CN102221502B - Multi-beam laser heterodyne second harmonic Young modulus measurement method - Google Patents

Abstract

The invention discloses a multi-beam laser heterodyne second harmonic Young modulus measurement method, which relates to a Young modulus measurement method and aims to solve the problem of relatively lower measurement accuracy caused by poor laser heterodyne beat frequency signal acquisition effects and low signal processing speed of conventional multi-beam laser heterodyne Young modulus measurement methods. In the method, a galvanometer is introduced into a light path, and optical frequency is added to optical signals incident at different moments according to Doppler effects, so that multi-beam heterodyne second harmonic signals are generated under the condition of meeting interference after light reflected for k times and the light reflected for k+2 times by a planar mirror permeate a thin glass plate, and information to be measured is successfully modulated into frequency differences of the intermediate frequency heterodyne second harmonic signals. In the process of measuring a Young modulus of a sample, a frequency value comprising a metal length variation value is obtained in a frequency domain, the amount of variation, along with the mass of a weight, of a sample length is obtained after signal demodulation, and the Young modulus of the sample can be calculated. The device and the method are applied to the measurement of the Young modulus.

Description

The method of multi-beam laser heterodyne second harmonic measuring young modulus

Technical field

The present invention relates to a kind of method of measuring young modulus.

Background technology

Young's modulus of elasticity has reflected the relation of material deformation and internal stress; Material receives external force to do the time spent, and deformation must take place; Its inside is stressed and the ratio of strain (being relative deformation) is called Young's modulus of elasticity; It is an important physical amount that characterizes solid material character, is the important parameter during the mechanical component selection in the engineering.In recent years, in engineering measuring technology, adopted feed rod thick stick method, Fiber Optical Sensor Based, CCD method, interferometric method, pulling method and diffraction approach etc. more; But the indirect measuring amount of these methods is more; Accidental error is bigger, and need carry out lot of data and handle, therefore; The measuring accuracy of these methods is lower, can't satisfy the requirement of present high-acruracy survey.

And in optical measuring method; Advantages such as the laser heterodyne measurement technology has that high room and time resolution, measuring speed are fast, precision is high, the linearity good, antijamming capability is strong, dynamic response is fast, good reproducibility and measurement range are big and enjoy Chinese scholars to pay close attention to; The laser heterodyne measurement technology has been inherited the plurality of advantages of heterodyne technology and Doppler technology, is one of present superhigh precision measuring method.This method has become one of significant technology of modern ultraprecise detection and surveying instrument, is widely used in ultra precise measurement, detection, process equipment, laser radar system etc.But the existing method of multi-beam laser heterodyne measurement Young modulus that adopts causes measuring accuracy lower owing to laser signal difference frequency signal collection effect arithmetic speed poor, signal Processing slowly.

Summary of the invention

In order to solve the existing method that adopts multi-beam laser heterodyne measurement Young modulus because the lower problem of measuring accuracy that laser difference frequency signal collection effect arithmetic speed poor, signal Processing causes slowly, thereby a kind of method of multi-beam laser heterodyne second harmonic measuring young modulus is provided.

The method of multi-beam laser heterodyne second harmonic measuring young modulus; It is based on, and the device of multi-beam laser heterodyne second harmonic measuring young modulus realizes; Said device based on multi-beam laser heterodyne second harmonic measuring young modulus comprises the device of multi-beam laser heterodyne measurement distance, and it is by H ₀Solid state laser, plane mirror, quarter-wave plate, galvanometer, galvanometer driving power, polarizing beam splitter mirror, convergent lens, thin glass plate, photodetector and signal processing system are formed, and the galvanometer driving power is used to drive the galvanometer vibration; The thin glass plate horizontal fixed is provided with a plane mirror apart from the d place directly over this thin glass plate, and the reflecting surface of said thin glass plate and plane mirror is relative and be parallel to each other H ₀Solid state laser, quarter-wave plate, galvanometer, polarizing beam splitter mirror, convergent lens, photodetector all are positioned at the below of thin glass plate, said H ₀The front surface of solid state laser emission of lasering beam to polarizing beam splitter mirror; After the quarter-wave plate transmission, be transmitted into the plane of incidence of galvanometer through this polarizing beam splitter mirror beam reflected; Folded light beam after vibration mirror reflected is transmitted through polarizing beam splitter mirror through quarter-wave plate once more; After said polarizing beam splitter mirror transmission, be incident to thin glass plate, this transmitted light beam is at the incident angle θ of the plane of incidence of this thin glass plate ₀Less than 90 and more than or equal to 0 degree; This transmitted light forms folded light beam and transmitted light beam through this thin glass plate; Said printing opacity bundle is incident to convergent lens once more through the folded light beam of plane reflection mirror reflection after the thin glass plate transmission; The folded light beam that forms through this thin glass plate front surface reflection also is incident to convergent lens; Convergent lens focuses to incident beam on the test surface of photodetector; The electrical signal of photodetector is connected with the signal input part of wave filter, and the signal output part of wave filter is connected with the signal input part of prime amplifier, and the signal output part of prime amplifier is connected with the signal input part of A/D converter; The signal output part of said A/D converter is connected with the signal input part of DSP digital signal processor; Be solidified with fft algorithm in the said DSP digital signal processor, the DSP digital signal processor is according to the distance that obtains after the signal demodulation that receives between plane mirror and the thin glass plate, and this distance equals length variations amount wiry to be measured;

The method of multi-beam laser heterodyne second harmonic measuring young modulus, it is realized by following steps:

Step 1, a long L; Mean diameter is that the tinsel to be measured of R ' hangs on the fixed support; Said lower end wiry to be measured is fixedly connected with counterweight, and said counterweight applies tensile force f so that said tinsel to be measured produces internal stress to tinsel to be measured under action of gravity; The bottom of said counterweight is fixedly connected with the non-reflecting surface of plane mirror, makes tinsel to be measured perpendicular to the reflecting surface of plane mirror, opens H then ₀Solid state laser, and control the galvanometer driving power simultaneously and drive galvanometer and begin vibration;

Step 2, signal processing system are gathered the signal of photodetector output, obtain the distance parameter between thin glass plate and the plane mirror, when plane mirror remains static, write down this distance parameter;

The quality m of step 3, increase counterweight,

Step 4, signal processing system are gathered the signal of photodetector output once more, obtain the distance parameter between thin glass plate and the plane mirror, when plane mirror remains static, write down this distance parameter,

Step 5, according to two distance parameters that step 2 and four obtains, obtain the variation delta d of distance between thin glass plate and the plane mirror, this variable in distance amount Δ d is the elongation Δ L of tinsel to be measured under the effect of quality m;

According to Hooke's law, obtain Young modulus wiry to be measured and be:

$E=\frac{\mathrm{FL}}{\mathrm{S\ΔL}}$

In the formula, S is a sectional area wiry to be measured, S=π R ' ²/ 4;

F is the pulling force on prolonging direction, is counterweight weight mg; Parameter g is an acceleration of gravity; Then, the Young modulus that power F is corresponding is:

$E=\frac{4\mathrm{mgL}}{\mathrm{\π}{R}^{\′2}\mathrm{\ΔL}}$

Step 6, in elastic limit wiry to be measured; Repeatedly increase the quality m of counterweight; Each increasing after the counterweight, execution in step five obtains a distance parameter, obtains corresponding variable in distance amount according to the distance parameter of this distance parameter and step 2 acquisition; And then the Young modulus of acquisition under power xmg effect, wherein x=1,2,3

The process of the acquisition distance parameter described in step 2 and the step 4 is:

Under the motion effect of galvanometer, become through the catoptrical frequency of vibration mirror reflected:

ω＝ω ₀(1+at/c)，

In the formula: ω ₀Be the laser angular frequency, a is a vibration acceleration, and c is the light velocity; Then t-l/c arrives the thin glass plate front surface constantly and by the catoptrical light field of this thin glass plate front surface reflection is:

$E_1\left(t\right)={\mathrm{\α}}_1{E}_0\exp \left\{i\right[{\mathrm{\ω}}_0(1+\frac{a(t-l/c)}{c})t+{\mathrm{\ω}}_0\frac{\frac{a{(t-l/c)}^2}{2}}{c}\left]\right\}$

Parameter E ₀The expression constant, l representes the distance of galvanometer to the thin glass plate front surface; Light through the transmission of thin glass plate front surface is repeatedly reflected by plane mirror in difference constantly, and its catoptrical expression formula is respectively:

$E_2\left(t\right)={\mathrm{\α}}_2{E}_0\exp \left\{i\right[{\mathrm{\ω}}_0(1+a\frac{t-\frac{l}{c}-\frac{2\mathrm{nd}\cos \mathrm{\θ}}{c}}{c})t+{\mathrm{\ω}}_0\frac{(a\frac{{(t-\frac{l}{c}-\frac{2\mathrm{nd}\cos \mathrm{\θ}}{c})}^2}{2}+2\mathrm{nd}\cos \mathrm{\θ})}{c}\left]\right\}$

$E_j\left(t\right)={\mathrm{\α}}_j{E}_0\exp \left\{i\right[{\mathrm{\ω}}_0(1+a\frac{t-\frac{l}{c}-\frac{2(j-1)\mathrm{nd}\cos \mathrm{\θ}}{c}}{c})t$

$+{\mathrm{\ω}}_0\frac{(a\frac{{(t-\frac{l}{c}-\frac{2(j-1)\mathrm{nd}\cos \mathrm{\θ}}{c})}^2}{2}+2(j-1)\mathrm{nd}\cos \mathrm{\θ})}{c}\left]\right\}$

Wherein, α ₁=r, α ₂=β β ' r ' ..., α _j=β β ' r ' ^(2j-3)The reflectivity that r is a light when surrounding medium is injected thin glass plate, transmissivity is β, r ' is the reflectivity of plane mirror; Transmissivity when reflected light penetrates thin glass plate between thin glass plate and the plane mirror is β ', and d is the distance between thin glass plate and the plane mirror; J is a nonnegative integer; N is the refractive index of medium between thin glass plate and plane mirror; θ is that incident light sees through refraction angle behind the thin glass plate;

Total light field that photodetector receives is:

E(t)＝E ₁(t)+E ₂(t)+…+E _j(t)

J representes the number of the light beam that photodetector receives; The photocurrent of photodetector output is expressed as:

$I=\frac{\mathrm{\ηe}}{\mathrm{hv}}\frac{1}{Z}\underset{D}{\∫\∫}\frac{1}{2}[E_1\left(t\right)+E_2\left(t\right)+...+E_j\left(t\right)+...]{[E_1\left(t\right)+E_2\left(t\right)+...+E_j\left(t\right)+...]}^{*}\mathrm{ds}$

Wherein, e is an electron charge, and Z is the intrinsic impedance of photodetector surfaces medium, and η is a quantum efficiency, and D is the area of the test surface of photodetector, and h is a Planck's constant, and v is a laser frequency;

Said photo-signal after filter filtering, the dc terms in the filtered signal, the electric current of intermediate frequency of the second harmonic signal of wave filter output is expressed as:

$I_{\mathrm{if}}=\frac{\mathrm{\ηe}}{2\mathrm{hv}}\frac{1}{Z}\underset{D}{\∫\∫}\underset{p=1}{\overset{\∞}{\mathrm{\Σ}}}\underset{j=p+2}{\overset{\∞}{\mathrm{\Σ}}}(E_p\left(t\right){E_j}^{*}\left(t\right)+{E_p}^{*}\left(t\right)E_j\left(t\right))\mathrm{ds}$

Bring the expression formula of the reflection light field of the reflection light field of thin glass plate front surface and plane mirror into following formula, this signal obtains current signal through the inner algorithm computation integration of DSP digital signal processor:

$I_{\mathrm{if}}=\frac{\mathrm{\ηe}}{\mathrm{hv}}\frac{\mathrm{\π}}{Z}\underset{p=1}{\overset{\∞}{\mathrm{\Σ}}}{\mathrm{\α}}_{p+2}{\mathrm{\α}}_p{E_0}^2\cos (\frac{8{\mathrm{\ω}}_0\mathrm{and}\cos \mathrm{\θ}}{c^2}t-\frac{{4\mathrm{\ω}}_0\mathrm{nd}\cos \mathrm{\θ}}{c}-\frac{4l{\mathrm{\ω}}_0\mathrm{and}\cos \mathrm{\θ}}{c^3}-\frac{8p{\mathrm{\ω}}_0{\mathrm{an}}^2{d}^2{\cos }^2\mathrm{\θ}}{c^3})$

Ignore 1/c ³Event after be reduced to:

$I_{\mathrm{if}}=\frac{\mathrm{\ηe}}{\mathrm{hv}}\frac{\mathrm{\π}}{Z}{E_0}^2\cos (\frac{{8\mathrm{\α\ω}}_0\mathrm{nd}\cos \mathrm{\θ}}{c^2}t-\frac{4{\mathrm{\ω}}_0\mathrm{nd}\cos \mathrm{\θ}}{c})\underset{p=1}{\overset{\∞}{\mathrm{\Σ}}}{\mathrm{\α}}_{p+2}{\mathrm{\α}}_p$

Wherein, p is a nonnegative integer;

The frequency of interference signal is designated as:

f＝8andcosθω ₀/(2πc ²)＝4andcosθω ₀/(πc ²)＝Kd

Can know by following formula, being directly proportional between the frequency of interference signal and plane mirror and the thin glass plate apart from d, scale-up factor K is:

K＝4ancosθω ₀/(πc ²)

With the light source angle frequencies omega ₀, between plane mirror and the thin glass plate refractive index n, refraction angle θ, the galvanometer acceleration of medium a is relevant;

The photocurrent expression formula of photodetector output obtains the second harmonic frequency crest on frequency spectrum through Fourier transform after, through the measurement second harmonic frequency, and then measure between thin glass plate and the plane mirror apart from d.

Xmg is in elastic limit wiry to be measured; Length wiry to be measured is 1m, and diameter of section is the steel wire of 0.25mm to 1mm.

In the system based on multi-beam laser heterodyne second harmonic measuring young modulus, apart from d >=20mm.

In the system based on multi-beam laser heterodyne second harmonic measuring young modulus, H ₀The light field of the laser beam that solid state laser is launched is:

E(t)＝E ₀exp(iω ₀t)，

Parameter i representes imaginary number; E ₀The expression constant; ω ₀The initial angle frequency of expression laser.

In the system based on multi-beam laser heterodyne second harmonic measuring young modulus, said galvanometer is Doppler's galvanometer, and the vibration equation of this galvanometer is:

x(t)＝a(t ²/2)，

T ∈ [0,0.001s], value is spaced apart 1 μ s; The Oscillation Amplitude of x (t) expression galvanometer; Parameter a representes the vibration acceleration of galvanometer, and span is 10 usually ²～10 ⁴M/s ²

The rate equation of this galvanometer is:

v(t)＝at

Beneficial effect: the second harmonic frequency that the photocurrent expression formula that the present invention exports through the measuring light electric explorer obtains on frequency spectrum after Fourier transform; The distance between thin glass plate and the plane mirror is measured in realization; And then acquisition measuring young modulus; Measuring accuracy of the present invention is higher, the fast operation of signal Processing.

Description of drawings

Fig. 1 is the configuration state synoptic diagram of device when Displacement Measurement of multi-beam laser heterodyne measurement micro-displacement of the present invention, is device of the present invention in the frame of broken lines wherein.Fig. 2 is a multi-beam laser principle of interference synoptic diagram.Fig. 3 is the Fourier transform spectrogram of multi-beam laser heterodyne signal.Under the different counterweight quality of Fig. 4 situation; The corresponding multi-beam laser heterodyne signal Fourier transform frequency spectrum of carbon steel wire length variations amount to be measured when applying different quality, wherein curve 41 corresponding counterweight quality are 0.25kg, curve 42 corresponding counterweight quality are 0.5kg; Curve 43 corresponding counterweight quality are 0.75kg; Curve 44 corresponding counterweight quality are 1.0kg, and curve 45 corresponding counterweight quality are 1.25kg, and curve 46 corresponding counterweight quality are 1.5kg; Curve 47 corresponding counterweight quality are 1.75kg, and curve 48 corresponding counterweight quality are 2.0kg.

Embodiment

Embodiment one, combination Fig. 1 explain this embodiment; The method of multi-beam laser heterodyne second harmonic measuring young modulus; It is based on, and the device of multi-beam laser heterodyne second harmonic measuring young modulus realizes; Said device based on multi-beam laser heterodyne second harmonic measuring young modulus comprises the device of multi-beam laser heterodyne measurement distance, and it is by H ₀Solid state laser 1, plane mirror 6, quarter-wave plate 3, galvanometer 2, galvanometer driving power, polarizing beam splitter mirror 4, convergent lens 9, thin glass plate 5, photodetector 10 and signal processing system are formed, and the galvanometer driving power is used to drive galvanometer 2 vibrations; Thin glass plate 5 horizontal fixed are provided with a plane mirror 6 apart from the d place directly over this thin glass plate 5, and the reflecting surface of said thin glass plate 5 and plane mirror 6 is relative and be parallel to each other H ₀Solid state laser 1, quarter-wave plate 3, galvanometer 2, polarizing beam splitter mirror 4, convergent lens 9, photodetector 10 all are positioned at the below of thin glass plate 5, said H ₀The front surface of solid state laser 1 emission of lasering beam to polarizing beam splitter mirror 4; After quarter-wave plate 3 transmissions, be transmitted into the plane of incidence of galvanometer 2 through these polarizing beam splitter mirror 4 beam reflected; Folded light beam after galvanometer 2 reflections is transmitted through polarizing beam splitter mirror 4 through quarter-wave plate 3 once more; After said polarizing beam splitter mirror 4 transmissions, be incident to thin glass plate 5, this transmitted light beam is at the incident angle θ of the plane of incidence of this thin glass plate 5 ₀Less than 90 and more than or equal to 0 degree; This transmitted light forms folded light beam and transmitted light beam through this thin glass plate 5; Said printing opacity bundle is incident to convergent lens 9 once more through the folded light beam of plane mirror 6 reflections after thin glass plate 5 transmissions; The folded light beam that forms through these thin glass plate 5 front surface reflections also is incident to convergent lens 9; Convergent lens 9 focuses to incident beam on the test surface of photodetector 10; The electrical signal of photodetector 10 is connected with the signal input part of wave filter 11, and the signal output part of wave filter 11 is connected with the signal input part of prime amplifier 12, and the signal output part of prime amplifier 12 is connected with the signal input part of A/D converter 13; The signal output part of said A/D converter 13 is connected with the signal input part of DSP digital signal processor 14; Be solidified with fft algorithm in the said DSP digital signal processor 14, DSP digital signal processor 14 is according to the distance that obtains after the signal demodulation that receives between plane mirror 6 and the thin glass plate 5, and this distance equals length variations amount wiry to be measured;

The method of multi-beam laser heterodyne second harmonic measuring young modulus, it is realized by following steps:

Step 1, a long L; Mean diameter is that the tinsel to be measured 8 of R ' hangs on the fixed support; The lower end of said tinsel to be measured 8 is fixedly connected with counterweight 7, and said counterweight 7 applies tensile force f so that said tinsel to be measured 8 produces internal stress to tinsel 8 to be measured under action of gravity; The bottom of said counterweight 7 is fixedly connected with the bottom surface of plane mirror 6, opens H then ₀Solid state laser 1;

Step 2, signal processing system are gathered the signal of photodetector 10 outputs; Obtain the distance parameter between thin glass plate 5 and the plane mirror 6; When plane mirror 6 remains static, write down this distance parameter, keep thin glass plate fixed in the experimentation always;

The quality m of step 3, increase counterweight;

Step 4, signal processing system are gathered the signal of photodetector 10 outputs once more, obtain the distance parameter between thin glass plate 5 and the plane mirror 6, when plane mirror 6 remains static, write down this distance parameter,

Step 5, according to two distance parameters that step 2 and four obtains, obtain the variation delta d of distance between thin glass plate 5 and the plane mirror 6, this variable in distance amount Δ d is the elongation Δ L of tinsel 8 to be measured under the effect of quality m;

According to Hooke's law, obtain Young modulus wiry to be measured and be:

$E=\frac{\mathrm{FL}}{\mathrm{S\ΔL}}---\left(1\right)$

In the formula, L and S are former length wiry and sectional area; S is a sectional area wiry to be measured, S=π R ' ²/ 4; F is the pulling force on prolonging direction, is counterweight weight mg; Parameter g is an acceleration of gravity; Then, the Young modulus that power F is corresponding is:

$E=\frac{4\mathrm{mgL}}{\mathrm{\π}{R}^{\′2}\mathrm{\ΔL}}---\left(2\right)$

Step 6, in elastic limit wiry to be measured, repeatedly increase the quality m of counterweight, increase after the counterweight at every turn, execution in step two to five obtains the Young modulus under power xmg effect, wherein x=1,2,3

As shown in Figure 2; Because light beam can constantly reflect and transmit thin glass plate between surface behind the thin glass plate and plane mirror; And this reflection and transmission for reflected light and transmitted light at infinity or the interference on the lens focal plane contribution is all arranged; So when interference is discussed, must consider repeatedly reflection and transmission effect, multi-beam laser promptly should be discussed interfere.

But; Because the optical mixing that transmit glass front of laser after the reflected light of glass front and plane reflection mirror reflection k time and k+1 time; The amplitude of two difference frequency signals that produce differs 2～3 one magnitude; Through after the Fourier transform, in order to collect laser difference frequency signal and the arithmetic speed that improves signal Processing preferably, so the E of our the k secondary reflection only considering to be detected here _kE behind the surperficial k+2 secondary reflection of light and back _K+2The humorous frequency difference of the secondary that optical mixing produced.

Under the situation of not considering thin glass plate self thickness, when laser with incident angle θ ₀During oblique incidence, establishing incident field is E (t)=E ₀Exp (i ω ₀T), the vibration equation of Doppler's galvanometer and rate equation are respectively x (t)=a (t ²/ 2) and v (t)=at.Because the motion of galvanometer, catoptrical frequency becomes ω=ω ₀(1+at/c), ω in the formula ₀Be the laser angular frequency, a is a vibration acceleration, and c is the light velocity.Then t-l/c arrives the reflection light field on thin glass plate surface constantly and is:

$E_1\left(t\right)={\mathrm{\α}}_1{E}_0\exp \left\{i\right[{\mathrm{\ω}}_0(1+\frac{a(t-l/c)}{c})t+{\mathrm{\ω}}_0\frac{\frac{a{(t-l/c)}^2}{2}}{c}\left]\right\}---\left(3\right)$

And constantly repeatedly reflected by plane mirror in difference through the light of thin glass plate transmission, its catoptrical expression formula is write as following form respectively:

$E_2\left(t\right)={\mathrm{\α}}_2{E}_0\exp \left\{i\right[{\mathrm{\ω}}_0(1+a\frac{t-\frac{l}{c}-\frac{2\mathrm{nd}\cos \mathrm{\θ}}{c}}{c})t+{\mathrm{\ω}}_0\frac{(a\frac{{(t-\frac{l}{c}-\frac{2\mathrm{nd}\cos \mathrm{\θ}}{c})}^2}{2}+2\mathrm{nd}\cos \mathrm{\θ})}{c}\left]\right\}$

. (4)

$E_j\left(t\right)={\mathrm{\α}}_j{E}_0\exp \left\{i\right[{\mathrm{\ω}}_0(1+a\frac{t-\frac{l}{c}-\frac{2(j-1)\mathrm{nd}\cos \mathrm{\θ}}{c}}{c})t$

$+{\mathrm{\ω}}_0\frac{(a\frac{{(t-\frac{l}{c}-\frac{2(j-1)\mathrm{nd}\cos \mathrm{\θ}}{c})}^2}{2}+2(j-1)\mathrm{nd}\cos \mathrm{\θ})}{c}\left]\right\}$

Wherein, α ₁=r, α ₂=β β ' r ' ..., α _j=β β ' r ' ^(2j-3)The reflectivity that r is a light when surrounding medium is injected thin glass plate, transmissivity is β, r ' is the reflectivity of plane mirror; Transmissivity when reflected light penetrates thin glass plate between thin glass plate and the plane mirror is β ', and d is the distance between thin glass plate and the plane mirror.N is the refractive index of medium between plane mirror and the thin glass plate, and θ is that incident light sees through refraction angle behind the thin glass plate.J is a nonnegative integer.

Like this, total light field of receiving of photodetector is expressed as:

E(t)＝E ₁(t)+E ₂(t)+…+E _j(t) (5)

Then the photocurrent of photodetector output is expressed as:

$I=\frac{\mathrm{\ηe}}{\mathrm{hv}}\frac{1}{Z}\underset{D}{\∫\∫}\frac{1}{2}[E_1\left(t\right)+E_2\left(t\right)+...+E_j\left(t\right)+...]{[E_1\left(t\right)+E_2\left(t\right)+...+E_j\left(t\right)+...]}^{*}\mathrm{ds}---\left(6\right)$

Wherein, e is an electron charge, and Z is the intrinsic impedance of photodetector surfaces medium, and η is a quantum efficiency, and D is the area of the test surface of photodetector, and h is a Planck's constant, and v is a laser frequency.

Because we point out only to consider E the principle part _kAnd E _K+2Therefore the second harmonic difference frequency signal that optical mixing produced, dc terms, only consider to exchange item here through filtering behind the low-pass filter, and this exchanges item and is commonly referred to electric current of intermediate frequency, and the electric current of intermediate frequency that arrangement obtains second harmonic signal is:

$I_{\mathrm{if}}=\frac{\mathrm{\ηe}}{2\mathrm{hv}}\frac{1}{Z}\underset{D}{\∫\∫}\underset{p=1}{\overset{\∞}{\mathrm{\Σ}}}\underset{j=p+2}{\overset{\∞}{\mathrm{\Σ}}}(E_p\left(t\right){E_j}^{*}\left(t\right)+{E_p}^{*}\left(t\right)E_j\left(t\right))\mathrm{ds}---\left(7\right)$

With (3) formula and (4) formula substitution (7) formula, net result is:

$I_{\mathrm{if}}=\frac{\mathrm{\ηe}}{\mathrm{hv}}\frac{\mathrm{\π}}{Z}\underset{p=1}{\overset{\∞}{\mathrm{\Σ}}}{\mathrm{\α}}_{p+2}{\mathrm{\α}}_p{E_0}^2\cos (\frac{8{\mathrm{\ω}}_0\mathrm{and}\cos \mathrm{\θ}}{c^2}t-\frac{{4\mathrm{\ω}}_0\mathrm{nd}\cos \mathrm{\θ}}{c}-\frac{4l{\mathrm{\ω}}_0\mathrm{and}\cos \mathrm{\θ}}{c^3}-\frac{8p{\mathrm{\ω}}_0{\mathrm{an}}^2{d}^2{\cos }^2\mathrm{\θ}}{c^3})---\left(8\right)$

Ignore 1/c ³Event after be reduced to:

$I_{\mathrm{if}}=\frac{\mathrm{\ηe}}{\mathrm{hv}}\frac{\mathrm{\π}}{Z}{E_0}^2\cos (\frac{{8\mathrm{\α\ω}}_0\mathrm{nd}\cos \mathrm{\θ}}{c^2}t-\frac{4{\mathrm{\ω}}_0\mathrm{nd}\cos \mathrm{\θ}}{c})\underset{p=1}{\overset{\∞}{\mathrm{\Σ}}}{\mathrm{\α}}_{p+2}{\mathrm{\α}}_p---\left(9\right)$

Wherein, p is a nonnegative integer.

Can see in intermediate frequency item difference on the frequency that multiple beam heterodyne second harmonic mensuration obtains and the phase differential information apart from d between plane mirror and the thin glass plate being arranged all through (9) formula.Be primarily aimed at intermediate frequency item intermediate frequency rate variance and analyze, because adopt Fourier transform to be easy to realize frequency measurement.At this moment, according to (9) formula, be designated as the frequency of interference signal:

f＝8and?cosθω ₀/(2πc ²)＝4and?cosθω ₀/(πc ²)＝Kd (10)

Can know according to (10) formula, being directly proportional between the frequency isoplanar catoptron of interference signal and the thin glass plate apart from d, scale-up factor is:

K＝4an?cosθω ₀/(πc ²) (11)

With the light source angle frequencies omega ₀, between plane mirror and the thin glass plate refractive index n, refraction angle θ, the galvanometer acceleration of medium a is relevant.

Should be noted that; Can find out that through (9) formula the photocurrent expression formula of detector output can be seen the second harmonic frequency crest after Fourier transform on frequency spectrum, through measuring second harmonic frequency; Just can measure between thin glass plate and the plane mirror apart from d; When d changes, just can measure the variation delta d of corresponding d according to (9) formula, known that Δ d just can calculate the testing sample Young modulus according to (2) formula.

Adopt method of emulation that the analog result of the described measuring method of this embodiment is carried out error analysis, detailed process is:

In order to verify the feasibility of multi-beam laser heterodyne second harmonic measuring method, former long L=(800.3 ± 0.5) mm that utilized MA TLAB software simulation uses screw-thread micrometer to measure the Young modulus of diameter as the carbon steel wire of 0.732mm.Used H _oSolid state laser wavelength X=2050nm, this laser is to eye-safe; Gravity acceleration g=9.80m/s ²Generally the refractive index of medium is got n=1 between plane mirror and the thin glass plate; The photosurface aperture of detector is R=1mm.Sensitivity 1A/W.Get Doppler's galvanometer acceleration a=2 * 10 ³M/s ²In experimentation, require in elastic limit, institute adds the counterweight quality and is increased to about 2kg according to certain step-length gradually by 0, simultaneously the numerical value Δ L of record difference moment length variations amounts and the quality m of corresponding counterweight.

Can see through emulation; The Fourier transform frequency spectrum of the multi-beam laser heterodyne second harmonic signal that obtains through signal Processing is as shown in Figure 3; Wherein solid line is under the laser oblique incidence situation, the Fourier transform frequency spectrum of corresponding multi-beam laser heterodyne second harmonic signal when measuring carbon steel wire length variations amount Δ L; Dotted line is under the laser normal incidence situation, the Fourier transform frequency spectrum of corresponding multi-beam laser heterodyne second harmonic signal when measuring carbon steel wire length variations amount Δ L.

From Fig. 3, can also see; Provided the theoretical curve under the situation of normal incidence in the experiment; Purpose is: in multi-beam laser heterodyne second harmonic signal spectrogram; The numerical value of the centre frequency of theoretical curve when the centre frequency of multi-beam laser heterodyne second harmonic signal frequency spectrum and normal incidence in the time of can obtaining oblique incidence simultaneously, like this, the ratio of two centre frequencies that are easy to obtain:

ζ＝cosθ (12)

Obtaining under the situation of centre frequency, can calculate the size of laser refraction angle θ behind thin glass plate,, therefore can obtain incident angle θ according to refraction law because the thickness of thin glass plate can be ignored through (12) formula ₀Size be:

${\mathrm{\θ}}_0=\stackrel{\·}{=}\mathrm{\θ}=\arccos \mathrm{\ξ}---\left(13\right)$

The numerical value of the K that asks through (11) formula at last finally obtains the value of variable in distance amount Δ d between thin glass plate and the plane mirror, because Δ d=Δ l, thereby can calculate the Young modulus of carbon steel wire under any incident angle situation according to (2) formula.

Simultaneously; Emulation has obtained under the different counterweight quality situation; The multi-beam laser heterodyne second harmonic signal Fourier transform frequency spectrum of correspondence was as shown in Figure 4 when multi-beam laser heterodyne second harmonic was measured carbon steel wire length variations amount; As can be seen from Figure 4, along with the increase of counterweight quality, the relative position of frequency spectrum reduces to the increase frequency that the low frequency direction moves promptly along with quality.Reason is: under the constant situation of carbon steel wire Young modulus; Counterweight quality and carbon steel wire length variations amount are proportional, and the distance that carbon steel wire length increases between thin glass plate and the plane mirror thereupon when the counterweight quality increases reduces thereupon, because the relation apart from d between frequency f and plane mirror and the thin glass plate is f=Kd; Under the constant situation of K; Frequency f and d are linear spectrum, and therefore, frequency also reduces the increase along with quality thereupon during reducing apart from d between plane mirror and the thin glass plate; The relative position of frequency spectrum moves to the low frequency direction, and Fig. 4 has verified the correctness of front theoretical analysis well.Need to prove that detection sensitivity is high, so the signal to noise ratio (S/N ratio) of the heterodyne second harmonic signal of Fig. 3 and Fig. 4 is very high because heterodyne detection is a kind of detection mode of nearly diffraction limit.

In theoretical derivation; The thickness of having ignored thin glass plate is not promptly considered the influence of the reflected light on surface behind the device to the heterodyne second harmonic signal; But in fact the thickness of thin glass plate is the 1mm that is generally less than that exists; For overcoming this influence; Can find out that according to (13) formula the frequency distribution of the multiple beam heterodyne second harmonic signal that the reflected light on surface produces behind the thin glass plate has added the interference that wave filter just can filters low heterodyne second harmonic signal near the zero-frequency of frequency spectrum in the experiment light path.Utilize above-mentioned multi-beam laser heterodyne second harmonic mensuration, continuous analog eight groups of data, obtained the simulation result of carbon steel wire length variations amount to be measured under the different counterweight quality situation, as shown in table 1.

Table 1:

Time	1	2	3	4	5	6	7	8
									m(kg)	0.25	0.50	0.75	1.00	1.25	1.50	1.75	2.00
ΔL(×10 -5m)	2.337857	4.675710	6.963858	9.301719	11.639581	13.977442	16.315297	18.653151
									E(×10 11N/m 2)	1.992916	1.992917	2.007142	2.003566	2.001426	2.000002	1.998987	1.998226

Because the theoretical value E of carbon steel wire Young modulus ₀=2 * 10 ¹¹N/m ², can calculate relative error according to the simulated data of table 1 and be:

$\mathrm{\η}=\frac{|E_0-\stackrel{\‾}{E|}}{\stackrel{\‾}{E}}\×100\%=\frac{|1.999398-2|\×{10}^{11}}{2\×{10}^{11}}\×100\%=0.03\%---\left(14\right)$

See that from analog result the order of magnitude of this method error is 10 ^-4, and the degree of accuracy that the optical lever method is measured only has 1mm; Simultaneously, when this method can avoid the optical lever method to measure because θ and 2 θ want smaller restriction, and approximate in the derivation and the systematic error brought.See that from simulated data the relative error of analog result is about 0.03%, meet actual conclusion, this method has reduced accidental error than few 2 of the indirect measuring amount of optical lever method, has improved measuring accuracy.This shows that the method for utilizing the multiple beam heterodyne method of quadratic harmonics to survey Young modulus is feasible.

Conclusion: the present invention is through introducing galvanometer in light path; Make the light signal of different incidents constantly add an optical frequency; Satisfying under the condition of interfering through the reflected light front surface of thin glass plate and the light that plane mirror repeatedly reflects like this; Produce multiple beam difference interference signal, thereby will treat that measurement information successfully is modulated in the difference on the frequency of intermediate frequency heterodyne second harmonic signal.In analog sample Young modulus process, the method has obtained comprising the frequency values of the information of metal length variable quantity at frequency domain, after the signal demodulation, can obtain the variable quantity of accurate sample length with the counterweight quality, finally obtains Young modulus through calculating.With the carbon steel wire is that example is carried out emulation experiment, and the relative error of Young modulus analog result is merely 0.03%, has significantly improved measuring accuracy.

Compare advantage such as the multi-beam laser heterodyne method of quadratic harmonics is surveyed Young modulus and had that high room and time resolution, measuring speed are fast, the linearity good, antijamming capability is strong, dynamic response is fast, good reproducibility and measurement range are big with other measuring methods; Experimental provision is simple in structure, power consumption is little, easy to operate; The experimental result error is little, the high many-sided advantage of precision.Simultaneously, because this method experimental phenomena is obvious, experimental data is reliable, so can in engineering design fields such as coherent laser windfinding radar, be widely used.

Claims (7)

1. the method for multi-beam laser heterodyne second harmonic measuring young modulus; It is based on, and the device of multi-beam laser heterodyne second harmonic measuring young modulus realizes; Said device based on multi-beam laser heterodyne second harmonic measuring young modulus comprises the device of multi-beam laser heterodyne measurement distance, and it is by H ₀Solid state laser (1), plane mirror (6), quarter-wave plate (3), galvanometer (2), galvanometer driving power, polarizing beam splitter mirror (4), convergent lens (9), thin glass plate (5), photodetector (10) and signal processing system are formed, and the galvanometer driving power is used to drive galvanometer (2) vibration; Thin glass plate (5) horizontal fixed is provided with a plane mirror (6) apart from the d place directly over this thin glass plate (5), and the reflecting surface of said thin glass plate (5) and plane mirror (6) is relative and be parallel to each other H ₀Solid state laser (1), quarter-wave plate (3), galvanometer (2), polarizing beam splitter mirror (4), convergent lens (9), photodetector (10) all are positioned at the below of thin glass plate (5), said H ₀The front surface of solid state laser (1) emission of lasering beam to polarizing beam splitter mirror (4); After quarter-wave plate (3) transmission, be transmitted into the plane of incidence of galvanometer (2) through this polarizing beam splitter mirror (4) beam reflected; Folded light beam after galvanometer (2) reflection is transmitted through polarizing beam splitter mirror (4) through quarter-wave plate (3) once more; After said polarizing beam splitter mirror (4) transmission, be incident to thin glass plate (5), this transmitted light beam is at the incident angle θ of the plane of incidence of this thin glass plate (5) ₀Less than 90 and more than or equal to 0 degree; This transmitted light forms folded light beam and transmitted light beam through this thin glass plate (5); Said printing opacity bundle is incident to convergent lens (9) once more through the folded light beam of plane mirror (6) reflection after thin glass plate (5) transmission; The folded light beam that forms through this thin glass plate (5) front surface reflection also is incident to convergent lens (9); Convergent lens (9) focuses to incident beam on the test surface of photodetector (10); The electrical signal of photodetector (10) is connected with the signal input part of wave filter (11); The signal output part of wave filter (11) is connected with the signal input part of prime amplifier (12); The signal output part of prime amplifier (12) is connected with the signal input part of A/D converter (13); The signal output part of said A/D converter (13) is connected with the signal input part of DSP digital signal processor (14), is solidified with fft algorithm in the said DSP digital signal processor (14), and DSP digital signal processor (14) obtains the distance between plane mirror (6) and the thin glass plate (5) according to after the signal demodulation that receives;

It is characterized in that: the method for multi-beam laser heterodyne second harmonic measuring young modulus, it is realized by following steps:

Step 1, a long L; Mean diameter is that the tinsel to be measured (8) of R ' hangs on the fixed support; The lower end of said tinsel to be measured (8) is fixedly connected with counterweight (7); Said counterweight (7) applies tensile force f so that said tinsel to be measured (8) produces internal stress to tinsel to be measured (8) under action of gravity; The bottom of said counterweight (7) is fixedly connected with the non-reflecting surface of plane mirror (6), makes tinsel to be measured (8) perpendicular to the reflecting surface of plane mirror (6), opens H then ₀Solid state laser (1), and control the galvanometer driving power simultaneously and drive galvanometer (2) and begin vibration;

Step 2, signal processing system are gathered the signal of photodetector (10) output, obtain the distance parameter between thin glass plate (5) and the plane mirror (6), when plane mirror (6) when remaining static, write down this distance parameter;

The quality m of step 3, increase counterweight,

Step 4, signal processing system are gathered the signal of photodetector (10) output once more, obtain the distance parameter between thin glass plate (5) and the plane mirror (6), when plane mirror (6) when remaining static, write down this distance parameter,

Step 5, according to two distance parameters that step 2 and four obtains, obtain the variation delta d of distance between thin glass plate (5) and the plane mirror (6), this variable in distance amount Δ d is the elongation Δ L of tinsel to be measured (8) under the effect of quality m:

According to Hooke's law, obtain Young modulus wiry to be measured and be:

$E=\frac{\mathrm{FL}}{\mathrm{S\ΔL}}$

In the formula, S is a sectional area wiry to be measured, S=π R '- ²/ 4;

F is the pulling force on prolonging direction, is counterweight weight mg; Parameter g is an acceleration of gravity; Then, the Young modulus that power F is corresponding is:

$E=\frac{4\mathrm{mgL}}{\mathrm{\π}{R}^{\′2}\mathrm{\ΔL}}$

Step 6, in elastic limit wiry to be measured; Repeatedly increase the quality m of counterweight; Each increasing after the counterweight, execution in step five obtains a distance parameter, obtains corresponding variable in distance amount according to the distance parameter of this distance parameter and step 2 acquisition; And then the Young modulus of acquisition under power xmg effect, wherein x=1,2,3

The process of the acquisition distance parameter described in step 2 and the step 4 is:

Under the motion effect of galvanometer (2), the catoptrical frequency that reflects through galvanometer (2) becomes:

ω＝ω ₀(1+at/c)，

In the formula: ω ₀Be the laser angular frequency, a is a vibration acceleration, and c is the light velocity; Then t-l/c arrives thin glass plate (5) front surface constantly and by the catoptrical light field of this thin glass plate (5) front surface reflection is:

$E_1\left(t\right)={\mathrm{\α}}_1{E}_0\exp \left\{i\right[{\mathrm{\ω}}_0(1+\frac{a(t-l/c)}{c})t+{\mathrm{\ω}}_0\frac{\frac{a{(t-l/c)}^2}{2}}{c}\left]\right\}$

Parameter E ₀Expression constant, l are represented the distance of galvanometer (2) to thin glass plate (5) front surface; Light through thin glass plate (5) front surface transmission is repeatedly reflected by plane mirror (6) in difference constantly, and its catoptrical expression formula is respectively:

$E_2\left(t\right)={\mathrm{\α}}_2{E}_0\exp \left\{i\right[{\mathrm{\ω}}_0(1+a\frac{t-\frac{l}{c}-\frac{2\mathrm{nd}\cos \mathrm{\θ}}{c}}{c})t+{\mathrm{\ω}}_0\frac{(a\frac{{(t-\frac{l}{c}-\frac{2\mathrm{nd}\cos \mathrm{\θ}}{c})}^2}{2}+2\mathrm{nd}\cos \mathrm{\θ})}{c}\left]\right\}$

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$E_j\left(t\right)={\mathrm{\α}}_j{E}_0\exp \left\{i\right[{\mathrm{\ω}}_0(1+a\frac{t-\frac{l}{c}-\frac{2(j-1)\mathrm{nd}\cos \mathrm{\θ}}{c}}{c})t$

$+{\mathrm{\ω}}_0\frac{(a\frac{{(t-\frac{l}{c}-\frac{2(j-1)\mathrm{nd}\cos \mathrm{\θ}}{c})}^2}{2}+2(j-1)\mathrm{nd}\cos \mathrm{\θ})}{c}\left]\right\}$

Wherein, α ₁=r, α ₂=β β ' r ' ..., α _j=β β ' r ' ^(2j-3)The reflectivity that r is a light when surrounding medium is injected thin glass plate (5); Transmissivity is β; R ' is the reflectivity of plane mirror (6), and the transmissivity when reflected light penetrates thin glass plate (5) between thin glass plate (5) and the plane mirror (6) is β ', and d is the distance between thin glass plate (5) and the plane mirror (6); J is a nonnegative integer; N is the refractive index of medium between thin glass plate and plane mirror; θ is that incident light sees through refraction angle behind the thin glass plate;

Total light field that photodetector receives is:

E(t)＝E ₁(t)+E ₂(t)+…+E _j(t)

J representes the number of the light beam that photodetector receives; The photocurrent of photodetector output is expressed as:

$I=\frac{\mathrm{\ηe}}{\mathrm{hv}}\frac{1}{Z}\underset{D}{\∫\∫}\frac{1}{2}[E_1\left(t\right)+E_2\left(t\right)+...+E_j\left(t\right)+...]{[E_1\left(t\right)+E_2\left(t\right)+...+E_j\left(t\right)+...]}^{*}\mathrm{ds}$

Wherein, e is an electron charge, and Z is the intrinsic impedance of photodetector surfaces medium, and η is a quantum efficiency, and D is the area of the test surface of photodetector (10), and h is a Planck's constant, and v is a laser frequency;

Said photo-signal after wave filter (11) filtering, the dc terms in the filtered signal, the electric current of intermediate frequency of the second harmonic signal of wave filter (11) output is expressed as:

$I_{\mathrm{if}}=\frac{\mathrm{\ηe}}{2\mathrm{hv}}\frac{1}{Z}\underset{D}{\∫\∫}\underset{p=1}{\overset{\∞}{\mathrm{\Σ}}}\underset{j=p+2}{\overset{\∞}{\mathrm{\Σ}}}(E_p\left(t\right){E_j}^{*}\left(t\right)+{E_p}^{*}\left(t\right)E_j\left(t\right))\mathrm{ds}$

Bring the expression formula of the reflection light field of the reflection light field of thin glass plate (5) front surface and plane mirror into following formula, this signal obtains current signal through the inner algorithm computation integration of DSP digital signal processor:

$I_{\mathrm{if}}=\frac{\mathrm{\ηe}}{\mathrm{hv}}\frac{\mathrm{\π}}{Z}\underset{p=1}{\overset{\∞}{\mathrm{\Σ}}}{\mathrm{\α}}_{p+2}{\mathrm{\α}}_p{E_0}^2\cos (\frac{8{\mathrm{\ω}}_0\mathrm{and}\cos \mathrm{\θ}}{c^2}t-\frac{{4\mathrm{\ω}}_0\mathrm{nd}\cos \mathrm{\θ}}{c}-\frac{4l{\mathrm{\ω}}_0\mathrm{and}\cos \mathrm{\θ}}{c^3}-\frac{8p{\mathrm{\ω}}_0{\mathrm{an}}^2{d}^2{\cos }^2\mathrm{\θ}}{c^3})$

Ignore 1/c ³Event after be reduced to:

$I_{\mathrm{if}}=\frac{\mathrm{\ηe}}{\mathrm{hv}}\frac{\mathrm{\π}}{Z}{E_0}^2\cos (\frac{{8\mathrm{\α\ω}}_0\mathrm{nd}\cos \mathrm{\θ}}{c^2}t-\frac{4{\mathrm{\ω}}_0\mathrm{nd}\cos \mathrm{\θ}}{c})\underset{p=1}{\overset{\∞}{\mathrm{\Σ}}}{\mathrm{\α}}_{p+2}{\mathrm{\α}}_p$

Wherein, p is a nonnegative integer;

The frequency of interference signal is designated as:

f＝8and?cosθω ₀/(2πc ²)＝4and?cosθω ₀/(πc ²)＝Kd

Scale-up factor K is:

K＝4an?cosθω ₀/(πc ²)

The photocurrent expression formula of photodetector (10) output obtains the second harmonic frequency crest on frequency spectrum through Fourier transform after, through the measurement second harmonic frequency, and then measure between thin glass plate (5) and the plane mirror (6) apart from d.

2. the method for multi-beam laser heterodyne second harmonic measuring young modulus according to claim 1 is characterized in that xmg is in elastic limit wiry to be measured.

3. the method for multi-beam laser heterodyne second harmonic measuring young modulus according to claim 1 is characterized in that tinsel to be measured (8) is a steel wire.

4. the method for multi-beam laser heterodyne second harmonic measuring young modulus according to claim 1, the length that it is characterized in that tinsel to be measured (8) is 1m, diameter of section is 0.25mm to 1mm.

5. the method for multi-beam laser heterodyne second harmonic measuring young modulus according to claim 1 is characterized in that in the system based on multi-beam laser heterodyne second harmonic measuring young modulus, apart from d >=20mm.

6. the method for multi-beam laser heterodyne second harmonic measuring young modulus according to claim 1 is characterized in that in the system based on multi-beam laser heterodyne second harmonic measuring young modulus H ₀The light field of the laser beam that solid state laser (1) is launched is:

E(t)＝E ₀exp(iω ₀t)，

Parameter i representes imaginary number; ω ₀The initial angle frequency of expression laser.

7. the method for multi-beam laser heterodyne second harmonic measuring young modulus according to claim 1; It is characterized in that in the system based on multi-beam laser heterodyne second harmonic measuring young modulus; Said galvanometer (6) is Doppler's galvanometer (6), and the vibration equation of this galvanometer (6) is:

x(t)＝a(t ²/2)，

T ∈ [0,0.001s], value is spaced apart 1 μ s; The Oscillation Amplitude of x (t) expression galvanometer (6); Parameter a representes the vibration acceleration of galvanometer, and span is 10 usually ²～10 ⁴M/s ²

The rate equation of this galvanometer (6) is:

v(t)＝at。

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