CN113834561B - System and method for extracting and compensating phase modulation depth in PGC phase demodulation - Google Patents
System and method for extracting and compensating phase modulation depth in PGC phase demodulation Download PDFInfo
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Abstract
A system and method for extracting and compensating phase modulation depth in PGC phase demodulation, after analog-digital sampling, the interference signal is divided into three paths after direct current filtering, one path is directly subjected to low-pass filtering, the other two paths are respectively multiplied with reference signals of first order and second order harmonic waves and subjected to low-pass filtering, three harmonic amplitude signals are obtained, and the harmonic amplitude signals and harmonic differential signals are mutually operated; combining Bessel function recurrence formulas; the invention relates to a new method for eliminating light source light intensity disturbance and Bessel function interference item under the condition of reducing operation memory as much as possible, and extracting C value from interference signal to make it compensate demodulation result.
Description
Technical Field
The present invention relates to the field of phase-generating carrier (PGC) demodulation, and in particular, to a system and method for extracting and compensating a phase modulation depth in PGC phase demodulation.
Background
The operation result of the existing PGC algorithm is difficult to eliminate light intensity disturbance and Bessel function term, the Bessel function term can be eliminated only by taking specific values, a large amount of operation is introduced to eliminate the phase modulation depth C value, the operation result of the follow-up improved algorithm is complicated in calculation result, a large amount of division is introduced, and the situation that the denominator is 0 is difficult to eliminate, so that stability is poor.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention aims to provide a system and a method for extracting and compensating the phase modulation depth in PGC phase demodulation, and a novel method for extracting C value by interference signals to compensate the demodulation result by eliminating light source light intensity disturbance and Bessel function interference items under the condition of reducing operation memory as much as possible.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
a system for extracting and compensating phase modulation depth in PGC phase demodulation comprises a direct current filter 1, wherein an interference signal is divided into three paths after being filtered by the direct current filter 1, and the three paths are respectively connected with input ends of a first low-pass filter 2, a first multiplier 3 and a second multiplier 4;
digital frequency synthesizer generating cos omega c t、cos2ω c the frequency multiplication signals of t are respectively connected to the input ends of the first multiplier 3 and the second multiplier 4;
the output end of the first low-pass filter 2 is connected with the input end of the first differentiator 5; the output end of the multiplier I3 is connected with the input end of the low-pass filter II 6; the output end of the multiplier II 4 is connected with the input end of the low-pass filter III 7;
the output end of the third low-pass filter 7 is connected with the input end of the second differentiator 8; the output end of the differentiator I5 and the output end of the low-pass filter II 6 are connected to the input end of the divider I9; the output end of the second low-pass filter 6 and the output end of the second differentiator 8 are connected to the input end of the second divider 10; the output ends of the divider I9 and the divider II 10 are connected to the input end of the differentiator 11; the output of the differentiator 11 is connected to the input of the integrator 12; the output of the integrator 12 is connected to the input of the high pass filter 13; the output end of the high-pass filter 13 is connected to the input end of the multiplier III 14; the output terminal of the multiplier three 14 outputs the demodulation result.
A method for extracting and compensating phase modulation depth in PGC phase demodulation comprises the following steps;
step 1: s (t) is shown by Bessel function for interference signals;
(1)
wherein A is DC and B is dryAmplitude of the signal, C is phase modulation depth, J 0 (C) As 0 th order Bessel function of the first kind, J 2n (C) And J 2n+1 (C) Bessel functions of the first type, respectively of even order and of odd order, n representing the order, ω c Is the angular frequency of the sinusoidal phase modulated signal,
the phase to be measured at the moment t is the phase to be measured, and t represents time; />
S (t) is I (t) after the direct current component is removed by a first direct current filter;
i (t) is an interference signal with the direct current component removed, and is obtained by expanding a Bessel function:
step 2:
frequency doubling reference signal cos omega generated by digital frequency synthesizer c t and double frequency reference signal cos2 omega c t are multiplied by the interference signal I (t) respectively, and low-pass filtering is carried out respectively to obtain a pair of phases to be detected
Orthogonal signal L of (2) 1 And L 2 The interference signal I (t) is low-pass filtered to obtain the phase to be measured>
Is a quadrature signal L of (a);
wherein LPF []For low-pass filtering operation, J 0 ()、J 1 ()、J 2 () The zero-th order, the first order and the second order Bessel functions are respectively adopted;
step 3:
quadrature signals L and L 2 After differentiation and respectively sum L 1 Dividing to obtain T and Z;
subtracting to obtain
Derivative of the phase to be measured
Through integration operation and filtering low-frequency noise, the phase to be measured is obtained
Step 4: c value, which is defined by the signal applied to the phase modulator by the signal generator, and the result from the previous step
Multiplying to obtain final result->
The invention has the beneficial effects that:
the invention extracts the phase modulation depth by applying three paths of operation, namely direct low-pass filtering, two paths of harmonic amplitude signals and harmonic differential signals obtained by differentiation of the two paths of harmonic amplitude signals, and then marks the size of the phase modulation depth from the interference signals, and compensates the amplitude modulation depth into a final operation result.
The method demodulates the signal to be detected from the interference signal by utilizing three paths of operations, eliminates the influence of light intensity interference, bessel function items and phase modulation depth, improves phase measurement precision, has good instantaneity, low harmonic distortion and large dynamic range, and can be widely applied to the fields of interference type optical fiber sensors, hydrophones, underground vibration measurement and the like.
Drawings
Fig. 1 is a schematic block diagram of a PGC improvement algorithm.
Fig. 2 is a schematic diagram of demodulation results when the simulated vibration signal is 1000 Hz.
FIG. 3 is a schematic diagram of the results of simulation experiment data with insensitive modulation depth.
Fig. 4 is a demodulation waveform diagram of the PGC improvement algorithm when c=2.
Fig. 5 is a waveform diagram of demodulation by PGC arctangent algorithm when c=2.
Detailed Description
The present invention will be described in further detail with reference to examples.
As shown in fig. 1-5: a system for extracting and compensating phase modulation depth in PGC phase demodulation comprises a DC filter 1, wherein interference signals are filtered by the DC filter 1; the input ends of the first low-pass filter 2, the first multiplier 3 and the second multiplier 4 are all connected with the interference signal I (t), and the digital frequency synthesizer generates cos omega c t、cos2ω c the frequency multiplication signals of t are respectively connected to the input ends of the first multiplier 3 and the second multiplier 4; the output end of the first low-pass filter 2 is connected with the input end of the first differentiator 5; the output end of the multiplier I3 is connected with the input end of the low-pass filter II 6; the output end of the multiplier II 4 is connected with the input end of the low-pass filter III 7; the output end of the third low-pass filter 7 is connected with the input end of the second differentiator 8; the output end of the differentiator I5 and the output end of the low-pass filter II 6 are connected to the input end of the divider I9; the output end of the second low-pass filter 6 and the output end of the second differentiator 8 are connected to the input end of the second divider 10; the output ends of the divider I9 and the divider II 10 are connected to the input end of the differentiator 11; the output of the differentiator 11 is connected to the input of the integrator 12; the output of integrator 12 is connected to a high passAn input of the filter 13; the output end of the high-pass filter 13 is connected to the input end of the multiplier III 14; the output terminal of the multiplier three 14 outputs the demodulation result.
The system obtains interference signals after analog-to-digital sampling, three paths of interference signals are obtained after direct current filtering, one path of interference signals is directly subjected to low-pass filtering, the other two paths of interference signals are multiplied with reference signals of first-order harmonic waves and second-order harmonic waves respectively and subjected to low-pass filtering, three harmonic amplitude signals are obtained, and the harmonic amplitude signals and harmonic differential signals are used for mutual operation; combining Bessel function recurrence formulas; and multiplying the magnitude of the calibration C in the interference signal into a final operation result, and eliminating the influence of light intensity disturbance, bessel function term and modulation depth through the operation.
Examples:
in the simulation experiment, the amplitude of C is obtained from the simulation modulation signal, and is compensated into a final operation result.
The specific parameters are set as follows:
the phase to be demodulated is cosine-changed, the amplitude is 2rad, the frequency is 1000Hz, the sine phase modulation frequency is 10kHz, the sampling rate is 200kHz, and the demodulation result is shown in figure 1. It can be seen from fig. 1 that the improved algorithm demodulation results in the recovery of the vibration signal.
The amplitude of the phase cosine to be demodulated is 2rad, the frequency is 100Hz, the sine phase modulation frequency is 5kHz, the sampling rate is 200kHz, C is changed in 1.3 rad-3.5 rad by taking 0.1rad as step length through setting the amplitude C of the simulation modulation signal, and each value is changed to record the corresponding demodulation phase amplitude, so that the condition that the demodulation phase amplitude changes along with the modulation depth C is obtained, as shown in figure 3, the method is insensitive to the change of the modulation depth C.
Let c=2, the remaining parameters are unchanged, the result of the modified algorithm demodulation is shown in fig. 4, and in the case of the same parameter setting, the result of the PGC-arctangent algorithm demodulation is shown in fig. 5. When the two C=2, the result of the arctangent demodulation is distorted, and the result of the improved algorithm demodulation can restore the vibration signal.
The embodiment shows that the PGC improved algorithm of the invention solves the requirements of C for taking a special value, is insensitive to the phase modulation depth and insensitive to the fluctuation of light intensity, and can effectively improve the phase demodulation precision.
Claims (1)
1. A method for extracting and compensating a phase modulation depth system in PGC phase demodulation, comprising the steps of;
step 1: s (t) is an interference signal Bessel function expansion expression;
wherein A is DC, B is amplitude of interference signal, C is phase modulation depth, J 0 (C) As 0 th order Bessel function of the first kind, J 2n (C) And J 2n+1 (C) Bessel functions of the first type, respectively of even order and of odd order, n representing the order, ω c Is the angular frequency of the sinusoidal phase modulated signal,
the phase to be measured at the moment t is the phase to be measured, and t represents time;
s (t) is I (t) after the direct current component is removed by a first direct current filter;
i (t) is an interference signal with the direct current component removed, and is obtained by expanding a Bessel function:
step 2:
frequency doubling reference signal cos omega generated by digital frequency synthesizer c t and double frequency reference signal cos2 omega c t are multiplied by the interference signal I (t) respectively, and low-pass filtering is carried out respectively to obtain a pair of phases to be detected
Orthogonal signal L of (2) 1 And L 2 The interference signal I (t) is low-pass filtered to obtain the phase to be measured>
Is a quadrature signal L of (a);
wherein LPF []For low-pass filtering operation, J 0 ()、J 1 ()、J 2 () The zero-th order, the first order and the second order Bessel functions are respectively adopted;
step 3:
quadrature signals L and L 2 After differentiation and respectively sum L 1 Dividing to obtain T and Z;
subtracting to obtain
Derivative of the phase to be measured
Through integration operation, filtering low frequency noise, obtaining the detected phase after>
Step 4: c value, which is defined by the signal applied to the phase modulator by the signal generator, and the result from the previous step
Multiplying to obtain final result->
The system for extracting and compensating the phase modulation depth in PGC phase demodulation comprises a first direct current filter, wherein an interference signal is divided into three paths after being filtered by the direct current filter (1), and the three paths are respectively connected with the input ends of a first low-pass filter (2), a first multiplier (3) and a second multiplier (4);
digital frequency synthesizer generating cos omega c t、cos2ω c the frequency multiplication signals of t are respectively connected to the input ends of the first multiplier (3) and the second multiplier (4);
the output end of the first low-pass filter (2) is connected with the input end of the first differentiator (5); the output end of the multiplier I (3) is connected with the input end of the low-pass filter II (6); the output end of the multiplier II (4) is connected with the input end of the low-pass filter III (7);
the output end of the third low-pass filter (7) is connected with the input end of the second differentiator (8); the output end of the first differentiator (5) and the output end of the second low-pass filter (6) are connected to the input end of the first divider (9); the output end of the low-pass filter II (6) and the output end of the differentiator II (8) are connected to the input end of the divider II (10); the output ends of the divider I (9) and the divider II (10) are connected to the input end of the differentiator (11); the output end of the differentiator (11) is connected to the input end of the integrator (12); the output end of the integrator (12) is connected to the input end of the high-pass filter (13); the output end of the high-pass filter (13) is connected to the input end of the multiplier III (14); the output end of the multiplier III (14) outputs the demodulation result.
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