Design method of acoustic holography system based on rotation and layer sequence multiplexing

Abstract

The application discloses a kind of based on rotation and layer sequence multiplexing acoustic holography system design method, belong to acoustic holography, passive acoustic phase modulation and multi-state sound field control technical field;The method comprises:1 establishes acoustic holography system, to the configuration order of first diffraction layer and second diffraction layer at first cascade position, second cascade position and the rotation angle of diffraction layer at second cascade position around propagation main shaft Limit multiple multiplexing states, and with multiple target output sound intensity distribution one-to-one correspondence;2 it is with limited angle spectrum propagation model to calculate predicted output sound intensity distribution, and based on sound intensity square error term and sound intensity separation term Joint loss function is constructed and two layer phase distributions are simultaneously optimized;3 the optimal phase distribution of two layers is converted into corresponding entity total thickness distribution respectively, to determine the passive phase modulation structure parameters of two diffraction layers, realize the repeatable switching of multiple target output sound intensity distribution.

Description

Technical Field

[0001] This invention relates to the fields of acoustic holography, passive acoustic phase modulation, and multi-state sound field control technology, and specifically to a design method for an acoustic holographic system based on rotation and layer sequence multiplexing. Background Technology

[0002] Acoustic holography can generate a target sound pressure or sound intensity distribution in a predetermined plane or spatial region by modulating the amplitude and phase of sound waves. Passive acoustic phase plates and acoustic metasurfaces, as passive wavefront modulation devices, can generate complex sound fields without configuring independent active drives for each modulation position; however, once their phase modulation structure is determined, the acoustic transmission relationship is fixed, and they are usually suitable for mapping between fixed input and fixed output.

[0003] To achieve a reconfigurable sound field, one existing approach employs a phased-array transducer array, applying amplitude or phase control to multiple array elements to electronically alter the output sound field. This approach requires driving, synchronization, and amplitude / phase calibration components that match the number of array elements; when the element spacing is small, the operating frequency is high, or the effective aperture is large, the number of driving channels, calibration errors, and hardware scale all increase the system implementation complexity.

[0004] Another approach employs a single-layer passive phase plate or a single-layer acoustic metasurface to transform a given input wave field into a predetermined target output sound intensity distribution. The phase modulation degrees of freedom for this type of device are primarily provided by the single-layer phase distribution, making it suitable for mapping between fixed inputs and fixed outputs. However, when switching between multiple target output sound intensity distributions is required, existing solutions typically necessitate changing the operating frequency, incident mode, or propagation distance, continuously adjusting the mechanical pose of the phase modulation structure, or replacing the phase modulation structure altogether. These methods may alter propagation conditions and impose additional requirements on pose positioning, repetitive assembly, and amplitude-phase calibration. Changing the operating frequency, incident mode, or propagation distance will result in inconsistent propagation conditions corresponding to different target outputs, affecting the stability and repeatability of sound field switching. Continuously adjusting the mechanical pose or replacing the phase modulation structure can easily introduce positioning errors, assembly errors, and amplitude-phase calibration errors, increasing the burden of system debugging and maintenance.

[0005] For existing solutions employing multi-layer passive phase modulation structures, the propagation between layers causes the output sound field to be simultaneously affected by inter-layer distances, phase distributions of each layer, and assembly alignment. Deviations in structural parameters or assembly positions may reduce the repeatability of the output sound field. For applications requiring the generation of multiple target output sound fields, multiplexing by switching input channels or incident modes alters propagation conditions and increases driving and calibration requirements. Replacing the phase modulation structure increases the burden of repetitive assembly and maintenance. On the other hand, if the optimization target only constrains the morphological error of the normalized sound field, insufficient sound intensity concentration in the target region or high residual sound intensity in the background region may occur. Therefore, under the condition that the input wave field and propagation distance remain unchanged, existing solutions struggle to simultaneously achieve morphological matching, sound intensity concentration, and stable switching of multiple target sound fields using the same set of phase modulation structures. Summary of the Invention

[0006] This invention addresses the challenges of existing passive acoustic phase modulation structures, which struggle to generate multiple stable and repeatable target sound intensity distributions under constant input wave field, interlayer propagation distance, and output propagation distance. Furthermore, it highlights the difficulty in simultaneously achieving sound field contour matching and background sound intensity suppression when multiple multiplexing states share a phase configuration. The invention proposes an acoustic holographic system design method based on rotation and layer sequence multiplexing. This method leverages the multi-dimensional controllability of cascaded diffraction arrangement, configuration order, and diffraction layer rotation angles, while comprehensively considering constraints such as interlayer diffraction propagation laws and sound field superposition interference. This allows multiple multiplexing modes under the same propagation conditions to generate target sound fields with excellent matching, thereby achieving conflict-free multiplexing control of multi-morphological sound fields under constant propagation parameters.

[0007] The present invention provides a design method for an acoustic holographic system based on rotation and layer sequence multiplexing, characterized by the following steps: S1, with the center of the input plane as the origin and the direction of sound propagation as the principal axis, establish mutually orthogonal points in a plane perpendicular to the principal axis of propagation. x Axial direction and y The axial direction; thus forming a three-dimensional rectangular coordinate system; An acoustic holographic system is established, comprising: an input plane, a first diffraction layer, a second diffraction layer, and a receiving plane; and a first cascade position and a second cascade position are sequentially arranged along the main propagation axis; wherein, the first and second diffraction layers represent fixed diffraction layer entities, and the first and second cascade positions represent fixed spatial positions along the main propagation axis; the meanings of the diffraction layer number and the cascade position number are independent of each other; the layer order referred to in this paper refers to the arrangement order of the two diffraction layers at the above two cascade positions; set up NEach multiplexing state is defined by the arrangement order of the first and second diffraction layers at the first and second cascade positions, and the rotation angle of the diffraction layer at the second cascade position about the propagation principal axis. When the first diffraction layer is set at the first cascade position, the second diffraction layer is set at the second cascade position, and this is recorded as the first state group; When the first diffraction layer is set at the second cascade position, the second diffraction layer is set at the first cascade position and is denoted as the second state group; The input plane is set in close contact with the incident surface of the diffraction layer at the first cascade position, and the input wave field on the input plane is directly loaded onto the incident surface, without setting an independent free propagation region between the two; The distance between the exit surface of the diffraction layer in the first cascade position and the incident surface of the diffraction layer in the second cascade position is defined as the interlayer propagation distance. d 1. And set the space between the two as the first propagation interval; The distance between the exiting surface of the diffraction layer in the second cascade position and the receiving plane is defined as the output propagation distance. d 2, and the space between the two is set as the second propagation interval; Preset on the receiving plane and N Each reuse state corresponds to one-to-one N Each target output sound intensity distribution has a corresponding effective signal region. Set the first phase distribution of the first diffraction layer and the second phase distribution of the second diffraction layer as parameters to be optimized; S2, determine the phase distribution at the first cascade position and the second cascade position according to the configuration order and rotation angle corresponding to each multiplexing state; wherein, the first phase distribution and the second phase distribution are fixed to the first diffraction layer and the second diffraction layer, respectively; for the k-th multiplexing state, Φ A,k This represents the phase distribution of the diffraction layer located at the first cascade position, Φ. B,k This represents the phase distribution of the diffraction layer located at the second cascade position after rotation according to the rotation angle of this multiplexing state; forward propagation calculations are performed on the input wave field under the current first and second phase distributions, such that the input wave field sequentially passes through the phase modulation at the first cascade position and the interlayer propagation distance. d The propagation corresponding to 1, the phase modulation at the second cascade position, and the output propagation distance d The propagation of 2 corresponds to the predicted output acoustic intensity distribution on the receiving plane, which corresponds to the corresponding multiplexing state. S3, the effective signal region of the target output acoustic intensity distribution corresponding to each multiplexing state is set as the target region of the corresponding multiplexing state, and the part of the discrete calculation region of the receiving plane other than the target region is set as the background region; according to N The predicted output sound intensity distribution and its corresponding N A joint loss function is constructed from the output sound intensity distribution of each target. Joint loss function Includes: a sound intensity squared error term used to constrain the difference between the normalized predicted output sound intensity distribution and the corresponding target output sound intensity distribution. L MSE And a sound intensity separation term used to constrain the ratio of the average sound intensity of the background region to the average sound intensity of the target region. L sep ; S4, with joint loss function Minimize as the optimization objective, so that N Each reused state participates in the optimization calculation, and the parameters to be optimized are updated synchronously during the optimization process until the first optimal phase distribution of the first diffraction layer and the second optimal phase distribution of the second diffraction layer are obtained. S5. Based on the sound velocity of the background propagation medium, the sound velocity of the diffraction layer material, and the operating frequency, the first optimal phase distribution and the second optimal phase distribution are converted into the first total thickness distribution and the second total thickness distribution of the material, respectively, thereby determining the passive phase modulation structure parameters of the first diffraction layer and the second diffraction layer.

[0008] The design method of this invention is also characterized by employing a band-limited angle spectrum propagation model for forward propagation calculation; and using equations (1a)-(1e) to predict the first... k Sound intensity distribution of the multiplexed output: (1a) (1b) (1c) (1d) (1e) In equations (1a)-(1e), k An index for the reuse status; For any horizontal coordinate position perpendicular to the main propagation axis; j Φ is the imaginary unit. A,k ( x , y ) and Φ B,k ( x , y ) are respectively the first kIn the multiplexing state, the horizontal coordinate position is at the first cascade position and the second cascade position. Phase distribution at; U in ( x , y () represents the horizontal coordinate position. Input fluctuation field at the location; U 1,k ( x , y () represents the lateral coordinate position after phase modulation at the first cascade location. The fluctuation field at that location; U prop1,k ( x , y () represents the interlayer propagation distance d 1. Lateral coordinate position after propagation The fluctuation field at that location; U 2,k ( x , y () indicates the lateral coordinate position after phase modulation at the second cascaded position. The fluctuation field at that location; U out,k ( x , y ) is the first k The horizontal coordinate position of each multiplexing state on the receiving plane (4) The output fluctuation field at that location; I raw,k ( x , y () represents the lateral coordinate position on the receiving plane (4). The unnormalized predicted output sound intensity characterization at the location; the above U in U 1,k U prop1,k U 2,k and U out,k Both represent the complex sound pressure level; F and F -1 These are the Fourier transform and the inverse Fourier transform, respectively. f x and f y respectively along x Axial direction and y Spatial frequency components along the axial direction; H ( ) is the angular spectrum propagation transfer function, which is obtained from equation (2); B( ) is the band-limited window function, which takes the value 1 when both the propagation condition λ²(fx²+fy²)≤1 and the non-aliasing sampling condition of the current discrete grid are satisfied, and takes the value 0 otherwise. Its frequency boundary is determined by the transverse sampling interval, the calculation window size and the propagation distance d. (2) In equation (2), For the propagation distance, and ∈{ d 1, d 2}; λ The operating wavelength in the background propagation medium, and λ = c 0 / f 0, c 0 represents the speed of sound in the background propagation medium. f 0 represents the operating frequency.

[0009] Furthermore, the joint loss function Construct according to equations (3a)-(3e): (3a) (3b) (3c) (3d) (3e) In equations (3a)-(3e), D is the discrete computational region of the receiving plane. M This represents the number of pixels within the discrete computation region D. I norm,k ( x , y )express I raw,k ( x , y The predicted output acoustic intensity distribution is obtained by performing minimum-maximum normalization for each multiplexing state; the maximum and minimum values ​​of the normalization are both obtained within the discrete computation region D, and when the maximum value equals the minimum value, the corresponding normalization result is set to zero. I target,k ( x , y () represents the horizontal coordinate position. Normalized to the [0,1]th position k The output sound intensity distribution of each target; Ω k For the first k The effective signal region of the target output sound intensity distribution; and The first k Each reuse state is in Ω k The unnormalized average sound intensity in the inner and background regions; ε is a positive number with the same dimensions as the unnormalized average sound intensity, used to prevent the denominator of the sound intensity separation term from being zero. γ The weighting coefficients for the sound intensity separation term are greater than 0.

[0010] Furthermore, in the first state group, different rotation angles are applied to the second diffraction layer at the second cascade position to determine each multiplexing state; In the second state group, different rotation angles are applied to the first diffraction layer at the second cascade position to determine each multiplexing state; The rotation angle is selected from a set of orthogonal rotation angles, which includes 0°, 90°, 180°, and 270°. All rotations are based on the propagation axis corresponding to the center of the input plane, with clockwise as the positive direction when viewed along the sound propagation direction, and the center of the input plane as the center of the lateral coordinate rotation.

[0011] Furthermore, the sound velocity in the diffraction layer solid material c p Greater than the speed of sound in the background propagation medium c 0; will the first i Any lateral coordinate position in the optimal phase distribution of the diffraction layer ( x , y The phase modulation at point ) is expressed as and will the i Lateral coordinate position in the optimal phase distribution of the diffraction layer ( x , y The total thickness of the solid at point ) is expressed as Then calculate the first according to formula (4). i Lateral coordinate position in the optimal phase distribution of the diffraction layer ( x , y Total thickness of the solid at ) , i =1,2: (4) In equation (4), h0 is the thickness of the uniform support substrate; where the left side of equation (4) represents the total thickness of the solid including the uniform support substrate, and the fractional term on the right side of equation (4) represents the phase modulation height. k 0 and k p These are the wavenumbers in the background propagation medium and the diffraction layer material, respectively. k 0=2 πf 0 / c 0, k p =2 πf 0 / c p .

[0012] The present invention provides an electronic device, including a memory and a processor, characterized in that the memory is used to store a program supporting the processor in performing the method described herein, and the processor is configured to execute the program stored in the memory.

[0013] The present invention discloses a computer-readable storage medium storing a computer program, characterized in that the computer program is executed by a processor to perform the steps of the method described thereon.

[0014] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention defines the multiplexing state by the arrangement order of the first and second diffraction layers at the first and second cascade positions, and the rotation angle of the diffraction layer at the second cascade position around the propagation principal axis. Changing the arrangement order alters the formation path of the intermediate wave field, and the rotation angle changes the spatial correspondence between the phase distribution at the second cascade position and the intermediate wave field. Under the condition that the input wave field, interlayer propagation distance, and output propagation distance remain unchanged, the same set of first and second phase distributions can adapt to multiple multiplexing states and form target output sound intensity distributions corresponding to each multiplexing state. Therefore, it is not necessary to design diffraction layer combinations with different phase distributions for each target output; multiple preset target sound fields can be obtained using the same set of diffraction layers, thereby reducing the number of diffraction layer groups and the workload of phase structure design required for multi-target sound field control.

[0015] 2. This invention enables multiple multiplexing states to jointly participate in the optimization of the first and second phase distributions, and constructs a joint loss function by setting a sound intensity squared error term and a sound intensity separation term. The sound intensity squared error term is used to constrain the morphological difference between the predicted output sound intensity distribution and the target output sound intensity distribution, while the sound intensity separation term is used to constrain the ratio of the average sound intensity in the background region to the average sound intensity in the target region. Therefore, the joint loss function can simultaneously constrain the contour matching degree of the target pattern and the residual sound intensity in the background region during the same optimization process, avoiding the optimization result from only satisfying the pattern contour while retaining a high sound intensity in the background region. This ensures that the output sound field corresponding to each multiplexing state has a identifiable target contour and that the sound intensity is relatively concentrated in the target region, thus facilitating the improvement of the reconstruction quality of the target sound field corresponding to different multiplexing states. Attached Figure Description

[0016] Figure 1 This is a schematic diagram showing the configuration order of the first diffraction layer 2 and the second diffraction layer 3 in four multiplexing states in one embodiment of the present invention, the rotation angle of the diffraction layer in the second cascade position and the target output sound intensity distribution of the corresponding numbers 0, 1, 2 and 3. Figure 2This is the normalized amplitude distribution of the predicted output corresponding to the four multiplexing states, calculated using a band-limited angle spectrum propagation model in one embodiment of the present invention. Figure 3 This is the normalized amplitude distribution of the output corresponding to the four reuse states obtained by cross-validation using a three-dimensional k-Wave model in one embodiment of the present invention. Detailed Implementation

[0017] The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments. The embodiments are used to illustrate the implementation process of the present invention, and are not intended to limit the scope of protection of the present invention; without departing from the technical concept defined by the claims, the relevant parameters, the target output sound intensity distribution form, and the number of multiplexing states can be adjusted according to the actual application.

[0018] In this embodiment, an acoustic holographic system design method based on rotation and layer sequence multiplexing aims to address how to construct multiple repeatable multiplexing states by exchanging the configuration order of the first and second diffraction layers and the rotation angle of the diffraction layer in the second cascade position around the propagation axis, under the condition that the input wave field, inter-layer propagation distance, and output propagation distance remain unchanged, and to form multiple target output sound intensity distributions corresponding to them; and how to balance the morphological matching of the target output sound intensity distribution and the sound intensity concentration of the target region relative to the background region in the joint optimization of the first phase distribution and the second phase distribution, while converting the first optimal phase distribution and the second optimal phase distribution into the first total thickness distribution and the second total thickness distribution of the entity, respectively. Specifically, the method includes the following steps: S1, with the center of input plane 1 as the origin and the direction of sound propagation as the principal axis, establish mutually orthogonal points in a plane perpendicular to the principal axis of propagation. x Axial direction and y The axial direction; thus forming a three-dimensional rectangular coordinate system; An acoustic holographic system is established, comprising: an input plane 1, a first diffraction layer 2, a second diffraction layer 3, and a receiving plane 4; and a first cascade position and a second cascade position are sequentially set along the main propagation axis. Here, the first and second diffraction layers represent fixed diffraction layer entities, and the first and second cascade positions represent fixed spatial positions along the main propagation axis. The diffraction layer numbers and cascade position numbers have independent meanings. The layer order referred to in this paper refers to the arrangement order of the two diffraction layers at the aforementioned two cascade positions.

[0019] set up N Each multiplexing state is defined by the arrangement order of the first diffraction layer 2 and the second diffraction layer 3 at the first cascade position and the second cascade position, as well as the rotation angle of the diffraction layer at the second cascade position around the propagation axis.

[0020] When the first diffraction layer 2 is set in the first cascade position, the second diffraction layer 3 is set in the second cascade position, and this is recorded as the first state group; When the first diffraction layer 2 is set in the second cascade position, the second diffraction layer 3 is set in the first cascade position and is denoted as the second state group.

[0021] In the first state group, different rotation angles are applied to the second diffraction layer at the second cascade position to determine each multiplexing state; In the second state group, different rotation angles are applied to the first diffraction layer at the second cascade position to determine each multiplexing state; The rotation angle is selected from a set of orthogonal rotation angles, which includes 0°, 90°, 180°, and 270°. All rotations are based on the propagation axis corresponding to the center of the input plane, with clockwise as the positive direction when viewed along the sound propagation direction, and the center of the input plane as the center of the lateral coordinate rotation.

[0022] In this embodiment, N=4. The four multiplexing states are numbered k=1, 2, 3, 4, with target numbers 0, 1, 2, 3 respectively. In the first state group, the first diffraction layer 2 is located at the first cascade position, and the second diffraction layer 3 is located at the second cascade position. The second diffraction layer 3 is rotated 0° and 180° respectively, corresponding to numbers 0 and 1. In the second state group, the second diffraction layer 3 is located at the first cascade position, and the first diffraction layer 2 is located at the second cascade position. The first diffraction layer 2 is rotated 90° and 270° respectively, corresponding to numbers 2 and 3. The configuration order swap changes the formation path of the intermediate wave field, and the rotation of the diffraction layer at the second cascade position changes the spatial correspondence between the phase pixels and the intermediate wave field.

[0023] like Figure 1 As shown, the four multiplexing states are, in order, the first diffraction layer 2 → the second diffraction layer 3 / 0°, the first diffraction layer 2 → the second diffraction layer 3 / 180°, the second diffraction layer 3 → the first diffraction layer 2 / 90° and the second diffraction layer 3 → the first diffraction layer 2 / 270°, and correspond to the numbers 0, 1, 2 and 3 respectively.

[0024] The input plane 1 is set in close contact with the incident surface of the diffraction layer at the first cascade position. The input wave field on the input plane 1 is directly loaded onto the incident surface, and there is no independent free propagation region between the two. The distance between the exit surface of the diffraction layer in the first cascade position and the incident surface of the diffraction layer in the second cascade position is defined as the interlayer propagation distance. d 1. And set the space between the two as the first propagation interval; The distance between the exiting surface of the diffraction layer in the second cascade position and the receiving plane 4 is defined as the output propagation distance. d2, and set the space between the two as the second propagation interval.

[0025] Preset on receiving plane 4 and N Each reuse state corresponds to one-to-one N Each target output sound intensity distribution has a corresponding effective signal region. The first phase distribution of the first diffraction layer 2 and the second phase distribution of the second diffraction layer 3 are set as parameters to be optimized.

[0026] In this embodiment, water is used as the background propagation medium, and the input sound source is a uniform circular coherent sound source with a diameter of 35 mm. The input plane 1 is coaxially and tightly attached to the diffraction layer located in the first cascade position, and the input wave field is directly applied to the incident surface of the diffraction layer. The effective aperture of the first diffraction layer 2 and the second diffraction layer 3 is 100 mm × 100 mm, and both are discrete into 200 × 200 phase pixels with a lateral sampling interval of 0.5 mm; the interlayer propagation distance is... d 1 and output propagation distance d 2. Both are 30 mm. The four multiplexing states use the same sound source, effective aperture, propagation distance, and receiving plane 4.

[0027] S2, determine the phase distribution at the first cascade position and the second cascade position according to the configuration order and rotation angle corresponding to each multiplexing state; wherein, the first phase distribution and the second phase distribution are fixed to the first diffraction layer and the second diffraction layer, respectively; for the k-th multiplexing state, Φ A,k This represents the phase distribution of the diffraction layer located at the first cascade position, Φ. B,k This represents the phase distribution of the diffraction layer located at the second cascade position after rotation according to the rotation angle of this multiplexing state; forward propagation calculations are performed on the input wave field under the current first and second phase distributions, such that the input wave field sequentially passes through the phase modulation at the first cascade position and the interlayer propagation distance. d The propagation corresponding to 1, the phase modulation at the second cascade position, and the output propagation distance d The propagation corresponding to 2 is used to obtain the predicted output acoustic intensity distribution corresponding to the corresponding multiplexing state on the receiving plane 4.

[0028] In step S2, the forward propagation calculation uses a band-limited angle spectrum propagation model, and uses equations (1a)-(1e) to predict the first... k Sound intensity distribution of the multiplexed output: (1a) (1b) (1c) (1d) (1e) In equations (1a)-(1e), k An index for the reuse status; For any horizontal coordinate position perpendicular to the main propagation axis; j Φ is the imaginary unit. A,k ( x , y ) and Φ B,k ( x , y ) are respectively the first k In the multiplexing state, the horizontal coordinate position is at the first cascade position and the second cascade position. Phase distribution at; U in ( x , y () represents the horizontal coordinate position. Input fluctuation field at the location; U 1,k ( x , y () represents the lateral coordinate position after phase modulation at the first cascade location. The fluctuation field at that location; U prop1,k ( x , y () represents the interlayer propagation distance d 1. Lateral coordinate position after propagation The fluctuation field at that location; U 2,k ( x , y () indicates the lateral coordinate position after phase modulation at the second cascaded position. The fluctuation field at that location; U out,k ( x , y ) is the first k The horizontal coordinate position of each multiplexing state on the receiving plane 4 The output fluctuation field at that location; I raw,k ( x , y () represents the lateral coordinate position on receiving plane 4. The unnormalized predicted output sound intensity characterization at the location; the above U in U 1,k U prop1,k U 2,k and U out,k Both represent the complex sound pressure amplitude. Equation (1e) omits the common sound intensity scaling factor for each reuse state; this omission does not affect the subsequent normalization results; F and F -1These are the Fourier transform and the inverse Fourier transform, respectively. f x and f y respectively along x Axial direction and y Spatial frequency components along the axial direction; H ( ) is the angular spectrum propagation transfer function, which is obtained from equation (2); B( ) is the band-limited window function, which is 1 when both the propagation condition λ²(fx²+fy²)≤1 and the non-aliasing sampling condition of the current discrete grid are satisfied, and 0 otherwise. Its frequency boundary is determined by the transverse sampling interval, the calculation window size and the propagation distance d.

[0029] (2) In equation (2), For the propagation distance, and ∈{ d 1, d 2}; λ The operating wavelength in the background propagation medium, and λ = c 0 / f 0, c 0 represents the speed of sound in the background propagation medium. f 0 represents the operating frequency.

[0030] Equations (1a) to (1e) correspond to two phase modulations and two propagation segments, respectively; in each discrete propagation segment, the angular spectrum propagation transfer function is... H ( ) and band-limited window function B Multiplying by ( ) retains only the spectral components that satisfy the propagation and discrete sampling conditions, in order to suppress spectral aliasing and eliminate the non-physical growth of evanescent components in numerical propagation.

[0031] S3, the effective signal region of the target output acoustic intensity distribution corresponding to each multiplexing state is set as the target region of the corresponding multiplexing state, and the part of the discrete calculation region of the receiving plane 4 other than the target region is set as the background region; according to N The predicted output sound intensity distribution and its corresponding N A joint loss function is constructed from the output sound intensity distribution of each target. Joint loss function Includes: a sound intensity squared error term used to constrain the difference between the normalized predicted output sound intensity distribution and the corresponding target output sound intensity distribution. L MSE And a sound intensity separation term used to constrain the ratio of the average sound intensity of the background region to the average sound intensity of the target region. L sep .

[0032] In step S3, the joint loss function is constructed according to equations (3a)-(3e). : (3a) (3b) (3c) (3d) (3e) In equations (3a)-(3e), D is the discrete computational region of the receiving plane 4. M This represents the number of pixels within the discrete computation region D. I norm,k ( x , y )express I raw,k ( x , y The predicted output acoustic intensity distribution is obtained by performing minimum-maximum normalization for each multiplexing state; the maximum and minimum values ​​of the normalization are both obtained within the discrete computation region D, and when the maximum value equals the minimum value, the corresponding normalization result is set to zero. I target,k ( x , y () represents the horizontal coordinate position. Normalized to the [0,1]th position k The output sound intensity distribution of each target; For the first k The effective signal region of the target output sound intensity distribution; and The first k A reuse state in The unnormalized average sound intensity in the inner and background regions; ε is a positive number with the same dimensions as the unnormalized average sound intensity, used to prevent the denominator of the sound intensity separation term from being zero. γ The weighting coefficients for the sound intensity separation term are greater than 0.

[0033] Target effective signal region Ω k The background region is determined by a binary mask corresponding to the digit strokes, and is the discrete computational region D excluding Ω. k The part other than that. In the joint loss function L MSE Normalized sound intensity is used. L sepUnnormalized average sound intensity is used; Pearson correlation coefficient (PCC) and peak signal-to-noise ratio (PSNR) are calculated using normalized sound intensity; sound intensity contrast (CR) is calculated as the ratio of the average unnormalized sound intensity of the target area to the average unnormalized sound intensity of the background area. The larger the CR value, the higher the concentration of sound intensity in the target area. Figure 2 and Figure 3 The display shows the normalized amplitude distribution obtained by dividing the amplitude of the output wave field from the receiving plane 4 by the maximum amplitude under each multiplexing state. The normalization range is [0,1]. This display processing is only used for sound field contour visualization and does not change the calculation method of the joint loss function and each evaluation index. It should be noted that... L sep The ratio of CR is in the opposite direction: L sep The ratio of the average sound intensity of the background area to the average sound intensity of the target area is used; a smaller value indicates better separation. For CR (Rapid Resonance), the ratio of the average sound intensity of the target area to the average sound intensity of the background area is used; a larger value indicates a higher degree of sound intensity concentration. Sound intensity and output wave field amplitude satisfy a square relationship, i.e. I =| U |²; Therefore, for Figure 2 and Figure 3 The maximum amplitude normalization method is used to display that the square of the normalized amplitude is equal to the sound intensity distribution obtained by normalizing to the maximum sound intensity.

[0034] S4, with joint loss function Minimize as the optimization objective, so that N Each reused state participates in the optimization calculation, and the parameters to be optimized are updated synchronously during the optimization process until the first optimal phase distribution of the first diffraction layer 2 and the second optimal phase distribution of the second diffraction layer 3 are obtained. Each iteration calculates the predicted output acoustic intensity distribution for the four multiplexed states, then summarizes the joint loss function and updates the two-layer phase distribution simultaneously. (Weight of the acoustic intensity separation term) γ The value is set to 35; the Adam optimizer is used, with an initial learning rate of 0.0005, a maximum number of iterations of 50, and both phase distributions are constrained to [0, 2]. π )Inside.

[0035] S5, based on the sound velocity of the background propagation medium, the sound velocity of the diffraction layer solid material, and the operating frequency, the first optimal phase distribution and the second optimal phase distribution are converted into the first total solid thickness distribution and the second total solid thickness distribution, respectively, and the passive phase modulation structure parameters of the first diffraction layer 2 and the second diffraction layer 3 are determined accordingly. In step S5, the sound velocity in the diffraction layer solid material... c p Greater than the speed of sound in the background propagation medium c 0; will the first iAny lateral coordinate position in the optimal phase distribution of the diffraction layer ( x , y The phase modulation at point ) is expressed as and will the i Lateral coordinate position in the optimal phase distribution of the diffraction layer ( x , y The total thickness of the solid at point ) is expressed as Then calculate the first according to formula (4). i Lateral coordinate position in the optimal phase distribution of the diffraction layer ( x , y Total thickness of the solid at ) , i =1,2: (4) In equation (4), The thickness of the uniform support substrate; where the left side of equation (4) represents the total thickness of the entity including the uniform support substrate, and the fractional term on the right side of equation (4) represents the phase modulation height. k 0 and k p These are the wavenumbers in the background propagation medium and the diffraction layer material, respectively. k 0=2 πf 0 / c 0, k p =2 πf 0 / c p .

[0036] The total thickness of the solid is calculated according to equation (4), and the minimum thickness of the total thickness distribution of the solid is the thickness of the uniform support base. In this embodiment =0.5 mm. The background propagation medium is water. Take 2 MHz, Take 1500 m / s, Take 1000 kg / m 3 ; Diffraction layer solid material =2400 m / s =1200 kg / m 3 Complete coverage 2 π The phase modulation height difference required for the phase range is approximately 2.0 mm, therefore the total thickness of the solid body ranges from approximately 0.5 to 2.5 mm.

[0037] Adopting based on kCross-validation was performed using a three-dimensional k-Wave model based on the spatial pseudospectral method: the transverse grid spacing was 0.5 mm, the axial grid spacing was 0.25 mm, and the phase modulation height range of 0–2.0 mm was discretized into 8 equal levels, corresponding to a total solid thickness range of approximately 0.5–2.5 mm; the absorption coefficients of water and the diffraction layer solid material were taken as 0.0022 dB·MHz. -2 ·cm -1 and 3 dB·MHz -2 ·cm -1 The power-law exponents are all 2, and the CFL number is 0.22. During cross-validation, the phase distribution is not re-optimized; instead, the same sound source, configuration order, rotation angle, and propagation distance as used in the band-limited spectral propagation model are employed to verify the relationship between the four multiplexed states and their corresponding output sound fields.

[0038] like Figure 2 As shown, the normalized amplitude distributions of the four multiplexing states obtained from the band-limited spectral propagation model range from 0 to 3. The four average indices are: MSE = 0.02070, PCC = 0.8206, PSNR = 16.93 dB, and CR = 81.54; the PCC range for each multiplexing state is 0.7886–0.8386, and the CR ranges from 64.12 to 89.75. Figure 3 As shown, the normalized amplitude distribution obtained by the three-dimensional k-Wave model maintains the correspondence between the digits 0 to 3 and the four multiplexed states, and the main outlines of the digits 0 to 3 are preserved.

[0039] In this embodiment, an electronic device includes a memory and a processor. The memory stores a program that supports the processor in executing the above-described method, and the processor is configured to execute the program stored in the memory.

[0040] In this embodiment, a computer-readable storage medium stores a computer program, which is executed by a processor to perform the steps of the above method.

Claims

1. A design method for an acoustic holographic system based on rotation and layer sequence multiplexing, characterized in that, Includes the following steps: S1, with the center of the input plane (1) as the origin and the direction of sound propagation as the main axis of propagation, establish mutually orthogonal points in a plane perpendicular to the direction of the main axis of propagation. x Axial direction and y Axial direction; This constitutes a three-dimensional rectangular coordinate system; An acoustic holographic system is established, comprising: an input plane (1), a first diffraction layer (2), a second diffraction layer (3), and a receiving plane (4); and a first cascade position and a second cascade position are sequentially set along the main propagation axis; wherein, the first diffraction layer and the second diffraction layer represent fixed diffraction layer entities, and the first cascade position and the second cascade position represent fixed spatial positions along the main propagation axis, and the meanings of the diffraction layer number and the cascade position number are independent of each other; the layer order referred to in this paper refers to the configuration order of the two diffraction layers at the above two cascade positions; set up N Each multiplexing state is defined by the arrangement order of the first diffraction layer (2) and the second diffraction layer (3) at the first cascade position and the second cascade position, and the rotation angle of the diffraction layer at the second cascade position around the propagation axis. When the first diffraction layer (2) is set at the first cascade position, the second diffraction layer (3) is set at the second cascade position and is recorded as the first state group; When the first diffraction layer (2) is set in the second cascade position, the second diffraction layer (3) is set in the first cascade position and is recorded as the second state group; The input plane (1) is set in close contact with the incident surface of the diffraction layer at the first cascade position. The input wave field on the input plane (1) is directly loaded onto the incident surface, and there is no independent free propagation interval between the two. The distance between the exit surface of the diffraction layer in the first cascade position and the incident surface of the diffraction layer in the second cascade position is defined as the interlayer propagation distance. d 1. And set the space between the two as the first propagation interval; The distance between the exiting surface of the diffraction layer in the second cascade position and the receiving plane (4) is set as the output propagation distance. d 2, and the space between the two is set as the second propagation interval; Preset on the receiving plane (4) and N Each reuse state corresponds to one-to-one N Each target output sound intensity distribution has a corresponding effective signal region. The first phase distribution of the first diffraction layer (2) and the second phase distribution of the second diffraction layer (3) are set as parameters to be optimized. S2, determine the phase distribution at the first and second cascade positions based on the configuration order and rotation angle corresponding to each multiplexing state; wherein the first and second phase distributions are fixedly corresponding to the first and second diffraction layers, respectively; perform forward propagation calculation on the input wave field under the current first and second phase distributions, so that the input wave field sequentially passes through the phase modulation at the first cascade position and the interlayer propagation distance. d The propagation corresponding to 1, the phase modulation at the second cascade position, and the output propagation distance d The propagation corresponding to 2 is carried out, thereby obtaining the predicted output acoustic intensity distribution corresponding to the corresponding multiplexing state on the receiving plane (4); S3, set the target effective signal region of the corresponding target output acoustic intensity distribution in each multiplexing state as the target region of the corresponding multiplexing state, and set the part of the discrete calculation region of the receiving plane (4) other than the target region as the background region; according to N The predicted output sound intensity distribution and its corresponding N A joint loss function is constructed from the output sound intensity distribution of each target. Joint loss function Includes: a sound intensity squared error term used to constrain the difference between the normalized predicted output sound intensity distribution and the corresponding target output sound intensity distribution. L MSE And a sound intensity separation term used to constrain the ratio of the average sound intensity of the background region to the average sound intensity of the target region. L sep ; S4, with joint loss function Minimize as the optimization objective, so that N Each reused state participates in the optimization calculation and updates the parameters to be optimized synchronously during the optimization process until the first optimal phase distribution of the first diffraction layer (2) and the second optimal phase distribution of the second diffraction layer (3) are obtained. S5. Based on the sound velocity of the background propagation medium, the sound velocity of the diffraction layer material, and the operating frequency, the first optimal phase distribution and the second optimal phase distribution are converted into the first total thickness distribution and the second total thickness distribution of the material, respectively, so as to determine the passive phase modulation structure parameters of the first diffraction layer (2) and the second diffraction layer (3).

2. The design method according to claim 1, characterized in that, Forward propagation calculations employ a band-limited spectral propagation model; and equations (1a)-(1e) are used to predict the first... k Sound intensity distribution of the multiplexed output: (1a) (1b) (1c) (1d) (1e) In equations (1a)-(1e), k An index for the reuse status; For any horizontal coordinate position perpendicular to the main propagation axis; j Φ is the imaginary unit. A,k ( x , y ) and Φ B,k ( x , y ) are respectively the first k In the multiplexing state, the horizontal coordinate position is at the first cascade position and the second cascade position. Phase distribution at; U in ( x , y () represents the horizontal coordinate position. Input fluctuation field at the location; U 1,k ( x , y () represents the lateral coordinate position after phase modulation at the first cascade location. The fluctuation field at that location; U prop1,k ( x , y () represents the interlayer propagation distance d 1. Lateral coordinate position after propagation The fluctuation field at that location; U 2,k ( x , y () indicates the lateral coordinate position after phase modulation at the second cascaded position. The fluctuation field at that location; U out,k ( x , y ) is the first k The horizontal coordinate position of each multiplexing state on the receiving plane (4) The output fluctuation field at that location; I raw,k ( x , y () represents the lateral coordinate position on the receiving plane (4). The unnormalized predicted output sound intensity characterization at the location; the above U in U 1,k U prop1,k U 2,k and U out,k Both represent the complex sound pressure level; F and F -1 These are the Fourier transform and the inverse Fourier transform, respectively. f x and f y respectively along x Axial direction and y Spatial frequency components along the axial direction; H ( ) is the angular spectrum propagation transfer function, which is obtained from equation (2); B( ) is the band-limited window function, which takes the value 1 when both the propagation condition λ²(fx²+fy²)≤1 and the non-aliasing sampling condition of the current discrete grid are satisfied, and takes the value 0 otherwise. Its frequency boundary is determined by the transverse sampling interval, the calculation window size and the propagation distance d. (2) In equation (2), For the propagation distance, and ∈{ d 1, d 2}; λ The operating wavelength in the background propagation medium, and λ = c 0 / f 0, c 0 represents the speed of sound in the background propagation medium. f 0 represents the operating frequency.

3. The design method according to claim 2, characterized in that, Joint loss function Construct according to equations (3a)-(3e): (3a) (3b) (3c) (3d) (3e) In equations (3a)-(3e), D is the discrete computational region of the receiving plane (4). M This represents the number of pixels within the discrete computation region D. I norm,k ( x , y )express I raw,k ( x , y The predicted output acoustic intensity distribution is obtained by performing minimum-maximum normalization for each multiplexing state; the maximum and minimum values ​​of the normalization are both obtained within the discrete computation region D, and when the maximum value equals the minimum value, the corresponding normalization result is set to zero. I target,k ( x , y () represents the horizontal coordinate position. Normalized to the [0,1]th position k The output sound intensity distribution of each target; Ω k For the first k The effective signal region of the target output sound intensity distribution; and The first k Each reuse state is in Ω k Unnormalized average sound intensity within the inner and background regions; ε is a positive number that prevents the denominator of the sound intensity separation term from being zero and has the same dimension as the unnormalized average sound intensity; γ The weighting coefficients for the sound intensity separation term are greater than 0.

4. The design method according to claim 1, characterized in that, In the first state group, different rotation angles are applied to the second diffraction layer at the second cascade position to determine each multiplexing state; In the second state group, different rotation angles are applied to the first diffraction layer at the second cascade position to determine each multiplexing state; The rotation angle is selected from a set of orthogonal rotation angles, which includes 0°, 90°, 180°, and 270°. All rotations are based on the propagation axis corresponding to the center of the input plane, with clockwise as the positive direction when viewed along the sound propagation direction, and the center of the input plane as the center of the lateral coordinate rotation.

5. The design method according to claim 1, characterized in that, Velocity of sound in diffraction layer solid material c p Greater than the speed of sound in the background propagation medium c 0; will the first i Any lateral coordinate position in the optimal phase distribution of the diffraction layer ( x , y The phase modulation at point ) is expressed as and the first i Lateral coordinate position in the optimal phase distribution of the diffraction layer ( x , y The total thickness of the solid at point ) is expressed as Then calculate the first according to formula (4). i Lateral coordinate position in the optimal phase distribution of the diffraction layer ( x , y Total thickness of the solid at ) , i =1,2: (4) In equation (4), h0 is the thickness of the uniform support substrate; where the left side of equation (4) represents the total thickness of the solid including the uniform support substrate, and the fractional term on the right side of equation (4) represents the phase modulation height. k 0 and k p These are the wavenumbers in the background propagation medium and the diffraction layer material, respectively. k 0=2 πf 0 / c 0, k p =2 πf 0 / c p .

6. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store a program that supports a processor in executing the method of any one of claims 1-5, the processor being configured to execute the program stored in the memory.

7. A computer-readable storage medium storing a computer program thereon, characterized in that, The computer program is executed by the processor to perform the steps of the method according to any one of claims 1-5.

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