Ultrasonic hollow plane array focusing method based on pseudo-inverse matrix solution

Abstract

The invention relates to an ultrasonic hollow plane array focusing method based on pseudo-inverse matrix solution, and belongs to the technical field of man-machine interaction and virtual reality. Based on a sound pressure radiation model of a circular piston, sound pressure distribution characteristics generated by a single emitter in a sound field are established, a mathematical relationship between the total sound field sound pressure of the whole array and excitation amplitudes of all the emitters is derived on the basis, and an ideal sound field distribution target is set, so that the sound field of the array is obtained. And inversely solving the optimal amplitude configuration of each transmitter by adopting a pseudo-inverse matrix algorithm so as to control the sound field. The method is used for solving the problems that focusing energy is dispersed and the focus shape tends to be oval due to the fact that the side lobe is too large during single-point focusing of the hollow plane ultrasonic array, the side lobe level is remarkably restrained, the focus energy concentration ratio and shape regularity are improved, and the focusing performance of the hollow plane array is effectively improved.

Description

Technical Field

[0001] This invention belongs to the fields of human-computer interaction and virtual reality technology, and in particular relates to a focusing method for ultrasonic hollow planar arrays based on pseudo-inverse matrix solving. Background Technology

[0002] With the rapid development of technology, digital interaction has penetrated every aspect of our lives. However, existing interaction methods mainly focus on vision and hearing, often neglecting another important human sensory system—touch. Haptic feedback technology aims to fill this gap, providing realistic tactile experiences through electronic devices and bringing users a more immersive interactive experience. Aerial displays and 3D display technologies from science fiction movies are gradually becoming a reality. The development of 3D imaging and aerial levitation technology allows people to see images or interfaces suspended in the air. The addition of depth cameras and markerless gesture tracking technology allows people to manipulate projected images or interfaces with their bare hands. If haptic feedback technology is added, it can provide tactile feedback when people touch or manipulate aerial images, improving the usability of the interactive system and enhancing the user experience. Furthermore, the application of haptic feedback technology in augmented reality and virtual reality will enhance the user's sense of immersion and realism, giving users a feeling of being actually there.

[0003] Haptic feedback technology has demonstrated immense potential in numerous fields. For instance, in virtual reality (VR) and augmented reality (AR), by providing realistic haptic feedback, users can gain a more immersive experience in virtual environments, enhancing their sense of presence. In manufacturing, haptic feedback technology can help workers complete tasks more accurately, improving productivity and quality. In human-computer interaction, haptic feedback technology can improve the usability and practicality of user interface design, making interactions more natural and intuitive. In medical rehabilitation, haptic feedback technology holds great potential in rehabilitation therapy, assisting patients with muscle training, pain management, and prosthetic control. It can also improve the usability of electronic devices; applying haptic feedback technology to mobile devices such as smartphones and tablets can improve input efficiency and accuracy while providing a unique user experience. Furthermore, it can be applied to accessibility design, helping visually or hearing impaired individuals better use electronic devices and improving their quality of life. In conclusion, research on haptic feedback technology has significant scientific and practical value, bringing many innovative and practical applications to our lives, improving quality of life and social development.

[0004] Haptic feedback technology can be mainly divided into two types: contact haptic feedback technology and non-contact haptic feedback technology. Contact haptic feedback technology requires the device to come into contact with the skin to generate tactile sensation. Moreover, devices that come into contact with the human body may hinder people's free movement in three-dimensional space and may also cause discomfort. Therefore, researchers have gradually focused their attention on non-contact haptic feedback technology. In the research of non-contact haptic feedback, aerial haptic feedback based on ultrasonic radiation pressure is a research hotspot both domestically and internationally.

[0005] Currently, aerial haptic feedback technology based on ultrasonic radiation pressure has matured in both principle and implementation, providing a novel tactile experience for fields such as virtual reality and human-computer interaction without the need for wearing devices. However, to achieve multimodal fusion interaction integrating vision, hearing, and touch, and to build a complete "visual, auditory, and tactile" integrated system, it is often necessary to arrange an ultrasonic transmitter array around the display to achieve compact hardware integration and functional integration.

[0006] While this integration method facilitates device miniaturization and overall integration, it also introduces new problems: because the central area of ​​the array is occupied by the display, the transmitters are distributed in a hollow planar shape, making uniform arrangement within the plane impossible. More importantly, when focusing on a target point in space, the transmitter distribution around the focal point exhibits significant asymmetry. This asymmetry disrupts the balance between constructive and destructive interference of sound waves superimposed at the focal point, resulting in excessively high sidelobes of sound energy around the main focal point. The direct consequence is a significant reduction in sound pressure in the focusing core area and severe energy dispersion, making it difficult to achieve high-intensity, high-precision point-to-point tactile feedback, greatly limiting the application effectiveness of this integrated solution in practical scenarios. Summary of the Invention

[0007] This invention provides a focusing method for ultrasonic hollow planar arrays based on pseudo-inverse matrix solving. This addresses the problem that existing ultrasonic hollow planar arrays, when focusing at a single point, suffer from an elliptical focusing area due to excessively large side lobes, making it difficult to achieve ideal circular focusing. This problem significantly reduces the concentration of ultrasonic energy at the focal point in practical applications, affecting focusing accuracy and control effect. The purpose of this invention is to effectively suppress side lobe levels by optimizing the array excitation signal, thereby significantly improving the symmetry of the focusing area and the focusing effect.

[0008] The technical solution adopted by this invention includes the following steps:

[0009] (1) Determine the shape of the hollow planar array and the number of transmitters;

[0010] (2) Based on the sound pressure radiation model of a circular piston, establish the relationship between a single transmitter and each point in its sound field, and derive the relationship between the total sound pressure of the array and the amplitude of each transmitter.

[0011] (3) Solve for the amplitude of each transmitter based on the desired sound pressure distribution of the sound field.

[0012] The hollow planar array in step (1) of the present invention refers to an array configuration in which the transmitting units are not uniformly distributed throughout the entire array plane, but are concentrated on the outer edge of the array, and the central region is empty.

[0013] The hollow planar array form described in this invention includes:

[0014] Annular hollow planar array: All transmitters are arranged along one or more concentric circular paths to form a ring structure;

[0015] Rectangular hollow planar array: The transmitters are arranged along a rectangular frame. Its shape can be regarded as the frame-like structure remaining after a large rectangular solid array is removed from the center of a small rectangular array.

[0016] Based on the selected hollow planar array geometry and its specific dimensional parameters, determine the total number N of transmitters contained in the array.

[0017] In step (2) of this invention, an accurate physical sound field model is established based on the circular piston sound pressure radiation model, and then the quantitative mathematical relationship between the total sound field pressure of the array and the amplitude of each transmitter is derived as follows:

[0018]

[0019] in It is the first in space The sound pressure amplitude at each point It is the first The amplitude of each transmitter It is the forward operator between the amplitude of the m-th spatial point and the amplitude of the n-th transmitter.

[0020] The specific process is as follows:

[0021] The first step is to establish an accurate mathematical model between the amplitude of the array transmitter and the spatial sound field distribution. In this process, it is necessary to clearly define the hollow planar array structure used, and then establish the mathematical relationship between the amplitude of the array transmitter and the total sound pressure of the sound field:

[0022] The instantaneous sound pressure at each point in the sound field of a single transmitter under delayed phase control is :

[0023]

[0024] in, It is the density of air. The amplitude of the transmitter, The radius of the transmitter, and The polar coordinates of the focus relative to the transmitter. It is a first-order Bessel function. For wave number, For the delay time of the transmitter, The imaginary unit, Angular frequency;

[0025] In the above formula, only two quantities are related to the characteristics of the sound source: the amplitude of the transmitter. and the transmitter delay time To facilitate description and more intuitive observation of the relationship between sound pressure and sound source, the above formula is simplified as follows:

[0026]

[0027] The delay time of each transmitter Calculate it using the following procedure:

[0028] Calculate the time required for the ultrasonic waves emitted by the transmitters on the ultrasonic transmitter array to reach the focal point. :

[0029]

[0030] Among them, (x n ,y n ,z n (x, y, z) represents the coordinates of the nth transmitter in the ultrasonic transmitter array, and (x, y, z) represents the coordinates of the focal point. It is the speed of sound in the air, and the arrival time of the sound is taken as the speed of sound. maximum value :

[0031]

[0032] Calculate the time delay of the drive signal of each transmitter in the ultrasonic transmitter array. :

[0033]

[0034] The above calculation The expression can be simplified as follows:

[0035]

[0036] The final abbreviation is:

[0037]

[0038] in, This is the forward operator between the instantaneous sound pressure amplitude and the transmitter amplitude;

[0039] Similarly, the sound pressure amplitude of the total sound field of the array can be obtained by linear superposition:

[0040]

[0041] in, This is the forward operator between the sound pressure amplitude of the total sound field of the array and the amplitude of the nth transmitter. The amplitude of the nth transmitter;

[0042]

[0043] When the sound pressure amplitudes at M points in space are specified or known, then:

[0044]

[0045] The number of M's here is determined based on the main lobe and side lobe in the desired sound field distribution. A rectangular hollow planar array can be used as the desired sound field by a similar square array, and a circular hollow planar array can be used as the desired sound field by a circular array.

[0046] Swap the left and right sides of the equation and expand the matrix as follows:

[0047]

[0048] In short:

[0049]

[0050] in It is the first in space The sound pressure amplitude at each point It is the first The amplitude of each transmitter It is the forward operator between the amplitude of the m-th spatial point and the amplitude of the n-th transmitter. It is a forward operator, a The matrix, yes The amplitude of a transmitter is a The vector, For the desired sound field distribution, it is The vector.

[0051] The process of solving the amplitude of each transmitter in step (3) of the present invention is as follows:

[0052] Based on the formula relating the total sound pressure level to the amplitude of each transmitter in step (2), the objective optimization function is set as follows:

[0053]

[0054] The goal is to solve for the amplitude of the array transmitter. So that the generated total sound field with by The specified desired sound field distribution should be as close as possible;

[0055] To address the aforementioned optimization problem, utilize Find its solution from the right inverse matrix:

[0056]

[0057] In the formula yes The conjugate transpose of .

[0058] calculate elements in The formula:

[0059]

[0060] It is the forward operator between the amplitude of the m-th spatial point and the amplitude of the n-th transmitter.

[0061] The desired sound field distribution is set. The method is as follows:

[0062] For a ring-shaped hollow planar array, the inner radius of its ring structure is used as the radius of the circle to construct a solid circular array as the desired sound field;

[0063] For a rectangular hollow planar array, the length of the shorter side of the rectangle is taken as the side length of the square, and a solid square array is constructed as the desired sound field. The number of emitters in this array is... ;

[0064] To reflect the sound pressure amplitude at the desired sound field focal point and radius Furthermore, considering that a rectangular array will produce side lobes in four directions (positive and negative X-axis and positive and negative Y-axis), the sound pressure amplitude is selected at five points: the focal center and the edges of the focal point in the positive and negative X and Y directions. and radius It can be calculated using the following formula:

[0065]

[0066]

[0067]

[0068] in, It refers to the sound pressure level of the i-th transmitter on the solid array that forms the desired sound field distribution. Let λ be the sound pressure amplitude of the desired sound field distribution, h be the distance from the focal point to the array, λ be the wavelength of the ultrasonic wave emitted by the transmitter, and d be the diameter of the transmitter.

[0069] If the coordinates of the focus are (x, y, z), then the positions of these five points are (x, y, z), (x+r, y, z), (xr, y, z), (x, y+r, z), and (x, yr, z), respectively, and the magnitudes of these five points are respectively ( , , (i.e., the desired sound field distribution) for( , , );

[0070] Finally, based on the aforementioned sound field distribution Overall sound field Calculate the amplitude u of N transmitters.

[0071] The advantages of this invention are as follows: By establishing a mathematical relationship between the total sound pressure of the array and the excitation amplitude of each transmitter, a complete sound field model is constructed; furthermore, an innovative reverse design approach is adopted, using a pseudo-inverse matrix algorithm to solve for the optimal amplitude configuration of each transmitter by setting an ideal sound field distribution target, thereby achieving control of the sound field. Sound field simulation observations and comparisons demonstrate that this method effectively suppresses asymmetric sidelobes, significantly optimizes the focusing area from an elliptical shape to a near-circular shape, and simultaneously improves the focus energy concentration and sound field control accuracy. This provides reliable technical support for the application of hollow arrays in fields such as ultrasonic haptic feedback, and can be applied to fields such as human-computer interaction and virtual reality. Attached Figure Description

[0072] Figure 1 This is a schematic diagram of the hollow planar array of the present invention;

[0073] Figure 2 This is the desired sound field distribution diagram of the present invention;

[0074] Figure 3 This is a schematic diagram of the selected location in this invention;

[0075] Figure 4 This is the initial amplitude distribution u0 diagram of this invention;

[0076] Figure 5 This is a distribution diagram of the sound pressure in the sound field under the initial amplitude u0 control of this invention;

[0077] Figure 6 The amplitude distribution u obtained by this invention H picture;

[0078] Figure 7 This invention u H Distribution diagram of sound pressure in the sound field under control;

[0079] Figure 8 This is a diagram showing the focal size of the sound field under the initial amplitude u0 control of this invention;

[0080] Figure 9 The amplitude u after solving this invention H Control the focal size diagram of the lower sound field;

[0081] Figure 10 This is a schematic diagram of the inverse matrix algorithm of the present invention. Detailed Implementation

[0082] The technical solution adopted by this invention includes the following steps:

[0083] (1) Determine the shape of the hollow planar array and the number of transmitters;

[0084] The hollow planar array refers to an array configuration where the transmitting units are not uniformly distributed across the entire array plane, but are concentrated at the outer edge of the array, with the central region being empty; the hollow planar array forms include:

[0085] Annular hollow planar array: All transmitters are arranged along one or more concentric circular paths to form a ring structure;

[0086] Rectangular hollow planar array: The transmitters are arranged along a rectangular frame. Its shape can be regarded as the frame-like structure remaining after a large rectangular solid array is removed from the central part of a small rectangular array.

[0087] Based on the selected hollow planar array geometry and its specific dimensional parameters, determine the total number N of transmitters contained in the array.

[0088] The following explanation will be based on a square hollow planar array as an example:

[0089] First, determine the geometric structure and dimensional parameters of the hollow planar array: as shown in the attached figure. Figure 1 As shown: The hollow planar array used in this example consists of a rectangular array with an outer contour dimension of 16x24. An 8x16 rectangular sub-array is removed from its central region, thus forming a rectangular hollow planar structure. This array contains a total of 256 ultrasonic transmitters, evenly distributed on the rectangular hollow planar array. (See attached image) Figure 4 and 5The image shows the sound pressure distribution of the array under its initial amplitude distribution and control before the optimization algorithm was applied. It is evident from the sound pressure distribution diagram that the side amplitude in the horizontal direction (x-axis) is significantly higher than that in the vertical direction (y-axis), resulting in an elliptical focusing area rather than an ideal circular focus point. This reflects the adverse effect of side lobe asymmetry on the focusing shape.

[0090] Then, based on the above array structure, we enter the derivation stage of the core pseudo-inverse matrix solving algorithm.

[0091] (2) Based on the sound pressure radiation model of a circular piston, establish the relationship between a single transmitter and its points in the sound field, and derive the relationship between the total sound pressure of the array and the amplitude of each transmitter. See [reference needed]. Figure 2 ;

[0092] The core idea of ​​this invention lies in employing a reverse design approach: starting from the desired sound field distribution, it works backwards to find the optimal excitation amplitudes of each transmitter required to achieve that sound field. Specifically, firstly, an accurate physical sound field model is established based on a circular piston sound pressure radiation model, and then the quantitative mathematical relationship between the total sound pressure of the array and the amplitudes of each transmitter is derived. Based on this, by setting a reasonable desired sound pressure distribution, the corresponding relationship is constructed, and the pseudo-inverse matrix method is used to obtain the transmitter amplitude solution that best approximates the target sound field in the least squares sense.

[0093] To implement the above algorithm, the first step is to establish an accurate mathematical model between the amplitude of the array transmitter and the spatial sound field distribution. In this process, it is necessary to clearly define the hollow planar array structure used, and then establish the mathematical relationship between the amplitude of the array transmitter and the total sound pressure of the sound field:

[0094] The instantaneous sound pressure at each point in the sound field of a single transmitter under delayed phase control is :

[0095]

[0096] in, It is the density of air. The amplitude of the transmitter, The radius of the transmitter, and The polar coordinates of the focus relative to the transmitter. It is a first-order Bessel function. For wave number, For the delay time of the transmitter, The imaginary unit, Angular frequency;

[0097] In the above formula, only two quantities are related to the characteristics of the sound source: the amplitude of the transmitter. and the transmitter delay time To facilitate description and more intuitive observation of the relationship between sound pressure and sound source, the above formula is simplified as follows:

[0098]

[0099] The delay time of each transmitter Calculate it using the following procedure:

[0100] Calculate the time required for the ultrasonic waves emitted by the transmitters on the ultrasonic transmitter array to reach the focal point. :

[0101]

[0102] Among them, (x n ,y n ,z n (x, y, z) represents the coordinates of the nth transmitter in the ultrasonic transmitter array, and (x, y, z) represents the coordinates of the focal point. It is the speed of sound in the air, and the arrival time of the sound is taken as the speed of sound. maximum value :

[0103]

[0104] Calculate the time delay of the drive signal of each transmitter in the ultrasonic transmitter array. :

[0105]

[0106] The above calculation The expression can be simplified as follows:

[0107]

[0108] The final abbreviation is:

[0109]

[0110] in, This is the forward operator between the instantaneous sound pressure amplitude and the transmitter amplitude;

[0111] Similarly, the sound pressure amplitude of the total sound field of the array can be obtained by linear superposition:

[0112]

[0113] in, This is the forward operator between the sound pressure amplitude of the total sound field of the array and the amplitude of the nth transmitter. The amplitude of the nth transmitter;

[0114]

[0115] When the sound pressure amplitudes at M points in space are specified or known, then:

[0116]

[0117] The number of M's here is determined based on the main lobe and side lobe in the desired sound field distribution. A rectangular hollow planar array can be used as the desired sound field by a similar square array, and a circular hollow planar array can be used as the desired sound field by a circular array.

[0118] Swap the left and right sides of the equation and expand the matrix as follows:

[0119]

[0120] In short:

[0121]

[0122] in It is the first in space The sound pressure amplitude at each point It is the first The amplitude of each transmitter It is the forward operator between the amplitude of the m-th spatial point and the amplitude of the n-th transmitter. It is a forward operator, a The matrix, yes The amplitude of a transmitter is a The vector, For the desired sound field distribution, it is The vector.

[0123] At this point, the relationship between the sound pressure amplitude of the array sound field and the sound source has been established. The next step is to solve and optimize it.

[0124] (3) Solve for the amplitude of each transmitter based on the set desired sound pressure distribution of the sound field;

[0125] Based on the formula relating the total sound pressure level to the amplitude of each transmitter in step (2), the objective optimization function is set as follows:

[0126]

[0127] The goal is to solve for the amplitude of the array transmitter. So that the generated total sound field with by The specified desired sound field distribution should be as close as possible;

[0128] Since the number of control points is usually less than the number of transmitters in the array, i.e., M is less than N, the number of columns in the matrix is ​​greater than the number of rows, and the number of unknowns is greater than the number of equations. There are infinitely many solutions. However, one special solution minimizes the u-norm and is called the minimum norm solution. Finding this minimum norm solution is equivalent to:

[0129]

[0130]

[0131] To address the aforementioned optimization problem, utilize Find its solution from the right inverse matrix:

[0132]

[0133] In the formula yes The conjugate transpose of .

[0134] calculate elements in The formula:

[0135]

[0136] It is the forward operator between the amplitude of the m-th spatial point and the amplitude of the n-th transmitter;

[0137] The desired sound field distribution is set. The method is as follows:

[0138] To optimize the focusing performance of the hollow planar array, the core of this invention lies in constructing a reasonable desired sound field distribution and then using this distribution to solve for the optimal excitation amplitude of each transmitter. By presetting the target sound pressure amplitude at multiple points on the target focusing plane and substituting them into the formula, the optimal amplitude of each transmitter that can approximate the desired sound field can be calculated.

[0139] Among them, the desired sound field distribution It refers to the sound field distribution that can be formed by a solid array with a similar number of elements to the current hollow planar array. Specifically:

[0140] For a ring-shaped hollow planar array, the inner radius of its ring structure is used as the radius of the circle to construct a solid circular array as the desired sound field;

[0141] For a rectangular hollow planar array, the length of the shorter side of the rectangle is taken as the side length of the square, and a solid square array is constructed as the desired sound field. The number of emitters in this array is... ;

[0142] To reflect the sound pressure amplitude at the desired sound field focal point and radius Furthermore, considering that a rectangular array will produce side lobes in four directions (positive and negative X-axis and positive and negative Y-axis), the sound pressure amplitude is selected at five points: the focal center and the edges of the focal point in the positive and negative X and Y directions. and radius It can be calculated using the following formula:

[0143]

[0144]

[0145]

[0146] in, It refers to the sound pressure level of the i-th transmitter on the solid array that forms the desired sound field distribution. Let h be the sound pressure amplitude of the desired sound field distribution, λ be the distance from the focal point to the array, λ be the wavelength of the ultrasonic wave emitted by the transmitter, and d be the diameter of the transmitter; see attached. Figure 2 For the desired sound field distribution, attached Figure 3 This is a schematic diagram of the selected location;

[0147] If the coordinates of the focus are (x, y, z), as shown in the attached figure. Figure 3 As shown, the positions of these five points are (x, y, z), (x+r, y, z), (xr, y, z), (x, y+r, z), and (x, yr, z), respectively, and the magnitudes of these five points are respectively ( , , (i.e., the desired sound field distribution) for( , , );

[0148] Finally, the amplitude u of the N transmitters is calculated using the above formula, and then the effect of the pseudo-inverse matrix is ​​observed through sound field simulation.

[0149] Appendix Figure 6 and 7 This refers to the amplitude and sound pressure distribution of the sound field under the control of the pseudo-inverse matrix algorithm. (The text abruptly ends here, likely due to an incomplete sentence or missing information.) Figure 3 and 4 The comparison clearly shows the attached Figure 7 In the mid-field distribution diagram, the side lobes along the X-axis are significantly higher than those along the Y-axis. This is further confirmed by the pseudo-inverse matrix algorithm. Figure 4The sound field distribution diagram clearly shows that the side lobes on the X-axis and Y-axis are roughly the same height, indicating that the sound energy is more symmetrical and concentrated around the focal point.

[0150] Appendix Figure 8 and 9 The diagram provides cross-sectional views of the sound pressure distribution along the X and Y axis centers before and after algorithm processing. The diagram uses a dashed line to indicate the sound pressure corresponding to half the maximum sound pressure (-6 dB). In engineering, the diameter of the region defined by this power half-width is often defined as the focal point size. From the data in the diagram, it can be calculated that under initial amplitude control, the diameter of the focal point is approximately 36 mm in the X-axis direction and only 10 mm in the Y-axis direction, with an aspect ratio of 3.6, exhibiting a significant elliptical shape. After pseudo-inverse matrix optimization, the focal diameter in the X-axis direction narrows to 32 mm, while it expands to 22 mm in the Y-axis direction, improving the aspect ratio to approximately 1.45, and the shape of the focal region significantly approaches a circle.

[0151] In summary, the experimental data and sound field simulation results demonstrate that the pseudo-inverse matrix solving algorithm used in this invention can effectively balance the sidelobe sound pressures of different axes by re-optimizing the distribution of array amplitude, thereby substantially improving the focusing effect of the hollow planar ultrasonic array, making the focusing area closer to a circle, and improving the accuracy and quality of single-point focusing.

Claims

1. An ultrasonic hollow planar array focusing method based on pseudo-inverse matrix solution, characterized in that, The method comprises the following steps: (1) determining the shape of the hollow planar array and the number of transmitters; (2) establishing the relationship between a single transmitter and each point in its sound field according to a sound pressure radiation model of a circular piston, and deducing the relationship between the total sound field sound pressure of the array and the amplitude of each transmitter; (3) solving the amplitude of each transmitter according to the set expected sound field sound pressure distribution.

2. The ultrasonic hollow planar array focusing method based on pseudo-inverse matrix solution according to claim 1, characterized in that, The hollow planar array in step (1) refers to a configuration in which the transmission units are not uniformly distributed on the entire array plane, but are concentratedly arranged on the peripheral edge of the array, and the central region is empty.

3. The ultrasonic hollow planar array focusing method based on pseudo-inverse matrix solution according to claim 2, characterized in that, The hollow planar array form includes: Ring-shaped hollow planar array: all transmitters are arranged along one or more concentric circular ring paths to form a ring structure; Rectangular hollow planar array: the transmitters are arranged along a rectangular frame, and the form can be regarded as a frame structure remaining after removing a small rectangular array from the center of a complete large-area rectangular solid array.

4. The ultrasonic hollow planar array focusing method based on pseudo-inverse matrix solution according to claim 1, 2 or 3, characterized in that: According to the selected hollow planar array geometric shape and specific size parameters, the total number N of transmitters included in the array is determined.

5. The ultrasonic hollow planar array focusing method based on pseudo-inverse matrix solution according to claim 1, characterized in that, In step (2), the inverse design idea is adopted, the optimal excitation amplitude of each transmitter required to achieve the expected sound field distribution target is solved in reverse, an accurate physical sound field model is established based on the sound pressure radiation model of the circular piston, and then the quantitative mathematical relationship between the total sound field sound pressure of the array and the amplitude of each transmitter is deduced as follows: ； wherein is the sound pressure amplitude at the mth point in space, is the amplitude of the nth emitter, is the forward operator between the mth spatial point amplitude and the nth emitter amplitude.

6. The ultrasonic hollow planar array focusing method based on pseudo-inverse matrix solution according to claim 5, characterized in that: The specific process is as follows: The first step is to establish an accurate mathematical model between the array transmitter amplitude and the spatial sound field distribution. In this process, the hollow planar array structure to be used needs to be clearly defined, and then the mathematical relationship between the array transmitter amplitude and the total sound field sound pressure is established: The instantaneous sound pressure of a point in the sound field of a single emitter under delay phase control is : ； wherein is the density of air, is the amplitude of the emitter, is the radius of the emitter, and is the polar coordinate of the focus relative to the emitter, is the first order Bessel function, is the wave number, is the delay time of the emitter, is the imaginary unit, is the angular frequency; In the above equation, there are only two quantities related to the source characteristics, namely the amplitude of the emitter and the delay time of the emitter For the sake of simplicity and to make the relationship between the sound pressure and the source more intuitive, the above equation is simplified as follows: ； where the delay time of each transmitter was calculated using the following procedure: calculating the time required for the ultrasound waves emitted by the emitters on the array of ultrasound emitters to reach the focal point : ； where (x n ,y n ,z n ) represents the coordinates of the nth transmitter on the array of ultrasonic transmitters, (x,y,z) are the coordinates of the focal point, is the propagation speed of the ultrasonic waves in air, taken as the maximum of the arrival times of the ultrasonic waves ； Computing a delay time for a drive signal of each transmitter of an array of ultrasonic transmitters : ； Simplifying the equation above as follows: ； Finally, it is simply denoted as: ； wherein, is the forward operator between the instantaneous sound pressure amplitude and the transmitter amplitude; Similarly, the sound pressure amplitude of the total sound field of the array can be obtained by linear superposition: ； wherein, is a forward operator between the amplitude of the sound pressure of the total sound field of the array and the amplitude of the nth transmitter, is the amplitude of the nth transmitter; ； When the sound pressure amplitudes at M points in space are specified or known, we have: ； Here, the number of M needs to be determined according to the main lobe and side lobe in the expected sound field distribution, wherein the rectangular hollow planar array can use a similar square array as the expected sound field, and the ring-shaped hollow planar array can use a circular planar array as the expected sound field; Exchange the left and right sides of the equation and expand the matrix as: ； Simply denoted as: ； in It is the first in space The sound pressure amplitude at each point It is the first The amplitude of each transmitter It is the forward operator between the amplitude of the m-th spatial point and the amplitude of the n-th transmitter. It is a forward operator, a The matrix, yes The amplitude of a transmitter is a The vector, For the desired sound field distribution, it is The vector.

7. The ultrasonic hollow planar array focusing method based on pseudo-inverse matrix solution according to claim 1, characterized in that: The process of solving the amplitude of each transmitter in step (3) is as follows: According to the formula of the relationship between the total sound pressure and the amplitude of each transmitter in step (2), the target optimization function is set as: ； The goal is to solve for the array transmitter amplitudes such that the resulting total sound field is as close as possible to the desired sound field distribution specified by ​ For the optimization problem above, the solution is found using the right inverse matrix of ​ ； wherein is the conjugate transpose of 8. The ultrasonic hollow planar array focusing method based on pseudo-inverse matrix solution according to claim 7, characterized in that, Computing the elements in the formula: ； is the forward operator between the mth spatial point amplitude and the nth transmitter amplitude.

9. The ultrasonic hollow planar array focusing method based on pseudo-inverse matrix solution according to claim 8, characterized in that, The set desired sound field distribution The method is as follows: For the ring-shaped hollow planar array, the inner radius of the ring structure is taken as the radius of the circle, and a circular solid array is constructed as the expected sound field. For a rectangular hollow planar array, the length of its rectangular short side is taken as the side length of a square, and a square solid array is constructed as the desired sound field, and the number of emitters of the array is ; In order to reflect the sound pressure amplitude at the desired sound field focal point and radius And considering that the rectangular array will have side lobes at the positive and negative directions of the X axis and the positive and negative directions of the Y axis, the sound pressure amplitudes at the positions of the focal point center and the five points at the edges of the focal point in the positive and negative directions of the X axis and the Y axis are selected, and the sound pressure amplitudes are and radius The sound pressure amplitudes can be calculated by the following formula: ； ； ； wherein, P(i) refers to the sound pressure of the i-th emitter on the solid array forming the desired sound field distribution, P(i) refers to the sound pressure of the i-th emitter on the solid array forming the desired sound field distribution, P refers to the amplitude of the sound pressure of the desired sound field distribution, h refers to the distance of the focal point from the array, l refers to the wavelength of the ultrasound emitted by the emitters, and d refers to the diameter of the emitters; If the focus coordinates are (x, y, z), then the positions of the five points are (x, y, z), (x+r, y, z), (x-r, y, z), (x, y+r, z), (x, y-r, z) respectively, and the amplitudes of the five points are ( , , ) respectively, that is, the expected sound field distribution is ( , , ).

10. The ultrasonic hollow planar array focusing method based on pseudo-inverse matrix solution according to claim 9, characterized in that, By the sound field distribution , total sound field The amplitude u of the N emitters is calculated.

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