CN102607612B - Low-coherence interference demodulation method based on monochrome frequency absolute phase - Google Patents
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Abstract
The invention provides a low-coherence interference demodulation method based on a monochrome frequency absolute phase, belonging to the field of optical fiber sensing. The low-coherence interference demodulation method based on the monochrome frequency absolute phase is widely applied to measurements of various static physical quantities, such as temperature, pressure, displacement and refractive index, and detection of object three-dimensional feature. According to the method, a Fabry-Perot sensor is selected as a sensing element for sensing external air pressure intensity variation, an optical wedge is used as an optical path difference space scanning element, and interference strips are formed in a partial area with an optical path difference of zero. The low-coherence interference demodulation method comprises the following steps of: firstly, carrying out Fourier conversion on an interference signal to obtain phase information which is aliased within a section of (-pi, pi); then selecting a phase with a standard frequency as a reference phase, carrying out phase unwrapping according to frequency-phase monotonous properties, and carrying out linear least-squares regression on the unwrapped phase so as to obtain a fitting straight intercept; and finally, dividing the intercept by an integer part of 2*pi, so as to obtain an interference order of a reference frequency; and finally, obtaining the absolute phase of the reference frequency by combining a relative phase obtained through the Fourier conversion. Therefore, the demodulation is realized.
Description
Technical field
The present invention relates to a kind of low coherence interference demodulation method based on monochrome frequency absolute phase, belong to sensory field of optic fibre.
Background technology
Low coherence interference can overcome the phase fuzzy problem existed in laser interference, measurement range is no longer confined to λ/4, there is measurement range in theory that do not limit, high precision, large range measuring can be carried out to a lot of absolute physical amount, low coherence interference technology is widely used at sensory field of optic fibre, the such as measurement of static physical amount (temperature, pressure, displacement and refractive index), the detection of object dimensional appearance and optical coherence tomography etc.
The envelope peak position of location low coherence interference striped or center crest location are the methods of the acquisition interference fringe translation information usually adopted, and these methods are all from interference fringe, directly obtain translation information carry out demodulation.In addition, phase information may be used for demodulation equally, and spatial frequency domain algorithm (SFDA), phase-shift method and dual wavelength algorithm etc. are all the demodulation methods proposed based on phase place.Generally, the demodulation method based on phase place is more responsive than the change of demodulation method to measurand based on envelope, can obtain higher demodulation accuracy.But precision that demodulation obtains is often not high directly to utilize phase slope to carry out, and the displacement that the phase place of monochrome frequency and measurand cause is directly related, and can be obtained by discrete Fourier (or phase shift algorithm), but the phase place obtained after Discrete Fourier Transform is aliasing in (-π, π) in interval, there is the uncertain problem of 2 π or order of interference, therefore first must determine that order of interference could recover absolute phase, so the recovery of absolute phase or the determination of order of interference are very important problems.We can utilize the intercept of the least square fitting launching rear phase place to determine order of interference, and relative to Direct Phase slope demodulation method, the method can obtain higher demodulation accuracy.
Summary of the invention
The object of the invention is to the precision improving phase demodulating method, utilize the order of interference of the intercept information determination monochrome frequency after phase unwrapping to recover its absolute phase, realize the wide range of low coherence interference, high-acruracy survey, a kind of low coherence interference demodulation method based on monochrome frequency absolute phase is provided.
Specific embodiment of the invention method:
Fabry-Perot (F-P) sensor is adopted to experience the change of ambient atmos pressure in the present invention, two faces of F-P cavity form sensing interferometer, wedge forms reception interferometer as optical path difference spacescan element, form interference fringe at the regional area of zero optical path difference, demodulation method comprises:
1st, first the method carries out Discrete Fourier Transform to the low coherence interference signal received, and obtain amplitude-frequency information and be aliasing in the phase information in (-π, π), the amplitude-versus-frequency curve of interference signal is made up of Gauss's carrier component of two groups of symmetries;
2nd, in positive frequency domain components part, the frequency that pressure-relative phase linearity is best in an order of interference is selected to carry out phase unwrapping as reference frequency;
3rd, using the relative phase of reference frequency as carrying out phase unwrapping with reference to phase place, to frequency-expansions afterwards phase place carry out least square linear fit and obtain Linear intercept after matching, by intercept divided by 2 π, the integral part obtained is the order of interference of reference frequency;
4th, Discrete Fourier Transform obtains the relative phase of reference frequency, obtains the order of interference of reference frequency, so just recover the absolute phase of reference frequency, thus can obtain pressure information, realize demodulation through the calculating process of above-mentioned 1st to the 3rd step.
The concrete grammar of the phase unwrapping described in the 3rd step is: phase place is along with the increase monotone decreasing of frequency, and this is the theoretical foundation of phase unwrapping.If reference frequency is chosen as Ω
j, its relative phase is
as the fixed phase of phase unwrapping, carry out phase unwrapping by recursive expression below:
Wherein, u () is step function.
Theoretical foundation of the present invention is:
Generally common wideband light source, its light source light spectrum is all Gaussian distribution or class Gaussian distribution, and therefore the light intensity of low coherence interference can be expressed as:
I(x)＝γexp{[-α(x-x
0)]
2}cos[β(x-x
0)] (1)
Wherein, α, β, γ are the constants relevant with light path system, x
0it is the corresponding coordinate in wedge in zero optical path difference position.
For simplifying the analysis, we define:
f(x)＝γexp[-(αx)
2] (2)
(2) the continuous Fourier of formula is transformed to F (j Ω), and F (j Ω) is Gaussian function equally, and Ω is frequency.The time shift converted according to continuous Fourier and frequency shift property, the continuous Fourier conversion of (1) formula can be expressed as:
The amplitude-versus-frequency curve of the Fourier conversion of interference signal is made up of two symmetrical Gaussian functions, the axis of symmetry of function lays respectively at Ω=β and Ω=-β place, system determines that rear β is a constant, in optical spectrum is analyzed, negative frequency component does not have actual physical significance, do not consider, therefore, amplitude-frequency function and phase frequency function can be expressed as:
A(jΩ)＝1/2F[j(Ω-β)] (4)
From (5) formula, we can find out that phase place is the linear function of frequency, and the external physical quantity of phase slope namely with tested is directly related, not by the impact of order of interference.If Ω
jthe reference frequency selected, Ω
jabsolute phase can be expressed as:
From order of interference angle, absolute phase can be write as again:
Wherein φ (Ω
j) be through Discrete Fourier Transform after the relative phase that obtains, n is order of interference.Simultaneous formula (6) and formula (7) can obtain:
φ(Ω
j)＝-xΩ
j+2nπ (8)
As can be seen from formula (8) we, the intercept of phase frequency curve be namely the n of 2 π doubly, wherein n is the order of interference of reference frequency.So, we just can obtain the order of interference of reference frequency by following formula:
Wherein, T is the intercept of the fitting a straight line of phase place after least square linear fit after frequency-expansion, and function int () is for returning nearest round values, and so, the absolute phase finally obtaining reference frequency can be expressed as:
Beneficial effect of the present invention and advantage are:
1, the inventive method utilizes the phase information of frequency domain to carry out demodulation, the acquisition of phase place can utilize Discrete Fourier Transform to obtain, and relative to the Fourier filtering often used in time-domain detection, need not carry out discrete Fourier inverse transformation, calculated amount reduces half, is applicable to high speed demodulation occasion;
2, the acquisition of phase place is except utilizing Discrete Fourier Transform, and phase-shift method can also be utilized to obtain, and operand can be reduced further;
3, the derivation of the inventive method is based on the wideband light source of Gaussian distribution, but is equally applicable to the wideband light source of other distributions;
4, the inventive method is relative to the Direct Phase Slope Method in frequency-domain demodulation, and demodulation accuracy is improved significantly;
Accompanying drawing explanation
Fig. 1 is spacescan type low coherence interference Fibre Optical Sensor atmospheric pressure demodulating equipment schematic diagram;
Fig. 2 is the partial frequency spectrum figure that the frame interference signal that gathers in actual demodulation device and Discrete Fourier Transform obtain, and wherein in (a), three curves are respectively: (1) is the frame original signal without any process under pressure 30kPa; (2) be after filtering after filtering signal; (3) be envelope signal; B () is partial frequency spectrum family curve;
Fig. 3 is pressure-relative phase linearity comparison diagram in the next order of interference of different frequency, and wherein (a) is frequency omega=1548 time pressure-relative phase figure; B () is frequency omega=1555 time pressure-relative phase figure; C () is frequency omega=1558 time pressure-relative phase figure; D () is frequency omega=1567 time pressure-relative phase figure;
Fig. 4 is comparison diagram before and after phase unwrapping under pressure 100kPa, and wherein, (a) is the aliasing phase place before phase unwrapping; B () is the linear phase after phase unwrapping;
Fig. 5 is the slope of phase place after least square linear fit and intercept figure after launching, and wherein, (a) is pressure-slope replot; B () is pressure-intercept figure;
Fig. 6 is pressure-relative phase figure that reference frequency Ω=1558 time obtain and the pressure-order of interference figure calculated by this inventive method, and wherein, (a) is pressure-relative phase figure; B () is pressure-order of interference figure;
Fig. 7 is the pressure-slope replot and pressure-absolute phase figure that adopt phase slope method and the inventive method to obtain respectively, wherein, and pressure-slope replot that (a) obtains for phase slope method; B pressure-absolute phase figure that () obtains for the inventive method;
Fig. 8 is demodulating error curve map, and wherein, (a) is the error of phase slope method; The error of (b) the inventive method;
In Fig. 1: 1-wideband light source, 2-photo-coupler, 3-(F-P) sensor, 4-self-focusing collimation lens, the 5-polarizer, 6-birefringent wedge, 7-analyzer, 8-line array CCD.
Embodiment
Embodiment
Accompanying drawing 1 is the low coherence interference demodulating equipment figure based on monochrome frequency absolute phase that the inventive method relates to, and in conjunction with the measurement of external atmospheric pressure, is described this method: demodulation method of the present invention is verified by experiment, see accompanying drawing 2-accompanying drawing 8.
The light that wideband light source (LED) 1 sends imports F-P sensor 3 through coupling mechanism 2, the change of atmospheric pressure is converted to optical path difference as the sensitive element experiencing external atmospheric pressure by F-P sensor, two faces of F-P cavity form sensing interferometer, the light signal modulated by F-P sensor is derived from the outlet of coupling mechanism 2, and transmission self-focusing collimation lens 4 successively, the polarizer 5, birefringent wedge 6 and analyzer 7, final arrival line array CCD 8, the F-P sensor that birefringent wedge 6 can see space distribution as forms reception interferometer, when 5 optical path differences caused and 3 optical path differences caused match, obvious low coherence interference striped can be produced at 8 corresponding regional areas.
The atmospheric pressure needed in experiment is produced by high precision, high stable pressure source, and this pressure source can reach the control accuracy of 10Pa, and controlling pressure in experiment is that interval increases to 170kPa from 30kPa dullness with 1kPa, and the time interval that pressure changes is 5 minutes.Effective pixel number of line array CCD is 3000 points, utilize the external sampling clock of pixel synchronizing pulse as capture card of CCD, the digital signal obtained after carrying out analog to digital conversion is made up of 3000 discrete data points, represents a CCD pixel separation between every two adjacent datas.
Accompanying drawing 2 is a frame interference signal of CCD output and the part amplitude-versus-frequency curve after Discrete Fourier Transform under 30kPa, and three curves wherein in accompanying drawing 2 (a) are respectively: (1) is the interference signal of a frame without any process; (2) be after filtering after filtering signal; (3) be envelope signal.Accompanying drawing 2 (b) is the part amplitude-versus-frequency curve after Discrete Fourier Transform, can find out that amplitude-versus-frequency curve is made up of the carrier component of two groups of symmetries, initial frequency according to the expansion of amplitude-versus-frequency curve selected phase is Ω=1547, and cutoff frequency is Ω=1572.The attached selection schematic diagram that Figure 3 shows that reference frequency, the selection of reference frequency determines according to the linearity of pressure-relative phase in an order of interference, relative phase is obtained by Discrete Fourier Transform, and wherein (a) is the pressure under frequency omega=1548-relative phase figure; B () is the pressure under frequency omega=1555-relative phase figure; C () is the pressure under frequency omega=1558-relative phase figure; D () is the pressure under frequency omega=1567-relative phase figure; As can be seen from accompanying drawing 3, there is bigger difference in the linearity of the pressure-relative phase under different frequencies, certainly, accompanying drawing 3 only gives the linearity comparison diagram under four frequencies, and their linearity is respectively 0.99582,0.99578,0.99984 and 0.98470.The scope of phase unwrapping is (1547,1572), and table 1 is the linearity contrast table of pressure-relative phase in the next order of interference of all frequencies within the scope of phase unwrapping:
Table 1 linearity contrast table
As can be seen from Table 1, the linearity under frequency omega=1558 is 0.99984 to the maximum, and therefore reference frequency is chosen as Ω
j=1558.
The concrete implementation step that the present invention is based on the low coherence interference demodulation method of monochrome frequency absolute phase is as follows:
1st, first Discrete Fourier Transform is carried out to the digitalized intervention signal obtained through capture card, time-domain signal x (n) is transformed into frequency domain X (k), wherein
through linearity analysis above, select Ω
j=1558 is reference frequency.
2nd, the relative phase of reference frequency that obtains of Discrete Fourier Transform
for fixed phase carries out phase unwrapping, the scope of phase unwrapping is (1547,1572), and phase unwrapping carries out according to recursive expression below:
Accompanying drawing 4 is comparison diagram before and after phase unwrapping under pressure 100kPa, accompanying drawing 4 (a) is for being aliasing in (-π before phase unwrapping, relative phase π), accompanying drawing 4 (b) is the phase place after above-mentioned phase unwrapping and the fitting a straight line after least square linear fit, can find out, frequency after phase unwrapping and the linear relationship between phase place obtain and well highlight, and this also demonstrates the correctness of phase developing method conversely.
Attachedly Figure 5 shows that the slope and intercept figure that obtain after phase unwrapping, least square linear fit, wherein accompanying drawing 5 (a) is pressure-slope replot, accompanying drawing 5 (b) is pressure-intercept figure, slope totally presents the relation of linear change continuously along with the change of pressure, phase slope can be directly utilized to carry out demodulation, and intercept presents obvious stepped change along with the change of pressure, this matches with theoretical analysis above.
Attachedly Figure 6 shows that reference frequency Ω
jthe relative phase (obtaining through Discrete Fourier Transform) of=1558 and order of interference figure, wherein accompanying drawing 6 (a) is pressure-relative phase figure, accompanying drawing 6 (b) is pressure-interference order of interference figure, relative phase and order of interference present one-to-one relationship, thus demonstrate the correctness of the inventive method.
In order to the feasibility of checking the inventive method quantitative further, the inventive method and Direct Phase Slope Method are contrasted from the linearity and demodulating error two aspects, accompanying drawing 7 and 8 is comparing result, wherein accompanying drawing 7 (a) the linearity analysis figure that is pressure-phase slope, although slope and pressure are still linear on the whole, the linearity is 0.9998129, but linearly bad in subrange, the pressure that in accompanying drawing 7, (b) obtains for the inventive method-absolute phase linearity analysis figure, no matter from entirety or local, pressure and absolute phase all show good linear relationship, the linearity is 0.9999816, the linearity of the method that the present invention proposes is compared phase slope method and is significantly improved, accompanying drawing 8 is the pressure of actual set and carries out the error comparison diagram between the pressure after cubic polynomial matching by the data that two kinds of methods obtain, accompanying drawing 8 (a) is depicted as the error of phase slope method, the error that shown in accompanying drawing 8 (b), the inventive method obtains, can find out, the method maximum error mentioned in invention is 0.15kPa, and the maximum error of phase slope method is up to 2kPa, demodulation accuracy can improve more than 13 times, and demodulation accuracy obtains obvious improvement.
Claims (2)
1., based on a low coherence interference demodulation method for monochrome frequency absolute phase, it is characterized in that the method comprises:
1st, first carry out Discrete Fourier Transform to interference signal, obtain amplitude-frequency information and be aliasing in the phase information in (-π, π), the amplitude-versus-frequency curve of interference signal is made up of the carrier component of two groups of symmetries;
2nd, in positive frequency domain components part, the frequency that pressure-relative phase linearity is best in an order of interference is selected to carry out phase unwrapping as reference frequency;
3rd, with the relative phase of reference frequency for fixed phase carries out phase unwrapping, then carry out to phase place after frequency-expansion the intercept that least square linear fit obtains straight line after matching, intercept is the order of interference of reference frequency divided by the integral part that 2 π obtain;
4th, Discrete Fourier Transform obtains the relative phase of reference frequency, obtains the order of interference of reference frequency, so just recover the absolute phase of reference frequency, thus obtain pressure information, realize demodulation through the calculating process of above-mentioned 1st to the 3rd step.
2. method according to claim 1, is characterized in that the concrete grammar of the phase unwrapping described in the 3rd step is: with reference frequency Ω
jrelative phase
for fixed phase, carry out phase unwrapping according to recursive expression below:
Wherein, u () is step function.
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| CN103542870B (en) * | 2013-10-12 | 2016-03-30 | 天津大学 | Ac modulation type low coherence interference demodulating system |
| CN103759748B (en) * | 2014-01-08 | 2015-12-30 | 天津大学 | Position-based is correlated with the quick low coherence interference demodulation method of dispersion characteristics |
| CN104730001A (en) * | 2015-04-16 | 2015-06-24 | 福州大学 | High-time-resolution high-precision elliptically-polarized measurement device and high-time-resolution high-precision elliptically-polarized measurement method |
| CN106643835B (en) * | 2015-11-03 | 2019-07-05 | 中国石油天然气股份有限公司 | Fabry-perot optical fiber chamber demodulation method and device and Fabry-perot optical fiber interferometer |
| CN109141700A (en) * | 2018-08-17 | 2019-01-04 | 天津大学 | The double light source low coherence interference pressure-temperature measuring systems of Fabry-perot optical fiber and method |
| CN115427766A (en) * | 2020-04-20 | 2022-12-02 | 北京佰为深科技发展有限公司 | Fabry-Perot sensor cavity length demodulation system and Fabry-Perot sensor cavity length demodulation method |
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