CN103968989A - Device and method for measuring micro impulse by means of linear frequency modulation multi-beam laser heterodyne quadratic harmonic method and torsional pendulum method - Google Patents

Abstract

The invention provides a device and method for measuring micro impulse by means of a linear frequency modulation multi-beam laser heterodyne quadratic harmonic method and a torsional pendulum method, and belongs to the field of optics. The device and method are aimed to solve the problems that according to an existing laser interference method for measuring the micro impulse, accidental errors are large and measurement precision is low. Linearly polarized light emitted from a linear frequency modulation laser device is reflected through a first plane reflection mirror and a second plane reflection mirror and then enters a plane standard lens, light beams penetrating through the front surface of the plane standard lens are reflected by the rear surface and the front surface of the plane standard lens in the plane standard mirror for many times, then multiple beams of reflection light are obtained, the beams of reflection light penetrate through the front surface of the plane standard lens, then the beams of the reflection light and the light beams reflected through the front surface of the plane standard lens penetrate through a vacuum window and are converged to a photosensitive face of a photoelectric detector outside a vacuum chamber through a convergence lens, the photoelectric detector outputs electric signals to a signal processing system, and the signal processing system obtains the micro impulse borne by a standard beam according to the electric signals received continuously. The device and method are suitable for measuring the micro impulse.

Description

Utilize linear frequency modulation multi-beam laser heterodyne second harmonic method and Inertia Based on Torsion Pendulum Method to measure the device and method of micro-momentum

Technical field

The invention belongs to optical field.

Background technology

Laser microthruster has extensive and deep application prospect at microsatellite attitude and track control field, it has than leaping high, large, the minimum momentum of momentum dynamic range is little, low in energy consumption, Energy Coupling efficiency is high and be easy to the significant advantages such as realization, lightweight and Digital Control, has been subject to Chinese scholars and has paid close attention to widely.And momentum is an important parameter of reflection laser microthruster performance, feature is that magnitude is little, is about 10 ^-7～10 ^-5ns.The people such as the Photonic Associates Phipps of group have proposed the micro impulse producing with rocking systematic survey laser microthruster in 1999, and carry out the test of microthruster performance parameter with it; 2002, the people such as Phipps improved the system of rocking again, and domestic Chinese University of Science and Technology and equipment Command technical college have also carried out correlative study subsequently.From the result of study of reporting both at home and abroad at present, on the one hand, the noise of measuring system can affect the precision of system, and in little momentum magnitude, systematic error has even reached 50%; Meanwhile, within power action time, target plane departs from focal plane, Energy Coupling Efficiency Decreasing, and this also can affect the measurement of micro-momentum, and therefore conventional little impulse measurement system is difficult to meet and measures requirement.

Laser interferance method can effectively solve above two problems that conventionally test system exists, and improves the measuring accuracy of system.The method that adopts two corner cubes to form variate replaces original light pointer method measurement to rock the angle of rotation, has greatly improved the precision of system; Rock the Push Technology quality of 2010 and be increased to 58g by original 0.2g, overcome out of focus problem.Result of study shows, the introducing of laser interferance method has greatly improved the performance of rocking test macro, can meet the test request of laser microthruster micro impulse.But because measuring amount is more indirectly, accidental error is larger, and therefore measuring accuracy can be very not high yet.

Summary of the invention

The present invention is larger in order to solve the accidental error of existing measurements by laser interferometry micro impulse, and the problem that measuring accuracy is low, has proposed to utilize linear frequency modulation multi-beam laser heterodyne second harmonic method and Inertia Based on Torsion Pendulum Method to measure the device and method of micro-momentum.

Utilize linear frequency modulation multi-beam laser heterodyne second harmonic method and Inertia Based on Torsion Pendulum Method to measure the device of micro-momentum, it comprises linear frequency modulation laser instrument, the first plane mirror, rocks system, pulsed laser, plane standard mirror, convergent lens, photodetector and signal processing system;

Described linear frequency modulation laser instrument, the first plane mirror, rock system, pulsed laser, plane standard mirror and convergent lens and be all positioned at vacuum chamber, on vacuum chamber, have a vacuum window;

The described system of rocking comprises Standard Beam, the second plane mirror and working medium target; On an end lower surface of Standard Beam, be adhesive with the second plane mirror, Standard Beam upper surface and the second plane mirror correspondence position are fixed with working medium target, Standard Beam is in the equilibrium state of level, and the target surface of working medium target is perpendicular to the optical axis of the laser beam of pulsed laser transmitting;

Linear frequency modulation laser instrument sends linear frequency modulation linearly polarized light, and described linear frequency modulation linearly polarized light is after the first plane mirror and the second plane mirror two secondary reflections, with θ ₀angle is incident to plane standard mirror; Through the light beam of the front surface transmission of plane standard mirror obtaining multi beam reflected light in plane standard mirror after the rear surface of plane standard mirror and front surface multiple reflections, this multi beam reflected light after the front surface transmission of plane standard mirror with light beam after the front surface reflection of plane standard mirror all by convergent lens with see through vacuum window and converge on the photosurface of the photodetector outside vacuum chamber;

Photodetector output electrical signals is to signal processing system; Described signal processing system, for according to the electric signal receiving continuously, obtains the suffered micro-momentum of Standard Beam.

Signal processing system comprises wave filter, prime amplifier, A/D change-over circuit and DSP microprocessor;

The input end of wave filter connects the electrical signal of photodetector; The output terminal of wave filter connects the input end of prime amplifier; The output terminal of pre-amplification circuit connects the input end of analog signal of A/D change-over circuit; The digital signal output end of A/D change-over circuit connects the input end of DSP microprocessor.

Described utilize linear frequency modulation multi-beam laser heterodyne second harmonic method and Inertia Based on Torsion Pendulum Method are measured the method for the micro-momentum of measurement device of micro-momentum, and the method comprises the following steps:

Step 1, open linear frequency modulation laser instrument and pulsed laser simultaneously;

Adopt pulsed laser to send pulse laser excitation working medium target, make working medium target produce plasma jet, the effect of regurgitating of the plasma jet that described working medium target produces is rotated Standard Beam;

Step 2, signal processing system are rocking the electric signal that in system swing process, continuous acquisition photodetector sends, and the electric signal of continuous acquisition is processed, adopt linear frequency modulation multi-beam laser heterodyne second harmonic method to measure light beam to be incident to the incidence angle θ of plane standard mirror ₀;

The pivot angle θ ' of step 3, Standard Beam presses formula θ '=θ ₀/ 2 obtain;

Step 4, obtain the suffered micro-momentum I ' of Standard Beam according to the pivot angle θ ' of Standard Beam, the computing formula of micro-momentum I ' is as follows:

$I^{\′}=\frac{2\mathrm{J\ω}}{D}\·{\mathrm{\θ}}^{\′}=\frac{4\mathrm{\πJ}}{{\mathrm{DT}}^{\′}}\·{\mathrm{\θ}}^{\′}=k^{\′}{\mathrm{\θ}}^{\′},$ Order $\frac{4\mathrm{\πJ}}{{\mathrm{DT}}^{\′}}=k^{\′},$ ? $I^{\′}=\frac{2\mathrm{J\ω}}{D}\·{\mathrm{\θ}}^{\′}=\frac{4\mathrm{\πJ}}{{\mathrm{DT}}^{\′}}\·{\mathrm{\θ}}^{\′}=k^{\′}{\mathrm{\θ}}^{\′};$

In formula, J is the moment of inertia of the system of rocking, and ω is damped frequency, and T ' rocks the damping period of system for this, and D is Standard Beam length.

The present invention is applicable to the measurement of micro-momentum.

For feature and the deficiency of traditional micro-impulse measurement system, propose the micro-impulse measurement method of rocking of a kind of linear frequency modulation multi-beam laser heterodyne second harmonic angle measurement herein, utilized rocking measuring system and having carried out the emulation experiment measurement of pulse laser and PVC working medium target coupling micro-momentum that produces of design herein.Result shows, this measuring method range of linearity is large and resolution is high, the advantage of this angle-measuring method is to rotation sensitive, insensitive to translation, therefore test macro also has compared with strong anti-interference ability vibration, and particularly low-frequency vibration can return to working state of system within several seconds, not only reduce measuring error, also reduced the requirement to measuring equipment and bad border of experiment.Meanwhile, less at rotational angle, while being less than 5 °, momentum and the incident angle surveyed are linear, and measuring error is less than 0.63%, can meet the requirement of laser microthruster impulse measurement, for the performance of assessment laser microthruster provides good measurement means.

Brief description of the drawings

Fig. 1 is the structural representation that utilizes linear frequency modulation multi-beam laser heterodyne second harmonic method and Inertia Based on Torsion Pendulum Method to measure the device of micro-momentum of the present invention;

Fig. 2 is multi-beam laser principle of interference schematic diagram;

Fig. 3 is the Fourier transform spectrogram of linear frequency modulation multi-beam laser heterodyne second harmonic signal;

Fig. 4 is spectrogram corresponding to micro-impulse measurement in different incidence angles situation.

Embodiment

Illustrate present embodiment with reference to Fig. 1, utilize linear frequency modulation multi-beam laser heterodyne second harmonic method and Inertia Based on Torsion Pendulum Method described in present embodiment are measured the device of micro-momentum, and it comprises linear frequency modulation laser instrument 1, the first plane mirror 2, rocks system, pulsed laser 6, plane standard mirror 7, convergent lens 8, photodetector 9 and signal processing system;

Described linear frequency modulation laser instrument 1, the first plane mirror 2, rock system, pulsed laser 6, plane standard mirror 7 and convergent lens 8 and be all positioned at vacuum chamber 14, on vacuum chamber 14, have a vacuum window 15;

The described system of rocking comprises Standard Beam 3, the second plane mirror 4 and working medium target 5; On an end lower surface of Standard Beam 3, be adhesive with the second plane mirror 4, Standard Beam 3 upper surfaces and the second plane mirror 4 correspondence positions are fixed with working medium target 5, Standard Beam 3 is in the equilibrium state of level, the optical axis of the laser beam that the target surface of working medium target 5 is launched perpendicular to pulsed laser 6;

Linear frequency modulation laser instrument 1 sends linear frequency modulation linearly polarized light, and described linear frequency modulation linearly polarized light is after the first plane mirror 2 and 4 liang of secondary reflections of the second plane mirror, with θ ₀angle is incident to plane standard mirror 7; Light beam through the front surface transmission of plane standard mirror 7 obtains multi beam reflected light after the interior rear surface through plane standard mirror 7 of plane standard mirror 7 and front surface multiple reflections, this multi beam reflected light after the front surface transmission of plane standard mirror 7 with light beam after 7 front surface reflections of plane standard mirror all by convergent lens 8 with see through vacuum window 15 and converge on the photosurface of the photodetector 9 outside vacuum chamber 14;

Photodetector 9 output electrical signals are to signal processing system; Described signal processing system, for according to the electric signal receiving continuously, obtains the suffered micro-momentum of Standard Beam 3.

In optical measuring method, advantages such as 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, reproducible and measurement range is large and enjoy Chinese scholars to pay close attention to, laser heterodyne measurement technology has been inherited the plurality of advantages of heterodyne technology, is one of current superhigh precision measuring method.The 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.

In order to collect good laser difference frequency signal and to improve the arithmetic speed of signal processing, utilize linear frequency modulation technology and heterodyne technology herein, propose a kind of high-precision linear frequency modulation multi-beam laser heterodyne second harmonic and measured the method for micro-momentum, utilize linear frequency modulation technology that parameter information to be measured is modulated in heterodyne signal second harmonic, by can accurately obtaining parameter information to be measured to the demodulation of heterodyne second harmonic.

The laser beam that pulsed laser 6 sends and 5 effects of working medium target produce plasma jet, and the effect of regurgitating is rotated Standard Beam 3.Simultaneously, open linear frequency modulation laser instrument 1, linearly polarized light is mapped on the second plane mirror 4 surfaces of pasting on Standard Beam 3 through the first plane mirror 2 is oblique, reflected light after the light of plane standard mirror 7 front surface transmissions is by the reflection of the rear surface of plane standard mirror 7 with together with light through 7 front surface reflections of plane standard mirror, be converged lens 8 and converge on photodetector 9 photosurfaces, after signal processing system, obtain not parameter information to be measured in the same time finally by the electric signal after photodetector 9 opto-electronic conversion.Like this, just can record the pivot angle of Standard Beam 3 by linear frequency modulation double light beam laser process of heterodyning, thereby measure the micro impulse of laser and the 5 effect generations of working medium target.

Embodiment two: present embodiment is described below in conjunction with Fig. 2, present embodiment is described further the device that utilizes linear frequency modulation multi-beam laser heterodyne second harmonic method and Inertia Based on Torsion Pendulum Method to measure micro-momentum described in embodiment one, and signal processing system comprises wave filter 10, prime amplifier 11, A/D change-over circuit 12 and DSP microprocessor 13;

The input end of wave filter 10 connects the electrical signal of photodetector 9; The output terminal of wave filter 10 connects the input end of prime amplifier 11; The output terminal of pre-amplification circuit 11 connects the input end of analog signal of A/D change-over circuit 12; The digital signal output end of A/D change-over circuit 12 connects the input end of DSP microprocessor 13.

Embodiment three: illustrate present embodiment with reference to Fig. 2, measure the method for the micro-momentum of measurement device of micro-momentum according to utilize linear frequency modulation multi-beam laser heterodyne second harmonic method and Inertia Based on Torsion Pendulum Method described in embodiment two, the method comprises the following steps:

Step 1, open linear frequency modulation laser instrument 1 and pulsed laser 6 simultaneously;

Adopt pulsed laser 6 to send pulse laser excitation working medium target 5, make working medium target 5 produce plasma jet, the effect of regurgitating of the plasma jet that described working medium target 5 produces is rotated Standard Beam 3;

Step 2, signal processing system are rocking the electric signal that in system swing process, continuous acquisition photodetector 9 sends, and the electric signal of continuous acquisition is processed, adopt linear frequency modulation multi-beam laser heterodyne second harmonic method to measure light beam to be incident to the incidence angle θ of plane standard mirror 7 ₀;

The pivot angle θ ' of step 3, Standard Beam 3 presses formula θ '=θ ₀/ 2 obtain;

Step 4, obtain the suffered micro-momentum I ' of Standard Beam 3 according to the pivot angle θ ' of Standard Beam 3, the computing formula of micro-momentum I ' is as follows:

$I^{\′}=\frac{2\mathrm{J\ω}}{D}\·{\mathrm{\θ}}^{\′}=\frac{4\mathrm{\πJ}}{{\mathrm{DT}}^{\′}}\·{\mathrm{\θ}}^{\′}=k^{\′}{\mathrm{\θ}}^{\′},$ Order $\frac{4\mathrm{\πJ}}{{\mathrm{DT}}^{\′}}=k^{\′},$ ? $I^{\′}=\frac{2\mathrm{J\ω}}{D}\·{\mathrm{\θ}}^{\′}=\frac{4\mathrm{\πJ}}{{\mathrm{DT}}^{\′}}\·{\mathrm{\θ}}^{\′}=k^{\′}{\mathrm{\θ}}^{\′};$

In formula, J is the moment of inertia of the system of rocking, and ω is damped frequency, and T ' rocks the damping period of system for this, and D is Standard Beam 3 length.

In present embodiment, k '=4 π J/DT '.The pivot angle θ ' of visible Standard Beam 3 is directly proportional to micro-momentum I ', under small angle approximation condition, as long as known the pivot angle θ ' of Standard Beam, just can obtain the size of micro-momentum I '.

Embodiment four: present embodiment is that utilize linear frequency modulation multi-beam laser heterodyne second harmonic method and Inertia Based on Torsion Pendulum Method described in embodiment three are measured to the further illustrating of method of micro-momentum, adopts linear frequency modulation multi-beam laser heterodyne second harmonic method to measure light beam to be incident to the incidence angle θ of plane standard mirror 7 in step 2 ₀acquisition methods:

Total light field E of the light beam of step 2 one, photodetector 9 _Σ(t):

E _Σ(t)＝E ₁(t)+E ₂(t)+...+E _m(t)；

Wherein: E ₁(t) be the reflection light field of light beam after 7 front surface reflections of plane standard mirror, and press formula

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

In above formula: α ₁for coefficient, α ₁=γ, γ is the reflectivity of light while injecting plane standard mirror 7 from surrounding medium; E ₀for incident field amplitude; ω ₀for incident field angular frequency; T is the time; K is the rate of change of modulating bandwidth, and t is the frequency modulation cycle, and △ F is modulating bandwidth; C is the light velocity;

E ₂(t) ..., E _m(t) for obtaining the catoptrical reflection light field of multi beam after the rear surface at plane standard mirror 7 and front surface multiple reflections;

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

Wherein, α ₂, α ₃..., α _mbe coefficient, and α ₂=β β ' γ ', α ₃=β β ' (γ ') ³, α _m=β β ' (γ ') ^(2m-3); β in formula is the transmissivity of light while injecting plane standard mirror 7 from surrounding medium, and β ' is the transmissivities of plane standard mirror 7 front and rear surfaces multiple reflections light while penetrating plane standard mirror 7, and γ ' is the reflectivity of plane standard mirror 7 rear surfaces; D is the thickness of plane standard mirror 7, and θ is refraction angle, and n is the refractive index of plane standard mirror 7, and l is the light path that arrives plane standard mirror 7, and m is more than or equal to 2 positive integer;

The photosurface of step 2 two, photodetector 9 is accepted light signal, and is translated into photocurrent, and the expression formula of described photocurrent is:

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

Wherein: e is electron charge, Z is the intrinsic impedance of photodetector 9 surface dielectrics, and η is quantum efficiency, D is the area of photodetector 9 photosurfaces, h is Planck's constant, and v is that linear frequency modulation laser instrument 1 sends linear frequency modulation linear polarization light frequency, represents complex conjugate No. *;

The photocurrent that step 2 three, photodetector 9 are exported is by wave filter 10 filtering, remove DC terms, the photocurrent that has only retained interchange item is called electric current of intermediate frequency, and described electric current of intermediate frequency is sent into DSP microprocessor 13 and processed after prime amplifier 11 and A/D change-over circuit 12;

Step 2 four, DSP microprocessor 13 adopt linear frequency modulation multiple beam heterodyne second harmonic mensuration to process to electric current of intermediate frequency, plane standard mirror 7 front and rear surfaces multiple reflections the light beam that transmits from plane standard mirror 7, only get the light and the direct light reflecting of plane of incidence standard mirror 7 that transmit for the p-1 time and the p+1 time and carry out mixing, electric current of intermediate frequency I _iFbe treated to:

$I_{\mathrm{IF}}=\frac{\mathrm{\ηe}}{\mathrm{hv}}\frac{\mathrm{\π}}{Z}{E}_0^2\underset{p=2}{\overset{m-2}{\mathrm{\Σ}}}{\mathrm{\α}}_{p+2}{\mathrm{\α}}_p\cos (\frac{8\mathrm{knd}\cos }{c}t-\frac{8\mathrm{knd}\cos \mathrm{\θ}(I+\mathrm{nd}\cos \mathrm{\θ})}{c^2});$

Wherein, p=2,3 ..., m-2;

Step 2 five, the electric current of intermediate frequency I that step 2 four is obtained _iFcarry out Fourier transform, obtain the frequency f of its heterodyne signal; According to electric current of intermediate frequency I _iFformula can know, the frequency f of heterodyne signal is designated as:

$\frac{8\mathrm{knd}\cos \mathrm{\θ}}{2\mathrm{\πc}}=\frac{4\mathrm{knd}\cos \mathrm{\θ}}{\mathrm{\πc}}=\mathrm{Kd};$

Step 2 six, the ratio ζ of the centre frequency of curve when the centre frequency of first main peak of linear frequency modulation multi-beam laser heterodyne secondary singal frequency spectrum and normal incidence while adopting linear frequency modulation multi-beam laser heterodyne second harmonic method to obtain oblique incidence, ζ=cos θ;

Step 2 seven, obtain the size of laser refraction angle θ after plane standard mirror according to the ζ=cos θ in step 2 five; Again according to refraction law relational expression obtain incidence angle θ ₀size be:

θ ₀＝arcsin[nsin(arccosζ)]。

As shown in Figure 2, because light beam can constantly reflect and reflect between the front and rear surfaces of plane standard mirror 7, and this reflection and refraction for reflected light and transmitted light, the interference at infinity or on convergent lens 8 focal planes 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.

But, because laser reflects the adjacent optical mixing that transmits plane standard mirror front surface for twice in reflected light and plane standard mirror 7 rear surfaces of plane standard mirror 7 front surfaces, the amplitude of two difference frequency signals that produce differs 2～3 orders of magnitude, after Fourier transform, in order can to collect good laser difference frequency signal and to improve the arithmetic speed of signal processing, so here we only consider the E of detected rear surface p-1 secondary reflection _p-1(t) E and after the p+1 secondary reflection of rear surface _p+1(t) the humorous frequency difference of secondary that optical mixing produces.What present embodiment adopted is linear frequency modulation multiple beam heterodyne second harmonic mensuration.

Suppose that linear frequency modulation laser 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)}；

Be l if arrive the light path of plane standard mirror 7 front surfaces, the t-l/c moment arrives the reflection light field of the direct reflection after plane standard mirror 7 front surfaces and is:

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

After the rear surface of plane standard mirror 7 and front surface multiple reflections, obtain the catoptrical reflection light field of multi beam and be respectively E ₂(t) ..., E _m(t);

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

Only get therein the E of p-1 secondary reflection _p-1(t) E and after the p+1 secondary reflection of rear surface _p+1(t).

The photosurface of photodetector 9 is accepted light signal, and is translated into photocurrent (electric signal), and filtering DC terms retains and exchanges item, the electric current of intermediate frequency I obtaining _iFbe treated to:

$I_{\mathrm{IF}}=\frac{\mathrm{\ηe}}{\mathrm{hv}}\frac{\mathrm{\π}}{Z}{E}_0^2\underset{p=2}{\overset{m-2}{\mathrm{\Σ}}}{\mathrm{\α}}_{p+2}{\mathrm{\α}}_p\cos (\frac{8\mathrm{knd}\cos }{c}t-\frac{8\mathrm{knd}\cos \mathrm{\θ}(I+\mathrm{nd}\cos \mathrm{\θ})}{c^2});$

From can learning of this formula, before variable t for angular velocity, the frequency f of heterodyne signal is designated as:

$\frac{8\mathrm{knd}\cos \mathrm{\θ}}{2\mathrm{\πc}}=\frac{4\mathrm{knd}\cos \mathrm{\θ}}{\mathrm{\πc}}=\mathrm{Kd};$

According to theoretical analysis above, refractive index n=1.493983 of normal conditions lower plane standard mirror; Linear frequency modulation laser wavelength is 1.55 μ m, frequency modulation cycle T=1ms, modulating bandwidth △ F=5GHz.The relation of utilized MATLAB emulation standard flat mirror thickness d and intermediate-freuqncy signal frequency, can see by emulation, the Fourier transform frequency spectrum of the linear frequency modulation multi-beam laser heterodyne second harmonic signal obtaining through signal processing as shown in Figure 3, wherein solid line is in laser oblique incidence situation, the Fourier transform frequency spectrum of corresponding linear frequency modulation multi-beam laser heterodyne second harmonic signal when measurement plane standard mirror thickness d; Dotted line is in laser normal incidence situation, the Fourier transform frequency spectrum of corresponding linear frequency modulation multi-beam laser heterodyne second harmonic signal when measurement plane standard mirror thickness d.

As can see from Figure 3, in experiment, provide the theoretical curve in the situation of normal incidence, object is: in Linear Frequency Modulation multi-beam laser heterodyne second harmonic 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 second harmonic 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=cos θ;

Obtain the size of laser refraction angle θ after plane standard mirror according to described ζ=cos θ formula; Again according to refraction law relational expression obtain incidence angle θ ₀size be θ ₀=arcsin[nsin (arccos ζ)].

In formula, K is scale-up factor,

The pivot angle θ '=θ of Standard Beam 3 ₀/ 2, obtain the suffered micro-momentum of Standard Beam 3

Add the variation of Standard Beam 3 front and back system cycles by measurement, calibrate the moment of inertia of system, the experimental result of demarcation is as shown in table 1, can be obtained the size of k ' value according to k '=4 π J/DT ' by calibration result.

Table 1 rocks parametric calibration result

Linear frequency modulation multi-beam laser heterodyne second harmonic based on Fig. 1 is designed is measured low-angle system, under the condition of work of 10Pa, utilize MATLAB analogue measurement working medium for PVC (Polyvinylchloride)+2%C, thickness is 180 μ m, the laser initial current of pulsed laser 6 is 5A, pulsewidth is 50ms, laser and the working medium target 5 micro-momentum producing that interacts, and verify the feasibility of linear frequency modulation multi-beam laser heterodyne second harmonic measuring method.Get equally Standard Beam 3 length D=15cm; Refractive index n=1.493983 of plane standard mirror 7, its thickness is 2cm; The wavelength of linear frequency modulation laser instrument 1 is 1.55 μ m, frequency modulation cycle T=1ms, modulating bandwidth △ F=5GHz.

Meanwhile, emulation has obtained different incidence angles θ ₀in situation, linear frequency modulation multi-beam laser heterodyne is measured Fourier transform frequency spectrum corresponding to minute angle as shown in Figure 4, and as can be seen from Figure 4, along with the increase of incident angle, the relative position of frequency spectrum moves along with incidence angle θ to low frequency direction ₀increase frequency reduce.Reason is: in the situation that plane standard mirror thickness is constant, Proportional coefficient K and frequency are proportional, in low-angle situation, in the time that incident angle increases, Proportional coefficient K reduces thereupon, is f=Kd because frequency f and Proportional coefficient K close, in the constant situation of d, frequency f and K are linear spectrum, and therefore, when K reduces, frequency also reduces the increase along with incident angle thereupon, the relative position of frequency spectrum moves to low frequency direction, and Fig. 4 has verified the correctness of theoretical analysis above well.

It should be noted that, because heterodyne detection is a kind of detection mode of nearly diffraction limit, detection sensitivity is high, and therefore the signal to noise ratio (S/N ratio) of the linear frequency modulation multi-beam laser heterodyne second harmonic signal of Fig. 3 and Fig. 4 is very high.

Utilize above-mentioned linear frequency modulation multi-beam laser heterodyne second harmonic mensuration, eight groups of data of continuous coverage, have obtained the simulated measurement result of the micro-momentum of testing sample in different incidence angles situation, as shown in table 2.

In table 2 different incidence angles situation, the actual value I ' ' of micro-momentum and simulated measurement value I '

Measure number of times	1	2	3	4	5	6	7	8
									θ 0(mrad)	5.976	6.723	7.470	8.217	8.964	9.711	10.458	11.205
I′′(×10 -6N·s)	22.183	24.956	27.729	30.502	33.275	36.048	38.820	41.593
									I′(×10 -6N·s)	22.133	25.115	27.595	30.566	33.038	35.998	38.953	41.411

It should be noted that: utilize the emulation experiment data of table 2, calculate the average measurement value of micro-momentum, the maximum relative error that finally can obtain measured value is less than 0.63%, and the measuring accuracy that can find out the method is very high.Simultaneously, analysis data it can also be seen that, the in the situation that of small angle approximation, the systematic error that environment brings and reading error are negligible in emulation, and the error in emulation experiment mainly comes from trueness error after Fast Fourier Transform (FFT) (FFT) and the round-off error in computation process.

Claims (4)

1. utilize linear frequency modulation multi-beam laser heterodyne second harmonic method and Inertia Based on Torsion Pendulum Method to measure the device of micro-momentum, it is characterized in that, it comprises linear frequency modulation laser instrument (1), the first plane mirror (2), rocks system, pulsed laser (6), plane standard mirror (7), convergent lens (8), photodetector (9) and signal processing system;

Described linear frequency modulation laser instrument (1), the first plane mirror (2), rock system, pulsed laser (6), plane standard mirror (7) and convergent lens (8) and be all positioned at vacuum chamber (14), on vacuum chamber (14), have a vacuum window (15);

The described system of rocking comprises Standard Beam (3), the second plane mirror (4) and working medium target (5); On an end lower surface of Standard Beam (3), be adhesive with the second plane mirror (4), Standard Beam (3) upper surface and the second plane mirror (4) correspondence position are fixed with working medium target (5), Standard Beam (3) is in the equilibrium state of level, and the target surface of working medium target (5) is perpendicular to the optical axis of the laser beam of pulsed laser (6) transmitting;

Linear frequency modulation laser instrument (1) sends linear frequency modulation linearly polarized light, and described linear frequency modulation linearly polarized light is after the first plane mirror (2) and the second plane mirror (4) two secondary reflections, with θ ₀angle is incident to plane standard mirror (7); Through the light beam of the front surface transmission of plane standard mirror (7), obtaining multi beam reflected light in plane standard mirror (7) after the rear surface of plane standard mirror (7) and front surface multiple reflections, this multi beam reflected light all converges on the photosurface of the photodetector (9) outside vacuum chamber (14) by convergent lens (8) with through vacuum window (15) with the light beam after plane standard mirror (7) front surface reflection after the front surface transmission of plane standard mirror (7);

Photodetector (9) output electrical signals is to signal processing system; Described signal processing system, for according to the electric signal receiving continuously, obtains the suffered micro-momentum of Standard Beam (3).

2. the device that utilizes linear frequency modulation multi-beam laser heterodyne second harmonic method and Inertia Based on Torsion Pendulum Method to measure micro-momentum according to claim 1, it is characterized in that, signal processing system comprises wave filter (10), prime amplifier (11), A/D change-over circuit (12) and DSP microprocessor (13);

The input end of wave filter (10) connects the electrical signal of photodetector (9); The output terminal of wave filter (10) connects the input end of prime amplifier (11); The output terminal of pre-amplification circuit (11) connects the input end of analog signal of A/D change-over circuit (12); The digital signal output end of A/D change-over circuit (12) connects the input end of DSP microprocessor (13).

3. described utilize linear frequency modulation multi-beam laser heterodyne second harmonic method and Inertia Based on Torsion Pendulum Method according to claim 2 are measured the method for the micro-momentum of measurement device of micro-momentum, it is characterized in that, the method comprises the following steps:

Step 1, open linear frequency modulation laser instrument (1) and pulsed laser (6) simultaneously;

Adopt pulsed laser (6) to send pulse laser excitation working medium target (5), make working medium target (5) produce plasma jet, the effect of regurgitating of the plasma jet that described working medium target (5) produces is rotated Standard Beam (3);

Step 2, signal processing system are rocking the electric signal that in system swing process, continuous acquisition photodetector (9) sends, and the electric signal of continuous acquisition is processed, adopt linear frequency modulation multi-beam laser heterodyne second harmonic method to measure light beam to be incident to the incidence angle θ of plane standard mirror (7) ₀;

The pivot angle θ ' of step 3, Standard Beam (3) presses formula θ '=θ ₀/ 2 obtain;

Step 4, obtain the suffered micro-momentum I ' of Standard Beam (3) according to the pivot angle θ ' of Standard Beam (3), the computing formula of micro-momentum I ' is as follows:

$I^{\′}=\frac{2\mathrm{J\ω}}{D}\·{\mathrm{\θ}}^{\′}=\frac{4\mathrm{\πJ}}{{\mathrm{DT}}^{\′}}\·{\mathrm{\θ}}^{\′}=k^{\′}{\mathrm{\θ}}^{\′},$ Order $\frac{4\mathrm{\πJ}}{{\mathrm{DT}}^{\′}}=k^{\′},$ ? $I^{\′}=\frac{2\mathrm{J\ω}}{D}\·{\mathrm{\θ}}^{\′}=\frac{4\mathrm{\πJ}}{{\mathrm{DT}}^{\′}}\·{\mathrm{\θ}}^{\′}=k^{\′}{\mathrm{\θ}}^{\′};$

In formula, J is the moment of inertia of the system of rocking, and ω is damped frequency, and T ' rocks the damping period of system for this, and D is Standard Beam (3) length.

4. the method for utilizing linear frequency modulation multi-beam laser heterodyne second harmonic method and Inertia Based on Torsion Pendulum Method to measure micro-momentum according to claim 3, it is characterized in that, in step 2, adopt linear frequency modulation multi-beam laser heterodyne second harmonic method to measure light beam to be incident to the incidence angle θ of plane standard mirror (7) ₀acquisition methods:

Total light field E of the light beam of step 2 one, photodetector (9) _Σ(t):

E _Σ(t)＝E ₁(t)+E ₂(t)+...+E _m(t)；

Wherein: E ₁(t) be the reflection light field of light beam after plane standard mirror (7) front surface reflection, and press formula

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

In above formula: α ₁for coefficient, α ₁=γ, γ is the reflectivity of light while injecting plane standard mirror (7) from surrounding medium; E ₀for incident field amplitude; ω ₀for incident field angular frequency; T is the time; K is the rate of change of modulating bandwidth, and t is the frequency modulation cycle, and △ F is modulating bandwidth; C is the light velocity;

E ₂(t) ..., E _m(t) for obtaining the catoptrical reflection light field of multi beam after the rear surface at plane standard mirror (7) and front surface multiple reflections;

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

Wherein, α ₂, α ₃..., α _mbe coefficient, and α ₂=β β ' γ ', α ₃=β β ' (γ ') ³, α _m=β β ' (γ ') ^(2m-3); β in formula is the transmissivity of light while injecting plane standard mirror (7) from surrounding medium, transmissivity when β ' is plane standard mirror (7) front and rear surfaces multiple reflections light ejaculation plane standard mirror (7), γ ' is the reflectivity of plane standard mirror (7) rear surface; D is the thickness of plane standard mirror (7), and θ is refraction angle, and n is the refractive index of plane standard mirror (7), and l is for arriving the light path of plane standard mirror (7), and m is more than or equal to 2 positive integer;

The photosurface of step 2 two, photodetector (9) is accepted light signal, and is translated into photocurrent, and the expression formula of described photocurrent is: $I=\frac{\mathrm{\ηe}}{\mathrm{hv}}\frac{1}{Z}\underset{D}{\∫\∫}\frac{1}{2}{[E_1\left(t\right)+E_2\left(t\right)+...+E_m\left(t\right)][E_1\left(t\right)+E_2\left(t\right)+...+E_m\left(t\right)]}^{*}\mathrm{ds}$

Wherein: e is electron charge, Z is the intrinsic impedance of photodetector (9) surface dielectric, η is quantum efficiency, D is the area of photodetector (9) photosurface, h is Planck's constant, v is that linear frequency modulation laser instrument (1) sends linear frequency modulation linear polarization light frequency, represents complex conjugate No. *;

The photocurrent of step 2 three, photodetector (9) output is by wave filter (10) filtering, remove DC terms, the photocurrent that has only retained interchange item is called electric current of intermediate frequency, and described electric current of intermediate frequency is sent into DSP microprocessor (13) and processed after prime amplifier (11) and A/D change-over circuit (12);

Step 2 four, DSP microprocessor (13) adopt linear frequency modulation multiple beam heterodyne second harmonic mensuration to process to electric current of intermediate frequency, the light beam transmitting at plane standard mirror (7) front and rear surfaces multiple reflections and from plane standard mirror (7), only get the light and the direct light reflecting of plane of incidence standard mirror (7) that transmit for the p-1 time and the p+1 time and carry out mixing, electric current of intermediate frequency I _iFbe treated to:

$I_{\mathrm{IF}}=\frac{\mathrm{\ηe}}{\mathrm{hv}}\frac{\mathrm{\π}}{Z}{E}_0^2\underset{p=2}{\overset{m-2}{\mathrm{\Σ}}}{\mathrm{\α}}_{p+2}{\mathrm{\α}}_p\cos (\frac{8\mathrm{knd}\cos }{c}t-\frac{8\mathrm{knd}\cos \mathrm{\θ}(I+\mathrm{nd}\cos \mathrm{\θ})}{c^2});$

Wherein, p=2,3 ..., m-2;

Step 2 five, the electric current of intermediate frequency I that step 2 four is obtained _iFcarry out Fourier transform, obtain the frequency f of its heterodyne signal; According to electric current of intermediate frequency I _iFformula can know, the frequency f of heterodyne signal is designated as:

$\frac{8\mathrm{knd}\cos \mathrm{\θ}}{2\mathrm{\πc}}=\frac{4\mathrm{knd}\cos \mathrm{\θ}}{\mathrm{\πc}}=\mathrm{Kd};$

Step 2 six, the ratio ζ of the centre frequency of curve when the centre frequency of first main peak of linear frequency modulation multi-beam laser heterodyne secondary singal frequency spectrum and normal incidence while adopting linear frequency modulation multi-beam laser heterodyne second harmonic method to obtain oblique incidence, ζ=cos θ;

Step 2 seven, obtain the size of laser refraction angle θ after plane standard mirror according to the ζ=cos θ in step 2 five; Again according to refraction law relational expression obtain incidence angle θ ₀size be: θ ₀=arcsin[nsin (arccos ζ)].