CN102889900B - The low coherence interference demodulation method of phase slope determination monochrome frequency order of interference - Google Patents

Abstract

The present invention relates to sensory field of optic fibre, the atmospheric pressure be specifically related to based on spatial polarization low coherence interference technology is measured, disclose a kind of low coherence interference demodulation method of phase slope determination monochrome frequency order of interference, the method utilizes the phase slope of low precision and calibration function to estimate the absolute phase of a specific monochrome frequency, and the phase differential that the absolute phase of estimation and Fourier converted between the relative phase that obtains gets its immediate integer divided by 2 π, just can obtain the absolute phase of this monochrome frequency, then absolute phase is utilized to realize the high precision demodulation of low coherence interference.The present invention is applicable to the signal transacting of low coherence interference striped, and object is the order of interference accurately determining a specific monochrome frequency, and 2 π eliminating phase place are uncertain, recovers the demodulation that absolute phase realizes low coherence interference.

Description

The low coherence interference demodulation method of phase slope determination monochrome frequency order of interference

Technical field

The present invention relates to sensory field of optic fibre, particularly relate to the defining method of a kind of monochrome frequency order of interference in low coherence interference technology.

Background technology

For the demodulation of low coherence interference striped, there has been proposed the signal processing method that many kinds are different, mostly can be classified as following three classes: interfere envelope peak probe method, phase peak or crest level time determine method, and spatial frequency domain algorithm.

Such as: G.S.Kino, the people such as S.S.C.Chim and P.Sandoz are respectively by Fourier, Hilbert and Wavelet converter technique is applied in low coherence interference for extracting interference envelope, demodulation (G.S.Kino is realized by envelope peak, and S.S.C.Chim, Applied optics 29,3775-3783 (1990); S.S.C.Chim, and G.S.Kino, Applied optics 31,2550-2553 (1992); P.Sandoz, Optics Letters 22,1065-1067 (1997) .).

1996, phase-shifting technique was incorporated into (K.G.Larkin, JOSAA 13,832-843 (1996) .) in low coherence interference signal transacting by K.G.Larkin, extracts interference envelope by phase-shift method; 1997, the people such as P.Sandoz are by constructing a step function for determining crest level time in conjunction with low coherence interference information and phase-shifting technique, realize high precision demodulation (P.Sandoz, R.Devillers, and A.Plata, Journal of modern optics 44,519-534 (1997) .); 2000, the people such as A.Harasaki propose one successively comparison algorithm, uncertainty (the A.Harasaki of 2 π of phase place is eliminated by comparing envelope demodulation result and phase demodulating result, J.Schmit, and J.C.Wyant, Applied optics 39,2107-2115 (2000) .).

Nineteen ninety-five, the people such as de Groot first proposed spatial frequency domain algorithm (SFD) (P.de Groot, and L.Deck, Journal of modern optics 42,389-401 (1995) .), and modified SFD algorithm (P.DeGroot was proposed in 2002, X.Colonna de Lega, J.Kramer, and M.Turzhitsky, Applied optics 41,4571-4578 (2002) .).SFD algorithm directly carries out demodulation by phase slope, and precision is lower; Modified SFD algorithm is by a monochrome frequency extracting in wideband light source and recover its absolute phase to realize demodulation, and this method can reach the precision of laser interference in theory and not have the problem of phase ambiguity.But, follow-on SFD algorithm is main in the determination of monochrome frequency order of interference relies on the empirical parameter obtained in actual treatment, need to carry out complicated phase bias analysis, compensate the phase drift that the factor such as dispersion due to birefringent wedge causes, if can not estimate to phase drift the erroneous judgement that just there will be order of interference preferably, and then occur that error is got on pseudo-rank, limit the application of method.

Summary of the invention

Based on above-mentioned prior art Problems existing, the present invention proposes a kind of low coherence interference demodulation method of phase slope determination monochrome frequency order of interference, utilize and simply, effectively demarcate disposal route, by setting up the demarcation relation between phase slope and a certain specific monochrome frequency absolute phase, achieve the order of interference of the phase slope determination monochrome frequency utilizing low precision.

The present invention proposes a kind of low coherence interference demodulation method of phase slope determination monochrome frequency order of interference, it is characterized in that, the phase slope of low precision and calibration function is utilized to estimate the absolute phase of a specific monochrome frequency, then the phase differential between the relative phase converting this monochrome frequency obtained by absolute phase and the Fourier of estimation determines its order of interference, recover the absolute phase of this monochrome frequency for low coherence interference demodulation, the method comprises the following steps:

Step (1), carry out calibration experiment, determine calibration function, atmospheric pressure is controlled with the pressure interval monotone increasing chosen in experiment, pressure range covers whole measurement range, choosing of pressure interval need meet: the phase changing capacity that pressure interval variation causes is no more than pi/2, specifically comprises following three steps:

Along with the monotone increasing of atmospheric pressure changes, obtain phase slope array σ respectively _iwith the specific monochrome frequency Ω of correspondence _krelative phase array φ _i(Ω _k), wherein, relative phase array φ (Ω _k) obtained by Fourier conversion, i be pressure change sequence number (i=1,2 ... N), the corresponding array sequence of initial pressure number 1, stops the corresponding array sequence N of pressure;

To relative phase array φ _i(Ω _k) carry out phase unwrapping to obtain absolute phase array according to recursive expression below

In above formula, floor [] function returns the maximum integer being less than or equal to parameter in bracket;

With phase slope array for independent variable, with the absolute phase array after launching for dependent variable, obtain calibration function expression formula E (σ) by cubic polynomial matching, calibration function meets fitting expression below:

In above formula, for the estimation absolute phase array obtained after cubic polynomial matching;

When step 2, demodulation, phase slope value σ is substituted into the calibration function E (σ) obtained in calibration experiment and obtains monochrome frequency Ω _kthe estimated value of absolute phase, by the estimated value of absolute phase array and Fourier, then the phase differential converted between the relative phase array obtained gets its immediate integer divided by 2 π, obtains monochrome frequency Ω _korder of interference, namely by expression formula determination order of interference below:

$m=\mathrm{int}\left[\frac{E\left(\mathrm{\σ}\right)-\mathrm{\φ}\left({\mathrm{\Ω}}_k\right)}{2\mathrm{\π}}\right]$

In above formula, m is order of interference, and int [] function returns the immediate round values of parameter in bracket, once determine order of interference, recovers its absolute phase for low coherence interference demodulation result by expression formula below:

Phase slope in described step 1 and described step 2, its acquisition comprises the following steps:

First, quick Fourier transformation is carried out to discrete interference signal x (n) of a frame gathered

$X\left(k\right)X\left(k\right)=\underset{n=0}{\overset{M-1}{\mathrm{\Σ}}}x\left(n\right)\exp [-j\frac{2\mathrm{\π}}{M}k]=A\left({\mathrm{\Ω}}_k\right)e^{\mathrm{i\φ}\left({\mathrm{\Ω}}_k\right)}$

Wherein, M is length and the effective picture dot number of CCD of a frame interference signal, and k is FFT sequence number, the monochrome frequency Ω that different sequence numbers is corresponding different _k, φ (Ω _k) be monochrome frequency Ω _krelative phase, A (Ω _k) be monochrome frequency Ω _kamplitude; Then, the component frequency (Ω that amplitude is higher is chosen _p, Ω _p+q), carry out phase unwrapping according to recursive expression below:

$\left\{\begin{array}{c}{\mathrm{\φ}}^{,}\left({\mathrm{\Ω}}_p\right)=\mathrm{\φ}\left({\mathrm{\Ω}}_p\right)\\ {\mathrm{\φ}}^{,}\left({\mathrm{\Ω}}_{p+i}\right)=\mathrm{\φ}\left({\mathrm{\Ω}}_{p+i}\right)-2\mathrm{\π}\×\left\{\mathrm{floor}\right[\frac{\mathrm{\φ}\left({\mathrm{\Ω}}_{p+i}\right)-{\mathrm{\φ}}^{,}\left({\mathrm{\Ω}}_{p+i-1}\right)}{2\mathrm{\π}}]+1\},i=1,...,q,\end{array}\right.$

In above formula, φ ' (Ω _k) be phase place after launching, p is FFT sequence number corresponding to initial frequency, and q is the length of the frequency range chosen; Finally, carry out least square linear fit to phase place after frequency-expansion and obtain fitting a straight line, the slope of straight line is phase slope σ.

Compared with prior art, the present invention does not relate to empirical parameter, does not need dynamically to estimate phase drift, compensate, and method is directly perceived, implements simple, has very strong applicability.Details are as follows for the concrete implementation result that the present invention reaches:

1, this method utilizes the phase slope of low precision and calibration function accurately can determine the order of interference of a specific monochrome frequency, and recover its absolute phase for low coherence interference demodulation in conjunction with relative phase, relative to Direct Phase Slope Method, demodulation accuracy has and significantly improves;

2, this method effectively can overcome the phase drift problem that the factor such as non-normal incidence, F-P end face reflection due to birefringent wedge dispersion, light causes, do not need dynamically to estimate phase place, compensate, and do not relate to experience estimation parameter, method is simple, be convenient to implement, there is very strong applicability;

3, monochrome frequency not necessarily centre frequency, may be used for determining that the order of interference of any one monochrome frequency is determined;

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 obtained after the frame interference signal gathered and quick Fourier transformation in actual demodulation device, and wherein (a) is the frame original interference signal under 130kPa; B () is spectrogram;

Fig. 3 is respectively the atmospheric pressure-phase slope curve and atmospheric pressure-relative phase curve that obtain in calibration experiment, and wherein (a) is atmospheric pressure-phase slope curve; B () is atmospheric pressure-relative phase curve;

Fig. 4 is absolute phase curve after the atmospheric pressure-expansion obtained in calibration experiment;

Fig. 5 is respectively the atmospheric pressure-relative phase curve and atmospheric pressure-phase differential curve that obtain in experiment demodulation, and wherein (a) is atmospheric pressure-relative phase curve; B () is atmospheric pressure-phase differential curve;

Fig. 6 is respectively order of interference and the estimation error curve of the monochrome frequency determined by the inventive method in experiment demodulation, and wherein (a) is atmospheric pressure-order of interference curve; B () is atmospheric pressure-estimation error curve;

Fig. 7 is respectively the monochrome frequency absolute phase curve of atmospheric pressure-phase slope curve of obtaining in experiment demodulation and atmospheric pressure-recover, and wherein (a) is atmospheric pressure-phase slope curve; B () is atmospheric pressure-absolute phase curve.

Embodiment

Below by specific embodiment and accompanying drawing, the invention will be further described, and following examples are descriptive, are not determinate, can not limit protection scope of the present invention with this.

Fig. 1 is the structural representation of a kind of spacescan type low coherence interference Fibre Optical Sensor atmospheric pressure demodulating equipment for atmospheric pressure measurement that the inventive method relates to;

Order of interference defining method of the present invention is verified by experiment, and its result is specifically see Fig. 2 to Fig. 7.

The light that wideband light source (LED) 1 sends is through coupling mechanism 2 introductory technique Fabry-Perot-type (F-P) sensor 3, the sensing chamber of F-P sensor is made up of fiber end face and flexible silicon diaphragm, silicon diaphragm generation elastic deformation can be caused when ambient atmosphere pressure changes, be F-P cavity long message by the convert information of atmospheric pressure, the light signal modulated by F-P sensor is derived from the outlet of coupling mechanism 2, and by optical path scanning device, when the optical path difference that 3 optical path differences caused and optical path scanning device produce matches, local significantly low coherence interference striped can be formed, interference fringe is accepted eventually through a CCD.Wherein, optical path scanning device is made up of self-focusing collimation lens 4, the polarizer 5, birefringent wedge 6 and analyzer 7, and birefringent wedge 6 can see the F-P sensor of space distribution as.

Produce the atmospheric pressure sources of the atmospheric pressure required for the confirmatory experiment of order of interference defining method of the present invention by high precision, high stable, this pressure source precision is 0.01kPa.The concrete steps of confirmatory experiment comprise:

1st step, carries out calibration experiment, determines calibration function, and controlling atmospheric pressure in calibration experiment is that interval is from 110kPa monotone increasing to 170kPa with 0.2kPa.The spectrogram that Fig. 2 (a) and (b) obtain after being respectively a frame original interference signal under 130kPa and quick Fourier transformation (FFT); Atmospheric pressure-phase slope the curve of Fig. 3 (a) for obtaining in calibration experiment, wherein, phase slope is obtained by step below: first, carries out Fourier conversion be transformed into frequency domain X (k) to original interference signal x (n) $X\left(k\right)=\underset{n=0}{\overset{M-1}{\mathrm{\Σ}}}x\left(n\right)\exp [-j\frac{2\mathrm{\π}}{M}k]=A\left({\mathrm{\Ω}}_k\right)e^{\mathrm{i\φ}\left({\mathrm{\Ω}}_k\right)},$ Wherein, M is

The length (in experimental provision as shown in Figure 1, the valid pixel of CCD is 3000, so M=3000) of one frame interference signal, φ (Ω _k) be monochrome frequency Ω _krelative phase, A (Ω _k) be monochrome frequency Ω _kamplitude, be (Ω according to the scope that the amplitude characteristic selected phase of Fig. 2 (b) launches ₁₅₇₂, Ω ₁₅₈₉), i.e. p=1572, q=17; Then, phase unwrapping is carried out according to recursive expression below:

Wherein floor [] function returns the maximum integer being less than or equal to parameter in bracket; Finally, carry out least square linear fit to phase place after expansion and obtain fitting a straight line, the slope of straight line is phase slope.A phase slope value can be obtained according to above-mentioned phase slope acquisition methods under each pressure, just can obtain the phase slope curve with atmospheric pressure change shown in Fig. 3 (a); Atmospheric pressure-monochrome frequency relative phase the curve of Fig. 3 (b) for obtaining in calibration experiment, wherein, monochrome frequency is chosen as Ω ₁₅₇₇, relative phase is obtained by Fourier conversion.

2nd step, to the relative phase array φ obtained in the 1st step _i(Ω ₁₅₇₇), i=1,2 ..., 301, carry out phase unwrapping according to recursive expression below:

Figure 4 shows that absolute phase curve after the atmospheric pressure-expansion obtained after recursive expression above.

3rd step, carries out cubic polynomial matching to the phase slope array obtained by the 1st step and the 2nd step and absolute phase array, and wherein, phase slope array is independent variable, and absolute phase array is dependent variable, can obtain calibration function wherein E (σ)=274.800+99.084 σ+5.595 σ ²+ 0.543 σ ³.

In order to the validity of verification method, We conducted demodulation confirmatory experiment, control in experiment demodulation atmospheric pressure with 0.2kPa be interval from 109.9kPa monotone increasing to 169.9kPa, the atmospheric pressure in this and calibration experiment is just in time spaced.Under each atmospheric pressure, all use same phase slope acquisition methods can obtain phase slope value σ above, and carry it into calibration function E (σ)=274.800+99.084 σ+5.595 σ obtained in calibration experiment ²+ 0.543 σ ³obtain monochrome frequency Ω ₁₅₇₇the estimated value of absolute phase, then utilize the absolute phase of estimation relative phase φ (the Ω obtained is converted with Fourier ₁₅₇₇) between phase differential determination order of interference.Atmospheric pressure-relative phase the curve and atmospheric pressure-phase differential curve that obtain in experiment demodulation is respectively shown in Fig. 5 (a) He (b), can find out, one-to-one relationship is presented between relative phase and phase differential, and phase differential curve has significantly " step-characteristic ", each " ladder " represents a specific order of interference.Then, order of interference determination formula is below utilized just can to obtain monochrome frequency Ω ₁₅₇₇order of interference: fig. 6 (a) and (b) are respectively the order of interference and corresponding estimation error that are obtained by order of interference determination formula above, and wherein estimation error is passed through obtain, as can be seen from estimation error curve, maximum estimation error is approximately " 0.2 ", less than effectively estimating 1/2 of interval " 0.5 ", illustrating that the inventive method is not only feasible, and having good reliability.Once determine order of interference, just monochrome frequency Ω can be recovered by expression formula below ₁₅₇₇absolute phase: thus utilize absolute phase to realize low coherence interference demodulation.Fig. 7 (a) and (b) are respectively the absolute phase curve directly utilizing phase slope and the inventive method to obtain, can find out, the atmospheric pressure that the inventive method obtains-absolute phase curve has the extraordinary linearity, and although the curve directly utilizing phase slope to obtain presents linearly on the whole, the linearity of local is poor.

Claims (2)

1. the low coherence interference demodulation method of a phase slope determination monochrome frequency order of interference, it is characterized in that, the phase slope of low precision and calibration function is utilized to estimate the absolute phase of a specific monochrome frequency, then the phase differential between the relative phase converting this monochrome frequency obtained by absolute phase and the Fourier of estimation determines its order of interference, recover the absolute phase of this monochrome frequency for low coherence interference demodulation, the method comprises the following steps:

Step (1), carry out calibration experiment, determine calibration function, atmospheric pressure is controlled with the pressure interval monotone increasing chosen in experiment, pressure range covers whole measurement range, choosing of pressure interval need meet: the phase changing capacity that pressure interval variation causes is no more than pi/2, specifically comprises following three steps:

Along with the monotone increasing of atmospheric pressure changes, obtain phase slope array σ respectively _iwith the specific monochrome frequency Ω of correspondence _krelative phase array φ _i(Ω _k), wherein, relative phase array φ (Ω _k) obtained by Fourier conversion, i is pressure change sequence number, i=1,2 ... N, the corresponding array sequence of initial pressure number 1, stops the corresponding array sequence N of pressure;

To relative phase array φ _i(Ω _k) carry out phase unwrapping to obtain absolute phase array according to recursive expression below

In above formula, floor [] function returns the maximum integer being less than or equal to parameter in bracket;

With phase slope array for independent variable, with the absolute phase array after launching for dependent variable, obtain calibration function expression formula E (σ) by cubic polynomial matching, calibration function meets fitting expression below:

In above formula, for the estimation absolute phase array obtained after cubic polynomial matching;

When step 2, demodulation, phase slope value σ is substituted into the calibration function E (σ) obtained in calibration experiment and obtains monochrome frequency Ω _kthe estimated value of absolute phase, by the estimated value of absolute phase array and Fourier, then the phase differential converted between the relative phase array obtained gets its immediate integer divided by 2 π, obtains monochrome frequency Ω _korder of interference, namely by expression formula determination order of interference below:

$m=\mathrm{int}\left[\frac{E\left(\mathrm{\σ}\right)-\mathrm{\φ}\left({\mathrm{\Ω}}_k\right)}{2\mathrm{\π}}\right]$

In above formula, m is order of interference, and int [] function returns the immediate round values of parameter in bracket, once determine order of interference, recovers its absolute phase for low coherence interference demodulation result by expression formula below:

2. the low coherence interference demodulation method of phase slope determination monochrome frequency order of interference as claimed in claim 1, is characterized in that, the phase slope in described step 1 and described step 2, and its acquisition comprises the following steps:

First, quick Fourier transformation is carried out to discrete interference signal x (n) of a frame gathered

$X\left(k\right)X\left(k\right)=\underset{n=0}{\overset{M-1}{\mathrm{\Σ}}}x\left(n\right)\exp [-j\frac{2\mathrm{\π}}{M}k]=A\left({\mathrm{\Ω}}_k\right)e^{\mathrm{i\φ}\left({\mathrm{\Ω}}_k\right)}$

Wherein, M is length and the effective picture dot number of CCD of a frame interference signal, and k is FFT sequence number, the monochrome frequency Ω that different sequence numbers is corresponding different _k, φ (Ω _k) be monochrome frequency Ω _krelative phase, A (Ω _k) be monochrome frequency Ω _kamplitude; Then, the component frequency Ω that amplitude is higher is chosen _p, Ω _p+q, carry out phase unwrapping according to recursive expression below:

$\left\{\begin{array}{c}{\mathrm{\φ}}^{,}\left({\mathrm{\Ω}}_p\right)=\mathrm{\φ}\left({\mathrm{\Ω}}_p\right)\\ {\mathrm{\φ}}^{,}\left({\mathrm{\Ω}}_{p+i}\right)=\mathrm{\φ}\left({\mathrm{\Ω}}_{p+i}\right)-2\mathrm{\π}\×\left\{\mathrm{floor}\right[\frac{\mathrm{\φ}\left({\mathrm{\Ω}}_{p+i}\right)-{\mathrm{\φ}}^{,}\left({\mathrm{\Ω}}_{p+i-1}\right)}{2\mathrm{\π}}]+1\},i=1,...,q\end{array}\right.$

In above formula, φ ' (Ω _k) be phase place after launching, p is FFT sequence number corresponding to initial frequency, and q is the length of the frequency range chosen; Finally, carry out least square linear fit to phase place after frequency-expansion and obtain fitting a straight line, the slope of straight line is phase slope σ.