CN100449356C - Triangular wave phase modulation method of resonant cavity optical fiber gyroscope and apparatus thereof - Google Patents

Abstract

This invention discloses one triangle wave phase modulation method and device of resonance chamber fiber top, wherein, the laser is connected to first couple device, first phase modulator, second couple device, third couple device, fourth couple device, second phase modulation device and first couple; the first phase modulation and first triangle wave signal generator are connected; the second phase modulation and second triangle signal generator are connected; the second couple device and first photoelectricity, first high speed digital signal processor and laser are connected; the fourth couple device is connected to fourth couple device, second photoelectricity detector, second high speed digital processor; the third couple device is connected to the fiber ring.

Description

The triangular wave phase modulation method of resonant cavity optical fiber gyroscope and device thereof

Technical field

The present invention relates to a kind of triangular wave phase modulation method and device thereof of resonant cavity optical fiber gyroscope.

Background technology

(Resonator Fiber Optic Gyro is to utilize optics Sagnac effect to realize a kind of high-precision inertia sensing device that detects rotating R-FOG) to resonant cavity optical fiber gyroscope.The noise that backscattering causes can bring bigger error to gyrosystem, and the key of inhibition backscattering is to suppress the carrier component of signal.The signal detection technique that generally adopts in optical fibre gyro system has sine wave phase modulation and sawtooth wave phase modulation (PM) at present.The sine wave phase modulation is unfavorable for the inhibition to the signal carrier component.Though the sawtooth wave phase modulation (PM) helps to suppress the signal carrier component, can introduce 2 π reset height out of true and the reset pulse that produces, thereby influence system accuracy.

The slope in gyro demodulation curve linear district can influence the precision of gyro, and thinks that in theory demodulation curve linear district slope is big more, and the precision of gyro is high more.The phase-modulation index of triangular wave phase modulation (PM) and modulating frequency can exert an influence to the slope of linear zone, and therefore, phase-modulation index and the modulating frequency of reasonably choosing the triangular wave phase modulation (PM) are extremely important for the precision that improves gyro.

Summary of the invention

The purpose of this invention is to provide and a kind ofly both can effectively suppress backscattering, can avoid the phase modulation technique of reset pulse again, and propose the choosing method of best phase-modulation index and optimum modulation frequency.

The triangular wave phase modulation method of resonant cavity optical fiber gyroscope comprises:

1) the laser instrument output light field is analyzed, by Fourier transform the laser of triangular wave phase modulation (PM) is expanded into each harmonics frequency component sum, fourier coefficient delivery with carrier frequency component, obtain the carrier component normalization amplitude of laser after the triangular wave phase modulation (PM) and the relation of phase-modulation index, obtaining carrier component normalization amplitude by Computer Simulation is 0 o'clock pairing phase-modulation index, obtain when phase-modulation index is π rad according to theoretical derivation result and simulation result, carrier component is 0, thereby determines that best phase-modulation index is π rad.;

2) utilization light field superposition principle obtains the light field transition function of fiber optic loop, by Fourier transform the laser of triangular wave phase modulation (PM) is expanded into each harmonics frequency component sum, each harmonics frequency component substitution light field transition function is obtained each harmonics frequency component through the light field expression formula after the fiber optic loop, after all these expression formula additions, obtain the output light field E of fiber optic loop _Out(t).Output light field got grip the back altogether and multiply each other with former expression formula, and get time average, obtain output intensity expression formula＜E _Out(t) E _Out ^*(t) 〉, output intensity be multiply by loss and the photoelectric conversion factors that coupling mechanism causes, can obtain the expression formula of the output voltage signal of photodetector $V_{\mathrm{PD}-\mathrm{out}}=\frac{1}{2}(1-{\mathrm{\&alpha;}}_{C2})N<E_{\mathrm{out}}\left(t\right)E_{\mathrm{out}}^{*}\left(t\right)>,$ Owing to do not have statistic in the expression formula, time-averaging operation is removed, obtain photodetector output voltage signal expression formula $V_{\mathrm{PD}-\mathrm{out}}=\frac{1}{2}(1-{\mathrm{\&alpha;}}_{C2})N{E}_{\mathrm{out}}\left(t\right)E_{\mathrm{out}}^{*}\left(t\right).$ With V _PD-outMake related operation with square-wave signal S (t), obtain restituted signal V _dPass through V _dTo resonance frequency deviation Δ f in Δ f=0 place's differentiate, and take absolute value, can obtain the demodulation rate of curve at tuning-points place and the relation of modulating frequency, by Computer Simulation, find that there is an optimum value in modulating frequency, make the demodulation rate of curve maximum at tuning-points place, this frequency is exactly an optimum modulation frequency.

3) by feedback, the square wave that triangular signal and high-low level is respectively 1V and-1V is made related operation, with related operation result and V _π/ 2 relatively, and the result who obtains when related operation is greater than V _π/ 2 o'clock, the triangular wave amplitude is reduced; The result who obtains when related operation equals V _π/ 2 o'clock, the triangular wave amplitude was constant; The result who obtains when related operation is less than V _π/ 2 o'clock, the triangular wave amplitude is increased.To export the triangular wave amplitude stabilization in half-wave voltage by the feedback algorithm of this dynamic adjustment.

The triangular wave phasing device of resonant cavity optical fiber gyroscope: the laser instrument and first coupling mechanism, first phase-modulator, second coupling mechanism, the 3rd coupling mechanism, the 4th coupling mechanism, second phase-modulator, first coupling mechanism joins, first phase-modulator and first triangular signal generator based the joining, second phase-modulator and second triangular signal generator based the joining, second coupling mechanism and first photodetector, first high speed digital signal processor, laser instrument joins, the 4th coupling mechanism and second photodetector, second high speed digital signal processor joins, and the 3rd coupling mechanism and fiber optic loop are joined.

Described phase-modulator internal module annexation is: A/D converter and high speed digital signal processor, D/A, amplifying circuit, touch/number converter joins.

The beneficial effect that the present invention has:

1) the present invention helps suppressing the noise that backscattering causes;

2) the present invention's 2 π reset pulses of having avoided the sawtooth wave phase modulation (PM) to bring influence that system accuracy is caused;

3) the present invention helps the amplitude of stable output triangular wave, helps overcoming environmental factor such as temperature to the influence that the triangular wave amplitude produces, and helps overcoming the influence that the autoexcitation vibration causes triangular wave.

Description of drawings

Fig. 1 is the triangular wave phasing device structural representation of resonant cavity optical fiber gyroscope;

Fig. 2 is a triangular signal generator based circuit block diagram of the present invention;

Fig. 3 is the amplifying circuit block diagram of triangular signal generator based circuit;

Fig. 4 is the waveform of triangle wave voltage signal;

Fig. 5 (a) is when adopting the triangular wave phase modulation (PM), the relation curve of the bias that the recruitment of carrier component normalization amplitude and phase-modulation index depart from optimum value;

Fig. 5 (b) is when adopting the sine wave phase modulation, the relation curve of the bias that the recruitment of carrier component normalization amplitude and phase-modulation index depart from optimum value;

Fig. 6 is the process flow diagram of triangular wave amplitude feedback algorithm of the present invention;

Fig. 7 is the demodulation curve that obtains under the different modulating frequency;

Fig. 8 is the relation between tuning-points place slope k and the modulating frequency F.

Embodiment

As shown in Figure 1, in the triangular wave phasing device of resonant cavity optical fiber gyroscope, the laser instrument 1 and first coupling mechanism 2, first phase-modulator 3, second coupling mechanism 7, the 3rd coupling mechanism 13, the 4th coupling mechanism 8, second phase-modulator 4, first coupling mechanism 2 joins, first phase-modulator 3 and first triangular signal generator based 5 joins, second phase-modulator 4 and second triangular signal generator based 6 joins, second coupling mechanism 7 and first photodetector 9, first high speed digital signal processor 11, laser instrument 1 joins, the 4th coupling mechanism 8 and second photodetector 10, second high speed digital signal processor 12 joins, and the 3rd coupling mechanism 13 joins with fiber optic loop 14.

The laser that is sent by laser instrument 1 is divided into two bundles through 50% the first coupling mechanisms 2, this two bundles laser carries out shift frequency through first phase-modulator 3 and second phase-modulator 4 respectively, be coupled into fiber optic loop 14 by the 3rd coupling mechanism 13 again, form (Counter Clockwise counterclockwise, CCW) and clockwise (Clockwise, CW) two resonance light beams are coupled to second photodetector 10 and first photodetector 9 by the 4th coupling mechanism 8 and second coupling mechanism 7 respectively.The control signal of first phase-modulator 3 and second phase-modulator 4 is triangular waves.The signal that comes out from first photodetector 9 extracts the resonance frequency deviation through first high speed digital signal processor 11, in order to control laser instrument output light frequency, thereby makes the CCW light path be locked in tuning-points; Export demodulation values from the signal that second photodetector 10 comes out through second high speed digital signal processor 12, this signal promptly reflects angular velocity of rotation.

As shown in Figure 2, triangular signal generator based annexation is: A/D converter and high speed digital signal processor, D/A, amplifying circuit, touch/number converter joins.

The triangular wave phase modulation method of resonant cavity optical fiber gyroscope comprises:

1) the laser instrument output light field is analyzed, by Fourier transform the laser of triangular wave phase modulation (PM) is expanded into each harmonics frequency component sum, fourier coefficient delivery with carrier frequency component, obtain the carrier component normalization amplitude of laser after the triangular wave phase modulation (PM) and the relation of phase-modulation index, obtaining carrier component normalization amplitude by Computer Simulation is 0 o'clock pairing phase-modulation index, obtain when phase-modulation index is π rad according to theoretical derivation result and simulation result, carrier component is 0, thereby determines that best phase-modulation index is π rad.;

2) utilization light field superposition principle obtains the light field transition function of fiber optic loop, by Fourier transform the laser of triangular wave phase modulation (PM) is expanded into each harmonics frequency component sum, each harmonics frequency component substitution light field transition function is obtained each harmonics frequency component through the light field expression formula after the fiber optic loop, after all these expression formula additions, obtain the output light field E of fiber optic loop _Out(t).Output light field got grip the back altogether and multiply each other with former expression formula, and get time average, obtain output intensity expression formula＜E _Out(t) E _Out ^*(t) 〉, output intensity be multiply by loss and the photoelectric conversion factors that coupling mechanism causes, can obtain the expression formula of the output voltage signal of photodetector $V_{\mathrm{PD}-\mathrm{out}}=\frac{1}{2}(1-{\mathrm{\&alpha;}}_{C2})N<E_{\mathrm{out}}\left(t\right)E_{\mathrm{out}}^{*}\left(t\right)>,$ Owing to do not have statistic in the expression formula, time-averaging operation is removed, obtain photodetector output voltage signal expression formula $V_{\mathrm{PD}-\mathrm{out}}=\frac{1}{2}(1-{\mathrm{\&alpha;}}_{C2})N{E}_{\mathrm{out}}\left(t\right)E_{\mathrm{out}}^{*}\left(t\right).$ With V _PD-outMake related operation with square-wave signal S (t), obtain restituted signal V _dPass through V _dTo resonance frequency deviation Δ f in Δ f=0 place's differentiate, and take absolute value, can obtain the demodulation rate of curve at tuning-points place and the relation of modulating frequency, by Computer Simulation, find that there is an optimum value in modulating frequency, make the demodulation rate of curve maximum at tuning-points place, this frequency is exactly an optimum modulation frequency.

3) by feedback, the square wave that triangular signal and high-low level is respectively 1V and-1V is made related operation, with related operation result and V _π/ 2 relatively, and the result who obtains when related operation is greater than V _π/ 2 o'clock, the triangular wave amplitude is reduced; The result who obtains when related operation equals V _π/ 2 o'clock, the triangular wave amplitude was constant; The result who obtains when related operation is less than V _π/ 2 o'clock, the triangular wave amplitude is increased.To export the triangular wave amplitude stabilization in half-wave voltage by the feedback algorithm of this dynamic adjustment.

Below by theoretical derivation and emulation triangular wave phase modulation method is described further.

1) best phase-modulation index determines

At first provide the laser light field when not passing through the triangular wave phase modulation (PM), that is, and the output light field of laser instrument:

In the formula, E ₀Be laser amplitude, f _cBe the laser center frequency,

Be first phase.If with the phase place of this road laser of triangular modulation, then entering fiber optic loop laser before can be expressed as the laser of CW light path before entering fiber optic loop:

In the formula, α _C1And α _C3Be respectively the insertion loss factor of first coupling mechanism 2 and the 4th coupling mechanism 8, α _PM2Be the insertion loss factor of second phase-modulator 4, v (t) is the triangle wave voltage signal that is used to drive second phase-modulator 4, V ₁Be the amplitude of triangle wave voltage signal, K is and the relevant parameter of second phase-modulator, 4 structures.Can obtain phase-modulation index M _p=KV ₁Fig. 2 has provided the oscillogram of the triangle wave voltage signal v (t) that is used to drive phase-modulator, and this triangular waveform can be expressed as:

$v\left(t\right)=\begin{array}{cc}& \end{array}\left\{\begin{array}{c}4F(t-\frac{q}{F}-\frac{1}{4F})[\frac{q}{F}<t\&le;(q+\frac{1}{2})\frac{1}{F}]\\ -4F(t-\frac{q}{F}-\frac{3}{4F})[(q+\frac{1}{2})\frac{1}{F}<t\&le;(q+1)\frac{1}{F}]\end{array}---\left(3\right)\right.$

In the formula, F is a modulating frequency, and q is an integer.Utilize fourier coefficient that (2) formula is launched, can be expressed as:

In the formula, A _nCan be expressed as:

$A_n=\left\{\begin{array}{cc}\frac{1}{2}\exp \left(3{\mathrm{jM}}_p\right)& (n=-\frac{2M_p}{\mathrm{\&pi;}})\\ \frac{1}{2}\exp (-{\mathrm{jM}}_p)& (n=\frac{{2M}_p}{\mathrm{\&pi;}})\\ \frac{{2M}_{p}j[\exp (-{\mathrm{jM}}_p)-\exp ({\mathrm{jM}}_p-\mathrm{n\&pi;j})]}{4{M_p}^2-{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="C20071006679500141.png,C20071006679500161.png"\; state="\{\{state\}\}">n</figure-callout>}}^2{\mathrm{\&pi;}}^2}& \left(\mathrm{otherwise}\right)\end{array}\right.---\left(5\right)$

According to (5) formula, can obtain through after the triangular wave phase modulation (PM) carrier component normalization amplitude | A ₀| with phase-modulation index M _pRelation:

$\left|A_0\right|=\left|\frac{\sin \left(M_p\right)}{M_p}\right|---\left(6\right)$

In like manner, can obtain through after the sine wave phase modulation carrier component normalization amplitude | A ' ₀| with phase-modulation index M ' _pRelation:

|A′ ₀|＝|J ₀(M′ _p)| (7)

In the formula, J ₀(x) be the Bessel function.

For the triangular wave phase modulation (PM), work as M _p=π _RadThe time, | A ₀| be 0; For the sine wave phase modulation, as M ' _pDuring=2.405rad, | A ' ₀| be 0.Therefore, M _p=π rad and M ' _p=2.405rad is respectively the optimum value of the phase-modulation index of triangular wave phase modulation (PM) and sine wave phase modulation.But can not make phase-modulation index accurately satisfy optimum value in the real system.Following formula has provided by phase-modulation index and has departed from the recruitment of the carrier component normalization amplitude that optimum value causes and the relation of the bias that phase-modulation index departs from optimum value:

$\mathrm{\&Delta;}\left|A_0\right|=\left|\frac{\sin (\mathrm{\&pi;}+\mathrm{\&Delta;}{M}_p)}{\mathrm{\&pi;}+\mathrm{\&Delta;}{M}_p}\right|---\left(8\right)$

Δ|A′ ₀|＝|J ₀(2.405+ΔM′ _p)| (9)

(8) formula is the result who is obtained by the triangular wave phase modulation (PM), and (9) formula is the result who is obtained by the sine wave phase modulation.In the formula, Δ | A ₀| and Δ | A ' ₀| be the recruitment that departs from the carrier component normalization amplitude that optimum value causes by phase-modulation index, Δ M _pWith Δ M ' _pBe the bias that phase-modulation index departs from optimum value.Fig. 5 has provided by phase-modulation index and has departed from the recruitment of the carrier component normalization amplitude that optimum value causes and the relation curve of the bias that phase-modulation index departs from optimum value, Fig. 5 (a) is the result of triangular wave phase modulation (PM), and Fig. 5 (b) is the result of sine wave phase modulation.Can find, when phase-modulation index departs from optimum value, the increment of the carrier component when adopting the triangular wave phase modulation (PM) increases soon when not adopting the sine wave phase modulation, promptly, the triangular wave phase modulation (PM) is subjected to the influence of phase modulation (PM) coefficient littler than the sine wave phase modulation, therefore, the triangular wave phase modulation (PM) more helps overcoming backscattering.

In addition, because there is not reset issues in the triangular wave phase modulation (PM), therefore, the influence that the reset pulse that can avoid the sawtooth wave phase modulation (PM) to bring causes system accuracy.

2) stablize the method for triangular wave amplitude

According to above analysis, the best phase-modulation index of triangular wave phase modulation (PM) is π rad.Fig. 2 has provided the output circuit of triangular signal.Triangular signal after process analog-digital chip DA is converted into simulating signal, amplifies back input phase modulator through amplifying circuit by high speed digital signal processor DSP output again.In order accurately to control the amplitude of triangular wave, make the half-wave voltage V of triangular wave amplitude stabilization at phase-modulator _π(V _πBe meant the voltage when the change amount that causes phase place is π rad), the amplitude of triangular wave is fed back monitoring, that is, the triangular signal of exporting is fed back to DSP by analog to digital converter AD, thereby the amplitude of triangular wave is dynamically adjusted.DSP realizes as related operation by triangular signal and square-wave signal the dynamic adjustment of triangular wave amplitude.The mathematic(al) representation of the used square-wave signal of related operation is:

$S\left(t\right)=\left\{\begin{array}{cc}1& [\frac{q}{F}+\frac{1}{4F}<t\&le;(q+\frac{1}{2})\frac{1}{F}+\frac{1}{4F}]\\ -1& [(q+\frac{1}{2})\frac{1}{F}+\frac{1}{4F}<t\&le;(q+1)\frac{1}{F}+\frac{1}{4F}]\end{array}\right.---\left(10\right)$

The mathematic(al) representation that triangular signal and square-wave signal are made related operation is:

$V_{\mathrm{tri}}=F{\&Integral;}_{1/\left(4F\right)}^{5/\left(4F\right)}{V}_{1}v\left(t\right)S_1\left(t\right)\mathrm{dt}$

$=F[{\&Integral;}_{1/\left(4F\right)}^{1/\left(2F\right)}4F{V}_1(t-\frac{1}{4F})\mathrm{dt}+{\&Integral;}_{1/\left(2F\right)}^{3/\left(4F\right)}-4F{V}_1(t-\frac{3}{4F})\mathrm{dt}$

$-{\&Integral;}_{3/\left(4F\right)}^{1/F}-4F{V}_1(t-\frac{3}{4F})\mathrm{dt}-{\&Integral;}_{1/\mathrm{<figure-callout\; id="5"\; label="F"\; filenames="C20071006679500141.png"\; state="\{\{state\}\}">F</figure-callout>}}^{5/\left(4F\right)}4F{V}_1(t-\frac{5}{4F})\mathrm{dt}]$

$=V_1/2---\left(11\right)$

Can find according to (11) formula:

(1) as triangular wave amplitude V ₁＞V _πThe time, make the V as a result that obtains behind the related operation _Tri＞V _π/ 2;

(2) as triangular wave amplitude V ₁=V _πThe time, make the V as a result that obtains behind the related operation _Tri=V _π/ 2;

(3) as triangular wave amplitude V ₁＜V _πThe time, make the V as a result that obtains behind the related operation _Tri＜V _π/ 2;

Therefore, can determine algorithm according to this characteristic to triangular wave amplitude FEEDBACK CONTROL.Fig. 6 has provided the process flow diagram of triangular wave amplitude feedback algorithm, among the figure, and Δ V ₁Adjustment amount for the triangular wave amplitude.

Because phase-modulator is a capacitive load, and operational amplification circuit connects capacitive load and can produce self-sustained oscillation, that is, the triangular signal of output can the overlapped high-frequency signal.Usually adopted in the past and reduced amplifying circuit depth of feedback (this method can reduce the stability of amplifying circuit etc.), perhaps feedback network adds electric capacity compensation (this method need be determined the value of electric capacity by the calculating of complexity, implements to bother) and carries out weakening.Fig. 3 has provided amplifying circuit of the present invention, and wherein, 15,16,17,18 is resistance, and 19 is amplifier, and 20,21,22,23 is filter capacitor.The characteristics of sort circuit are on the basis of positive amplifying circuit, have been connected in series a resistance 18 in output, like this, resistance 18 just with phase-modulator equivalent electric capacity formed a RC low-pass filter, thereby with the self-sustained oscillation target signal filter of high frequency.The characteristics of this method are to implement very simply, and can change resistance in real time according to actual effect, make the output of triangular wave reach best effect.

3) choosing method of optimum modulation frequency

Below by theoretical derivation and emulation choosing of optimum modulation frequency analyzed.Utilize the light field superposition principle, the light field of fiber optic loop delivery outlet can be expressed as:

$\&times;\underset{n=-\&infin;}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{A}_n\exp \left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="C20071006679500141.png,C20071006679500161.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}{f}_{n}t\right)h_n\exp \left(j{\mathrm{\&phi;}}_n\right)---\left(12\right)$

In the formula, f _n=f _c+ nF, other parameter is as follows::

$h_n=(1-{\mathrm{\&alpha;}}_{C4})\sqrt{1-\mathrm{\&rho;}\&CenterDot;\frac{{(1-Q)}^2}{{(1-Q)}^2+4Q{\sin }^2[\mathrm{\&pi;}(\mathrm{\&Delta;f}+\mathrm{nF})/\mathrm{FSR}]}}---\left(12a\right)$

$\mathrm{\&rho;}=1-\frac{{(T-\mathrm{TQ}-R)}^2}{(1-{\mathrm{\&alpha;}}_{C4}){(1-Q)}^2}---\left(12b\right)$

${\mathrm{\&phi;}}_n=\arctan \left\{\frac{R\sin [2\mathrm{\&pi;}(\mathrm{\&Delta;f}+\mathrm{nF})/\mathrm{FSR}]}{T+(\mathrm{TQ}+R)Q-(2\mathrm{TQ}+R)\cos [2\mathrm{\&pi;}(\mathrm{\&Delta;f}+\mathrm{nF})/\mathrm{FSR}]}\right\}---\left(12c\right)$

$T=\sqrt{1-k_C}\sqrt{1-{\mathrm{\&alpha;}}_{C4}},$ $R=k_C(1-{\mathrm{\&alpha;}}_{C4})\sqrt{1-{\mathrm{\&alpha;}}_L},$ $Q=\sqrt{1-{\mathrm{\&alpha;}}_L}\sqrt{1-k_C}\sqrt{1-{\mathrm{\&alpha;}}_{C4}}---\left(12d\right)$

In the formula, k _CIt is the coupling coefficient of the 3rd coupling mechanism 13; α _C4It is the insertion loss factor of the 3rd coupling mechanism 13; α _LFor light by the loss factor behind the fiber optic loop transmission primaries; Δ f=f _c-f _R, f _RResonance frequency for fiber optic loop; FSR is free spectrum width, and FSR=c/ (n _rL), L is the fiber lengths of fiber optic loop, n _rBe optical fibre refractivity, c is the light velocity in the vacuum; Formula (12a) and (12c) represent the amplitude of fiber optic loop transition function and bit position mutually respectively; Formula (12b) is the resonance degree of depth of fiber optic loop.

The output signal of first photodetector 9 can be expressed as:

$V_{\mathrm{PD}-\mathrm{out}}=\frac{1}{2}(1-{\mathrm{\&alpha;}}_{C2})N<E_{\mathrm{out}}\left(t\right)E_{\mathrm{out}}^{*}\left(t\right)>$

$=\frac{1}{2}(1-{\mathrm{\&alpha;}}_{C2})N{E}_{\mathrm{out}}\left(t\right)E_{\mathrm{out}}^{*}\left(t\right)$

$=P\underset{n=-\&infin;}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\underset{n^{\&prime;}=-\&infin;}{\overset{\&infin;}{\mathrm{\&Sigma;}}}{A}_n\left(M_p\right)A_{n^{\&prime;}}^{*}\left(M_p\right)\exp \left[\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="C20071006679500141.png,C20071006679500161.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}(n-n^{\&prime;})\mathrm{Ft}\right]h_n{h}_{n^{\&prime;}}\exp \left[j({\mathrm{\&phi;}}_n-{\mathrm{\&phi;}}_{n^{\&prime;}})\right]---\left(13\right)$

In the formula, angle brackets express time average alpha _C2Be the insertion loss factor of second coupling mechanism 7, N is the photoelectric conversion factors of first photodetector 9, and parameter P can be expressed as:

$P=\frac{1}{8}(1-{\mathrm{\&alpha;}}_{C_2})(1-{\mathrm{\&alpha;}}_{C_2})(1-{\mathrm{\&alpha;}}_{C_3})(1-{\mathrm{\&alpha;}}_{\mathrm{PM}2}){\mathrm{NI}}_0---\left(14\right)$

In the formula, I ₀Output intensity for laser instrument.The restituted signal of gyro is to pass through V _PD-outObtain as related operation with square-wave signal S (t).Used square-wave signal S (t) can be expressed as:

$S\left(t\right)=\left\{\begin{array}{cc}1& [\frac{q}{F}<t\&le;(q+\frac{1}{2})\frac{1}{F}]\\ -1& [(q+\frac{1}{2})\frac{1}{F}<t\&le;(q+1)\frac{1}{F}]\end{array}\right.---\left(15\right)$

Therefore, restituted signal can be expressed as:

$V_d=\mathrm{DF}{\&Integral;}_0^{1/F}{V}_{\mathrm{PD}-\mathrm{out}}S\left(t\right)\mathrm{dt}$

$=\mathrm{DF}({\&Integral;}_0^{1/\left(2F\right)}{V}_{\mathrm{PD}-\mathrm{out}}\mathrm{dt}-{\&Integral;}_{1/\left(2F\right)}^{1/F}{V}_{\mathrm{PD}-\mathrm{out}}\mathrm{dt})$

$=\mathrm{PD}\underset{n=-\&infin;}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\left\{\underset{n^{\&prime;}=-\&infin;}{\overset{n^{\&prime;}=n-1}{\mathrm{\&Sigma;}}}{A}_n\left(M_p\right)A_{n^{\&prime;}}^{*}\left(M_p\right)h_n{h}_{n^{\&prime;}}\exp \right[j({\mathrm{\&phi;}}_n-{\mathrm{\&phi;}}_{n^{\&prime;}})]\frac{\exp \left[\mathrm{j\&pi;}(n-n^{\&prime;})\right]-1}{\mathrm{j\&pi;}(n-n^{\&prime;})}$

$+\underset{n^{\&prime;}=n+1}{\overset{n^{\&prime;}=\&infin;}{\mathrm{\&Sigma;}}}{A}_n\left(M_p\right)A_{n^{\&prime;}}^{*}\left(M_p\right)h_n{h}_{n^{\&prime;}}\exp \left[j({\mathrm{\&phi;}}_n-{\mathrm{\&phi;}}_{n^{\&prime;}})\right]\frac{\exp \left[\mathrm{j\&pi;}(n-n^{\&prime;})\right]-1}{\mathrm{j\&pi;}(n-n^{\&prime;})}\}---\left(16\right)$

In the formula, D is the gain that produces by after 11 demodulation of first high speed digital signal processor.Fig. 7 has provided modulating frequency and has been respectively F=20kHz, the demodulation curve that obtains when F=60kHz and F=120kHz.Other parameter is as follows: L=12m, n _r=1.45, k _C=0.05, α _C=6.67%, α _L=1.14%, M _p=π rad (best phase-modulation index), I ₀=1mW, D=1, N=6.25V/mW.Can find the linear zone slope that different modulating frequencies is corresponding different.In order to improve the precision of gyro, must choose best modulating frequency and make linear zone slope maximum.According to formula (16), the slope at tuning-points place can be expressed as:

$k={\left|\frac{d{V}_d}{\mathrm{d\&Delta;f}}\right|}_{\mathrm{\&Delta;f}=0}$

$=\left|\mathrm{PD}\underset{n=-\&infin;}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\right(\underset{n^{\&prime;}=-\&infin;}{\overset{n^{\&prime;}=n-1}{\mathrm{\&Sigma;}}}{A}_n\left(M_p\right)A_{n^{\&prime;}}^{*}\left(M_p\right)\frac{\exp \left[\mathrm{j\&pi;}(n-n^{\&prime;})\right]-1}{\mathrm{j\&pi;}(n-n^{\&prime;})}\left\{h_n^{\&prime;}{h}_{n^{\&prime;}}\exp \right[j({\mathrm{\&phi;}}_n-{\mathrm{\&phi;}}_{n^{\&prime;}})]$

$+h_n{h}_{n^{\&prime;}}^{\&prime;}\exp \left[j({\mathrm{\&phi;}}_n-{\mathrm{\&phi;}}_{n^{\&prime;}})\right]+j({\mathrm{\&phi;}}_n^{\&prime;}-{\mathrm{\&phi;}}_{n^{\&prime;}}^{\&prime;})h_n{h}_{n^{\&prime;}}\exp \left[j({\mathrm{\&phi;}}_n-{\mathrm{\&phi;}}_{n^{\&prime;}})\right]\}$

$+\underset{n^{\&prime;}=n+1}{\overset{n^{\&prime;}=\&infin;}{\mathrm{\&Sigma;}}}{A}_n\left(M_p\right)A_{n^{\&prime;}}^{*}\left(M_p\right)\frac{\exp \left[\mathrm{j\&pi;}(n-n^{\&prime;})\right]-1}{\mathrm{j\&pi;}(n-n^{\&prime;})}\left\{h_n^{\&prime;}{h}_{n^{\&prime;}}\exp \right[j({\mathrm{\&phi;}}_n-{\mathrm{\&phi;}}_{n^{\&prime;}})]$

$+h_n{h}_{n^{\&prime;}}^{\&prime;}\exp \left[j({\mathrm{\&phi;}}_n-{\mathrm{\&phi;}}_{n^{\&prime;}})\right]+j({\mathrm{\&phi;}}_n^{\&prime;}-{\mathrm{\&phi;}}_{n^{\&prime;}}^{\&prime;})h_n{h}_{n^{\&prime;}}\exp \left[j({\mathrm{\&phi;}}_n-{\mathrm{\&phi;}}_{n^{\&prime;}})\right]\left\}\right){|}_{\mathrm{\&Delta;f}=0}---\left(17\right)$

Fig. 8 has provided the relation between tuning-points place slope k and the modulating frequency F, and correlation parameter is the same.Can find that modulating frequency F exists an optimum value to make tuning-points place slope k obtain maximal value, this modulating frequency is exactly an optimum modulation frequency.

Claims (3)

1. the triangular wave phase modulation method of a resonant cavity optical fiber gyroscope is characterized in that comprising:

1) the laser instrument output light field is analyzed, by Fourier transform the laser of triangular wave phase modulation (PM) is expanded into each harmonics frequency component sum, fourier coefficient delivery with carrier frequency component, obtain the carrier component normalization amplitude of laser after the triangular wave phase modulation (PM) and the relation of phase-modulation index, obtaining carrier component normalization amplitude by Computer Simulation is 0 o'clock pairing phase-modulation index, obtain when phase-modulation index is π rad according to theoretical derivation result and simulation result, carrier component is 0, thereby determines that best phase-modulation index is π rad;

2) utilization light field superposition principle obtains the light field transition function of fiber optic loop, by Fourier transform the laser of triangular wave phase modulation (PM) is expanded into each harmonics frequency component sum, each harmonics frequency component substitution light field transition function is obtained each harmonics frequency component through the light field expression formula after the fiber optic loop, after all these expression formula additions, obtain the output light field E of fiber optic loop _Out(t), output light field got grip the back altogether and multiply each other with former expression formula, and get time average, obtain output intensity expression formula＜E _Out(t) E _Out ^*(t) 〉, output intensity be multiply by loss and the photoelectric conversion factors that coupling mechanism causes, can obtain the expression formula of the output voltage signal of photodetector $V_{\mathrm{PD}-\mathrm{out}}=\frac{1}{2}(1-{\mathrm{\&alpha;}}_{C2})n<E_{\mathrm{out}}\left(t\right)E_{\mathrm{out}}^{*}\left(t\right)>,$ Owing to do not have statistic in the expression formula, time-averaging operation is removed, obtain photodetector output voltage signal expression formula $V_{\mathrm{PD}-\mathrm{out}}=\frac{1}{2}(1-{\mathrm{\&alpha;}}_{C2}){\mathrm{NE}}_{\mathrm{out}}\left(t\right)E_{\mathrm{out}}^{*}\left(t\right),$ With V _PD-outMake related operation with square-wave signal S (t), obtain restituted signal V _d, pass through V _dResonance frequency deviation Δ f in Δ f=0 place's differentiate, and is taken absolute value, obtain the demodulation rate of curve at tuning-points place and the relation of modulating frequency, by Computer Simulation, find that there is an optimum value in modulating frequency, make the demodulation rate of curve maximum at tuning-points place, this frequency is exactly an optimum modulation frequency;

3) by feedback circuit and high speed digital signal processor, with triangular signal and high-low level be respectively 1V and-square wave of 1V makes related operation, with related operation result and V _π/ 2 relatively, and the result who obtains when related operation is greater than V _π/ 2 o'clock, the triangular wave amplitude is reduced; The result who obtains when related operation equals V _π/ 2 o'clock, the triangular wave amplitude was constant; The result who obtains when related operation is less than V _π/ 2 o'clock, the triangular wave amplitude is increased, will export the triangular wave amplitude stabilization in half-wave voltage by the feedback algorithm of this dynamic adjustment.

2. the triangular wave phasing device of a resonant cavity optical fiber gyroscope, it is characterized in that laser instrument (1) and first coupling mechanism (2), first phase-modulator (3), second coupling mechanism (7), the 3rd coupling mechanism (13), the 4th coupling mechanism (8), second phase-modulator (4), first coupling mechanism (2) joins, first phase-modulator (3) joins with first triangular signal generator based (5), second phase-modulator (4) joins with second triangular signal generator based (6), second coupling mechanism (7) and first photodetector (9), first high speed digital signal processor (11), laser instrument (1) joins, the 4th coupling mechanism (8) and second photodetector (10), second high speed digital signal processor (12) joins, and the 3rd coupling mechanism (13) joins with fiber optic loop (14).

3. the triangular wave phasing device of a kind of resonant cavity optical fiber gyroscope according to claim 2, it is characterized in that described phase-modulator internal module annexation is: A/D converter and high speed digital signal processor, D/A, amplifying circuit, A/D converter join.

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