CN103940844A - Device and method for measuring linear expansion coefficient of metal by virtue of linear-frequency-modulation multi-beam laser heterodyne - Google Patents

Abstract

The invention relates to a device and a method for measuring a linear expansion coefficient of metal by virtue of a linear-frequency-modulation multi-beam laser heterodyne, belonging to the field of the measurement of linear expansion coefficients of materials and solving the problem that measuring errors are too large because more parameters need to be directly measured and the operation is complex in an existing linear expansion coefficient measuring method. According to the device and the method, to-be-measured parameter information is modulated into the frequency difference of heterodyne signals by virtue of a linear frequency modulation technique based on the linear frequency modulation and a laser heterodyne technique, a plurality of to-be-measured parameters can be simultaneously obtained by demodulating the laser heterodyne signals, and the accurate information of the to-be-measured parameters is obtained by virtue of weighted average treatment. The device and the method are applied to ultra-precise measurement, detection, processing equipment, laser radar systems and the like; an experimental phenomenon is obvious, and the experimental data is reliable; the device and the method are particularly applied to engineering design fields of coherence laser wind-finding radars and the like.

Description

Linear frequency modulation multi-beam laser heterodyne is measured the device and method of expansion coefficients of metal wire

Technical field

The invention belongs to the linear expansion coefficient fields of measurement of material.

Background technology

The hot expansion property of object has reflected the attribute of material itself, after conventionally solid being heated one-dimensional square upwards the variation of length be called line expand.Measure the linear expansion coefficient of material, not only significant to the development of new material, and be one of important indicator of the selection of material.In the process such as manufacture, the processing of material of Structural Design, machinery and instrument, all must consider the thermal expansion character of material.Otherwise, will affect the stability of structure and the precision of instrument.It is improper to consider, even can cause the damage of engineering, instrument malfunctioning, and defect in processing welding and failure etc.At present, the mensuration of expansion coefficients of metal wire is had to the measuring methods such as optical lever method, reading microscope method, electrothermal way and laser interferance method.

In the process of measuring by these methods, because the parameter that needs are directly measured is too much, operate more complicated, to such an extent as to systematic error and the accidental error of experiment are bigger than normal, for example, while surveying linear expansion coefficient with optical lever method, because the employing of approximate formula and complicated operation make its systematic error bigger than normal, meanwhile, the accidental error that is equipped with unreasonable introducing due to reading device is also larger, to such an extent as to its relative error reaches 4.4%; Systematic error that the accidental error that reading microscope method causes due to vision and the delay of electrothermal way actual temperature and sensor cause etc. has all limited its measuring accuracy greatly; Laser interferance method is because the interference fringe of this device is sharp carefully, resolution is high, experimental implementation is simple simultaneously, thereby greatly reduce experimental error, realize the accurate measurement of linear expansion coefficient, the relative error of measuring can be 2%, but the accidental error that this method exists vision to cause in the time reading number of interference fringes, causes precision to improve again, can not meet the requirement that current superhigh precision is measured.

Summary of the invention

The present invention needs in existing linear expansion coefficient measuring method in order to solve that the parameter directly measured is many, complicated operation, to such an extent as to measuring error problem bigger than normal, and the device and method of linear frequency modulation multi-beam laser heterodyne measurement expansion coefficients of metal wire is now provided.

Linear frequency modulation multi-beam laser heterodyne is measured the device of expansion coefficients of metal wire, and it comprises: linear frequency modulation laser instrument, thin glass plate, plane mirror, electrothermal furnace, temperature controller, convergent lens and a photodetector;

The linear frequency modulation laser of linear frequency modulation laser instrument output incides the front surface of thin glass plate, and incidence angle θ ₀for acute angle, thin glass plate be reflected light and refract light by this laser beam splitter, thin glass plate reflexes to this reflected light on convergent lens, thin glass plate refracts to this refract light on a plane mirror, the rear surface of this plane mirror and thin glass plate will obtain No. two reflected light of multi beam after this refract light multiple reflections, No. two reflected light of this multi beam refract on convergent lens through thin glass plate, and the light that convergent lens is received converges on the photosurface of photodetector;

Electrothermal furnace is used to Metallic rod homogeneous heating to be measured, and temperature controller is for controlling and detect the temperature of electrothermal furnace;

A plane mirror is fixed on one end of Metallic rod to be measured, and vertical with the axis of Metallic rod to be measured, and thin glass plate and a plane mirror be arranged in parallel, and distance between thin glass plate and a plane mirror is between 20mm to 30mm.

Linear frequency modulation multi-beam laser heterodyne based on said apparatus is measured the method for expansion coefficients of metal wire, and the method comprises the following steps:

Step 1: open linear frequency modulation laser the linear frequency modulation laser that linear frequency modulation laser instrument sends is incided on thin glass plate, and ensure incidence angle θ ₀for acute angle; Open electrothermal furnace and temperature controller, the temperature of temperature controller control electrothermal furnace also gathers the temperature of Metallic rod to be measured simultaneously;

Step 2: gather the signal of the photocurrent I of photodetector output, thereby and the DC terms of this photocurrent I is carried out to filtering acquisition electric current of intermediate frequency I _iF;

Step 3: the electric current of intermediate frequency I that step 2 is obtained _iFanalyze, obtain the frequency f of interference signal _p:

$f_p=\frac{2\mathrm{pknd}\cos \mathrm{\θ}}{\mathrm{\πc}}=K_{p}d,$

Wherein, p is nonnegative integer, for the rate of change of the modulating bandwidth of linear frequency modulation laser instrument, T is the frequency modulation cycle, △ F is modulating bandwidth, n is the refractive index of medium between thin glass plate and a plane mirror, d is the distance between thin glass plate and a plane mirror, θ is the refraction angle that incident light transmits thin glass plate, the light velocity that c is incident light, K _pscale-up factor between frequency and the refraction angle θ cosine of expression intermediate frequency heterodyne signal;

Step 4: the frequency f of utilizing interference signal _pobtain the distance d between thin glass plate and a plane mirror, obtain the change of distance amount △ d between thin glass plate and a plane mirror,

△d＝d ₀-d，

Wherein, d ₀represent the initial distance between thin glass plate and a plane mirror;

Step 5: utilize following formula to obtain the linear expansion coefficient α of Metallic rod to be measured,

$\mathrm{\α}=\frac{\mathrm{\Δd}}{l_0\mathrm{\ΔT}},$

Wherein, l ₀represent the initial length of Metallic rod to be measured, △ T=T ₁-T ₂represent the temperature variation of Metallic rod to be measured, T ₁represent the temperature of Metallic rod to be measured under room temperature, T ₂the temperature of Metallic rod to be measured when distance between expression thin glass plate and a plane mirror is d.

Linear frequency modulation multi-beam laser heterodyne of the present invention is measured the device and method of expansion coefficients of metal wire, based on linear frequency modulation technology and heterodyne technology, utilize linear frequency modulation technology that parameter information to be measured is modulated in heterodyne signal, by can accurately obtaining parameter information to be measured to the demodulation of heterodyne, in this parameter information measuring process, measuring speed is fast, the linearity good, antijamming capability is strong, dynamic response is fast, reproducible and measurement range is large; Apparatus structure of the present invention is simple, power consumption is little, easy to operate; The method of the invention experimental result error is little, precision is high; Test as an example of brass example, the relative error that linear expansion coefficient is measured is only 0.1%.The present invention is applicable to ultra precise measurement, detection, process equipment, laser radar system etc., and experimental phenomena of the present invention is obvious, and experimental data is reliable, is especially useful in the engineering design fields such as coherent laser windfinding radar.

Brief description of the drawings

Fig. 1 is the structural representation that the linear frequency modulation multi-beam laser heterodyne described in embodiment one is measured the device of expansion coefficients of metal wire.

Fig. 2 is the principle of interference schematic diagram of linear frequency modulation multi-beam laser between thin glass plate and a plane mirror; Wherein E represents to incide the laser on thin glass plate, E ₁for the laser of thin glass plate front surface reflection, E ₂to E _mthe laser that represents the refraction of thin glass plate rear surface, d represents the distance between thin glass plate and a plane mirror.

Fig. 3 is the structural representation that the linear frequency modulation multi-beam laser heterodyne described in embodiment two is measured the device of expansion coefficients of metal wire.

Fig. 4 is the structural representation that the linear frequency modulation multi-beam laser heterodyne described in embodiment three is measured the device of expansion coefficients of metal wire.

Fig. 5 is the structural representation that the linear frequency modulation multi-beam laser heterodyne described in embodiment four is measured the device of expansion coefficients of metal wire.

Fig. 6 be room temperature at 15 DEG C, the Fourier transform spectrogram of linear frequency modulation multi-beam laser heterodyne signal.

Embodiment

Embodiment one: see figures.1.and.2 and illustrate present embodiment, linear frequency modulation multi-beam laser heterodyne described in present embodiment is measured the device of expansion coefficients of metal wire, and it comprises: linear frequency modulation laser instrument 1, thin glass plate 2, plane mirror 3, electrothermal furnace 4, temperature controller 6, convergent lens 7 and a photodetector 8;

The linear frequency modulation laser that linear frequency modulation laser instrument 1 is exported incides the front surface of thin glass plate 2, and incidence angle θ ₀for acute angle, thin glass plate 2 be reflected light and refract light by this laser beam splitter, thin glass plate 2 reflexes to this reflected light on convergent lens 7, thin glass plate 2 refracts to this refract light on a plane mirror 3, this plane mirror 3 will obtain No. two reflected light of multi beam with the rear surface of thin glass plate 2 after this refract light multiple reflections, No. two reflected light of this multi beam refract on convergent lens 7 through thin glass plate 2, and the light that convergent lens 7 is received converges on the photosurface of photodetector 8;

Electrothermal furnace 4 is used to Metallic rod 5 homogeneous heatings to be measured, and temperature controller 6 is for controlling and detect the temperature of electrothermal furnace 4;

A plane mirror 3 is fixed on one end of Metallic rod 5 to be measured, and vertical with the axis of Metallic rod 5 to be measured, and thin glass plate 2 and a plane mirror 3 be arranged in parallel, and distance between thin glass plate 2 and a plane mirror 3 is between 20mm to 30mm.

Temperature controller 6 described in present embodiment is digital readout temperature controller, and this digital readout temperature controller is convenient to reading, easy to operate, can make measuring process easy.

Embodiment two: illustrate present embodiment with reference to Fig. 3, present embodiment is that the device of the linear frequency modulation multi-beam laser heterodyne measurement expansion coefficients of metal wire described in embodiment one is described further, in present embodiment, it also comprises: data handling system 9;

The electric signal input end of the electrical signal connection data disposal system 9 of photodetector 8; In described data handling system 9, be embedded with the module that software is realized, described module comprises with lower unit:

The signal gathering unit of the photocurrent I that collection photodetector 8 is exported;

To the filtering of carrying out of photocurrent I, thereby obtain electric current of intermediate frequency I _iFfilter unit;

Utilize electric current of intermediate frequency I _iFobtain the frequency f of interference signal _punit;

Utilize the frequency f of interference signal _pobtain the unit of the distance d between thin glass plate 2 and a plane mirror 3;

Obtain the unit of the change of distance amount △ d between thin glass plate 2 and a plane mirror 3 according to the distance d between thin glass plate 2 and a plane mirror 3;

Utilize change of distance amount △ d between thin glass plate 2 and a plane mirror 3 to obtain the unit of the linear expansion coefficient α of Metallic rod 5 to be measured.

Embodiment three: illustrate present embodiment with reference to Fig. 4, present embodiment is that the device of the linear frequency modulation multi-beam laser heterodyne measurement expansion coefficients of metal wire described in embodiment one is described further, in present embodiment, it also comprises: wave filter 9-1, amplifier 9-2, A/D converter 9-3 and DSP9-4;

The electrical signal of photodetector 8 connects the electric signal input end of wave filter 9-1, the electrical signal of wave filter 9-1 connects the electric signal input end of amplifier 9-2, the electrical signal of amplifier 9-2 connects the input end of analog signal of A/D converter 9-3, and the digital signal output end of A/D converter 9-3 connects the digital signal input end of DSP9-4;

In described DSP9-4, be embedded with the module that software is realized, this module comprises with lower unit:

Gather the electric current of intermediate frequency I of A/D converter 9-3 output _iFsignal gathering unit;

Utilize electric current of intermediate frequency I _iFobtain the frequency f of interference signal _punit;

Utilize the frequency f of interference signal _pobtain the unit of the distance d between thin glass plate 2 and a plane mirror 3;

Obtain the unit of the change of distance amount △ d between thin glass plate 2 and a plane mirror 3 according to the distance d between thin glass plate 2 and a plane mirror 3;

Utilize change of distance amount △ d between thin glass plate 2 and a plane mirror 3 to obtain the unit of the linear expansion coefficient α of Metallic rod 5 to be measured.

The temperature probe of digital readout temperature controller, by platinum resistance thermometer sensor,, is obtained the signal of representation temperature; And desired temperature uses " setting knob " to regulate, two signals, through selector switch and A/D converter, can be distinguished display measurement temperature and design temperature on charactron.Electrothermal furnace approaches design temperature to testing sample homogeneous heating, automatically disconnects heater circuit by relay; At measuring state, show the current temperature detecting.

Embodiment four: illustrate present embodiment with reference to Fig. 5, present embodiment is that the device of the linear frequency modulation multi-beam laser heterodyne measurement expansion coefficients of metal wire described in embodiment one is described further, in present embodiment, it also comprises: No. two plane mirrors 10;

The laser that linear frequency modulation laser instrument 1 is exported incides on No. two plane mirrors 10, and No. two plane mirrors 10 are the front surface to thin glass plate 2 by this laser reflection, and incidence angle θ ₀for acute angle.

Embodiment five: present embodiment is that the device of the linear frequency modulation multi-beam laser heterodyne measurement expansion coefficients of metal wire described in embodiment one is described further, in present embodiment, the frequency modulation cycle of described linear frequency modulation laser instrument 1 is 1ms, modulating bandwidth is 5GHz, and the wavelength of Output of laser is 1.55 μ m.

Embodiment six: present embodiment is that the device of the linear frequency modulation multi-beam laser heterodyne measurement expansion coefficients of metal wire described in embodiment one is described further, in present embodiment, incidence angle θ ₀it is 15.26 °.

Embodiment seven: present embodiment is that the device of the linear frequency modulation multi-beam laser heterodyne measurement expansion coefficients of metal wire described in embodiment one is described further, and in present embodiment, the thickness of described thin glass plate 2 is greater than 0mm and is less than 1mm.

Embodiment eight: present embodiment is that the device of the linear frequency modulation multi-beam laser heterodyne measurement expansion coefficients of metal wire described in embodiment one is described further, in present embodiment, the frequency f of interference signal _pfor:

$f_p=\frac{2\mathrm{pknd}\cos \mathrm{\θ}}{\mathrm{\πc}}=K_{p}d,$

Wherein, p is nonnegative integer, for the rate of change of the modulating bandwidth of linear frequency modulation laser instrument 1, T is the frequency modulation cycle, △ F is modulating bandwidth, n is the refractive index of medium between thin glass plate 2 and a plane mirror 3, d is the distance between thin glass plate 2 and a plane mirror 3, θ is the refraction angle that incident light transmits thin glass plate 2, the light velocity that c is incident light, K _pscale-up factor between frequency and the refraction angle θ cosine of expression intermediate frequency heterodyne signal.

Embodiment nine: present embodiment is that the device that linear frequency modulation multi-beam laser heterodyne described in embodiment one is measured to expansion coefficients of metal wire is described further, in present embodiment, utilizes following formula to obtain the linear expansion coefficient α of Metallic rod 5 to be measured,

$\mathrm{\α}=\frac{\mathrm{\Δd}}{l_0\mathrm{\ΔT}},$

Wherein, l ₀represent the initial length of Metallic rod 5 to be measured, △ T=T ₁-T ₂represent the temperature variation of Metallic rod 5 to be measured, T ₁represent the temperature of Metallic rod 5 to be measured under room temperature, T ₂the temperature of Metallic rod 5 to be measured when distance between expression thin glass plate 2 and a plane mirror 3 is d.

Embodiment ten: the linear frequency modulation multi-beam laser heterodyne based on embodiment one is measured the method for expansion coefficients of metal wire, and in present embodiment, the method comprises the following steps:

Step 1: open linear frequency modulation laser 1 the linear frequency modulation laser that linear frequency modulation laser instrument 1 sends is incided on thin glass plate 2, and ensure incidence angle θ ₀for acute angle; Open electrothermal furnace 4 and temperature controller 6, temperature controller 6 gathers the temperature of Metallic rod 5 to be measured simultaneously;

Step 2: the signal of the photocurrent I that collection photodetector 8 is exported, thus and the DC terms of this photocurrent I is carried out to filtering acquisition electric current of intermediate frequency I _iF;

Step 3: the electric current of intermediate frequency I that step 2 is obtained _iFanalyze, obtain the frequency f of interference signal _p:

$f_p=\frac{2\mathrm{pknd}\cos \mathrm{\θ}}{\mathrm{\πc}}=K_{p}d,$

Wherein, p is nonnegative integer, for the rate of change of the modulating bandwidth of linear frequency modulation laser instrument 1, T is the frequency modulation cycle, △ F is modulating bandwidth, n is the refractive index of medium between thin glass plate 2 and a plane mirror 3, d is the distance between thin glass plate 2 and a plane mirror 3, θ is the refraction angle that incident light transmits thin glass plate 2, the light velocity that c is incident light, K _pscale-up factor between frequency and the refraction angle θ cosine of expression intermediate frequency heterodyne signal;

Step 4: the frequency f of utilizing interference signal _pobtain the distance d between thin glass plate 2 and a plane mirror 3, obtain the change of distance amount △ d between thin glass plate 2 and a plane mirror 3,

△d＝d ₀-d，

Wherein, d ₀represent the initial distance between thin glass plate 2 and a plane mirror 3;

Step 5: utilize following formula to obtain the linear expansion coefficient α of Metallic rod 5 to be measured,

$\mathrm{\α}=\frac{\mathrm{\Δd}}{l_0\mathrm{\ΔT}},$

Wherein, l ₀represent the initial length of Metallic rod 5 to be measured, △ T=T ₁-T ₂represent the temperature variation of Metallic rod 5 to be measured, T ₁represent the temperature of Metallic rod 5 to be measured under room temperature, T ₂the temperature of Metallic rod 5 to be measured when distance between expression thin glass plate 2 and a plane mirror 3 is d.

As shown in Figure 2, because light beam can constantly reflect and reflect between thin glass plate and a plane mirror, and this reflection and refraction for reflected light and transmitted light, the interference at infinity or on lens focal plane has contribution, so in the time that interference is discussed, must consider multiple reflections and refraction effect, multi-beam laser should be discussed and interfere.

In the situation that not considering thin glass plate self thickness, the laser after linear frequency modulation is with incidence angle θ ₀when oblique incidence, the mathematic(al) representation of incident field is:

E(t)＝E ₀exp{i(ω ₀t+kt ²)} (1)

Wherein, for the rate of change of the modulating bandwidth of linear frequency modulation laser instrument, T is the frequency modulation cycle, and △ F is modulating bandwidth; E ₀for incident field amplitude, t is the time, ω ₀for light field angular frequency.If arriving the light path of thin glass plate front surface is L, the reflection light field that moment arrives thin glass plate front surface is:

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

Wherein, α ₁=r, the reflectivity that r is thin glass plate.

And through the light of thin glass plate transmission not in the same time by plane mirror multiple reflections and transmit thin glass plate, the light field expression formula of its transmitted light can be write respectively as following form:

$\left\{\begin{array}{c}{E}_2\left(t\right)={\mathrm{\α}}_2{E}_0\exp \left\{i\right[{\mathrm{\ω}}_0(t-\frac{L+2\mathrm{nd}\cos \mathrm{\θ}}{c})+k{(t-\frac{L+2\mathrm{nd}\cos \mathrm{\θ}}{c})}^2+\frac{{2\mathrm{\ω}}_0\mathrm{nd}\cos \mathrm{\θ}}{c}\left]\right\}\\ E_3\left(t\right)={\mathrm{\α}}_3{E}_0\exp \left\{i\right[{\mathrm{\ω}}_0(t-\frac{L+4\mathrm{nd}\cos \mathrm{\θ}}{c})+k{(t-\frac{L+4\mathrm{nd}\cos \mathrm{\θ}}{c})}^2+\frac{{4\mathrm{\ω}}_0\mathrm{nd}\cos \mathrm{\θ}}{c}\left]\right\}\\ ...\\ E_m\left(t\right)={\mathrm{\α}}_m{E}_0\exp \left\{i\right[{\mathrm{\ω}}_0(t-\frac{L+2(m-1)\mathrm{nd}\cos \mathrm{\θ}}{c})+k{(t-\frac{L+2(m-1)\mathrm{nd}\cos \mathrm{\θ}}{c})}^2+\frac{2(m-1){\mathrm{\ω}}_0\mathrm{nd}\cos \mathrm{\θ}}{c}\left]\right\}\end{array}\right.---\left(3\right)$

Wherein, α ₂=β ²r' ..., α _m=β ²r' ^m-1r ^m-2, the transmissivity that β is thin glass plate, the reflectivity that r' is plane mirror, d is the distance between thin glass plate and plane mirror, and θ is that incident light transmits the refraction angle after thin glass plate, and n is the refractive index of medium between thin glass plate and plane mirror, the value of subscript m is 2,3,4 ...Owing to having ignored the thickness of thin glass plate, therefore do not consider the impact of thin glass plate rear surface.

Like this, total light field that detector receives can be expressed as:

E′(t)＝E ₁(t)+E ₂(t)+L+E _m(t)+… (4)

The photocurrent of detector output can be expressed as:

$I=\frac{\mathrm{\ηe}}{\mathrm{h\ν}}\frac{1}{Z}\underset{D}{\∫\∫}\frac{1}{2}{[E_1\left(t\right)+E_2\left(t\right)+...+E_m\left(t\right)+...][E_1\left(t\right)+E_2\left(t\right)+...+E_m\left(t\right)+...]}^{*}\mathrm{ds}---\left(5\right)$

Wherein, e is electron charge, and Z is the intrinsic impedance of detector surface medium, and η is quantum efficiency, and h is Planck's constant, and ν is laser frequency, represents complex conjugate No. *.

Because heterodyne signal DC terms can filtering after low-pass filter, therefore, only to consider here to exchange, this exchanges and is commonly referred to electric current of intermediate frequency, and the electric current of intermediate frequency that arrangement can obtain linear frequency modulation heterodyne signal is:

$I_{\mathrm{if}}=\frac{\mathrm{\ηe}}{2\mathrm{h\ν}}\frac{1}{Z}\underset{D}{\∫\∫}\underset{p=0}{\overset{m-1}{\mathrm{\Σ}}}\underset{j=0}{\overset{m-p}{\mathrm{\Σ}}}(E_j\left(t\right){E_{j+p}}^{*}\left(t\right)+{E_j}^{*}\left(t\right)E_{j+p}\left(t\right))\mathrm{ds}---\left(6\right)$

By (2) formula and (3) formula substitution (6) formula, net result is:

$I_{\mathrm{IF}}=\frac{\mathrm{\ηe}}{\mathrm{h\ν}}\frac{\mathrm{\π}}{Z}{E}_0^2\underset{p=0}{\overset{m-1}{\mathrm{\Σ}}}\underset{j=0}{\overset{m-p}{\mathrm{\Σ}}}{\mathrm{\α}}_{j+p}{\mathrm{\α}}_j\cos (\frac{4\mathrm{pknd}\cos \mathrm{\θ}}{c}t-\frac{4\mathrm{pknd}\cos \mathrm{\θ}(L+\mathrm{nd}\cos \mathrm{\θ})}{c^2})---\left(7\right)$

Wherein, p and j are nonnegative integer.

Can see in the intermediate frequency item difference on the frequency that linear frequency modulation multiple beam heterodyne measurement method obtains and phase differential, there is the information of distance d between thin glass plate and plane mirror by (7) formula.Analyze mainly for intermediate frequency item intermediate frequency rate variance, because adopt Fourier transform to be easy to realize frequency measurement.Now, according to (7) formula, the frequency of linear frequency modulation multi-beam laser heterodyne signal can be designated as:

$f_p=\frac{2\mathrm{pknd}\cos \mathrm{\θ}}{\mathrm{\πc}}=K_{p}d---\left(8\right)$

Should be noted that, can find out by (7) formula, the photocurrent expression formula of detector output can be seen linear frequency modulation multi-beam laser heterodyne signal frequency crest after Fourier transform on frequency spectrum, by measuring multi-beam laser heterodyne signal frequency, just can measure the distance d between thin glass plate and plane mirror, in the time that d changes, the variable quantity △ d that just can measure according to (8) formula corresponding d, has known that △ d just can calculate testing sample linear expansion coefficient according to (9) formula.

$\mathrm{\α}=\frac{\mathrm{\Δd}}{l_0\mathrm{\ΔT}}---\left(9\right)$

Based on the multi-beam laser heterodyne of linear frequency modulation shown in Fig. 2 measurement scheme, measure long 150mm, diameter is the brass metal bar linear expansion coefficient of Φ 18mm, and verifies the feasibility of multi-beam laser heterodyne measuring method.The temperature controller device configuring in measurement is XMT type digital displaying temperature adjusting apparatus; Linear frequency modulation laser wavelength is 1.55 μ m, frequency modulation cycle T=1ms, modulating bandwidth △ F=5GHz.

Can see according to (7) formula emulation, when metal bar is during in 15 DEG C of room temperatures, the Fourier transform frequency spectrum of the linear frequency modulation multi-beam laser heterodyne signal obtaining through signal processing as shown in Figure 6, wherein solid line is in 15 DEG C of room temperatures and laser oblique incidence situation, the Fourier transform frequency spectrum of corresponding linear frequency modulation multi-beam laser heterodyne signal while measuring metal bar length variations amount △ l; Dotted line is in 15 DEG C of room temperatures and laser normal incidence situation, the Fourier transform frequency spectrum of corresponding linear frequency modulation multi-beam laser heterodyne signal while measuring metal bar length variations amount △ l.

As can see from Figure 6, in experiment, provide the theoretical curve in the situation of normal incidence, object is: in Linear Frequency Modulation multi-beam laser heterodyne signal spectrum figure, the numerical value of the centre frequency of theoretical curve when the centre frequency of first main peak of linear frequency modulation multi-beam laser heterodyne signal spectrum and normal incidence can simultaneously obtain oblique incidence time, like this, be easy to the ratio of two centre frequencies that obtain:

ζ＝cosθ (10)

In theoretical derivation, the impact of the reflected light that thickness of having ignored thin glass plate do not consider device rear surface on linear frequency modulation multi-beam laser heterodyne signal, but in fact the thickness of thin glass plate is the 1mm that is generally less than existing, for overcoming this impact, can find out according to (10) formula, the frequency distribution of the linear frequency modulation multiple beam heterodyne signal that the reflected light of thin glass plate rear surface produces, near the zero-frequency of frequency spectrum, has added the interference that wave filter just can filtering low frequency heterodyne signal in experiment light path.Utilize above-mentioned linear frequency modulation multi-beam laser heterodyne mensuration, eight groups of data of continuous coverage, have obtained laser incidence angle θ ₀=15.26 ° time, in different temperatures situation, the measurement result of metal bar length variations amount to be measured, as shown in table 1.

In table 1 different temperatures T situation, the measurement result of metal bar length variations amount

It should be noted that: in table 1,15 DEG C is the temperature in laboratory.Meanwhile, can derive relevant each data according to the simulation experiment result in table 1:

(1) temperature T standard uncertainty σ _c(△ T)

Duplicate measurements , type A standard uncertainty the limiting error Δ that temperature controller is introduced ₁=0.002 DEG C, type B standard uncertainty

(2) length l ₀standard uncertainty σ _c(l ₀)

Use vernier caliper duplicate measurements , type A standard uncertainty:

${\mathrm{\σ}}_A={\left\{\right[\underset{i=1}{\overset{8}{\mathrm{\Σ}}}{(l_{0i}-\stackrel{\‾}{l_0})}^2]/8\×(8-1)\}}^{1/2}=0.009\mathrm{mm},$

The limiting error Δ that vernier caliper is introduced ₂=0.02mm, type B standard uncertainty σ _c(l ₀)=(0.009 ²+ 0.012 ²) ¹/ ²=0.015mm.

Utilize the experimental data of table 1, the average measurement value of the linear expansion coefficient of metal bar is

The standard uncertainty of linear expansion coefficient is

The measurement result of linear expansion coefficient can be expressed as:

And the theoretical value of the linear expansion coefficient of metal bar is 2.06 × 10 ^-5/ DEG C, the relative error that so just can obtain measurement result is:

$\mathrm{\η}=\left|\frac{{\mathrm{\α}}_{\exp }-{\mathrm{\α}}_{\mathrm{theory}}}{{\mathrm{\α}}_{\mathrm{theory}}}\right|\×100\%=\left|\frac{(2.057952-2.06)\×{10}^{-5}}{2.06\×{10}^{-5}}\right|\×100\%=0.1\%$

Can find out by data processing, the relative measurement error that records linear expansion coefficient with linear frequency modulation multi-beam laser heterodyne method measurement mechanism is only 0.1%, and compared with traditional measuring method, the measured result of the method has better precision.Meanwhile, analyze data and it can also be seen that, the in the situation that of sample homogeneous heating, environmental error is negligible in experiment.Error in experiment mainly comes from the limiting error of measurement mechanism, and trueness error after Fast Fourier Transform (FFT) (FFT) and the round-off error in computation process, can reduce limiting error by the measuring accuracy that improves measurement mechanism, reduce trueness error and the round-off error in computation process, the finally further measuring accuracy that improves after Fast Fourier Transform (FFT) (FFT) by improving Processing for Data Analysis in Physics.

Claims (10)

1. linear frequency modulation multi-beam laser heterodyne is measured the device of expansion coefficients of metal wire, it is characterized in that, it comprises: linear frequency modulation laser instrument (1), thin glass plate (2), a plane mirror (3), electrothermal furnace (4), temperature controller (6), convergent lens (7) and photodetector (8);

The linear frequency modulation laser of linear frequency modulation laser instrument (1) output incides the front surface of thin glass plate (2), and incidence angle θ ₀for acute angle, thin glass plate (2) be reflected light and refract light by this laser beam splitter, thin glass plate (2) reflexes to this reflected light on convergent lens (7), thin glass plate (2) refracts to this refract light on a plane mirror (3), this plane mirror (3) will obtain No. two reflected light of multi beam with the rear surface of thin glass plate (2) after this refract light multiple reflections, No. two reflected light of this multi beam refract on convergent lens (7) through thin glass plate (2), the light that convergent lens (7) is received converges on the photosurface of photodetector (8),

Electrothermal furnace (4) is used to Metallic rod to be measured (5) homogeneous heating, and temperature controller (6) is for controlling and detect the temperature of electrothermal furnace (4);

A plane mirror (3) is fixed on one end of Metallic rod to be measured (5), and vertical with the axis of Metallic rod to be measured (5), thin glass plate (2) and a plane mirror (3) be arranged in parallel, and distance between thin glass plate (2) and a plane mirror (3) is between 20mm to 30mm.

2. linear frequency modulation multi-beam laser heterodyne according to claim 1 is measured the device of expansion coefficients of metal wire, it is characterized in that, it also comprises: data handling system (9);

The electric signal input end of the electrical signal connection data disposal system (9) of photodetector (8); In described data handling system (9), be embedded with the module that software is realized, described module comprises with lower unit:

Gather the signal gathering unit of the photocurrent I of photodetector (8) output;

To the filtering of carrying out of photocurrent I, thereby obtain electric current of intermediate frequency I _iFfilter unit;

Utilize electric current of intermediate frequency I _iFobtain the frequency f of interference signal _punit;

Utilize the frequency f of interference signal _pobtain the unit of the distance d between thin glass plate (2) and a plane mirror (3);

Obtain the unit of the change of distance amount △ d between thin glass plate (2) and a plane mirror (3) according to the distance d between thin glass plate (2) and a plane mirror (3);

Utilize change of distance amount △ d between thin glass plate (2) and a plane mirror (3) to obtain the unit of the linear expansion coefficient α of Metallic rod to be measured (5).

3. linear frequency modulation multi-beam laser heterodyne according to claim 1 is measured the device of expansion coefficients of metal wire, it is characterized in that, it also comprises: wave filter (9-1), amplifier (9-2), A/D converter (9-3) and DSP (9-4);

The electrical signal of photodetector (8) connects the electric signal input end of wave filter (9-1), the electrical signal of wave filter (9-1) connects the electric signal input end of amplifier (9-2), the electrical signal of amplifier (9-2) connects the input end of analog signal of A/D converter (9-3), and the digital signal output end of A/D converter (9-3) connects the digital signal input end of DSP (9-4);

In described DSP (9-4), be embedded with the module that software is realized, this module comprises with lower unit:

Gather the electric current of intermediate frequency I of A/D converter (9-3) output _iFsignal gathering unit;

Utilize electric current of intermediate frequency I _iFobtain the frequency f of interference signal _punit;

Utilize the frequency f of interference signal _pobtain the unit of the distance d between thin glass plate (2) and a plane mirror (3);

Obtain the unit of the change of distance amount △ d between thin glass plate (2) and a plane mirror (3) according to the distance d between thin glass plate (2) and a plane mirror (3);

Utilize change of distance amount △ d between thin glass plate (2) and a plane mirror (3) to obtain the unit of the linear expansion coefficient α of Metallic rod to be measured (5).

4. the device of measuring expansion coefficients of metal wire according to the linear frequency modulation multi-beam laser heterodyne described in claim 1,2 or 3, is characterized in that, it also comprises: No. two plane mirrors (10);

It is upper that the laser of linear frequency modulation laser instrument (1) output incides No. two plane mirrors (10), and No. two plane mirrors (10) are the front surface to thin glass plate (2) by this laser reflection, and incidence angle θ ₀for acute angle.

5. linear frequency modulation multi-beam laser heterodyne according to claim 4 is measured the device of expansion coefficients of metal wire, it is characterized in that, the frequency modulation cycle of described linear frequency modulation laser instrument (1) is 1ms, and modulating bandwidth is 5GHz, and the wavelength of Output of laser is 1.55 μ m.

6. linear frequency modulation multi-beam laser heterodyne according to claim 5 is measured the device of expansion coefficients of metal wire, it is characterized in that incidence angle θ ₀it is 15.26 °.

7. linear frequency modulation multi-beam laser heterodyne according to claim 6 is measured the device of expansion coefficients of metal wire, it is characterized in that, the thickness of described thin glass plate (2) is greater than 0mm and is less than 1mm.

8. the device of measuring expansion coefficients of metal wire according to the linear frequency modulation multi-beam laser heterodyne described in claim 2 or 3, is characterized in that the frequency f of interference signal _pfor:

$f_p=\frac{2\mathrm{pknd}\cos \mathrm{\θ}}{\mathrm{\πc}}=K_{p}d,$

Wherein, p is nonnegative integer, for the rate of change of the modulating bandwidth of linear frequency modulation laser instrument (1), T is the frequency modulation cycle, △ F is modulating bandwidth, n is the refractive index of medium between thin glass plate (2) and a plane mirror (3), d is the distance between thin glass plate (2) and a plane mirror (3), θ is the refraction angle that incident light transmits thin glass plate (2), the light velocity that c is incident light, K _pscale-up factor between frequency and the refraction angle θ cosine of expression intermediate frequency heterodyne signal.

9. linear frequency modulation multi-beam laser heterodyne according to claim 8 is measured the device of expansion coefficients of metal wire, it is characterized in that, utilizes following formula to obtain the linear expansion coefficient α of Metallic rod to be measured (5),

$\mathrm{\α}=\frac{\mathrm{\Δd}}{l_0\mathrm{\ΔT}},$

Wherein, l ₀represent the initial length of Metallic rod to be measured (5), △ T=T ₁-T ₂represent the temperature variation of Metallic rod to be measured (5), T ₁represent the temperature of Metallic rod to be measured (5) under room temperature, T ₂the temperature of Metallic rod to be measured (5) when distance between expression thin glass plate (2) and a plane mirror (3) is d.

10. the method based on measure expansion coefficients of metal wire according to the linear frequency modulation multi-beam laser heterodyne of claim 1, is characterized in that, the method comprises the following steps:

Step 1: opening linear frequency modulation laser that linear frequency modulation laser (1) sends linear frequency modulation laser instrument (1), to incide thin glass plate (2) upper, and ensure incidence angle θ ₀for acute angle; Open electrothermal furnace (4) and temperature controller (6), temperature controller (6) gathers the temperature of Metallic rod to be measured (5) simultaneously;

Step 2: gather the signal of the photocurrent I of photodetector (8) output, thereby and the DC terms of this photocurrent I is carried out to filtering acquisition electric current of intermediate frequency I _iF;

Step 3: the electric current of intermediate frequency I that step 2 is obtained _iFanalyze, obtain the frequency f of interference signal _p:

$f_p=\frac{2\mathrm{pknd}\cos \mathrm{\θ}}{\mathrm{\πc}}=K_{p}d,$

Wherein, p is nonnegative integer, for the rate of change of the modulating bandwidth of linear frequency modulation laser instrument (1), T is the frequency modulation cycle, △ F is modulating bandwidth, n is the refractive index of medium between thin glass plate (2) and a plane mirror (3), d is the distance between thin glass plate (2) and a plane mirror (3), θ is the refraction angle that incident light transmits thin glass plate (2), the light velocity that c is incident light, K _pscale-up factor between frequency and the refraction angle θ cosine of expression intermediate frequency heterodyne signal;

Step 4: the frequency f of utilizing interference signal _pobtain the distance d between thin glass plate (2) and a plane mirror (3), obtain the change of distance amount △ d between thin glass plate (2) and a plane mirror (3),

△d＝d ₀-d，

Wherein, d ₀represent the initial distance between thin glass plate (2) and a plane mirror (3);

Step 5: utilize following formula to obtain the linear expansion coefficient α of Metallic rod to be measured (5),

$\mathrm{\α}=\frac{\mathrm{\Δd}}{l_0\mathrm{\ΔT}},$

Wherein, l ₀represent the initial length of Metallic rod to be measured (5), △ T=T ₁-T ₂represent the temperature variation of Metallic rod to be measured (5), T ₁represent the temperature of Metallic rod to be measured (5) under room temperature, T ₂the temperature of Metallic rod to be measured (5) when distance between expression thin glass plate (2) and a plane mirror (3) is d.