Fiber grating float type density sensor device

Abstract

The application belongs to the technical field of density sensors, and relates to a fiber grating float type density sensing device based on laser sweeping technology. A pi-phase shift fiber grator is used as a sensitive element to improve sensitivity based on the advantage of narrow linewidth. A laser sweeping technology is used to establish a modulation-demodulation system to improve resolution and response time and realize real-time measurement and high-speed measurement. A gas molecule absorption cell is used as a standard wavelength reference to improve measurement accuracy based on the fact that a gas molecule absorption line is not affected by changes in external temperature and other factors. A cross-correlation algorithm is used to calculate the shift of the center wavelength of the pi-phase shift fiber grator relative to the absorption peak of the gas molecule absorption cell to improve measurement accuracy. When the density of the liquid to be measured changes, the buoyancy of the microcrystalline glass float changes, the pi-phase shift fiber grator senses the buoyancy, generates strain, and the center wavelength shifts. The time interval between the center wavelength and the absorption peak of the gas molecule absorption cell is calculated to demodulate the density of the liquid to be measured.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of density sensors, and particularly relates to a fiber bragg grating float type density sensing device based on laser sweep frequency technology. BACKGROUND

[0002] Liquid density as one of the important physical parameters of matter, has important significance in the field of oil exploration, ocean observation, biopharmaceuticals, etc. With the progress of society and the development of science and technology, the measurement of liquid density tends to be high precision and real-time. The traditional glass float meter is designed based on Archimedes principle. The density is obtained by reading the immersion depth of the glass float in the measured sample. Manual operation and manual reading are required during use, which cannot realize the automation of measurement and has poor reproducibility. In addition, due to the different standard densities of various liquids, the temperature of the liquid during on-site measurement usually deviates from the standard temperature. Therefore, the temperature must be measured synchronously during measurement, and then the standard density at the standard temperature is converted through the temperature and density conversion table. It does not have real-time performance, which significantly reduces the production efficiency. Fiber grating sensor has the advantages that other types of sensors do not have: small size, light weight, anti-electromagnetic interference, good repeatability, etc. In recent years, it has developed rapidly and is widely used in measuring temperature, strain, displacement, pressure, flow, etc. Especially in various engineering fields such as aerospace, large mechanical and electrical equipment, bridge construction, etc. It plays an important role. In the research of using fiber grating as the sensitive element of the density sensor, the previous measurement equipment or method has the problem of low resolution based on the wavelength resolution of the spectrometer, which cannot meet the requirements of engineering measurement accuracy. For example, the resonant cylinder liquid density sensor disclosed in Chinese patent 201711240055.X includes a shell and a vibrating cylinder arranged in the shell and extending axially along the shell. An exciter for driving the vibrating cylinder to vibrate and a pickup for detecting the vibration frequency of the vibrating cylinder are also arranged in the shell. The exciter and the pickup are in direct contact with the vibrating cylinder. The shell includes a side surface and two upper and lower end surfaces connected as one body. The side surface and the two upper and lower end surfaces are welded as one body through corrugated pipes. The shell side surface outer surface is fixedly installed with a mounting bracket for fixing the resonant cylinder liquid density sensor. The vibrating cylinder and the shell form a closed cavity, and the exciter and the pickup are fixed in the cavity. The exciter and the pickup are respectively screwed to the shell. The exciter and the pickup are respectively and symmetrically installed on both sides of the vibrating cylinder. The exciter is arranged perpendicular to the shell axis. The vibrating cylinder side surface is opposite to the exciter end surface. The pickup is arranged perpendicular to the shell axis. The vibrating cylinder side surface is opposite to the pickup end surface. The exciter includes two excitation units. The pickup includes one or two pickup units. The excitation unit includes an excitation coil and a first metal box for mounting the excitation coil. The first metal box is screwed to the shell. The pickup unit includes a pickup coil and a second metal box for mounting the pickup coil. The second metal box is screwed to the shell.The X disclosed new fiber grating density sensor based on differential pressure method, including protective shell: cylindrical, first beam is arranged in the direction of diameter near the top, second beam is arranged in the direction of diameter near the bottom, the length of the first beam and the second beam is same with the diameter, and they are parallel to each other;The first corrugated diaphragm is fixed on the top of the protective shell along the horizontal plane, and the second corrugated diaphragm is fixed on the bottom of the protective shell along the horizontal plane;The two corrugated diaphragms are parallel to each other;The first metal sensitization structure is fixed on the first beam and contacts with the first corrugated diaphragm, and the second metal sensitization structure is fixed on the second beam and contacts with the second corrugated diaphragm;The metal sensitization structure and the beam form an isosceles triangle, and the contact point with the corrugated diaphragm is the vertex of the isosceles triangle, and the contact point with the corrugated diaphragm is located on the axis of the protective shell;The first fiber grating is fixed between the two hips of the first metal sensitization structure;The second fiber grating is fixed between the two hips of the second metal sensitization structure;The protective shell has a fiber lead-out hole;The two corrugated diaphragms adopt the same material and geometric structure;The two metal sensitization structures adopt the same material and geometric structure;The two fiber gratings have the same center wavelength;The liquid density sensing device based on double Bragg fiber grating disclosed in Chinese patent 201521007652.4, the output end of the broadband light source is connected with the input end of the optical isolator, the output end of the optical isolator is fixed on the upper support rod through the upper optical fiber clamp, and is connected with one end of the Bragg fiber grating FBG1, the other end of the Bragg fiber grating FBG1 is fixed on the cylinder, the other end of the Bragg fiber grating FBG1 is connected with one end of the Bragg fiber grating FBG2, the other end of the FBG2 is fixed on the lower support rod through the lower optical fiber clamp, and is connected with the input end of the optical spectrum analyzer;The upper support rod and the lower support rod are fixed on the horizontally placed base through the vertical support rod, and the upper support rod and the lower support rod are parallel and perpendicular to the vertical support rod;The Bragg wavelength and the transmission spectrum of the Bragg fiber grating FBG1 and the Bragg fiber grating FBG2 are the same.

[0003] The laser sweep frequency technology is mainly used for the sensing system with a narrow line width laser as a light source, and different wavelengths of laser are obtained by changing the injection current of the narrow line width laser during measurement, so that the laser sweep frequency technology has the advantages of high resolution, rapid response and high speed measurement. In order to solve the problems of limited measurement method and device or precision, high cost, and even safety hazards in the prior art, a liquid density sensing device with simple structure, ultra-high resolution, easy operation and good repeatability is developed and designed. SUMMARY

[0004] The purpose of the present application is to overcome the shortcomings of the prior art, and to develop and design a fiber grating float type density sensing device based on laser sweep frequency technology, which obtains the density of the liquid to be measured through the corresponding relationship between the liquid density and the wavelength of the pi-phase shift fiber grating.

[0005] To achieve the above objectives, the main structure of the fiber optic grating float-type density sensing device of the present invention includes a laser, an optical beam splitter, an optical circulator, a gas molecule absorption cell, a π-phase-shift fiber grating, a photodetector, a data acquisition module, a control module, a voltage output module, a current controller, a temperature controller, a buoyancy hook, and a microcrystalline glass float. The laser is connected to the optical circulator and the gas molecule absorption cell via the optical beam splitter. The optical circulator is connected to the π-phase-shift fiber grating and the photodetector. The gas molecule absorption cell is also connected to the photodetector. The photodetector is connected to the laser via the data acquisition module, the control module, the voltage output module, and the current controller, forming a loop. In addition, the laser is also connected to the temperature controller, and the π-phase-shift fiber grating is connected to the buoyancy hook with a microcrystalline glass float at its end.

[0006] When using the fiber optic grating float-type density sensing device of the present invention, a microcrystalline glass float is inserted into a container containing the liquid to be measured, and both the buoyancy hook and the container are set on a vibration isolation platform; when the density of the liquid to be measured changes, the buoyancy force on the microcrystalline glass float changes, and this change is transmitted to the π-phase-shift fiber grating. The density of the liquid to be measured is obtained based on the correspondence between the center wavelength of the π-phase-shift fiber grating and the density of the liquid to be measured.

[0007] The laser involved in this invention is a narrow-linewidth laser used to provide a light source, and the wavelength of its output laser is related to its driving current. An optical beam splitter divides the laser light from the laser into two beams: one beam is used for reference and connected to a gas molecule absorption cell, and the other beam is used for measurement and connected to a π-phase-shift fiber grating via an optical circulator. The gas molecule absorption cell has an optical absorption peak, and the reference gas molecule absorption peak has high frequency stability, enabling real-time calibration of the laser's output wavelength. The π-phase-shift fiber grating is the sensing element: a π-PSFBG, which introduces a phase shift at the center of the fiber Bragg grating, creating a Fabry-Perot cavity where each side is a mirror formed by a grating, resulting in a sharp resonance peak in the transmission spectrum. A photodetector is used to receive the transmitted light signal from the gas molecule absorption cell and the π-phase-shift fiber grating. The system receives reflected light signals and converts them into electrical signals; the data acquisition module collects voltage signals output by the photodetector; the control module controls the voltage output module to output periodic sawtooth wave signals for modulating the current controller; the voltage output module can output modulation signals of various waveforms, including but not limited to step signals, sine signals, and sawtooth wave signals; the current controller drives the laser, and the wavelength of the laser changes when the driving current changes; the temperature controller regulates the operating temperature of the laser; the buoyancy hook is used to bind the π-phase-shift fiber grating and transmit the buoyancy force to the π-phase-shift fiber grating; the microcrystalline glass float senses the buoyancy of the liquid to be tested; the container holds the liquid to be tested; and the vibration isolation platform is used to install the buoyancy hook and support the container, protecting it from environmental vibrations.

[0008] This invention relates to a fiber optic grating float-type density sensing device based on laser frequency sweeping technology. It establishes a correspondence between liquid density and the center wavelength of a π-phase-shifted fiber grating (BPGF). Liquid density is measured by inverting and analyzing the wavelength variation data of the BPGF. The resolution and range are adjusted by changing the performance parameters of the laser and the BPGF, as well as the amplitude of the sawtooth wave signal, to suit different measurement scenarios. To demodulate the center wavelength of the BPGF, a periodic sawtooth wave signal modulates the current controller, driving the laser wavelength to change periodically. Density information is demodulated by calculating the time delay of the BPGF's center wavelength relative to the absorption peak of the gas molecule absorption cell within one cycle. To improve measurement resolution, the output spectral signals of the gas molecule absorption cell and the BPGF's center wavelength are differentiated within one frequency sweep cycle to obtain an error signal. The two error signals are cross-correlated to obtain the center wavelength difference, which is then used to demodulate the density information.

[0009] Compared with existing technologies, this invention uses a π-phase-shift fiber grating as the sensing element, leveraging its narrow linewidth to improve sensitivity; it employs laser frequency sweeping technology to establish a modulation-demodulation system, improving resolution and response time for real-time and high-speed measurements; it uses a gas molecule absorption cell as a standard wavelength reference, improving measurement accuracy because the gas molecule absorption line is unaffected by changes in external factors such as temperature; it uses a cross-correlation algorithm to calculate the shift of the center wavelength of the π-phase-shift fiber grating relative to the absorption peak of the gas molecule absorption cell, further enhancing measurement precision; when the density of the liquid to be measured changes, it causes a change in the buoyancy of the microcrystalline glass float. Through the buoyancy hook, the π-phase-shift fiber grating senses the buoyancy and generates a strain of the same direction and magnitude, shifting its center wavelength. By calculating the time interval between this center wavelength and the absorption peak of the gas molecule absorption cell, the density of the liquid to be measured is demodulated; its structure is simple, with high measurement accuracy and signal-to-noise ratio, and its cost is far lower than that of commercially available densitometers. Attached image description:

[0010] Figure 1 This is a schematic diagram of the main structure of the present invention.

[0011] Figure 2 This is a schematic diagram of the spectral signals of the gas molecule absorption cell and the π-phase-shifted fiber grating during laser frequency sweeping, as per the present invention.

[0012] Figure 3 This is a schematic diagram of the error signal of the gas molecule absorption cell and π-phase-shifted fiber grating involved in the present invention.

[0013] Figure 4 This is a schematic diagram of the cross-correlation signal product involved in the present invention. Detailed implementation method:

[0014] The present invention will be further described below with reference to the embodiments and accompanying drawings.

[0015] Example 1:

[0016] This embodiment relates to a fiber Bragg grating float-type density sensing device. The main structure includes a laser 1, an optical beamsplitter 2, an optical circulator 3, a gas molecule absorption cell 4, a π-phase-shift fiber Bragg grating 5, a photodetector 6, a data acquisition module 7, a control module 8, a voltage output module 9, a current controller 10, a temperature controller 11, a buoyancy hook 12, a microcrystalline glass float 13, a container 14, and a vibration isolation platform 15. The laser 1 is connected to the optical beamsplitter 2, which splits the optical signal input from the laser 1 into two beams: one beam for measurement, connected sequentially to the optical circulator 3 and the π-phase-shift fiber Bragg grating 5; and the other beam for reference, connected to the gas molecule absorption cell 4. The third port of the optical circulator 3 and the gas molecule absorption cell 4 are both connected to the photodetector 6. Based on this, the photodetector 6 can... The system can receive the reflected signal from the π-phase-shift fiber grating 5 and measure the transmission spectrum. The photodetector 6 is connected to the laser 1 in sequence through the data acquisition module 7, the control module 8, the voltage output module 9, and the current controller 10. The data acquisition module 7 transmits the collected voltage signal to the control module 8 for recording and further processing. The control module 8 controls the voltage output module 9 to output a modulation signal with a set waveform. After obtaining the modulation signal, the current controller 10 adjusts the wavelength of the laser output by the laser 1. The laser 1 is also connected to the temperature controller 11. The π-phase-shift fiber grating 5 is connected to the buoyancy hook 12. The end of the buoyancy hook 12 is provided with a microcrystalline glass float 13, which extends into the container 14. Both the buoyancy hook 12 and the container 14 are set on the vibration isolation platform 15.

[0017] The laser 1 involved in this embodiment is a tunable laser with a center wavelength of 1550nm. The wavelength of its output optical signal is related to the driving current output by the current controller 11. The optical beam splitter 2 has three ports. The optical signal input from the first port is output from the second and third ports at a set splitting ratio. Without considering losses, the sum of the output light intensities of the second and third ports is equal to the input light intensity of the first port, splitting the laser into two output paths: one path passes through the gas molecule absorption cell 4 as a reference optical path, with the absorption peak of the gas molecule absorption cell 4 as the reference wavelength standard; the other path passes through the optical circulator 3 and the π-phase-shift fiber grating 5 as a measurement optical path. The optical circulator 3 has three ports. The optical signal input from the first port is output only from the second port, and the optical signal input from the second port is output only from the third port. The gas molecule absorption line of the gas molecule absorption cell 4 has high frequency stability. The wavelength of the π-phase-shift fiber grating 5 is unaffected by factors such as ambient temperature and can be used as a reference wavelength standard. The π-phase-shift fiber grating 5 is attached to the buoyancy transfer hook 12. According to Archimedes' principle, when the density of the liquid to be measured in the container 14 changes, the buoyancy force on the microcrystalline glass float 13 connected to the buoyancy transfer hook 12 changes accordingly, generating stresses of equal magnitude and opposite direction on the π-phase-shift fiber grating 5. Therefore, there is a corresponding relationship between the center wavelength of the π-phase-shift fiber grating 5 and the density of the liquid to be measured. The photodetector 6 can simultaneously receive two optical signals: one is the transmitted light signal from the gas molecule absorption cell 4, and the other is the reflected light signal from the π-phase-shift fiber grating 5, and converts the optical signals into electrical signals. The control module 8 is used to record and process the voltage signal collected by the data acquisition module 7, and controls the voltage output module 9 to output a specified modulation signal. The voltage output module 9 uses a sawtooth wave signal as the modulation signal.

[0018] In this embodiment, a fiber optic grating float-type density sensing device is used as follows: The optical beam splitter 2 splits the optical signal input from the laser 1 into a measurement optical path and a reference optical path. The photodetector 6 converts the optical signals from the reference and sensing optical paths into electrical signals. The data acquisition module 7 synchronously acquires data, obtaining the spectral signals of the sensing and reference optical paths in the time domain, and transmits them to the control module 8 for recording, storage, and signal processing. Based on the processing results, the control module 8 controls the voltage output module 9 to output a periodic sawtooth wave signal, which is loaded onto the current controller 10, changing the injection current and output wavelength of the laser 1. The wavelength of the laser output by the laser 1 is related to the change in the sawtooth wave signal. By analyzing the signal... Figure 2 Differentiating the spectra of the center wavelength of the π-phase-shifted fiber grating 5 and the absorption peak of the gas molecule absorption cell 4, as shown, yields... Figure 3 The respective error signals are shown, and then cross-correlation calculation is performed on the error signals, the results are as follows. Figure 4 As shown, the time delay of the center wavelength of the π-phase-shifted fiber grating 5 relative to the absorption peak of the gas molecule absorption cell 4 is known.

[0019] This embodiment relates to a fiber optic grating float-type density sensing device. To measure the density of a liquid, a π-phase-shift fiber grating 5 is attached to a buoyancy hook 12. When the microcrystalline glass float 14 comes into contact with the liquid, it is affected by its own weight and the buoyancy of the liquid, causing the buoyancy hook 12 to deform under tension. This results in a shift in the central reflected wavelength of the π-phase-shift fiber grating 5. According to the relationship between the buoyancy of the microcrystalline glass float 14 and the central wavelength of the π-phase-shift fiber grating 5: The density of the liquid to be tested is calculated. To improve the measurement resolution, the output spectral signals of the gas molecule absorption cell 4 and the center wavelength of the π-phase-shift fiber grating 5 are differentiated within one frequency sweep cycle to obtain the error signal. The cross-correlation of the two error signals is calculated to obtain the center wavelength difference. The density information is demodulated through the wavelength difference. The maximum value of the cross-correlation result is represented by the abscissa as the time delay of the π-phase-shift fiber grating 5 relative to the gas molecule absorption cell 4. To achieve high-precision and rapid demodulation of the center wavelength of the π-phase-shift fiber grating 5, a modulation system based on laser frequency sweep technology is used. The laser 1 is scanned by a periodic sawtooth wave input signal, causing the laser to... The output wavelength of the optical device 1 exhibits a periodic change. Based on the fact that the laser passing through the gas molecule absorption cell 4 and the laser passing through the π-phase-shifting fiber grating 5 have the same wavelength at each moment within a scanning cycle, the absorption peak of the gas molecule absorption cell 4, which has high frequency stability, is used as the reference wavelength standard to compensate for the wavelength drift of the laser frequency sweeping system caused by environmental noise in real time. When the density of the liquid under test changes, causing the center wavelength of the π-phase-shifting fiber grating 5 to change, the change in the center wavelength of the π-phase-shifting fiber grating 5 is known by calculating the time difference between the absorption peak of the gas molecule absorption cell 4 and the center wavelength of the π-phase-shifting fiber grating 5 within a cycle.

[0020] The derivation process of the relationship between the buoyancy force on the microcrystalline glass float 14 and the center wavelength of the π-phase-shift fiber grating 5 involved in this embodiment is as follows:

[0021] F T =F M -F A =m·g-ρ·V·g=g·(m-ρ·V) (1)

[0022] Among them, F T F is the net force acting on the microcrystalline glass float 14. M For the weight of the microcrystalline glass float 14, F A The buoyancy force experienced by the microcrystalline glass float 14 when it comes into contact with the liquid being measured is, according to Archimedes' principle, F A The density ρ of the liquid being measured and the volume V of the liquid displaced by the microcrystalline glass float 14 are related. For a cylindrical microcrystalline glass float 14, V = π·r 2 ·h, we get:

[0023] F T =g·(m-ρ·π·r) 2 ·h) (2)

[0024] The axial strain of the π-phase-shifting fiber grating 5 is:

[0025] Where, σ T Let A be the axial pressure on the π-phase-shifting fiber grating 5, A be the cross-sectional area of ​​the π-phase-shifting fiber grating 5, and E be the Young's modulus of the π-phase-shifting fiber grating 5.

[0026] As can be seen from formula (3), all environmental factors that cause changes in h will lead to a resultant force F acting on the π-phase-shifted fiber grating 5. T Based on this change, the density of the liquid under test can be obtained by measuring the axial strain of the π-phase-shifting fiber grating 5;

[0027] The wavelength selection mechanism of π-phase-shifted fiber Bragg grating 5 sensing is: λ B =2·n eff ·Λ(4)

[0028] Where, λ B n eff Λ and Λ represent the center wavelength, effective refractive index, and grating period of the π-phase-shifted fiber grating 5, respectively. When axial strain causes n eff When Λ changes, due to the photoelastic effect, the center wavelength λ B Movement occurred: Where, Δλ B C represents the drift of the center wavelength of the π-phase-shifted fiber grating 5. e The elastic coefficient;

[0029] The relationship between the density change of the liquid under test and the center wavelength change of the π-phase-shift fiber grating 5, obtained from formulas (1)-(5), is as follows:

Claims

1. A fiber optic grating float-type density sensing device, the main structure of which includes a laser, an optical beam splitter, an optical circulator, a gas molecule absorption cell, a π-phase-shifting fiber optic grating, a photodetector, a data acquisition module, a control module, a voltage output module, a current controller, a temperature controller, a buoyancy hook, and a microcrystalline glass float, characterized in that, The laser is connected to an optical circulator and a gas molecule absorption cell via an optical beam splitter. The optical circulator is connected to a π-phase-shift fiber grating and a photodetector. The gas molecule absorption cell is also connected to the photodetector. The photodetector is connected to the laser via a data acquisition module, a control module, a voltage output module, and a current controller to form a loop. In addition, the laser is also connected to a temperature controller. The π-phase-shift fiber grating is connected to a buoyancy hook with a microcrystalline glass float at the end. The laser is a narrow linewidth laser, and the π-phase-shift fiber grating is the sensing element: π-PSFBG. A phase shift is introduced at the center of the fiber Bragg grating to create a Fabry-Perot cavity where each side is a mirror formed by the grating.

2. The fiber optic grating float-type density sensing device according to claim 1, characterized in that, Lasers are used to provide a light source, and the wavelength of the output laser light is related to the driving current.

3. The fiber optic grating float-type density sensing device according to claim 2, characterized in that, An optical beam splitter splits the laser light from the laser into two beams: one beam is used for reference and connected to a gas molecule absorption cell, and the other beam is used for measurement and connected to a π-phase-shifted fiber grating via an optical circulator.

4. The fiber optic grating float-type density sensing device according to claim 3, characterized in that, The gas molecule absorption cell has an optical absorption peak, and the emission wavelength of the laser is calibrated in real time with reference to the gas molecule absorption peak.

5. The fiber optic grating float-type density sensing device according to claim 4, characterized in that, Photodetectors are used to receive the transmitted light signal from the gas molecule absorption cell and the reflected light signal from the π-phase-shifted fiber optic grating, and convert them into electrical signals.

6. The fiber optic grating float-type density sensing device according to claim 5, characterized in that, The data acquisition module is used to collect the voltage signal output by the photodetector; the control module controls the voltage output module to output a periodic sawtooth wave signal for modulating the current controller; the voltage output module outputs modulated signals of various waveforms. The current controller is used to drive the laser, and the wavelength of the laser changes when the driving current changes.

7. A fiber optic grating float-type density sensing device according to claim 6, characterized in that, Temperature controllers are used to regulate the operating temperature of the laser.

8. A fiber optic grating float-type density sensing device according to any one of claims 1-7, characterized in that, In use, the microcrystalline glass float is inserted into a container filled with the liquid to be tested, and both the buoyancy hook and the container are placed on a vibration isolation platform. When the density of the liquid to be tested changes, the buoyancy force on the microcrystalline glass float changes, and this change is transmitted to the π-phase-shift fiber grating. The density of the liquid to be tested is obtained based on the correspondence between the center wavelength of the π-phase-shift fiber grating and the density of the liquid to be tested.

9. A fiber optic grating float-type density sensing device according to claim 8, characterized in that, Based on laser frequency sweeping technology, a correspondence between liquid density and the center wavelength of a π-phase-shifted fiber grating is established. Liquid density is measured by inverting and analyzing the wavelength variation data of the π-phase-shifted fiber grating. The resolution and range are adjusted by changing the performance parameters of the laser and the π-phase-shifted fiber grating, as well as the amplitude of the sawtooth wave signal. A periodic sawtooth wave signal is used to modulate the current controller, driving the laser wavelength to change periodically. The density information is demodulated by calculating the time delay of the center wavelength of the π-phase-shifted fiber grating relative to the absorption peak of the gas molecule absorption cell within one cycle. For the absorption peak of the gas molecule absorption cell and the center wavelength of the π-phase-shifted fiber grating, the output spectral signals of the two are differentiated within one frequency sweeping cycle to obtain the error signal. The cross-correlation of the two error signals is calculated to obtain the center wavelength difference, and the density is demodulated using the wavelength difference.

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