Flexible ultrasonic array for measuring curved objects with scattering elements.

Abstract

A system and method for acoustically measuring curved objects is provided. A flexible sheet (20) is provided with an array of acoustic transducers (10) and wrapped around a curved object (Obj) such that the acoustic transducers (10) are in acoustic contact with the curved object (Obj). The acoustic transducers (10) are used to generate and / or measure acoustic waves (W) at variable positions depending on the shape of the curved object (Obj). While the flexible sheet (20) is wrapped around the curved object (Obj), spatial coordinates (X,Y,Z) of the acoustic transducers (10) are determined. In particular, the spatial coordinates are determined based on respective subsets (Ta,Tb,Tc) of travel times that are used to calculate the wave directions of the respective acoustic waves (Wa,Wb,Wc) arriving at the respective subarrays (10a,10b,10c) from a common origin, e.g. a scattering element (S) inside the curved 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 objects and materials, such as tissue. For example, mammography and other acoustic images can be generated using pulse-echo measurements performed by acoustic transducers. Information about the materials and structures inside an object or tissue can be extracted from measured properties of the acoustic waves traversing and / or reflecting off the material infrastructure, such as the amplitude, frequency, phase, and / or time between the transmitted pulse and the received echo. When pulse-echo and / or tomographic measurements are performed between different transducers, reconstruction of the imaged ultrasound may rely on a priori knowledge of the (relative) positions of the transducers. However, with conformable, flexible, and / or stretchable ultrasound arrays, the positions between the elements of the different transducers may be unknown, hindering image reconstruction.

[0003] As background, US Patent Application Publication No. 2020 / 0278327 describes phased array calibration for geometry and aberration correction. Various techniques for calibrating the geometry of an ultrasound transducer having multiple transducer elements include providing an acoustic reflector that spans an area traversed by multiple beam paths of ultrasound transmitted from all (or at least some) transducer elements to a focal region, causing the transducer elements to transmit the ultrasound to the focal region, measuring the reflection of the ultrasound from the acoustic reflector, and determining optimal geometric parameters associated with 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 relate to an acoustic system and method for measuring curved objects. A flexible sheet comprises an array of transducers distributed on a sheet surface of the flexible sheet that acoustically contacts the curved object. The transducers are configured to generate and / or measure acoustic waves. These waves can be generated and measured according to variable positions of the transducers relative to each other. The spatial coordinates of the variable positions (in three-dimensional space) depend on the deformation of the sheet surface in contact with the curved object. As will be appreciated, the a priori unknown (relative) spatial coordinates can be determined by the acoustic system itself using various methods described herein.

[0007] A set of arrival times is determined from acoustic waves originating from a common origin and arriving at different transducers in the array. Preferably, the common origin is formed by one or more common scattering elements inside the curved object. Alternatively or additionally, one or more transducers in the array can be used as the common origin. The set of arrival times is organized (divided) into different subsets. Each subset of arrival times is selected to correspond to a respective subarray of transducers spanning a respective subarea of ​​the flexible sheet at a respective surface coordinate along the sheet surface. Based on the respective subset of arrival times of each subarray of transducers, a respective wave direction is determined, where each portion of the acoustic wave arrives at each of the subareas originating from the common origin. A modeled shape of the sheet surface can be determined based at least in part on the respective wave direction as a function of the surface coordinate of the respective subarea. The spatial coordinates of the transducers can be determined based on the modeled shape of the sheet surface. Alternatively, or in addition to wave direction, other aspects can be derived from the arrival times, such as the distance between each transducer and the common scattering element and / or the distance (direct and indirect) to other transducers. Other or additional features may also be used in modeling the shape of the sheet surface. For example, predefined surface coordinates and distances of the transducers may serve to constrain the shape to fit. For example, the shape may be constrained to a predefined (functional) parameterization, or may remain as a free-form mesh of interconnected sub-arrays.

[0008] These and other features, aspects, and advantages of the presently disclosed apparatus, systems, and methods will become better understood from the following description, appended claims, and accompanying drawings. [Brief description of the drawings]

[0009] [Figure 1A] FIG. 1 is a perspective view of an acoustic system including a flexible sheet having an array of transducers. [Figure 1B] FIG. 13 is a cross-sectional view of a flexible sheet in which transducers contact a curved object and measure acoustic waves emanating from a common scattering element. [Figure 1C] FIG. 1 illustrates the wave direction of acoustic waves arriving at different sub-areas of a flexible sheet and the distance to a common scattering element. [Figure 2A] FIG. 13 illustrates determining a modeled shape of the sheet surface based on the direction of each wave as a function of the surface coordinates of each sub-area. [Figure 2B] FIG. 13 illustrates determining a modeled shape of the sheet surface based on the direction of each wave as a function of the surface coordinates of each sub-area. [Figure 2C] FIG. 13 illustrates determining a modeled shape of the sheet surface based on the direction of each wave as a function of the surface coordinates of each sub-area. [Figure 3A] FIG. 1 illustrates steps for determining a modeled shape using multiple scattering elements. [Figure 3B] FIG. 1 illustrates steps for determining a modeled shape using multiple scattering elements. [Figure 4A] FIG. 13 illustrates determining the direction of each wave based on a subset of arrival times. [Figure 4B] FIG. 13 illustrates determining the angle of the wave direction using a two-dimensional sub-array of transducers covering a sub-area of ​​a flexible sheet. [Figure 5A] FIG. 2 illustrates the steps of computing a linear Radon transform for each subarray of the transducer. [Figure 5B] FIG. 2 illustrates the steps of computing a linear Radon transform for each subarray of the transducer. [Figure 5C] FIG. 2 illustrates the steps of computing a linear Radon transform for each subarray of the transducer. [Figure 6A]Using the Radon transform, we show how to derive the direction of each wave and determine the modeled shape, and these directions can be fitted together via a common point of origin. [Figure 6B] Using the Radon transform, we show how to derive the direction of each wave and determine the modeled shape, and these directions can be fitted together via a common point of origin. [Figure 6C] Using the Radon transform, we show how to derive the direction of each wave and determine the modeled shape, and these directions can be fitted together via a common point of origin. [Figure 6D] Using the Radon transform, we show how to derive the direction of each wave and determine the modeled shape, and these directions can be fitted together via a common point of origin. [Figure 7A] 1 illustrates the use of the Radon transform to separate measurements from different scattering elements. [Figure 7B] 1 illustrates the use of the Radon transform to separate measurements from different scattering elements. [Figure 7C] 1 illustrates the use of the Radon transform to separate measurements from different scattering elements. [Figure 8A] 13 illustrates the use of deimaging to separate measurements from different scattering elements. [Figure 8B] 13 illustrates the use of deimaging to separate measurements from different scattering elements. [Figure 8C] 13 illustrates the use of deimaging to separate measurements from different scattering elements. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0010] The terms used to describe certain embodiments are not intended to limit the invention. As used herein, the singular forms "a," "an," and "the" are intended to include the plural, 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 "comprising" specify the presence of the stated features, but do not exclude the presence or addition of one or more other features. It will be further understood that when a particular step of a method is referred to after another step, it may directly follow the other step, unless otherwise stated, or one or more intermediate steps may be performed before performing the particular step. Similarly, when a connection between structures or components is described, it will be understood that this connection may be established directly or through an intermediate structure or component, unless otherwise specified.

[0011] The present invention will now be described more fully 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. Embodiments may be described with reference to schematic and / or cross-sectional illustrations of potentially idealized embodiments and intermediate structures of the invention. In the specification and drawings, like numbers refer to like elements throughout. Related terms and derivatives thereof should be construed to refer to the orientation as described then or as shown in the drawings under discussion. These related terms are for convenience of description and do not require that the system be constructed or operated in a particular orientation, unless specifically stated otherwise.

[0012] Figure 1A shows a perspective view of an acoustic system 100 comprising a flexible sheet 20 with an array of transducers 10. Figure 1B shows a cross-sectional view of the flexible sheet 20 where the transducers 10 contact a curved object "Obj" and measure acoustic waves "Wa", "Wb", "Wc" emanating from a common scattering element "S". Figure 1C shows the wave directions θa, θb, θc where the acoustic waves arrive at different sub-areas 20a, 20b, 20c of the flexible sheet 20 and the distances "Das", "Dbs", "Dcs" to the common scattering element "S".

[0013] In some embodiments, an array of transducers 10 is distributed on a sheet surface 20s of a flexible sheet 20 that is in acoustic contact with the curved object "Obj". In one embodiment, the transducers 10 are configured to generate and / or measure acoustic waves "W" at variable positions relative to each other. For example, one or more acoustic transducers generate acoustic waves and one or more acoustic transducers measure acoustic waves. Preferably, each acoustic transducer is capable of both generating and measuring acoustic waves. In one embodiment, some acoustic transducers are used to generate acoustic waves and other acoustic transducers are used to measure the generated acoustic waves. The role of an acoustic transducer to generate or to measure acoustic waves may be fixed or variable, or an acoustic transducer may perform both roles simultaneously or successively. It is also conceivable that the acoustic transducers 10 distributed on the flexible sheet 20 are used only for measurement. For example, the acoustic waves scattered from the common scattering element "S" may originate from another acoustic wave source, e.g., another acoustic wave source than the flexible sheet.

[0014] As noted, the spatial coordinates (X,Y,Z) of the variably positioned transducers in three-dimensional space depend on the deformation of the sheet surface 20s, which in turn can be coupled to the contacting curved object "Obj". For example, the flexible sheet 20 can be at least partially wrapped around the curved object "Obj" and / or cover the surface of the object including the curvature. This allows the flexible sheet 20 and the array of transducers 10 to have a non-planar shape.

[0015] In some embodiments, the shape of the flexible sheet 20 and / or the (relative) spatial coordinates of the transducer 10 are determined in situ, for example, using a controller 30 operatively coupled to the transducer 10 to transmit and receive electrical signals that are converted to acoustic signals, and vice versa. For example, the controller 30 is configured and / or programmed to perform operational steps according to the methods and systems described herein. Typically, the controller may be under the control of hardware and / or software. Aspects of the present disclosure may be embodied as a (non-transitory) computer-readable medium that stores instructions that, when executed by one or more processors, cause the controller to perform the methods described herein.

[0016] Some embodiments include determining a set of arrival times "T" of acoustic waves "W" emanating from a common origin for different transducers in the array. In a preferred embodiment, the common origin is formed by a common scattering element "S" inside the curved object "Obj", for example as shown. For example, the set of arrival times "T" of acoustic waves "W" is based on the respective time intervals between the generation of acoustic waves "W" by one or more source transducers (within the array and / or separate from the array) and the measurement of the resulting acoustic waves by the receiving transducers in the respective sub-arrays 10a, 10b, 10c after the common scattering element "S" scatters the waves along respective paths between the source transducers and the receiving transducers. Alternatively, or in addition, the common point of origin may be formed by a direct source of the acoustic waves, e.g. one of the transducers in the array, or by another transducer, e.g. another transducer applied at or near a particular location within the object (e.g. on the opposite side of the object to the array), and / or another source transducer that sends acoustic waves to the common scattering element "S".

[0017] Some embodiments comprise organizing the set of arrival times T into various subsets. In one embodiment, each subset of arrival times "Ta", Tb, Tc corresponds to a respective subarray 10a, 10b, 10c of the transducer 10 spanning a respective subarea 20a, 20b, 20c of the flexible sheet 20 at a respective surface coordinate (Sx, Sy) along the sheet surface 20s. An embodiment comprises determining, based on the respective subset of arrival times "Ta", Tb, Tc at each subarray 10a, 10b, 10b of the transducer 10, a respective wave direction θa, θb, θc of the respective portions of the acoustic waves "Wa", "Wb", "Wc" arriving at the respective subarea 20a, 20b, 20c originating from a common point of origin, e.g., scattering element "S". Another or further embodiment comprises determining a modeled shape 20m of the sheet surface 20s based at least in part on the respective wave directions θa, θb, θc as a function of the surface coordinates (Sx, Sy) of the respective sub-areas 20a, 20b, 20c. The spatial coordinates (X,Y,Z) of the transducer 10 can thus be determined based on the modeled shape 20m of the sheet surface 20s.

[0018] In some embodiments, the shape of the sheeting surface 20s is modeled primarily or exclusively based on the respective wave directions θa, θb, θc. In one embodiment, subareas of the sheeting surface are modeled, at least initially, facing angles relative to one another based on the respective wave directions. For example, if a common scattering element "S" is at a relatively large distance from a set of subareas, the angle between the subareas may be similar or the same as the relative wave directions. Alternatively, or in addition, the relative position or distance of the common scattering element "S" with respect to one or more subareas may be modeled, assumed, or measured. In one embodiment, the position of the modeled scattering element "M" is variable, for example, determined by a fitting and / or iterative procedure. In another or further embodiment, the position of the modeled scattering element "M" is predetermined or otherwise assumed.

[0019] Some embodiments comprise determining respective distances "Das", "Dbs", "Dcs" between each sub-area 20a, 20b, 20c and the common scattering element "S" or other origin. The modeled shape 20m of the sheet surface 20s can thus be determined or constrained based at least in part on one or more of the respective distances "Das", "Dbs", "Dcs". In one embodiment, the respective distances are determined relative to the centre of the respective sub-area. In another or further embodiment, an average distance is determined based on one or more, preferably all, transducers in the sub-array. In principle, any other position can be selected for the sub-areas. In principle, if the distance between the common scattering element "S" and one of the sub-areas is measured, other distances can also be derived. Preferably, each of the distances "Das", "Dbs", "Dcs" is measured respectively to improve the constraint on the modeled shape. In principle, if the distance between the common scattering element "S" and each of the transducers 10 could be accurately measured, this could be used to determine the modelled shape 20m even independently of the respective wave directions θa, θb, θc. However, in practice this may be difficult to model accurately, for example due to limitations in accuracy and / or interference. It is therefore preferable to use one or more measured distances as a further constraint on the modelled shape 20m that is based at least in part on the wave directions.

[0020] As will be appreciated, the respective distances "Das", "Dbs", "Dcs" between each sub-area 20a, 20b, 20c and the common scattering element "S" can be determined based on the arrival times "Ta", Tb, Tc. For example, the respective distances "Das", "Dbs", "Dcs" between each sub-area 20a, 20b, 20c and the common scattering element "S" are determined based on the time interval between the generation and measurement of the respective acoustic waves. In some embodiments, at least one transducer in each sub-array 10a, 10b, 10c is configured to generate a respective acoustic wave and measure the resulting acoustic waves "Wa", "Wb", "Wc" reflected back from the common scattering element "S", and the respective distances "Das", "Dbs", "Dcs" between each sub-area 20a, 20b, 20c and the common scattering element "S" are determined based on the time interval between the generation and measurement of the respective acoustic wave.

[0021] In one embodiment, the time interval between transmission and reception of acoustic waves in each subarray 10a is about 2 round trip times. * corresponds to Tas. For example, the (one-way) travel time "Ta" it takes for an acoustic wave "Wa" to travel from the common scattering element "S" to the subarray 10a is calculated as half the round trip time. In another or further embodiment, the distance "Das" between the corresponding subarea 20a and the common scattering element "S" is calculated by multiplying the one-way travel time by the (wave) velocity "C". Similarly, the round trip time can be multiplied by an "effective" velocity, which in the pulse-echo case can be considered as half the actual wave velocity in the medium.

[0022] In principle, the speed of the acoustic waves can be predetermined, measured, assumed, and / or modeled (e.g., as a parameter). In one embodiment, the speed of the acoustic waves is predetermined between a pair of transducers at a known distance between them, e.g., using measurements through the object or a model object. In another or further embodiment, one or more pairs of transducers in an array are used to measure the speed of the acoustic waves, e.g., by assuming that the surface distance between the nearest adjacent transducers is similar or the same as the distance through the object. In another or further embodiment, the speed of the acoustic waves is assumed, e.g., based on known wave transmission characteristics of the object. In another or further embodiment, the speed of the acoustic waves is used as a parameter in modeling the layout / shape of the sheet. In some embodiments, the speed "C" is assumed to be constant throughout the object. In other or further embodiments, the speed "C" can be variable, e.g., depending on the substructure inside the object. For example, the substructure can be determined by the acoustic system itself, e.g., iteratively.

[0023] In some embodiments, the acoustic waves generated by one source transducer are also measured by multiple receiving transducers in different subarrays. This can provide faster data than just measuring the reflected waves back to the same subarray. In one embodiment, one or more transducers in the first subarray 10a are configured to generate respective acoustic waves, and the transducers in the (another) second subarray 10b and the third subarray 10c are configured to measure the respective acoustic waves refracted (or reflected) at the common scattering element "S". In another or further embodiment, the transducers in the first subarray 10a are also configured to measure the respective acoustic waves reflected back from the common scattering element "S". For example, this round trip wave can be used to determine the respective round trip time and / or distance "Das" between the first subarray 10a and the common scattering element "S". This information can also be used to determine the distances "Dbs", "Dcs" between the common scattering element "S" and the other subarrays 10b, 10c. For example, one-way travel time (or distance) between a scattering element and the second sub-array S→10B can be obtained by subtracting half the round trip time 10a→S→10a from the travel time between the different transducers 10a→S→10B. Alternatively or in addition to determining one or more distances "Das", "Dbs", "Dcs" to the common scattering element "S", other or further constraints can also be used in combination with the wave directions θa, θb, θc to determine the modelled shape 20m.

[0024] In some embodiments, each transducer or subarray of transducers has a set of predefined surface coordinates (Sx,Sy) along the sheet surface 20s. Typically, the spatial coordinates (X,Y,Z) of the acoustic transducers 10 are determined based at least in part on the predefined surface coordinates (Sx,Sy) (while the flexible sheet 20 is wrapped around the curved object "Obj"). In one embodiment, the surface coordinates (Sx,Sy) comprise the two-dimensional coordinates of the respective position of each transducer and / or subarray, 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 order or relative position of each transducer, which, e.g. in combination with a known distance between the transducers, allows the calculation of the actual position.

[0025] In another or further embodiment, the transducers in the array have a predefined surface distance between them along the sheet surface 20s (e.g., denoted by "Sp", "Ss", "Sab", "Sac", "Sbc"). An embodiment comprises determining the spatial coordinates (X,Y,Z) of the acoustic transducers 10 (while the flexible sheet 20 is wrapped around the curved object "Obj") based at least in part on the predefined surface distance. In an embodiment, the predefined surface distance comprises a distance "Sp" between (closest) adjacent transducers, e.g., a fixed or variable periodic distance. For example, the respective surface distances "Sab", "Sac", "Sbc" between any set of transducers or between subarrays 10a, 10b, 10c are calculated based on the periodic distance "Sp" 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 distances "Sab" between the sets of transducers or subarrays 10a, 10b are calculated based on a table storing the respective (absolute) surface positions (Xa,Ya,Xb,Yb) (e.g. measured in millimeters from an origin) of each transducer or subarray. For example, the absolute surface positions can be subtracted from the table to determine the relative positions between the transducers (ΔXab=Xa-Xb, ΔYab=Ya-Yb), the distances being calculated according to the Pythagorean theorem (Dab 2 =ΔXab 2 +ΔYab 2) can be used to calculate the distance D ab. In another or further embodiment, a table is used that directly stores, for one or more (preferably each) transducer, the respective surface distance D ab to one or more, preferably all other transducers in the array. In this way, the surface distance can be quickly read out for any pair of transducers and / or subarrays. As will be appreciated, the given surface coordinates (Sx, Sy) and / or distance are preferably measured along the surface of the flexible sheet 20 when the sheet is flat, e.g., placed on a horizontal flat surface. Typically, the distance along the flexible sheet can represent the maximum distance that can be shortened if the sheet is curved around an object. The distance through the object can be described as a direct Euclidean distance (shortest line segment), which is, for example, shorter than the surface distance along the curved sheet surface.

[0026] In some embodiments, the flexible sheet 20 is stretchable, allowing for a variable surface distance between the acoustic transducers 10 along the sheet surface 20s. In one embodiment, the acoustic transducer 10 is further configured to generate and / or measure guided waves traveling inside and / or along the sheet surface 20s to determine the variable surface distance Dab. In another or further embodiment, the distance between the transducers along the sheet surface is measured using guided waves, preferably traveling along and / or within the flexible sheet 20, or another interface / connection between the transducers. In one embodiment, the waves measuring the distance between the transducers comprise Lamb waves, e.g., extensional A0 and / or bending S0 guided waves. In another or further embodiment, the waves measuring the distance between the transducers comprise interface waves, e.g., Scholte waves traveling along the sheet / tissue interface. When used in combination with an interface where the sheet is solid, the waves can be referred to as Stoneley waves. Regular compression waves for tissue, or compression / shear waves when the sample is solid, can also be used to determine the 3D shape of the transducer sheet. For example, the measured distance between the transducers can be used as a substitute for the predetermined distance, or can be further used to correct the predetermined distance in case of stretching / compression. In particular, in the case of a stretchable transducer sheet, it can be advantageous to determine the distance between the transducers on the transducer sheet separately from the 3D shape of the transducer sheet, by using guided waves traveling along the transducer sheet for the former and bulk compression / shear waves for the latter. One advantage is that the minimum degree of freedom can be used for the inversion of the 3D shape, allowing for a more complex 3D shape reconstruction or a more robust reconstruction process of the transducer sheet.

[0027] Some embodiments (not shown) comprise determining the spatial coordinates (X,Y,Z) of the acoustic transducer 10 based at least in part on a set of travel times of acoustic waves transmitted directly (e.g. along a straight line through the object without a common scattering element "S") between different transducers of different subarrays. For example, the transducers and / or subarrays at least partially face each other on different sides of the curved object "Obj". One embodiment comprises using the subarrays of receiving transducers to determine the wave direction of each of the acoustic waves transmitted from a particular source transducer or transducers. In this way, the angle of the receiving subarray with respect to the source transducer or transducers can be determined, similar to the case of the scattering elements. Another or further embodiment comprises determining a set of Euclidean (direct) distances through the object between the different transducers based on the set of travel times, for example by multiplying by the wave speed "C".

[0028] Typically, the travel time can be determined based on the time difference measured between a first timestamp of transmitting an acoustic wave with a first transducer and a second timestamp of receiving the acoustic wave with the same or another transducer. For example, the travel time can be determined for an acoustic wave traveling back and forth between a transducer and a scattering element, and / or traveling between a pair of transducers, and / or traveling between one transducer, a scattering element, and another transducer. The travel time is sometimes called the time of flight. The same acoustic wave (or another acoustic wave) transmitted from the first acoustic transducer can also be received by a third acoustic transducer, resulting in another timestamp that is used to determine the travel time between the first acoustic transducer and the third acoustic transducer. This can be done for each transducer in the array to obtain a subset of the travel times. Similarly, the travel time between the second transducer and the third transducer can be determined. These measurements can be performed sequentially and / or in parallel between any pair of transducers in the array and / or through at least one common scattering element to obtain a desired set of travel times. For example, acoustic waves can be transmitted with a unique signature (e.g., frequency) to distinguish the origin of each of the acoustic waves. The travel time can also be determined in opposite directions for any pair. Also, by repeating the measurements in the same or opposite directions, the average or median travel time between any pair can be determined. For example, this can be done to mitigate any noise.

[0029] In some embodiments, the acoustic system 100 is configured to function as a reflection-based acoustic device. In other or further embodiments, the acoustic system 100 is configured to function as a tomography-based acoustic device. Other or further types of acoustic devices, such as photoacoustic devices, are also conceivable. In principle, each acoustic transducer may comprise, for example, 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. Preferably, each subarray is formed by an area with a plurality of acoustic transducers, for example at least 2, 4, 10, 20, 50, 100 or more (adjacent) transducers forming a localized array. Typically, each subarray has an area of ​​less than 1 mm 2 From 1000mm 2 Between 10 mm and 20 mm, preferably 2 From 100mm 2 For example, a sheet of area 10×10 mm may be formed on a local sub-area of ​​the sheet between 2 The subarray comprises a local array of 100 transducers with a pitch of 1 mm.

[0030] In a preferred embodiment, the acoustic system 100 is configured to generate an image of the curved object "Obj" using an array of acoustic transducers 10, for example using the same or another controller. Most preferably, 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 at least in part based on the wave directions θa, θb, θc. For example, the acoustic system 100 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 inside of the curved object "Obj" can 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) controller may be configured to generate images or other measurements of structures and / or properties measured within the curved object "Obj" using a set of amplitudes of (same or other) acoustic waves "W" sent through the curved object "Obj" between different transducers (tomography and / or reflection) or back to the same transducer (reflection).

[0031] As will be appreciated, the measurement signals (and the particular processing of these 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 arrangement of the transducers relative to the object. For example, in a reflection measurement, the echo time combined with, e.g., the amplitude or other properties of the acoustic signal returning to the same or other transducers may be processed to determine the structure and / or properties of the material in the reflection path, the origin and destination of the path being determined by the spatial arrangement of one or more transducers relative to the object. If the respective paths for the different signals can be located, e.g., mapped to the object, the signals can be combined to generate an image or other measurement. Thus, measurements of structures and / or properties inside the object may be processed based on acoustic signals (e.g., reflection and / or tomography) measured according to the spatial coordinates (X,Y,Z) of the transducers determined as described herein.

[0032] In one embodiment, imaging or other measurements of the object are performed after determining the spatial coordinates (X,Y,Z) of the acoustic transducer 10. In another or further embodiment, the spatial coordinates (X,Y,Z) of the acoustic transducer 10 are determined while measurements of the curved object "Obj" are being made or intermittently between such measurements. For example, tomographic and / or reflection-based measurements can be performed on a body while its shape is changing (e.g. due to respiratory movements) by constantly updating the measurement positions of the transducers. In principle, the same or similar acoustic signals used to determine the spatial coordinates can also be used to image the object. For example, the structure and / or properties inside the object can be determined based on the reflection and / or absorption of acoustic waves between the same or different transducers.

[0033] In some embodiments, the modeled shape 20m of the flexible sheet 20 is determined by a constrained fit using the wave directions θa, θb, θc as inputs. Various constraints can be applied to the modeled shape 20m to allow a convergent fit, such as a predetermined surface distance between different subarrays. 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 of subarrays. In another or further embodiment, the model is constrained by a maximum curvature (e.g., minimum radius) of the sheet and / or object. For example, the sheet is assumed to have a certain flexibility and / or bending property. For example, the object is assumed to have a certain maximum curvature (e.g., minimum radius). In another or further embodiment, the model is constrained by a maximum stretchability of the flexible sheet 20. For example, the flexible sheet 20 may not be substantially stretchable so that any predetermined distance along the sheet surface can be fixed. Or, the flexible sheet 20 may have some stretchability so that the predetermined distance along the sheet surface can be variable, e.g., adjusted by a variable magnification depending on the model. In some embodiments, the model is constrained by the predetermined positions of the transducers on the surface (surface coordinates). For example, the predetermined positions are set in the model as constraints on the maximum distance between the transducers through the object and / or on a fixed distance along the sheet surface. Instead of a free-form surface, the shape can be restricted to a specific shape, e.g., spherical, cylindrical, etc. This can limit the number of free parameters to allow a more constrained (easier) fit.

[0034] In one embodiment, the fitting is performed by an iterative procedure, e.g., minimizing the difference between the actual measurements and the expected measurements based on the modeled shape 20m and / or scattering elements "S". In another or further embodiment, the fitting is performed analytically, e.g., directly calculating the best fit. Also, a combination of calculation and / or fitting routines is possible. Also, other algorithms such as machine learning / artificial intelligence can be used to calculate, e.g., the most likely shape of the flexible sheet. In some embodiments, multiple fits are performed for different subsets of transducers to determine the local shape or curvature of the corresponding sub-compartment area of ​​the sheet. For example, multiple fits can be combined to provide the overall shape. In some embodiments, the fitting is performed globally using all measurements. For example, this may be performed after determining the general shape based on local fits or a predetermined general shape of the object.

[0035] An embodiment comprises determining a set of current spatial coordinates (X,Y,Z) of the acoustic transducer 10 by adjusting the predefined spatial coordinates (X,Y,Z) according to the wave directions θa, θb, θc. A selection of one or more predefined shapes, e.g., sphere, cylinder, etc., can be input to the controller as an initial assumed shape. This can facilitate fitting the shape. In another or further embodiment, the set of predefined spatial coordinates comprises previously measured and / or fitted coordinates of the acoustic transducer 10. For example, the spatial coordinates of the acoustic transducer 10 and / or the modeled shape 20m are measured or updated continuously or intermittently to track objects that may change shape (e.g., the body when breathing). Alternatively or in addition to modeling the sheet surface as a (free-form) mesh, it can also be envisaged to model the sheet surface as a continuous parameterized surface, e.g. according to a surface equation of a predefined shape.

[0036] In some embodiments, the modeled shape is constrained to fit by a function related to the shape or parameters that is determined by the predefined parameters. An embodiment comprises calculating the modeled shape 20m based on a predefined parameterized shape with variable scaling parameters and / or a set of coordinates. For example, the coordinates may include the (x0, y0, z0) origin of the shape. The use of parameterized shapes may limit the number of free parameters compared to more general meshes. For example, the set of scaling parameters and / or coordinates is fitted according to the wave directions θa, θb, θc and / or other measurements or constraints. In some embodiments, the modeled shape 20m can be parameterized as a (subdivision area of) a sphere or an ellipsoid. An ellipsoid is a surface that can be obtained from a sphere by directional scaling, or more generally by deforming the sphere by an affine transformation. For example, an ellipsoid can be uniquely defined by six parameters (x0, y0, z0, a, b, c). These can be determined by a set of at least seven independent measurements. In practice, more measurements may be required, since the information of the measurements may not be orthogonal and the signal-to-noise ratio (SNR) may be limited. For example, the acoustic system is used to measure cellular tissue (of the breast). In this case, the initial mesh shape and / or the parameterized functional surface may be determined using a portion of a sphere. 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 tube that may have an unknown or variable diameter. Also, other parameterized shapes may be envisaged, such as, for example, a (frustum) cone shape. For example, the acoustic system is used to measure other parts of the body, or any other curved object.

[0037] 2A-2C show the steps of determining a modeled shape 20m of the sheet surface 20s based on the respective wave directions θa, θb, θc as a function of the surface coordinates (Sx, Sy) of each sub-area 20a, 20b, 20c.

[0038] In some embodiments, determining the modeled shape 20m comprises determining a set of line segments. In one embodiment, each line segment remains fixedly connected to a respective sub-area 20a, 20b, 20c. In another or further embodiment, each fixedly connected line segment intersects the respective sub-area at a fixed angle corresponding to the respective wave direction θa, θb, θc at which the acoustic waves "Wa", "Wb", "Wc" arrive at the respective sub-area 20a, 20b, 20c. Other or further embodiments comprise orienting the sub-areas 20a, 20b, 20c to intersect the fixedly connected line segments at a common origin "M", which corresponds to, for example, a common scattering element "S" or a model of another origin.

[0039] In some embodiments, one or more, preferably all, of the line segments are modeled having fixed lengths corresponding to the distances "Das", "Dbs", "Dcs" between each subarea 20a, 20b, 20c and the common scattering element "S". In one embodiment, the subareas 20a, 20b, 20c are oriented and / or translated to overlap respective ends of a fixed connecting and fixed length line segment at a common origin M. In principle, the position and orientation of each subarea can be uniquely determined, for example, using the direction and length of the fixed connecting line segment, without requiring further predetermined knowledge of the subarray. For example, not only the orientation but also the position of the subareas can be changed to align the direction and length of the line segment to the common origin.

[0040] In some embodiments, the subareas 20a, 20b, 20c of the modeled shape 20m are oriented according to their respective wave directions θa, θb, θc, and adjacent subareas 20a, 20b, 20c remain connected to each other (at their respective ends therebetween) according to their size "Sn" and relative positions, e.g., surface coordinates (Sx,Sy). In one embodiment, the size and / or relative positions of the subareas are determined based on the surface coordinates (Sx,Sy) of the transducers and / or subarrays. In one embodiment, adjacent subareas connect to each other to form a linked chain or mesh. In one embodiment, the order of the subareas in the chain or mesh is determined based on their relative positions. In another or further embodiment, the length of each chain or mesh element is determined based on the respective size of the subareas. In general, the surface of the sheet may vary in more than one direction. Thus, the mesh may vary in multiple directions as well. Typically, this may include local stretching and / or compression of the subareas, which may be modeled, for example, as parameters that change their respective tolerances or predetermined sizes. In one embodiment, the subareas are modeled to form an interconnected (2-dimensional) mesh with parameterized or freeform shape.

[0041] 3A and 3B show steps for determining a modeled shape 20m using multiple scattering elements S1, S2.

[0042] Some embodiments comprise determining a first set of arrival times of acoustic waves "W" interacting with a first scattering element "S1" inside the curved object "Obj". Other or further embodiments comprise determining a second set of arrival times of acoustic waves "W" interacting with a distinct second scattering element "S2" inside the curved object "Obj". An embodiment comprises splitting and / or collapsing each set of arrival times into a respective set of subsets corresponding to the subarrays 10a, 10b, 10c. Other or further embodiments comprise determining, based on the two sets of subsets for each scattering element "S1", S2 and for each subarray 10a, 10b, 10c, at least two wave directions θa1, θb1, θc1, θa2, θb2, θc2, respectively, of the acoustic waves arriving at each subarray from two directions originating from the first scattering element "S1" or the second scattering element "S2", respectively. Another or further embodiment comprises determining a modeled shape 20m of the sheet surface 20s based at least in part on the directions of at least two waves per subarray as a function of the surface coordinates (Sx, Sy) of the subarea. Thus, the spatial coordinates (X, Y, Z) of the transducer 10 can be determined based on the modeled shape 20m of the sheet surface 20s.

[0043] As will be appreciated, the use of more than one scattering element can further constrain the possible modeled shapes 20m that match the measured direction. Preferably, a set of scattering elements is selected that can be sufficiently isolated. In one embodiment, a set is selected that includes at least two distinct scattering elements, the scattering elements being laterally spaced apart from each other. In this way, the scattering elements can be distinguished, for example, by windowing different angles of the incident wave. In one embodiment, a set is selected that includes at least two distinct scattering elements that are at different depths. In this way, the scattering elements can be distinguished, for example, by windowing different arrival times.

[0044] Alternative or further embodiments comprise determining at least two distances Das1 and Das2, Dbs1 and Dbs2, Dcs1 and Dcs2, respectively, between each sub-area 20a, 20b, 20c and at least two distinct scattering elements S1, S2 within the curved object "Obj". Thus, the modelled shape 20m of the sheeting surface 20s can be determined at least in part based on one or more of the at least two distances per sub-area.

[0045] FIG. 4A illustrates determining the respective wave directions θa based on a subset of arrival times “Ta”. In some embodiments, for example as illustrated, acoustic waves “Wa” arriving from a common origin, e.g., from scattering elements and / or other transducers, may arrive at different transducers in the subarray at different times. In one embodiment, the time difference “Δt” within the subset of arrival times “Ta” depends on the respective wave directions θa of the acoustic waves “Wa”, e.g., the angle with respect to the surface normal of the subarray. For example, if the acoustic waves “Wa” arrive with wave directions θa substantially parallel to the surface normal, there may be little or no time difference “Δt” between the different arrival times “Ta”. On the other hand, if the wave directions θa make a large angle with respect to the surface normal, there may be a significant time difference “Δt”. In another or further embodiment, the time difference “Δt” within the subset of arrival times “Ta” depends on the wave speed “C” of the acoustic waves. For example, the slower the acoustic wave, the larger the time difference "Δt" and vice versa. In another or further embodiment, the time difference "Δt" within a subset of arrival times "Ta" depends on the surface distance ΔS between the set of transducers measuring the respective time difference. For example, the further apart the transducers are, the larger the time difference "Δt" and vice versa. In a preferred embodiment, the arrival times of the subset are measured for each transducer in the subarray. From this subset, the overall trend of the time difference can be determined more accurately, for example, by determining the slope of the arrival times as a function of transducer position.

[0046] In one embodiment, the wave direction θa of the sub-area is expressed by the relationship θa=sin -1 C·Δt / ΔS, or any equivalent formula. More sophisticated methods and equations can also be used, such as the (linear) Radon transform, which is further described below. Typically, these equations can work most easily if the incident acoustic wave is a good approximation of a plane wave. This may be the case, for example, when the distance to the wave's origin is, for example, at least 10 times larger than the size of the subarray. For example, this can be easily ensured by using a minimum arrival time. Furthermore, the transducers in the subarray can be assumed to be located approximately in a plane. This can be ensured, for example, by limiting the extent of the subarray and / or by adding local stiffness to keep each subarray in an approximately planar form. Instead of using the plane wave equation, in principle the equations can also be adapted to take into account curved wavefronts, which can be a function of the distance to the origin. Instead of assuming a planar subarray, the equations can also allow for local curvatures, for example by further fitting the positions of the individual transducers according to the globally modeled shape and local curvature of the flexible sheet.

[0047] FIG. 4B illustrates the steps of determining the angles θa, Φa of the wave direction using a two-dimensional subarray 10a of transducers 10 covering a subarea 20a of the flexible sheet. It will be understood that although the embodiments described herein can be described with reference to an illustration of a one-dimensional array of transducers, the contents can be generally applied to two-dimensional arrays. In the case of a two-dimensional array, the direction of each wave can be described by two angular coordinates, for example using a polar angle θa with respect to the surface normal, and an azimuth angle Φa that determines the direction around the normal. For example, the azimuth angle Φa can be determined by interpolating lines through the subarrays where the acoustic waves arrive simultaneously (and taking the azimuth direction perpendicular to those lines). Similarly, the polar angle θa can be calculated by determining the time difference Δt (along the azimuth direction) perpendicular to the line of simultaneous arrival and the surface distance ΔS. Alternatively or additionally, more sophisticated methods and equations can be used, such as the 2D linear Radon transform.

[0048] 5A shows a modeled transducer 10 arranged according to a curved shape and configured to measure acoustic waves from a common scattering element "S." The lighter shaded areas indicate particular subarrays.

[0049] Figure 5B shows a scatter plot of the arrival times "T" obtained for each transducer in the array as a function of their respective surface coordinates "Sx". For reference, the array is drawn above as a straight line, but the arrival times are calculated for the shape shown in the previous figure.

[0050] FIG. 5C shows the linear Radon transform of a subset of arrival times for a particular subarray shown in the previous figure. The Radon transform measures the propagation direction of a plane wave and the arrival time as the center of the subarray. For example, this can be mathematically formulated as follows:

[0051]

number

[0052] Where:

[0053]

number

[0054] For example, the calculation may include selecting a window of the recorded wavefield, e.g. the subarray through which the light points, defining the zero position in the transformation as the center position of the array, and then performing the transformation. After transforming back to the time domain, the recorded response can be shown as a function of the light ray parameters and the origin traveltime (e.g. the arrival time at x=0). For visualization, the envelope of the rf signal can be shown. For example, taking the maximum as a function of the origin traveltime can give a single peak that indicates the best estimate of the propagation direction.

[0055] Figure 6A shows the steps to calculate the (dominant) wave direction θ based on a linear Radon transform with respect to arrival times on each sub-area of ​​the transducer array. For example, each point in the scatter plot of the Radon transform on the left is converted to the respective angle using the formula shown in the figure. For this, we use the effective wave speed "C" which can be considered as half the actual wave speed in the case of a pulse-echo experiment (because each wave can cross paths back and forth). The converted points are plotted in a histogram shown on the right. The peaks of the histograms can be fitted together to obtain the wave direction θ on each sub-array. Figure 6B shows the respective peaks indicating the wave direction measured on each of the sub-arrays. For comparison, the dots at the top of the figure show the expected location of the peaks if the array is not curved. In effect, the shift of the peaks can be used to indicate the amount of curvature. Figure 6C shows the line segments at the respective angles corresponding to the wave directions starting from the modeled shape of the plane. As shown, the line segments do not intersect a common point in this case because the sub-arrays are not properly oriented. Figure 6D shows a modeled shape 20m where the line segments fit through a common origin. In this case, the shape roughly corresponds to the actual input arrangement of the transducers.

[0056] FIG. 7A shows an arrangement of different scattering elements, each scattering element transmitting / refracting a respective wave to each subarray. FIG. 7B shows the arrival time T (e.g., round trip time) as a function of surface coordinate Sx. As shown, each subarray can detect multiple arrival times corresponding to different scattering elements. For some of the transducers, there may be substantial overlap between the arrival times, as shown for example for the subarrays in the dashed-dotted box. FIG. 7C shows the corresponding Radon transform of the subarray data of the previous figure. As this plot shows, the data that is substantially overlapping in the plot shown previously can be well separated in the Radon transform thanks to the different wave directions of the scattering elements S1, S3, S5. Thus, in some embodiments, the Radon transform is used to separate the data corresponding to one of the scattering elements in the case of multiple scattering elements.

[0057] FIG. 8A shows a curved object with multiple scattering elements imaged without considering the curvature of the array to be measured. As shown, the image with the imaging coordinates (Ix, Iz) can be highly distorted without correcting for the actual transducer position. Nevertheless, it may be possible to recognize the separate scattering elements. FIG. 8B shows the same image, but filtered to retain only the data corresponding to one of the scattering elements. This is also called windowing. FIG. 8C shows the de-imaging of the filtered image. As shown, this can be used to effectively isolate the arrival time of a single scattering element. This can be used as input to the previously described method of calculating the direction of each wave relative to this single scattering element. Thus, some embodiments comprise one or more of the steps of generating an (ultrasound) image based on the arrival times of all transducers in the array (e.g., without taking into account the respective positions of the transducers); selecting a single (isolated) scattering element based on the imaging data and filtering out the imaging data corresponding to the other scattering elements to generate a filtered image; inverting the filtered image to generate a set of filtered arrival times T for the selected common scattering element "S"; and performing the steps described herein based on the set of filtered arrival times T, e.g., calculating the wave directions θa, θb, θc of the respective portions of the acoustic waves "Wa", "Wb", "Wc" arriving at the sub-array from the selected common scattering element "S". In some cases, this procedure can be repeated for one or more other selected scattering elements, each time resulting in a respective set of wave directions and / or distances for the respective scattering elements. For example, a fitting of a modeled shape such as that shown in Figures 3A-3B can thus be used.

[0058] Although features are described herein as part of the same or different embodiments for clarity and concise description, 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 the specific systems and devices can also be embodied as a corresponding method of acoustically measuring a curved object. In one embodiment, the method comprises providing a flexible sheet having an array of acoustic transducers distributed on a sheet surface of the flexible sheet. In another or further embodiment, the method comprises wrapping the flexible sheet at least partially around the curved object "Obj" such that the acoustic transducers acoustically contact the curved object "Obj" from different sides. In another or further embodiment, the method comprises generating and / or measuring acoustic waves at variable positions around the curved object using the acoustic transducers. For example, the spatial coordinates of the variable positions in three-dimensional space depend on the deformation of the sheet surface wrapping around the curved object. In another or further embodiment, the method comprises determining the spatial coordinates of the acoustic transducers, preferably while the flexible sheet is wrapped around the curved object "Obj". In a preferred embodiment, the method further comprises imaging and / or measuring the curved object based on the acoustic waves generated and / or measured by the acoustic transducer and their spatial coordinates determined based on the set of travel times. These and other aspects may also be embodied as a computer readable medium storing instructions that, when executed, cause execution of the methods and systems described herein.

[0059] Although embodiments have been shown for various layouts of acoustic transducers on a flexible sheet, alternative methods can be envisioned by those skilled in the art having the benefit of the present disclosure to achieve similar functions and results. For example, the flexible sheet may be omitted if the transducers or subarrays are placed directly on the curved object to be measured. Instead of the flexible sheet, other or similar structures, such as flexible wires and / or nets between the transducers, can also be used to hold the transducers together. The various elements of the described and illustrated embodiments provide certain advantages, such as an acoustic device that is adaptable for self-calibration. Of course, it should be understood that any one of the above embodiments or processes can be combined with one or more other embodiments or processes to provide further improvements in design and discovery and adaptation of advantages. It is understood that the present disclosure provides certain advantages for acoustic imaging and is generally applicable to any application in which the respective positions of acoustic transducers are determined. In interpreting the appended claims, it should be understood that the word "comprising" does not exclude the presence of other elements or acts than those recited in a given claim. The word "a" or "an" preceding an element does not exclude the presence of a plurality of such elements. Any reference signs in the claims do not limit their scope. Several "means" may be represented by the same or different items or implemented structures or functions. Any of the disclosed devices 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 combining their respective features. However, the mere fact that certain means are recited in mutually different claims does not indicate that a combination of these means cannot also be used advantageously. Thus, embodiments of the present invention include all practical combinations of claims, each of which may in principle refer to any preceding claim, unless clearly excluded by the context.

Claims

1. An acoustic system (100) for measuring a curved object (Obj), said acoustic system comprising: a flexible sheet (20) comprising an array of transducers (10) distributed on a sheet surface (20s) of the flexible sheet (20) in acoustic contact with the curved object (Obj), wherein the transducers (10) are configured to measure acoustic waves (W) at variable positions relative to one another, and wherein spatial coordinates (X, Y, Z) of the variable positions in three-dimensional space depend on the deformation of the sheet surface (20s) in contact with the curved object (Obj); A controller (30), determining a set of arrival times (T) of acoustic waves (W) emanating from a common origin for different transducers in the array; organizing the set of arrival times (T) into different subsets, each subset of arrival times (Ta, Tb, Tc) corresponding to a respective sub-array (10a, 10b, 10c) of the transducers (10) spanning a respective sub-area (20a, 20b, 20c) of the flexible sheet (20) at a respective surface coordinate (Sx, Sy) along the sheet surface (20s); determining respective wave directions (θa, θb, θc) of the respective portions of the acoustic waves (Wa, Wb, Wc) originating from the common origin and arriving at the respective sub-areas (20a, 20b, 20c) based on the respective subsets of arrival times (Ta, Tb, Tc) for each sub-array (10a, 10b, 10c) of the transducer (10); determining a modeled shape (20m) of the sheet surface (20s) based at least in part on the respective wave directions (θa, θb, θc) as a function of the surface coordinates (Sx, Sy) of each sub-area (20a, 20b, 20c); a controller (30) configured to determine the spatial coordinates (X, Y, Z) of the transducer (10) based on the modeled shape (20m) of the seat surface (20s); An acoustic system (100) comprising:

2. 2. The acoustic system of claim 1, wherein the common point of origin is formed by a selected common scattering element (S) within the curved object (Obj), and wherein the set of arrival times (T) of the acoustic waves (W) are based on respective time intervals between generation of the acoustic waves (W) by one or more source transducers and measurement of the resulting acoustic waves by a receiving transducer in each of the sub-arrays (10 a, 10 b, 10 c) after the common scattering element (S) has scattered the resulting acoustic waves along respective paths between the source transducers and a receiving transducer.

3. determining the modeled shape (20m) determining a set of line segments, each line segment remaining fixedly connected to a respective sub-area (20a, 20b, 20c), and each fixedly connected line segment crossing the respective sub-area at a fixed angle corresponding to the respective wave direction (θa, θb, θc) of the acoustic waves (Wa, Wb, Wc) arriving at the respective sub-area (20a, 20b, 20c); orienting said sub-areas (20a, 20b, 20c) to intersect these fixedly connected line segments at a common origin (M) corresponding to said model of common origin; Equipped with The sound system of claim 1 .

4. 4. The acoustic system of claim 1, wherein one or more of the line segments are modeled with fixed lengths corresponding to distances (Das, Dbs, Dcs) between the respective sub-areas (20a, 20b, 20c) and the common origin (M), wherein the sub-areas (20a, 20b, 20c) are oriented and / or translated to overlap respective ends of the fixedly connected fixed-length line segments at the common origin (M).

5. The controller (30) determining respective distances (Das, Dbs, Dcs) between each of the sub-areas (20a, 20b, 20c) and the common origin based on the arrival times (Ta, Tb, Tc); and further configured to determine the modeled shape (20m) of the seat surface (20s) based on one or more of the respective distances (Das, Dbs, Dcs). The sound system of claim 1 .

6. 2. The acoustic system of claim 1, wherein at least one transducer in each sub-array (10a, 10b, 10c) is configured to generate a respective acoustic wave and measure the resulting acoustic wave (Wa, Wb, Wc) reflected back from a common scattering element (S) within the object (Obj), and wherein respective distances (Das, Dbs, Dcs) between the respective sub-areas (20a, 20b, 20c) and the common scattering element (S) are determined based on a time interval between the generation and measurement of the respective acoustic wave.

7. 2. The acoustic system of claim 1, wherein the sub-areas (20a, 20b, 20c) in the modeled shape (20m) are oriented according to their respective wave directions (θa, θb, θc), while adjacent sub-areas (20a, 20b, 20c) remain interconnected at their respective ends therebetween according to their respective sizes (Sn) and relative surface positions.

8. 2. The acoustic system of claim 1, wherein the modeled shape (20m) of the flexible sheet (20) is determined by a constraint fit using the wave directions (θa, θb, θc) as input, and wherein the fit is further constrained by one or more of the surface coordinates (Sx, Sy) of each of the subarrays, the size (Ss) of each of the subarrays, the respective surface distances (Sab, Sac, Sbc, Sp) between a pair of subarrays or a pair of transducers, the respective distances (Sas, Sbs, Scs) between each subarray and the common origin, the Euclidean distance between a pair of transducers through the object, and / or a function related to parameters describing the modeled shape (20m).

9. 2. The acoustic system of claim 1, wherein the controller is configured to calculate each wave direction (θa, θb, θc) using a linear Randon transform of each subset of the arrival times (Ta, Tb, Tc) as a function of one or more surface coordinates (Sx, Sy) of the transducers in the respective sub-array.

10. The controller (30) generating an ultrasound image based on the arrival times of all transducers in the array; selecting a single scattering element based on the ultrasound image; filtering out imaging data in the ultrasound image corresponding to other scattering elements to generate a filtered image; inversely imaging the filtered image to generate a filtered set of arrival times (T) for the selected single scattering element; and determining the wave direction (θ, θ, θ) of each portion of the acoustic wave (Wa, Wb, Wc) arriving on the sub-array based on the filtered set of arrival times (T) corresponding to the selected single scattering element. The sound system of claim 1 .

11. The controller (30) determining a first set of arrival times of an acoustic wave (W) that has interacted with a first scattering element (S1) within the curved object (Obj); determining a second set of arrival times of the acoustic wave (W) that has interacted with a second distinct scattering element (S2) within the curved object (Obj); dividing each set of arrival times into a respective set of subsets corresponding to said sub-arrays (10a, 10b, 10c); determining, based on the two sets of subsets for each scattering element (S1, S2) and each sub-array (10a, 10b, 10c), at least two wave directions (θa1, θb1, θc1; θa2, θb2, θc2) for each of the acoustic waves arriving at the respective sub-array from two directions originating from the first or second scattering element (S1, S2), respectively; determining a modeled shape (20m) of the sheet surface (20s) based at least in part on at least two wave directions for each subarray as a function of the surface coordinates (Sx, Sy) of the subarea; and determining the spatial coordinates (X, Y, Z) of the transducer (10) based on the modeled shape (20m) of the seat surface (20s). The sound system of claim 1 .

12. 2. The acoustic system of claim 1, wherein the controller is further configured to determine the spatial coordinates (X, Y, Z) of the acoustic transducer (10) based at least in part on a set of travel times of acoustic waves transmitted directly between different sub-arrays of transducers that are at least partially opposite each other on different sides of the curved object (Obj).

13. 2. The acoustic system of claim 1, wherein the controller (30) is configured to generate an image of the curved object (Obj) using the array of acoustic transducers (10), wherein 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 at least in part based on the directions (θa, θb, θc) of the waves.

14. A method for acoustically measuring a curved object (Obj), comprising: providing a flexible sheet (20) having an array of acoustic transducers (10) distributed on a sheet surface (20s) of said flexible sheet (20); wrapping the flexible sheet (20) at least partially around the curved object (Obj) such that the acoustic transducer (10) is in acoustic contact with the curved object (Obj); using the acoustic transducer (10) to measure acoustic 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 around the curved object (Obj); determining the spatial coordinates (X, Y, Z) of the acoustic transducer (10) based on a set of travel times (Ta, Tb, Tc) of the acoustic waves (W) sent through the curved object (Obj) originating from a common origin while the flexible sheet (20) is wrapped around the curved object (Obj), where: the set of arrival times (T) is organized into different subsets, each subset of arrival times (Ta, Tb, Tc) corresponding to a respective sub-array (10a, 10b, 10c) of the transducers (10) spanning a respective sub-area (20a, 20b, 20c) of the flexible sheet (20) at a respective surface coordinate (Sx, Sy) along the sheet surface (20s); determining respective wave directions (θa, θb, θc) of respective portions of the acoustic waves (Wa, Wb, Wc) emanating from the common origin and arriving at the respective sub-areas (20a, 20b, 20c) based on respective subsets of the arrival times (Ta, Tb, Tc) of each sub-array (10a, 10b, 10c) of the transducer (10); a modeled shape (20m) of the sheet surface (20s) is determined based at least in part on the respective wave directions (θa, θb, θc) as a function of the surface coordinates (Sx, Sy) of each sub-area (20a, 20b, 20c); the spatial coordinates (X, Y, Z) of the transducer (10) are determined based on the modeled shape (20m) of the seat surface (20s); method.

15. A non-transitory computer-readable medium storing instructions that, when executed by an audio system, cause the audio system to: controlling a set of acoustic transducers (10) to measure acoustic waves (W) at variable positions on the periphery of a curved object (Obj), wherein the spatial coordinates (X, Y, Z) of said variable positions in three-dimensional space depend on said periphery of said curved object (Obj); determining the spatial coordinates (X, Y, Z) of the acoustic transducer (10) based on a set of travel times (Ta, Tb, Tc) of the acoustic waves (W) transmitted through the curved object (Obj) originating from a common point of origin; generating an image of the object 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); where: the set of arrival times (T) is organized into different subsets, each subset of arrival times (Ta, Tb, Tc) corresponding to a respective sub-array (10a, 10b, 10c) of the transducers (10) spanning a respective sub-area (20a, 20b, 20c) of the flexible sheet (20) at a respective surface coordinate (Sx, Sy) along the sheet surface (20s); determining respective wave directions (θa, θb, θc) of the respective portions of the acoustic waves (Wa, Wb, Wc) arriving at the respective sub-areas (20a, 20b, 20c) originating from the common point of origin based on the respective subsets of arrival times (Ta, Tb, Tc) of each sub-array (10a, 10b, 10c) of the transducer (10); determining a modeled shape (20m) of the sheet surface (20s) based at least in part on the respective wave directions (θa, θb, θc) as a function of the surface coordinates (Sx, Sy) of each sub-area (20a, 20b, 20c); determining the spatial coordinates (X, Y, Z) of the transducer (10) based on the modeled shape (20m) of the seat surface (20s); Non-transitory computer-readable medium.

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