阅读说明：本技术 基于散射声场分离算法在浅海信道中测量方法 (Method for measuring shallow sea channel based on scattering sound field separation algorithm ) 是由 肖妍 李金凤 商德江 赵明月 于 2021-09-15 设计创作，主要内容包括：本发明公开了基于散射声场分离算法在浅海信道中测量方法,包括以下步骤：建立基于弹性结构的浅海信道散射声场模型,采用双层柱面阵列进行声压数据采样,提取浅海信道中两同轴柱形全息面上的复声压数据。提取两柱形全息面数据,计算全息面声压角谱。采用柱面声场分离技术对两柱形测量全息面声压数据进行分解,分离得到散射声场。重构散射声场,计算声场重构误差。对重建面的声压角谱进行波数域加窗,对加窗后的重建声压角谱进行傅里叶逆变换获得重建面声压。通过有限元软件对声场进行仿真,获取更为精准的两柱形全息面复声压数据,通过声场分离算法,有效的分离得到入射声和散射声,重构散射声场。(The invention discloses a method for measuring in a shallow sea channel based on a scattering sound field separation algorithm, which comprises the following steps: a shallow sea channel scattering sound field model based on an elastic structure is established, sound pressure data sampling is carried out by adopting a double-layer cylindrical surface array, and complex sound pressure data on two coaxial cylindrical holographic surfaces in a shallow sea channel are extracted. And extracting the data of the two cylindrical holographic surfaces and calculating the sound pressure angle spectrum of the holographic surface. And decomposing the sound pressure data of the two cylindrical measurement holographic surfaces by adopting a cylindrical sound field separation technology, and separating to obtain a scattering sound field. And reconstructing a scattering sound field and calculating a sound field reconstruction error. And windowing the sound pressure angle spectrum of the reconstruction surface in a wave number domain, and performing Fourier inverse transformation on the windowed reconstruction sound pressure angle spectrum to obtain the sound pressure of the reconstruction surface. The sound field is simulated through finite element software, more accurate complex sound pressure data of the two cylindrical holographic surfaces is obtained, incident sound and scattered sound are effectively obtained through separation of a sound field separation algorithm, and the scattered sound field is reconstructed.)

1. The method for measuring in the shallow sea channel based on the scattering sound field separation algorithm is characterized by comprising the following steps:

the method comprises the following steps: establishing a shallow sea channel scattering sound field model based on an elastic structure, sampling sound pressure data by adopting a double-layer cylindrical surface array, and extracting complex sound pressure data on two coaxial cylindrical holographic surfaces in a shallow sea channel;

step two: extracting two cylindrical holographic surface data, and calculating a holographic surface sound pressure angle spectrum;

step three: decomposing the sound pressure data of the two cylindrical measurement holographic surfaces by adopting a cylindrical sound field separation technology, and separating to obtain a scattering sound field;

step four: reconstructing a scattering sound field, calculating a sound field reconstruction error, windowing a sound pressure angle spectrum of a reconstruction surface in a wave number domain, and performing Fourier inverse transformation on the windowed reconstruction sound pressure angle spectrum to obtain the sound pressure of the reconstruction surface.

2. The method for measuring in shallow sea channel based on scattered sound field separation algorithm as claimed in claim 1, wherein the step one is to combine the model to be analyzed and the finite space three-dimensional size to establish the elastic structure shallow sea channel sound field model and to perform meshing, and the water area mesh is to perform meshing by using free tetrahedral mesh according to the rule of not less than six points in one wavelength.

3. The method for measuring in shallow sea channel based on scattered sound field separation algorithm according to claim 1, wherein step two is defined as a medium which is continuous and has no energy consumption problem in the process of moving for an ideal fluid medium, and the propagation law equation of sound wave in the ideal fluid medium under the three-dimensional environment is expressed as three basic equations:

in the formulae (1) and (2), ρ₀Representing the propagation medium density in acoustics; in the formula (3), ρ' is an excess of density, which indicates a difference between the density in the presence and absence of a sound field in the medium, and is a physical variable related to time and space. C in formula (3)₀Representing the speed of sound propagation within the medium; in the expressions (1) and (2), v and p represent the particle vibration velocity and the sound pressure in the sound field, respectively.

4. The scattered sound field separation algorithm-based method for measuring in shallow sea channels according to claim 1, wherein the scattered field excited by the sound source in step three and the scattered sound field excited by the boundary reflection are regarded as the scattered sound field of the target, and the sound source has a sound source 1 and a sound source 2, and the two sound sources are distributed on both sides of the two holographic surfaces.

5. The method for measuring in shallow sea channel based on scattered sound field separation algorithm according to claim 1, wherein the step four performs windowing process on the continuous sound pressure signal to reduce the spectrum leakage error generated by finite truncation of the continuous sound pressure signal during the reconstruction of the cylindrical near-field acoustic hologram.

6. The method for measuring in shallow sea channel based on the scattered sound field separation algorithm according to claim 1, wherein in the calculation process of the reconstruction in the fourth step, the wave number domain is windowed to filter out high wave number errors, wherein the adopted filter is a low-pass circularly symmetric index filter:

wherein the content of the first and second substances,α is a steepness factor of the window function; k is a radical of_cTo cut off the beam.

Technical Field

The invention relates to a measuring method for target identification in a shallow sea channel in the field of acoustic holography, in particular to a measuring method in the shallow sea channel based on a scattering sound field separation algorithm.

Background

The acoustic holography is an acoustic imaging technology formed by introducing the holography theory to the acoustic field, and is divided into the following steps according to different imaging distances: near-field acoustic holography, far-field acoustic holography, conventional acoustic holography. Compared with the traditional holographic technology, the near-field acoustic holography not only contains far-field propagation wave components but also contains near-field evanescent wave components due to the selection of the position of the measuring surface, so that the limitation of Rayleigh distance is broken through, and a noise source and a visual space sound field can be accurately identified. Due to the advantages and the characteristics, the near-field acoustic holography has wide application prospect in the aspect of sound source analysis, and becomes one of important methods for identifying and positioning a noise source. The core of the near-field acoustic holography technology is a holographic transformation algorithm thereof. The basic principle is that acoustic quantities such as sound pressure or vibration speed of a target radiation sound field obtained by matrix measurement are utilized, and different reconstruction algorithms are utilized to carry out visual reconstruction or prediction on the sound field.

The conventional near-field acoustic holography has strict requirements on the environment, and requires that sound sources are all on the same side of a measuring surface, and the other side of the measuring surface is in a free-field environment. And in the measuring environment of actual engineering, the method is difficult to guarantee. At this time, the reconstruction result is difficult to guarantee due to interference of reflection, scattering and the like of other targets, and even the judgment is completely influenced. Therefore, research into NAH technology for non-free fields is becoming an increasingly critical issue.

For the problem of target sound scattering, the most original is an integral equation method, the basic principle of which is a Helmholtz integral formula, a scattering sound field of a target with any complex shape can be theoretically calculated, but the integral equation is difficult to solve, but has obvious defects of instability of solution and huge calculation amount. Rayleigh provides a separation variable, and a simple series is solved by combining boundary conditions, so that the method can provide a strict analytic solution for infinite-length cylinders, spheres and the like and is only suitable for regular shape targets, and in addition, the solution of the method is in an infinite series form, so that the convergence ratio of the solution is poor. The strict theoretical solutions that have been proposed are only applicable to some simple targets. Thus, for the scattered sound field calculation of complex targets, a variety of numerical and approximation solutions have emerged. Such as: t matrix method, physical acoustic calculation method, bright spot model and plate element theory. The finite element method is a very common numerical calculation method, and the calculation is completed by carrying out discretization approximation and linear superposition on the regions, but when the problem of a scattering sound field is separately processed, particularly when a complex large-size target and high-frequency calculation is carried out, the calculation speed is low, and the requirement on computer hardware is high. Compared with a finite element method, the boundary element method has high calculation precision and reduced calculation amount, but is faced with inverse calculation of a large-order matrix, so that the modeling of the target with a complex shape is very difficult.

Disclosure of Invention

The invention aims to provide a method for measuring in a shallow sea channel based on a scattering sound field separation algorithm, which effectively separates incident sound and scattering sound through the sound field separation algorithm to reconstruct a scattering sound field. A new research approach is provided for solving the problems of analyzing and measuring the characteristics of the target scattering sound field so as to solve the problems in the background technology.

In order to achieve the purpose, the invention provides the following technical scheme:

the method for measuring in the shallow sea channel based on the scattering sound field separation algorithm comprises the following steps:

the method comprises the following steps: establishing a shallow sea channel scattering sound field model based on an elastic structure, sampling sound pressure data by adopting a double-layer cylindrical surface array, and extracting complex sound pressure data on two coaxial cylindrical holographic surfaces in a shallow sea channel;

step two: extracting two cylindrical holographic surface data, and calculating a holographic surface sound pressure angle spectrum;

step three: decomposing the sound pressure data of the two cylindrical measurement holographic surfaces by adopting a cylindrical sound field separation technology, and separating to obtain a scattering sound field;

step four: and reconstructing a scattering sound field and calculating a sound field reconstruction error. And windowing the sound pressure angle spectrum of the reconstruction surface in a wave number domain. And carrying out Fourier inverse transformation on the windowed reconstructed sound pressure angle spectrum to obtain reconstructed surface sound pressure.

And further, combining a model to be analyzed and the three-dimensional size of the finite space, establishing a shallow sea channel sound field model of the elastic structure, and performing grid division, wherein the water area grid adopts a free tetrahedral grid to perform grid division according to the rule that no less than six points in one wavelength.

Further, step two defines an ideal fluid medium as a medium which is continuous and has no energy consumption problem in the process of movement, and the propagation law equation of sound waves in the ideal fluid medium in a three-dimensional environment is expressed as three basic equations:

in the formulae (1) and (2), ρ₀Representing the propagation medium density in acoustics; in the formula (3), ρ' is an excess of density, which indicates a difference between the density in the presence and absence of a sound field in the medium, and is a physical variable related to time and space. C in formula (3)₀Representing the speed of sound propagation within the medium; in the expressions (1) and (2), v and p represent the particle vibration velocity and the sound pressure in the sound field, respectively.

Further, the scattered field excited by the sound source in the step three and the scattered field excited by the boundary reflection are regarded as the scattered sound field of the target, the sound source is provided with a sound source 1 and a sound source 2, and the two sound sources are distributed on two sides of the two holographic surfaces.

Furthermore, the step four carries out windowing processing on the continuous sound pressure signals, and reduces the frequency spectrum leakage error generated by carrying out limited truncation on the continuous sound pressure signals in the reconstruction process of the cylindrical surface near-field acoustic holography.

Further, windowing is performed on the wave number domain in the reconstruction calculation process in the step four, and high wave number errors are filtered, wherein the adopted filter is a low-pass circularly symmetric exponential filter:

wherein the content of the first and second substances,α is a steepness factor of the window function; k is a radical of_cTo cut off the beam.

Compared with the prior art, the invention has the beneficial effects that: according to the method for measuring the sound field in the shallow sea channel based on the scattering sound field separation algorithm, the sound field is simulated through finite element software, more accurate complex sound pressure data of the two cylindrical holographic surfaces is obtained, incident sound and scattering sound are effectively obtained through the sound field separation algorithm, and the scattering sound field is reconstructed. A new research approach is provided for solving the problems of analyzing and measuring the characteristics of the target scattering sound field.

Drawings

FIG. 1 is a flow chart of a method of the present invention;

FIG. 2 is a point sound source-elastic ball shallow sea channel scattering sound field model established in step one of the present invention;

FIG. 3 is a diagram showing the relationship between the sound source and the two measuring planes in step two of the present invention;

fig. 4(a) is a front view of sound pressure data extraction in the second step;

FIG. 4(b) is a view of the sound pressure data extracted in step two taken along the X-Z plane;

FIG. 5 is a plot of acoustic pressure versus contrast axis position selected in the present invention;

FIG. 6(a) shows a holographic surface distance target z_HWhen the distance is equal to 0.17m, the sound pressure amplitude of the target on the holographic surface 1 is compared;

FIG. 6(b) shows a holographic surface distance target z_HWhen the distance is equal to 0.2m, the sound pressure amplitude of the target on the holographic surface 2 is compared;

FIG. 6(c) shows a holographic surface distance target z_HWhen the sound source is equal to 0.17m, comparing the sound pressure amplitude of the sound source on the holographic surface 1;

FIG. 6(d) shows a holographic surface distance target z_HWhen the sound source is equal to 0.2m, the sound pressure amplitude of the sound source on the holographic surface 2 is compared;

FIG. 7(a) shows a holographic surface distance target z_HWhen the distance is equal to 0.17m, the sound pressure amplitude of the target on the holographic surface 1 is compared;

FIG. 7(b) shows a holographic surface distance target z_H0.2m, the target is holographicComparing the sound pressure amplitude on the surface 2;

FIG. 7(c) shows a holographic surface distance target z_HWhen the sound source is equal to 0.17m, comparing the sound pressure amplitude of the sound source on the holographic surface 1;

FIG. 7(d) shows a holographic surface distance target z_HWhen the sound source is 0.2m, the sound pressure amplitude of the sound source on the holographic surface 2 is compared.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

A method for measuring in a shallow sea channel based on a scattered sound field separation algorithm is shown in figure 1 and comprises the following steps:

the method comprises the following steps: and establishing a point sound source-elastic ball-based shallow sea channel scattering sound field model, and extracting complex sound pressure data on a holographic surface in a shallow sea channel.

Combining a model to be analyzed and a finite space three-dimensional size, establishing a point sound source-elastic sphere shallow sea channel sound field model, and when establishing a grid model, adopting finite element simulation software COMSOL to establish the model, as shown in figure 2, and carrying out grid division, wherein a grid of a water area adopts free tetrahedral grids to carry out grid division according to the rule of no less than six points in one wavelength, a in figure 2 represents an infinite soft boundary of a sea surface, b represents an infinite hard boundary of a sea bottom, c represents boundary reflection, d represents incident sound, e represents scattered sound, f represents scattered sound reflected by the boundary, g represents a sound source, and M represents a measurement matrix.

Step two: and extracting the data of the two cylindrical holographic surfaces and calculating the sound pressure angle spectrum of the holographic surface.

An ideal fluid medium can be generally defined as a medium that is continuous and does not present energy consumption problems during movement. In a three-dimensional environment, the propagation law equation of sound waves in an ideal fluid medium can be expressed as three nearest equations, and the expressions of the three nearest equations are as follows:

in the formulae (1) and (2), ρ₀Representing the propagation medium density in acoustics; in the formula (3), ρ' is an excess of density, which indicates a difference between the density in the presence and absence of a sound field in the medium, and is a physical variable related to time and space. C in formula (3)₀Representing the speed of sound propagation within the medium; in the expressions (1) and (2), v and p represent the particle vibration velocity and the sound pressure in the sound field, respectively.

The three equations (1), (2) and (3) are combined to obtain a medium-small amplitude wave fluctuation equation in the uniform and static ideal fluid:

v in the above formula (4)²For the Laplace operator, the functional relation expression based on the rectangular coordinate system is as follows:

if x is r cos θ and y is r sin θ, the Helmholtz equation may be converted from the rectangular coordinate system to the Laplace operator whose cylindrical coordinate system corresponds to the cylindrical coordinate system by the following expression:

solving a Helmholtz equation under a cylindrical coordinate system by using a separation variable method, firstly rewriting a partial differential equation into a form of a product of several ordinary differential equations, and assuming that the form of the equation solution can be written as:

p(r,θ,z)＝R(r)Θ(θ)Z(z) (7)

the Helmholtz equation in the cylindrical coordinate system can be obtained:

in the formula (8), the first term in parentheses is related to only the variables R and θ, the second term in parentheses is related to only the variable Z, and the independent variable R appears only in R, the independent variable θ appears only in Θ, and the independent variable Z appears only in Z, that is, the independent variables R, θ, Z are three variables independent of each other. If the equation is to be true, it must be satisfied that the terms in the two brackets are both constants. Then, these two constants are respectively denoted as k_zAnd k_rIs provided with

Wherein constant k_rSatisfy the requirement of

At the same time, can be rewritten as

If the above equation (12) is satisfied, the condition that the terms on the left and right sides of the equation are both constant is also satisfied, and therefore, the constant n is selected²Let it satisfy the following equation

Substituting the above expression (13) into the equation and dividing by r on both sides of the equation²R, can be obtained

The equation is a Bessel equation.

As can be seen from the knowledge of mathematical physics equations, the solution of the Bezier equation comprises a first class of Bezier functions J_n(k_rr) and Bessel function Y of the second type_n(k_rr), wherein the Bessel function of the second type, also called Newman function, may be given the notation N_nAnd (4) performing representation. The solution can be made by a linear combination of a first type of Bezier equation and a second type of Bezier equation

R(r)＝C₁J_n(k_rr)+C₂Y_n(k_rr) (15)

Expressed, the equation (15) represents a standing wave solution of the Bessel equation, where C₁、C₂Is an arbitrary constant.

The travelling wave general solution expression of the Bessel equation needs to be linearly expressed by a first-class Hankel function and a second-class Hankel function

Wherein the Hankel function of the first kindCorresponding to outwardly diverging waves, Hankel functions of the second kindCorresponding to inwardly converging waves.

In whichSelect k_zThere is no limitation on the time, however, in the discussion above, defaultsNamely have

When k is_zWhen > k, k_rShould be written asIs an imaginary number, and should be rewritten as a modified bessel equation.

The solution of this equation may be defined by a first class of modified Bessel function I_n(k′_rr) and a second class of modified Bessel function K_n(k′_rr) linear representation in whichIt should be noted that the modified Bessel function K of the second kind_n(k′_rr) the modification results corresponding to the first type of hankerr function, and the modified bessel function of the first type corresponds to the modification results of the hankerr function of the second type.

Summarizing the above analysis and derivation, the general solution expression of Helmholtz equation under the cylindrical coordinate system can be obtained as

In the formula (18), D₁(k_zz) and D)₂(k_zz) can be any constant.

Will P_n(r,k_z) Defined as the spatial Fourier transform of the sound pressure at position r with respect to the circumferential and axial variables θ and z, i.e. the cylindrical wave number spectrum:

step three: and decomposing the measured holographic surface sound pressure data by adopting a cylindrical surface sound field separation technology, and separating to obtain a scattering sound field.

The bi-cylindrical sound field separation, as the name implies, needs two holographic measurement cylindrical surfaces when applying the technology, and the spatial distribution of the holographic surface and the sound source is as shown in fig. 3 below.

In FIG. 3, S_H1And S_H2Respectively, radius is r_H1And r_H2The holographic cylindrical surface of (1) has two sound sources, respectively A and B, in the analysis space, wherein A represents a sound source 2, B represents a sound source 1, the two sound sources are distributed on two sides of the two holographic surfaces, and the sound source 1 is distributed on the holographic cylindrical surface S_H1Inside, the sound source 2 is located in the holographic cylinder S_H2Besides, according to the superposition principle of sound fields, the total sound field on the holographic surface is the sum of the radiation sound fields of the two sound sources and can be recorded as

p(r_H1,θ,z)＝p^I(r_H1,θ,z)+p^II(r_H1,θ,z) (20)

p(r_H2,θ,z)＝p^I(r_H2,θ,z)+p^II(r_H2,θ,z) (21)

In formulae (20) and (21), p^I(r_H1θ, z) and p^II(r_H1θ, z) respectively represent the sound source 1 and the sound source 2 on the holographic cylinder S_H1The value of the sound pressure generated, p^I(r_H2θ, z) and p^II(r_H2θ, z) respectively represent the sound source 1 and the sound source 2 on the holographic cylinder S_H2The value of the sound pressure generated.

The sound pressure in the wave number domain can be obtained by performing spatial Fourier transform on the sound pressure in the spatial domain, namely the cylindrical spectrum of the sound wave, and the sound pressure in the wave number domain can be obtained by performing spatial Fourier transform on the sound pressure in the spatial domain:

according to the near-field acoustic holography theory, the sound pressure cylindrical wave spectrums between different cylindrical surfaces have a certain conversion relation, so that an expression which describes that the same sound source is arranged on the holographic surface S can be obtained_H1And a holographic surface S_H2Relationship of cylinder spectrum of sound pressure generated above:

by combining the above equations (24) and (25), the sound source 1 can be solved on the holographic surface S_H1And S_H2Generated sound pressure spectrum and sound source 2 on hologram surface S_H1And S_H2The generated sound pressure spectrum has the following specific formula:

step four: and reconstructing a scattering sound field and calculating a sound field reconstruction error. And windowing the sound pressure angle spectrum of the reconstruction surface in a wave number domain. And carrying out Fourier inverse transformation on the windowed reconstructed sound pressure angle spectrum to obtain reconstructed surface sound pressure.

In the actual operation process of the holographic measurement surface, the sound pressure signal at a discrete point of a certain area on the holographic surface can only be selected in the holographic aperture, that is, a finite truncation is performed on the continuous sound pressure signal, so a spectrum leakage error is generated in the reconstruction process of the near-field acoustic holography, and the condition is generally called as a "finite aperture effect" or a "window effect". The "finite aperture effect" is the sound pressure angle spectrum P (k) on the holographic surface_x,k_y,z_H) The main cause of calculation errors.

Discrete Fourier transforms have a process of wave-number domain sampling in which "wrap-around errors," also commonly referred to as aperture repeat effects, occur. The inclusion of the above errors leads to distortion of the reconstruction result.

The reconstruction process is very sensitive to errors of spatial frequency, so that appropriate measures must be taken to suppress interference of errors of high spatial frequency components, and an effective method is to window a wave number domain in the calculation process and filter out high wave number errors. Among them, the most commonly used filter is a low-pass circularly symmetric exponential filter:

wherein the content of the first and second substances,α is a steepness factor of the window function; k is a radical of_cTo cut off the beam.

The beneficial effects of the invention are verified as follows:

the method is subjected to a simulation experiment under the conditions of COMSOL numerical calculation and MATLAB simulation:

the simulation parameters are as follows:

verifying and simulating a plastic spherical shell of a channel:

the target spherical shell is made of PVC material with the density of 1380kg/m³PoissonRatio 0.31, Young's modulus 3.5X 10⁹Pa

The radius r of the sphere is 0.15m, and the center of the spherical shell with the thickness of 0.01m is positioned at the origin.

The point sound source position: (0.5,0,0).

Setting a channel environment: 12.8m 5 m.

Parameters of the fluid medium: water, density 1000kg/m³The speed of sound is 1500 m/s.

Model boundary conditions: the upper boundary of the model is an interface of the water surface and the air, and is an absolute soft boundary, the reflection coefficient is-1, the lower boundary is an absolute hard boundary, and the reflection coefficient is 1.

Calculating the frequency: f is 200Hz-2 kHz.

Holographic surface measurement parameters: and rectangular cylindrical holographic surfaces, wherein the axial height L of the holographic surfaces is 4m, the circumferential angle interval is 10 degrees, the axial sampling interval dz is 0.04m, and the distances from the holographic surfaces to the center of the target sphere are 0.17m, 0.20m, 0.25m, 0.30m, 0.35m, 0.40m and 0.45 m.

Distance of reconstruction surface from center of target sphere: 0.17m and 0.20 m.

The sound pressure data extraction is shown in fig. 4, fig. 4(a) is a front view of sound pressure data extraction, fig. 4(b) is a view of an X-Z plane of sound pressure data extraction, fig. 5 is a graph of selected sound pressure values versus axial positions, and the axial sound pressure simulation result is shown in fig. 6, wherein fig. 6(a) is a graph of a holographic plane distance from a target Z_HWhen the value is 0.17m, the sound pressure amplitude of the target at the holographic surface 1 is compared. FIG. 6(b) shows a holographic surface distance target z_HWhen the target is 0.2m, the sound pressure amplitude of the target on the holographic surface 2 is compared. FIG. 6(c) shows a holographic surface distance target z_HWhen the sound source is 0.17m, the sound pressure amplitude of the sound source is compared at the holographic surface 1. FIG. 6(d) shows a holographic surface distance target z_HWhen the sound source is 0.2m, the sound pressure amplitude of the sound source on the holographic surface 2 is compared.

Wherein FIG. 7 is a three-dimensional effect contrast diagram, and FIG. 7(a) is a holographic surface distance target z_HWhen the value is 0.17m, the sound pressure amplitude of the target at the holographic surface 1 is compared. FIG. 7(b) shows a holographic surface distance target z_HWhen the target is 0.2m, the sound pressure amplitude of the target on the holographic surface 2 is compared. FIG. 7(c) shows a holographic surface distance target z_HWhen the sound source is 0.17m, the sound pressure amplitude of the sound source is compared at the holographic surface 1. FIG. 7(d) shows a holographic surface distance target z_HWhen the thickness is equal to 0.2m,the sound pressure amplitude of the sound source on the holographic surface 2 is compared.

The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be able to cover the technical solutions and the inventive concepts of the present invention within the technical scope of the present invention.