CN101256234A - Method for modeling lens sound field - Google Patents

Abstract

The invention provides a modeling method of lens sound field, comprising: initializing the parameter definition; establishing coordinate system; calculating the refraction angle of sound wave and amplitude, phase of sound pressure based on ray property of sound wave; further calculating complex sound pressure of each point on the first surface; calculating complex sound pressure of each point in the second concave of lens; calculating the refraction angle of interface and amplitude, phase of sound pressure after sound wave emitting based; calculating the complex sound pressure of each point on the second surface; calculating the sound pressure field of the back of the lens. The said method more adequately considers the wave property of sound property of sound wave on the based of considering ray property and sound property of sound wave, with higher computation speed. The invention lucubrates the establishing method of lens sound field model and presents emulational computer result.

Description

A kind of method for modeling lens sound field

(1) technical field

What the present invention relates to is a kind of modeling method of sound field.The method for building up of the sound-field model behind specifically a kind of sound wave scioptics.

(2) background technology

The high-resolution imaging sonar survey under water with marine resources development in have widely and to use.Utilizing sound lens to carry out wave beam formation is a kind of new wave beam formation method, can obtain higher resolution with smaller volume and power consumption.

In the designing and developing of lens sonar, a key link is after analyzing the sound wave scioptics, focuses on the position of focus, and sonar performance index such as resolution, secondary lobe, detection angle of release.In design and theoretical analysis stage, these indexs can and can only obtain by the mathematical model of calculating lens sound field.Kevin Fink, Computer Simulation of Pressure Fields Generated by Acoustic LensBeamformers, University of Washington, 1994[D] and Bian Hongyu, Sang Enfang etc., Simulation research on acoustic lens beamforming, Harbin Engineering University's journal has been introduced the method that the mixture model that utilizes ray acoustics and wave acoustics to constitute carries out the sound field modeling in 2004.1 the list of references.But these methods also exist some to need improvements, have not for example considered the undulatory property of sound wave fully, can not adapt to well lens sound field is carried out modeling and simulation etc.

(3) summary of the invention

The object of the present invention is to provide a kind of undulatory property of considering sound wave more fully, can carry out the method for modeling lens sound field of modeling and simulation better to lens sound field.

The object of the present invention is achieved like this:

8) initial parameter definition, the frequency and the acoustic pressure amplitude of definition sound wave, the parameters,acoustic of external agency and sound lens;

9) setting up coordinate system, is the x axle with the thickness direction of sound lens, when calculating the sound field of lens inside, is initial point O with the center of front interface ₁, arbitrfary point Q is so that (x, r represent that θ) wherein x was the some Q plane vertical with the x axle and the intersection point x of x axle in the space ₁Apart from O ₁Distance, r is Qx in this plane ₁The length of line segment, θ is Qx in this plane ₁The straight line and the angle of direction vertically upward; When calculating the sound field of lens outside, initial point O ₂Be positioned at the plane that the edge surrounded of lens rear interface and the intersection point of x axle, other definition is the same;

10) sound wave is injected lens from external agency by the front interface of lens, according to the refractive direction of the ray calculating sound wave of sound wave and amplitude, the phase place of acoustic pressure;

11) cross O ₁Plane perpendicular to x is designated as plane 1, further calculates the multiple acoustic pressure of each point on the plane 1;

12) every bit on the plane 1 is regarded as sphere wavelet source,, calculated the multiple acoustic pressure of the inner each point of second concave surface of lens according to the undulatory property of sound wave;

13) penetrate the refraction angle of rear interface and amplitude, the phase place of acoustic pressure according to ray calculating sound wave once more;

14) cross O ₂Plane perpendicular to x is designated as plane 2, calculates the multiple acoustic pressure of each point on the plane 2;

8) calculate the sonic pressure field at lens rear portion according to the 5th method that goes on foot.

In the lens sonar design process, must on the basis of calculating the lens sound field distribution, analyze parameters such as focal position, main lobe width, beam pattern, these parameters are inseparable with sonar detection resolution with the sound lens design.Method of the present invention is considered in original method to have considered the undulatory property of sound wave more fully, and had higher computing velocity on the basis of the ray of sound wave and undulatory property simultaneously.The bright detailed method for building up of discussing the lens sound field model of we, and provided the simulation calculation result.Than original method, the bright undulatory property that begins to introduce sound wave from first interface of we, simulation result meets the truth of sound field more.Utilize method of the present invention not only can obtain sound field and distribute, can also obtain the important indicator of lens sonars such as focal position, main lobe width, beam pattern, established theoretical foundation for acoustic lens beamforming is applied to imaging sonar.

(4) description of drawings

Fig. 1, Fig. 2 are the coordinate system synoptic diagram;

Fig. 3 is the medium parameter synoptic diagram;

The sound field distribution plan that Fig. 4 goes out for simulation calculation.

(5) embodiment

For example the present invention is done description in more detail below in conjunction with accompanying drawing:

1. initial parameter definition

The frequency of definition sound wave is f, and initial amplitude is A0.

If sound wave enters medium 1 (Fig. 3) by medium 1 after by the sound lens of being made by medium 2 again.The density and the velocity of sound of definition medium 1 are ρ ₁, c ₁, the density of medium 2 and the velocity of sound are ρ ₂, c ₂, the acoustic attenuation coefficient in medium 1, the medium 2 is respectively α ₁, α ₂l ₁And l ₂Be respectively the physical path length of sonic propagation in medium 1 and medium 2.

2. set up coordinate system, for realizing the focusing of sound wave, lens are concavees lens.

When calculating the sound field of lens inside, be initial point O with the center of front interface ₁, be the x axle with the thickness direction of lens, arbitrfary point Q is so that (x, r represent that θ) wherein x was the some Q plane vertical with the x axle and the intersection point x of x axle in the space ₁Apart from the distance of initial point, r is Qx in this plane ₁The length of line segment, θ is Qx in this plane ₁The straight line and the angle of direction vertically upward; When calculating the sound field of lens outside, initial point O ₂Be positioned at behind the lens rear interface center, other definition the same (Fig. 1, Fig. 2) perpendicular to the plane of x axle.

3. according to the refractive direction and the multiple acoustic pressure of the ray calculating sound wave of sound wave

When if sound wave is injected medium 2 by medium 1, with O ₁The angle of x axle is β ₁, the incident angle of other positions can be obtained by the geometric configuration equation of lens.By top definition, the acoustic pressure of sound wave and the lens crossing point of axes Q1 of place is:

$p_1=(A_0-{\mathrm{\α}}_1{l}_1)\frac{\exp (-\mathrm{ik}{l}_1)}{l_1}$

Refraction angle β ₂Can calculate according to following formula:

$\frac{\sin {\mathrm{\β}}_1}{\sin {\mathrm{\β}}_2}=\frac{c_1}{c_2}$

Refraction coefficient when sound wave incides medium 2 by medium 1 can be expressed as:

${\mathrm{<figure-callout\; id="12"\; label="T"\; filenames="A20081006429200083.png"\; state="\{\{state\}\}">T</figure-callout>}}_{12}=\frac{2{\mathrm{\&rho;}}_2{c}_2\cos {\mathrm{\&beta;}}_1}{{\mathrm{\&rho;}}_2{c}_2\cos {\mathrm{\&beta;}}_1+{\mathrm{\&rho;}}_1{c}_1\cos {\mathrm{\&beta;}}_2}$

Incide in the lens, the acoustic pressure that Q2 is ordered is:

$p_2=p_1\&CenterDot;{\mathrm{<figure-callout\; id="12"\; label="T"\; filenames="A20081006429200083.png"\; state="\{\{state\}\}">T</figure-callout>}}_{12}=\frac{2{\mathrm{\&rho;}}_2{c}_2\cos {\mathrm{\&beta;}}_1}{{\mathrm{\&rho;}}_2{c}_2\cos {\mathrm{\&beta;}}_1+{\mathrm{\&rho;}}_1{c}_1\cos {\mathrm{\&beta;}}_2}(A_0-{\mathrm{\&alpha;}}_1{l}_1)\frac{\exp (-\mathrm{ik}{l}_1)}{l_1}$

Can calculate the acoustic pressure and the sound ray direction of the inner each point of lens front interface according to this.

4. cross O ₁Plane perpendicular to x is designated as plane 1, further calculates the multiple acoustic pressure of each point on the plane 1.

Can calculate the physical pathway of each point sonic propagation 1 process on the front interface according to the interface equation of lens, calculate the acoustic pressure and the direction of each point on the plane 1 thus to the plane.

5. calculate the multiple acoustic pressure of the inner each point of rear interface according to the undulatory property of sound wave.

Regarding the every bit on the plane 1 as sphere wavelet source, is center emission sphere wavelet with each wavelet source, is exactly the stack of these wavelets in the sound pressure amplitude of its anterior sonic pressure field, will consider their relative amplitude and phase place simultaneously.The amplitude of each wavelet is maximum on the direction of propagation of original wavefront, and minimum is 0 on its opposite direction.

The inner any point Q4 of lens rear interface (x ₄, r ₄, θ ₄) acoustic pressure located can be expressed as:

$P(x_4,r_4,{\mathrm{\&theta;}}_4)=-\frac{1}{2\mathrm{\&pi;}}{\&Integral;\&Integral;P}_3\frac{\&PartialD;}{\&PartialD;x}\left[\frac{\exp (-\mathrm{ikR}(r_3,{\mathrm{\&theta;}}_3,x_4,r_4,{\mathrm{\&theta;}}_4))}{R(r_3,{\mathrm{\&theta;}}_3,x_4,r_4,{\mathrm{\&theta;}}_4)}\right]\&CenterDot;r_{3}d{r}_3{\mathrm{d\&theta;}}_3$

Wherein:

P ₃Be Q3 on the plane 1 (0, r ₃, θ ₃) the multiple acoustic pressure at some place, calculate by the 4th step.

$k=\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}=\frac{2\mathrm{\&pi;f}}{c}$ Be wave number, λ is a wavelength, and c is the velocity of sound in the medium.

R is the distance between a Q4 and Q3.

Be the Green function of point source, it has described the interference point source as sonic pressure field.

Launch partial differential, integration becomes:

$P(x_4,r_4,{\mathrm{\&theta;}}_4)=\frac{1}{2\mathrm{\&pi;}}{\&Integral;\&Integral;P}_3\frac{(-\mathrm{ik}-\frac{1}{R})x_4\exp (-\mathrm{ikR}(r_3,{\mathrm{\&theta;}}_3,x_4,r_4,{\mathrm{\&theta;}}_4))}{R^2(r_3,{\mathrm{\&theta;}}_3,x_4,r_4,{\mathrm{\&theta;}}_4)}{r}_3{\mathrm{dr}}_3{\mathrm{d\&theta;}}_3$

Wave length of sound is bigger because R is relative, and following formula can be reduced to:

$P(x_4,r_r,{\mathrm{\&theta;}}_4)=\frac{\mathrm{ik}{x}_4}{2\mathrm{\&pi;}}{\&Integral;\&Integral;P}_3\frac{\exp (-\mathrm{ikR}(r_3,{\mathrm{\&theta;}}_3,x_4,r_4,{\mathrm{\&theta;}}_4))}{R^2(r_3,{\mathrm{\&theta;}}_3,x_4,r_4,{\mathrm{\&theta;}}_4)}{r}_3{\mathrm{dr}}_3{\mathrm{d\&theta;}}_3$

Can calculate the multiple acoustic pressure of the inner each point of lens rear interface according to this.

6. the incident angle when the rear interface Equation for Calculating of calculating according to the 3rd step to maximum sound ray direction of the inner each point contribution of second concave surface of lens and lens goes out this sound ray and injects rear interface, incident sound pressure is got the value that the 5th step calculated, once more according to the refraction angle of ray calculating sound wave and amplitude, the phase place of acoustic pressure.

7, cross O ₂Plane perpendicular to x is designated as plane 2, further calculates the multiple acoustic pressure of each point on the plane 2.

8, calculate the sonic pressure field at lens rear portion according to the method identical with the 5th step.

The sound field that can calculate behind the sound wave scioptics by above 8 steps distributes.

Distribute according to acoustic pressure, can obtain the important indicator of lens sonars such as focal position, main lobe width, beam pattern.

Fig. 4 is the beam pattern after the incident acoustic wave of different angles focuses on.

Claims (3)

1, a kind of method for modeling lens sound field is characterized in that:

1) initial parameter definition, the frequency and the acoustic pressure amplitude of definition sound wave, the parameters,acoustic of external agency and sound lens;

2) setting up coordinate system, is the x axle with the thickness direction of sound lens, when calculating the sound field of lens inside, is initial point O with the center of front interface ₁, arbitrfary point Q is so that (x, r represent that θ) wherein x was the some Q plane vertical with the x axle and the intersection point x of x axle in the space ₁Apart from O ₁Distance, r is Qx in this plane ₁The length of line segment, θ is Qx in this plane ₁The straight line and the angle of direction vertically upward; When calculating the sound field of lens outside, initial point O ₂Be positioned at the plane that the edge surrounded of lens rear interface and the intersection point of x axle, other definition is the same;

3) sound wave is injected lens from external agency by the front interface of lens, according to the refractive direction of the ray calculating sound wave of sound wave and amplitude, the phase place of acoustic pressure;

4) cross O ₁Plane perpendicular to x is designated as plane 1, further calculates the multiple acoustic pressure of each point on the plane 1;

5) every bit on the plane 1 is regarded as sphere wavelet source,, calculated the multiple acoustic pressure of the inner each point of second concave surface of lens according to the undulatory property of sound wave;

6) penetrate the refraction angle of rear interface and amplitude, the phase place of acoustic pressure according to ray calculating sound wave once more;

7) cross O ₂Plane perpendicular to x is designated as plane 2, calculates the multiple acoustic pressure of each point on the plane 2;

8) calculate the sonic pressure field at lens rear portion according to the 5th method that goes on foot.

2, method for modeling lens sound field according to claim 1 is characterized in that: refractive direction and the amplitude of acoustic pressure, the method for phase place of described ray calculating sound wave according to sound wave are:

When if sound wave is injected medium 2 by medium 1, with O ₁The angle of x axle is β ₁, the incident angle of other positions can be obtained by the geometric configuration equation of lens, and the acoustic pressure of sound wave and the lens crossing point of axes Q1 of place is:

$p_1=(A_0-{\mathrm{\&alpha;}}_1{l}_1)\frac{\exp (-\mathrm{ik}{l}_1)}{l_1}$

Refraction angle β ₂Can calculate according to following formula:

$\frac{\sin {\mathrm{\&beta;}}_1}{\sin {\mathrm{\&beta;}}_2}=\frac{c_1}{c_2}$

Refraction coefficient when sound wave incides medium 2 by medium 1 is expressed as:

$T_{12}=\frac{2{\mathrm{\&rho;}}_2{c}_2\cos {\mathrm{\&beta;}}_1}{{\mathrm{\&rho;}}_2{c}_2\cos {\mathrm{\&beta;}}_1+{\mathrm{\&rho;}}_1{c}_1\cos {\mathrm{\&beta;}}_2}$

Incide in the lens, the acoustic pressure that Q2 is ordered is:

$p_2=p_1\&CenterDot;T_{12}=\frac{2{\mathrm{\&rho;}}_2{c}_2\cos {\mathrm{\&beta;}}_1}{{\mathrm{\&rho;}}_2{c}_2\cos {\mathrm{\&beta;}}_1+{\mathrm{\&rho;}}_1{c}_1\cos {\mathrm{\&beta;}}_2}(A_0-{\mathrm{\&alpha;}}_1{l}_1)\frac{\exp (-\mathrm{ik}{l}_1)}{l_1}$

Calculate the acoustic pressure and the sound ray direction of the inner each point of lens front interface according to this.

3, method for modeling lens sound field according to claim 1 and 2 is characterized in that: the method that described undulatory property according to sound wave is calculated the multiple acoustic pressure of the inner each point of rear interface is:

Regard the every bit on the plane 1 as sphere wavelet source, with each wavelet source is center emission sphere wavelet, is exactly the stack of these wavelets in the sound pressure amplitude of its anterior sonic pressure field, and the amplitude of each wavelet is maximum on the direction of propagation of original wavefront, minimum is 0 on its opposite direction

The inner any point Q4 of lens rear interface (x ₄, r ₄, θ ₄) acoustic pressure located can be expressed as:

$P(x_4,r_4,{\mathrm{\&theta;}}_4)=-\frac{1}{2\mathrm{\&pi;}}{\&Integral;\&Integral;P}_3\frac{\&PartialD;}{\&PartialD;x}\left[\frac{\exp (-\mathrm{ikR}(r_3,{\mathrm{\&theta;}}_3,x_4,r_4,{\mathrm{\&theta;}}_4))}{R(r_3,{\mathrm{\&theta;}}_3,x_4,r_4,{\mathrm{\&theta;}}_4)}\right]\&CenterDot;r_{3}d{r}_3{\mathrm{d\&theta;}}_3$

Wherein:

P ₃Be Q3 on the plane 1 (0, r ₃, θ ₃) the multiple acoustic pressure at some place,

$k=\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}=\frac{2\mathrm{\&pi;f}}{c}$ Be wave number, λ is a wavelength, and c is the velocity of sound in the medium,

R is the distance between a Q4 and Q3,

Be the Green function of point source, it has described the interference point source as sonic pressure field,

Launch partial differential, integration becomes:

$P(x_4,r_4,{\mathrm{\&theta;}}_4)=\frac{1}{2\mathrm{\&pi;}}{\&Integral;\&Integral;P}_3\frac{(-\mathrm{ik}-\frac{1}{R})x_4\exp (-\mathrm{ikR}(r_3,{\mathrm{\&theta;}}_3,x_4,r_4,{\mathrm{\&theta;}}_4))}{R^2(r_3,{\mathrm{\&theta;}}_3,x_4,r_4,{\mathrm{\&theta;}}_4)}{r}_3{\mathrm{dr}}_3{\mathrm{d\&theta;}}_3$

Wave length of sound is bigger because R is relative, and following formula can be reduced to:

$P(x_4,r_r,{\mathrm{\&theta;}}_4)=\frac{\mathrm{ik}{x}_4}{2\mathrm{\&pi;}}{\&Integral;\&Integral;P}_3\frac{\exp (-\mathrm{ikR}(r_3,{\mathrm{\&theta;}}_3,x_4,r_4,{\mathrm{\&theta;}}_4))}{R^2(r_3,{\mathrm{\&theta;}}_3,x_4,r_4,{\mathrm{\&theta;}}_4)}{r}_3{\mathrm{dr}}_3{\mathrm{d\&theta;}}_3$

Calculate the multiple acoustic pressure of the inner each point of lens rear interface according to this.

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