CN102175647B - Device and method for measuring electrostriction coefficient by multi-beam laser heterodyne method - Google Patents

Abstract

The invention relates to a device and a method for measuring electrostriction coefficient by multi-beam laser heterodyne method, which relate to the field of measurement technology, in particular to a measurement technology of electrostriction coefficient. It solves the problem that the measurement accuracy of the existing measurement methods for the electrostrictive coefficients of various piezoelectric crystals cannot meet the requirements of the existing high-precision measurement field. The present invention is designed based on the laser heterodyne technology and the Doppler effect. In the optical path, the device uses a galvanometer to perform frequency modulation on the incident light at different times, and obtains a multi-beam laser heterodyne signal. Contains multiple frequency values, and each frequency value contains the information of the parameter to be measured. After demodulation, multiple values of the parameter to be measured can be obtained at the same time, and the obtained multiple parameter values are weighted and averaged to obtain a high-precision parameter to be measured. A simulation experiment is carried out on lead zirconate titanate (PZT) piezoelectric ceramics to verify the method of the invention, and the relative measurement error is only 0.98%.

Description

The device and method of multi-beam laser heterodyne measurement electrostriction coefficient

Technical field

The present invention relates to field of measuring technique, be specifically related to a kind of measuring technique of electrostriction coefficient.

Background technology

Relate in the Mechatronic Systems and device of automatic control at all; Driver often is considered to one of the most key factor that limits its performance and life-span; And in numerous type of drivers, the piezoelectric driver is fast because of its response, bearing capacity is high, energy consumption is low and price is low etc., and characteristics receive much concern.At present; The piezoelectric driver successfully is applied in numerous technical fields such as laser resonant cavity, precision positioning, Precision Machining, intelligence structure, bioengineering, Aero-Space, telecommunications, auto industry, joint of robot, medicine equipment, and is forming an industry that has a high potential.Therefore, the exploitation for piezoelectric new material, new technology and driver new technology has received increasingly extensive attention with application.At occurring in nature, most of crystal all have piezoelectric effect, yet the piezoelectric effect of most of crystal is very faint, does not have practical value.Quartz is a well behaved piezoelectric in the crystal.Along with science and technology development, made piezoelectric ceramics is come out one after another like barium titanate, lead zirconate titanate polycrystalline piezoelectrics such as (PZT), and uses more and more widely.

The electrostriction coefficient of piezoelectric crystal has reflected the attribute of material itself, measures the electrostriction coefficient of material, and is not only significant to the development of new material, and is one of important indicator of the selection of material.At present, the method for mensuration electrostriction coefficient mainly contains laser interferance method, optical lever method, capacitance method, electric vortex method and Digital Speckle Correlation Method etc.But all there is the shortcoming of self in every kind of method, so precision can't improve again, can not satisfy the requirement of present high-acruracy survey.

And in optical measuring method; The laser heterodyne measurement technology enjoys 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, and the relative error of its measurement can reach 1%.Advantage such as this method 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; Become one of significant technology of modern ultraprecise detection and surveying instrument, be widely used in ultra precise measurement, detection, process equipment, laser radar system etc.

Traditional difference interference is two-beam interference, and the heterodyne signal frequency spectrum only contains single-frequency information, obtains single parameter value to be measured after the demodulation.

Summary of the invention

For the measuring accuracy of the measuring method of the electrostriction coefficient that solves existing various piezoelectric crystals can not satisfy the problem of the requirement of existing high-accuracy field of measurement, the present invention proposes a kind of device and method of multi-beam laser heterodyne measurement electrostriction coefficient.

The device of multi-beam laser heterodyne measurement electrostriction coefficient of the present invention is made up of Ho solid state laser, quarter-wave plate, galvanometer, first plane mirror, polarizing beam splitter mirror PBS, convergent lens, thin glass plate, second plane mirror, piezoelectric ceramic tube to be measured, two-dimentional adjustment rack, high-voltage power supply, photodetector and signal processing system;

The linearly polarized light that the Ho solid state laser sends is incident to polarizing beam splitter mirror PBS after the first plane reflection mirror reflection; Light beam after this polarizing beam splitter mirror PBS reflection is incident to the light receiving surface of galvanometer after the quarter-wave plate transmission; Light beam through this vibration mirror reflected is sent to polarizing beam splitter mirror PBS once more after the quarter-wave plate transmission; Light beam after this polarizing beam splitter mirror PBS transmission is incident to thin glass plate; Light beam after this thin glass plate transmission is incident to second plane mirror; This light beam reflects repeatedly between the thin glass plate that is parallel to each other and second plane mirror repeatedly, obtains the light beam of multi beam after the thin glass plate transmission and converges to through convergent lens on the photosurface of photodetector, and said photodetector output electric signal is given signal processing system; Distance between the thin glass plate and second plane mirror is d;

The center, the back side of said second plane mirror is fixedly connected with an end of piezoelectric ceramic tube to be measured; The other end of this piezoelectric ceramic tube to be measured is fixed on the two-dimentional adjustment rack; The inside surface of said piezoelectric ceramic tube to be measured is connected with two voltage output ends of high-voltage power supply through electrode respectively with outside surface, and this piezoelectric ceramic tube to be measured produces axial deformation under the effect of voltage.

Adopt the device of above-mentioned multi-beam laser heterodyne measurement electrostriction coefficient to realize that the method that electrostriction coefficient is measured is:

At first; Through adjusting two-dimentional adjustment rack; The reflecting surface and the thin glass plate of second plane mirror that is fixedly connected with piezoelectric ceramic tube to be measured are parallel to each other, wait highly between two flat boards, and to make between reflecting surface and the thin glass plate of second plane mirror be 20mm apart from d;

Then, will be connected with outside surface with the inside surface of piezoelectric ceramic tube to be measured through electrode respectively, and the driving power of opening galvanometer makes galvanometer begin vibration with two electrode outputs of high-voltage power supply; Simultaneously, open the Ho solid state laser,

At last; Regulate the output voltage signal U of said high-voltage power supply; The electric signal of synchronous signal disposal system continuous acquisition photodetector output; And the signal that collects handled, and then obtain the variable in distance amount between second plane mirror and the thin glass plate, obtain the electrostriction coefficient of piezoelectric ceramic tube to be measured according to this variable in distance amount and the voltage signal of high-voltage power supply output this moment:

$\mathrm{\α}=\frac{\mathrm{\Δ}{\mathrm{ld}}_0}{\mathrm{lU}}---\left(1\right)$

In the formula, Δ l is the length increment of electroceramics pipe behind the making alive, promptly equals the variable in distance amount between second plane mirror and the thin glass plate, and l is the length of piezoelectric ceramic tube to be measured; d ₀It is the wall thickness (all being unit) of piezoelectric ceramic tube to be measured with mm.

The present invention is on the laser heterodyne measurement technical foundation; Proposed a kind of scheme of multi-beam laser heterodyne measurement electrostriction coefficient, proposed a kind of multi-beam laser heterodyne measurement method that improves the heterodyne measurement precision, promptly in light path, utilized galvanometer that difference incident light is constantly carried out frequency modulation (PFM) based on this scheme; Obtained the multi-beam laser heterodyne signal; Comprise a plurality of frequency values in its signal spectrum simultaneously, each frequency values all comprises parameter information to be measured, can obtain a plurality of parameter values to be measured simultaneously through after the demodulation; To the multiple parameter values weighted mean that obtains, improved the precision of parameter to be measured.This paper has carried out theoretical analysis in detail to the method, at last lead zirconate titanate (PZT) piezoelectric ceramics has been carried out the emulation experiment checking, and measuring relative errors is merely 0.98%.

Description of drawings

Fig. 1 is the structural representation of the device of multi-beam laser heterodyne measurement electrostriction coefficient of the present invention.

Fig. 2 is the cut-open view of piezoelectric ceramic tube 7 to be measured.

Fig. 3 is the multi-beam laser principle of interference figure between the thin glass plate and second plane mirror.

Fig. 4 is the Fourier transform spectrogram of multi-beam laser heterodyne signal.

Fig. 5 is the corresponding spectrogram of PZT length variations measurement amount under the different voltage condition; Among the figure; From left to right, every curve high-voltage power supply output voltage respectively is under the situation of 800V, 700V, 600V, 500V, 400V, 300V, 200V and 100V, the spectrum curve of acquisition.

Embodiment

Embodiment one: referring to Fig. 1 this embodiment is described, the device of the described multi-beam laser heterodyne measurement of this embodiment electrostriction coefficient is by Ho solid state laser 2, quarter-wave plate 12, galvanometer 13, first plane mirror 3, polarizing beam splitter mirror PBS11, convergent lens 10, thin glass plate 9, second plane mirror 6, piezoelectric ceramic tube to be measured 7, two-dimentional adjustment rack 8, high-voltage power supply, photodetector 4 and signal processing system 5;

The linearly polarized light that Ho solid state laser 2 sends is incident to polarizing beam splitter mirror PBS11 after 3 reflections of first plane mirror; Light beam after this polarizing beam splitter mirror PBS11 reflection is incident to the light receiving surface of galvanometer 13 after quarter-wave plate 12 transmissions; After quarter-wave plate 12 transmissions, be sent to polarizing beam splitter mirror PBS11 once more through these galvanometer 13 beam reflected; Light beam after this polarizing beam splitter mirror PBS11 transmission is incident to thin glass plate 9; Light beam after these thin glass plate 9 transmissions is incident to second plane mirror 6; This light beam reflects repeatedly between the thin glass plate that is parallel to each other 9 and second plane mirror 6 repeatedly, obtains the light beam of multi beam after thin glass plate 9 transmissions and converges to through convergent lens 10 on the photosurface of photodetector 4, and said photodetector 4 output electric signal are given signal processing system 5; Distance between the thin glass plate 9 and second plane mirror 6 is d;

The center, the back side of said second plane mirror 6 is fixedly connected with an end of piezoelectric ceramic tube 7 to be measured; The other end of this piezoelectric ceramic tube 7 to be measured is fixed on the two-dimentional adjustment rack 8; The inside surface 7-1 of said piezoelectric ceramic tube to be measured 7 is connected with two voltage output ends of high-voltage power supply through electrode 1 respectively with outside surface 7-2, and this piezoelectric ceramic tube 7 to be measured produces axial deformation under the effect of voltage.

In this embodiment is 20mm apart from the general value of d.

Galvanometer 13 in this embodiment is done the even straight-line oscillation of quickening under the driving power effect, can incide galvanometer 13 surperficial laser constantly to difference and carry out frequency modulation (PFM).Said galvanometer 13 is Doppler's galvanometer, and its vibration equation and rate equation are respectively x (t)=a (t ²/ 2) and v (t)=at, a is the vibration acceleration of galvanometer.

Embodiment two: this embodiment is that the structure of the signal processing system 5 in the device of embodiment one described multi-beam laser heterodyne measurement electrostriction coefficient is done further to limit; Signal processing system 5 in this embodiment is made up of filtering circuit 5-1, pre-amplification circuit 5-2, analog to digital conversion circuit A/D and control circuit DSP; The electric signal that said filtering circuit 5-1 exports the photodetector 4 that receives carries out sending to pre-amplification circuit 5-2 after the filtering; Signal after said pre-amplification circuit 5-2 amplifies is exported to analog to digital conversion circuit A/D, and the signal after analog-digital conversion circuit as described A/D will change sends to control circuit DSP.

Embodiment three: this embodiment is described to be to adopt the device of embodiment one or two described multi-beam laser heterodyne measurement electrostriction coefficients to realize the method that electrostriction coefficient is measured, and the process of this method is:

At first; Through adjusting two-dimentional adjustment rack 8; The reflecting surface and the thin glass plate 9 of second plane mirror 6 that is fixedly connected with piezoelectric ceramic tube 7 to be measured are parallel to each other, wait highly between two flat boards, and to make between reflecting surface and the thin glass plate 9 of second plane mirror 6 be 20mm apart from d;

Then, will be connected with outside surface with the inside surface of piezoelectric ceramic tube 7 to be measured through electrode respectively, and the driving power of opening galvanometer 13 makes galvanometer 13 begin vibration with two electrode outputs of high-voltage power supply; Simultaneously, open Ho solid state laser 2,

At last; Regulate the output voltage signal U of said high-voltage power supply; The electric signal of synchronous signal disposal system 5 continuous acquisition photodetectors 4 outputs; And the signal that collects handled, and then obtain the variable in distance amount between second plane mirror 6 and the thin glass plate 9, obtain the electrostriction coefficient of piezoelectric ceramic tube 7 to be measured according to this variable in distance amount and the voltage signal of high-voltage power supply output this moment:

$\mathrm{\α}=\frac{\mathrm{\Δ}{\mathrm{ld}}_0}{\mathrm{lU}}---\left(1\right)$

In the formula, Δ l is the length increment of piezoelectric ceramic tube 7 to be measured behind the making alive, promptly equals the variable in distance amount between second plane mirror 6 and the thin glass plate 9, and l is the length of piezoelectric ceramic tube 7 to be measured; d ₀It is the wall thickness (all being unit) of piezoelectric ceramic tube 7 to be measured with mm.

Object with piezoelectric effect is called piezoelectrics, has now found that the multiple object with piezoelectric property, and monocrystalline, polycrystalline (polycrystalline ceramics) and some amorphous solid are wherein arranged.Piezoelectric ceramic tube to be measured among the present invention is a kind of piezoelectric ceramics of tubular, and its profile and structure are as shown in Figure 2.It is processed by lead zirconate titanate (PZT), and the surfaces externally and internally of piezoelectric ceramic tube 7 to be measured is silver-plated, as electrode; Connect and draw lead, just can execute impressed voltage, when applying positive voltage, inside surface ground connection at its outside surface to it; Piezoelectric ceramic tube 7 to be measured prolongs its axial elongation; Otherwise when its outside surface applied negative voltage, inside surface ground connection, piezoelectric ceramic tube 7 to be measured prolonged its axial shortening.

After representing that with E piezoelectric ceramic tube 7 surfaces externally and internallies to be measured add voltage, the electric field intensity of the radial electric field that between surfaces externally and internally, forms then has:

ε＝αE (2)

In the formula, α representes the electrostriction coefficient of piezoelectric ceramic tube 7 to be measured in the almost zone; ε representes the strain that piezoelectric ceramic tube to be measured 7 is axial; And

U is if be added in the voltage of piezoelectric ceramic tube 7 surfaces externally and internallies to be measured, then has:

$\frac{\mathrm{\Δl}}{l}=\mathrm{\α}\frac{U}{d_0}---\left(3\right)$

Finally can obtain:

$\mathrm{\α}=\frac{\mathrm{\Δ}{\mathrm{ld}}_0}{\mathrm{lU}}---\left(1\right)$

In the above-mentioned formula, d ₀Can directly measure with vernier caliper with l; Voltage U can be read by digital voltmeter, because during added change in voltage, the variation delta l of length l is very little; Can't use conventional length measurement method to solve; So need to adopt high-precision mensuration to measure this small quantity of electrostriction coefficient, this embodiment adopts embodiment one described device to accurately measure this small quantity, and then realizes the accurate measurement of electrostriction coefficient.The principle of the measurement device small quantity under the embodiment one is:

In the time can producing axial flexible deformation under the effect of piezoelectric ceramic tube 7 to be measured at high tension voltage, drive 6 motions of second plane mirror, make that the distance between this second plane mirror 6 and the thin glass plate 9 changes.Signal processing system in this embodiment can be carried out demodulation to the electric signal that photodetector obtains; Thereby obtain the variable in distance amount Δ d between second plane mirror 6 and the thin glass plate 9; And this Δ d equates with the axial deformation amount Δ l of piezoelectric ceramic tube 7 to be measured; The voltage signal of high-voltage power supply output just can obtain the electrostriction coefficient that this presses piezoelectric ceramic tube 7 to be measured during according to this deformation quantity Δ l and this deformation of generation.

Embodiment four: this embodiment is the further qualification to the method for the measurement of embodiment three described electrostriction coefficients; This embodiment is to the electric signal of signal processing system 5 according to 4 outputs of continuous acquisition photodetector; And the signal that collects handled; And then the process that obtains the variable in distance amount between second plane mirror 6 and the thin glass plate 9 further specifies, and this process is:

The incident angle of light beam oblique incidence to the thin glass plate 9 after this polarizing beam splitter mirror PBS11 transmission is θ 0, and the incident field of this moment is:

E(t)＝E ₀exp(iω ₀t)， (4)

E in the formula ₀Be constant, i representes imaginary number, ω ₀Be the laser angular frequency, this angular frequency is:

ω ₀＝(1+at/c)/ω (5)

ω is the incident light frequency of thin glass plate 9 in the formula, and a is the vibration acceleration of galvanometer 13, and c is the light velocity;

Then arrive thin glass plate surface constantly and be by the catoptrical light field of this surface reflection at t-l/c:

$E_1\left(t\right)={\mathrm{\α}}_1{E}_0\exp \left\{i\right[{\mathrm{\ω}}_0(1+\frac{a(t-l/c)}{c})t+{\mathrm{\ω}}_0\frac{\frac{a{(t-l/c)}^2}{2}}{c}\left]\right\}---\left(6\right)$

In the formula, l representes galvanometer 13 to the distance between the thin glass plate 9, and through the light of thin glass plate transmission in difference constantly by the m-1 secondary reflection of second plane mirror 6, the light field that obtains the m-1 bundle transmitted light of thin glass plate altogether is respectively:

$\begin{array}{c}{E}_2\left(t\right)={\mathrm{\α}}_2{E}_0\exp \left\{i\right[{\mathrm{\ω}}_0(1+a\frac{t-\frac{l}{c}-\frac{2\mathrm{nd}\cos \mathrm{\θ}}{c}}{c})t+{\mathrm{\ω}}_0\frac{(a\frac{{(t-\frac{l}{c}-\frac{2\mathrm{nd}\cos \mathrm{\θ}}{c})}^2}{2}+2\mathrm{nd}\cos \mathrm{\θ})}{c}\left]\right\}\\ .\\ .\\ .\\ .\\ .\\ .\end{array}---\left(7\right)$

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

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

Wherein, α ₁=r, α ₂=β β ' r ' ..., α _m=β β ' r ' ^(2m-3), the reflectivity that r is a light when surrounding medium is injected thin glass plate 9, transmissivity is β, and r ' is the reflectivity of second plane mirror 6, and the transmissivity when reflected light penetrates thin glass plate 9 between the thin glass plate and second plane mirror 6 is β '.

Total light field that photodetector 4 receives is:

E(t)＝E ₁(t)+E ₂(t)+…+E _m(t) (8)

Then the photocurrent of photodetector 4 outputs is:

$I=\frac{\mathrm{\&eta;e}}{\mathrm{hv}}\frac{1}{Z}\underset{\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="HDA0000045689400000011.png"\; state="\{\{state\}\}">D</figure-callout>}}{\&Integral;\&Integral;}\frac{1}{2}[E_1\left(t\right)+E_2\left(t\right)+...+E_m\left(t\right)]{[E_1\left(t\right)+E_2\left(t\right)+...+E_m\left(t\right)]}^{*}\mathrm{ds}$ (9)

$=\frac{\mathrm{\&eta;e}}{2\mathrm{hv}}\frac{1}{Z}\underset{D}{\&Integral;\&Integral;}[\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{E_j}^2\left(t\right)+\underset{p=1}{\overset{m-1}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{m-p}{\mathrm{\&Sigma;}}}{(E}_j\left(t\right){E_{j+p}}^{*}\left(t\right)+{E_j}^{*}\left(t\right)E_{j+p}\left(t\right))]\mathrm{ds}$

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

Because dc terms is through can filtering behind the low-pass filter 5-1, therefore, only to consider here to exchange, this exchanges and is commonly referred to electric current of intermediate frequency, and arrangement can get electric current of intermediate frequency and be:

$I_{\mathrm{if}}=\frac{\mathrm{\&eta;e}}{2\mathrm{hv}}\frac{1}{Z}\underset{s}{\&Integral;\&Integral;}\underset{p=1}{\overset{m-1}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{m-p}{\mathrm{\&Sigma;}}}(E_j\left(t\right){E_{j+p}}^{*}\left(t\right)+{E_j}^{*}\left(t\right)E_{j+p}\left(t\right))\mathrm{ds}---\left(10\right)$

With (6) formula and (7) formula substitution (10) formula, be through the computed in software integral result:

$I_{\mathrm{if}}=\frac{\mathrm{\&eta;e}}{\mathrm{hv}}\frac{\mathrm{\&pi;}}{Z}\underset{p=1}{\overset{m-1}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{m-p}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_j{\mathrm{\&alpha;}}_{j+p}{E_0}^2\cos [(\frac{{4\mathrm{\&omega;}}_0\mathrm{anpd}\cos \mathrm{\&theta;}}{c^2}-\frac{{2\mathrm{\&omega;}}_0\mathrm{anpd}\cos \mathrm{\&theta;}}{c^3})t+{\mathrm{\&omega;}}_0(\frac{{\mathrm{an}}^2{p}^2{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA0000045689400000011.png"\; state="\{\{state\}\}">d</figure-callout>}}^2{\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="HDA0000045689400000011.png"\; state="\{\{state\}\}">cos</figure-callout>}}^2\mathrm{\&theta;}}{c^3}-\frac{2\mathrm{npd}\cos \mathrm{\&theta;}}{c})]---\left(11\right)$

Ignore 1/c ³Event after can be reduced to:

$I_{\mathrm{if}}=\frac{\mathrm{\&eta;e}}{\mathrm{hv}}\frac{\mathrm{\&pi;}}{Z}\underset{p=1}{\overset{m-1}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{m-p}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_j{\mathrm{\&alpha;}}_{j+p}{E_0}^2\cos (\frac{{4\mathrm{\&omega;}}_0\mathrm{anpd}\cos \mathrm{\&theta;}}{c^2}t-{\mathrm{\&omega;}}_0\frac{2\mathrm{npd}\cos \mathrm{\&theta;}}{c})---\left(12\right)$

(12) formula can be designated as:

$I_{\mathrm{if}}=\frac{\mathrm{\&eta;e}}{\mathrm{hv}}\frac{\mathrm{\&pi;}}{Z}\underset{p=1}{\overset{m-1}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{m-p}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_j{\mathrm{\&alpha;}}_{j+p}{E_0}^2\cos [\mathrm{\&Omega;}\left(p\right)t-\mathrm{\&Phi;}\left(p\right)]=\frac{\mathrm{\&eta;e}}{\mathrm{hv}}\frac{\mathrm{\&pi;}}{Z}{E_0}^2\underset{p=1}{\overset{m-1}{\mathrm{\&Sigma;}}}\cos [\mathrm{\&Omega;}\left(p\right)t-\mathrm{\&Phi;}\left(p\right)]\left(\underset{j=1}{\overset{m-p}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_j{\mathrm{\&alpha;}}_{j+p}\right)---\left(13\right)$

Wherein:

$\mathrm{\&Omega;}\left(p\right)=\frac{{4\mathrm{\&omega;}}_0\mathrm{anpd}\cos \mathrm{\&theta;}}{c^2}---\left(14\right)$

$\mathrm{\&Phi;}\left(p\right)=\frac{{2\mathrm{\&omega;}}_0\mathrm{npd}\cos \mathrm{\&theta;}}{c^2}---\left(15\right)$

Here, p gets natural number;

Can see that through (13) formula the information apart from d is all arranged in intermediate frequency item difference on the frequency that multiple beam heterodyne measurement method obtains and the phase differential between the thin glass plate 9 and second plane mirror 6.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 (13) formula, can be designated as the frequency of interference signal:

f _p＝Ω(p)＝K _pd (16)

That is: the distance between second plane mirror 6 and the thin glass plate 9 is:

d＝Ω(p)/K _p

Can know that according to (14) formula the frequency of interference signal is directly proportional with testing distance, scale-up factor is:

$K_p=\frac{{4\mathrm{\&omega;}}_0\mathrm{anp}\cos \mathrm{\&theta;}}{c^2}---\left(17\right)$

With the light source angle frequencies omega ₀, refractive index n, refraction angle θ and the galvanometer 13 constant a of medium are relevant between thin glass plate and second plane mirror 6,

When d changes, measure the variation delta d of corresponding d according to (16) formula, Δ d obtains final variable in distance amount to the measured value weighted mean then.

Should be noted that through (13) formula and (17) formula and can find out that the photocurrent of detector output is by the humorous wave component of difference; Each respectively corresponding natural multiple of frequency that is to say that the side frequency difference is a fixed value, after Fourier transform, on frequency spectrum, can see different harmonic frequency crests; Through measuring different harmonic frequencies; Just can measure between the thin glass plate and second plane mirror 6 apart from d, when d changes, just can measure the variation delta d of corresponding d according to (16) formula; Δ d just can improve the measuring accuracy of Δ d to the measured value weighted mean after handling so then.

Adopted the multi-beam laser principle of interference in the measuring method of this embodiment; Referring to shown in Figure 2; Because light beam can constantly reflect and reflect between the thin glass plate and second plane mirror, and this reflection and refraction for reflected light and transmitted light at infinity or the interference on the lens focal plane contribution is all arranged, so when the discussion interference; Must consider repeatedly reflection and refraction effect, multi-beam laser promptly should be discussed interfere.

Embodiment five: this embodiment is to adopt the method for emulation experiment that the feasibility of the method for the measurement of electrostriction coefficient of the present invention is done further checking

The pressure measurement piezoelectric ceramic tube 7 to be measured of treating in this embodiment is selected long 15.00mm for use; Thickness is the piezoelectric ceramic tube of the PZT material of 1.50mm; Adopt the MATLAB software simulation to measure the electrostriction coefficient of this piezoelectric ceramic tube 7 to be measured, this electrostriction coefficient theoretical value of pressing the PZT material of piezoelectric ceramic tube 7 to be measured is 1.85 * 10 ^-9M/V, the feasibility of checking multi-beam laser heterodyne measurement method below.

Employed Ho solid state laser wavelength X=2050nm, this laser is to eye-safe; Generally the refractive index of medium is got n=1 between second plane mirror 6 and the thin glass plate; The photosurface aperture of detector is D=1mm.Sensitivity 1A/W.Getting Doppler's galvanometer 13 vibration equations is: x (t)=a (t ²/ 2), get a=4 * 10 in the formula ⁶M/s ²In experimentation, the voltage that requires to be added in piezoelectric ceramics slowly is increased to about 800V according to certain step-length by 0, simultaneously the numerical value Δ l of record length variable quantity.

Can see through emulation; The Fourier transform frequency spectrum of the multi-beam laser heterodyne signal that obtains through signal Processing is as shown in Figure 4; Wherein solid line is under the laser oblique incidence situation, the Fourier transform frequency spectrum of corresponding multi-beam laser heterodyne signal when measuring PZT 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 signal when measuring PZT length variations amount Δ l.

Solid line can be found out from Fig. 4, the spectrum distribution of multi-beam laser heterodyne signal, and its frequency spectrum is spacedly distributed, and conforms to the front theoretical analysis.Simultaneously; From Fig. 4, can also see; Provided the theoretical curve under the situation of normal incidence in the experiment, purpose is: in multi-beam laser heterodyne signal spectrogram, and the numerical value of the centre frequency of theoretical curve when the centre frequency of first main peak of multi-beam laser heterodyne signal frequency spectrum and normal incidence in the time of can obtaining oblique incidence simultaneously; The ratio of two centre frequencies that like this, are easy to obtain:

ζ＝cosθ (18)

Obtaining under the situation of centre frequency, can calculate the size of laser refraction angle θ behind thin glass plate through (18) formula, and then can obtain incident angle θ according to refraction law ₀Size, the K that asks through (16) formula at last _pNumerical value, finally obtain the value of variable in distance amount Δ d between the thin glass plate and second plane mirror 6 because Δ d=Δ l, thereby according to

Can calculate the electrostriction coefficient of PZT under any incident angle situation.

Simultaneously; Emulation has obtained under the different voltage condition; Multi-beam laser heterodyne signal Fourier transform frequency spectrum corresponding during multi-beam laser heterodyne measurement PZT length variations amount is as shown in Figure 5; As can be seen from Figure 5, along with the increase of voltage, the relative position of frequency spectrum reduces to the increase frequency that the low frequency direction moves promptly along with voltage.Reason is: under the constant situation of PZT electrostriction coefficient; Voltage and PZT length variations amount are proportional; The distance that PZT length increases between the thin glass plate and second plane mirror 6 thereupon when voltage increases reduces thereupon, because the relation apart from d between frequency f p and second plane mirror 6 and the lens is f _p=K _pD, K _pUnder the constant situation, frequency f _pBe linear spectrum with d, therefore, frequency also reduces the increase along with voltage thereupon during reducing apart from d between second plane mirror 6 and the lens, and the relative position of frequency spectrum moves to the low frequency direction, and Fig. 5 has verified the correctness of front theoretical analysis well.Need to prove, for the physical relationship of frequency with change in voltage is described, only provided the situation of the unimodal spectrogram after the multiple beam heterodyne FFT conversion among Fig. 5, launch to see and be similar to Fig. 4 multimodal Fourier transform spectrogram when carrying out Fig. 5 frequency spectrum.Simultaneously, because heterodyne detection is a kind of detection mode of nearly diffraction limit, detection sensitivity is high, so the signal to noise ratio (S/N ratio) of the heterodyne signal of Fig. 4 and Fig. 5 is very high.

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 heterodyne signal; But in fact the thickness of thin glass plate is the 1mm that is generally less than that exists, and for overcoming this influence, can find out according to (17) formula; The frequency distribution of the multiple beam heterodyne signal that the reflected light on surface produces behind the thin glass plate has added the interference that wave filter just can the filters low heterodyne signal in the experiment light path near the zero-frequency of frequency spectrum.Utilize above-mentioned multi-beam laser heterodyne measurement method, eight groups of data of continuous coverage have obtained the simulated measurement result of PZT length variations amount to be measured under the different voltage condition, and are as shown in table 1.

Under the different voltage condition of table 1, the simulated measurement result of PZT length variations amount and corresponding electrostriction coefficient

Need to prove: utilize the emulation experiment data of table 1, the average measurement value that can calculate the electrostriction coefficient of PZT according to (3) formula is 1.83178 * 10 ^-9M/V, so just can obtain measuring relative errors is 0.98%, the measuring accuracy that can find out this method is very high.Simultaneously; The analysis data it can also be seen that; Slowly increasing under the voltage condition, systematic error that environment brings and reading error are negligible in emulation, and the error in the emulation experiment mainly comes from trueness error and the round-off error in the computation process after the Fast Fourier Transform (FFT) (FFT).

The present invention is through introducing galvanometer 13 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 of thin glass plate and the light of more than 3 reflection of first plane mirror 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 signal.In measuring samples electrostriction coefficient process; The method has obtained comprising a plurality of frequency values of the information of metal length variable quantity simultaneously at frequency domain; Obtain a plurality of length variations amounts after the signal demodulation, can obtain accurate sample length with the change in current amount through weighted mean.With the iron-nickel alloy is that example experimentizes, and the relative error that electrostriction coefficient is measured is merely 0.98%, has significantly improved measuring accuracy.

Compare advantage such as the multi-beam laser process of heterodyning is surveyed electrostriction coefficient 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 method; 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.Get in touch because the exploitation of this experiment and new material has directly,, can in engineering design fields such as coherent laser windfinding radar, be widely used so have actual using value.

Claims (5)

1. The device for measuring electrostrictive coefficient by multi-beam laser heterodyne method is characterized in that the device is composed of Ho solid-state laser (2), quarter wave plate (12), vibrating mirror (13), first plane reflection mirror (3), polarizing beam splitter PBS (11), converging lens (10), thin glass plate (9), second plane mirror (6), piezoelectric ceramic tube to be tested (7), two-dimensional adjustment frame (8), high-voltage power supply, photoelectric detector (4) and signal processing system (5); The linearly polarized light emitted by the Ho solid-state laser (2) is reflected by the first plane reflector (3) and then enters the polarizing beam splitter PBS (11), and the beam reflected by the polarizing beam splitter PBS (11) is quarter-split One of the wave plates (12) is transmitted and incident on the light-receiving surface of the vibrating mirror (13), and the light beam reflected by the vibrating mirror (13) is transmitted to the polarizing beam splitter after being transmitted by the quarter wave plate (12) again PBS (11), the light beam transmitted through the polarizing beam splitter PBS (11) is incident on the thin glass plate (9), and the light beam transmitted through the thin glass plate (9) is incident on the second plane mirror (6) , the light beams transmitted through the thin glass plate (9) are repeatedly refracted between the thin glass plate (9) parallel to each other and the second plane mirror (6), and multiple beams are transmitted through the thin glass plate (9). The subsequent light beams are converged to the photosensitive surface of the photodetector (4) through the converging lens (10), and the photodetector (4) outputs an electrical signal to the signal processing system (5); the thin glass plate (9) and the second The distance between the plane mirrors (6) is d; The back center of the second plane mirror (6) is fixedly connected to one end of the piezoelectric ceramic tube (7) to be tested, and the other end of the piezoelectric ceramic tube (7) to be tested is fixed on the two-dimensional adjustment frame (8) Above, the inner surface (7-1) and the outer surface (7-2) of the piezoelectric ceramic tube (7) to be tested are respectively connected to the two voltage output terminals of the high-voltage power supply through the electrode (1). The electroceramic tube (7) produces axial deformation under the action of voltage. 2. The device for measuring electrostrictive coefficient by multi-beam laser heterodyne method according to claim 1, characterized in that, the distance d is 20mm. 3. multi-beam laser heterodyne method according to claim 1 measures the device of electrostrictive coefficient, it is characterized in that, described vibrating mirror (13) is a Doppler vibrating mirror, and its vibration equation and velocity equation are respectively x (t)=a(t ² /2) and v(t)=at, a is the vibration acceleration of the vibrating mirror. 4. the multi-beam laser heterodyne method according to claim 1 measures the device of electrostrictive coefficient, it is characterized in that, described signal processing system (5) is made of filter circuit (5-1), preamplifier circuit (5 -2), an analog-to-digital conversion circuit (A/D) and a control circuit DSP are composed, and the filter circuit (5-1) sends to the preamplifier after filtering the electrical signal output by the photodetector (4) received circuit (5-2), the signal amplified by the preamplifier circuit (5-2) is output to the analog-to-digital conversion circuit (A/D), and the analog-to-digital conversion circuit (A/D) converts the The signal is sent to the control circuit DSP. 5. adopt the method for measuring electrostrictive coefficient to realize the device of electrostrictive coefficient measuring by multi-beam laser heterodyne method claimed in claim 1, it is characterized in that the process of this method is: First, by adjusting the two-dimensional adjustment frame (8), the reflection surface of the second flat mirror (6) fixedly connected with the piezoelectric ceramic tube (7) to be tested and the thin glass plate (9) are parallel to each other, and the two flat plates Equal height between, and make the distance d between the reflective surface of the second flat mirror (6) and the thin glass plate (9) be 20mm; Then, connect the two electrode output terminals of the high-voltage power supply to the inner surface and the outer surface of the piezoelectric ceramic tube (7) to be measured through the electrodes respectively, and open the driving power of the vibrating mirror (13) to make the vibrating mirror (13) start vibration; at the same time, turn on the Ho solid-state laser (2), Finally, the output voltage signal U of the high-voltage power supply is adjusted, and at the same time, the signal processing system (5) continuously collects the electrical signal output by the photodetector (4), and processes the collected signal, and then obtains the second plane mirror ( 6) and the distance variation between the thin glass plate (9), obtain the electrostrictive coefficient of the piezoelectric ceramic tube (7) to be measured according to the distance variation and the voltage signal output by the high-voltage power supply at this time: In the formula, Δl is the length increment of the piezoelectric ceramic tube (7) to be measured after the voltage is applied, which is equal to the distance variation between the second plane reflector (6) and the thin glass plate (9), and l is the Measure the length of the piezoelectric ceramic tube (7); _d0 is the wall thickness of the piezoelectric ceramic tube (7) to be measured.

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