CN102608222B - Non-contact wave velocity extracting method of like surface acoustic wave of plating layer structure - Google Patents

Abstract

The invention discloses a non-contact wave velocity extracting method of a like surface acoustic wave of a plating layer structure, and belongs to the technical field of non-destructive testing. In the research of the elastic characteristic of a plating/coating layer, under the condition that the characteristics of a substrate material are known, through the relationship of wave velocity and wavelength or frequency, namely a frequency dispersion curve, the elastic characteristic of the plating/collating layer can be inverted. The V (z) curve formed by the interferences of a drain like surfaceacoustic wave and a direct reflection wave namely a vertical wave comprises much information at the aspect of a material micro structure. According to the invention, based on a defocusing measurementsystem, a wide-frequency pulse is utilized to act as an excitation source, ultrasonic waves comprising multiple frequency components are received, and the V (z) curve of the material and vibration cycle thereof are obtained through an improved two-dimensional fourier transform technology, thus the extraction of the wave velocity of the like surface wave of the plating layer is realized. Accordingto the invention, the wave velocity of like surface acoustic waves of different materials can be extracted; and the wave velocity of the like surface acoustic waves in the wide-frequency range can beextracted, and a single-frequency pointwise mode is replaced; and the wave velocity of like surface acoustic waves in different frequency bands can be extracted.

Description

The method that the contactless velocity of wave of a kind of coating structure class surface wave extracts

Technical field

The invention belongs to field of non destructive testing, be specifically related to the method that the contactless velocity of wave of a kind of coating structure class surface wave extracts.

Background technology

Plating/coating material is widely used in the fields such as Aero-Space, machinery, oil, chemical industry, nuclear power and micro element and little manufacturing, and its major function is the surfacecti proteons such as anticorrosion (Corrosion), rub resistance (Friction), anti-oxidant (Oxidation).Except in conventional mechanical equipment, generally using plating/coating to make the retarding surface burn into of part, member reduces wear, realizes lengthening the life, in special trade, also have many special function of surface requirements, such as the camouflage coating of the corrosion-inhibiting coating of the nonskid coating of ship deck, boats and ships seawater pipeline, military aircraft, high efficiency heat absorption coating in the solar facilities and opto-electronic conversion coating etc.Aspect the new material research and development, plated surface/coating technology is mainly used to prepare various new materials, and the amorphous silicon membrane for preparing such as the using plasma chemical vapour deposition technique is widely applied.In the process of plating or spraying, to inevitably introduce the defectives such as hole, fine cracks, especially in the process of spraying, the grain size of sprayed on material, sticky limit can affect defect concentration (being the volume fraction of hole, defects i.e.cracks) greatly, the form of binding deficient, distribution, direction, final decision the elastic property of plating/coating material.In addition, oxidation and corrosion also can produce material impact to the elastic modulus of plating/coating material, and plating/coating Young modulus is to carry out the requisite parameter of stress-strain analysis, and coating also directly depends on elastic modulus to the drag of thermal shock.Because plating/coating and its plating/to be coated with front material property normally different, even identical coating spraying its characteristic on different structures is not identical yet, so in the process of application plating/coating, it is very necessary that structure is carried out mechanics property analysis.

Adopt the method for the destructive traditional mechanics performance tests such as stretching can't satisfy the demand of plating/being coated with the structural mechanical property test.In detecting as main non-destructive take the measurement acoustic velocity, the many information that comprised the material microstructure aspect by the formed V of interference (z) curve of leaky surface wave and direct reflection wave, with ultrasonic microscope as the velocity of wave survey instrument, can be applied to detect the material mechanical character such as crystal structure, elastic modulus, unrelieved stress, inherent vice, so that ultrasonic microscope has obtained to use more and more widely at aspects such as characteristic of material mechanics test and quantitative Non-Destructive Testings.

Measurement is one of very promising measuring method of field of non destructive testing to elastic properties of materials character to utilize ultrasound wave.In the isotropy homogeneous material, surface wave (Surface acoustic wave, SAW) be called again R wave (Rayleigh SAW), in the research of plating/coating elastic property, propagate because surface wave or class surface wave (Rayleigh-like SAW) are limited in the top layer of structure---be generally in the thickness of a wavelength, when the wavelength of class surface wave during less than plating/coating thickness, its fluctuation behavior has comprised the information of a large amount of platings/coating material characteristic; When the wavelength of class surface wave during greater than plating/coating thickness, its fluctuation behavior also can be subject to the impact of matrix material characteristic.Therefore, in the situation of known matrix material characteristic, by the relation of velocity of wave and wavelength or frequency---be dispersion curve, can be finally inversed by the elastic property of plating/coating.

In order to achieve the above object, the accurate extraction of velocity of wave seems particularly necessary.Present for the most mode that adopts the single-frequency pointwise to extract of class surface wave velocity of wave extraction, determine the velocity of wave of class surface wave by Vz oscillation period in measurement V (z) curve, but its shortcoming is the extraction of single-frequency velocity of wave and the measurement that is not suitable for the wideband pulse signal.Therefore, need to develop a cover based on the class surface wave velocity of wave extracting method of wideband pulse signal.

Summary of the invention

The objective of the invention is to propose a kind of advanced person's material velocity of wave extracting method in order to solve the continuously problem of extraction of coating structure class surface wave velocity of wave wideband.

Step 1): establish the formula that velocity of wave extracts.

Here need to prove, because the load effect of water, leak the velocity of wave of class surface wave and class surface wave and not quite identical, but owing to the density of the measured material density much larger than water, difference between the two is negligible.To no longer region class surface wave and leakage class surface wave in the elaboration afterwards.In the process that velocity of wave extracts, according to V (z) curve theory, can carry out according to following formula the calculating of velocity of wave:

$v_{\mathrm{SAW}}=v_w\·{[1-{(1-\frac{v_w}{2\·f\·\mathrm{Vz}})}^2]}^{-1/2}$

Wherein: Vz is V (z) curve oscillation period, v _wBe the ultrasonic velocity in the water, f is the excitation frequency of transducer, v _SAWClass surface wave velocity of wave for material.Be the key that velocity of wave extracts V (z) curve oscillation period of measuring measured material.

Step 2): test system building.

In order conveniently to defocus stepping measurement, built the test macro that a cover defocuses stepping measurement, as shown in Figure 1.This test macro mainly comprises: sample 1, tank and water 2, transducer 3, mobile platform 4, pulse excitation/receiving instrument 5, oscillograph 6, gpib bus 7, PXI general control system 8, shift servo motor 9, turning axle 10.Wherein, transducer 3 is installed below mobile platform 4, transducer 3 links to each other with pulse excitation/receiving instrument 5, pulse excitation/receiving instrument 5 links to each other with oscillograph 6, oscillograph 6 links to each other with PXI general control system 8 by gpib bus 7, PXI general control system 8 links to each other with shift servo motor 9, and PXI general control system 8 links to each other with turning axle 10 simultaneously.

Step 3): the focusing surface data acquisition.

Tested sample is placed the focusing surface of transducer, pulse excitation/receiving instrument 5 is converted to accepting state after the pulse that to send a bandwidth be 10-200MHz, after receiving reflected signal, signal is transmitted into oscillograph 6, and oscillographic sample frequency is f _S, f _SBe 0.5-5GHz, sampling number is N _s, N _sSpan be the 10000-100000 point.Through after the oscillographic low-pass filtering, be stored into PXI general control system 8 by gpib bus 7.

Step 4): defocus measurement.

Transducer is moved one vertically downward apart from Vz ₀, Vz ₀Span be 1-50 μ m, after mobile finishing, carry out the data collection, sample frequency is f _S, sampling number is N _sAfter gather finishing again with transducer mobile Vz vertically downward ₀Carry out data acquisition, so move in circles, be total to displacement z, the span of z is 2-20mm, therefore will obtain M group voltage data, and M is by z and Vz ₀The common decision is the 40-20000 group.

Step 5): the time domain Fourier transform.

All data are arranged along defocus distance, the data that record are carried out the time domain Fourier transform:

$A_i\left[k\right]=\underset{n=0}{\overset{N_s-1}{\mathrm{\&Sigma;}}}{x}_i\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;nk}/N_s}$

Wherein: A _iBe the spectrum value after the time domain Fourier transform, x _iRepresent one group of voltage data, i=0,1,2L M-1, k=0,1,2L N _s-1, j represents imaginary part.

Step 6): spatial fourier transform.

In order to obtain accurate oscillation period of Vz, need to the result of time domain Fourier transform be carried out along the spatial fourier transform of defocus distance direction again, defocus distance z is converted into z ^-1The territory:

$B_i\left[k\right]=\underset{m=0}{\overset{M-1}{\mathrm{\&Sigma;}}}{A}_m\left[k\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;mi}/M}$

Wherein: B _iBe the spectrum value after the spatial fourier transform, A _mRepresent along the spectrum value that defocuses the time domain Fourier transform of direction, i=0,1,2L M-1, k=0,1,2L N _s-1, j represents imaginary part.Along z ^-1The peak of curve in territory is the inverse of Vz oscillation period.

Step 7): mode is followed the trail of.

Class surface-wave mode peak value in the 1-100MHz scope is followed the trail of, can be found out continuous Vz value oscillation period of this frequency band.

Step 8): velocity of wave extracts.

With the ultrasonic velocity v in the water _W, the frequency f that each peak value is corresponding and Vz substitution oscillation period step 1) shown in formula, can obtain continuous class surface wave velocity of wave v in this frequency band _SAW

The present invention has the following advantages: 1) can the class surface wave velocity of wave of different materials be extracted; 2) can in wide frequency range, extract class surface wave velocity of wave, replace the mode of single-frequency pointwise; 3) can the class surface wave velocity of wave in the different frequency section be extracted.

Description of drawings

Fig. 1 defocuses the measuring system schematic diagram;

Fig. 2 class surface wave propagation schematic diagram;

Fig. 3 focusing surface time domain waveform figure;

Time domain waveform figure under the different defocus distance of Fig. 4;

Fig. 5 time domain Fourier transform figure;

V (z) oscillating curve figure under Figure 64 0MHz frequency;

Fig. 7 spatial fourier transform figure;

Z under Figure 84 0MHz frequency ^-1The territory curve map;

Fig. 9 wideband mode tracking map;

Figure 10 class surface wave velocity of wave extracts figure;

Embodiment

Below in conjunction with instantiation content of the present invention is described in further detail:

Step 1): establish the formula that velocity of wave extracts.

In the situation that the single-frequency excitation/receiving, leaky surface wave shown in Figure 2 is propagated in the schematic diagram, and the time that the direct reflection echo I of upper surface propagates was respectively with the travel-time of leaking class surface wave L:

${\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">t</figure-callout>}}_1=\frac{2(R-\mathrm{Vz})}{v_w}---\left(1\right)$

${\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">t</figure-callout>}}_2=\frac{2(R-\frac{\mathrm{Vz}}{\cos {\mathrm{\&theta;}}_{\mathrm{SAW}}})}{v_w}+\frac{2\&CenterDot;\mathrm{Vz}\&CenterDot;\tan {\mathrm{\&theta;}}_{\mathrm{SAW}}}{v_{\mathrm{SAW}}}---\left(2\right)$

Wherein R is focused radius, and Vz is defocus distance, v _wBe the ultrasonic velocity of water, θ _SAWFor producing the Rayleigh angle of class surface wave, v _SAWClass surface wave velocity of wave for material.Therefore both mistimings are:

$\mathrm{Vt}=t_2-{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">t</figure-callout>}}_1=\frac{2(1-\cos {\mathrm{\&theta;}}_{\mathrm{SAW}})}{v_w}\&CenterDot;\mathrm{Vz}---\left(3\right)$

That is:

$\cos {\mathrm{\&theta;}}_{\mathrm{SAW}}=1-\frac{v_w\&CenterDot;\mathrm{<figure-callout\; id="2"\; label="Vt"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">Vt</figure-callout>}}{2\&CenterDot;\mathrm{Vz}}---\left(4\right)$

With the Snell law:

$\sin {\mathrm{\&theta;}}_{\mathrm{SAW}}=\frac{v_w}{v_{\mathrm{SAW}}}$ Or ${\mathrm{\&theta;}}_{\mathrm{SAW}}={\sin }^{-1}\left(\frac{v_w}{v_{\mathrm{SAW}}}\right)$

After the substitution (4), can get:

$\frac{v_w}{v_{\mathrm{SAW}}}=\sqrt{1-{(1-\frac{v_w}{2}\&CenterDot;\frac{\mathrm{Vt}}{\mathrm{Vz}})}^2}---\left(5\right)$

If when this moment, Vz just was the oscillation period of a V (z) curve, 1/Vt then was the excitation frequency f of transducer.If Vz can determine, just can use following formula to carry out the calculating of class surface wave velocity of wave:

$v_{\mathrm{SAW}}=v_w\&CenterDot;{[1-{(1-\frac{v_w}{2\&CenterDot;f\&CenterDot;\mathrm{Vz}})}^2]}^{-1/2}---\left(6\right)$

Therefore, V (z) curve of measurement measured material becomes the emphasis of velocity of wave extraction oscillation period.

Step 2): test system building.

In order conveniently to defocus stepping measurement, built the test macro that a cover defocuses stepping measurement, as shown in Figure 1.This test macro mainly comprises: sample 1, tank and water 2, transducer 3, mobile platform 4, pulse excitation/receiving instrument 5, oscillograph 6, gpib bus 7, PXI general control system 8, shift servo motor 9, turning axle 10.Wherein, transducer 3 is installed below mobile platform 4, transducer 3 links to each other with pulse excitation/receiving instrument 5, pulse excitation/receiving instrument 5 links to each other with oscillograph 6, oscillograph 6 links to each other with PXI general control system 8 by gpib bus 7, PXI general control system 8 links to each other with shift servo motor 9, and PXI general control system 8 links to each other with turning axle 10 simultaneously.

Step 3): the focusing surface data acquisition.

On fused quartz, plate 10 μ m nickel as sample, its overall dimensions is 40mm * 50mm * 6.01mm, fused quartz is of a size of 40mm * 50mm * 6mm, nickel coating is of a size of 40mm * 50mm * 0.01mm, transducer 3 is focused on the upper surface of sample, after the pulse that to send a bandwidth be 10-200MHz, be converted to accepting state by pulse excitation/receiving instrument 5, after receiving reflected signal, signal is transmitted into oscillograph 6 oscillographic sample frequency f _S=5GHz, sampling number N _s=10000.Through after the oscillographic low-pass filtering, the time domain waveform that is stored into PXI general control system 8 focusing surfaces by gpib bus 7 as shown in Figure 3.

Step 4): defocus measurement.

Transducer is moved Vz towards the sample direction ₀=5 μ m carry out the voltage data collection after mobile finishing, collection is moved Vz with transducer towards the sample direction after finishing again ₀=5 μ m carry out data acquisition, sample frequency f _S=5GHz, sampling number N _s=10000, so move in circles, altogether therefore mobile 2mm will obtain 400 groups of voltage datas, and the voltage data of focusing surface is included in the interior M=401 group voltage data that obtains altogether.All data are arranged along defocus distance, as shown in table 1, can obtain final time domain waveform figure.As shown in Figure 4.

Table 1 voltage data schematic diagram

Step 5): the time domain Fourier transform.

The data that record are carried out the time domain Fourier transform.

$A_i\left[k\right]=\underset{n=0}{\overset{N_s-1}{\mathrm{\&Sigma;}}}{x}_i\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;nk}/N_s}$

Wherein: A _iBe the spectrum value after the time domain Fourier transform, x _iRepresent one group of voltage data, i=0,1,2L M-1, k=0,1,2L N _s-1, j represents imaginary part, N _s=10000, that is:

x ₀[0]＝-0.000340089，x ₀[1]＝0.0006463861，x ₀[2]＝0.0005572123，L，x ₀[9999]＝0.0008652910

x ₁[0]＝0.0003648533，x ₁[1]＝0.0008660445，x ₁[2]＝0.0006378149，L，x ₁[9999]＝0.0005013446

x ₂[0]＝-0.000257757，x ₂[1]＝0.0007262812，x ₂[2]＝0.0007337191，L，x ₂[9999]＝-0.0006.47777

x ₄₀₀[0]＝-0.000422574，x ₄₀₀[1]＝0.0004863551，x ₄₀₀[2]＝0.0006377586，L，x ₄₀₀[9999]＝0.0006225912

$A_0\left[0\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_0\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;0/10000}=x_0\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;0/10000}+x_0\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;0/10000}$

$+x_0\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;0/10000}+L+x_0\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;0/10000}$

$A_0\left[1\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_0\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;1/10000}=x_0\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;1/10000}+x_0\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;1/10000}$

$+x_0\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;1/10000}+L+x_0\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;1/10000}$

$A_0\left[2\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_0\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;2/10000}=x_0\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;2/10000}+x_0\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;2/10000}$

$+x_0\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;2/10000}+L+x_0\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;2/10000}$

M

$A_0\left[9999\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_0\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;9999/10000}=x_0\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;9999/10000}+x_0\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;9999/10000}$

$+x_0\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;9999/10000}+L+x_0\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;9999/10000}$

$A_1\left[0\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_1\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;0/10000}=x_1\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;0/10000}+x_1\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;0/10000}$

$+x_1\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;0/10000}+L+x_1\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;0/10000}$

$A_1\left[1\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_1\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;1/10000}=x_1\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;1/10000}+x_1\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;1/10000}$

$+x_1\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;1/10000}+L+x_1\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;1/10000}$

$A_1\left[2\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_1\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;2/10000}=x_1\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;2/10000}+x_1\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;2/10000}$

$+x_1\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;2/10000}+L+x_1\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;2/10000}$

M

$A_1\left[9999\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_1\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;9999/10000}=x_1\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;9999/10000}+x_1\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;9999/10000}$

$+x_1\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;9999/10000}+L+x_1\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;9999/10000}$

$A_2\left[0\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_2\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;0/10000}=x_2\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;0/10000}+x_2\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;0/10000}$

$+x_2\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;0/10000}+L+x_2\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;0/10000}$

$A_2\left[1\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_2\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;1/10000}=x_2\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;1/10000}+x_2\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;1/10000}$

$+x_2\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;1/10000}+L+x_2\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;1/10000}$

$A_2\left[2\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_2\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;2/10000}=x_2\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;2/10000}+x_2\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;2/10000}$

$+x_2\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;2/10000}+L+x_2\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;2/10000}$

M

$A_2\left[9999\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_2\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;9999/10000}=x_2\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;9999/10000}+x_2\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;9999/10000}$

$+x_2\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;9999/10000}+L+x_2\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;9999/10000}$

M

$A_{400}\left[0\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_{400}\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;0/10000}=x_{400}\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;0/10000}+x_{400}\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;0/10000}$

$+x_{400}\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;0/10000}+L+x_{400}\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;0/10000}$

$A_{400}\left[1\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_{400}\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;1/10000}=x_{400}\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;1/10000}+x_{400}\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;1/10000}$

$+x_{400}\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;1/10000}+L+x_{400}\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;1/10000}$

$A_{400}\left[2\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_{400}\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;2/10000}=x_{400}\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;2/10000}+x_{400}\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;2/10000}$

$+x_{400}\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;2/10000}+L+x_{400}\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;2/10000}$

M

$A_{400}\left[9999\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_{400}\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;9999/10000}=x_{400}\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;9999/10000}+x_{400}\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;9999/10000}$

$+x_{400}\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;9999/10000}+L+x_{400}\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;9999/10000}$

Gained A _i[k], i=0,1,2L M-1, k=0,1,2L N _s-1, such as table 2, shown in Figure 5.

Table 2A _i[k] schematic diagram data

Oscillating curve along defocus distance under the characteristic frequency is V (z) curve, is Vz its oscillation period.For example, the oscillating curve under the 40MHz frequency as shown in Figure 6.

Step 6): spatial fourier transform.

In order to obtain accurate oscillation period of Vz, need to the result of time domain Fourier transform be carried out along the spatial fourier transform of defocus distance direction again, defocus distance z is converted into z ^-1The territory:

$B_i\left[k\right]=\underset{m=0}{\overset{M-1}{\mathrm{\&Sigma;}}}{A}_m\left[k\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;mi}/M}$

Wherein: B _iBe the spectrum value after the spatial fourier transform, A _mRepresent along the spectrum value that defocuses the time domain Fourier transform of direction, i=0,1,2L M-1, k=0,1,2L N _s-1, M=401, j represents imaginary part, that is:

$B_0\left[0\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;0/401}=A_0\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;0/401}+A_1\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;0/401}$

$+A_2\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;0/401}+L++A_{400}\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;0/401}$

$B_1\left[0\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;1/401}=A_0\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;1/401}+A_1\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;1/401}$

$+A_2\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;1/401}+L++A_{400}\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;1/401}$

$B_2\left[0\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;2/401}=A_0\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;2/401}+A_1\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;2/401}$

$+A_2\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;2/401}+L++A_{400}\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;2/401}$

M

$B_{400}\left[0\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;400/401}=A_0\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;400/401}+A_1\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;400/401}$

$+A_2\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;400/401}+L++A_{400}\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;400/401}$

$B_0\left[1\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;0/401}=A_0\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;0/401}+A_1\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;0/401}$

$+A_2\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;0/401}+L++A_{400}\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;0/401}$

$B_1\left[1\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;1/401}=A_0\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;1/401}+A_1\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;1/401}$

$+A_2\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;1/401}+L++A_{400}\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;1/401}$

$B_2\left[1\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;2/401}=A_0\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;2/401}+A_1\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;2/401}$

$+A_2\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;2/401}+L++A_{400}\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;2/401}$

M

$B_{400}\left[1\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;400/401}=A_0\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;400/401}+A_1\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;400/401}$

$+A_2\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;400/401}+L++A_{400}\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;400/401}$

$B_0\left[2\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;0/401}=A_0\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;0/401}+A_1\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;0/401}$

$+A_2\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;0/401}+L++A_{400}\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;0/401}$

$B_1\left[2\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;1/401}=A_0\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;1/401}+A_1\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;1/401}$

$+A_2\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;1/401}+L++A_{400}\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;1/401}$

$B_2\left[2\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;2/401}=A_0\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;2/401}+A_1\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;2/401}$

$+A_2\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;2/401}+L++A_{400}\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;2/401}$

M

$B_{400}\left[2\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;400/401}=A_0\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;400/401}+A_1\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;400/401}$

$+A_2\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;400/401}+L++A_{400}\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;400/401}$

M

$B_0\left[9999\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;0/401}=A_0\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;0/401}+A_1\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;0/401}$

$+A_2\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;0/401}+L++A_{400}\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;0/401}$

$B_1\left[9999\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;1/401}=A_0\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;1/401}+A_1\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;1/401}$

$+A_2\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;1/401}+L++A_{400}\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;1/401}$

$B_2\left[9999\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;2/401}=A_0\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;2/401}+A_1\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;2/401}$

$+A_2\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;2/401}+L++A_{400}\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;2/401}$

M

$B_{400}\left[9999\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;400/401}=A_0\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;400/401}+A_1\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;400/401}$

$+A_2\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;400/401}+L++A_{400}\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122106520000011.png,HDA0000122106520000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;400/401}$

Gained B _i[k], i=0,1,2L M-1, k=0,1,2L N _s-1, such as table 3, shown in Figure 7.

Table 3B _i[k] schematic diagram data

Under the characteristic frequency along z ^-1The peak of curve in territory is the inverse of Vz oscillation period.For example, z under the 40MHz frequency ^-1The curve in territory as shown in Figure 8.

Step 7): mode is followed the trail of.

Peak value to class surface-wave mode in the 10-100MHz scope is followed the trail of, and can find out the continuous Vz value of this frequency band, as shown in Figure 9.

Step 8): velocity of wave extracts.

With the ultrasonic velocity v in the water _W=1500m/s, the frequency that each peak value is corresponding and Vz bring formula (6) into, can obtain continuous surface wave velocity of wave in this frequency band.As shown in figure 10.Theoretical value and experiment value coincide good.

The present invention has the following advantages: 1) can the class surface wave velocity of wave of different materials be extracted; 2) can in wide frequency range, extract class surface wave velocity of wave, replace the mode of single-frequency pointwise; 3) can the class surface wave velocity of wave in the different frequency section be extracted.

Claims (1)

1. the method extracted of the contactless velocity of wave of a coating structure class surface wave is characterized in that the method carries out in accordance with the following steps:

Step 1): establish the formula that velocity of wave extracts;

In the process that velocity of wave extracts, according to V (z) curve theory, carry out the calculating of velocity of wave according to following formula:

$v_{\mathrm{SAW}}=v_w\&CenterDot;{[1-{(1-\frac{v_w}{2\&CenterDot;f\&CenterDot;\mathrm{Vz}})}^2]}^{-1/2}$

Wherein: Vz is V (z) curve oscillation period, v _wBe the ultrasonic velocity of water, f is the excitation frequency of transducer, v _SAWClass surface wave velocity of wave for material;

Step 2): test system building;

This test macro comprises: sample (1), tank and water (2), transducer (3), mobile platform (4), pulse excitation/receiving instrument (5), oscillograph (6), gpib bus (7), PXI general control system (8), shift servo motor (9), turning axle (10); Wherein, transducer (3) is installed below mobile platform (4), transducer (3) links to each other with pulse excitation/receiving instrument (5), pulse excitation/receiving instrument (5) links to each other with oscillograph (6), oscillograph (6) links to each other with PXI general control system (8) by gpib bus (7), PXI general control system (8) links to each other with shift servo motor (9), and PXI general control system (8) links to each other with turning axle (10) simultaneously;

Step 3): the focusing surface data acquisition;

Sample is placed the focusing surface of transducer, pulse excitation/receiving instrument (5) is converted to accepting state after the pulse of sending a 10-200MHz, after receiving reflected signal, signal is transmitted into oscillograph (6), and oscillographic sample frequency is f _S, f _SBe 0.5-5GHz, sampling number is N _sThrough after the oscillographic low-pass filtering, be stored into PXI general control system (8) by gpib bus (7);

Step 4): defocus measurement;

Transducer is moved one vertically downward apart from Vz ₀, Vz ₀Span be 1-50 μ m, after mobile finishing, carry out the data collection, sample frequency is f _S, sampling number is N _sAfter gather finishing again with transducer mobile Vz vertically downward ₀Carry out data acquisition, so repeated acquisition is total to displacement z, and the span of z is 2-20mm, obtains M group voltage data;

Step 5): the time domain Fourier transform;

All data are arranged along defocus distance, the voltage data that records is carried out the time domain Fourier transform;

Step 6): spatial fourier transform

Result to the time domain Fourier transform carries out along the spatial fourier transform of defocus distance direction again, and defocus distance z is converted into z ^-1The territory;

Step 7): mode is followed the trail of

To spatial frequency z ^-1Class surface-wave mode peak value in the territory is followed the trail of, and gives up the peak-data in the 0-1MHz, finds out the continuous Vz value of this frequency band;

Step 8): velocity of wave extracts

The frequency f that velocity of wave, each peak value of water is corresponding and Vz substitution step 1) shown in formula, namely obtain continuous class surface wave velocity of wave v _SAW

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