Acoustic radiation force calculation method and system of concave ellipsoid weak focusing transducer

Abstract

The invention relates to an acoustic radiation force calculation method and system for a concave ellipsoid weak focusing transducer. The method comprises the following steps: establishing an acoustic radiation force test scene for testing the acoustic radiation force of the transducer; calculating the unit area of the transducer based on the data of the acoustic radiation force test scene; and calculating the acoustic radiation force of the transducer based on the unit projection area. The system is used for realizing the method. Compared with the prior art, the acoustic radiation force calculation method for the concave ellipsoid weak focusing transducer provides more powerful support for analysis of acoustic radiation force characteristics and performance of the concave ellipsoid weak focusing transducer.

Description

Technical Field

[0001] The present invention relates to the field of acoustics, and in particular to a method and system for calculating the acoustic radiation force of a concave ellipsoidal weakly focused transducer. Background Art

[0002] An ultrasonic transducer is a device that can convert electrical energy into ultrasonic energy and vice versa. In a specific application scenario, the ultrasonic waves emitted by the transducer will exert a force on an object, namely, the acoustic radiation force. In the biomedical field, the acoustic radiation force of a focused transducer is used for ultrasonic imaging, ultrasonic therapy, etc. For example, high-intensity focused ultrasound (HIFU) therapy technology uses the high-intensity sound waves generated by a focused transducer to focus on the diseased tissue, and denatures the diseased tissue through biological effects such as thermal effect, mechanical effect, and cavitation effect to achieve the purpose of treatment. During the treatment process, precise control of the acoustic radiation force is the key to ensuring the therapeutic effect and safety. With the continuous development of materials science, electronic technology, etc., the performance of ultrasonic transducers has been continuously improved, enabling focused transducers to generate focused sound waves more efficiently. For example, the performance of piezoelectric ceramic materials has been continuously improved, enabling transducers to operate at higher frequencies and have higher energy conversion efficiency; new transducer structure designs, such as the concave shape design of focused ultrasonic piezoelectric ceramics, can better focus ultrasound into a thin beam and increase the sound intensity at the focus. The transducer is the core component of therapeutic ultrasound equipment, and the measurement of the sound power radiated by the focused transducer is very important for the safety and effectiveness of treatment. The acoustic radiation force method is currently the most widely used sound power measurement method recognized by the International Electrotechnical Commission (IEC). Among them, the calculation of the acoustic radiation force has a great influence on the accuracy of measuring the ultrasonic power emitted by the focused transducer. Most ultrasonic transducers are spherical focusing transducers, cylindrical focusing transducers and annular concave transducers. Therefore, the calculated acoustic radiation force is also mostly calculated for the above three corresponding acoustic radiation forces. The above three transducers are characterized by point focusing or line focusing, and the concave ellipsoid shape enables the transducer to concentrate the ultrasonic energy in a specific elliptical focal area as a weak focusing form, thereby increasing the energy density. Compared with the first three, the transducer has a smaller focusing angle, a relatively low focusing degree, and a larger focusing area. Therefore, the calculation form of the acoustic radiation force of the above three transducers does not use the calculation of the concave ellipsoid shape transducer.

[0003] Therefore, it is a technical problem to be solved to provide a method for calculating the acoustic radiation force of a transducer that is applicable to a concave ellipsoidal shape. Summary of the invention

[0004] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and to provide a method and system for calculating the acoustic radiation force of a concave ellipsoidal weakly focused transducer, which is specifically used for concave ellipsoidal transducers and integrates the angular span in two directions of the ellipsoidal surface, which is more accurate than approximate calculation using spherical integral.

[0005] The purpose of the present invention can be achieved by the following technical solutions:

[0006] According to a first aspect of the present invention, a method for calculating the acoustic radiation force of a concave ellipsoidal weakly focused transducer is provided, the method comprising:

[0007] Build an acoustic radiation force test scene: place a convex conical reflective target at any position between the transducer and the focus, and align the central axis of the convex conical reflective target with the central axis of the transducer surface, take the focus of the transducer as the origin of the coordinate system, take the central axis as the Z axis of the coordinate system, and randomly select a point on the convex conical reflective target as the target point;

[0008] Calculation of transducer unit area: obtaining angle parameters of the acoustic ray incident on the target point, and calculating the transducer unit projection area based on the angle parameters, wherein the angle parameters include the angle of the transducer's half-angle aperture in the XZ plane of the coordinate system, the angle of the half-angle aperture in the YZ plane of the coordinate system, the incident angle of the acoustic ray and the normal line of the convex conical reflective target surface, and the angle of the acoustic ray and the Z axis;

[0009] Acoustic radiation force calculation: The acoustic radiation force of the transducer is calculated based on the unit projection area.

[0010] As a preferred technical solution, the calculation method of the unit projected area is:

[0011]

[0012] Wherein, a represents the length of the long semi-axis of the concave ellipsoid of the transducer, b represents the length of the short semi-axis of the concave ellipsoid of the transducer; c represents the speed of sound; represents a function related to the angle of the half-angle aperture of the transducer in the XZ plane of the coordinate system and the angle of the half-angle aperture in the YZ plane of the coordinate system, and

[0013] As a preferred technical solution, the method for obtaining the acoustic radiation force is:

[0014] Acquire sound data of the sound wave ray entering the target point, wherein the sound data includes sound intensity and sound speed;

[0015] The acoustic radiation force within a unit area is calculated based on the sound intensity and sound velocity, and its expression is:

[0016]

[0017] Where F represents the acoustic radiation force; c represents the speed of sound; I represents the sound intensity; γ represents the angle between the sound wave ray and the Z axis; r f represents the pressure reflection coefficient at the interface between water and target, and 0≤rf ≤1; ζ represents the inclination angle of the convex conical reflective target surface as ζ=δ+γ, δ represents the incident angle of the acoustic ray and the normal line of the convex conical reflective target surface, and γ represents the angle between the acoustic ray and the Z axis;

[0018] Obtain the relationship between the unit area and the unit projection area, and convert the acoustic radiation force calculation within the unit area into the acoustic radiation force calculation within the unit projection;

[0019] Based on the unit projected area, the acoustic radiation force of the transducer is calculated by integration.

[0020] As a preferred technical solution, the relationship between the unit area and the unit projection area is: IdS′=I0dS, where I represents the sound intensity at any point on the concave ellipsoid of the transducer; dS′ represents the unit area; I0 represents the sound intensity at the projection; and dS represents the unit projection area.

[0021] As a preferred technical solution, the method for integrally calculating the acoustic radiation force of the transducer is:

[0022]

[0023] Where I0 represents the sound intensity at the projection point; c represents the sound velocity; α represents the angle of the half-angle aperture of the transducer in the XZ plane of the coordinate system; β represents the angle of the half-angle aperture in the YZ plane of the coordinate system; γ represents the angle between the sound wave ray and the Z axis; the pressure reflection coefficient at the interface between water and the target, and 0≤r f ≤1; ζ represents the inclination angle of the convex conical reflective target surface as ζ=δ+γ, δ represents the incident angle of the acoustic ray and the normal line of the convex conical reflective target surface, γ represents the angle between the acoustic ray and the Z axis; a represents the long semi-axis length of the concave ellipsoid of the transducer, b represents the short semi-axis length of the concave ellipsoid of the transducer; c represents the speed of sound; represents a function related to the angle of the half-angle aperture of the transducer in the XZ plane of the coordinate system and the angle of the half-angle aperture in the YZ plane of the coordinate system, and

[0024] According to a second aspect of the present invention, there is provided an acoustic radiation force calculation system for a concave ellipsoidal weakly focused transducer, the system comprising an acoustic radiation force testing device: used to perform an acoustic radiation force test in an acoustic radiation force testing scenario, wherein the acoustic radiation force testing scenario is to place a convex conical reflection target at any position between the transducer and the focus, and the central axis of the convex conical reflection target is aligned with the central axis of the transducer surface, the focus of the transducer is used as the origin of the coordinate system, the central axis is used as the Z axis of the coordinate system, and a point on the convex conical reflection target is randomly selected as the target point;

[0025] Data acquisition device: used to collect the sound data and angle parameters generated by the sound radiation force test device when performing the sound radiation force test;

[0026] Acoustic radiation force calculation module: Based on the acoustic data and angle parameters collected by the data acquisition module, the steps of the above method are executed to obtain the acoustic radiation force of the transducer.

[0027] Compared with the prior art, the present invention proposes a method for calculating the acoustic radiation force specifically for a concave ellipsoidal weakly focusing transducer. The area is integrated from the opening angles in two directions of the concave ellipsoidal surface of the transducer. Compared with the prior art which only integrates the area through one opening angle, the method proposed in the present invention eliminates the need to use spherical surface integrals for approximate calculations when calculating the acoustic radiation force of a concave ellipsoidal weakly focusing transducer, thereby increasing the accuracy of the area calculation of the concave ellipsoidal surface, thereby improving the accuracy of the calculation of the acoustic radiation force, and providing more powerful support for analyzing the characteristics and performance of the acoustic radiation force of a concave ellipsoidal weakly focusing transducer. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 is a flow chart of the method of the present invention;

[0029] Figure 2 It is a schematic diagram of the focused sound field of the radiation surface of the concave ellipsoidal transducer of the present invention;

[0030] Figure 3 It is a schematic diagram of the acoustic radiation force test scenario of the present invention. DETAILED DESCRIPTION

[0031] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0032] Unless otherwise defined, the technical terms or scientific terms involved in this application should be understood by people with ordinary skills in the technical field to which this application belongs. The words "one", "a", "a", "the" and the like involved in this application do not indicate a quantitative limitation, and may represent the singular or plural. The terms "include", "comprise", "have" and any of their variations involved in this application are intended to cover non-exclusive inclusions; for example, a process, method, system, product or device that includes a series of steps or modules (units) is not limited to the listed steps or units, but may also include steps or units that are not listed, or may also include other steps or units inherent to these processes, methods, products or devices. The words "connect", "connected", "coupled" and the like involved in this application are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. The "multiple" involved in this application refers to two or more. "And / or" describes the association relationship of associated objects, indicating that there may be three relationships, for example, "A and / or B" can represent: A exists alone, A and B exist at the same time, and B exists alone. The character " / " generally indicates that the objects before and after are in an "or" relationship. The terms "first", "second", "third", etc. involved in this application are only used to distinguish similar objects and do not represent a specific ordering of the objects.

[0033] The present invention uses geometric acoustic theory and Langiven radiation pressure principle to propose a method for calculating the acoustic radiation force of a concave ellipsoidal weakly focused transducer. The method provides a more accurate and efficient calculation method for its research and application by calculating the acoustic radiation force of a concave ellipsoidal weakly focused transducer. The method flow is as follows: Figure 1 shown.

[0034] In this embodiment, it is assumed that there is a concave ellipsoidal focused ultrasonic transducer that satisfies geometric acoustics, the sound intensity on its surface is a constant I0, the focal spot diameter is zero, the sound energy is not lost during propagation, and the sound energy flow is the same within the same solid angle passing through the focus, as shown in the schematic diagram. Figure 2 As shown, in order to facilitate the acoustic radiation force test, the following Figure 3 The coordinate system shown serves as the acoustic radiation force test scenario.

[0035] exist Figure 2In the figure, the radius of curvature or geometric focal length of the transducer is set to R, and its ellipsoid semi-aperture angle is α in the XZ plane and β in the YZ plane, wherein a unit area is dS′, and the unit area is perpendicular to the sound wave at point Q and the sound intensity is set to I. The unit area is extended from the focus O to the surface of the sound source, and a unit projection area dS can be generated on the radiation surface of the transducer, and the sound intensity at the unit projection is I0. When diffraction is ignored (i.e., in the geometric limit or high-frequency limit), the relationship between the unit area and the unit projection area is: IdS′=I0dS, wherein I represents the sound intensity at any point on the concave ellipsoidal surface of the transducer; dS′ represents the unit area; I0 represents the sound intensity at the projection; dS represents the unit projection area.

[0036] exist Figure 3 In the acoustic radiation force test scenario, a convex conical reflective target is placed at any position between the transducer and the focus, and the convex conical reflective target is large enough to intersect all the acoustic energy. The central axis of the convex conical reflective target is aligned with the central axis of the transducer surface, the focus of the transducer is used as the origin of the coordinate system, the central axis is used as the Z axis of the coordinate system, and a point on the convex conical reflective target is randomly selected as the target point.

[0037] Now let a sound wave ray be shot into the target point P with sound intensity I, then the sound wave ray is equivalent to an extremely thin plane wave sound beam, and the normal line at the target point on the convex conical reflection target is represented by n, the incident angle between the sound wave ray and the normal line is represented by δ, and the angle between the sound wave ray and the Z axis is represented by γ, then the inclination angle of the surface of the convex conical reflection target is ζ=δ+γ.

[0038] According to the Langiven radiation pressure principle, the energy density of the plane wave pulse flow (i.e., radiation pressure) is expressed as: P r =I / c, and at the target point P, the axial component of the incident acoustic pulse energy density is Icosγ / c, and the axial component of the reflected acoustic pulse energy density is Among them, r f Indicates the pressure reflection coefficient at the interface between water and target 0≤r f ≤1, then at point P, the radiation pressure can be expressed as:

[0039]

[0040] Among them, P r represents the sound radiation force; I represents the sound intensity; c represents the sound speed.

[0041] Because the fully focused sound wave ray is composed of many small sound wave rays, then at the incident point P, its sound wave ray can be regarded as composed of multiple small sound wave rays, and the area of ​​each small sound wave ray on the transducer surface is the unit area dS, then the sound radiation force caused by the small sound wave ray in the unit area is:

[0042]

[0043] Since, in the unit area and unit projected area, IdS′=I0dS, its acoustic radiation force can also be:

[0044]

[0045] Where F represents the acoustic radiation force; c represents the speed of sound; I and I0 both represent the sound intensity; γ represents the angle between the sound wave ray and the Z axis; r f represents the pressure reflection coefficient at the interface between water and target, and 0≤r f ≤1; ζ represents the inclination angle of the convex conical reflective target surface is ζ=δ+γ, δ represents the incident angle of the acoustic ray and the normal line of the convex conical reflective target surface, and γ represents the angle between the acoustic ray and the Z axis.

[0046] It can be seen from the above formula that if the acoustic radiation force F is to be solved, dS′ or dS can be solved. Because the light intensity of the acoustic wave ray is a known constant under the projection condition, therefore, in this embodiment, the calculation unit projection area, i.e., dS, is selected. In detail, its expression is:

[0047]

[0048] Wherein, a represents the length of the long semi-axis of the concave ellipsoid of the transducer, b represents the length of the short semi-axis of the concave ellipsoid of the transducer; c represents the speed of sound; represents a function related to the angle of the half-angle aperture of the transducer in the XZ plane of the coordinate system and the angle of the half-angle aperture in the YZ plane of the coordinate system, and

[0049] Substitute the calculated dS into By calculating in, the calculation expression of the acoustic radiation force of the transducer can be obtained as follows:

[0050]

[0051] Where I0 represents the sound intensity at the projection point; c represents the sound velocity; α represents the angle of the half-angle aperture of the transducer in the XZ plane of the coordinate system; β represents the angle of the half-angle aperture in the YZ plane of the coordinate system; γ represents the angle between the sound wave ray and the Z axis; the pressure reflection coefficient at the interface between water and the target, and 0≤r f≤1; ζ represents the inclination angle of the convex conical reflective target surface as ζ=δ+γ, δ represents the incident angle of the acoustic ray and the normal line of the convex conical reflective target surface, γ represents the angle between the acoustic ray and the Z axis; a represents the long semi-axis length of the concave ellipsoid of the transducer, b represents the short semi-axis length of the concave ellipsoid of the transducer; c represents the speed of sound; represents a function related to the angle of the half-angle aperture of the transducer in the XZ plane of the coordinate system and the angle of the half-angle aperture in the YZ plane of the coordinate system, and

[0052] The above formula can be used to calculate the acoustic radiation force of the concave ellipsoidal transducer.

[0053] The above is an introduction to the method embodiment. The following is a further explanation of the scheme of the present invention through a system embodiment. In this embodiment, a system for calculating the acoustic radiation force of a concave ellipsoidal weakly focused transducer is also provided, and the system includes:

[0054] Acoustic radiation force test device: used to perform acoustic radiation force test in the acoustic radiation force test scenario. In the acoustic radiation force test scenario, a convex conical reflective target is placed at any position between the transducer and the focus, and the central axis of the convex conical reflective target is aligned with the central axis of the transducer surface. The focus of the transducer is taken as the origin of the coordinate system, the central axis is taken as the Z axis of the coordinate system, and a point on the convex conical reflective target is randomly selected as the target point.

[0055] Data acquisition device: used to collect the sound data and angle parameters generated by the sound radiation force testing device when conducting the sound radiation force test.

[0056] Acoustic radiation force calculation module: Based on the acoustic data and angle parameters collected by the data acquisition module, the steps of the above method are executed to obtain the acoustic radiation force of the transducer.

[0057] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working process of the described module can refer to the corresponding process in the aforementioned method embodiment, and will not be repeated here.

[0058] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed by the present invention, and these modifications or replacements should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A method for calculating the acoustic radiation force of a concave ellipsoidal weakly focused transducer, characterized in that: The method includes: Build an acoustic radiation force test scene: place a convex conical reflective target at any position between the transducer and the focus, and align the central axis of the convex conical reflective target with the central axis of the transducer surface, take the focus of the transducer as the origin of the coordinate system, take the central axis as the Z axis of the coordinate system, and randomly select a point on the convex conical reflective target as the target point; Calculation of transducer unit area: obtaining angle parameters of the acoustic ray incident on the target point, and calculating the transducer unit projection area based on the angle parameters, wherein the angle parameters include the angle of the transducer's half-angle aperture in the XZ plane of the coordinate system, the angle of the half-angle aperture in the YZ plane of the coordinate system, the incident angle of the acoustic ray and the normal line of the convex conical reflective target surface, and the angle of the acoustic ray and the Z axis; Acoustic radiation force calculation: The acoustic radiation force of the transducer is calculated based on the unit projection area.

2. The method for calculating the acoustic radiation force of a concave ellipsoidal weakly focused transducer according to claim 1, characterized in that: The calculation method of the unit projected area is: Wherein, a represents the length of the long semi-axis of the concave ellipsoid of the transducer, b represents the length of the short semi-axis of the concave ellipsoid of the transducer; c represents the speed of sound; represents a function related to the angle of the half-angle aperture of the transducer in the XZ plane of the coordinate system and the angle of the half-angle aperture in the YZ plane of the coordinate system, and 3. The method for calculating the acoustic radiation force of a concave ellipsoidal weakly focused transducer according to claim 2, characterized in that: The method for obtaining the acoustic radiation force is: Acquire sound data of the sound wave ray entering the target point, wherein the sound data includes sound intensity and sound speed; The acoustic radiation force within a unit area is calculated based on the sound intensity and sound velocity, and its expression is: Where F represents the acoustic radiation force; c represents the speed of sound; I represents the sound intensity; γ represents the angle between the sound wave ray and the Z axis; the pressure reflection coefficient at the interface between water and the target, and 0≤r f ≤1; ζ represents the inclination angle of the convex conical reflective target surface as ζ=δ+γ, δ represents the incident angle of the acoustic ray and the normal line of the convex conical reflective target surface, and γ represents the angle between the acoustic ray and the Z axis; Obtain the relationship between the unit area and the unit projection area, and convert the acoustic radiation force calculation within the unit area into the acoustic radiation force calculation within the unit projection; Based on the unit projected area, the acoustic radiation force of the transducer is calculated by integration.

4. The method for calculating the acoustic radiation force of a concave ellipsoidal weakly focused transducer according to claim 3, characterized in that: The relationship between the unit area and the unit projection area is: IdS′=I0dS, where I represents the sound intensity at any point on the concave ellipsoid of the transducer; dS′ represents the unit area; I0 represents the sound intensity at the projection; and dS represents the unit projection area.

5. The method for calculating the acoustic radiation force of a concave ellipsoidal weakly focused transducer according to claim 3, characterized in that: The method for integrally calculating the acoustic radiation force of the transducer is: Where I0 represents the sound intensity at the projection point; c represents the speed of sound; α represents the angle of the half-angle aperture of the transducer in the XZ plane of the coordinate system; β represents the angle of the half-angle aperture in the YZ plane of the coordinate system; γ represents the angle between the sound wave ray and the Z axis; r f represents the pressure reflection coefficient at the interface between water and target, and 0≤r f ≤1; ζ represents the inclination angle of the convex conical reflective target surface as ζ=δ+γ, δ represents the incident angle of the acoustic ray and the normal line of the convex conical reflective target surface, γ represents the angle between the acoustic ray and the Z axis; a represents the long semi-axis length of the concave ellipsoid of the transducer, b represents the short semi-axis length of the concave ellipsoid of the transducer; c represents the speed of sound; represents a function related to the angle of the half-angle aperture of the transducer in the XZ plane of the coordinate system and the angle of the half-angle aperture in the YZ plane of the coordinate system, and 6. A system for calculating the acoustic radiation force of a concave ellipsoidal weakly focused transducer, characterized in that: The system includes an acoustic radiation force testing device: used for performing an acoustic radiation force test in an acoustic radiation force testing scenario, wherein the acoustic radiation force testing scenario is to place a convex conical reflective target at any position between a transducer and a focus, and the central axis of the convex conical reflective target is aligned with the central axis of the transducer surface, the focus of the transducer is used as the origin of the coordinate system, the central axis is used as the Z axis of the coordinate system, and a point on the convex conical reflective target is randomly selected as a target point; Data acquisition device: used to collect the sound data and angle parameters generated by the sound radiation force test device when performing the sound radiation force test; Acoustic radiation force calculation module: Based on the acoustic data and angle parameters collected by the data acquisition module, the following steps are performed to calculate the acoustic radiation force of the transducer: Calculation of transducer unit area: obtaining angle parameters of the acoustic ray incident on the target point, and calculating the transducer unit projection area based on the angle parameters, wherein the angle parameters include the angle of the transducer's half-angle aperture in the XZ plane of the coordinate system, the angle of the half-angle aperture in the YZ plane of the coordinate system, the incident angle of the acoustic ray and the normal line of the convex conical reflective target surface, and the angle of the acoustic ray and the Z axis; Acoustic radiation force calculation: The acoustic radiation force of the transducer is calculated based on the unit projection area.

7. The acoustic radiation force calculation system of a concave ellipsoidal weakly focused transducer according to claim 6, characterized in that: The calculation method of the unit projected area is: Wherein, a represents the length of the long semi-axis of the concave ellipsoid of the transducer, b represents the length of the short semi-axis of the concave ellipsoid of the transducer; c represents the speed of sound; represents a function related to the angle of the half-angle aperture of the transducer in the XZ plane of the coordinate system and the angle of the half-angle aperture in the YZ plane of the coordinate system, and 8. The acoustic radiation force calculation system of a concave ellipsoidal weakly focused transducer according to claim 7, characterized in that: The method for obtaining the acoustic radiation force is: Acquire sound data of the sound wave ray entering the target point, wherein the sound data includes sound intensity and sound speed; The acoustic radiation force within a unit area is calculated based on the sound intensity and sound velocity, and its expression is: Where F represents the acoustic radiation force; c represents the speed of sound; I represents the sound intensity; γ represents the angle between the sound wave ray and the Z axis; r f represents the pressure reflection coefficient at the interface between water and target, and 0≤r f ≤1; ζ represents the inclination angle of the convex conical reflective target surface as ζ=δ+γ, δ represents the incident angle of the acoustic ray and the normal line of the convex conical reflective target surface, and γ represents the angle between the acoustic ray and the Z axis; Obtain the relationship between the unit area and the unit projection area, and convert the acoustic radiation force calculation within the unit area into the acoustic radiation force calculation within the unit projection; Based on the unit projected area, the acoustic radiation force of the transducer is calculated by integration.

9. The acoustic radiation force calculation system of a concave ellipsoidal weakly focused transducer according to claim 8, characterized in that: The relationship between the unit area and the unit projection area is: IdS′=I0dS, where I represents the sound intensity at any point on the concave ellipsoid of the transducer; dS′ represents the unit area; I0 represents the sound intensity at the projection; and dS represents the unit projection area.

10. The acoustic radiation force calculation system of a concave ellipsoidal weakly focused transducer according to claim 8, characterized in that: The method for integrally calculating the acoustic radiation force of the transducer is: Where I0 represents the sound intensity at the projection point; c represents the speed of sound; α represents the angle of the half-angle aperture of the transducer in the XZ plane of the coordinate system; β represents the angle of the half-angle aperture in the YZ plane of the coordinate system; γ represents the angle between the sound wave ray and the Z axis; r f represents the pressure reflection coefficient at the interface between water and target, and 0≤r f ≤1; ζ represents the inclination angle of the convex conical reflective target surface as ζ=δ+γ, δ represents the incident angle of the acoustic ray and the normal line of the convex conical reflective target surface, γ represents the angle between the acoustic ray and the Z axis; a represents the long semi-axis length of the concave ellipsoid of the transducer, b represents the short semi-axis length of the concave ellipsoid of the transducer; c represents the speed of sound; represents a function related to the angle of the half-angle aperture of the transducer in the XZ plane of the coordinate system and the angle of the half-angle aperture in the YZ plane of the coordinate system, and

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