CN103697923A - Method for demodulating extrinsic fiber Fabry-Perot interferometer cavity length - Google Patents

Abstract

The invention discloses a method for demodulating the extrinsic fiber Fabry-Perot interferometer cavity length. The method comprises the following steps: step 1, measuring the intensity value of original light entering an F-P cavity through an optical power meter; step 2, measuring the intensity value of light reflected back from the F-P cavity through the optical power meter; step 3, substituting the measured intensity values of the incident light and the reflected light in a cavity length expression; step 4, obtaining an F-P cavity length solution by using a multi-wavelength intensity demodulation method. The method can extend the demodulation range of the fiber Fabry-Perot Interferometer cavity length. Compared with a conventional fiber Fabry-Perot interferometer cavity light intensity demodulation method, the method is more accurate, and the measuring accuracy can reach 0.1 microns. A measuring system is simple in device, and easy to operate, and measured data are accurate.

Description

A kind of method that demodulation extrinsic type fiber F-P is long

Technical field

The invention belongs to Fibre Optical Sensor application, particularly proposed the long new method in light intensity signal demodulation F-P chamber that a kind of utilization is returned from optical fiber extrinsic type Fabry-Perot (EFPI) cavity reflection.

Background technology

Along with the development of modern surveying technology, Fibre Optical Sensor is more and more subject to people's attention.Optical fibre Fabry-perot (F-P) sensor has that measuring accuracy is high, response band is wide, miniature, anti-strong electromagnetic, is convenient to the advantages such as remote measurement with respect to other Fibre Optical Sensors, thereby is used for the rugged surroundings such as high temperature, inflammable and explosive, strong electromagnetic.Fabry-perot optical fiber sensor-based system mainly comprises two parts, Fabry-perot optical fiber pressure transducer and signal demodulating system for perception external information, the two performance separately and the cooperate degree of combining use directly affect the performance of sensor-based system, so high-precision optical fiber Fabry-Perot sensor technology and reliable and stable high speed signal demodulation techniques all obtain larger concern.

The Fiber Optic Fabry-Perot Sensor overwhelming majority for physical quantities such as displacement, temperature, pressure, stress, strain, voltage, electric field, magnetic field, vibration and refractive indexes realizes by the demodulation that Fabry-Perot-type cavity chamber is grown.For realizing the cavity length demodulating of Fiber Optic Fabry-Perot Sensor, various demodulation schemes are suggested in succession, and common demodulation method is divided into phase demodulating method and intensity demodulation method.

Phase demodulating method be subject to quantization error and environmental impact little, demodulation accuracy is high, but the Fourier transform demodulation method for Fiber Optic Fabry-Perot Sensor cavity length demodulating meets the approximate hypothesis of two-beam interference based on Fabry-Perot multiple-beam interference at present, the range of application that has limited the Fiber Optic Fabry-Perot Sensor cavity length demodulating principle based on Fourier transform, makes the method be confined to the cavity length demodulating of low fineness Fabry-Perot-type cavity.

Intensity demodulation method generally adopts monochromatic source, directly utilizes interference output intensity to solve fiber Fabry-Pérot cavity chamber long.Intensity demodulation method realizes simply, direct and cost is low, is the method that Fiber Optic Fabry-Perot Sensor is the most often used.But traditional intensity demodulation method adopts single wavelength light source to carry out demodulation by the relation of reflective light intensity and chamber length.The long relation in reflective light intensity and chamber is a class cosine function, interferes long solution the in corresponding a plurality of chambeies of output intensity value for one, is the long multivalued function in chamber, by interfering output intensity cannot direct solution chamber long.For meeting the relation of the long approximately linear of reflective light intensity and chamber, must make Fabry-Perot sensor measurement scope very limited by be limited to ± λ/8 of the change of cavity length of Fiber Optic Fabry-Perot Sensor, practical value is had a greatly reduced quality.

Summary of the invention

The object of the invention is the problem existing in order to solve above-mentioned intensity demodulation method, propose a kind of new demodulation method.When external environment variation changes the chamber length in F-P chamber, the method can demodulate the definite chamber long value in F-P chamber, improves the degree of accuracy of traditional intensity demodulation method, can expand demodulation scope simultaneously.

The method that demodulation extrinsic type fiber Fabry-Pérot cavity is long, comprises following step:

Step 1: the original light intensity value that is incident to F-P chamber by light power meter measurement;

Step 2: measure the light intensity value returning from F-P cavity reflection by light power meter;

Step 3: by the long expression formula of the incident measuring and reflective light intensity value substitution chamber;

Step 4: utilize multi-wavelength intensity demodulation method to obtain long solution the in chamber in F-P chamber;

The invention has the advantages that:

(1) demodulation method of the present invention can expand the long demodulation scope in fiber Fabry-Pérot cavity chamber.

(2) the more traditional fiber Fabry-Pérot cavity light intensity demodulation method of demodulation method of the present invention is more accurate, and measuring accuracy can reach 0.1um.

(3) measuring system device of the present invention is simple, easy operating, and measurement data is accurate.

Accompanying drawing explanation

Fig. 1 is incident intensity optical system for testing;

Fig. 2 is reflective light intensity optical system for testing;

Fig. 3 is the analogous diagram of the long relation of reflective light intensity and chamber under dual wavelength;

Fig. 4 is the analogous diagram of the long relation of reflective light intensity and chamber under three-wavelength;

Fig. 5 utilizes SM125 to demarcate the long optical system for testing in chamber, F-P chamber;

Fig. 6 utilizes the chamber long value of SM125 (FBG) demodulator demarcation and the chamber long value comparison diagram that multi-wavelength demodulation method is tried to achieve.

In figure:

1-with the DFB diode laser 2 of single-mode tail fiber-close ripple WDM 3-three port circulators

4-Fiber Optic Fabry-Perot Sensor, 5-partial wave WDM, 6-light power meter

7-SM125 (FBG) demodulator, 8-flange

Embodiment

Below in conjunction with embodiment and accompanying drawing, the present invention is described in detail.

The present invention is a kind of long method of demodulation extrinsic type fiber Fabry-Pérot cavity, measure the device using and comprise the DFB(distributed feedback laser with single-mode tail fiber) diode laser 1, close ripple WDM(wavelength division multiplexer) 2, circulator 3, Fiber Optic Fabry-Perot Sensor (F-P chamber) 4, partial wave WDM(wavelength division multiplexer) 5, light power meter 6, flange 8 and SM125 (FBG) demodulator 7.

Laser instrument 1 comprises laser instrument A ₁, laser instrument A ₂..., laser instrument A _n;

Light power meter 6 comprises light power meter A ₁, light power meter A ₂..., light power meter A _n;

Comprise following step:

Step 1: the original light intensity value that is incident to F-P chamber 4 by light power meter measurement.

As shown in Figure 1, by fixed wave length λ ₁the DFB diode laser A with single-mode tail fiber of=1540nm ₁by a flange 8, be connected with first port of three end circulators 3, a light power meter of second port access of three end circulators 3, records laser instrument A ₁light intensity, light intensity is now the original light intensity value I that is incident to F-P chamber 4 ₁₀.

By laser instrument A ₁from flange 8, extract, change fixed wave length λ into ₂the DFB diode laser A of=1550nm ₂, all the other interfaces are constant, record laser instrument A ₂incident intensity value I ₂₀.

By laser instrument A ₂from flange 8, extract, change fixed wave length λ into ₃the laser instrument A of=1570nm ₃, record laser instrument A ₃incident intensity value I ₃₀.

In like manner, by laser instrument A _n-1from flange 8, extract, changing fixed wave length into is λ _nlaser instrument A _n, record laser instrument A _nincident intensity value I _n0.

The selection of DFB diode laser wavelength can be chosen from 1550nm wave band, and wavelength interval 10nm～20nm not etc., can not select according to actual conditions.

Step 2: measure the light intensity value being reflected back from F-P chamber 4 by light power meter 6.

As shown in Figure 2, by laser instrument A _nfrom flange 8, extract, by laser instrument A ₁, laser instrument A ₂..., laser instrument A _nwith close ripple WDM2 and be connected, the light ECDC ripple WDM2 of the different wave length that N laser instrument sends is coupled in same single-mode fiber, this optical fiber is connected with first port of three end circulators 3 by flange 8, second port of three end circulators 3 connects the 3rd port access partial wave WDM5 of F-P chamber 4, three end circulators 3 by another flange 8.

Laser instrument A ₁, laser instrument A ₂..., laser instrument A _nby closing ripple WDM2, be coupled into after same single-mode fiber, incide F-P chamber 4, the light intensity signal being reflected back through F-P chamber 4 just includes the chamber long message of Fa-Po cavity, and exports by the 3rd port of circulator 3.The 3rd port is connected with partial wave WDM5, and N reflected light signal after partial wave WDM5 beam splitting accesses respectively light power meter A ₁, light power meter A ₂..., light power meter A _n, N light power meter monitored respectively, obtains and N the reflective light intensity value I that incident wave is corresponding _1R, I _2R, I _3R..., I _nR.

Step 3: by the long expression formula of the incident measuring and reflective light intensity value substitution chamber.

Because F-P chamber 4 end faces adopt antiradar reflectivities, EFPI(Non-intrinsic Fabry-Perot chamber) reflective light intensity can use formula (1) expression, i.e. two-beam interference:

$I_R=\frac{2R(1-\cos \mathrm{\φ})}{1+R^2-2R\cos \mathrm{\φ}}{I}_0---\left(1\right)$

Wherein, R is the reflectivity of F-P chamber 4 fiber end faces, is about 4%,

φ is phase place, I ₀for incident intensity, the wavelength that λ is incident light wave.

According to the reflective light intensity formula (1) of intensity demodulation method, can obtain the long expression formula in chamber is:

$L=\frac{\mathrm{\λ}}{4\mathrm{\π}}\arccos \frac{I(1+R^2)-2R}{2R(I-1)}+\frac{\mathrm{m\λ}}{2}---\left(2\right)$

Wherein, $I=\frac{I_R}{I_0},m=\mathrm{0,1,2}....$

Definition the reflective light intensity value substitution measuring can be obtained to it for constant, and the long expression formula in chamber can be abbreviated as:

$L=C+\frac{\mathrm{m\λ}}{2}---\left(3\right)$

In actual measurement, I ₁₀, I ₂₀, I ₃₀..., I _n0, I _1R, I _2R, I _3R..., I _nRbe all to determine numerical value, by the definition of I:

$I=\frac{I_R}{I_0}---\left(4\right)$

Just can obtain the normalization reflective light intensity value of N incident wave:

$I_1=\frac{I_{1R}}{I_{10}}---\left(5\right)$

$I_2=\frac{I_{2R}}{I_{20}}---\left(6\right)$

$I_3=\frac{I_{3R}}{I_{30}}---\left(7\right)$

……

$I_n=\frac{I_{\mathrm{nR}}}{I_{n0}}---\left(8\right)$

By the chamber in F-P chamber, grown the definition of expression formula (2) and C:

$C=\frac{\mathrm{\λ}}{4\mathrm{\π}}\arccos \left[\frac{I+{\mathrm{IR}}^2-2R}{2R(I-1)}\right]---\left(9\right)$

Can obtain:

${\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="HDA0000442205330000012.png"\; state="\{\{state\}\}">C</figure-callout>}}_1=\frac{{\mathrm{\&lambda;}}_1}{4\mathrm{\&pi;}}\arccos \left[\frac{I_1+{I_{1}R}^2-2R}{2R(I_1-1)}\right]---\left(10\right)$

${\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA0000442205330000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_2=\frac{{\mathrm{\&lambda;}}_2}{4\mathrm{\&pi;}}\arccos \left[\frac{I_2+{I_{2}R}^2-2R}{2R(I_2-1)}\right]---\left(11\right)$

${\mathrm{<figure-callout\; id="3"\; label="C"\; filenames="HDA0000442205330000011.png,HDA0000442205330000012.png"\; state="\{\{state\}\}">C</figure-callout>}}_3=\frac{{\mathrm{\&lambda;}}_3}{4\mathrm{\&pi;}}\arccos \left[\frac{I_3+{I_{3}R}^2-2R}{2R(I_3-1)}\right]---\left(12\right)$

……

$C_n=\frac{{\mathrm{\&lambda;}}_{\mathrm{<figure-callout\; id="4"\; label="n"\; filenames="HDA0000442205330000031.png"\; state="\{\{state\}\}">n</figure-callout>}}}{4\mathrm{\&pi;}}\arccos \left[\frac{I_n+{I_{n}R}^2-2R}{2R(I_n-1)}\right]---\left(13\right)$

Value difference substitution formula (10) (11) (12) (13) by formula (5) (6) (7) (8), just can obtain C ₁, C ₂, C ₃, C ₄value, now, C ₁, C ₂, C ₃, C ₄for known parameters.

The long value in chamber just can be expressed as by these three known parameters:

$L={\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="HDA0000442205330000012.png"\; state="\{\{state\}\}">C</figure-callout>}}_1+\frac{{\mathrm{<figure-callout\; id="1"\; label="m"\; filenames="HDA0000442205330000012.png"\; state="\{\{state\}\}">m</figure-callout>}}_1{\mathrm{\&lambda;}}_1}{2}$

$L={\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA0000442205330000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_2+\frac{{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="HDA0000442205330000031.png"\; state="\{\{state\}\}">m</figure-callout>}}_2{\mathrm{\&lambda;}}_2}{2}$

$L={\mathrm{<figure-callout\; id="3"\; label="C"\; filenames="HDA0000442205330000011.png,HDA0000442205330000012.png"\; state="\{\{state\}\}">C</figure-callout>}}_3+\frac{{\mathrm{<figure-callout\; id="3"\; label="m"\; filenames="HDA0000442205330000011.png,HDA0000442205330000012.png"\; state="\{\{state\}\}">m</figure-callout>}}_3{\mathrm{\&lambda;}}_3}{2}$

……

$L=C_n+\frac{m_n{\mathrm{\&lambda;}}_{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000442205330000031.png"\; state="\{\{state\}\}">n</figure-callout>}}}{2}$

Wherein, m ₁, m ₂, m ₃..., m _nfor uncertain value.

Step 4: utilize multi-wavelength intensity demodulation method to obtain long solution the in chamber in F-P chamber 4.

Expect the definite solution in F-P chamber, by following three steps, realize:

First, at definite change of cavity length scope [L _a, L _b] in, for first incident wavelength, according to known reflective light intensity value, the long expression formula in chamber can be written as:

$L={\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="HDA0000442205330000012.png"\; state="\{\{state\}\}">C</figure-callout>}}_1+\frac{{\mathrm{<figure-callout\; id="1"\; label="m"\; filenames="HDA0000442205330000012.png"\; state="\{\{state\}\}">m</figure-callout>}}_1{\mathrm{\&lambda;}}_1}{2}---\left(14\right)$

Wherein: C ₁for determined value, m ₁round numbers, so just can obtain the long disaggregation { L in a chamber within the scope of demodulation ₁₁, L ₁₂..., L _1k1.

Then, introduce second incident wavelength, the long expression formula in chamber can be written as simultaneously:

$L={\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA0000442205330000031.png"\; state="\{\{state\}\}">C</figure-callout>}}_2+\frac{{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="HDA0000442205330000031.png"\; state="\{\{state\}\}">m</figure-callout>}}_2{\mathrm{\&lambda;}}_2}{2}---\left(15\right)$

Wherein: C ₂value is determined, first group of solution is brought in formula (15), according to the second bundle reflection of light light intensity value, is meeting under the condition that m is integer, can obtain again the long { L of solution in new a series of chambeies ₂₁, L ₂₂..., L _2k2, this solution meets equation (14) and equation (15) simultaneously, visible, { L ₂₁, L ₂₂..., L _2k2∈ { L ₁₁, L ₁₂..., L _1k1, K ₂<K ₁.

Then, in order to reduce the number of solution, obtain unique correct solution corresponding with Fa-Po cavity chamber length, introduce the 3rd incident wavelength, the long expression formula in chamber can be written as:

$L={\mathrm{<figure-callout\; id="3"\; label="C"\; filenames="HDA0000442205330000011.png,HDA0000442205330000012.png"\; state="\{\{state\}\}">C</figure-callout>}}_3+\frac{{\mathrm{<figure-callout\; id="3"\; label="m"\; filenames="HDA0000442205330000011.png,HDA0000442205330000012.png"\; state="\{\{state\}\}">m</figure-callout>}}_3{\mathrm{\&lambda;}}_3}{2}---\left(16\right)$

Use the same method and can obtain the 3rd group of solution { L ₃₁, L ₃₂..., L _3k3, and { L ₃₁, L ₃₂..., L _3k3∈ { L ₂₁, L ₂₂..., L _2k2∈ { L ₁₁, L ₁₂..., L _1k1, K ₃<K ₂<K ₁.Visible, the 3rd group of solution meets equation (14), equation (15) and equation (16) simultaneously.

By that analogy, introduce N incident wavelength, the long expression formula in chamber can be written as:

$L=C_n+\frac{m_n{\mathrm{\&lambda;}}_n}{2}---\left(17\right)$

Use the same method, can obtain N group and separate { L _n1, L _n2..., L _nkn, and { L _n1, L _n2..., L _nkn∈ { L _{(n-1) 1}, L _{(n-1) 2}..., L _{(n-1) k (n-1)}∈ ... ∈ { L ₁₁, L ₁₂..., L _1k1, K _n< ... <K ₃<K ₂<K ₁.Visible, N group solution meets equation (14), equation (15), equation (16), equation (17) simultaneously, finally obtains the long correct solution in chamber, F-P chamber within the scope of demodulation.

The present invention, by introducing a plurality of incident wavelengths, just can obtain unique corresponding to the long correct solution in chamber, F-P chamber within the scope of demodulation.

For this principle of clearer explanation, existing describe by illustrating: on the basis of existing test condition, first suppose that change of cavity length scope is between 109um～114um.From the analogous diagram of the long relation of reflective light intensity and chamber,, in accompanying drawing 3(figure, solid line represents laser instrument A ₁during incident, the relation between chamber, F-P chamber length and reflective light intensity; Dotted line represents laser instrument A ₂during incident, the relation between chamber, F-P chamber length and reflective light intensity), can find out, only exist

scope in, its light intensity and chamber are long linear, surpass this scope, the long solution in chamber just becomes not unique.When scope is grown in chamber at 109um～114um, as can be seen from the figure, by adding an incident wavelength, can reduce the number of solution.Because of A=A ', B=B ', is now two solutions.Certainly, the chamber in the not corresponding F-P of one of them solution chamber is long.At this moment, then introduce the 3rd incident wavelength, while representing respectively three laser instrument incident as tri-curves of accompanying drawing 4(, the relation between chamber, F-P chamber length and reflective light intensity), just can within the scope of demodulation, obtain the long solution in unique correct chamber.From above theory, can know, select suitable incident wavelength just can obtain in the larger context the long solution in unique chamber.

Step 5: the accuracy to described method is assessed.

Utilize SM125 (FBG) demodulator fixed to the chamber progress rower in F-P chamber.As accompanying drawing 5, optical fiber Fabry-Perot sensor 4 is accessed in SM125 (FBG) demodulator 7 by wire jumper, open the demodulation interface of SM125 on computing machine, move and obtain the accurate chamber long value in F-P chamber 4.Wherein, the long change in chamber, F-P chamber is by optical fiber Fabry-Perot sensor 4 is exerted pressure and obtained.With matlab, write corresponding program, obtain the error contrast between demodulation value and exact value, in accompanying drawing 6(figure, actual chamber, the F-P chamber long value that solid line representative obtains with SM125 (FBG) demodulator; Demodulation chamber, the F-P chamber long value that dotted line representative obtains with above-mentioned multi-wavelength demodulation method).

The present invention, on the basis of existing fiber Fabry-Perot-type cavity intensity demodulation method, has proposed a kind of new demodulating algorithm.This algorithm measurement precision is high, and demodulation scope is large, can obtain the long solution in unique correct chamber within the scope of the change of cavity length of 5um.

Claims (1)

1. the long method of demodulation extrinsic type fiber Fabry-Pérot cavity, measures that the device using comprises laser module, closing ripple WDM, to close wave-wave division multiplexer, circulator, Fiber Optic Fabry-Perot Sensor be that F-P chamber, partial wave WDM are partial wave wavelength division multiplexer, light power meter;

Laser module comprises n laser instrument, is respectively laser instrument A ₁, laser instrument A ₂..., laser instrument A _n;

Light power meter module comprises n light power meter, is respectively light power meter A ₁, light power meter A ₂..., light power meter A _n;

Method comprises following step:

Step 1: the original light intensity value that is incident to F-P chamber by light power meter measurement;

By laser instrument A ₁be connected with first port of three end circulators, a light power meter of second port access of three end circulators, records laser instrument A ₁light intensity, light intensity is now the original light intensity value I that is incident to F-P chamber ₁₀;

By laser instrument A ₁change laser instrument A into ₂, record laser instrument A ₂incident intensity value I ₂₀;

Change successively laser instrument, finally measure laser instrument A ₁, laser instrument A ₂..., laser instrument A _nincident intensity value I ₁₀, I ₂₀..., I _n0;

Step 2: measure the light intensity value returning from F-P cavity reflection by light power meter;

By laser instrument A ₁, laser instrument A ₂..., laser instrument A _nwith close ripple WDM and be connected, the light ECDC ripple WDM of the different wave length that N laser instrument sends is coupled in same single-mode fiber, optical fiber is connected with first port of three end circulators, second port of three end circulators connects F-P chamber, the 3rd port access partial wave WDM of three end circulators, partial wave WDM connects respectively light power meter A ₁, light power meter A ₂..., light power meter A _n, N light power meter obtains N and sends the corresponding reflective light intensity value I of incident wave with laser instrument _1R, I _2R, I _3R..., I _nR;

Step 3: by the long expression formula of the incident measuring and reflective light intensity value substitution chamber;

The long expression formula in chamber is:

$L=C+\frac{\mathrm{m\&lambda;}}{2}---\left(3\right)$

Wherein: $C=\frac{\mathrm{\&lambda;}}{4\mathrm{\&pi;}}\arccos \left[\frac{I+{\mathrm{IR}}^2-2R}{2R(I-1)}\right],$ C does not have physical meaning, $I=\frac{I_R}{I_0},m=\mathrm{0,1},2...,$ I ₀for incident intensity, I _rfor reflective light intensity, the wavelength that λ is incident light wave;

By the incident intensity I in step 1 ₁₀, I ₂₀..., I _n0, by the reflective light intensity I in step 2 _1R, I _2R..., I _nRbring into

obtain the normalization reflective light intensity value of N incident wave:

$I_n=\frac{I_{\mathrm{nR}}}{I_{n0}}---\left(8\right)$

According to I _nobtain N C value:

$C_n=\frac{{\mathrm{\&lambda;}}_n}{4\mathrm{\&pi;}}\arccos \left[\frac{I_n+{I_{n}R}^2-2R}{2R(I_n-1)}\right]---\left(13\right)$

Wherein, λ _nthe wavelength that represents n incident light wave;

By C _n, I _nbring the long expression formula in chamber into, obtain N long expression formula of chamber:

$L=C_1+\frac{m_1{\mathrm{\&lambda;}}_1}{2}$

$L=C_2+\frac{m_2{\mathrm{\&lambda;}}_2}{2}$

……

$L=C_n+\frac{m_n{\mathrm{\&lambda;}}_n}{2}$

Wherein, m ₁, m ₂..., m _nfor uncertain value;

Step 4: utilize multi-wavelength intensity demodulation method to obtain long solution the in chamber in F-P chamber;

Change of cavity length scope [L _a, L _b] be known;

For first incident wavelength, the long expression formula in chamber is:

$L=C_1+\frac{m_1{\mathrm{\&lambda;}}_1}{2}---\left(14\right)$

Wherein: C ₁for determined value, m ₁round numbers, obtains the long disaggregation { L in first group of chamber within the scope of demodulation ₁₁, L ₁₂..., L _1k1, K ₁it is the long number of separating in first group of chamber;

For second incident wavelength, the long expression formula in chamber is:

$L=C_2+\frac{m_2{\mathrm{\&lambda;}}_2}{2}---\left(15\right)$

Wherein: C ₂value is determined, the long disaggregation in first group of chamber is brought in above formula (15), is meeting under the condition that m is integer, obtains the long { L of solution in second group of chamber ₂₁, L ₂₂..., L _2k2, K ₂be the long number of separating in second group of chamber, { L ₂₁, L ₂₂..., L _2k2∈ { L ₁₁, L ₁₂..., L _1k1, K ₂<K ₁;

Then, by that analogy, introduce N incident wavelength, the long expression formula in chamber is:

$L=C_n+\frac{m_n{\mathrm{\&lambda;}}_n}{2}---\left(17\right)$

Wherein, C _nvalue is determined, the long disaggregation in N-1 group chamber is brought in above formula (17), is meeting m _nunder condition for integer, obtain N group and separate { L _n1, L _n2..., L _nkn, K _nbe the long number of separating in N group chamber, and { L _n1, L _n2..., L _nkn∈ { L _{(n-1) 1}, L _{(n-1) 2}..., L _{(n-1) k (n-1)}∈ ... ∈ { L ₁₁, L ₁₂..., L _1k1, K _n< ... <K ₃<K ₂<K ₁;

Finally obtain the long correct solution in chamber, F-P chamber within the scope of demodulation.

Images