CN102305682B - Device and method for measuring micro impulse by torsional pendulum method for modulating multi-beam laser heterodyne by using doppler galvanometer sine - Google Patents

Abstract

The invention relates to a device and a method for measuring a micro impulse by a torsional pendulum method for modulating multi-beam laser heterodyne by using doppler galvanometer sine, and belongs to the technical field of micro impulse measurement. By the device and the method, the problem that the measurement precision of parameter values to be measured is low because only one single parameter value to be measured can be acquired by the conventional heterodyne interference method for measuring the micro impulse of a micro thrustor is solved. The device consists of a digital signal processing system, a photoelectric detector, a pulse laser device, a torsional pendulum system, an H0 solid laser device, a polarization beam splitter (PBS), a quarter wave plate, a galvanometer, a plane standard lens and a convergent lens. The method comprises the following steps of: switching on driving power supplies of the H0 solid laser device and the galvanometer; exciting a working medium target by using pulse laser emitted by a pulse laser device, and making the working medium target produce plasma ejection to make the beam of a standard beam rotate; and acquiring signals emitted by the photoelectric detector by using the digital signal processing system, and processing the signals to acquire the micro impulse I' of the beam of the standard beam. The device and the method are suitable for measuring the micro impulse of the micro thrustor.

Description

The Inertia Based on Torsion Pendulum Method of Doppler galvanometer Sine Modulated multi-beam laser heterodyne is measured the device and method of little momentum

Technical field

The Inertia Based on Torsion Pendulum Method that the present invention relates to a kind of Doppler galvanometer Sine Modulated multi-beam laser heterodyne is measured the device and method of little momentum, belongs to little impulse measurement technical field.

Background technology

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

Laser interferance method can effectively solve above two problems that the 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 Push Technology quality in 2010 and be increased to 58g by original 0.2g, overcome the out of focus problem.Result of study shows that the introducing of laser interferance method has greatly improved the performance of rocking test macro, can satisfy the test request of laser microthruster micro impulse.But because measuring amount is more indirectly, accidental error is larger, so measuring accuracy can be very not high yet.

And in optical measuring method, the advantages such as high room and time resolution, measuring speed are fast, precision is high, the linearity good, antijamming capability is strong, dynamic response is fast owing to having for the laser heterodyne measurement technology, good reproducibility and measurement range are large enjoy Chinese scholars to pay close attention to, the laser heterodyne measurement technology has been inherited the plurality of advantages of heterodyne technology and Doppler technology, is one of present superhigh precision measuring method.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 and 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, and the measuring accuracy of the parameter value to be measured that this method obtains is low.

Summary of the invention

The objective of the invention is to solve the method for the little momentum that has employing heterodyne interferometry measurement microthruster now owing to can only obtain single parameter value to be measured, so that the low problem of the measuring accuracy of parameter value to be measured, provide a kind of Inertia Based on Torsion Pendulum Method of Doppler galvanometer Sine Modulated multi-beam laser heterodyne to measure the device and method of little momentum.

The Inertia Based on Torsion Pendulum Method of Doppler galvanometer Sine Modulated multi-beam laser heterodyne of the present invention is measured the device of little momentum, this device by digital information processing system, photodetector, pulsed laser, rock system, H ₀Solid state laser, polarizing beam splitter mirror PBS, quarter-wave plate, galvanometer, plane standard mirror and convergent lens form,

Wherein said H ₀Solid state laser, rock system, quarter-wave plate, galvanometer, polarizing beam splitter mirror PBS, convergent lens and plane standard mirror and be positioned at vacuum chamber, this vacuum chamber has the first vacuum window and the second vacuum window, and the described system of rocking is comprised of Standard Beam, plane mirror and working medium target; Plane at the end of crossbeam of Standard Beam is adhesive with plane mirror, is symmetrically fixed with the working medium target on the opposite side plane of this crossbeam relative with this plane mirror, and the reflecting surface of described plane mirror is vertical with the swaying direction of the crossbeam of Standard Beam; This Standard Beam is in the equilibrium state of level, and the optical axis of the laser beam of the target surface of described working medium target and pulsed laser emission is perpendicular;

H ₀Solid state laser Emission Lasers bundle is to the front surface of polarizing beam splitter mirror PBS, the folded light beam of this polarizing beam splitter mirror PBS is transmitted into the plane of incidence of galvanometer after the quarter-wave plate transmission, again after the quarter-wave plate transmission, be emitted to polarizing beam splitter mirror PBS through the folded light beam after the vibration mirror reflected, be incident to the plane of incidence of pasting the plane mirror on Standard Beam after this polarizing beam splitter mirror PBS transmission, the folded light beam of this plane mirror is with incidence angle θ ₀Oblique incidence is to plane standard mirror, after the utilizing emitted light of this plane standard mirror front surface converges by convergent lens with the light that transmits front surface through its rear surface Multi reflection, the first vacuum window through this vacuum chamber focuses on the photosurface of photodetector, the photodetector output electrical signals is to digital information processing system, the setting position of the second vacuum window is corresponding with the position of pulsed laser, is used for observing the duty of the system of rocking; Described digital information processing system is used for obtaining the suffered little momentum of crossbeam of Standard Beam according to the signal that receives continuously.

The Inertia Based on Torsion Pendulum Method of the Doppler galvanometer Sine Modulated multi-beam laser heterodyne based on said apparatus of the present invention is measured the method for little momentum, and the process of the method is:

At first, open H ₀Solid state laser, and open the driving power of galvanometer, make galvanometer begin to do simple harmonic oscillation;

Simultaneously, adopt pulsed laser to send pulse laser excitation working medium target, make this working medium target produce plasma jet, the effect of regurgitating of the plasma spraying that produces is rotated the crossbeam of Standard Beam;

The digital information processing system signal that the continuous acquisition photodetector sends in rocking system's swing process, and all signals of continuous acquisition are processed, the suffered little momentum I ' of crossbeam of Standard Beam obtained.

The suffered little momentum of the crossbeam of described Standard Beam is that described little momentum I ' is according to the crossbeam swing angle θ ' acquisition of Standard Beam with the relational expression of crossbeam swing angle θ ':

I′＝k·θ′，

K=4 π J/DT in the formula, wherein J is the moment of inertia of the system of rocking, and T rocks the damping period of system for this, and D is crossbeam length;

The pivot angle θ ' of described Standard Beam is:

${\mathrm{\θ}}^{\′}=\frac{{\mathrm{\θ}}_0}{2},$

In the formula, θ ₀It is the incident angle of plane standard mirror.

The crossbeam swing angle θ ' of described Standard Beam is the signal of the photodetector that constantly obtains according to difference, obtains by the multi-beam laser heterodyne method, and detailed process is:

The folded light beam of plane mirror is with incidence angle θ ₀Oblique incidence is to plane standard mirror, and the incident field of this moment is:

E(t)＝E _lexp(iω ₀t)，

E in the formula _lBe constant, i represents imaginary number, ω ₀Be the laser angular frequency;

The vibration equation of galvanometer is:

x(t)＝x ₀ cos(ω _ct)，

The rate equation of galvanometer is:

v(t)＝-ω _cx ₀sin(ω _ct)，

X in the formula ₀Be the amplitude of Doppler galvanometer vibration, ω _cBe the angular frequency of Doppler galvanometer, c is the light velocity, and t is the time,

Because the vibration of galvanometer, the catoptrical frequency of plane standard mirror is:

ω＝ω ₀(1-2ω _cx ₀sin(ω _ct)/c)，

The reflection light field that then constantly arrives plane standard mirror front surface at tl/c is:

E ₀(t)＝α ₀E _lexp{i[ω ₀(1-2ω _cx ₀sin(ω _c(t-l/c))/c)

(t-l/c)+ω ₀x ₀cos(ω _c(t-l/c))/c]}

α in the formula ₀To be light inject the reflection coefficient of plane standard mirror front surface from surrounding medium for=r, r, l be galvanometer to the light path of plane standard mirror,

Through the light of plane standard mirror front surface transmission difference constantly by plane standard mirror between its front surface and rear surface by rear surface continuous reflection and transmission m time, the light field that the m that obtains plane standard mirror restraints the light that transmits plane standard mirror front surface is respectively:

E ₁(t)＝α ₁E _lexp{i[ω ₀(1-2ω _cx ₀sin(ωc(t-(L+2ndcosθ)/c))/c)

(t-(L+2ndcosθ)/c)+ω ₀x ₀cos(ω _c(t-(L+2ndcosθ)/c))/c]}

E ₃(t)＝α ₂E _lexp{i[ω ₀(1-2ω _cx ₀sin(ω _c(t-(L+4ndcosθ)/c))/c)

(t-(L+4ndcosθ)/c)+ω ₀x ₀cos(ω _c(t-(L+4ndcosθ)/c))/c]}

E ₃(t)＝α ₃E _lexp{i[ω ₀(1-2ω _cx ₀sin(ω _c(t-(L+6ndcosθ)/c))/c)

(t-(L+6ndcosθ)/c)+ω ₀x ₀cos(ω _c(t-(L+6ndcosθ)/c))/c]}，

·

·

·

E _m(t)＝α _mE _lexp{i[ω ₀(1-2ω _cx ₀sin(ω _c(t-(L+2mndcosθ)/c))/c)

(t-(L+2mndcosθ)/c)+ω ₀x ₀cos(ω _c(t-(L+2mndcosθ)/c))/c]}

Wherein, parameter alpha ₁=β β ' r ' ..., α _m=β β ' r ' ^(2m-1), β is the transmission coefficient of plane standard mirror front surface, the transmission coefficient when β ' transmits plane standard mirror for light, r ' is the reflectivity of standard mirror rear surface, plane, and d is the thickness of plane standard mirror, and θ is the refraction angle of plane standard mirror, m is nonnegative integer, and n is the refractive index of plane standard mirror;

Total light field that photodetector receives is:

E(t)＝E ₀(t)+E ₁(t)+E ₂(t)+…+E _m(t)，

Then the photocurrent of photodetector output is:

$I=\frac{\mathrm{\ηe}}{\mathrm{hv}}\frac{1}{Z}\underset{S}{\∫\∫}\frac{1}{2}[E_0\left(t\right)+E_1\left(t\right)+E_2\left(t\right)+...+E_m\left(t\right)]{[E_0\left(t\right)+E_1\left(t\right)+E_2\left(t\right)+...+E_m\left(t\right)]}^{*}\mathrm{ds}$

$=\frac{\mathrm{\ηe}}{2\mathrm{hv}}\frac{1}{Z}\underset{S}{\∫\∫}[\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{E_j}^2\left(t\right)+\underset{p=1}{\overset{m-1}{\mathrm{\Σ}}}\underset{j-1}{\overset{m-p}{\mathrm{\Σ}}}(E_j\left(t\right){E_{j+p}}^{*}\left(t\right)+{E_j}^{*}\left(t\right)E_{j+p}\left(t\right))]\mathrm{ds},$

Wherein, e is electron charge, and η is quantum efficiency, and h is Planck's constant, and v is laser frequency, and Z is the intrinsic impedance of photodetector surfaces medium, and S is the area of photodetector photosurface, * number expression complex conjugate;

Following formula is put in order the acquisition electric current of intermediate frequency is:

$I_{\mathrm{IF}}=\frac{\mathrm{\ηe}}{2\mathrm{hv}}\frac{1}{Z}\underset{S}{\∫\∫}\underset{p=1}{\overset{m-1}{\mathrm{\Σ}}}\underset{j=0}{\overset{m-p}{\mathrm{\Σ}}}(E_j\left(t\right){E_{j+p}}^{*}\left(t\right)+{E_j}^{*}\left(t\right)E_{j+p}\left(t\right))\mathrm{ds},$

With the formula substitution following formula of all light fields, acquisition result of calculation is:

$I_{\mathrm{IF}}=\frac{\mathrm{\ηe}}{\mathrm{hv}}\frac{\mathrm{\π}}{Z}{E}_0^2\underset{p=1}{\overset{m-1}{\mathrm{\Σ}}}\underset{j=0}{\overset{m-p}{\mathrm{\Σ}}}{\mathrm{\α}}_{j+p}{\mathrm{\α}}_j\cos [\frac{4\mathrm{pnd}\cos \mathrm{\θ}{\mathrm{\ω}}_0{\mathrm{\ω}}_c^2{x}_0}{c^2}t+\frac{2{\mathrm{\ω}}_0{x}_0}{c}-\frac{2\mathrm{pnd}{\mathrm{\ω}}_0\cos \mathrm{\θ}}{c}$

$-\frac{4\mathrm{pnd}\cos \mathrm{\θ}{\mathrm{\ω}}_0{\mathrm{\ω}}_c^2{x}_0(l+2\mathrm{pnd}\cos \mathrm{\θ})}{c^3}],$

Ignore 1/c ³Event after following formula be reduced to:

$I_{\mathrm{IF}}=\frac{\mathrm{\ηe}}{\mathrm{hv}}\frac{\mathrm{\π}}{Z}{E}_0^2\underset{p=1}{\overset{m-1}{\mathrm{\Σ}}}\underset{j=0}{\overset{m-p}{\mathrm{\Σ}}}{\mathrm{\α}}_{j+p}{\mathrm{\α}}_j\cos [\frac{4\mathrm{pnd}\cos \mathrm{\θ}{\mathrm{\ω}}_0{\mathrm{\ω}}_c^2{x}_0}{c^2}t+\frac{2{\mathrm{\ω}}_0{x}_0}{c}-\frac{2\mathrm{pnd}{\mathrm{\ω}}_0\cos \mathrm{\θ}}{c}],$

P and j are positive integer in the formula;

According to following formula, the frequency of interference signal is designated as:

$f_p=4\mathrm{pnd}\cos \mathrm{\θ}{\mathrm{\ω}}_0{\mathrm{\ω}}_c^2{x}_0/\left(2\mathrm{\π}{c}^2\right)2\mathrm{pnd}\cos \mathrm{\θ}{\mathrm{\ω}}_0{\mathrm{\ω}}_c^2{x}_0/\left(\mathrm{\π}{c}^2\right)=K_{p}d,$

In the formula $K_p=2\mathrm{pn}{\mathrm{\ω}}_0{\mathrm{\ω}}_c^2{x}_0\cos \mathrm{\θ}/\left(\mathrm{\π}{c}^2\right),$

The numerical value of the centre frequency of theoretical curve when the centre frequency of first main peak of multi-beam laser heterodyne signal spectrum and normal incidence during according to the oblique incidence among the multi-beam laser heterodyne signal spectrum figure obtains the ratio of two centre frequencies:

ζ＝cosθ

And then the size of acquisition laser refraction angle θ behind the standard mirror of plane, according to refraction law acquisition incidence angle θ be:

θ ₀＝arcsin[nsin(arccosζ)]

According to

${\mathrm{\θ}}^{\′}=\frac{{\mathrm{\θ}}_0}{2}$

Obtain the pivot angle θ ' of Standard Beam.

Advantage of the present invention is: the present invention is on the laser heterodyne measurement technical foundation, proposed in light path, to utilize the Sine Modulated Doppler galvanometer that difference incident light frequency is constantly carried out Sine Modulated, obtained Sine Modulated multi-beam laser heterodyne signal, comprise simultaneously a plurality of frequency values in its signal spectrum, each frequency values comprises parameter information to be measured, can obtain simultaneously a plurality of parameter values to be measured through after the demodulation, to the multiple parameter values weighted mean that obtains, improve the precision of parameter to be measured.

Measured little momentum of working medium target by emulation experiment, it measures relative error only is 0.4%.

The present invention is based on heterodyne technology and Doppler effect, parameter information to be measured is loaded in the difference on the frequency of heterodyne signal, after the signal demodulation, can obtain simultaneously a plurality of parameter values to be measured, process the measuring accuracy that can improve parameter to be measured through weighted mean.Little momentum that laser and the effect of working medium target are produced is converted into the rotational angle of the system of rocking, and measures this micro-corner by the multi-beam laser heterodyne method, thereby calculates little momentum.

Description of drawings

Fig. 1 is the structural representation of apparatus of the present invention;

Fig. 2 is the multi-beam laser principle of interference figure between the front and rear surfaces of plane standard mirror;

Fig. 3 is the Fourier transform spectrogram of multi-beam laser heterodyne signal;

Fig. 4 is plane standard mirror spectrogram corresponding to little impulse measurement in the different incidence angles situation of light beam, and leftmost lines are the spectrogram in the 11.205mrad situation among the figure, and the rightest lines are the spectrogram in the 5.976mrad situation among the figure.

Embodiment

Embodiment one: present embodiment is described below in conjunction with Fig. 1, the Inertia Based on Torsion Pendulum Method of the described Doppler galvanometer Sine Modulated of present embodiment multi-beam laser heterodyne is measured the device of little momentum, this device by digital information processing system 1, photodetector 2, pulsed laser 6, rock system, H ₀ Solid state laser 10, polarizing beam splitter mirror PBS11, quarter-wave plate 12, galvanometer 13, plane standard mirror 14 and convergent lens 15 form,

Wherein said H ₀ Solid state laser 10, rock system, quarter-wave plate 12, galvanometer 13, polarizing beam splitter mirror PBS11, convergent lens 15 and plane standard mirror 14 and be positioned at vacuum chamber 4, this vacuum chamber 4 has the first vacuum window 3 and the second vacuum window 5, and the described system of rocking is comprised of Standard Beam 8, plane mirror 9 and working medium target 7; Plane at the end of crossbeam of Standard Beam 8 is adhesive with plane mirror 9, be symmetrically fixed with working medium target 7 on the opposite side plane of this crossbeam relative with this plane mirror 9, the reflecting surface of described plane mirror 9 is vertical with the swaying direction of the crossbeam of Standard Beam 8; This Standard Beam 8 is in the equilibrium state of level, and the optical axis of the laser beam of the target surface of described working medium target 7 and pulsed laser 6 emissions is perpendicular;

H ₀ Solid state laser 10 Emission Lasers bundles are to the front surface of polarizing beam splitter mirror PBS11, the folded light beam of this polarizing beam splitter mirror PBS11 is transmitted into the plane of incidence of galvanometer 13 after quarter-wave plate 12 transmissions, folded light beam after galvanometer 13 reflections is emitted to polarizing beam splitter mirror PBS 11 again after quarter-wave plate 12 transmissions, be incident to the plane of incidence of the plane mirror 9 of pasting on Standard Beam 8 after this polarizing beam splitter mirror PBS 11 transmissions, the folded light beam of this plane mirror 9 is with incidence angle θ ₀Oblique incidence is to plane standard mirror 14, after the utilizing emitted light of these plane standard mirror 14 front surfaces converges by convergent lens 15 with the light that transmits front surface through its rear surface Multi reflection, the first vacuum window 3 through this vacuum chamber 4 focuses on the photosurface of photodetector 2, photodetector 2 output electrical signals are to digital information processing system 1, the setting position of the second vacuum window 5 is corresponding with the position of pulsed laser 6, is used for observing the duty of the system of rocking; Described digital information processing system 1 is used for obtaining the suffered little momentum of crossbeam of Standard Beam 8 according to the signal that receives continuously.

Galvanometer 13 in the present embodiment can carry out frequency modulation (PFM) to the laser that difference incides the galvanometer surface constantly.

This device in use, at first, pulsed laser 6 produces plasma jets with 7 effects of working medium target, the effect of regurgitating of plasma is rotated the crossbeam of the Standard Beam 8 of the system of rocking.Simultaneously, open H ₀Solid state laser 10, make linearly polarized light successively through shining on galvanometer 13 front surfaces behind polarizing beam splitter mirror PBS11 and the quarter-wave plate 12, and the different reflected light of constantly being modulated by galvanometer 13 are pasted on plane mirror 9 surfaces on the Standard Beam 8 through seeing through oblique being mapped to of polarizing beam splitter mirror PBS11 behind the quarter-wave plate 12, reflected light is converged with the light through plane standard mirror 14 front surface reflections after the light of plane standard mirror 14 front surface transmissions is by the reflection of the rear surface of plane standard mirror 14 on the photosurface that lens 15 converge to photodetector 2, finally by the electric signal after photodetector 2 opto-electronic conversion through wave filter 17, prime amplifier 16, obtain different parameter informations constantly to be measured behind modulus converter A/D and the digital signal processing controller DSP.Like this, just can record by the multi-beam laser heterodyne method angle of the crossbeam rotation of Standard Beam 8, thereby measure the micro impulse of laser and the 7 effect generations of working medium target.

Embodiment two: present embodiment is further specifying embodiment one, digital information processing system 1 is by wave filter 17, prime amplifier 16, modulus converter A/D and digital signal processing controller DSP form, wave filter 17 carries out the signal of photodetector 2 outputs to send to prime amplifier 16 after the filtering, this prime amplifier 16 sends to modulus converter A/D after the signal that receives is amplified, modulus converter A/D becomes digital signal to send to the digital signal processing controller DSP analog signal conversion that receives, be solidified with fft algorithm in this digital signal processing controller DSP, the digital signal processing controller DSP is used for the signal that receives is continuously processed, and obtains the suffered little momentum of crossbeam of Standard Beam 8 after the demodulation.

Embodiment three: present embodiment is for to the further specifying of embodiment one or two, and described galvanometer 13 is Doppler galvanometer, and its simple harmonic oscillation equation and rate equation are respectively x (t)=x ₀Cos (ω _cT) and v (t)=-ω _cx ₀Sin (ω _cT),

X in the formula ₀Be the amplitude of Doppler galvanometer vibration, ω _cBe the angular frequency of Doppler galvanometer, c is the light velocity, and t is the time.

Embodiment four: present embodiment is for to embodiment one, two or three further specify, and described working medium target 7 is targets of making of working medium.

Embodiment five: present embodiment is described below in conjunction with Fig. 1 and Fig. 2, present embodiment is to measure the method for little momentum based on the Inertia Based on Torsion Pendulum Method of the Doppler galvanometer Sine Modulated multi-beam laser heterodyne of embodiment one to four described device, and the process of the method is:

At first, open H ₀ Solid state laser 10, and open the driving power of galvanometer 13, make galvanometer 13 begin to do simple harmonic oscillation;

Simultaneously, adopt pulsed laser 6 to send pulse laser excitation working medium target 7, make this working medium target 7 produce plasma jet, the effect of regurgitating of the plasma spraying that produces is rotated the crossbeam of Standard Beam 8;

Digital information processing system 1 signal that continuous acquisition photodetector 2 sends in rocking system's swing process, and all signals of continuous acquisition are processed, the suffered little momentum I ' of crossbeam of Standard Beam 8 obtained.

Embodiment six: present embodiment is further specifying embodiment five, the suffered little momentum of the crossbeam of described Standard Beam 8 is that described little momentum I ' is according to the crossbeam swing angle θ ' acquisition of Standard Beam 8 with the relational expression of crossbeam swing angle θ ':

I′＝k·θ′，

K=4 π J/DT in the formula, wherein J is the moment of inertia of the system of rocking, and T rocks the damping period of system for this, and D is crossbeam length;

The pivot angle θ ' of described Standard Beam 8 is:

${\mathrm{\θ}}^{\′}=\frac{{\mathrm{\θ}}_0}{2},$

In the formula, θ ₀It is the incident angle of plane standard mirror 14.

Embodiment seven: present embodiment is described below in conjunction with Fig. 1 to Fig. 4, present embodiment is further specifying embodiment five or six, the crossbeam swing angle θ ' of described Standard Beam 8 is signals of the photodetector 2 that constantly obtains according to difference, obtain by the multi-beam laser heterodyne method, detailed process is:

The folded light beam of plane mirror 9 is with incidence angle θ ₀Oblique incidence is to plane standard mirror 14, and the incident field of this moment is:

E(t)＝E _lexp(iω ₀t)，

E in the formula _lBe constant, i represents imaginary number, ω ₀Be the laser angular frequency;

The vibration equation of galvanometer 13 is:

x(t)＝x ₀cos(ω _ct)，

The rate equation of galvanometer 13 is:

v(t)＝-ω _cx ₀sin(ω _ct)，

X in the formula ₀Be the amplitude of Doppler galvanometer vibration, ω _cBe the angular frequency of Doppler galvanometer, c is the light velocity, and t is the time,

Because the vibration of galvanometer 13, the catoptrical frequency of plane standard mirror 14 is:

ω＝ω ₀(1-2ω _cx ₀sin(ω _ct)/c)，

The reflection light field that then constantly arrives plane standard mirror 14 front surfaces at t-l/c is:

E ₀(t)＝α ₀E _lexp{i[ω ₀(1-2ω _cx ₀sin(ω _c(t-l/c))/c)

(t-l/c)+ω ₀x ₀cos(ω _c(t-l/c))/c]}

α in the formula ₀To be light inject the reflection coefficient of plane standard mirror 14 front surfaces from surrounding medium for=r, r, l be galvanometer 13 to the light path of plane standard mirror 14,

Through the light of plane standard mirror 14 front surface transmissions difference constantly by plane standard mirror 14 between its front surface and rear surface by rear surface continuous reflection and transmission m time, the light field that the m that obtains plane standard mirror 14 restraints the light that transmits plane standard mirror 14 front surfaces is respectively:

E ₁(t)＝α ₁E _lexp{i[ω ₀(1-2ω _cx ₀sin(ω _c(t-(L+2ndcosθ)/c))/c)

(t-(L+2ndcosθ)/c)+ω ₀x ₀cos(ω _c(t-(L+2ndcosθ)/c))/c]}

E ₂(t)＝α ₂E _lexp{i[ω ₀(1-2ω _cx ₀sin(ω _c(t-(L+4ndcosθ)/c))/c)

(t-(L+4ndcosθ)/c)+ω ₀x ₀cos(ω _c(t-(L+4ndcosθ)/c))/c]}

E ₃(t)＝α ₃E _lexp{i[ω ₀(1-2ω _cx ₀sin(ω _c(t-(L+6ndcosθ)/c))/c)

(t-(L+6ndcosθ)/c)+ω ₀x ₀cos(ω _c(t-(L+6ndcosθ)/c))/c]}，

·

·

·

E _m(t)＝α _mE _lexp{i[ω ₀(1-2ω _cx ₀sin(ω _c(t-(L+2mndcosθ)/c))/c)

(t-(L+2mndcosθ)/c)+ω ₀x ₀cos(ω _c(t-(L+2mndcosθ)/c))/c]}

Wherein, parameter alpha ₁=β β ' r ' ..., α _m=β β ' r ' ^(2m-1)β is the transmission coefficient of plane standard mirror 14 front surfaces, transmission coefficient when β ' transmits plane standard mirror 14 for light, r ' is the reflectivity of standard mirror 14 rear surfaces, plane, d is the thickness of plane standard mirror 14, θ is the refraction angle of plane standard mirror 14, and m is nonnegative integer, and n is the refractive index of plane standard mirror 14;

Total light field that photodetector 2 receives is:

E(t)＝E ₀(t)+E ₁(t)+E ₂(t)+…+E _m(t)，

Then the photocurrent of photodetector 2 outputs is:

$I=\frac{\mathrm{\ηe}}{\mathrm{hv}}\frac{1}{Z}\underset{S}{\∫\∫}\frac{1}{2}[E_0\left(t\right)+E_1\left(t\right)+E_2\left(t\right)+...+E_m\left(t\right)]{[E_0\left(t\right)+E_1\left(t\right)+E_2\left(t\right)+...+E_m\left(t\right)]}^{*}\mathrm{ds}$

$=\frac{\mathrm{\ηe}}{2\mathrm{hv}}\frac{1}{Z}\underset{S}{\∫\∫}[\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{E_j}^2\left(t\right)+\underset{p=1}{\overset{m-1}{\mathrm{\Σ}}}\underset{j=1}{\overset{m-p}{\mathrm{\Σ}}}(E_j\left(t\right){E_{j+p}}^{*}\left(t\right)+{E_j}^{*}\left(t\right)E_{j+p}\left(t\right))]\mathrm{ds},$

Wherein, e is electron charge, and η is quantum efficiency, and h is Planck's constant, and v is laser frequency, and Z is the intrinsic impedance of photodetector 2 surface dielectrics, and S is the area of photodetector 2 photosurfaces, * number expression complex conjugate;

Following formula is put in order the acquisition electric current of intermediate frequency is:

$I_{\mathrm{IF}}=\frac{\mathrm{\ηe}}{2\mathrm{hv}}\frac{1}{Z}\underset{S}{\∫\∫}\underset{p=1}{\overset{m-1}{\mathrm{\Σ}}}\underset{j=0}{\overset{m-p}{\mathrm{\Σ}}}(E_j\left(t\right){E_{j+p}}^{*}\left(t\right)+{E_j}^{*}\left(t\right)E_{j+p}\left(t\right))\mathrm{ds},$

With the formula substitution following formula of all light fields, acquisition result of calculation is:

$I_{\mathrm{IF}}=\frac{\mathrm{\ηe}}{\mathrm{hv}}\frac{\mathrm{\π}}{Z}{E}_0^2\underset{p=1}{\overset{m-1}{\mathrm{\Σ}}}\underset{j=0}{\overset{m-p}{\mathrm{\Σ}}}{\mathrm{\α}}_{j+p}{\mathrm{\α}}_j\cos [\frac{4\mathrm{pnd}\cos {{\mathrm{\θ\ω}}_0\mathrm{\ω}}_c^2{x}_0}{c^2}t+\frac{2{\mathrm{\ω}}_0{x}_0}{c}-\frac{2\mathrm{pnd}{\mathrm{\ω}}_0\cos \mathrm{\θ}}{c}$

$-\frac{4\mathrm{pnd}\cos {\mathrm{\θ\ω}}_0{\mathrm{\ω}}_c^2{x}_0(l+2\mathrm{pnd}\cos \mathrm{\θ})}{c^3}],$

Ignore 1/c ³Event after following formula be reduced to:

$I_{\mathrm{IF}}=\frac{\mathrm{\ηe}}{\mathrm{hv}}\frac{\mathrm{\π}}{Z}{E}_0^2\underset{p=1}{\overset{m-1}{\mathrm{\Σ}}}\underset{j=0}{\overset{m-p}{\mathrm{\Σ}}}{\mathrm{\α}}_{j+p}{\mathrm{\α}}_j\cos [\frac{4\mathrm{pnd}\cos {\mathrm{\θ\ω}}_0{\mathrm{\ω}}_c^2{x}_0}{c^2}t+\frac{{2\mathrm{\ω}}_0{x}_0}{c}-\frac{2\mathrm{pnd}{\mathrm{\ω}}_0\cos \mathrm{\θ}}{c}],$

P and j are positive integer in the formula;

According to following formula, the frequency of interference signal is designated as:

$f_p=4\mathrm{pnd}\cos {\mathrm{\θ\ω}}_0{\mathrm{\ω}}_c^2{x}_0/\left({2\mathrm{\πc}}^2\right)=2\mathrm{pnd}\cos {\mathrm{\θ\ω}}_0{\mathrm{\ω}}_c^2{x}_0/\left({\mathrm{\πc}}^2\right)=K_{p}d,$

In the formula $K_p=2\mathrm{pn}{\mathrm{\ω}}_0{\mathrm{\ω}}_c^2{x}_0\cos \mathrm{\θ}/\left({\mathrm{\πc}}^2\right),$

The numerical value of the centre frequency of theoretical curve when the centre frequency of first main peak of multi-beam laser heterodyne signal spectrum and normal incidence during according to the oblique incidence among the multi-beam laser heterodyne signal spectrum figure obtains the ratio of two centre frequencies:

ζ＝cosθ

And then the size of acquisition laser refraction angle θ behind plane standard mirror 14, obtain incidence angle θ according to refraction law ₀For:

θ ₀＝arcsin[nsin(arccosζ)]

According to

${\mathrm{\θ}}^{\′}=\frac{{\mathrm{\θ}}_0}{2}$

Obtain the pivot angle θ ' of Standard Beam 8.

Shown in Figure 2, because light beam can constantly reflect and reflect between the front and rear surfaces of plane standard mirror 14, and this reflection and refraction for reflected light and transmitted light at infinity or the interference on the lens focal plane contribution is arranged, so when interference is discussed, must consider Multi reflection and refraction effect, multi-beam laser namely should be discussed interfere.

Obtain electric current of intermediate frequency I in arrangement _IFProcess in because DC terms is through can filtering behind the low-pass filter, therefore, only consider here to exchange, this exchanges item and is commonly referred to electric current of intermediate frequency.

By ignoring 1/c ³Event after electric current of intermediate frequency I _IFFormula of reduction, can see that the information of the thickness d of plane standard mirror is arranged in the intermediate frequency item difference on the frequency that multiple beam heterodyne measurement method obtains and the phase differential.Analyze mainly for intermediate frequency item intermediate frequency rate variance, because adopt Fourier transform to be easy to realize frequency measurement.According to the expression formula of the frequency f of interference signal as can be known, the frequency of interference signal is directly proportional with the thickness of plane standard mirror 14.

According to top theoretical analysis, get H ₀Wavelength X=the 2050nm of solid state laser 10, this laser is to eye-safe; The refractive index n of normal conditions lower plane standard mirror 14=1.493983; The photosurface aperture of photodetector 2 is R=1mm.Sensitivity 1A/W.The amplitude x of galvanometer 13 ₀=0.0001m.Utilize the relation of MATLAB emulation plane standard mirror 14 thickness and intermediate-freuqncy signal frequency, can see by emulation, the Fourier transform frequency spectrum of processing the multi-beam laser heterodyne signal obtain through signal as shown in Figure 3, wherein solid line is in the laser oblique incidence situation, the Fourier transform frequency spectrum of corresponding multi-beam laser heterodyne signal during measurement plane standard mirror 14 thickness d; Dotted line is in the laser normal incidence situation, the Fourier transform frequency spectrum of corresponding multi-beam laser heterodyne signal during the standard mirror 14 mirror thickness d of plane.

Solid line can be found out from Fig. 3, 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. 3, can also see, provided the theoretical curve in the situation of normal incidence in the experiment, purpose is: in 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 multi-beam laser heterodyne signal spectrum and normal incidence in the time of can obtaining oblique incidence simultaneously, like this, be easy to the ratio of two centre frequencies obtaining:

ζ＝cosθ，

Obtaining in the situation of centre frequency, can calculate the size of laser refraction angle θ behind plane standard mirror 14 by following formula, therefore can obtain incidence angle θ according to refraction law ₀Size be:

θ ₀＝arcsin[nsin(arccosζ)]，

The relational expression that is easy to thus to obtain momentum I ' and refraction angle θ is:

$I^{\′}=\frac{k\·\arcsin \left\{n\sin \right[\arccos \left(\cos \mathrm{\θ}\right)\left]\right\}}{2}.$

Simulation result:

Adopt the variation that adds Standard Beam 8 front and back system cycles by measuring, calibrate the moment of inertia of the system of rocking, the experimental result of demarcation is as shown in table 1, can obtain the size of k value according to calibration result.

Table 1

Measure low-angle system based on the designed multi-beam laser heterodyne of apparatus of the present invention, under the condition of work of 10.0Pa, utilize the MATLAB software simulation to measure working medium and be PVC (Polyvinylchloride)+2%C, thickness is 180 μ m, the laser initial current is 5A, pulsewidth is 50ms, little momentum that laser and working medium target 7 interact and produce, and the feasibility of checking multi-beam laser heterodyne measuring method.Get H ₀ Solid state laser 10 wavelength X=2050nm; Standard Beam 8 long D=15cm; The refractive index n of plane standard mirror 14=1.493983, its thickness are 2cm; The photosurface aperture of detector is R=1mm, sensitivity 1A/W.

Simultaneously, emulation has obtained different incidence angles θ ₀In the situation, multi-beam laser heterodyne is measured multi-beam laser heterodyne signal Fourier transform frequency spectrum corresponding to minute angle as shown in Figure 4, as can be seen from Figure 4, along with the increase of incident angle, the relative position of frequency spectrum reduces to the increase frequency that the low frequency direction moves namely along with angle.Reason is: in the constant situation of plane standard mirror 14 thickness, Proportional coefficient K and frequency are proportional, and in the low-angle situation, Proportional coefficient K reduces thereupon when incident angle increases, because frequency f _pWith Proportional coefficient K _pThe pass is f _p=K _pD, in the constant situation of d, frequency f _pAnd K _pBe linear spectrum, therefore, K _pFrequency also reduces thereupon when reducing, and namely along with the increase of incident angle, the relative position of frequency spectrum moves to the low frequency direction, and Fig. 4 has verified the correctness of the inventive method well.

Need to prove that 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. 3 and Fig. 4 is very high.

Utilize above-mentioned Sine Modulated multi-beam laser heterodyne mensuration, continuous analog eight groups of data, obtained the simulation result of the little momentum of testing sample in the different incidence angles situation, as shown in table 2.

Table 2 different incidence angles θ ₀In the situation, the actual value I of little momentum _ActualWith simulation value I (k=7.42409372e-3)

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 Actual(×10 -6N·s)	22.183	24.956	27.729	30.502	33.275	36.048	38.820	41.593
									I′(×10 -6N·s)	22.074	25.001	27.699	30.392	33.303	35.986	38.887	41.561

Need to prove: utilize the emulation experiment data of table 2, can calculate the mean value of little momentum, the maximum relative error that finally can obtain the analogue value can find out that less than 0.4% the measuring accuracy of the method is very high.Simultaneously, the analysis data it can also be seen that, in the situation of small angle approximation, the systematic error that environment brings and reading error are negligible in emulation, and the error in the emulation experiment mainly comes from trueness error after the Fast Fourier Transform (FFT) (FFT) and the round-off error in the computation process.

The present invention is directed to characteristics and the deficiency of traditional little impulse measurement system, proposed a kind ofly based on the little impulse measurement method of rocking of multi-beam laser heterodyne angle measurement, utilized device of the present invention to carry out the emulation experiment measurement of pulse laser and PVC working medium target coupling little momentum that produces.The 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 than 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.Simultaneously, when rotational angle less (less than 5 °), little momentum and the incident angle surveyed are linear, and measuring error is less than 0.4%, can satisfy the requirement of laser microthruster impulse measurement, for the performance of assessing laser microthruster provides good measurement means.

Claims (6)

1. the Inertia Based on Torsion Pendulum Method of a Doppler galvanometer Sine Modulated multi-beam laser heterodyne is measured the device of little momentum, it is characterized in that: this device by digital information processing system (1), photodetector (2), pulsed laser (6), rock system, H ₀Solid state laser (10), polarizing beam splitter mirror PBS(11), quarter-wave plate (12), galvanometer (13), plane standard mirror (14) and convergent lens (15) form,

Wherein said H ₀Solid state laser (10), rock system, quarter-wave plate (12), galvanometer (13), polarizing beam splitter mirror PBS(11), convergent lens (15) and plane standard mirror (14) be positioned at vacuum chamber (4), this vacuum chamber (4) has the first vacuum window (3) and the second vacuum window (5), and the described system of rocking is comprised of Standard Beam (8), plane mirror (9) and working medium target (7); Plane at the end of crossbeam of Standard Beam (8) is adhesive with plane mirror (9), be symmetrically fixed with working medium target (7) on the opposite side plane of this crossbeam relative with this plane mirror (9), the reflecting surface of described plane mirror (9) is vertical with the swaying direction of the crossbeam of Standard Beam (8); This Standard Beam (8) is in the equilibrium state of level, and the optical axis of the laser beam of the target surface of described working medium target (7) and pulsed laser (6) emission is perpendicular;

H ₀Solid state laser (10) Emission Lasers bundle is to polarizing beam splitter mirror PBS(11) front surface, this polarizing beam splitter mirror PBS(11) folded light beam is transmitted into the plane of incidence of galvanometer (13) after quarter-wave plate (12) transmission, folded light beam after galvanometer (13) reflection is emitted to polarizing beam splitter mirror PBS(11 again after quarter-wave plate (12) transmission), through this polarizing beam splitter mirror PBS(11) be incident to the plane of incidence of the plane mirror (9) of pasting on Standard Beam (8) after the transmission, the folded light beam of this plane mirror (9) is with incidence angle θ ₀Oblique incidence is to plane standard mirror (14), after the reflected light of this plane standard mirror (14) front surface converges by convergent lens (15) with the light that transmits front surface through its rear surface Multi reflection, the first vacuum window (3) through this vacuum chamber (4) focuses on the photosurface of photodetector (2), photodetector (2) output electrical signals is to digital information processing system (1), the setting position of the second vacuum window (5) is corresponding with the position of pulsed laser (6), is used for observing the duty of the system of rocking; Described digital information processing system (1) is used for obtaining the suffered little momentum of crossbeam of Standard Beam (8) according to the signal that receives continuously, and described galvanometer (13) is Doppler galvanometer, and its simple harmonic oscillation equation and rate equation are respectively x (t)=x ₀Cos (ω _cT) and v (t)=-ω _cx ₀Sin (ω _cT),

X in the formula ₀Be the amplitude of Doppler galvanometer vibration, ω _cBe the angular frequency of Doppler galvanometer, c is the light velocity, and t is the time.

2. the Inertia Based on Torsion Pendulum Method of Doppler galvanometer Sine Modulated multi-beam laser heterodyne according to claim 1 is measured the device of little momentum, it is characterized in that: digital information processing system (1) is by wave filter (17), prime amplifier (16), analog to digital converter (A/D) and digital signal processing controller (DSP) form, wave filter (17) carries out the signal of photodetector (2) output to send to prime amplifier (16) after the filtering, this prime amplifier (16) sends to analog to digital converter (A/D) after the signal that receives is amplified, analog to digital converter (A/D) becomes digital signal to send to digital signal processing controller (DSP) analog signal conversion that receives, be solidified with fft algorithm in this digital signal processing controller (DSP), digital signal processing controller (DSP) is used for the signal that receives is continuously processed, and obtains the suffered little momentum of crossbeam of Standard Beam (8) after the demodulation.

3. the Inertia Based on Torsion Pendulum Method of Doppler galvanometer Sine Modulated multi-beam laser heterodyne according to claim 1 is measured the device of little momentum, it is characterized in that: described working medium target (7) is the target of making of working medium.

4. the Inertia Based on Torsion Pendulum Method based on the described Doppler galvanometer Sine Modulated of the claim 1 multi-beam laser heterodyne Inertia Based on Torsion Pendulum Method of Doppler galvanometer Sine Modulated multi-beam laser heterodyne of measuring the device of little momentum is measured the method for little momentum, it is characterized in that the process of the method is:

At first, open H ₀Solid state laser (10), and open the driving power of galvanometer (13), make galvanometer (13) begin to do simple harmonic oscillation;

Simultaneously, adopt pulsed laser (6) to send pulse laser excitation working medium target (7), make this working medium target (7) produce plasma jet, the effect of regurgitating of the plasma spraying that produces is rotated the crossbeam of Standard Beam (8);

Digital information processing system (1) signal that continuous acquisition photodetector (2) sends in rocking system's swing process, and all signals of continuous acquisition are processed, the suffered little momentum I ' of crossbeam of Standard Beam (8) obtained.

5. the Inertia Based on Torsion Pendulum Method of Doppler galvanometer Sine Modulated multi-beam laser heterodyne according to claim 4 is measured the method for little momentum, it is characterized in that: the suffered little momentum of the crossbeam of described Standard Beam (8) is that described little momentum I ' is according to the crossbeam swing angle θ ' acquisition of Standard Beam (8) with the relational expression of crossbeam swing angle θ ':

I′＝k·θ′，

K=4 π J/DT in the formula, wherein J is the moment of inertia of the system of rocking, and T rocks the damping period of system for this, and D is crossbeam length;

The pivot angle θ ' of described Standard Beam (8) is:

${\mathrm{\θ}}^{\′}=\frac{{\mathrm{\θ}}_0}{2},$

In the formula, θ ₀It is the incident angle of plane standard mirror (14).

6. the Inertia Based on Torsion Pendulum Method of Doppler galvanometer Sine Modulated multi-beam laser heterodyne according to claim 5 is measured the method for little momentum, it is characterized in that: the crossbeam swing angle θ ' of described Standard Beam (8) is the signal of the photodetector (2) that constantly obtains according to difference, obtain by the multi-beam laser heterodyne method, detailed process is:

The folded light beam of plane mirror (9) is with incidence angle θ ₀Oblique incidence is to plane standard mirror (14), and the incident field of this moment is:

E(t)＝E _lexp(iω ₀t)，

E in the formula _lBe constant, i represents imaginary number, ω ₀Be the laser angular frequency;

The vibration equation of galvanometer (13) is:

x(t)＝x ₀cos(ω _ct)，

The rate equation of galvanometer (13) is:

v(t)＝-ω _cx ₀sin(ω _ct)，

X in the formula ₀Be the amplitude of Doppler galvanometer vibration, ω _cBe the angular frequency of Doppler galvanometer, c is the light velocity, and t is the time,

Because the vibration of galvanometer (13), the catoptrical frequency of plane standard mirror (14) is:

ω＝ω ₀(1-2ω _cx ₀sin(ω _ct)/c)，

The reflection light field that then constantly arrives plane standard mirror (14) front surface at t-l/c is:

E ₀(t)＝α ₀E _lexp{i[ω ₀(1-2ω _cx ₀sin(ω _c(t-l/c))/c)

(t-l/c)+ω ₀x ₀cos(ω _c(t-l/c))/c]}

α in the formula ₀To be light inject the reflection coefficient of plane standard mirror (14) front surface from surrounding medium for=r, r, l be galvanometer (13) to the light path of plane standard mirror (14),

Through the light of plane standard mirror (14) front surface transmission difference constantly by plane standard mirror (14) between its front surface and rear surface by rear surface continuous reflection and transmission m time, the light field that the m that obtains plane standard mirror (14) restraints the light that transmits plane standard mirror (14) front surface is respectively:

E ₁(t)＝α ₁E _lexp{i[ω ₀(1-2ω _cx ₀sin(ω _c(t-(L+2nd cosθ)/c))/c)

(t-(L+2nd cosθ)/c)+ω ₀x ₀cos(ω _c(t-(L+2nd cosθ)/c))/c]}

E ₂(t)＝α ₂E _lexp{i[ω ₀(1-2ω _cx ₀sin(ω _c(t-(L+4nd cosθ)/c))/c)

(t-(L+4nd cosθ)/c)+ω ₀x ₀cos(ω _c(t-(L+4nd cosθ)/c))/c]}

E ₃(t)＝α ₃E _lexp{i[ω ₀(1-2ω _cx ₀sin(ω _c(t-(L+6nd cosθ)/c))/c)

(t-(L+6nd cosθ)/c)+ω ₀x ₀cos(ω _c(t-(L+6nd cosθ)/c))/c]}，

E _m(t)＝α _mE _lexp{i[ω ₀(1-2ω _cx ₀sin(ω _c(t-(L+2mnd cosθ)/c))/c)

(t-(L+2mnd cosθ)/c)+ω ₀x ₀cos(ω _c(t-(L+2mnd cosθ)/c))/c]}

Wherein, parameter alpha ₁=β β ' r ' ..., α _m=β β ' r ' ^(2m-1)β is the transmission coefficient of plane standard mirror (14) front surface, transmission coefficient when β ' transmits plane standard mirror (14) for light, r ' is the reflectivity of plane standard mirror (14) rear surface, d is the thickness of plane standard mirror (14), θ is the refraction angle of plane standard mirror (14), and m is nonnegative integer, and n is the refractive index of plane standard mirror (14);

Total light field that photodetector (2) receives is:

E(t)＝E ₀(t)+E ₁(t)+E ₂(t)+…+E _m(t)，

Then the photocurrent of photodetector (2) output is:

$I=\frac{\mathrm{\ηe}}{\mathrm{hv}}\frac{1}{Z}\underset{S}{\∫\∫}\frac{1}{2}{[E_0\left(t\right)+E_1\left(t\right)+E_2\left(t\right)+\·\·\·+E_m\left(t\right)][E_0\left(t\right)+E_1\left(t\right)+E_2\left(t\right)+\·\·\·+E_m\left(t\right)]}^{*}\mathrm{ds}$

$=\frac{\mathrm{\ηe}}{2\mathrm{hv}}\frac{1}{Z}\underset{S}{\∫\∫}[\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{E_j}^2\left(t\right)+\underset{p=1}{\overset{m-1}{\mathrm{\Σ}}}\underset{j=1}{\overset{m-p}{\mathrm{\Σ}}}(E_j\left(t\right){E_{j+p}}^{*}\left(t\right)+{E_j}^{*}\left(t\right)E_{j+p}\left(t\right))]\mathrm{ds},$

Wherein, e is electron charge, and η is quantum efficiency, and h is Planck's constant, and v is laser frequency, and Z is the intrinsic impedance of photodetector (2) surface dielectric, and S is the area of photodetector (2) photosurface, * number expression complex conjugate;

Following formula is put in order the acquisition electric current of intermediate frequency is:

$I_{\mathrm{IF}}=\frac{\mathrm{\ηe}}{2\mathrm{hv}}\frac{1}{Z}\underset{S}{\∫\∫}\underset{p=1}{\overset{m-1}{\mathrm{\Σ}}}\underset{j=0}{\overset{m-p}{\mathrm{\Σ}}}(E_j\left(t\right){E_{j+p}}^{*}\left(t\right)+{E_j}^{*}\left(t\right)E_{j+p}\left(t\right))\mathrm{ds},$

With the formula substitution following formula of all light fields, acquisition result of calculation is:

$I_{\mathrm{IF}}=\frac{\mathrm{\ηe}}{\mathrm{hv}}\frac{\mathrm{\π}}{Z}{E}_0^2\underset{p=1}{\overset{m-1}{\mathrm{\Σ}}}\underset{j=0}{\overset{m-p}{\mathrm{\Σ}}}{\mathrm{\α}}_{j+p}{\mathrm{\α}}_j\cos [\frac{4\mathrm{pnd}\cos \mathrm{\θ}{\mathrm{\ω}}_0{\mathrm{\ω}}_c^2{x}_0}{c^2}t+\frac{2{\mathrm{\ω}}_0{x}_0}{c}-\frac{2\mathrm{pnd}{\mathrm{\ω}}_0\cos \mathrm{\θ}}{c},$

$-\frac{4\mathrm{pnd}\cos \mathrm{\θ}{\mathrm{\ω}}_0{\mathrm{\ω}}_c^2{x}_0(l+2\mathrm{pnd}\cos \mathrm{\θ})}{c^3}]$

Ignore 1/c ³Event after following formula be reduced to:

$I_{\mathrm{IF}}=\frac{\mathrm{\ηe}}{\mathrm{hv}}\frac{\mathrm{\π}}{Z}{E}_0^2\underset{p=1}{\overset{m-1}{\mathrm{\Σ}}}\underset{j=0}{\overset{m-p}{\mathrm{\Σ}}}{\mathrm{\α}}_{j+p}{\mathrm{\α}}_j\cos [\frac{4\mathrm{pnd}\cos \mathrm{\θ}{\mathrm{\ω}}_0{\mathrm{\ω}}_c^2{x}_0}{c^2}t+\frac{2{\mathrm{\ω}}_0{x}_0}{c}-\frac{2\mathrm{pnd}{\mathrm{\ω}}_0\cos \mathrm{\θ}}{c}],$

P and j are positive integer in the formula;

According to following formula, the frequency of interference signal is designated as:

$f_p=4\mathrm{pnd}\cos {\mathrm{\θ\ω}}_0{\mathrm{\ω}}_c^2{x}_0/\left({2\mathrm{\πc}}^2\right)=2\mathrm{pnd}\cos \mathrm{\θ}{\mathrm{\ω}}_0{\mathrm{\ω}}_c^2{x}_0/\left(\mathrm{\π}{c}^2\right)=K_{p}d,$

In the formula $K_p=2\mathrm{pn}{\mathrm{\ω}}_0{\mathrm{\ω}}_c^2{x}_0\cos \mathrm{\θ}/\left({\mathrm{\πc}}^2\right),$

The numerical value of the centre frequency of theoretical curve when the centre frequency of first main peak of multi-beam laser heterodyne signal spectrum and normal incidence during according to the oblique incidence among the multi-beam laser heterodyne signal spectrum figure obtains the ratio of two centre frequencies:

ζ＝cosθ

And then the size of acquisition laser refraction angle θ behind plane standard mirror (14), obtain incidence angle θ according to refraction law ₀For:

θ ₀＝arcsin[nsin(arccosζ)]

According to

${\mathrm{\θ}}^{\′}=\frac{{\mathrm{\θ}}_0}{2}$

Obtain the pivot angle θ ' of Standard Beam (8).

Images