A self-calibrating flexible ultrasonic array for measuring curved objects

Abstract

Acoustic system (100) and method for measuring a curved object (Obj). A flexible sheet (20) is provided having an array of acoustic transducers (10) arranged on a surface (20s) of the sheet (20). The sheet (20) at least partially encases the object (Obj) such that different transducers (10a, 10b, 10c) acoustically contact the object (Obj) from different sides. The transducers (10) are used to generate and / or measure acoustic waves (W) at variable positions around the curved object (Obj). The spatial coordinates (X,Y,Z) of the variable positions in three-dimensional space depend on the deformation of the sheet surface (20s) encasing the object (Obj). The spatial coordinates (X,Y,Z) of the transducer (10) are determined based on a set of propagation times (Tab,Tbc,Tac) of the sound waves (W) transmitted through the object (Obj), for example between different transducers (10a,10b), while the sheet (20) envelops the object (Obj).

Description

[Technical field]

[0001] The present disclosure relates to acoustic systems and methods for measuring curved objects. [Background technology]

[0002] Acoustic systems have a variety of applications for measuring materials and objects such as tissue. For example, mammography or other acoustic images can be produced using pulse-echo measurements performed by acoustic transducers. Information about the material or structure inside the object or tissue can be derived from measured properties of the acoustic waves transmitted and / or reflected from the material internal structure, such as the amplitude, frequency, phase, and / or time between the emitted pulse and the received echo. When pulse-echo and / or tomography measurements are performed between different transducers, reconstruction of the imaged ultrasound may depend on a priori knowledge of the (relative) positions of the transducers. However, in conformable, flexible and / or stretchable ultrasound arrays, the inter-element positions of the different transducers may be unknown, hindering image reconstruction.

[0003] As background, US Patent Application Publication No. 2020 / 0278327 discloses phased array calibration for alignment and aberration correction. Various techniques for calibrating an array of ultrasonic transducers having multiple transducer elements include providing an acoustic reflector over an area traversed by multiple beam paths of ultrasound emitted from all (or at least some) transducer elements to a focal region, causing the transducer elements to emit ultrasound to the focal region, measuring the reflection of the ultrasound from the acoustic reflector, and determining optimal array parameters for the transducer elements based at least in part on the measured reflection. Unfortunately, calibration cannot be performed (in situ) during imaging. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] US Patent Application Publication No. 2020 / 0278327 Summary of the Invention [Problem to be solved by the invention]

[0005] For example, there is a need for improved acoustic systems and methods that can easily measure curved objects having variable geometries. [Means for solving the problem]

[0006] Aspects of the present disclosure are directed to acoustic systems and methods for measuring curved objects. A flexible sheet is configured to at least partially encase the curved object. The flexible sheet comprises an array of acoustic transducers arranged on a surface of the flexible sheet for acoustically contacting the curved object from different sides. The acoustic transducers are configured to generate and / or measure acoustic waves at variable positions relative to each other. The spatial coordinates of the variable positions in three-dimensional space typically depend on the deformation of the sheet surface encasing the curved object. Advantageously, the spatial coordinates of the acoustic transducers can be determined while the flexible sheet encases the curved object. In particular, the spatial coordinates can be determined based on a set of propagation times of acoustic waves transmitted through the curved object between various combinations of transducers arranged, for example, on different sides of the curved object. The positions of the transducers thus determined can be used to process the acoustic signals of the transducers to generate images and / or measure other material properties and internal structures inside the object. [Brief description of the drawings]

[0007] These and other features, aspects, and advantages of the presently disclosed apparatus, systems, and methods may become better understood from the following description, appended claims, and accompanying drawings, in which:

[0008] [Figure 1A] FIG. 1 is a perspective view of an acoustic system having a flexible sheet with an array of transducers. [Figure 1B] FIG. 1 is a cross-sectional view of a flexible sheet at least partially wrapped around a curved object. [Figure 2A]FIG. 1 illustrates the shape of a flexible sheet modeled based on the propagation time and / or relative distance measured between transducers on the surface of the sheet. [Figure 2B] FIG. 1 illustrates various parameterizations of the modeled shape. [Figure 3A] FIG. 1 illustrates an example of a curved object. [Figure 3B] FIG. 1 illustrates the measurement of a curved object having convex and concave regions. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0009] The terms used to describe particular embodiments are not intended to limit the invention. As used herein, the singular forms "a," "an," and "the" are intended to include the plural forms unless the context clearly indicates otherwise. The term "and / or" includes any and all combinations of one or more of the associated listed items. It will be understood that the terms "comprises" and / or "comprises" specify the presence of the stated features but do not exclude the presence or addition of one or more other features. When a particular step of a method is referred to as following another step, it will be further understood that the other step may follow directly, unless otherwise specified, or one or more intermediate steps may be performed prior to performing the particular step. Similarly, when a connection between structures or components is described, it will be understood that the connection may be made directly or through an intermediate structure or component, unless otherwise specified.

[0010] The present invention will now be described in detail with reference to the accompanying drawings, in which embodiments of the invention are shown. In the drawings, absolute and relative sizes of systems, components, layers, and regions may be exaggerated for clarity. The embodiments may be described with reference to schematic and / or cross-sectional views of idealized embodiments and intermediate structures of the invention. Like numbers refer to like elements throughout this specification and the drawings. Relative language and its derivations should be interpreted to refer to the orientation shown in the description or drawings being discussed. These relative language is for convenience of description and does not require that the system be constructed or operated in a particular orientation unless otherwise specified.

[0011] Figure 1A is a perspective view of an acoustic system 100 for measuring a curved object "Obj". Figure 1B shows a cross-sectional view of a flexible sheet 20 wrapped at least partially around the curved object "Obj".

[0012] In an embodiment, the flexible sheet 20 comprises an array of acoustic transducers 10. For example, the transducers are arranged on the sheet surface 20s of the flexible sheet 20. For example, the transducers form a one or two dimensional array. In this way, the transducers (10) can be used to acoustically contact a curved object "Obj" from different sides, for example, at least partially facing each other at the periphery of the object. In one embodiment, the acoustic transducers 10 are configured to generate and / or measure sound waves "W" at variable positions relative to each other, determined at the periphery of the curved object "Obj". The spatial coordinates (X,Y,Z) in the three-dimensional space of the variable positions thus depend on the deformation of the sheet surface 20s enveloping the curved object "Obj". In one embodiment, the control unit 30 is configured to determine the spatial coordinates (X,Y,Z) of the acoustic transducers 10, preferably while the flexible sheet 20 is wrapped around the curved object "Obj".

[0013] In an embodiment, the spatial coordinates are determined based on a set of propagation times Tab, Tbc, Tac of the acoustic wave "W" transmitted through the curved object "Obj". Preferably, the set of propagation times includes or consists of the propagation times Tab, Tbc, Tac of the acoustic wave "W" between different transducers 10a, 10b, 10c on different sides of the curved object "Obj", most preferably along a direct (shortest) path through the object. For example, the propagation time between a pair of transducers 10a, 10b is determined based on a measured time difference Tab between a first timestamp Ta of the transmission of the acoustic wave at the first transducer 10a and a second timestamp Tb of the reception of the acoustic wave at the second transducer 10b. For example, determining the respective timestamps and / or propagation times may include one or more of: detecting the peak of the acoustic wave, cross-correlating the emitted wave measured on the transducer with the arriving pressure pulse, determining the start of the received wave, measuring the difference between the phase of the received signal and the phase of the transmitted signal (the arrival time may appear as a linear phase over frequency in the frequency domain). The propagation time may also be referred to as the time of flight. The same acoustic wave (or another acoustic wave) transmitted from the first acoustic transducer 10a may also be received by the third acoustic transducer 10c, resulting in another time stamp that is used to determine the propagation time Tac between the first acoustic transducer 10a and the third acoustic transducer 10c. Similarly, the propagation time Tbc may be determined between the second transducer 10b and the third transducer 10c. These measurements may be performed sequentially and / or in parallel between any pair of transducers in the array to generate a desired set of propagation times. For example, acoustic waves may be transmitted with a unique signature (e.g., frequency) to distinguish the respective origins of the acoustic waves. Propagation times may also be determined in opposite directions for any pair. Also, the average or median propagation time may be determined between any pair by repeating the measurements in the same or opposite directions. For example, this may be done to mitigate any noise.

[0014] In an embodiment, the acoustic system 100 is configured to function as a tomography-based acoustic device. In other or further embodiments, the acoustic system 100 is configured to function as a reflection-based acoustic device. Also other or further types of acoustic devices, such as photoacoustic devices, may be envisaged. In principle, each acoustic transducer comprises one or more acoustic elements capable of converting between acoustic and electrical signals. For example, each acoustic element may comprise a piezoelectric structure, a membrane, etc. In one embodiment, each acoustic transducer is formed by an area with a number of acoustic elements, forming for example a local array. Typically, each transducer has an area of ​​0.1 to 10 mm. 2 , preferably 0.2 to 1 mm 2 For example, a local area of ​​0.5×0.5 mm 2 The area of ​​the transducer is 40 x 40 μm with 50 μm spacing. 2 It includes a local array of 100 pillars.

[0015] In an embodiment, the (same or another) control unit is configured to generate an image of the curved object "Obj" using an array of acoustic transducers 10. In one embodiment, the image is generated based on acoustic waves generated and / or measured by the acoustic transducers 10 and their spatial coordinates (X,Y,Z) determined based on a set of propagation times Tab, Tbc, Tac. For example, the acoustic system is configured as an ultrasound imaging device. Typically, the image includes structures and / or properties measured inside the curved object "Obj" using the array of acoustic transducers 10. Other measurements of the surface and / or interior of the curved object "Obj" may also be envisaged. Preferably, the measured properties of the acoustic signals include one or more of the arrival time, amplitude, frequency and / or phase of the acoustic signals. For example, the (same or other) control unit is configured to generate images or other measurements of structures and / or properties measured within the curved object "Obj" using sets of amplitudes of (same or other) acoustic waves "W" transmitted through the curved object "Obj" between different transducers (tomography and / or reflection) or returning to the same transducer (reflection).

[0016] As will be appreciated, the measured signals (and the particular processing of those signals, e.g. to generate an image) may depend on the actual (relative) positions of the transducers. For example, in a tomographic measurement, the amplitude or other properties of the acoustic signal between a pair of transducers may be processed to determine the structure and / or properties of the material in the path between the transducers, the origin and destination of the path being determined by the spatial position of one or more transducers relative to the object. For example, in a reflection measurement, the reverberation time may be processed, e.g. in combination with the amplitude or other properties of the sound wave returning to the same or a transducer, to determine the structure and / or properties of the material in the reflected path, the origin and destination of the path being determined by the spatial position of the transducer relative to the object. When the respective paths of the different signals can be mapped to a configuration, e.g. the object, the signals may be combined to generate an image or other measurement. Thus, measurements of the internal structure and / or properties of the object may be processed based on the measured acoustic signals (e.g. reflection and / or tomography) according to the spatial coordinates (X,Y,Z) of the transducers determined as described herein.

[0017] In an embodiment, the determination of the spatial coordinates (X,Y,Z) of the acoustic transducer 10 is followed by imaging or other measurements of the object. In other or further embodiments, the spatial coordinates (X,Y,Z) of the acoustic transducer 10 are determined while measurements of the curved object "Obj" are being made, or are determined intermittently during such measurements. For example, tomography and / or reflection-based measurements can be performed on the body, allowing for changes in the shape of the body (e.g. due to breathing movements) by constantly updating the measured position of the transducer.

[0018] In principle, the same or similar acoustic signals used to determine spatial coordinates can also be used for imaging of objects. For example, the internal structure and / or properties of an object can be determined based on the reflection and / or absorption of acoustic waves between different transducers. Typically, the measured propagation time between a pair of transducers is the time it takes for a wave to propagate a direct path between the transducers, penetrating any material between the transducers. Direct waves allow relatively easy reconstruction of the (Euclidean) distance between the transducers, and mapping or imaging properties of structures along the (direct) path can also be obtained.

[0019] Alternatively, or in addition, indirect paths may also be considered, such as sound waves reflecting off internal structures of an object and reaching the same or different transducers. For example, if sound waves are reflected off scattering elements from a particular internal structure or from different transducers, the respective reflection times (to the originating transducer or to other transducers) may reconstruct the respective distances between a particular internal structure and each transducer. This may also determine the spatial coordinates (X,Y,Z) of the acoustic transducer 10 itself. Indirect waves reflecting off internal structures may also be used to image the structure, for example after the spatial coordinates (X,Y,Z) of the acoustic transducer 10 have been determined, or in an iterative manner in which the spatial coordinates are changed until a self-consistent image is constructed.

[0020] In an embodiment, sound waves in a first frequency range are used to determine a set of flight times for determining the spatial coordinates (X,Y,Z) of the acoustic transducer 10. In another or further embodiment, sound waves in a second frequency range are used to determine an image or other measurement of the object. In one embodiment, the first frequency range is selected to have minimal interaction with the material and / or internal structure of the object. This allows the waves to propagate relatively unhindered through the object. For example, the signal strength and / or flight time are relatively unaffected by the material and / or internal structure of the object. In another or further embodiment, the second frequency range is selected to have more interaction with the material and / or internal structure of the object. For example, the second frequency is selected so that the sound waves are reflected and / or absorbed, facilitating reflection and / or tomographic measurements. In one embodiment, the second frequency range is different from, e.g., higher than, the first frequency range. Alternatively, the first and second frequency ranges can be the same or similar. For example, to perform tomography and / or reflection-based measurements, a frequency range may be selected that produces a relatively constant wave velocity while producing sufficient absorption or reflection in the internal structure of the object.

[0021] Depending on the type of measurement, different ultrasound frequencies may be used. For example, tomography-based measurements typically use ultrasound frequencies of 1 to 5 MHz, preferably 2 to 3 MHz. Reflection-based measurements typically use higher ultrasound frequencies, for example frequencies higher than 3.5 MHz, preferably frequencies higher than 7 MHz. For example, cardiac / liver imaging typically uses a frequency of 3.5 MHz, while carotid artery imaging typically uses a frequency of 7 MHz. Photoacoustic measurements typically use lower ultrasound frequencies, for example frequencies lower than 2 MHz. The frequency also depends on the size of the structure being imaged.

[0022] In an embodiment, each transducer has a set of predefined surface coordinates (Sx, Sy) along the sheet surface 20s. In another or further embodiment, the control unit 30 is configured to determine the spatial coordinates (X, Y, Z) of the acoustic transducer 10 (while the flexible sheet 20 is wrapped around the curved object "Obj") further based on the predefined surface coordinates (Sx, Sy). In one embodiment, the surface coordinates (Sx, Sy) comprise two-dimensional coordinates of the respective position of each transducer, e.g. a set of absolute (X, Y) positions measured from an origin on the sheet, and / or relative positions measured between the transducers. In another or further embodiment, the surface coordinates (Sx, Sy) comprise the relative position or column of each transducer, from which the actual position can be calculated, e.g. in combination with a known distance between the transducers.

[0023] In an embodiment, the transducers in the array have a predefined surface distance between them, particularly along the sheet surface 20s (e.g., Dp, Dab as shown). In another or further embodiment, the control unit 30 is configured to determine the spatial coordinates (X, Y, Z) of the acoustic transducers 10 (while the flexible sheet 20 is wrapped around the curved object "Obj") further based on the predefined surface distance (D and / or Dab). In one embodiment, the predefined surface distance D comprises a distance between (closest) adjacent transducers, e.g., a fixed or variable periodic distance. For example, the respective surface distance Dab between any pair of transducers 10a, 10b is calculated based on the periodic distance D and a set of relative surface coordinates (e.g., counting the number of transducers along a row or column). In another or further embodiment, the respective surface distance Dab between pairs of transducers 10a, 10b is calculated based on a table that stores the respective (absolute) surface positions (Xa, Ya; Xb, Yb) of each transducer (e.g., measured in cm from the origin). For example, the absolute surface positions from the table are subtracted to determine the relative positions between the transducers (ΔXab=Xa-Xb; ΔYab=Ya-Yb), and the Pythagorean theorem (Dab 2 =ΔXab 2 +ΔYab 2) the distances may be calculated using. In an alternative or further embodiment, a table is used which directly stores, for one or more (preferably each) transducer, the respective surface distance D ab to one or more, preferably every other transducer in the array. In this way the surface distances for any pair of transducers in the array may be quickly obtained.

[0024] As will be appreciated, the given surface coordinates (Sx, Sy) and / or distances (D, Dab) are preferably measured along the surface of the flexible sheet 20 when the sheet is flat, e.g., placed on a horizontal plane. Typically, the distance along the flexible sheet may represent the maximum distance that can be shortened when the sheet is curved around an object. The distance through the object may be referred to as the direct Euclidean distance (shortest line segment or chord), which is shorter than the surface distance, e.g., along the curved sheet surface. Alternatively, it may be assumed that the flexible sheet 20, adapted to the object to be measured, e.g., stretched, has a certain inherent curvature. For example, an essentially concave sheet may be stretched or compressed to envelop a convex object.

[0025] FIG. 2A shows a modeled shape 20m of the flexible sheet 20 based on the propagation times and / or relative distances Eab, Eac, Ebc measured between the transducers 10a, 10b, 10c on the sheet surface 20s. An embodiment includes determining the modeled shape 20m of the sheet surface 20s, for example by a controller. For example, the modeled shape is calculated based on the propagation times Tab, Tbc, Tac between pairs of transducers 10a, 10b; 10b, 10c; 10a, 10c. In one embodiment, each transducer has a modeled position that is constrained to the sheet surface 20s. In another or further embodiment, the modeled positions of the transducers are constrained by a set of predetermined surface coordinates (Sx, Sy) of the acoustic transducers 10 on the flexible sheet 20 and / or a surface distance Dab therebetween along the sheet surface 20s.

[0026] In one embodiment, the degree of curvature Rab of the sheet surface 20s is determined based on a set of propagation times Tab, Tbc, and Tac between one or more pairs of transducers. For example, the degree of curvature Rab may be limited according to the bendability of the flexible sheet 20 and / or the expected curvature of the object. In one embodiment, the shape of the sheet surface 20s is determined based on one or more degrees of curvature Rab of the flexible sheet 20 between respective pairs of transducers.

[0027] In an embodiment, a Euclidean distance Eab is determined between the pair of transducers 10a, 10b based on the flight time Tab of the sound wave "W" transmitted through the curved object "Obj" between the first transducer 10a and the second transducer 10b of the pair of transducers 10a, 10b. In one embodiment, the Euclidean distance through the object is determined based on the flight time of the sound wave through the object and the wave speed "C". For example, the speed of the sound wave may be predetermined, measured, assumed, and / or modeled (e.g., as a parameter). In one embodiment, the speed of the sound wave is predetermined, for example, using measurements through the object or a model object between pairs of transducers at known distances between them. In another or further embodiment, the speed of the sound wave for one or more pairs of transducers in the array is measured, for example, by assuming that the surface distance between the nearest adjacent transducers is similar or identical to the distance through the object. In another or further embodiment, the speed of the sound wave is assumed, for example, based on known wave transmission properties of the object. In another or further embodiment, the speed of the sound waves is used as a parameter for modeling the layout / shape of the sheet. In one embodiment, the speed "C" is assumed to be constant throughout the object. In another or further embodiment, the speed "C" may be variable, for example depending on the internal structure of the interior of the object. For example, the internal structure may be determined by the acoustic system itself, for example iteratively. For example, a pulse-echo mode is used.

[0028] In an embodiment, the spatial coordinates (X, Y, Z) of the acoustic transducers 10 are determined by comparing the Euclidean distance Eab and the surface distance Dab for each pair of transducers 10a, 10b of at least a subset 10a, 10b; 10a, 10c; 10b, 10c of the array of transducers 10. In one embodiment, the Euclidean distance Eab between the pair of transducers 10a, 10b is determined based on the propagation time Tab of the acoustic wave "W" transmitted through the curved object "Obj" between the first transducer 10a and the second transducer 10b of the pair of transducers 10a, 10b. In another or further embodiment, the surface distance Dab along the sheet surface 20s between the first transducer 10a and the second transducer 10b is based on predetermined information about the relative or absolute position of the transducers 10.

[0029] Typically, the respective Euclidean distances Eab between the pairs of transducers 10a, 10b will be shorter than the respective surface distances Dab depending on the degree of curvature of the flexible sheet 20. For example, if the sheet has a relatively high degree of curvature between the pair of transducers 10a, 10b, the Euclidean distance Eab therebetween will be relatively short. For example, if the sheet has a relatively low degree of curvature between the pair of transducers 10a, 10b, the Euclidean distance Eab therebetween will be relatively long, e.g., approaching the surface distance Dab if the sheet is essentially uncurved between the transducers. It will be appreciated that this is used to determine the degree of curvature between the various pairs of transducers.

[0030] In an embodiment, the spatial coordinates (X,Y,Z) of the acoustic transducers 10 are determined by calculating, for each pair of transducers 10a, 10b; 10b, 10c of at least a subset 10a, 10b; 10a, 10c; 10b, 10c of the array of transducers 10, a set of curvatures Rab, Rbc that compare the respective Euclidean distances Eab, Ebc with the respective surface distances Dab, Dbc. In one embodiment, the curvature between a pair of transducers is determined by assuming that the arc length between the transducers is equal to their relative surface distance Dab (optionally scaled by the sheet stretch / compression factor). In another or further embodiment, the curvature between a pair of transducers is determined by assuming that the radius of curvature between the pair of transducers is constant. For example, a combination of a particular arc length and the Euclidean distance between the points may determine a particular radius of curvature. In principle, the radius of curvature may be different for different parts of the sheet surface 20s, may be assumed to be the same, or may be modeled with a particular shape.

[0031] Preferably, each subset for determining the respective curvatures includes at least three transducers for determining a relative distance / flight time triangle, and more preferably includes at least four transducers for determining a three-dimensional shape (e.g., a three-sided pyramid) based on the distance between each pair of transducers in the subset. For example, the control unit is configured to determine a mesh surface in which each transducer is formed at the center of each node and / or each mesh element of the mesh. For example, the curvature of each of the line segments in the mesh is based on the set of determined curvatures. Of course, a surface model can generally be fitted to any set of measurements. In one embodiment, the entire curve is fitted based on all the measurement data, e.g., full inversion.

[0032] In an embodiment, the spatial coordinates (X, Y, Z) of the acoustic transducer 10 are determined using a model of the seat surface 20s including the respective positions of the modeled transducers on the modeled seat surface. In one embodiment, the model is used to calculate a set of modeled propagation times between the modeled transducers. In another or further embodiment, the modeled propagation times depend on the respective distances between the modeled transducers. In another or further embodiment, the respective distances between the modeled transducers depend on the respective positions on the modeled seat surface and the variable geometry of the modeled seat surface. In another or further embodiment, the variable geometry of the modeled seat surface is adjusted such that the modeled propagation times match the set of measured propagation times Tab, Tbc, Tac. In another or further embodiment, the spatial coordinates (X, Y, Z) of the acoustic transducer 10 are determined based on the respective positions of the modeled transducers on the modeled seat surface.

[0033] To allow for a convergent fit, various constraints may be applied to the modeled surfaces. In one embodiment, the model is constrained by assuming continuity of the sheet surface and / or its curvature. For example, the sheet is modeled as an interconnected mesh. In another or further embodiment, the model is constrained by the maximum curvature (e.g., minimum radius) of the sheet and / or the object. For example, the sheet is assumed to have some flexibility and / or bendability. For example, the object is assumed to have a constant maximum curvature (e.g., minimum radius). In another or further embodiment, the model is constrained by the maximum stretchability of flexible sheet 20. For example, if flexible sheet 20 is essentially inelastic, any predefined distance along the sheet surface may be fixed, or if flexible sheet 20 has some stretchability, the predefined distance along the sheet surface may be variable, e.g., adjusted by a variable scaling factor according to the model. For example, flexible sheet 20 may be allowed some stretching and / or compression to encase a spherical object.

[0034] In an embodiment, the distance between the transducers along the sheet surface is preferably measured using (guided) waves propagating along and / or within the flexible sheet 20 or another interface / connection between the transducers. In one embodiment, the waves for measuring the inter-transducer distance include Lamb waves, e.g., tension (A0) and / or bending (S0) guided waves. In another or further embodiment, the waves for measuring the inter-transducer distance include interface waves (e.g., Scholte waves) propagating along the sheet / tissue interface. If the sheet is used in combination with a solid, the interface waves may be called Stoneley waves. Ordinary compression waves (for tissue, or compression / shear waves if the sample is solid) may also be used to determine the 3D shape of the transducer sheet. For example, the measured distance between the transducers may be used as a substitute for a predetermined distance or in addition to correct the predetermined distance in the case of tension / compression. In particular, for the case of stretchable transducer sheets, it may be advantageous to determine the distance between the transducers on the transducer sheet separately from the 3D shape of the transducer sheet (using guided waves propagating along the transducer sheet for the former and bulk waves (compression / shear waves) for the latter). One advantage is that for the inversion of the 3D shape, minimal degrees of freedom are used, allowing for the reconstruction of more complex 3D shapes of the transducer sheet or a more robust reconstruction process.

[0035] In an embodiment, the model is constrained by predefined positions of the transducers on the surface (surface coordinates). For example, predefined positions are set in the model as constraints on the maximum distance between the transducers through the object and / or a fixed distance along the sheet surface. Instead of a freeform surface, the shape can be constrained to a specific shape, e.g., spherical, cylindrical, etc. This limits the number of free parameters and allows for a more constrained (simpler) fit.

[0036] In one embodiment, the fitting is performed in an iterative procedure, e.g., minimizing the difference between the modeled and measured propagation times. In other or further embodiments, the fitting is performed analytically, e.g., directly calculating the best fit. Also, a combination of computational and / or fitting routines is possible. Other algorithms, such as machine learning / artificial intelligence, may also be used, e.g., to calculate the most likely shape of the flexible sheet.

[0037] In an embodiment, multiple fits are performed on different subsets of transducers to determine the local shape or curvature of the corresponding subsection region of the sheet. For example, multiple fits may be combined to provide the overall shape. In one embodiment, a subset of two transducers is used to form a line that determines a specific distance between two transducers. The modeled sheet may then be curved between the transducers to fit the specific distance. In another or further embodiment, a subset of three transducers is used to form a triangle that determines a specific distance between three transducers. The modeled sheet may then be curved between the transducers to fit the specific distance. In another or further embodiment, a subset of four transducers may form a three-sided pyramid (e.g., with one center point surrounded by three other points). Using a subset of four or more points may allow a more direct determination of the three-dimensional shape of the subsection region of the sheet. Also, more transducers may be included in the fit. In an embodiment, the fit is performed globally using all measured propagation times. For example, this may be performed after a general shape is determined based on local fits or a predefined general shape of the object.

[0038] In an embodiment, the set of current spatial coordinates (X,Y,Z) of the acoustic transducer 10 is determined by adjusting a set of predefined spatial coordinates of the acoustic transducer 10 according to a set of propagation times Tab, Tbc, Tac. In one embodiment, the set of predefined spatial coordinates includes a set of initial coordinates based on an initial assumed shape of the curved object "Obj". For example, a selection of one or more predefined shapes such as a sphere, a cylinder, etc. may be input (e.g., to the control unit) as the initial assumed shape. This may facilitate shape adaptation. In another or further embodiment, the set of predefined spatial coordinates includes previously measured and / or adapted coordinates of the acoustic transducer 10. For example, the spatial coordinates of the acoustic transducer 10 are measured or updated continuously or intermittently to track an object whose shape may change (e.g., a body when breathing). Instead of or in addition to modeling the sheet surface as a mesh, it is also envisaged to model the sheet surface as a continuously parameterized surface, for example according to a surface equation of a predefined shape.

[0039] In an embodiment, the propagation time Tac of the sound wave "W" transmitted through the curved object "Obj" between the first acoustic transducer 10a and the third transducer 10c is measured. In one embodiment, the second transducer 10b is placed between the first acoustic transducer 10a and the third transducer 10c along a surface path on the sheet surface of the flexible sheet. In another or further embodiment, the spatial coordinates Xb, Yb, Zb of the second transducer 10b are determined based at least in part on interpolating the predetermined surface coordinates and / or surface distances Dab, Dbc of the second transducer 10b relative to the first acoustic transducer 10a and the third transducer 10c on the modeled surface 20m of the flexible sheet 20. For example, if the second transducer 10b is known from a given distance and / or coordinate of a transducer array located along the surface between the first acoustic transducer 10a and the third transducer 10c, and the layout of the surface is modeled based on, for example, various propagation times between the first acoustic transducer 10a and the third transducer 10c, the position of the second transducer 10b can be interpolated. This can be used instead of or in addition to direct measurements of sound waves between the first acoustic transducer 10a and the second transducer 10b and / or between the third transducer 10c and the second transducer 10b.

[0040] FIG. 2B shows various parameterizations of the modeled shape 20m. In an embodiment, the modeled shape of the flexible sheet is based on a predefined parameterized shape with a set of variable scaling parameters a, b, c and / or coordinates. For example, the coordinates may include the origin of the shape (x0, y0, z0). Using a parameterized shape may limit the number of free parameters compared to a more general mesh. For example, the set of scaling parameters and / or coordinates is adapted according to a set of measured propagation times Tab, Tbc, Tac. In an embodiment, the modeled shape 20m may be parameterized as a (subsection area of) a sphere or an ellipsoid. An ellipsoid is a surface that can be obtained from a sphere by deforming the sphere by directional scaling, or more generally by an affine transformation. For example, an ellipsoid may be uniquely defined by six parameters (x0, y0, z0, a, b, c). These may be determined by a set of at least seven independent measurements. In practice, more measurements may be required since the information of the measurements is not orthogonal and the signal-to-noise (SNR) may be limited. To improve the orthogonality / independence of the different measurements, the transducers are preferably chosen to be scattered at different positions around the object.

[0041] FIG. 3A shows examples of various curved objects "OBj". In an embodiment, the acoustic system is used to measure (breast) tissue. In this case, the initial mesh shape and / or the parameterized functional surface may be determined using a portion of a sphere. Similarly, other tissues or other structures may have a (partial) spherical shape. In other or further embodiments, the curved object "Obj" may have a tubular or cylindrical shape. For example, the acoustic system may be used to measure the inside of a pipe, which may have an unknown or variable diameter. Similarly, other parameterized shapes may be envisaged, such as a conical (frustum) shape or any surface that can be described by an analytical function, etc. For example, the acoustic system is used to measure other parts of the body or any other curved object. As will be appreciated, the method and system may be advantageously used to measure curved objects with convex features that allow sound waves to propagate through the object between different transducers, e.g. at least partially facing each other. Alternatively or in addition, the curved object may include concave features.

[0042] FIG. 3B illustrates the measurement of a curved object "Obj" having convex and concave subsection areas Av, Ac. In one embodiment, the convex subsection area of ​​the flexible sheet 20 is determined based on one or more acoustic signals being blocked along a path between a pair of acoustic transducers 10a, 10i through the convex subsection area. It will be appreciated that the convex subsection area of ​​the flexible sheet 20 as viewed from the front side facing the object corresponds to the concave subsection area Ac of the object, and vice versa, the convex subsection area Av of the object corresponds to the concave subsection area of ​​the flexible sheet 20. For example, the first transducer 10a emits an acoustic signal that is received by transducers 10c and 10d but not 10i because an edge or periphery of the object formed in the concave subsection area Ac may block the direct path. The absence of such a signal at transducer 10i may be used to infer the concave subsection area of ​​the object and / or the convex subsection area of ​​the flexible sheet 20. Alternatively, or in addition, the proximity of transducer 10d to transducer 10a (and / or other transducers, such as 10c) may also be used to determine the local shape of the sheet surface.

[0043] For clarity and conciseness of description, features are described herein as part of the same or different embodiments, it will be understood that the scope of the invention may include embodiments having all or some combination of the described features. The aspects described with reference to specific systems and devices may be implemented as corresponding methods for acoustically measuring curved objects. In one embodiment, the method includes providing a flexible sheet 20 with an array of acoustic transducers 10 arranged on a sheet surface 20s of the flexible sheet 20. In another or further embodiment, the method includes at least partially wrapping the flexible sheet 20 around the curved object "Obj" such that the acoustic transducers 10 acoustically contact the curved object "Obj" from different sides. In another or further embodiment, the method includes using the acoustic transducers 10 to generate and / or measure acoustic waves "W" at variable positions around the curved object "Obj". For example, the spatial coordinates (X,Y,Z) of the variable positions in three-dimensional space depend on the deformation of the sheet surface 20s enveloping the curved object "Obj". In another or further embodiment, the method includes determining the spatial coordinates (X,Y,Z) of the acoustic transducers 10, preferably while the flexible sheet 20 is wrapped around the curved object "Obj". In a preferred embodiment, the method further includes imaging and / or measuring the curved object based on the acoustic waves generated and / or measured by the acoustic transducers 10 and their spatial coordinates (X,Y,Z) determined based on the set of propagation times Tab, Tbc, Tac. Advantageously, the same transducers 10a, 10b, 10c used for imaging and / or measuring the curved object are used for determining the spatial coordinates (X,Y,Z) and vice versa. Thus, no further reference transducers are required to determine the spatial coordinates. Furthermore, the acoustic transducers of the array 10 used for both determining the spatial coordinates and imaging and / or measuring the curved object may all be located in the same two-dimensional plane (if the flexible sheet 20 is laid flat). The sheet may be relatively thin and / or flexible, for example, since no additional transducers are required out of plane from the array. These and other aspects may be embodied as a (non-transitory) computer readable medium storing instructions that, when executed, cause the methods and systems described herein to perform.

[0044] Although embodiments have been shown for various layouts of acoustic transducers on a flexible sheet, alternative methods may be envisioned by those skilled in the art having the benefit of this disclosure to achieve similar functions and results. For example, the flexible sheet may be omitted if the transducers are placed directly on the curved object to be measured. Also, other or similar structures, such as flexible wires and / or nets between the transducers, may be used instead of the flexible sheet to hold the transducers together. The various elements of the described and shown embodiments provide certain advantages, such as a self-calibrating adaptive acoustic device. Of course, it will be understood that any one of the above embodiments or processes may be combined with one or more other embodiments or processes to provide further improvements in design and finding and adapting advantages. It will be understood that the present disclosure provides certain advantages for acoustic imaging and may be generally applied to any application in which the respective positions of acoustic transducers are determined.

[0045] In interpreting the appended claims, it is to be understood that the word "comprising" does not exclude the presence of elements or acts other than those recited in a given claim, and the word "a" or "an" preceding an element does not exclude the presence of a plurality of such elements, and any reference sign in a claim does not limit its scope, and that a plurality of "means" may be represented by the same or different items or by the structure or function implemented, and that the disclosed apparatus or parts thereof may be combined together or separated into further parts, unless otherwise specified. When a claim refers to another claim, this may indicate synergistic advantages achieved by the combination of the respective features. However, the mere fact that certain means are recited in mutually different claims does not indicate that the combination of these means cannot be used advantageously. Thus, the present embodiment includes all possible combinations of the claims, and each claim may in principle refer to the preceding claims, unless clearly excluded by the context.

[0046] (Additional Note) (Appendix 1) a flexible sheet (20) configured to at least partially encase a curved object (Obj), said flexible sheet (20) comprising an array of acoustic transducers (10) arranged on a sheet surface (20s) of said flexible sheet (20) for acoustically contacting said curved object (Obj) from different sides, said acoustic transducers (10) being configured to generate and / or measure sound waves (W) at variable positions relative to one another, the spatial coordinates (X,Y,Z) of the variable positions in three-dimensional space being dependent on the deformation of said sheet surface (20s) encasing said curved object (Obj); a control unit (30) configured to determine spatial coordinates (X, Y, Z) of the acoustic transducer (10) based on a set of propagation times (Tab, Tbc, Tac) of the sound waves (W) transmitted through the curved object (Obj) while the flexible sheet (20) is encasing the curved object (Obj); Equipped with An acoustic system (100) for measuring a curved object (Obj).

[0047] (Appendix 2) 2. The acoustic system of claim 1, wherein the set of propagation times (Tab, Tbc, Tac) includes or consists only of propagation times of the sound wave (W) transmitted through the curved object (Obj) between different acoustic transducers (10a, 10b, 10c) of an array of the acoustic transducers (10) disposed on the sheet surface (20s) and acoustically contacting the curved object (Obj) on different sides of a periphery of the curved object (Obj).

[0048] (Appendix 3) the control unit (30) is configured to generate an image of the curved object (Obj) using the array of acoustic transducers (10); the image is generated based on the acoustic waves generated and / or measured by the acoustic transducer (10) and their spatial coordinates (X, Y, Z) determined based on the set of propagation times (Tab, Tbc, Tac), 3. The acoustic system according to claim 1 or 2.

[0049] (Appendix 4) Each of the acoustic transducers has a set of predetermined surface coordinates (Sx, Sy) and / or predetermined surface distances (Dp, Dab) between the acoustic transducers along the seat surface (20s); the control unit (30) is configured to determine the spatial coordinates (X, Y, Z) of the acoustic transducer (10) further based on the predetermined surface coordinates (Sx, Sy) and / or the predetermined surface distance (Dp, Dab), 4. An acoustic system according to any one of claims 1 to 3.

[0050] (Appendix 5) the control unit (30) is configured to determine a modeled shape (20m) of the seat surface (20s); the modeled shape (20m) is calculated based on the propagation times (Tab, Tbc, Tac) between pairs of the acoustic transducers (10a, 10b; 10b, 10c; 10a, 10c); each said acoustic transducer has a modeled position that is constrained to said sheet surface (20s), said modeled positions of said acoustic transducers being further constrained by a set of predetermined surface coordinates (Sx, Sy) of said acoustic transducers (10) on said flexible sheet (20) and / or a surface distance (Dab) between said acoustic transducers (10) along said sheet surface (20s); 5. An acoustic system according to any one of claims 1 to 4.

[0051] (Appendix 6) the flexible sheet (20) is stretchable, allowing for a variable surface distance (Dab) between the acoustic transducers (10) along the sheet surface (20s); the acoustic transducer (10) is further configured to generate and / or measure guided waves propagating within and / or along the sheet surface (20s) to determine the variable surface distance (Dab), 6. An acoustic system according to any one of claims 1 to 5.

[0052] (Appendix 7) 7. The acoustic system of claim 1, wherein the control unit (30) is configured to calculate the modeled shape based on a predetermined parameterized shape according to an analytical function defined by variable scaling parameters (a, b, c) and / or a set of coordinates.

[0053] (Appendix 8) 8. The acoustic system of claim 1, wherein the control unit (30) is configured to determine a set of current spatial coordinates (X, Y, Z) of the acoustic transducer (10) by adjusting a set of predetermined spatial coordinates of the acoustic transducer (10) according to the set of propagation times (Tab, Tbc, Tac).

[0054] (Appendix 9) 9. The acoustic system of any one of claims 1 to 8, wherein the control unit (30) is configured to determine the convex subsection area of ​​the flexible sheet (20) based on one or more acoustic signals intercepted along a path between the pair of acoustic transducers (10a, 10i) through a convex subsection area.

[0055] (Appendix 10) The control unit (30) controls, for each pair of the acoustic transducers (10a, 10b) in at least a subset (10a, 10b; 10a, 10c; 10b, 10c) of the array of the acoustic transducers (10), a Euclidean distance (Eab) between the pair of acoustic transducers (10a, 10b) based on a propagation time (Tab) of an acoustic wave (W) transmitted through the curved object (Obj) between a first acoustic transducer (10a) and a second acoustic transducer (10b) of the pair of acoustic transducers (10a, 10b); a surface distance (Dab) along the seat surface (20s) between the first acoustic transducer (10a) and the second acoustic transducer (10b) based on predetermined information regarding the relative or absolute position of the acoustic transducers (10); and determining the spatial coordinates (X, Y, Z) of the acoustic transducer (10) by comparing 10. The acoustic system of any one of claims 1 to 9.

[0056] (Appendix 11) a degree of curvature (R ab ) of the seat surface (20s) is determined based on the set of propagation times (T ab , T bc , T ac ) between one or more of the acoustic transducers (10); the shape of the sheet surface (20s) is determined based on one or more degrees of curvature (Rab) of the flexible sheet (20) between each pair of transducers; the control unit (30) is configured to determine the spatial coordinates (X, Y, Z) of the acoustic transducers (10) for each pair of the acoustic transducers (10a, 10b) of at least a subset (10a, 10b; 10a, 10c; 10b, 10c) of the array of the acoustic transducers (10) by calculating a set of curvatures (Rab, Rbc) by comparing the respective Euclidean distances (Eab, Ebc) with the respective surface distances (Dab, Dbc), 11. An acoustic system according to any one of claims 1 to 10.

[0057] (Appendix 12) the control unit (30) is configured to determine the spatial coordinates (X, Y, Z) of the acoustic transducers (10) using a model of the seat surface (20s) including respective positions of modeled acoustic transducers on the modeled seat surface; the model is used to calculate a set of modeled propagation times between the modeled acoustic transducers; the modeled propagation times being dependent on respective distances between the modeled acoustic transducers; the respective distances between the modeled acoustic transducers being dependent on their respective positions on the modeled seat surface and on the variable geometry of the modeled seat surface; the deformable shape of the modeled seat surface is adjusted such that the modeled propagation times match the set of measured propagation times (Tab, Tbc, Tac); the spatial coordinates (X,Y,Z) of the acoustic transducers (10) are determined based on the respective positions of the modeled acoustic transducers on the modeled seat; 12. An acoustic system according to any one of claims 1 to 11.

[0058] (Appendix 13) the control unit (30) is configured to measure a time of flight (Tac) of an acoustic wave (W) transmitted through a curved object (Obj) between a first acoustic transducer (10a) and a third transducer (10c); a second transducer (10b) is disposed along a surface path on the sheet surface of the flexible sheet between the first acoustic transducer (10a) and the third transducer (10c); the control unit (30) is configured to determine spatial coordinates (Xb, Yb, Zb) of the second transducer (10b) based on at least partially interpolating surface distances (Dab, Dbc) of the second transducer (10b) relative to the first acoustic transducer (10a) and the third transducer (10c) on a modeled sheet surface (20m) of the flexible sheet (20) and / or predetermined surface coordinates. 13. An acoustic system according to any one of claims 1 to 12.

[0059] (Appendix 14) providing a flexible sheet (20) with an array of acoustic transducers (10) arranged on a sheet surface (20s) of said flexible sheet (20); at least partially enveloping the curved object (Obj) with the flexible sheet (20) such that the acoustic transducers (10) are in acoustic contact with the curved object (Obj) from different sides; using the acoustic transducer (10) to generate and / or measure sound waves (W) at variable positions around the curved object (Obj), the spatial coordinates (X,Y,Z) of the variable positions in three-dimensional space depending on the deformation of the sheet surface (20s) enveloping the curved object (Obj); determining the spatial coordinates (X,Y,Z) of the acoustic transducer (10) based on a set of propagation times (Tab,Tbc,Tac) of the sound waves (W) transmitted through the curved object (Obj) while the flexible sheet (20) is encasing the curved object (Obj); Equipped with A method for acoustically measuring a curved object (Obj).

[0060] (Appendix 15) When implemented by an acoustic system (100) according to any one of claims 1 to 13, the acoustic system further comprises: - controlling a set of acoustic transducers (10) to generate and / or measure sound waves (W) at variable positions around a curved object (Obj), the spatial coordinates (X,Y,Z) of said variable positions in three-dimensional space depending on the circumference of said curved object (Obj); determining the spatial coordinates (X,Y,Z) of the acoustic transducer (10) based on a set of propagation times (Tab,Tbc,Tac) of the acoustic wave (W) transmitted through the curved object (Obj); generating an image by processing acoustic signals measured from at least a subset of said acoustic transducers (10), said acoustic signals being processed based on said determined spatial coordinates (X,Y,Z); A non-transitory computer-readable medium storing instructions to cause a

Claims

1. A flexible sheet (20) configured to at least partially wrap a curved object (Obj), wherein the flexible sheet (20) has an array of acoustic transducers (10) disposed on a sheet surface (20s) of the flexible sheet (20) for acoustically contacting the curved object (Obj) from different sides, the acoustic transducers (10) being configured to generate and / or measure sound waves (W) at variable positions relative to each other, and spatial coordinates (X, Y, Z) of the variable positions in a three-dimensional space depending on a deformation of the sheet surface (20s) that wraps the curved object (Obj); and the flexible sheet (20), a control unit (30) configured to determine the spatial coordinates (X, Y, Z) of the acoustic transducers (10) based on a set of propagation times (Tab, Tbc, Tac) of the sound waves (W) transmitted through the curved object (Obj) while the flexible sheet (20) wraps the curved object (Obj); comprising an acoustic system (100) for measuring a curved object (Obj).

2. The acoustic system according to claim 1, wherein the set of propagation times (Tab, Tbc, Tac) includes or consists only of propagation times of the sound waves (W) transmitted through the curved object (Obj) between different acoustic transducers (10a, 10b, 10c) of the array of acoustic transducers (10) disposed on the sheet surface (20s) and acoustically contacting the curved object (Obj) on different sides of a periphery of the curved object (Obj).

3. The control unit (30) is configured to generate an image of the curved object (Obj) using the array of acoustic transducers (10), the image being generated based on sound waves generated and / or measured by the acoustic transducers (10) and their spatial coordinates (X, Y, Z) determined based on the set of propagation times (Tab, Tbc, Tac); The acoustic system according to claim 1 or 2.

4. Each of the acoustic transducers has a set of predetermined surface coordinates (Sx, Sy) and / or a set of predetermined surface distances (Dp, Dab) between the acoustic transducers along the sheet surface (20s), the control unit (30) being configured to further determine the spatial coordinates (X, Y, Z) of the acoustic transducers (10) based on the predetermined surface coordinates (Sx, Sy) and / or the predetermined surface distances (Dp, Dab). The acoustic system according to claim 1 or 2.

5. The control unit (30) is configured to determine a modeled shape (20m) of the seat surface (20s), The modeled shape (20m) is calculated based on the propagation times (Tab, Tbc, Tac) between pairs of the acoustic transducers (10a, 10b; 10b, 10c; 10a, 10c), Each of the acoustic transducers has a modeled position bound to the seat surface (20s), and the modeled position of the acoustic transducer is further bounded by a set of predetermined surface coordinates (Sx, Sy) of the acoustic transducer (10) on the flexible sheet (20) and / or a surface distance (Dab) between the acoustic transducers (10) along the seat surface (20s). The acoustic system according to claim 1 or 2.

6. The flexible sheet (20) is stretchable, allowing a variable surface distance (Dab) along the seat surface (20s) between the acoustic transducers (10), The acoustic transducers (10) are further configured to generate and / or measure guided waves propagating inside and / or along the seat surface (20s) in order to determine the variable surface distance (Dab). The acoustic system according to claim 1 or 2.

7. The control unit (30) is configured to calculate the modeled shape based on a predetermined parameterized shape according to an analysis function defined by a variable scaling parameter (a, b, c) and / or a set of coordinates, for the acoustic system according to claim 1 or 2.

8. The control unit (30) is configured to determine a set of current spatial coordinates (X, Y, Z) of the acoustic transducers (10) by adjusting a set of predetermined spatial coordinates of the acoustic transducers (10) according to the set of propagation times (Tab, Tbc, Tac), for the acoustic system according to claim 1 or 2.

9. The control unit (30) is configured to determine the convex sub-section region of the flexible sheet (20) based on one or more acoustic signals blocked along a path between pairs of the acoustic transducers (10a, 10i) passing through the convex sub-section region, for the acoustic system according to claim 1 or 2.

10. The control unit (30) determines, for each pair of the acoustic transducers (10a, 10b) within at least a subset (10a, 10b; 10a, 10c; 10b, 10c) of the array of the acoustic transducers (10), the Euclidean distance (Eab) between the pair of acoustic transducers (10a, 10b) based on the propagation time (Tab) of a sound wave (W) transmitted through the curved object (Obj) between the first acoustic transducer (10a) and the second acoustic transducer (10b) of the pair of acoustic transducers (10a, 10b), and the surface distance (Dab) along the sheet surface (20s) between the first acoustic transducer (10a) and the second acoustic transducer (10b) based on predetermined information regarding the relative or absolute position of the acoustic transducers (10), and is configured to determine the spatial coordinates (X, Y, Z) of the acoustic transducers (10) by comparing the two. The acoustic system according to claim 1 or 2.

11. The degree of curvature (Rab) of the sheet surface (20s) is determined based on a set of the propagation times (Tab, Tbc, Tac) between one or more of the acoustic transducers (10), The shape of the sheet surface (20s) is determined based on one or more of the degrees of curvature (Rab) of the flexible sheet (20) between respective pairs of transducers. The control unit (30) is configured to determine the spatial coordinates (X, Y, Z) of the acoustic transducers (10) by calculating a set of curvatures (Rab, Rbc) by comparing the respective Euclidean distances (Eab, Ebc) and the respective surface distances (Dab, Dbc) for each pair of the acoustic transducers (10a, 10b) of at least a subset (10a, 10b; 10a, 10c; 10b, 10c) of the array of the acoustic transducers (10). The acoustic system according to claim 1 or 2.

12. The control unit (30) is configured to determine the spatial coordinates (X, Y, Z) of the acoustic transducers (10) using a model of the sheet surface (20s) that includes the respective positions of modeled acoustic transducers on the modeled sheet surface, the model being used to calculate a set of modeled propagation times between the modeled acoustic transducers, the modeled propagation times depending on the respective distances between the modeled acoustic transducers. Each distance between the modeled acoustic transducers depends on each position on the modeled sheet surface and the variable shape of the modeled sheet surface, The variable shape of the modeled sheet surface is adjusted to fit a set of propagation times (Tab, Tbc, Tac) at which the modeled propagation times are measured, The spatial coordinates (X, Y, Z) of the acoustic transducer (10) are determined based on the respective positions of the modeled acoustic transducers on the modeled sheet, The acoustic system according to claim 1 or 2.

13. The control unit (30) is configured to measure the propagation time (Tac) of a sound wave (W) transmitted through a curved object (Obj) between the first acoustic transducer (10a) and the third transducer (10c), The second transducer (10b) is arranged along a surface path on the sheet surface of the flexible sheet between the first acoustic transducer (10a) and the third transducer (10c), The control unit (30) is configured to determine the spatial coordinates (Xb, Yb, Zb) of the second transducer (10b) based at least in part on interpolating the surface distances (Dab, Dbc) and / or predetermined surface coordinates of the second transducer (10b) with respect to the first acoustic transducer (10a) and the third transducer (10c) on the modeled sheet surface (20m) of the flexible sheet (20), The acoustic system according to claim 1 or 2.

14. Providing an array of acoustic transducers (10) arranged on the sheet surface (20s) of the flexible sheet (20), At least partially wrapping the curved object (Obj) with the flexible sheet (20) such that the acoustic transducers (10) acoustically contact the curved object (Obj) from different sides, Using the acoustic transducer (10) to generate and / or measure sound waves (W) at variable positions around the curved object (Obj), wherein the spatial coordinates (X, Y, Z) of the variable positions in three-dimensional space depend on the deformation of the sheet surface (20s) wrapping the curved object (Obj), While the flexible sheet (20) wraps the curved object (Obj), based on a set of propagation times (Tab, Tbc, Tac) of the sound wave (W) transmitted through the curved object (Obj), determining the spatial coordinates (X, Y, Z) of the acoustic transducer (10); comprising; A method for acoustically measuring a curved object (Obj).

15. When executed by the acoustic system (100) according to claim 1 or 2, the acoustic system is caused to control a set of acoustic transducers (10) to generate and / or measure sound waves (W) at variable positions around the curved object (Obj), wherein the spatial coordinates (X, Y, Z) of the variable positions in the three-dimensional space depend on the periphery of the curved object (Obj); determine the spatial coordinates (X, Y, Z) of the acoustic transducer (10) based on a set of propagation times (Tab, Tbc, Tac) of the sound wave (W) transmitted through the curved object (Obj); generate an image by processing acoustic signals measured from at least a subset of the acoustic transducers (10), wherein the acoustic signals are processed based on the determined spatial coordinates (X, Y, Z); a program for causing the above to be performed.

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