CN106124032B - Digital measurement method and device for modulation delay of optical frequency modulator - Google Patents

Digital measurement method and device for modulation delay of optical frequency modulator Download PDF

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CN106124032B
CN106124032B CN201610724499.XA CN201610724499A CN106124032B CN 106124032 B CN106124032 B CN 106124032B CN 201610724499 A CN201610724499 A CN 201610724499A CN 106124032 B CN106124032 B CN 106124032B
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梁志国
朱振宇
张合富
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Beijing Changcheng Institute of Metrology and Measurement AVIC
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    • G01—MEASURING; TESTING
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Abstract

The invention relates to a digital measurement method and a digital measurement device for modulation delay of an optical frequency modulator, and belongs to the technical field of photoelectric measurement. The device comprises a frequency stabilized laser, a polaroid, a lambda/2 wave plate, a spectroscope, a frequency shifter, a reflector, a measured optical frequency modulator, a modulation signal source, a reflector, a semi-transparent semi-reflecting mirror, a polaroid 11, a photoelectric detector, a digital oscilloscope and an electronic computer. The measured object is the delay time between the excitation control signal of the optical frequency modulator and the regulated optical frequency signal; the heterodyne laser interferometry apparatus is used to obtain a laser frequency modulation signal waveform for the optical frequency modulator and convert the optical signal to an electrical signal. The method can obtain good convergence, has high measurement accuracy, and has good self-adaptability to the conditions that the carrier wave is not stable and the amplitude envelope changes violently.

Description

Digital measurement method and device for modulation delay of optical frequency modulator
Technical Field
The invention relates to a digital measurement method and a digital measurement device for modulation delay of an optical frequency modulator, and belongs to the technical field of photoelectric measurement.
Background
The laser vibration measurer is a universal, basic vibration and impact measuring instrument, has high precision, no contact and no additional interference and influence on the measured object, and has measurement and calibration as the moving quantity value (displacement, speed and acceleration) and measurement principle based on laser Doppler effect. Usually, the measurement and calibration are carried out by exciting through a standard vibration table, measuring values by a standard laser vibration meter and measuring and calibrating other laser vibration meters, so that the frequency band is narrow, the accuracy is low and the tracing problem exists.
After the optical frequency modulator appears, the optical frequency modulator performs frequency regulation on measuring light emitted by the laser vibration meter by an optical frequency regulation technology and then feeds the measuring light back to the laser vibration meter, so that the problem of measurement and calibration of the laser vibration meter is solved. However, the problem of measuring the delay characteristic of the optical frequency modulator itself is not solved, and the greatest difficulty is that the control signal of the optical frequency modulator itself is a frequency modulation signal in which a radio frequency sine wave is a carrier wave and an audio frequency sine wave is a modulation waveform, a frequency modulation effect is generated on a passing optical frequency signal through a sound wave vibration mode and a light wave diffraction effect in the middle, and finally a frequency modulation result is generated on a passing laser signal, and the optical frequency modulator belongs to an optical, mechanical and electrical system integrating mechanical, electronic and optical effects, wherein the part needing to be accurately measured is the delay time of the modulation optical frequency signal on an excited electrical modulation signal. The response is not of the same physical magnitude as the stimulus.
How to evaluate the regulation response delay of the optical frequency modulator to the excitation optical frequency and the problem of magnitude traceability are the practical problems that the technology must face. The basic object of the present invention is to solve the problem of metering the modulation delay of the optical frequency modulator itself. Namely, the modulation delay of the optical frequency modulator is quantitatively measured, and the delay time of the output optical frequency signal relative to the input optical frequency modulation signal is quantitatively measured, so that a technical basis is provided for the measurement traceability of the demodulation delay time of the laser vibrometer.
In essence, the delay time of the sinusoidal vibration waveform demodulated and output by the laser vibration meter relative to the sinusoidal modulation signal of the analog vibration comprises three delay parts of demodulation delay of the laser vibration meter, modulation delay of the optical frequency modulator and electrical modulation delay in the sinusoidal frequency modulation process, and only the modulation delay of the optical frequency modulator and the demodulation delay of the laser vibration meter are difficult to separate in the delay time. The measurement range of the invention covers a wide delay range from nanosecond to second, and the delay measurement accuracy can be better than 0.1% magnitude.
Disclosure of Invention
The invention aims to provide a digital measurement method and a digital measurement device for modulation delay of an optical frequency modulator aiming at the problems of measurement and measurement calibration of the modulation delay time of the optical frequency modulator.
The core idea of the invention is as follows: dividing the laser generated by the frequency stabilized laser into two parts, one part is directly fed into the laser with the frequency f0The carrier frequency of the (t) sine wave modulation of (a) is fcAnd obtaining the returned laser light with the frequency regulated,the other path shifts the frequency f by a frequency shifterd>fcThen combining the two divided laser beams to perform beat frequency interference; obtaining heterodyne frequency modulation signals y (t) shifted to a radio frequency range by a photoelectric detector, simultaneously carrying out waveform measurement on FM signals x (t) and heterodyne frequency modulation signals y (t) output by the photoelectric detector in a high-speed data acquisition mode, demodulating a sequence of modulation sine waves a (t) from a measurement sequence of the signals x (t) by a delay-free digital frequency demodulation method, demodulating an optical frequency response sequence b (t) of the modulation sine waves a (t) from the measurement sequence of the signals y (t), and finally obtaining the phase delay of the optical frequency response b (t) of a measured optical frequency modulator to the modulation signals a (t)
Figure GDA0002780774330000021
Using the time difference t corresponding to the phase delayabThe trigger delay to be measured solves the problem of measurement and calibration of the delay time of the measured optical frequency modulator; if the delay time difference is large, the target frequency f needs to be decreased0So that t isab<1/f0；
The non-delay digital frequency demodulation method is a non-delay digital demodulation algorithm based on sine wave four-parameter waveform fitting, and is used for demodulating the instantaneous frequency of an FM signal x (t), so that a modulated sine wave a (t) and an optical frequency response sequence b (t) are respectively obtained, the method can obtain good convergence, has high measurement accuracy, and can realize good self-adaption to non-stability of a carrier wave and severe amplitude envelope change;
the purpose of the invention is realized by the following technical scheme.
A digital measurement method and device for modulation delay of an optical frequency modulator comprises a measurement device for the optical frequency modulator and a digital measurement method for modulation delay of the optical frequency modulator;
the measuring device for the optical frequency modulator is called as the device for short, and comprises a frequency stabilized laser, a polaroid, a lambda/2 wave plate, a spectroscope, a frequency shifter, a reflector, a measured optical frequency modulator, a modulation signal source, a reflector, a semi-transparent semi-reflective mirror, a polaroid, a photoelectric detector, a digital oscilloscope and an electronic computer;
a digital measurement method for modulation delay of an optical frequency modulator is called as the method for short, and comprises the following steps:
1) the frequency stabilized laser emitted by the frequency stabilized laser is divided into two parts by the polaroid, the lambda/2 wave plate and the spectroscope, and one part is frequency-shifted f by the frequency shifterdThen, the light beam passes through the reflector, passes through the semi-transparent semi-reflecting mirror to interfere with the other path of combined beam, and enters the photoelectric detector through the polarizing film to be received; the other path of the light beam passes through a reflector and is injected into a measured optical frequency modulator, is modulated by an FM signal x (t) output by a modulation signal source in the measured optical frequency modulator and then is output, is reflected by a semi-transparent mirror, then is subjected to beam combination interference with the previous path of laser, and is received by a photoelectric detector through a polarizing film; the signal output by the photodetector is a carrier frequency equal to the shift frequency fdHeterodyne frequency modulated signal y (t);
the FM signal is a sine modulation signal and is expressed by a formula (1):
x(t)＝Axcos(2π×fx(t)×t+ψx)+Dx； (1)
wherein A isxIs the amplitude of x (t), fxFrequency of x (t)xIs the phase of x (t), DxAn offset of x (t);
heterodyne fm signal y (t) is represented by equation (2):
y(t)＝Aycos(2π×fy(t)×t+ψy)+Dy； (2)
wherein A isxIs the amplitude of x (t), fxFrequency of x (t)xIs the phase of x (t), DxOffset of heterodyne frequency modulation signal y (t);
2) signals x (t) and y (t) are synchronously acquired by a digital oscilloscope to respectively obtain acquisition sequences x1,x2,…,xnAnd y1,y2,…,yn；
3) Respectively carrying out non-delay digital frequency demodulation on the acquisition sequences of the signals x (t) and y (t) output by the step 2) by an electronic computer according to a non-delay digital frequency demodulation method, and then respectively carrying out non-delay digital frequency demodulation on the acquisition sequences of y (t)i(i＝1,2,…N), the obtained frequency demodulation waveform sequence is called a heterodyne frequency demodulation waveform sequence and is recorded as:
Figure GDA0002780774330000031
acquisition sequence x of x (t)iThe frequency demodulation waveform sequence obtained (i ═ 1,2, …, n) is referred to as an FM frequency demodulation waveform sequence, and is written as:
Figure GDA0002780774330000032
in order to ensure that the water-soluble organic acid,
Figure GDA0002780774330000036
Figure GDA0002780774330000035
4) respectively carrying out least square waveform fitting on the FM frequency demodulation waveform sequence and the heterodyne frequency demodulation waveform sequence output by the step 3) by using a four-parameter sine wave fitting method, which specifically comprises the following steps:
4.1) using a four-parameter sine wave fitting method to the FM frequency demodulation waveform sequence a output by the 3)1，a2，…，aMPerforming least square waveform fitting, wherein the functional expression of the waveform least square fitting curve is shown as the following formula (3):
Figure GDA0002780774330000041
wherein A isaIs the fitted sinusoidal waveform amplitude;
Figure GDA0002780774330000042
fitting the sine wave frequency; phi is aaFitting the initial phase of the sine waveform; daFitting a sine waveform direct current component; is called a (t)i) FM fitting result, wherein pi is circumferential rate;
the fitted residual root mean square value of the FM frequency demodulation waveform sequence is shown in formula (4):
Figure GDA0002780774330000043
ρafitting residual root mean square values of the FM frequency demodulation waveform sequence;
4.2) demodulating waveform sequence b to heterodyne frequency by using four-parameter sine wave fitting method1，b2，…，bMPerforming least square waveform fitting, wherein the functional expression of a waveform least square fitting curve is shown as the formula (5):
Figure GDA0002780774330000044
wherein A isbA sinusoidal waveform amplitude fitted for a heterodyne frequency demodulation waveform sequence;
Figure GDA0002780774330000045
fitting a sine wave frequency for the heterodyne frequency demodulation waveform sequence;
Figure GDA0002780774330000046
a sinusoidal waveform initial phase fitted for a heterodyne frequency demodulation waveform sequence; dbFitting a sine waveform direct current component; b (t)i) Is the heterodyne fitting result;
the residual root mean square value of the heterodyne frequency demodulation waveform sequence fitting is as follows:
Figure GDA0002780774330000047
where ρ isbA residual root mean square value fitted for the heterodyne frequency demodulation waveform sequence;
5) calculating the trigger delay to be measured and the corresponding phase difference according to the result in the step 4);
wherein the trigger delay to be measured is calculated by equation (7):
Figure GDA0002780774330000048
wherein the content of the first and second substances,
Figure GDA0002780774330000049
a phase difference corresponding to the trigger delay to be measured;
to this end, from 1) to 5), the trigger delay measurement of the optical frequency modulator to be measured is completed, i.e. a digital measurement method of the modulation delay of the optical frequency modulator;
3) the delay-free digital frequency demodulation method comprises the following specific steps:
a. setting the sequence length n and the sampling rate v of the acquired waveform according to the carrier frequency of the detected signal; setting a principle to ensure that more than 20 sampling points are required in each carrier waveform period; limiting the lower limit value of n to 10000; wherein, the detected signal is a frequency modulation signal waveform y (t);
b. acquiring the detected signal in the step a to obtain a data acquisition sequence of a frequency modulation signal waveform y (t), and recording the data acquisition sequence as: y isiI is 1,2, …, n, where i represents the number of sampling points in the synchronous sampling sequence;
b. acquiring the detected signal in the step a to obtain a data acquisition sequence of a frequency modulation signal waveform y (t), and recording the data acquisition sequence as: y isiI is 1,2, …, n, where i represents the number of sampling points in the synchronous sampling sequence;
c. in the waveform acquisition sequence yiThe leading edge intercepts a segment of the waveform less than one carrier period, noted as: y isi，i＝1,2,…,m1；
Performing sine fitting on the sequence of the waveform segment of the frequency modulation signal output by the step c) by using an electronic computer according to the process of the step 4) to obtain the instantaneous frequency f of the fitted sine wave1The method specifically comprises the following steps:
c.1 assuming that the measured waveform of the intercepted waveform segment is approximate to a sine wave with a waveform of
ys(t)＝Ay sin(2πfyt+ψy)+Dy (8)
Wherein, ys(t) measured waveform of the intercepted waveform segment, AyAmplitude of a sine wave, fyIs the frequency, ψ, of a sine waveyIs the initial phase of a sine wave, DyAmplitude deviation of the measured waveform of the intercepted waveform segment;
a waveform segment of less than one carrier cycle is truncated at the leading edge of the waveform acquisition sequence,
Figure GDA0002780774330000051
i＝1,2,…,m1
Figure GDA0002780774330000052
wherein, the sampling time interval delta tau is 1/v;
c.2 computer Pair acquisition sequence
Figure GDA0002780774330000053
(i＝1,2,…,m1) And performing four-parameter fitting on the sine waveform to obtain a fitting signal:
Figure GDA0002780774330000054
wherein, ys(i) In order to fit the signal to the signal,
Figure GDA0002780774330000055
in order to fit the amplitude of the sine wave,
Figure GDA0002780774330000056
in order to fit the angular frequency of the sine wave,
Figure GDA0002780774330000057
to fit the initial phase of the sine wave,
Figure GDA0002780774330000058
fitting the direct current component value of the sine wave;
fitting frequency
Figure GDA0002780774330000059
Comprises the following steps:
Figure GDA00027807743300000510
the fitting frequency
Figure GDA00027807743300000511
Is a point (1+ m)1) Instantaneous frequency at/2;
c.3, fitting four parameters of a sine waveform, specifically:
assume that the target frequency to be estimated is f0，ω0＝2πf0V, the number of signals contained in the sine wave sampling sequence to be estimated is p (0) and is less than one period<p<1) The occupied time length of the waveform is tau; then, f 01/tau, another factor q is selected (e.g. q 1 × 10)-5) So that the estimated sinusoidal frequency f0>q/τ; thus, f0∈[q/τ,1/τ]The specific process is as follows:
c3. setting a fitting iteration stop condition to be he；
heIs in the range of 1 × 10-18To 1X 10-20xx; preferred is heIs 1 × 10-20；
c3. From the known time t1,t2,...,tm1Sine wave acquisition sample y1,y2,...,ym1. The signal waveform obtained by the point counting method occupies a time length of tau (m)1-1)/v; selecting a factor q (e.g. q 1 × 10)-5) Determining the target frequency f0Existence interval of [ q/τ,1/τ ]]；
c3. Determining an iteration left boundary frequency: f. ofL＝q/τ；ωL＝2πfLV,/v; iteration right boundary frequency: f. ofR＝1/τ；ωR＝2πfR/v；
c3. Command the median frequency: omegaM＝(ωR+ωL) 2; calculating respective fitting residual errors rho (omega) on the left boundary frequency, the right boundary frequency and the median frequency by using a three-parameter fitting formulaL)、ρ(ωM) And ρ (ω)R)；
c3. Judging whether rho (omega) is fifeL)<η·ρ(ωM) Wherein eta is a criterion factor and the value range is 1-1.5;
if ρ (ω)L)<η·ρ(ωM) Then let ω beR＝ρ(ωM)，ωLRepeatedly executing the processes from the fourth step to the fifth step without changing;
c3. sixthly, if rho (omega)L)≥η·ρ(ωM) Then there must be ωR<2ω0Determining the left boundary frequency of the iteration as omegaL(ii) a Iterative right boundary frequency omegaR(ii) a The median frequency was chosen according to the preferred method: omegaM＝ωL+0.618×(ωR-ωL)
And ωT＝ωR-0.618×(ωR-ωL)；
c3. Is on omegaLPerforming three-parameter sine curve fitting to obtain AL、
Figure GDA0002780774330000068
DL、ρL(ii) a At omegaRPerforming three-parameter sine curve fitting to obtain AR、
Figure GDA0002780774330000069
DR、ρR(ii) a At omegaMPerforming three-parameter sine curve fitting to obtain AM、
Figure GDA00027807743300000611
DM、ρM(ii) a At omegaTPerforming three-parameter sine curve fitting to obtain AT、
Figure GDA00027807743300000610
DT、ρT；
c3. And if ρM<ρTThen ρ is ρMHas omega0∈[ωT,ωR]，ωL＝ωT，ωT＝ωM；ωM＝ωL+0.618×(ωR-ωL)；
If ρM>ρTThen ρ is ρTHas omega0∈[ωL,ωM]，ωR＝ωM，ωM＝ωT；ωT＝ωR-0.618×(ωR-ωL)；
c3. Determination of whether or not a self-pinch is | (ρ)M(k)-ρT(k))/ρT(k)|＜heIf yes, the iteration is stopped, and ρ is ρTThen, obtaining the parameter of the four-parameter fitting sine curve as A ═ AT、ω＝ωT、
Figure GDA0002780774330000061
D＝DTRho, finishing the fitting process; ρ ═ ρMThen, obtaining the parameter of the four-parameter fitting sine curve as A ═ AM、ω＝ωM、
Figure GDA0002780774330000062
D＝DMRho, finishing the fitting process; otherwise, repeating c3. -c3. triple-point process;
d. storing instantaneous frequency of output sinusoidal model
Figure GDA0002780774330000063
Is the frequency of the measured sinusoidal model;
e. to be less than
Figure GDA0002780774330000064
Cycle length (e.g. of
Figure GDA0002780774330000065
) The corresponding sequence time length is the length m of the next fitting sequence2Sequence center position from m1Moving a sampling point backwards at position/2, executing the processes c and d on a new data segment, and obtaining the instantaneous frequency of the output sinusoidal model
Figure GDA0002780774330000066
Repeatedly executing the sliding fitting process until the end point of the data sequence;
obtaining a transient frequency sequence:
Figure GDA0002780774330000067
a demodulated waveform output for signal waveform y (t);
to this end, from a to e, the delay-free digital frequency demodulation method is completed.
Advantageous effects
Compared with other optical frequency modulator measuring methods and devices, the optical frequency modulator delay time measuring method and device provided by the invention have the following beneficial effects:
1. the method and the device for measuring the delay time of the optical frequency modulator provided by the invention use a heterodyne laser interference measuring device to obtain the waveform of an output signal of the measured optical frequency modulator, and simultaneously carry out waveform measurement on a modulation signal x (t) of the measured optical frequency modulator and an output signal y (t) of the measured optical frequency modulator in a high-speed data acquisition mode, thereby realizing the measurement and comparison of optical quantity values aiming at the time delay among different physical quantity values of electrical quantity values;
2. the method and the device for measuring the delay time of the optical frequency modulator provided by the invention adopt a non-delay digital frequency demodulation mode, demodulate a sequence of a modulation sine wave a (t) from a measurement sequence of a signal x (t), demodulate an optical frequency response sequence b (t) of the modulation sine wave a (t) from the measurement sequence of a signal y (t), and finally obtain the optical frequency response b (t) of the measured optical frequency modulator for the phase delay of the modulation signal a (t)
Figure GDA0002780774330000071
Higher measurement accuracy is obtained compared with other hardware demodulation methods, no extra demodulation delay error is introduced, and finally the time difference t corresponding to the phase delay is usedabThe problem of measurement and calibration of delay time of a measured optical frequency modulator is solved;
3. the method and the device for measuring the delay time of the optical frequency modulator acquire a signal waveform sequence by means of a high-speed data acquisition and quantization technology, use a model section less than one carrier period to carry out delay-free digital frequency demodulation on the signal waveform, and have higher time resolution and minimum filtering effect compared with xxx, thereby realizing the accurate demodulation of instantaneous frequency on the waveform of a laser frequency modulation signal x (t) and an output signal y (t) of the measured optical frequency modulator, and further solving the problems of accurate measurement and value traceability of the delay time of the measured optical frequency modulator;
4. the method for measuring the delay time of the optical frequency modulator uses a least square optimal estimation mode, so that the method has high measurement accuracy, high model demodulation resolution and high demodulation efficiency;
5. the method and the device for measuring the delay time of the optical frequency modulator demodulate the frequency modulation signal in a sliding model mode, have high time resolution, absolutely convergent algorithm and good adaptivity to non-stationary waveforms, and can conveniently carry out traceability calibration.
Drawings
FIG. 1 is a schematic diagram of an apparatus and method for measuring delay time of an optical frequency modulator according to the present invention;
reference numbers in fig. 1: 1-frequency stabilized laser, 2-polaroid, 3-lambda/2 wave plate, 4-spectroscope, 5-frequency shifter, 6-reflector, 7-measured optical frequency modulator, 8-modulation signal source, 9-reflector, 10-semi-transparent semi-reflector, 11-polaroid, 12-photoelectric detector, 13-digital oscilloscope and 14-electronic computer.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
Examples
The structure of the measuring method and the device of the optical frequency modulator is shown in figure 1, and the measuring method and the device comprise a frequency stabilized laser 1, a polaroid 2, a lambda/2 wave plate 3, a spectroscope 4, a frequency shifter 5, a reflector 6, a measured optical frequency modulator 7, a modulation signal source 8, a reflector 9, a half-transmitting and half-reflecting mirror 10, a polaroid 11, a photoelectric detector 12, a digital oscilloscope 13 and an electronic computer 14.
Specifically, in this embodiment:
firstly, the frequency stabilized laser emitted by the frequency stabilized laser 1 is divided into two parts by the polaroid 2, the lambda/2 wave plate 3 and the spectroscope 4, and one part is frequency-shifted f by the frequency shifter 5dThen, the beam passes through the reflector 9, the semi-transparent semi-reflecting mirror 10 to interfere with the other path of combined beam, and enters the photoelectric detector 12 through the polarizing plate 11 to be received; the other path is injected into the measured optical frequency modulator 7 via the mirror 6, and the measured optical frequency modulator 7 receives the sine-modulated FM signal x (t) a output from the modulation signal source 8xcos(2π×fx(t)×t+ψx)+DxThe modulated output is reflected by the half mirror 10, interferes with the previous laser beam, and is received by the photodetector 12 through the polarizer 11. The signal output by photodetector 12 is at a carrier frequency equal to the shift frequency fdFrequency modulation signal y (t) aycos(2π×fy(t)×t+ψy)+Dy；
Secondly, signals x (t) and y (t) are synchronously acquired by a digital oscilloscope 13 to respectively obtain acquisition sequences x1,x2,…,xnAnd y1,y2,…,yn；
Thirdly, after the computer 14 adopts the non-delay digital frequency demodulation algorithm to respectively carry out the non-delay digital frequency demodulation on x (t) and y (t), the waveform y (t) of the wave form is measuredi(i ═ 1,2, …, n) of the obtained frequency demodulation waveform sequence:
Figure GDA0002780774330000081
the waveform x (t) of which is a measurement sequence xi(i ═ 1,2, …, n) of the obtained frequency demodulation waveform sequence:
Figure GDA0002780774330000082
then the process of the first step is carried out,
Figure GDA0002780774330000088
Figure GDA0002780774330000086
fourth, with a four parameter sine waveFitting method for sine waveform sequence a1,a2,…,aMAnd performing least square waveform fitting, wherein the function expression of a waveform least square fitting curve is as follows:
Figure GDA0002780774330000087
the fitted residual root mean square value is:
Figure GDA0002780774330000091
wherein A isaFitting the amplitude of the sine waveform;
Figure GDA0002780774330000092
fitting the sine wave frequency; phi is aaFitting the initial phase of the sine waveform; daFitting a sine waveform direct current component; rhoaFitting residual root mean square values;
using four-parameter sine wave fitting method to align sine wave sequence b1,b2,…,bMAnd performing least square waveform fitting, wherein the function expression of a waveform least square fitting curve is as follows:
Figure GDA0002780774330000093
the fitted residual root mean square value is:
Figure GDA0002780774330000094
wherein A isbFitting the amplitude of the sine waveform;
Figure GDA0002780774330000095
fitting the sine wave frequency; phi is abFitting the initial phase of the sine waveform; dbFitting a sine waveform direct current component; rhobTo fit the residual errorA root mean square value;
fifth, the trigger delay t to be measuredabBy corresponding phase difference phiabCan be expressed as:
Figure GDA0002780774330000096
thereby completing the trigger delay t of the measured optical frequency modulatorabThe measurement process of (2);
the delay-free digital frequency demodulation algorithm comprises the following steps:
A. setting the sequence length n and the sampling rate v of the acquired waveform according to the carrier frequency of the detected signal; the rule is set to ensure that there are more than 20 samples per carrier waveform period. Limiting the lower limit value of n to 10000;
B. the data acquisition sequence of the frequency modulation signal waveform is as follows: y isiI is 1,2, …, n, where i represents the number of sampling points in the synchronous sampling sequence;
C. intercepting a waveform segment, y, of less than one carrier period at the leading edge of a waveform acquisition sequencei，i＝1,2,…,m1
Using computer to make sine fitting on the waveform segment sequence of the modulated signal according to the process described in c.3 to obtain instantaneous frequency f of fitted sine wave1The method specifically comprises the following steps:
c.1 supposing that the measured waveform of the intercepted waveform segment is approximate to a sine wave, and the waveform is
y(t)＝Ay sin(2πfyt+ψy)+Dy (17)
Wherein A isyAmplitude of a sine wave, fyIs the frequency, ψ, of a sine waveyIs the initial phase of the sine wave;
intercepting a waveform segment, y, of less than one carrier period at the leading edge of a waveform acquisition sequencei，i＝1,2,…,m1
yi＝y(ti)＝y((i-1)·Δτ)，i＝1,2,…,m1 (18)
Wherein, the sampling time interval delta tau is 1/v;
c.2 computer-to-acquisition sequence yi，(i＝1,2,…,m1) And performing four-parameter fitting on the sine waveform to obtain a fitting signal:
Figure GDA0002780774330000101
wherein the content of the first and second substances,
Figure GDA0002780774330000102
in order to fit the amplitude of the sine wave,
Figure GDA0002780774330000103
in order to fit the angular frequency of the sine wave,
Figure GDA0002780774330000104
to fit the initial phase of the sine wave,
Figure GDA0002780774330000105
fitting the direct current component value of the sine wave;
fitting frequency
Figure GDA0002780774330000106
Comprises the following steps:
Figure GDA0002780774330000107
the fitting frequency
Figure GDA0002780774330000108
As point (1+ m)1) Instantaneous frequency at/2;
c.3 sine waveform four-parameter fitting process
Assume that the target frequency to be estimated is f0，ω0＝2πf0V, the number of signals contained in the sine wave sampling sequence to be estimated is p (0) and is less than one period<p<1) The occupied time length of the waveform is tau; then, f 01/tau, another factor q is selected (e.g. q 1 × 10)-5) So that the estimated target frequency f0>q/τ; thus, f0∈[q/τ,1/τ]The method comprises the following steps:
setting a fitting iteration stop condition to be he(ii) a (optionally h)e＝1×10-20)
From the known time t1,t2,...,tm1Sine wave acquisition sample y1,y2,...,ym1(ii) a The signal waveform obtained by the point counting method occupies a time length of tau (m)1-1)/v; selecting a factor q (e.g. q 1 × 10)-5) Determining the target frequency f0Existence interval of [ q/τ,1/τ ]]；
Determining an iteration left boundary frequency: f. ofL＝q/τ；ωL＝2πfLV,/v; iteration right boundary frequency: f. ofR＝1/τ；ωR＝2πfR/v；
Command the median frequency: omegaM＝(ωR+ωL) 2; calculating respective fitting residual errors rho (omega) on the left boundary frequency, the right boundary frequency and the median frequency by using a three-parameter fitting formulaL)、ρ(ωM) And ρ (ω)R)；
Judging whether rho (omega) is fifeL)<η·ρ(ωM) Wherein eta is a criterion factor and the value range is 1-1.5;
if ρ (ω)L)<η·ρ(ωM) Then let ω beR＝ρ(ωM)，ωLRepeatedly executing the processes from the fourth step to the fifth step without changing;
sixthly, if rho (omega)L)≥η·ρ(ωM) Then there must be ωR<2ω0Determining the left boundary frequency of the iteration as omegaL(ii) a Iterative right boundary frequency omegaR(ii) a The median frequency was chosen according to the preferred method: omegaM＝ωL+0.618×(ωR-ωL) And ωT＝ωR-0.618×(ωR-ωL)；
Is on omegaLPerforming three-parameter sine curve fitting to obtain AL、
Figure GDA0002780774330000109
DL、ρL(ii) a At omegaRPerforming three-parameter sine curve fitting to obtain AR、
Figure GDA00027807743300001010
DR、ρR(ii) a At omegaMPerforming three-parameter sine curve fitting to obtain AM、
Figure GDA00027807743300001011
DM、ρM(ii) a At omegaTPerforming three-parameter sine curve fitting to obtain AT、
Figure GDA00027807743300001012
DT、ρT；
And if ρM<ρTThen ρ is ρMHas omega0∈[ωT,ωR]，ωL＝ωT，ωT＝ωM；ωM＝ωL+0.618×(ωR-ωL) (ii) a If ρM>ρTThen ρ is ρTHas omega0∈[ωL,ωM]，ωR＝ωM，ωM＝ωT；ωT＝ωR-0.618×(ωR-ωL)；
Determination of whether or not a self-pinch is | (ρ)M(k)-ρT(k))/ρT(k)|＜heIf yes, the iteration is stopped, and ρ is ρTThen, obtaining the parameter of the four-parameter fitting sine curve as A ═ AT、ω＝ωT、
Figure GDA0002780774330000111
D＝DTRho, finishing the fitting process; ρ ═ ρMThen, obtaining the parameter of the four-parameter fitting sine curve as A ═ AM、ω＝ωM、
Figure GDA0002780774330000112
D＝DMRho, finishing the fitting process; otherwise, the process of quietness-self-polishing is repeated;
d. storing instantaneous frequency of output sinusoidal model
Figure GDA0002780774330000113
Is the frequency of the measured sinusoidal model;
e. to be less than
Figure GDA0002780774330000114
Cycle length (e.g. of
Figure GDA0002780774330000115
) The corresponding sequence time length is the length m of the next fitting sequence2Sequence center position from m1Moving a sampling point backwards at position/2, executing the processes c and d on a new data segment, and obtaining the instantaneous frequency of the output sinusoidal model
Figure GDA0002780774330000116
Repeatedly executing the sliding fitting process until the end point of the data sequence;
obtaining a transient frequency sequence:
Figure GDA0002780774330000117
is the demodulated waveform output of signal waveform y (t).
While the foregoing is directed to the preferred embodiment of the present invention, it is not intended that the invention be limited to the embodiment and the drawings disclosed herein. Equivalents and modifications may be made without departing from the spirit of the disclosure and the scope of the invention.

Claims (5)

1. A digital measurement method for modulation delay of an optical frequency modulator is characterized in that:
the digital measurement method is a non-delay digital demodulation algorithm based on sine wave four-parameter waveform fitting to demodulate the instantaneous frequency of an FM signal x (t), so as to respectively obtain a modulated sine wave a (t) and an optical frequency response sequence b (t);
the measuring device of the supported optical frequency modulator comprises a frequency stabilized laser, a first polaroid, a lambda/2 wave plate, a spectroscope, a frequency shifter, a reflector, a measured optical frequency modulator, a modulation signal source, a reflector, a semi-transmitting and semi-reflecting mirror, a second polaroid, a photoelectric detector, a digital oscilloscope and an electronic computer;
the digital measurement method comprises the following specific steps:
1) the frequency stabilized laser emitted by the frequency stabilized laser is divided into two parts by the first polaroid, the lambda/2 wave plate and the spectroscope, and one part is subjected to frequency shift f by the frequency shifterdThen, the light beam passes through the reflector, passes through the semi-transparent semi-reflecting mirror to interfere with the other path of combined beam, and enters the photoelectric detector through the second polaroid to be received; the other path of the signal is injected into a tested optical frequency modulator through a reflector, is modulated according to an FM signal x (t) output by a modulation signal source in the tested optical frequency modulator and then is output, is reflected by a semi-transparent mirror, then is subjected to beam combination interference with the previous path of laser, and is received by a photoelectric detector through a second polarizing film; the signal output by the photodetector is a carrier frequency less than the shift frequency fdHeterodyne frequency modulated signal y (t);
2) signals x (t) and y (t) are synchronously acquired by a digital oscilloscope to respectively obtain acquisition sequences xi(i ═ 1,2, …, n) and yi(i ═ 1,2, …, n), i denotes the sample point number in the synchronous sample sequence;
3) respectively carrying out non-delay digital frequency demodulation on the acquisition sequences of the signals x (t) and y (t) output in the step 2) by an electronic computer according to a non-delay digital frequency demodulation method, and then respectively carrying out non-delay digital frequency demodulation on the acquisition sequences of y (t)i(i ═ 1,2, …, n), the obtained frequency demodulation waveform sequence, called heterodyne frequency demodulation waveform sequence, is written as:
Figure FDA0003098042110000011
acquisition sequence x of x (t)iThe frequency demodulation waveform sequence obtained (i ═ 1,2, …, n) is referred to as an FM frequency demodulation waveform sequence, and is written as:
Figure FDA0003098042110000012
Figure FDA0003098042110000013
in order to ensure that the water-soluble organic acid,
Figure FDA0003098042110000014
Figure FDA0003098042110000015
4) respectively carrying out least square waveform fitting on the FM frequency demodulation waveform sequence and the heterodyne frequency demodulation waveform sequence output in the step 3) by using a four-parameter sine wave fitting method;
5) calculating the trigger delay to be measured and the corresponding phase difference according to the result in the step 4); the phase difference corresponding to the trigger delay to be measured is recorded as
Figure FDA0003098042110000016
Determining the time difference t corresponding to the phase differenceabI.e. the trigger delay to be measured, if the delay time difference is large, the target frequency f needs to be reduced0So that t isab<1/f0。
2. A method of digitally measuring the modulation delay of an optical frequency modulator as recited in claim 1, further characterized by:
the FM signal in the step 1) is a sine modulation signal and is expressed by a formula (1):
x(t)＝Axcos(2π×fx(t)×t+ψx)+Dx； (1)
wherein A isxIs the amplitude of x (t), fxFrequency of x (t)xIs the phase of x (t), DxAn offset of x (t);
heterodyne fm signal y (t) is represented by equation (2):
y(t)＝Aycos(2π×fy(t)×t+ψy)+Dy； (2)
wherein A isyIs the amplitude of the (y) and (t),fyfrequency of y (t), psiyIs the phase of y (t), DyThe offset of heterodyne fm signal y (t).
3. A method of digitally measuring the modulation delay of an optical frequency modulator as recited in claim 1, further characterized by:
the step 4) is specifically as follows:
4.1) using a four-parameter sine wave fitting method to the FM frequency demodulation waveform sequence a output by the step 3)1，a2，…，aMPerforming least square waveform fitting, wherein the functional expression of the waveform least square fitting curve is shown as the following formula (3):
Figure FDA0003098042110000021
wherein A isaIs the fitted sinusoidal waveform amplitude;
Figure FDA0003098042110000022
fitting the sine wave frequency; phi is aaFitting the initial phase of the sine waveform; daFitting a sine waveform direct current component; title a (t)i) Is the FM fitting result, and pi is the circumferential ratio;
the fitted residual root mean square value of the FM frequency demodulation waveform sequence is shown in formula (4):
Figure FDA0003098042110000023
ρafitting residual root mean square values of the FM frequency demodulation waveform sequence;
4.2) demodulating waveform sequence b to heterodyne frequency by using four-parameter sine wave fitting method1，b2，…，bMPerforming least square waveform fitting, wherein the functional expression of a waveform least square fitting curve is shown as the formula (5):
Figure FDA0003098042110000031
wherein A isbA sinusoidal waveform amplitude fitted for a heterodyne frequency demodulation waveform sequence;
Figure FDA0003098042110000032
fitting a sine wave frequency for the heterodyne frequency demodulation waveform sequence;
Figure FDA0003098042110000033
a sinusoidal waveform initial phase fitted for a heterodyne frequency demodulation waveform sequence; dbFitting a sine waveform direct current component; b (t)i) Is the heterodyne fitting result;
the residual root mean square value of the heterodyne frequency demodulation waveform sequence fitting is as follows:
Figure FDA0003098042110000034
where ρ isbA residual root mean square value fitted for the heterodyne frequency demodulation waveform sequence.
4. A method of digitally measuring the modulation delay of an optical frequency modulator as recited in claim 1, further characterized by:
the step 5) is specifically as follows: the trigger delay to be measured is calculated by equation (7):
Figure FDA0003098042110000035
wherein the content of the first and second substances,
Figure FDA0003098042110000036
the phase difference corresponding to the trigger delay to be measured.
5. A method of digitally measuring the modulation delay of an optical frequency modulator as recited in claim 1, further characterized by:
the delay-free digital frequency demodulation method in the step 3) comprises the following specific steps:
a. setting the sequence length n and the sampling rate v of the acquired waveform according to the carrier frequency of the detected signal; setting a principle to ensure that more than 20 sampling points are required in each carrier waveform period; limiting the lower limit value of n to 10000; wherein, the measured signal is a heterodyne frequency modulation signal y (t);
b. and (b) acquiring the detected signal in the step a, obtaining a data acquisition sequence of the heterodyne frequency modulation signal y (t) with the length of n, and recording the data acquisition sequence as: y isi(i ═ 1,2, …, n), where i denotes the sample point number in the synchronous sample sequence;
c. in the waveform acquisition sequence yiThe front edge being taken over a length m1A wave segment of
Figure FDA0003098042110000037
Figure FDA0003098042110000038
Performing sine fitting on the sequence of the waveform segment of the frequency modulation signal output in the step c) by using an electronic computer according to the process in the step 4) to obtain the instantaneous frequency f of the fitted sine wave1The method specifically comprises the following steps:
c.1 assuming that the measured waveform of the intercepted waveform segment is approximate to a sine wave with a waveform of
ys(t)＝Aysin(2πfyt+ψy)+Dy (8)
Wherein, ys(t) measured waveform of the intercepted waveform segment, AyAmplitude of the intercepted waveform segment, fyFor the frequency, psi, of the intercepted waveform segmentyFor the initial phase of the truncated waveform segment, DyAmplitude offset of the intercepted waveform segment;
a waveform segment of less than one carrier cycle is truncated at the leading edge of the waveform acquisition sequence,
Figure FDA0003098042110000041
Figure FDA0003098042110000042
wherein, the sampling time interval delta tau is 1/v;
c.2 computer Pair acquisition sequence
Figure FDA0003098042110000043
Performing four-parameter fitting on a sine waveform to obtain a fitting signal:
Figure FDA0003098042110000044
wherein, ys(i) In order to fit the signal to the signal,
Figure FDA0003098042110000045
in order to fit the amplitude of the sine wave,
Figure FDA0003098042110000046
in order to fit the angular frequency of the sine wave,
Figure FDA0003098042110000047
to fit the initial phase of the sine wave,
Figure FDA0003098042110000048
fitting the direct current component value of the sine wave;
fitting frequency
Figure FDA0003098042110000049
Comprises the following steps:
Figure FDA00030980421100000410
the fitting frequency
Figure FDA00030980421100000411
Is a point (1+ m)1) Instantaneous frequency at/2;
c.3, fitting four parameters of a sine waveform, specifically:
assume that the target frequency to be estimated is f0，ω0＝2πf0V, the number of signals contained in the sine wave sampling sequence to be estimated is p (0) and is less than one period<p<1) The occupied time length of the waveform is tau; then, f01/tau, selecting another factor q 1 × 10-5So that the estimated sine wave frequency f0>q/τ; thus, f0∈[q/τ,1/τ]The specific process is as follows:
c3. setting a fitting iteration stop condition to be he；
heIs in the range of 1 × 10-18To 1X 10-20；
c3. From the known time t1,t2,...,tm1Sine wave acquisition sample y1,y2,...,ym1(ii) a The signal waveform obtained by the point counting method occupies a time length of tau (m)1-1)/v; selecting a factor q and determining a target frequency f0Existence interval of [ q/τ,1/τ ]]；
c3. Determining an iteration left boundary frequency: f. ofL＝q/τ；ωL＝2πfLV,/v; iteration right boundary frequency: f. ofR＝1/τ；ωR＝2πfR/v；
c3. Command the median frequency: omegaM＝(ωR+ωL) 2; calculating respective fitting residual errors rho (omega) on the left boundary frequency, the right boundary frequency and the median frequency by using a three-parameter fitting formulaL)、ρ(ωM) And ρ (ω)R)；
c3. Judging whether rho (omega) is fifeL)<η·ρ(ωM) Wherein eta is a criterion factor and the value range is 1-1.5;
if ρ (ω)L)<η·ρ(ωM) Then let ω beR＝ρ(ωM)，ωLRepeatedly executing the steps c3.(4) to c3. without changingA process;
c3. sixthly, if rho (omega)L)≥η·ρ(ωM) Then there must be ωR<2ω0Determining the left boundary frequency of the iteration as omegaL(ii) a Iterative right boundary frequency omegaR(ii) a The median frequency was chosen according to the preferred method: omegaM＝ωL+0.618×(ωR-ωL)
And ωT＝ωR-0.618×(ωR-ωL)；
c3. Is on omegaLPerforming three-parameter sine curve fitting to obtain AL、
Figure FDA0003098042110000051
DL、ρL(ii) a At omegaRPerforming three-parameter sine curve fitting to obtain AR、
Figure FDA0003098042110000052
DR、ρR(ii) a At omegaMPerforming three-parameter sine curve fitting to obtain AM、
Figure FDA0003098042110000053
DM、ρM(ii) a At omegaTPerforming three-parameter sine curve fitting to obtain AT、
Figure FDA0003098042110000054
DT、ρT；
c3. And if ρM<ρTThen ρ is ρMHas omega0∈[ωT,ωR]，ωL＝ωT，ωT＝ωM；ωM＝ωL+0.618×(ωR-ωL) (ii) a If ρM>ρTThen ρ is ρTHas omega0∈[ωL,ωM]，ωR＝ωM，ωM＝ωT；ωT＝ωR-0.618×(ωR-ωL)；
c3. Determination of whether or not a self-pinch is | (ρ)M(k)-ρT(k))/ρT(k)|＜heIf yes, the iteration is stopped, and ρ is ρTThen, obtaining the parameter of the four-parameter fitting sine curve as A ═ AT、ω＝ωT、
Figure FDA0003098042110000055
D＝DTRho, finishing the fitting process; ρ ═ ρMThen, obtaining the parameter of the four-parameter fitting sine curve as A ═ AM、ω＝ωM、
Figure FDA0003098042110000056
D＝DMRho, finishing the fitting process; otherwise, repeating c3. -c3. triple-point process;
d. storing instantaneous frequency of output sinusoidal model
Figure FDA0003098042110000057
Is the frequency of the measured sinusoidal model;
e. to be provided with
Figure FDA0003098042110000058
The sequence time length corresponding to the period length is the length m of the next fitting sequence2Sequence center position from m1Moving a sampling point backwards at position/2, executing the processes c and d on a new data segment, and obtaining the instantaneous frequency of the output sinusoidal model
Figure FDA0003098042110000059
Repeatedly executing the sliding fitting process until the end point of the data sequence;
obtaining a temporal frequency sequence consisting of fitted frequencies:
Figure FDA00030980421100000510
is the demodulated waveform output of signal waveform y (t).
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