averaging operator, - r is a set of available average directions, and

[0231] - At is a duration over which the inter-directional signal is averaged.

[0232] The averaging operator M can be defined in two different ways. In particular, the averaging operator M can be defined as envelope averaging; in this case, the inter-directional signal can be written as: is the arithmetic averaging operator on the variable x. With such an averaging operator M, an inter-directional signal of Gaussian shape as illustrated in Figure 13 is obtained.

[0233] Alternatively, the averaging operator M can be defined as phase averaging with realignment. In this case, we start by forcing the phase of all coherent backscatter cones to 0 by multiplying by an alignment signal, typically the conjugate of the signal corresponding to the same instant, the same mean angle 7 and 0 a zero angular aperture. An averaging is then performed before moving on to the intensity. In this case, the inter-directional signal is: (expression 1) where — is the conjugate.

[0234] Alternatively, we can write:

[0235] The two expressions above each allow us to obtain a respective inter-directional signal for a time of interest “T” considered:

[0236] - the first expression (expression 1) allows to obtain a first interdirectional signal,

[0237] - the second expression (expression 2) allows to obtain a second interdirectional signal.

[0238] These first and second inter-directional signals are different, since they have slightly different theoretical expressions (the first inter-directional signal is equal to the second inter-directional signal multiplied by a constant), but in both cases, the phases are realigned before averaging.

[0239] Whichever expression is used (expression 1 or expression 2), we obtain an inter-directional signal of the form illustrated in figure 14.

[0240] The observed difference between the two types of averaging (envelope averaging as shown in Figure 13 / phase averaging as shown in Figure 14) comes from the destructive interference of the incoherent background (constant as a function of the angular aperture) during phase averaging, which leaves only the coherent backscattering cone.

[0241] 3.5. Determination of one (or more) characteristics from interdirectional signals

[0242] For each time of interest “T” considered, the inter-directional signal obtained can be broken down into two parts:

[0243] - an incoherent part, which corresponds to a chaotic background of multiple diffusion; this incoherent part is present from the start on all the angular openings in a homogeneous manner, as illustrated in figure 15,

[0244] - a coherent part, called “coherent backscattering cone”, which corresponds to signals still in phase which constructively interfere with each other; this coherent part is concentrated around the small angular openings.

[0245] For the inter-directional signal obtained after envelope averaging, the two parts that compose it can be easily identified, for example by using the difference between the zero angular aperture and the large angular apertures or by calculating the function of the form f(x) = 1 + exp(-ax 2 ) closest to the data.

[0246] For the inter-directional signal obtained after phase averaging, the averaging has the effect of causing the coherent backscattering cones to interfere constructively and the incoherent part of the signal to interfere destructively. Therefore, only the coherent part remains. In all cases, the inter-directional signal obtained is highly time-dependent. First, its intensity decreases, theoretically in t (-3 / 2) (if we are independent of the effects of diffusion, directivity and spatial masking).

[0247] This theoretical trend depends on the hypothesis of strong diffusion in the medium, with a number of diffusers high enough to generate a Gaussian march of the acoustic wave, and this in a homogeneous manner.

[0248] The study of the intensity of the inter-directional signal (coherent or incoherent part, both being equal), therefore makes it possible to validate the hypotheses made on the environment, as well as to locate the areas of strong diffusion.

[0249] Furthermore, the angular extension of the coherent part of the interdirectional signal decreases over time. The theory states that the coherent part of the interdirectional signal behaves like a Gaussian as a function of the angular aperture, a Gaussian whose variance evolves over time (1 / t 2 ).

[0250] The study of the temporal evolution of the angular extension of the coherent backscattering cone makes it possible to trace physical parameters of the medium, such as the diffusion constant D or the mean free diffusion path L (proportional to the diffusion constant). These are linked to the slope of the angular extension as a function of time of the Gaussian component of the inter-directional signal (coherent part).

[0251] Indeed, the theory tells us: s(5, t) a 1 + e - / ( fc2<5 ) p Our | e mO y enna g e en envelope (intensity), and phase averaging.

[0252] If we choose the Gaussian which best corresponds to the coherent cone and we report the inverse of its angular variance over time, we obtain in theory for phase averaging:

[0253] In practice, we verify through simulations that we actually obtain the inverse of the linear standard deviation as a function of time, as illustrated in Figure 16. 4. Conclusions

[0254] The method described above allows an improvement of the signal-to-noise ratio of inter-directional signals calculated for different times of interest “T”.

[0255] The use of directional waves eliminates the need to emit and receive waves on the surface of the medium to be studied.

[0256] Furthermore, the study of the temporal evolution of the coherent backscattering cone (which thins with depth) rather than the incoherent halo (as proposed in documents WO 2020 / 117789 and WO 2019 / 104340) makes it possible to characterize the medium in a more robust manner.

[0257] In the case of phase averaging of inter-directional signals determined for different times of interest “T”, the constructive interference of the coherent scattering cones allows an additional SNR gain as well as ease in estimating its angular extension.

[0258] In the foregoing description, the invention was described in the case of the use of plane waves. The reader will appreciate that the invention can be implemented using other types of strongly directional waves, such as spiral waves.

[0259] Similarly in the foregoing description, the invention was described with reference to a Ti-T transducer array n having a linear geometry. It is quite obvious to those skilled in the art that the Ti-T transducer network n may have other shapes such as a curved or matrix shape.

[0260] In the case of a matrix probe, therefore two-dimensional, the previous method is generalized by defining two-dimensional plane or spiral waves. These plane or spiral waves are nothing other than the combination of a plane or spiral wave along one axis with a plane or spiral wave along the other axis, thus giving delay laws defined in Cartesian, cylindrical or polar reference frames.

Claims

CLAIMS 1. Method for analyzing a diffusing medium, characterized in that the method comprises the following steps: - the acquisition (101), by an acquisition system including a transmitter and a receiver, of signals, in response to the emission of a wave in the medium propagating in a desired emission direction, - the calculation (102), from the acquired signals, of a plurality of directional signals, each directional signal being representative of the evolution over time of a wave reflected by the medium and propagating in a chosen direction of reception, each directional signal being associated with a respective pair of emission and reception directions, - estimating (103) a set of inter-directional signals for different times of interest (T), from the plurality of directional signals, each inter-directional signal being representative of the backscattering of the medium at a respective time of interest (T), as a function of an angular aperture corresponding to an angle between the direction of emission and the direction of reception, - determining (104) at least one characteristic of the environment as a function of a temporal evolution of the estimated inter-directional signals.

2. Method according to claim 1, in which the estimation step comprises, for each time of interest (T) considered, the following steps: - selecting (1011) a first subgroup (P1) of directional signals from among the plurality of directional signals, the directional signals of the first subgroup (P1) being associated with pairs of transmission and reception directions having an identical first average direction, the first average direction corresponding to a bisector between the transmission and reception directions of each pair, - selecting (1012) at least one second subgroup (P2) of directional signals from among the plurality of directional signals, the directional signals of the second subgroup being associated with pairs of emission directions and receiving having an identical second average direction, the second average direction being different from the first average direction, - calculating (1013), from the directional signals of the first subgroup (P1), a first set of elementary inter-directional signals (SE1, SEn) for different instants (t) around the time of interest (T), each elementary signal of the first set being representative of the backscattering of the medium at the first average direction and at a respective instant (t), as a function of the angular aperture, - calculating (1014), from the directional signals of the second subgroup (P2), a second set of elementary inter-directional signals (SE1', SEn') for different instants (t) around the time of interest (T), each elementary signal of the second set being representative of the backscattering of the medium at the second average direction and at a respective instant (t), as a function of the angular aperture, - combine (1015) the elementary inter-directional signals of the first and second sets in order to obtain the inter-directional signal for the time of interest (T) considered.

3. Method according to claim 2, in which each elementary inter-directional signal is a complex signal obtained by Hilbert transform or demodulation, the combination sub-step consisting of: - extract the modules of the elementary inter-directional signals (SE1 -SEn, (SE1'-SEn') of the first and second sets, and - calculate the average of said modules in order to obtain the inter-directional signal for the time of interest (T) considered.

4. Method according to claim 2, in which each elementary inter-directional signal is a complex signal obtained by Hilbert transform or demodulation, the combination sub-step consisting of: - align the elementary inter-directional signals of the first and second sets with each other by multiplying each elementary inter-directional signal by a complex number having an alignment argument to obtain aligned elementary inter-directional signals, - calculate the average of the aligned elementary inter-directional signals in order to obtain the inter-directional signal for the time of interest (T) considered.

5. Method according to claim 4, in which the alignment argument is chosen in order to maximize the energy of the final inter-directional signal for the time of interest (T) considered around the zero angular aperture.

6. Method according to claim 1, in which the estimation step comprises, for each time of interest (T) considered, the following steps: - selecting a first subgroup of directional signals from among the plurality of directional signals, the directional signals of the first subgroup being associated with pairs of transmission and reception directions having an identical first transmission direction, - selecting at least a second subgroup of directional signals from among the plurality of directional signals, the directional signals of the second subgroup being associated with pairs of transmission and reception directions having an identical second transmission direction, the second transmission direction being different from the first transmission direction, - calculating, from the directional signals of the first subgroup, a first set of elementary inter-directional signals for different instants (t) around the time of interest (T), each elementary signal being representative of the backscattering of the medium at the first direction of emission and at a respective instant (t), as a function of the angular aperture, - calculating, from the directional signals of the second subgroup, a second set of elementary inter-directional signals for different instants (t) around the time of interest (T), each elementary signal being representative of the backscattering of the medium at the second direction of emission and at a respective instant (t), as a function of the angular aperture, combine the elementary inter-directional signals of the first and second sets in order to obtain the inter-directional signal for the time of interest (T) considered.

7. Method according to claim 6, in which each elementary inter-directional signal is a complex signal obtained by Hilbert transform or demodulation, the combination sub-step consisting of: - extract the modules of the elementary inter-directional signals of the first and second sets, and - calculate the average of said modules in order to obtain the inter-directional signal for the time of interest (T) considered.

8. Method according to any one of claims 1 to 7, in which the step of determining at least one characteristic of the medium comprises the following sub-steps: - for each estimated inter-directional signal: o extract a Gaussian component representative of a coherent backscattering cone, o calculate a width of the Gaussian component, - calculate a reduction factor from the widths calculated for the different times of interest (T), said factor being representative of the reduction in the widths calculated for the different times of interest (T), - define a characteristic of the environment from the reduction factor.

9. Method according to any one of claims 1 to 8, in which the transmitter and the receiver consist of a transducer network, each directional signal being representative of the evolution over time: - an acoustic wave reflected by the medium and propagating in a desired reception direction, - in response to the emission of an acoustic wave in the medium propagating in a desired emission direction.

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