CN102539541A - Method for non-contact wave velocity extraction of Rayleigh wave of anisotropic blocky material - Google Patents

Abstract

The invention discloses a method for the non-contact wave velocity extraction of a Rayleigh wave of an anisotropic blocky material, and the method belongs to the technical field of nondestructive examination. In the nondestructive examination for mainly measuring the wave velocity of an acoustic wave, a V(z) curve formed by the interference of a leaky surface wave and a directly reflected wave, namely a longitudinal wave, comprises much information at the microstructure aspect of the material; the method is based on a defocusing measurement system; a wide-frequency pulse is utilized as an excitation source; an ultrasonic wave comprising a plurality of frequency components is received; and the V(z) curve of the material and an oscillating period thereof are obtained through an improved two-dimensional Fourier transform technique, so as to achieve the extraction of the wave velocity of the Lamb wave of the blocky material. By using the method, the wave velocities of the Rayleigh waves of different materials can be extracted; the wave velocity of the Rayleigh wave can be extracted in a wide frequency scope; a single-frequency point-by-point way is replaced; the wave velocities of the Rayleigh waves in different frequency ranges can be extracted; an averaged value is selected as the wave velocity of the Rayleigh wave of the material; and the random error caused by an accidental factor in a single-frequency extraction process is avoided.

Description

The method that the contactless velocity of wave of a kind of isotropy block materials R wave extracts

Technical field

The invention belongs to the Non-Destructive Testing field, be specifically related to a kind of velocity of wave method for distilling isotropy block materials R wave.

Background technology

Along with constantly advancing of material science, various functional form materials continue to bring out, but receive preparation technology's influence, and the physical dimension of a lot of new materials is very limited, for example metallic glass, block nanometer material etc.Therefore, adopt the method for destructive traditional mechanics performance tests such as stretching can't satisfy the demand of new material.In the non-destructive that with the measurement of sound velocity of wave is the master detects; The many information that comprise the material microstructure aspect by leaky surface wave and the direct reflection formed V of wave interference (z) curve; With ultrasonic microscope as the velocity of wave survey instrument; Can be applied to detect material mechanical character such as crystal structure, elastic modulus, unrelieved stress, inherent vice, make ultrasonic microscope obtain application 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 in Non-Destructive Testing field to elastic properties of materials character to utilize ultrasound wave.In the isotropy homogeneous material; Surface wave (Surface acoustic wave; SAW) be called R wave (Rayleigh SAW) again; Its fluctuation behavior has comprised the information of lot of materials characteristic, therefore, and through the surface wave velocity of wave of measuring block materials and the elastic property that longitudinal wave velocity can be finally inversed by material.

In order to achieve the above object, the accurate extraction of velocity of wave seems particularly necessary.At present extract the modes that great majority adopt the single-frequency pointwise to extract for the R wave velocity of wave, through measuring the velocity of wave that Vz oscillation period in V (z) curve confirms surface wave, but its shortcoming is extraction of single-frequency velocity of wave and the measurement that is not suitable for the wideband pulse signal.Therefore, need develop the surface wave velocity of wave method for distilling of a cover based on the 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 method for distilling in order to solve the problem that the continuous velocity of wave of isotropy block materials R wave wideband extracts.

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

Here need to prove that because the load effect of water, the velocity of wave of leaky surface wave and surface wave is also 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 distinguish surface wave and leaky surface wave in the elaboration afterwards.In the process that velocity of wave extracts,, can carry out the calculating of velocity of wave according to following formula according to V (z) curve theory:

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

Wherein: Vz is V (z) curve oscillation period, v _wBe the ultrasonic velocity in the water, f is the excitation frequency of transducer, v _SAWSurface 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.

Defocus stepping measurement for ease, built one and overlapped the test macro that 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, and pulse excitation/receiving instrument 5 links to each other with oscillograph 6, and oscillograph 6 links to each other with PXI general control system 8 through 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: focusing surface data acquisition.

The block tested sample is placed the focusing surface of transducer, and pulse excitation/receiving instrument 5 converts accepting state into after the pulse that to send a bandwidth be 10-200MHz, after receiving reflected signal, signal is transmitted into oscillograph 6, and oscillographic SF is f _S, f _SBe 0.5-5GHz, sampling number is N _s, N _sSpan be the 10000-100000 point.Through behind the oscillographic LPF, advance PXI general control system 8 through gpib bus 7 storages.

Step 4): defocus measurement.

Transducer is moved one vertically downward apart from Vz ₀, Vz ₀Span be 1-50 μ m, wait move to accomplish laggard line data collection, SF is f _S, sampling number is N _sAgain transducer is moved Vz vertically downward after gathering end 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 ₀Common decision is the 40-20000 group.

Step 5): time domain Fourier transform.

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

$A_i\left[k\right]=\underset{n=0}{\overset{N_s-1}{\mathrm{\&Sigma;}}}{x}_i\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;nk}/N_s}$

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 the result of time domain Fourier transform be carried out along the spatial fourier transform of defocus distance direction again, z is converted into z with defocus distance ^-1The territory:

$B_i\left[k\right]=\underset{m=0}{\overset{M-1}{\mathrm{\&Sigma;}}}{A}_m\left[k\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;mi}/M}$

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.

Peak value in the 1-100MHz scope is followed the trail of, and can find out continuous Vz value oscillation period of this frequency band.

Step 8): velocity of wave extracts.

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

The present invention has the following advantages: 1) can the R wave velocity of wave of different materials be extracted; 2) can in wide frequency range, extract, replace the mode of single-frequency pointwise the R wave velocity of wave; 3) can the R wave velocity of wave in the different frequency section be extracted, selects value after average as the R wave velocity of wave of material, when having avoided single-frequency to extract because the stochastic error that accidentalia has caused.

Description of drawings

Fig. 1: defocus the measuring system synoptic diagram;

Fig. 2: surface wave propagation synoptic diagram;

Fig. 3: focusing surface time domain waveform figure;

Fig. 4: the time domain waveform figure under the different defocus distance;

Fig. 5: time domain Fourier transform figure;

Fig. 6: V under the 7.5MHz frequency (z) oscillating curve figure;

Fig. 7: spatial fourier transform figure;

Fig. 8: z under the 7.5MHz frequency ^-1The territory curve map;

Fig. 9: wideband mode tracking map;

Figure 10: the surface wave velocity of wave extracts figure;

Embodiment

Below in conjunction with instantiation content of the present invention is done further detailed description:

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

Under the situation of single-frequency excitation/reception, leaky surface wave shown in Figure 2 is propagated in the synoptic diagram, and time that the direct reflection echo I of upper surface propagates and the travel-time of leaky surface wave L are respectively:

${\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">t</figure-callout>}}_1=\frac{2(R-\mathrm{Vz})}{v_w}---\left(1\right)$

${\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">t</figure-callout>}}_2=\frac{2(R-\frac{\mathrm{Vz}}{\cos {\mathrm{\&theta;}}_{\mathrm{SAW}}})}{v_w}+\frac{2\&CenterDot;\mathrm{Vz}\&CenterDot;\tan {\mathrm{\&theta;}}_{\mathrm{SAW}}}{v_{\mathrm{SAW}}}---\left(2\right)$

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

$\mathrm{Vt}=t_2-{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">t</figure-callout>}}_1=\frac{2(1-\cos {\mathrm{\&theta;}}_{\mathrm{SAW}})}{v_w}\&CenterDot;\mathrm{Vz}---\left(3\right)$

That is:

$\cos {\mathrm{\&theta;}}_{\mathrm{SAW}}=1-\frac{v_w\&CenterDot;\mathrm{<figure-callout\; id="2"\; label="Vt"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">Vt</figure-callout>}}{2\&CenterDot;\mathrm{Vz}}---\left(4\right)$

With the Snell law:

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

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 confirm, just can use following formula to carry out the calculating of 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.

Defocus stepping measurement for ease, built one and overlapped the test macro that 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, and pulse excitation/receiving instrument 5 links to each other with oscillograph 6, and oscillograph 6 links to each other with PXI general control system 8 through 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): focusing surface data acquisition.

With the rectangular parallelepiped tungsten carbide is tested sample; It is of a size of 40mm * 40mm * 10mm; Transducer 3 is focused on the upper surface of sample, after the pulse that to send a bandwidth be 10-200MHz, convert accepting state through pulse excitation/receiving instrument 5 into, after receiving reflected signal; Signal is transmitted into oscillograph 6, oscillographic SF f _S=2.5GHz, sampling number N _s=10000.Through behind the oscillographic LPF, advance the PXI general control system through gpib bus 7 storages, the time domain waveform of focusing surface is as shown in Figure 3.

Step 4): defocus measurement.

Transducer is moved Vz towards the sample direction ₀=10 μ m carry out the voltage data collection after waiting to move completion, and collection is moved Vz with transducer towards the sample direction after finishing again ₀=10 μ m carry out data acquisition, SF f _S=2.5GHz, sampling number N _s=10000, so move in circles, move 4mm altogether, therefore will obtain 400 groups of voltage datas, in being included in, the voltage data of focusing surface obtains M=401 group voltage data 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 synoptic diagram

Step 5): time domain Fourier transform.

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

$A_i\left[k\right]=\underset{n=0}{\overset{N_s-1}{\mathrm{\&Sigma;}}}{x}_i\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;nk}/N_s}$

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]＝-0.008985937，x ₀[1]＝-0.007846875，x ₀[2]＝-0.007509375，L，x ₀[9999]＝-0.011221875

x ₁[0]＝-0.006519375，x ₁[1]＝-0.007625000，x ₁[2]＝-0.007091250，L，x ₁[9999]＝-0.011399375

x ₂[0]＝-0.007612500，x ₂[1]＝-0.009487500，x ₂[2]＝-0.009637500，L，x ₂[9999]＝-0.011362500

L

x ₄₀₀[0]＝-0.018224968，x ₄₀₀[1]＝-0.018341468，x ₄₀₀[2]＝-0.018210406，L，x ₄₀₀[9999]＝-0.008985062

$A_0\left[0\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_0\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;0/10000}=x_0\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;0/10000}+x_0\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;0/10000}$

$+x_0\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;0/10000}+L+x_0\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;0/10000}$

$A_0\left[1\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_0\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;1/10000}=x_0\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;1/10000}+x_0\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;1/10000}$

$+x_0\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;1/10000}+L+x_0\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;1/10000}$

$A_0\left[2\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_0\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;2/10000}=x_0\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;2/10000}+x_0\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;2/10000}$

$+x_0\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;2/10000}+L+x_0\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;2/10000}$

M

$A_0\left[9999\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_0\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;9999/10000}=x_0\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;9999/10000}+x_0\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;9999/10000}$

$+x_0\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;9999/10000}+L+x_0\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;9999/10000}$

$A_1\left[0\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_1\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;0/10000}=x_1\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;0/10000}+x_1\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;0/10000}$

$+x_1\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;0/10000}+L+x_1\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;0/10000}$

$A_1\left[1\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_1\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;1/10000}=x_1\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;1/10000}+x_1\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;1/10000}$

$+x_1\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;1/10000}+L+x_1\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;1/10000}$

$A_1\left[2\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_1\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;2/10000}=x_1\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;2/10000}+x_1\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;2/10000}$

$+x_1\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;2/10000}+L+x_1\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;2/10000}$

M

$A_1\left[9999\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_1\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;9999/10000}=x_1\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;9999/10000}+x_1\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;9999/10000}$

$+x_1\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;9999/10000}+L+x_1\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;9999/10000}$

$A_2\left[0\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_2\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;0/10000}=x_2\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;0/10000}+x_2\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;0/10000}$

$+x_2\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;0/10000}+L+x_2\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;0/10000}$

$A_2\left[1\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_2\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;1/10000}=x_2\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;1/10000}+x_2\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;1/10000}$

$+x_2\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;1/10000}+L+x_2\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;1/10000}$

$A_2\left[2\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_2\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;2/10000}=x_2\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;2/10000}+x_2\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;2/10000}$

$+x_2\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;2/10000}+L+x_2\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;2/10000}$

M

$A_2\left[9999\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_2\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;9999/10000}=x_2\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;9999/10000}+x_2\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;9999/10000}$

$+x_2\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;9999/10000}+L+x_2\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;9999/10000}$

M

$A_{400}\left[0\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_{400}\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;0/10000}=x_{400}\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;0/10000}+x_{400}\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;0/10000}$

$+x_{400}\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;0/10000}+L+x_{400}\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;0/10000}$

$A_{400}\left[1\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_{400}\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;1/10000}=x_{400}\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;1/10000}+x_{400}\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;1/10000}$

$+x_{400}\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;1/10000}+L+x_{400}\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;1/10000}$

$A_{400}\left[2\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_{400}\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;2/10000}=x_{400}\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;2/10000}+x_{400}\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;2/10000}$

$+x_{400}\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;2/10000}+L+x_{400}\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;2/10000}$

M

$A_{400}\left[9999\right]=\underset{n=0}{\overset{9999}{\mathrm{\&Sigma;}}}{x}_{400}\left[n\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;n}\&CenterDot;9999/10000}=x_{400}\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;9999/10000}+x_{400}\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;9999/10000}$

$+x_{400}\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;9999/10000}+L+x_{400}\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;9999\&CenterDot;9999/10000}$

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

Table 2 A _i[k] schematic diagram data

The oscillating curve of CF lower edge defocus distance is V (z) curve, is Vz its oscillation period.For example, the oscillating curve under the 7.5MHz frequency is as shown in Figure 6.

Step 6): spatial fourier transform.

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

$B_i\left[k\right]=\underset{m=0}{\overset{M-1}{\mathrm{\&Sigma;}}}{A}_m\left[k\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;mi}/M}$

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:

$B_0\left[0\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;0/401}=A_0\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;0/401}+A_1\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;0/401}$

$+A_2\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;0/401}+L++A_{400}\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;0/401}$

$B_1\left[0\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;1/401}=A_0\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;1/401}+A_1\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;1/401}$

$+A_2\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;1/401}+L++A_{400}\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;1/401}$

$B_2\left[0\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;2/401}=A_0\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;2/401}+A_1\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;2/401}$

$+A_2\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;2/401}+L++A_{400}\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;2/401}$

M

$B_{400}\left[0\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;400/401}=A_0\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;400/401}+A_1\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;400/401}$

$+A_2\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;400/401}+L++A_{400}\left[0\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;400/401}$

$B_0\left[1\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;0/401}=A_0\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;0/401}+A_1\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;0/401}$

$+A_2\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;0/401}+L++A_{400}\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;0/401}$

$B_1\left[1\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;1/401}=A_0\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;1/401}+A_1\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;1/401}$

$+A_2\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;1/401}+L++A_{400}\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;1/401}$

$B_2\left[1\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;2/401}=A_0\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;2/401}+A_1\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;2/401}$

$+A_2\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;2/401}+L++A_{400}\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;2/401}$

M

$B_{400}\left[1\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;400/401}=A_0\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;400/401}+A_1\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;400/401}$

$+A_2\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;400/401}+L++A_{400}\left[1\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;400/401}$

$B_0\left[2\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;0/401}=A_0\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;0/401}+A_1\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;0/401}$

$+A_2\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;0/401}+L++A_{400}\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;0/401}$

$B_1\left[2\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;1/401}=A_0\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;1/401}+A_1\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;1/401}$

$+A_2\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;1/401}+L++A_{400}\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;1/401}$

$B_2\left[2\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;2/401}=A_0\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;2/401}+A_1\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;2/401}$

$+A_2\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;2/401}+L++A_{400}\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;2/401}$

M

$B_{400}\left[2\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;400/401}=A_0\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;400/401}+A_1\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;400/401}$

$+A_2\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;400/401}+L++A_{400}\left[2\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;400/401}$

M

$B_0\left[9999\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;0/401}=A_0\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;0/401}+A_1\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;0/401}$

$+A_2\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;0/401}+L++A_{400}\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;0/401}$

$B_1\left[9999\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;1/401}=A_0\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;1/401}+A_1\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;1/401}$

$+A_2\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;1/401}+L++A_{400}\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;1/401}$

$B_2\left[9999\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;2/401}=A_0\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;2/401}+A_1\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;2/401}$

$+A_2\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;2/401}+L++A_{400}\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;2/401}$

M

$B_{400}\left[9999\right]=\underset{m=0}{\overset{400}{\mathrm{\&Sigma;}}}{A}_m\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;m\&CenterDot;400/401}=A_0\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;0\&CenterDot;400/401}+A_1\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;1\&CenterDot;400/401}$

$+A_2\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;2\&CenterDot;400/401}+L++A_{400}\left[9999\right]e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000122101780000011.png,HDA0000122101780000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}\&CenterDot;400\&CenterDot;400/401}$

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

Table 3 B _i[k] schematic diagram data

CF lower edge z ^-1The peak of curve in territory is the inverse of Vz oscillation period.For example, z under the 7.5MHz frequency ^-1The curve in territory is as shown in Figure 8.

Step 7): mode is followed the trail of.

Peak value in the 2.5-22.5MHz scope is followed the trail of, and can find out the continuous Vz value of this frequency band, and is as shown in Figure 9.

Step 8): velocity of wave extracts.

With the ultrasonic velocity v in the water _W=1500m/s, frequency and Vz that each peak value is corresponding bring formula (6) into, can obtain surface wave velocity of wave continuous in this frequency band.The theoretical surface wave-wave speed of tungsten carbide is 2680m/s, and the average velocity of wave of the surface wave that records is 2668m/s, and both are merely 12m/s at error, and it is very high to extract precision.Shown in figure 10.

The present invention has the following advantages: 1) can the R wave velocity of wave of different materials be extracted; 2) can in wide frequency range, extract, replace the mode of single-frequency pointwise the R wave velocity of wave; 3) can the R wave velocity of wave in the different frequency section be extracted, selects value after average as the R wave velocity of wave of material, when having avoided single-frequency to extract because the stochastic error that accidentalia has caused.

Claims (1)

1. the method extracted of the contactless velocity of wave of an isotropy block materials R wave is characterized in that this method carries out according to following steps:

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

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

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

Wherein: Vz is V (z) curve oscillation period, v _wBe the ultrasonic velocity of water, f is the excitation frequency of transducer, v _SAWSurface 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), and pulse excitation/receiving instrument (5) links to each other with oscillograph (6), and oscillograph (6) links to each other with PXI general control system (8) through 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): focusing surface data acquisition;

Sample is placed the focusing surface of transducer, and pulse excitation/receiving instrument (5) converts accepting state into after the pulse of sending a 10-200MHz, after receiving reflected signal, signal is transmitted into oscillograph (6), and oscillographic SF is f _S, f _SBe 0.5-5GHz, sampling number is N _sThrough behind the oscillographic LPF, advance PXI general control system (8) through gpib bus (7) storage;

Step 4): defocus measurement;

Transducer is moved one vertically downward apart from Vz ₀, Vz ₀Span be 1-50 μ m, wait move to accomplish laggard line data collection, SF is f _S, sampling number is N _sAgain transducer is moved Vz vertically downward after gathering end 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): 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 z is converted into z with defocus distance ^-1The territory;

Step 7): mode is followed the trail of

To spatial frequency z ^-1Peak value in the territory is followed the trail of, and finds out the continuous Vz value of this frequency band;

Step 8): velocity of wave extracts

Formula shown in frequency f that velocity of wave, each peak value of water is corresponding and the Vz substitution step 1) promptly obtains continuous surface wave velocity of wave v _SAW

Images