CN103954392B - What micro-momentum device was rocked in the measurement of linear frequency modulation multi-beam laser heterodyne rocks micro-impulse measurement method - Google Patents

Abstract

The measurement of linear frequency modulation multi-beam laser heterodyne is rocked the device of micro-momentum and is rocked micro-impulse measurement method based on this device, relates to and rocks micro-impulse measurement technical field.Solve the problem that measuring accuracy that other existing measurement rocks the apparatus and method of micro-momentum is low.The laser action that pulse laser emission goes out produces plasma spraying in working medium target, the effect of regurgitating makes Standard Beam rotate, while Standard Beam rotates, chirped laser device continues to launch chirped laser, chirped laser is incident to flat normal mirror after the first plane mirror and the reflection of the second plane mirror, the front surface of flat normal mirror and rear surface are all reflected chirped laser and are converged on the photosurface of photodetector by convergent lens, electric signal is sent to the pivot angle θ ' that signal processing system obtains Standard Beam by photodetector, micro-momentum I ' that the laser that sends of pulsed laser and the effect of working medium target produce is obtained again according to formula.The present invention is applicable to rock micro-impulse measurement.

Description

Torsional pendulum micro-impulse measuring method of torsional pendulum micro-impulse measuring device based on linear frequency modulation multi-beam laser heterodyne

Technical Field

The invention relates to the technical field of torsional pendulum micro-impulse measurement.

Background

The laser micro thruster has wide and deep application prospect in the field of micro satellite attitude and orbit control, has the remarkable advantages of high specific impulse, large impulse dynamic range, small minimum impulse, low power consumption, high energy coupling efficiency, easiness in realization, light weight, digital control and the like, and is widely concerned by scholars at home and abroad. The impulse is an important parameter reflecting the performance of the laser micro thruster, and is characterized by small magnitude of about 10^-7～10^-5N · s. The Photonic Assciates group Phipps et al proposed in 1999 to measure the micro-impulse generated by the laser micro-thruster with a torsional pendulum system and use it to perform the performance parameter test of the micro-thruster; in 2002, Phipps et al improved the torsion pendulum system, and then Chinese science and technology university and Equipment Command technology college in China also carried out related research. From the research results reported at home and abroad at present, on one hand, the noise of the measurement system can influence the precision of the system, and the system error even reaches 50% at a small impulse magnitude; meanwhile, in the force action time, the target plane deviates from the focal plane, the energy coupling efficiency is reduced, and the measurement of micro-impulse is influenced, so that the conventional small-impulse measurement system is difficult to meet the measurement requirement.

The laser interferometry can effectively solve the two problems of the conventional test system and improve the measurement precision of the system. The method of forming differential measurement by two corner cubes replaces the original optical pointer method to measure the torsional pendulum rotation angle, thereby greatly improving the precision of the system; the mass of the torsional pendulum propulsion technology in 2010 is increased from the original 0.2g to 58g, and the defocusing problem is solved. Research results show that the performance of the torsional pendulum test system is greatly improved by introducing the laser interferometry, and the test requirement of the micro impulse of the laser micro thruster can be met. However, the indirect measurement quantity is large, and the accidental error is large, so that the measurement accuracy is not high.

Disclosure of Invention

The invention provides a device for measuring torsional pendulum micro-impulse by linear frequency modulation multi-beam laser heterodyne and a torsional pendulum micro-impulse measuring method based on the device, aiming at solving the problem of low measuring precision of the existing device and method for measuring torsional pendulum micro-impulse.

The device for measuring torsional pendulum micro impulse by using chirp multi-beam laser heterodyne comprises a linear frequency modulation laser, a first plane reflector, a second plane reflector, a plane standard mirror, a standard beam, a vacuum chamber, a pulse laser, a working medium target, a converging lens, a photoelectric detector and a signal processing system,

the linear frequency modulation laser, the first plane reflector, the second plane reflector, the plane standard mirror, the standard beam, the pulse laser, the working medium target and the convergent lens are all arranged in a vacuum chamber,

a rotating shaft is fixed at the center of the standard beam,

the working medium target is pasted on the upper surface of the standard beam, the second plane reflector is pasted on the lower surface of the standard beam, the working medium target and the second plane reflector are both positioned at the same end of the standard beam,

the laser emitted by the pulse laser acts on the working medium target to generate plasma jet, the standard beam rotates under the action of back spray, the linear frequency modulation laser continuously emits linear frequency modulation laser while the standard beam rotates, the linear frequency modulation laser is reflected by the first plane reflecting mirror and the second plane reflecting mirror and then enters the plane standard mirror, the front surface and the rear surface of the plane standard mirror reflect the linear frequency modulation laser and converge on the photosensitive surface of the photoelectric detector through the converging lens, and the electric signal output end of the photoelectric detector is connected with the electric signal input end of the signal processing system.

The signal processing system comprises a filter, a preamplifier, an A/D converter and a DSP, wherein the electric signal input end of the filter is used as the electric signal input end of the signal processing system and is connected with the electric signal output end of the photoelectric detector, the filtering signal output end of the filter is connected with the filtering signal input end of the preamplifier, the amplifying signal output end of the preamplifier is connected with the analog signal input end of the A/D converter, and the digital signal output end of the A/D converter is connected with the digital signal input end of the DSP.

The vacuum chamber is provided with a vacuum window, and the vacuum window is used for converging light in the vacuum chamber onto a photosensitive surface of a photoelectric detector outside the vacuum chamber.

The torsional pendulum micro-impulse measuring method of the device for measuring torsional pendulum micro-impulse based on the linear frequency modulation multi-beam laser heterodyne is realized by the following processes:

switching a pulse laser, a linear frequency modulation laser, a photoelectric detector and a signal processing system to a working state, converting a received optical signal into an electric signal by the photoelectric detector, sending the electric signal to the signal processing system, obtaining a swing angle theta' of a standard beam by the signal processing system according to the received continuous electric signal,

according to the following steps:

$I^{\′}=\frac{2J\mathrm{\ω}}{D}\·{\mathrm{\θ}}^{\′}=\frac{4\mathrm{\π}J}{{\mathrm{DT}}^{\′}}\·{\mathrm{\θ}}^{\′}$ (formula one),

obtaining micro impulse I ' generated by the action of laser emitted by a pulse laser and a working medium target, wherein J is the moment of inertia of a torsional pendulum system, omega is damping frequency, T ' is damping period, D is standard beam length, and k is 4 pi J/DT ':

i ═ k · θ' (equation two).

The signal processing system obtains the swing angle theta' of the standard beam according to the received continuous electric signals by the following processes:

when the linear frequency modulation laser continuously emits linear frequency modulation laser at an incidence angle theta₀When the light is obliquely incident to the plane standard mirror, the incident light field E (t) of the plane standard mirror is as follows:

E(t)＝E₀exp{i(ω₀t+k′t²) A (formula three) is calculated,

wherein,for the rate of change of the bandwidth of the modulation, T is the frequency modulation period, Δ F is the bandwidth of the modulation, E₀For the amplitude of the incident light field, t is time, omega₀For the incident field angle frequency, i represents an imaginary number,

setting the optical path of the linear frequency modulation laser reaching the front surface of the plane standard mirror as l, and then the linear frequency modulation laser reaches the reflected light field E of the front surface of the plane standard mirror at the t-l/c moment₁(t) is:

$E_1\left(t\right)={\mathrm{\α}}_1{E}_0\exp \{i\[{\mathrm{\ω}}_0(t-\frac{l}{c})+k^{\′}{(t-\frac{l}{c})}^2\]\}$ (formula four) of the reaction solution,

the light transmitted by the front surface of the plane standard mirror is reflected and refracted for multiple times by the front surface and the rear surface of the plane standard mirror at different moments, and the light field of the reflected light obtained by each reflection is as follows:

$\left\{\begin{array}{c}{E}_2\left(t\right)={\mathrm{\α}}_2{E}_0\exp \{i\[{\mathrm{\ω}}_0(t-\frac{l+2ndcos\mathrm{\θ}}{c})+k^{\′}{(t-\frac{l+2ndcos\mathrm{\θ}}{c})}^2+\frac{2{\mathrm{\ω}}_{0}ndcos\mathrm{\θ}}{c}\]\}\\ E_3\left(t\right)={\mathrm{\α}}_3{E}_0\exp \{i\[{\mathrm{\ω}}_0(t-\frac{l+4ndcos\mathrm{\θ}}{c})+k^{\′}{(t-\frac{l+4ndcos\mathrm{\θ}}{c})}^2+\frac{4{\mathrm{\ω}}_{0}ndcos\mathrm{\θ}}{c}\]\}\\ \·\\ \·\\ \·\\ E_m\left(t\right)={\mathrm{\α}}_m{E}_0\exp \{i\[{\mathrm{\ω}}_0(t-\frac{l+2(m-1)nd\cos \mathrm{\θ}}{c})+k^{\′}{(t-\frac{l+2(m-1)nd\cos \mathrm{\θ}}{c})}^2+\frac{2(m-1){\mathrm{\ω}}_{0}ndcos\mathrm{\θ}}{c}\]\}\\ \·\\ \·\\ \·\end{array}\right.$

(formula five) of the reaction solution,

wherein m is a non-negative integer α₁＝r，α_m＝ββ′r′^(2m-3)(m is not less than 2), r is the reflectance when light enters the planar standard mirror from the surrounding medium, β is the transmittance when light enters the planar standard mirror from the surrounding medium, r 'is the reflectance of the rear surface of the planar standard mirror, β' is the transmittance when light enters the surrounding medium from the inside of the planar standard mirror, d is the thickness of the planar standard mirror, theta is the refraction angle, n is the refractive index of the planar standard mirror, c is the speed of light,

the total light field E' (t) received by the photodetector is:

E′(t)＝E₁(t)+E₂(t)+...+E_m(t) +. - (equation six),

the photocurrent I output by the photodetector is:

$I=\frac{\mathrm{\η}e}{hv}\frac{1}{Z}\underset{D}{\∫\∫}\frac{1}{2}\[E_1\left(t\right)+E_2\left(t\right)+...+E_m\left(t\right)+...\]{\[E_1\left(t\right)+E_2\left(t\right)+...+E_m\left(t\right)+...\]}^{*}ds$ (formula seven) of the reaction mixture,

wherein e is the electron electric quantity, Z is the intrinsic impedance of the surface medium of the photoelectric detector, eta is the quantum efficiency, D is the area of the photosensitive surface of the photoelectric detector, h is the Planck constant, v is the laser frequency, and the sign indicates the complex conjugate,

obtaining the intermediate frequency current I according to the formula_IFComprises the following steps:

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

substituting the formula four and the formula five into the formula eight, and arranging to obtain:

$I_{IF}=\frac{\mathrm{\η}e}{hv}\frac{\mathrm{\π}}{Z}{E}_0^2\underset{p=0}{\overset{m-1}{\Σ}}\underset{j=0}{\overset{m-p}{\Σ}}{\mathrm{\α}}_{j+p}{\mathrm{\α}}_{j}cos(\frac{4{\mathrm{pk}}^{\′}ndcos\mathrm{\θ}}{c}t-\frac{4{\mathrm{pk}}^{\′}ndcos\mathrm{\θ}(l+ndcos\mathrm{\θ})}{c^2})$ (the ninth formula),

fourier transform is carried out on the frequency difference of the intermediate frequency term in the formula nine to obtain the frequency f of the interference signal_pComprises the following steps:

$f_p=\frac{2{\mathrm{pk}}^{\′}ndcos\mathrm{\θ}}{\mathrm{\π}c}=K_{p}cos\mathrm{\θ}$ (formula ten) of the above-mentioned formula,

thereby obtaining a value of angle of refraction θ, where K_pIs a proportionality coefficient, and

the refraction angle theta and the incidence angle theta can be known according to the law of refraction₀The relationship of (1) is:

θ₀arcsin (nsin θ) (formula eleven),

the incident angle theta can be known according to the geometrical relation of the incident light path₀The relationship of the swing angle theta' with the standard beam (3) is as follows:

${\mathrm{\θ}}^{\′}=\frac{{\mathrm{\θ}}_0}{2}=\frac{arcsin\left(nsin\mathrm{\θ}\right)}{2}$ (formula twelve),

and substituting the value of the swing angle theta 'of the standard beam obtained in the formula twelve into the formula two to obtain the micro impulse I' generated by the action of the laser emitted by the pulse laser and the working medium target.

Has the advantages that: the torsional pendulum micro-impulse measuring method provided by the invention has the advantages of large linear range and high resolution, and the angle measuring method is sensitive to rotation and insensitive to translation, so that the device also has strong anti-interference capability on vibration, particularly low-frequency vibration, and can be recovered to a system working state within a few seconds, thereby not only reducing the measuring error, but also reducing the requirements on measuring equipment and experimental environment. Meanwhile, when the rotation angle is small (less than 5 degrees), the measured impulse and the incident angle are in a linear relation, the measurement error is less than 0.48 percent, the requirement of measuring the impulse of the laser micro thruster can be met, and a good measurement means is provided for evaluating the performance of the laser micro thruster.

Drawings

Fig. 1 is a schematic structural diagram of a device for measuring torsional pendulum micro-impulse by using chirped multi-beam laser heterodyne according to a first embodiment and a second embodiment;

FIG. 2 is a schematic diagram of the principle of linear frequency modulation multi-beam laser interference of a planar standard mirror;

FIG. 3 is a spectrum diagram of micro-impulse measurements at different incident angles.

Detailed Description

First embodiment, the present embodiment is described with reference to fig. 1, and the apparatus for measuring torsional pendulum micro impulse by linear frequency modulation multi-beam laser heterodyne according to the present embodiment includes a linear frequency modulation laser 5, a first plane mirror 6, a second plane mirror 4, a plane standard mirror 7, a standard beam 3, a vacuum chamber 11, a pulse laser 1, a working medium target 2, a converging lens 8, a photodetector 9, and a signal processing system 10,

the linear frequency modulation laser 5, the first plane reflector 6, the second plane reflector 4, the plane standard mirror 7, the standard beam 3, the pulse laser 1, the working medium target 2 and the convergent lens 8 are all arranged in a vacuum chamber 11,

a rotating shaft is fixed at the center of the standard beam 3,

the working medium target 2 is adhered to the upper surface of the standard beam 3, the second plane reflector 4 is adhered to the lower surface of the standard beam 3, the working medium target 2 and the second plane reflector 4 are both positioned at the same end of the standard beam 3,

the laser emitted by the pulse laser acts on the working medium target 2 to generate plasma jet, the standard beam 3 rotates under the action of back spray, the linear frequency modulation laser 5 continuously emits linear frequency modulation laser while the standard beam 3 rotates, the linear frequency modulation laser is reflected by the first plane reflecting mirror 6 and the second plane reflecting mirror 4 and then enters the plane standard mirror 7, the front surface and the rear surface of the plane standard mirror 7 reflect the linear frequency modulation laser and converge on the photosensitive surface of the photoelectric detector 9 through the converging lens 8, and the electric signal output end of the photoelectric detector 9 is connected with the electric signal input end of the signal processing system 10.

Second embodiment, the present embodiment is described with reference to fig. 1, and the difference between the present embodiment and the apparatus for measuring torsional pendulum micro-impulse by chirped multi-beam laser heterodyne described in the first embodiment is that, the signal processing system 10 comprises a filter 10-1, a preamplifier 10-2, an A/D converter 10-3 and a DSP10-4, wherein an electric signal input end of the filter 10-1 is connected with an electric signal output end of the photoelectric detector 9 as an electric signal input end of the signal processing system 10, a filtering signal output end of the filter 10-1 is connected with a filtering signal input end of the preamplifier 10-2, an amplifying signal output end of the preamplifier 10-2 is connected with an analog signal input end of the A/D converter 10-3, and a digital signal output end of the A/D converter 10-3 is connected with a digital signal input end of the DSP 10-4.

Third embodiment, the present embodiment is described with reference to fig. 1, and the difference between the present embodiment and the apparatus for measuring torsional micro-impulse by chirped multi-beam laser heterodyne according to the first embodiment is that the vacuum window is used to converge light in the vacuum chamber 11 onto the photosensitive surface of the photodetector 9 outside the vacuum chamber 11.

In a fourth embodiment, the method for measuring torsional pendulum micro-impulse of the device for measuring torsional pendulum micro-impulse by using chirp multi-beam laser heterodyne according to the second embodiment is implemented by the following steps:

the pulse laser 1, the linear frequency modulation laser 5, the photoelectric detector 9 and the signal processing system 10 are switched to a working state, the photoelectric detector 9 converts the received optical signals into electric signals and sends the electric signals to the signal processing system 10, the signal processing system 10 obtains the swing angle theta' of the standard beam 3 according to the received continuous electric signals,

according to the following steps:

$I^{\′}=\frac{2J\mathrm{\ω}}{D}\·{\mathrm{\θ}}^{\′}=\frac{4\mathrm{\π}J}{{\mathrm{DT}}^{\′}}\·{\mathrm{\θ}}^{\′}$ (formula one),

obtaining micro impulse I ' generated by the action of laser emitted by a pulse laser 1 and a working medium target, wherein J is the moment of inertia of a torsional pendulum system, omega is a damping frequency, T ' is a damping period, D is the length of a standard beam 3, and k is 4 pi J/DT ':

i ═ k · θ' (equation two).

Fifth embodiment, the present embodiment is described with reference to fig. 2, and the difference between the present embodiment and the method for measuring torsional pendulum micro-impulse of the apparatus for measuring torsional pendulum micro-impulse based on chirped multi-beam laser heterodyne described in fourth embodiment is that the signal processing system 10 obtains the pivot angle θ' of the standard beam 3 according to the received continuous electrical signal by the following processes:

when the chirped laser light continuously emitted from the chirped laser 5 is at the incident angle theta₀When the light is obliquely incident on the planar standard mirror 7, the incident light field e (t) of the planar standard mirror 7 is:

E(t)＝E₀exp{i(ω₀t+k′t²) A (formula three) is calculated,

wherein,for the rate of change of the bandwidth of the modulation, T is the frequency modulation period, Δ F is the bandwidth of the modulation, E₀For the amplitude of the incident light field, t is time, omega₀For the incident field angle frequency, i represents an imaginary number,

if the optical path of the linear frequency modulation laser reaching the front surface of the plane standard mirror 7 is set to be l, the linear frequency modulation laser reaches the reflected light field E of the front surface of the plane standard mirror 7 at the time of t-l/c₁(t) is:

$E_1\left(t\right)={\mathrm{\α}}_1{E}_0\exp \{i\[{\mathrm{\ω}}_0(t-\frac{l}{c})+k^{\′}{(t-\frac{l}{c})}^2\]\}$ (formula four) of the reaction solution,

the light transmitted by the front surface of the plane standard mirror 7 is reflected and refracted for multiple times by the front surface and the back surface of the plane standard mirror 7 at different times, and the light field of the reflected light obtained by each reflection is as follows:

$\left\{\begin{array}{c}{E}_2\left(t\right)={\mathrm{\α}}_2{E}_0\exp \{i\[{\mathrm{\ω}}_0(t-\frac{l+2ndcos\mathrm{\θ}}{c})+k^{\′}{(t-\frac{l+2ndcos\mathrm{\θ}}{c})}^2+\frac{2{\mathrm{\ω}}_{0}ndcos\mathrm{\θ}}{c}\]\}\\ E_3\left(t\right)={\mathrm{\α}}_3{E}_0\exp \{i\[{\mathrm{\ω}}_0(t-\frac{l+4ndcos\mathrm{\θ}}{c})+k^{\′}{(t-\frac{l+4ndcos\mathrm{\θ}}{c})}^2+\frac{4{\mathrm{\ω}}_{0}ndcos\mathrm{\θ}}{c}\]\}\\ \·\\ \·\\ \·\\ E_m\left(t\right)={\mathrm{\α}}_m{E}_0\exp \{i\[{\mathrm{\ω}}_0(t-\frac{l+2(m-1)nd\cos \mathrm{\θ}}{c})+k^{\′}{(t-\frac{l+2(m-1)nd\cos \mathrm{\θ}}{c})}^2+\frac{2(m-1){\mathrm{\ω}}_{0}ndcos\mathrm{\θ}}{c}\]\}\\ \·\\ \·\\ \·\end{array}\right.$

(formula five) of the reaction solution,

wherein m is a non-negative integer α₁＝r，α_m＝ββ′r′^(2m-3)(m.gtoreq.2), r is the reflectance when light enters the planar standard mirror 7 from the surrounding medium, β is the transmittance when light enters the planar standard mirror 7 from the surrounding medium, r 'is the reflectance of the rear surface of the planar standard mirror 7, β' is the transmittance when light enters the surrounding medium from the inside of the planar standard mirror 7, d is the thickness of the planar standard mirror 7, theta is the refraction angle, n is the refraction index of the planar standard mirror 7, c is the speed of light,

the total light field E' (t) received by the photodetector 9 is:

E′(t)＝E₁(t)+E₂(t)+...+E_m(t) +. - (equation six),

the photocurrent I output by the photodetector 9 is then:

$I=\frac{\mathrm{\η}e}{hv}\frac{1}{Z}\underset{D}{\∫\∫}\frac{1}{2}\[E_1\left(t\right)+E_2\left(t\right)+...+E_m\left(t\right)+...\]{\[E_1\left(t\right)+E_2\left(t\right)+...+E_m\left(t\right)+...\]}^{*}ds$ (formula seven) of the reaction mixture,

wherein e is the electron quantity, Z is the intrinsic impedance of the surface medium of the photoelectric detector 9, η is the quantum efficiency, D is the area of the photosensitive surface of the photoelectric detector 9, h is the Planck constant, v is the laser frequency, the number indicates the complex conjugate,

obtaining the intermediate frequency current I according to the formula_IFComprises the following steps:

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

substituting the formula four and the formula five into the formula eight, and arranging to obtain:

$I_{IF}=\frac{\mathrm{\η}e}{hv}\frac{\mathrm{\π}}{Z}{E}_0^2\underset{p=0}{\overset{m-1}{\Σ}}\underset{j=0}{\overset{m-p}{\Σ}}{\mathrm{\α}}_{j+p}{\mathrm{\α}}_{j}cos(\frac{4{\mathrm{pk}}^{\′}ndcos\mathrm{\θ}}{c}t-\frac{4{\mathrm{pk}}^{\′}ndcos\mathrm{\θ}(l+ndcos\mathrm{\θ})}{c^2})$ (the ninth formula),

fourier transform is carried out on the frequency difference of the intermediate frequency term in the formula nine to obtain the frequency f of the interference signal_pComprises the following steps:

$f_p=\frac{2{\mathrm{pk}}^{\′}ndcos\mathrm{\θ}}{\mathrm{\π}c}=K_{p}cos\mathrm{\θ}$ (formula ten) of the above-mentioned formula,

thereby obtaining a value of angle of refraction θ, where K_pIs a proportionality coefficient, and $K_p=\frac{2pknd}{\mathrm{\π}c},$

the refraction angle theta and the incidence angle theta can be known according to the law of refraction₀The relationship of (1) is:

θ₀arcsin (nsin θ) (formula eleven),

the incident angle theta can be known according to the geometrical relation of the incident light path₀The relationship with the pivot angle θ' of the standard beam 3 is:

${\mathrm{\θ}}^{\′}=\frac{{\mathrm{\θ}}_0}{2}=\frac{arcsin\left(nsin\mathrm{\θ}\right)}{2}$ (formula twelve),

and substituting the value of the swing angle theta 'of the standard beam 3 obtained in the formula twelve into the formula two to obtain the micro impulse I' generated by the action of the laser emitted by the pulse laser 1 and the working medium target 2.

In the embodiment, the moment of inertia of the system is calibrated by measuring the change of the system period before and after the standard beam 3 is added, and the proportionality coefficient K can be obtained according to the calibration result_pThe value of (c).

In the device for measuring torsional pendulum micro-impulse by linear frequency modulation multi-beam laser heterodyne shown in fig. 1, under the working condition of 10Pa, MATLAB is used for analog measurement of the micro-impulse generated by interaction of laser and working medium, wherein the working medium is PVC (polyvinyl chloride) + 2% C, the thickness is 180 μm, the laser initial current is 5A, the pulse width is 50ms, and the possibility of the linear frequency modulation multi-beam laser measurement method is verified, and the heterodyne multi-beam laser measurement method is characterized in that the length D of a heterodyne beam is 15cm, the refractive index n of a planar standard mirror is 1.493983, and the thickness is 3 cm; the wavelength of the linear frequency modulation laser is 1.55 μm, the scanning period T is 1ms, and the modulation bandwidth delta F is 5 GHz.

The simulation obtains different incidence angles theta₀In this case, the fourier transform spectrum corresponding to the minute angle of the chirped multi-beam laser heterodyne measurement is shown in fig. 3, and it can be seen from fig. 3 that θ is dependent on the incident angle₀The relative position of the frequency spectrum shifts towards the low frequency direction, i.e. with the angle of incidence theta₀Is increased, the frequency is decreased. This is because, at the proportionality coefficient K_pWithout change, due to the frequency f of the interference signal_pAngle of incidence theta₀Has a relationship of f_p＝K_pcosθ＝K_pcos[arcsin(sinθ₀/n)]Angle of incidence theta₀And the frequency f of the interference signal_pIs in inverse proportion to the incident angle theta₀As the angle increases, cos θ decreases, and thus, with angle of incidence θ₀The relative position of the frequency spectrum shifts towards the low frequency direction.

By using the inventionThe measuring method continuously measures eight groups of data to obtain different incidence angles theta₀The simulation measurement result of the micro impulse of the sample to be measured under the condition is shown in the following table:

the average measured value of the micro impulse is calculated by using the simulation experiment data in the table, the maximum relative error of the finally obtained measured value is less than 0.48%, meanwhile, under the condition of small angle approximation, the system error and the reading error brought by the environment can be ignored in the simulation, and the error in the simulation experiment mainly comes from the precision error after the fast Fourier change and the rounding error in the calculation process.

Claims (1)

1. A torsional pendulum micro impulse measuring method of a linear frequency modulation multi-beam laser heterodyne torsional pendulum micro impulse measuring device relates to a device comprising a linear frequency modulation laser (5), a first plane reflector (6), a second plane reflector (4), a plane standard mirror (7), a standard beam (3), a vacuum chamber (11), a pulse laser (1), a working medium target (2), a converging lens (8), a photoelectric detector (9) and a signal processing system (10),

the linear frequency modulation laser (5), the first plane reflector (6), the second plane reflector (4), the plane standard mirror (7), the standard beam (3), the pulse laser (1), the working medium target (2) and the convergent lens (8) are all arranged in a vacuum chamber (11),

a rotating shaft is fixed at the center of the standard beam (3),

the working medium target (2) is pasted on the upper surface of the standard beam (3), the second plane reflector (4) is pasted on the lower surface of the standard beam (3), the working medium target (2) and the second plane reflector (4) are both positioned at the same end of the standard beam (3),

the laser emitted by the pulse laser acts on the working medium target (2) to generate plasma jet, the standard beam (3) rotates under the action of back spray, the linear frequency modulation laser (5) continuously emits linear frequency modulation laser while the standard beam (3) rotates, the linear frequency modulation laser is reflected by the first plane reflecting mirror (6) and the second plane reflecting mirror (4) and then enters the plane standard mirror (7), the front surface and the rear surface of the plane standard mirror (7) reflect the linear frequency modulation laser and converge the linear frequency modulation laser on the photosensitive surface of the photoelectric detector (9) through the converging lens (8), and the electric signal output end of the photoelectric detector (9) is connected with the electric signal input end of the signal processing system (10);

the signal processing system (10) comprises a filter (10-1), a preamplifier (10-2), an A/D converter (10-3) and a DSP (10-4), wherein an electric signal input end of the filter (10-1) is connected with an electric signal output end of a photoelectric detector (9) as an electric signal input end of the signal processing system (10), a filtering signal output end of the filter (10-1) is connected with a filtering signal input end of the preamplifier (10-2), an amplifying signal output end of the preamplifier (10-2) is connected with an analog signal input end of the A/D converter (10-3), and a digital signal output end of the A/D converter (10-3) is connected with a digital signal input end of the DSP (10-4);

the vacuum chamber (11) is provided with a vacuum window for converging the light in the vacuum chamber (11) to the vacuum chamber

(11) The external photoelectric detector (9) is arranged on the photosensitive surface;

the torsional pendulum micro-impulse measuring method of the linear frequency modulation multi-beam laser heterodyne torsional pendulum micro-impulse measuring device is realized by the following processes:

the pulse laser (1), the linear frequency modulation laser (5), the photoelectric detector (9) and the signal processing system (10) are switched to a working state, the photoelectric detector (9) converts received optical signals into electric signals and sends the electric signals to the signal processing system (10), the signal processing system (10) obtains the swing angle theta' of the standard beam (3) according to the received continuous electric signals,

according to the following steps:

$I^{\′}=\frac{2J\mathrm{\ω}}{D}\·{\mathrm{\θ}}^{\′}=\frac{4\mathrm{\π}J}{{\mathrm{DT}}^{\′}}\·{\mathrm{\θ}}^{\′}$ (formula one),

obtaining micro impulse I ' generated by the action of laser emitted by a pulse laser (1) and a working medium target (2), wherein J is the rotational inertia of a torsional pendulum system, omega is damping frequency, T ' is damping period, D is the length of a standard beam (3), and k is 4 pi J/DT ':

i '═ k · θ' (equation two);

the method is characterized in that the signal processing system (10) obtains the swing angle theta' of the standard beam (3) according to the received continuous electric signals by the following steps:

when the linear frequency modulation laser (5) continuously emits linear frequency modulation laser at an incidence angle theta₀When the light is obliquely incident to the plane standard mirror (7), the incident light field E (t) of the plane standard mirror (7) is as follows:

E(t)＝E₀exp{i(ω₀t+k′t²) A (formula three) is calculated,

wherein,for the rate of change of the bandwidth of the modulation, T is the period of the modulation, △ F isBandwidth of modulation, E₀For the amplitude of the incident light field, t is time, omega₀For the incident field angle frequency, i represents an imaginary number,

setting the optical path of the linear frequency modulation laser reaching the front surface of the plane standard mirror (7) as l, and then the linear frequency modulation laser reaches the reflected light field E of the front surface of the plane standard mirror (7) at the time of t-l/c₁(t) is:

$E_1\left(t\right)={\mathrm{\α}}_1{E}_0\exp \{i\[{\mathrm{\ω}}_0(t-\frac{l}{c})+k^{\′}{\left(t-\frac{l}{c}\right)}^2\]\}$ (formula four) of the reaction solution,

the light transmitted by the front surface of the plane standard mirror (7) is reflected and refracted for multiple times by the front surface and the back surface of the plane standard mirror (7) at different times, and the light field of the reflected light obtained by each reflection is as follows:

$\left\{\begin{array}{c}{E}_2\left(t\right)={\mathrm{\α}}_2{E}_0\exp \{i\[{\mathrm{\ω}}_0(t-\frac{l+2ndcos\mathrm{\θ}}{c})+k^{\′}{\left(t-\frac{l+2ndcos\mathrm{\θ}}{c}\right)}^2+\frac{2{\mathrm{\ω}}_{0}ndcos\mathrm{\θ}}{c}\]\}\\ E_3\left(t\right)={\mathrm{\α}}_3{E}_0\exp \{i\[{\mathrm{\ω}}_0(t-\frac{l+4ndcos\mathrm{\θ}}{c})+k^{\′}{\left(t-\frac{l+2ndcos\mathrm{\θ}}{c}\right)}^2+\frac{4{\mathrm{\ω}}_{0}ndcos\mathrm{\θ}}{c}\]\}\\ \·\\ \·\\ \·\\ E_m\left(t\right)={\mathrm{\α}}_m{E}_0\exp \{i\[{\mathrm{\ω}}_0(t-\frac{l+2(m-1)nd\cos \mathrm{\θ}}{c})+k^{\′}{(t-\frac{l+2(m-1)nd\cos \mathrm{\θ}}{c})}^2+\frac{2(m-1){\mathrm{\ω}}_{0}ndcos\mathrm{\θ}}{c}\]\}\\ \·\\ \·\\ \·\end{array}\right.$

(formula five) of the reaction solution,

wherein m is a non-negative integer α₁＝r，α_m＝ββ′r′^(2m-3)(m is not less than 2), r is the reflectance when light enters the planar standard mirror (7) from the surrounding medium, β is the transmittance when light enters the planar standard mirror (7) from the surrounding medium, r 'is the reflectance of the rear surface of the planar standard mirror (7), β' is the transmittance when light enters the surrounding medium from the inside of the planar standard mirror (7), d is the thickness of the planar standard mirror (7), theta is the refraction angle, n is the refraction index of the planar standard mirror (7), c is the speed of light,

the total light field E' (t) received by the photodetector (9) is:

E′(t)＝E₁(t)+E₂(t)+...+E_m(t) +. - (equation six),

the photocurrent I output by the photodetector (9) is then:

$I=\frac{\mathrm{\η}e}{hv}\frac{1}{Z}\underset{D}{\∫\∫}\frac{1}{2}\[E_1\left(t\right)+E_2\left(t\right)+...+E_m\left(t\right)+...\]{\[E_1\left(t\right)+E_2\left(t\right)+...+E_m\left(t\right)+...\]}^{*}ds$ (formula seven) of the reaction mixture,

wherein e is the electron electric quantity, Z is the intrinsic impedance of the surface medium of the photoelectric detector (9), eta is the quantum efficiency, D is the area of the photosensitive surface of the photoelectric detector (9), h is the Planck constant, v is the laser frequency, and the sign indicates complex conjugate,

obtaining the intermediate frequency current I according to the formula_IFComprises the following steps:

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

substituting the formula four and the formula five into the formula eight, and arranging to obtain:

$I_{IF}=\frac{\mathrm{\η}e}{hv}\frac{\mathrm{\π}}{Z}{E}_0^2\underset{p=0}{\overset{m-1}{\mathrm{\Σ}}}\underset{j=0}{\overset{m-p}{\mathrm{\Σ}}}{\mathrm{\α}}_{j+p}{\mathrm{\α}}_j\cos (\frac{4{\mathrm{pk}}^{\′}nd\cos \mathrm{\θ}}{c}t-\frac{4{\mathrm{pk}}^{\′}nd\cos \mathrm{\θ}(l+nd\cos \mathrm{\θ})}{c^2})$ (the ninth formula),

fourier transform is carried out on the frequency difference of the intermediate frequency term in the formula nine to obtain the frequency f of the interference signal_pComprises the following steps:

$f_p=\frac{2{\mathrm{pk}}^{\′}ndcos\mathrm{\θ}}{\mathrm{\π}c}=K_{p}cos\mathrm{\θ}$ (formula ten) of the above-mentioned formula,

thereby obtaining a value of angle of refraction θ, where K_pIs a proportionality coefficient, and

the refraction angle theta and the incidence angle theta can be known according to the law of refraction₀The relationship of (1) is:

θ₀arcsin (nsin θ) (formula eleven),

the incident angle theta can be known according to the geometrical relation of the incident light path₀The relationship of the swing angle theta' with the standard beam (3) is as follows:

${\mathrm{\θ}}^{\′}=\frac{{\mathrm{\θ}}_0}{2}=\frac{arcsin\left(nsin\mathrm{\θ}\right)}{2}$ (formula twelve),

and substituting the value of the swing angle theta 'of the standard beam (3) obtained in the formula twelve into the formula two to obtain the micro impulse I' generated by the action of the laser emitted by the pulse laser (1) and the working medium target (2).