RU2805128C1 - Crack opening rate measuring device - Google Patents

Abstract

FIELD: measuring methods.

SUBSTANCE: studying processes of destruction of materials for measuring the magnitude and rate of crack opening. The device contains one or more optical fibers with Bragg gratings with a reflection coefficient at a resonant wavelength from 10 to 90%, optical fibers are fixed on the surface of the material, the attachment points of the optical fibers are located at a distance of 10 mm to 20 mm, the output end of the optical fiber with Bragg gratings is connected to its photodetector, one or more semiconductor lasers are connected to one or more optical fibers with Bragg gratings through fiber circulators, the port of each of the circulators is connected to its photodetector, spectrum half-width _LD radiation of a semiconductor laser is chosen significantly less than the half-width of the spectrum _FBG reflections of the fiber Bragg grating, photodetectors and the pulse synchronizer of the current generator are connected to the outputs of a multichannel analog-to-digital converter, the crack opening rate is determined from the delay time between the pulse synchronizer signal and the signal of the reflected radiation by the Bragg grating.

EFFECT: decrease in the sensitivity of the device to pulsed electromagnetic interference and an increase in thermal stability.

1 cl, 2 dwg

Description

The invention relates to the field of measurement technology and can be used in studying the processes of destruction of materials with the formation of cracks to measure the size and speed of crack opening.

The presence of cracks in the materials of building structures, engineering structures, and devices for various purposes can have a significant impact on the performance characteristics of such objects or devices. Therefore, information about the mechanical characteristics of materials is necessary for the design and operation of such objects. One of the material parameters is the speed of crack opening, and the mechanical parameters of the entire structure or object depend on the size of the crack opening. The most detailed description of methods for determining the parameters of cracks in materials and structures is given for the construction industry. There are state standards, in particular, GOST 31937-2011 “Buildings and structures. Rules for inspection and monitoring of technical condition", GOST 8829-2018 "Reinforced concrete and prefabricated concrete building products. Load test methods. Rules for assessing strength, stiffness and crack resistance", GOST R 59115.6—2021 "Justification of the strength of equipment and pipelines of nuclear power plants. Methods for determining the crack resistance characteristics of structural materials", GOST 24846-2019 "Soils. Methods for measuring deformations of the foundations of buildings and structures,” as well as guidelines and recommendations, such as RD 153-34.1-21.326-2001 “Guidelines for the inspection of building structures of industrial buildings and thermal power plant structures. Part 1. Reinforced concrete and concrete structures" or "Methodological recommendations for determining the width of cracks in reinforced concrete elements. 1982, Kyiv: NIISK Gosstroy USSR, 29 S., regulating measurements in the construction industry. Basically, so-called beacons or gap gauges, as well as ultrasonic or optical measuring devices are used to monitor and measure the width of cracks in building structures. Such devices are intended for monitoring slow processes and cannot be used to determine the rate of crack opening under high-speed pulsed mechanical action.

There are also other methods and devices for determining the rate of crack opening, such as, for example, the method and device described in RF patent No. 2603939 (Method for determining the rate of crack growth in a sample and a device for this), in which the operating principle is based on recording changes in heat flow through sample. This method is also not applicable in the case of high-speed crack opening.

One of the modern trends in the development of systems for monitoring the condition of building structures and engineering structures is the use of optical fibers. A review of devices and methods of their use is presented in the journal “Sensors” (Mattia Francesco Bado and Joan R. Casas Review. A Review of Recent Distributed Optical Fiber Sensors Applications for Civil Engineering Structural Health Monitoring. Sensors 2021, 21, 1818. doi: 10.3390/ s21051818). Basically, the review describes systems based on the use of backscattering - stimulated Raman scattering, Brillouin scattering and Rayleigh scattering, as a result of which it is difficult to achieve high spatial resolution, and the use of time separation in such systems does not allow recording rapid changes in the scattering medium. The examples given in the review relate to slow cracking of a material with a characteristic time of 10 – 20 minutes, and the maximum measurement sampling rate is 1 kHz. That is, such systems are unsuitable for determining the speed of crack opening under high-speed mechanical impact on the material under study. The sensors and systems based on fiber Bragg gratings described in the review are also designed to study relatively slow processes.

A method for determining places of pre-fracture of structures using optical fibers is described in RF patent No. 2316757 (patent of the Russian Federation 2316757 “Method for determining places of pre-fracture of structures”, publ. IPC G01N 21/88, G01N 3/32, 02/10/2008 Bulletin No. 4). The speed of crack propagation in this invention is determined by the time of rupture of individual optical fibers. The disadvantage of this method is the impossibility of determining the width of the crack and the rate of its increase, as well as the impossibility of using it with a single optical fiber.

In the method for diagnosing the reliability and maximum service life of multilayer structures made of composite materials (RF patent No. 2633288), the magnitude of the mechanical and temperature effects on it is determined by measuring the spectral position of the peaks of Bragg gratings, which is a relatively slow method of measuring inapplicable for rapid crack opening, and also requires complex and expensive measuring equipment. Close in purpose and principle of operation to the method described above (RF patent No. 2633288) is a device for collecting information on the magnitude of dynamic effects on flexible structures and the state of end optical fiber detectors, described in RF patent No. 2648008, which has the same disadvantages when used for measuring parameters of rapid crack opening.

Fracture detection using optical fibers is used to monitor hydraulic fracturing used in the extraction of hydrocarbons and other minerals. For example, in RF patents No. 2672117 (Method for determining the internal system of cracks in a rock mass) and No. 2648743 (Monitoring of hydraulic fracturing), optical fibers are used as a sensor, backscattering in which is used to determine the distance to the scattering point by the delay of the returned impulse. That is, according to the principle of operation of the sensor, these methods do not differ from those described in the literature review in the journal “Sensors” (see above); accordingly, they have all the same disadvantages.

In some cases, optical fibers can be replaced with strain gauge sensors that change their electrical resistance when stretched or compressed. Strain-resistor sensors in systems for measuring deformation parameters are used, for example, in US Pat. RF No. 2548600 (Adhesive semiconductor strain gauge strain sensor for strength tests), No. 125334 (Strain resistor sensor for measuring strains and stresses in the thickness of building materials and rocks), No. 2349874 (Strain resistor strain sensor).

The prototype of the claimed invention is a device that implements a method for measuring the length of a crack and the speed of its development in bending and tensile structural elements (RF patent No. 2596694, Method for measuring the length of a crack and the speed of its development in bending and tensile structural elements, G01B 7/00, publ. 09/10/2016 Bulletin No. 25), given in the description of the specified patent. The prototype has the following claims.

1. A method for measuring the length of a crack and the rate of its development in bending and tensile structural elements, characterized in that at a distance of 10-20 mm from the cross section of the element in which the crack is located, strain gauges with a base of 5-20 mm for metal elements and tensile elements are glued , and with a base of 20-50 mm for concrete and reinforced concrete elements to the right and left of the crack on both side walls of the element so that 2-3 strain gauges are located along the length of the crack perpendicular to the crack, and 2-3 strain gauges are located above the visible top of the crack; the distance between strain gauges is taken equal to 30-50 mm; then the electrical resistance of the strain gauges is measured, after which the element is loaded or unloaded with an experimental load F, a value not exceeding the maximum load on the element according to the material strength criterion or according to the permissible deflection of the element, calculated theoretically (taking into account the crack), and the electrical resistance of the strain gauges is again measured, and relative deformations are calculated using the formula:

,

where k is the strain sensitivity coefficient of strain gauges; R _0i - initial electrical resistance of the i-th strain gauge before loading (unloading); R _1i - electrical resistance of the i-th strain gauge after loading (unloading); for statistics, a test load is applied 3-5 times and R _0i , R _1i and ε _i are measured each time; the obtained average values of relative deformations are shown on the diagram of deformations ε _i along the height of the cross section of the element on both sides of the crack for each side wall of the element; straight lines are drawn through the vertices of the strain ordinates perpendicular to the side walls of the element until they intersect with the walls and the distance from these intersection points to the wall of the element from which the crack begins is measured; From the distances measured on the ε _i diagrams, taking into account the scales, the values of the crack lengths are calculated And on the surfaces of the side walls of the element and the average length of the crack:

,

Based on the results of 3-5 measurements of the crack length l _mp at the initial time and after some time t, the crack growth rate under load is determined using the formula:

,

where l _mp (t) is the length of the crack after some time t ; l _mp (0) is the length of the crack at the initial time.

2. The method for determining the length of a crack according to claim 1, characterized in that in reinforced concrete elements, deformations are measured only in the tensile zone of concrete, because in a compressed zone, the deformation diagram, depending on the load value, can be curvilinear, and strain gauges are glued to the surface of the concrete in the tension zone at a distance from the working reinforcement of 2-3 reinforcement diameters to eliminate its influence on the local deformation of concrete.

The disadvantage of the prototype is the difficulty of its use in systems with magnetic-pulse loading, due to the influence of a strong pulsed magnetic field on strain gauge sensors and electrical conductors connecting the strain gauge sensors with an electronic signal processing system. The existing problem of electromagnetic compatibility cannot be solved by simply replacing strain gauges with optical fibers with Bragg gratings, due to the difference in their operating principle and technical characteristics. A disadvantage of strain gauge sensors and the prototype in particular is the need to use temperature compensation if measurements are made over a wide range of ambient temperatures. Strain gauge sensors cannot be used in strong electromagnetic fields, such as microwave fields.

The purpose of the claimed invention is to reduce sensitivity to pulsed electromagnetic interference and increase thermal stability.

This goal is achieved due to the fact that the device contains one or more optical fibers with Bragg gratings with a reflectance at the resonant wavelength from 10% to 90%, the optical fibers are fixed on the surface of the material under study perpendicular to the slot on the material sample, the attachment points of the optical fibers located at a distance from 10 mm to 20 mm, the output end of each of the optical fibers with Bragg gratings is connected to its own photodetector,

one or more semiconductor lasers are connected to one or more optical fibers with Bragg gratings through fiber circulators, another port of each of the circulators is connected to its own photodetector,

The half-width of the spectrum σ _LD of the semiconductor laser radiation is chosen significantly less than the half-width of the spectrum σ _FBG of the reflection of the fiber Bragg grating

the operating wavelength of the semiconductor laser is set in the range from λ _FBG +0.4 σ _FBG to λ _FBG +1.3σ _FBG , where λ _FBG is the resonant reflection wavelength of the fiber Bragg grating,

photodetectors and a pulse synchronizer of the current generator are connected to the outputs of a multichannel analog-to-digital converter,

by the delay time between the signal of the pulse synchronizer and the signal of the reflected radiation by the Bragg grating, the speed of crack opening in the direction parallel to the slot of the material sample is determined; by the magnitude of the signal - the width of the crack in the process of opening; by the duration of the pulse reflected by the Bragg grating - the speed of crack expansion; by the delay between the pulse synchronizer and interruption of the passage of light through the optical fiber - the time until the fiber is destroyed due to exceeding the permissible value of fiber stretching, the relative position of the operating wavelength of the semiconductor laser and the reflection spectrum of the Bragg grating is determined by the ratio of the power passed through the fiber with the Bragg grating and the reflected power.

The essence of the invention is illustrated by two figures: Fig. 1 – block diagram of the proposed device, Fig. 2 – oscillogram of output signals. In fig. 1: sample of the material under study, 2 – cutout, 3 – flat curved conductor, 4 – pulsed current generator, 5 – optical fiber, 6 – fiber Bragg grating, 7 – crack, 8 – semiconductor laser with a Peltier element, 9 – circulator, 10 – photodetector of radiation transmitted through the optical fiber, 11 – photodetector of radiation reflected by the Bragg grating, 12 – analog-to-digital converter, 13 – personal computer, 14 – points of attachment of the optical fiber to the sample, 15 – power supply unit of the Peltier element.

The shape of the sample under study, the location of optical fibers on the test sample, and the connection diagram of the optical and electronic parts of the device are shown in Fig. 1. A flat-shaped sample of the material under study 1 has a slot 2, rounded inside the sample, or a chevron type inside which there is a flat conductor 3 whose surfaces inside the slot do not touch, except for the curved section. Flat conductor 3 is in contact with the outer side of the sample along the entire length of gap 2, excluding the curved section. A flat conductor is electrically connected to a pulse current generator 4. An optical fiber 5 with a Bragg grating 6 is attached to the material sample, crossing an existing crack 7 or the most likely location of crack formation. A semiconductor laser with a Peltier element is connected by an optical fiber to one input of the circulator 9. The input end of the optical fiber 5 is connected to the first output of the circulator 9. The output end of the optical fiber 5 is connected to the photodetector 10 of radiation passing through the optical fiber. The photodetector 11 of the radiation reflected by the Bragg grating is optically connected to the second output of the circulator 9. The pulse current generator is electrically connected to the input of the analog-to-digital converter 13. Photodetectors 10 and 12 are electrically connected to the inputs of the analog-to-digital converter 13. The fiber is attached to the test sample at attachment points 14 The Peltier element power supply 15 is connected to the Peltier element of the semiconductor laser. The analog-to-digital converter 12 is connected to a personal computer 13.

The operating principle of the proposed device is as follows. The optical radiation of the semiconductor laser 8 is introduced into the optical fiber, transmitted to the input of the circulator 9, passes through the circulator and is introduced into the optical fiber 5 with a fiber Bragg grating 6. The wavelength of the radiation of the semiconductor laser 8 is selected in accordance with the claims: from λ _FBG +0.4 σ _FBG up to λ _FBG +1.3σ _FBG . The wavelength of the laser 8 is adjusted by cooling or heating it using a Peltier element, mechanically coupled to the body of the semiconductor laser 8, by adjusting the current flowing through the Peltier element, performed using the power supply of the Peltier element 15.

The radiation reflected by the fiber Bragg grating passes back through the optical fiber 5 into the circulator 9, exits through the second output of the circulator 9 and enters the input of the reflected radiation photodetector module 11. The radiation passed through the fiber 5 with the Bragg grating 6 enters the input of the photodetector module 10. The output signals from the photodetector modules 10 and 11 are supplied to the corresponding inputs of the analog-to-digital converter 12. The clock pulse of the pulse current generator 4 is also transmitted to the analog-to-digital converter 12.

When a current pulse is applied through a flat conductor 3, the current flowing through the conductor 3, due to its interaction with the resulting magnetic field, produces a mechanical effect on the edges of the slot 2. The mechanical effect - loading, is transmitted through the sample material and, with sufficient force of influence, produces a partial destruction of the material in the form of a crack 7, which over time spreads along the axis of the slot 2 and expands in the perpendicular direction, i.e. the crack opens.

The appearance of a crack in the material of the test sample 1 and its further opening leads to an elongation of the fiber Bragg grating, and the elongation of the grating leads to an increase in its resonant wavelength λ _FBG . When using a semiconductor laser 8 with a narrow spectral width (in accordance with the claims of the invention: “the half-width of the spectrum σ _LD of the semiconductor laser radiation is chosen significantly less than the half-width of the spectrum σ _FBG of the reflection of the fiber Bragg grating”), a change in λ _FBG leads to a change in the value of the output voltage, both reflected and and transmitted radiation. The analog-to-digital converter 12 converts analog signals into digital ones and transmits data to a personal computer 13 for subsequent calculation of the parameters of the crack opening process.

The choice of a Bragg grating reflectivity at the resonant wavelength from 10% to 90% is due to the following reasons. In the inventive device, it is important to determine the power of both reflected and transmitted optical fiber radiation, which, as will be shown below, is necessary to determine the ratio of these powers. If one of the indicated values is significantly smaller than the other, then when determining the latter, a worse signal-to-noise ratio will occur. Accordingly, the power ratio will be determined with a greater error than in the case of comparable power values. The specified range of reflection coefficient is conditional: with a higher or lower reflection coefficient, the device remains operational, but the quality of the device will be lower. At low radiation power passing through an optical fiber with a Bragg grating, the accuracy of determining the moment of optical fiber rupture will also decrease due to a deterioration in the signal-to-noise ratio.

The choice of the laser operating length ranging from λ _FBG +0.4σ _FBG to λ _FBG +1.3σ _FBG , where λ _FBG is the resonant reflection wavelength of the fiber Bragg grating, is due to the following reason. Since when an optical fiber with a Bragg grating is elongated, the resonant wavelength increases, in order to achieve the largest recorded range of elongation, the operating wavelength of the laser must be located on the falling portion of the spectral dependence of the grating reflection, that is, the laser wavelength must be greater than the resonant wavelength of the grating . When the grating elongation is small, the change in its wavelength is also small. Therefore, to determine the thickness of a crack in a material during its opening, it is necessary to ensure a good signal-to-noise ratio. Accordingly, the power of reflected radiation should not be too small. The minimum operating wavelength λ _FBG +1.3σ _FBG selected in the claimed invention approximately corresponds to a level of 0.18 from the maximum value, and λ _FBG +0.4σ _FBG to a level of 0.85. The specified range of the operating wavelength of a semiconductor laser is also arbitrary. It is important that a good signal-to-noise ratio is ensured even when influenced by some temperature instability in the wavelength and power of the semiconductor laser, as well as the resonant wavelength of the Bragg grating. At wavelengths greater than λ _FBG +1.3σ _FBG , the signal-to-noise ratio can be considered poor, and at wavelengths shorter than λ _FBG +0.4σ _FBG , there is a decrease in sensitivity to small extensions of the Bragg grating due to the flat portion of the spectral dependence of reflection near the maximum - resonant wavelength.

Crack opening speed in the longitudinal direction is determined by the formula:

(1),

where L is the distance between the slot in the sample of the material under study and the fiber Bragg grating, τ _p is the delay time for the beginning of a change in the power of the radiation reflected from the fiber Bragg grating relative to the synchronization pulse of the pulse generator.

In general, the speed of crack opening may depend on the distance and, accordingly, may be different when using different optical fibers attached to the sample.

The change in crack width Δ l during the opening process (i.e. in time t ) is determined by the formula:

(2),

where Δλ( t ) is the change in the resonant wavelength of the fiber Bragg grating, k is the proportionality coefficient equal to 1.2·10 ³ nm for a single-mode quartz fiber at a radiation wavelength of 1550 nm. In turn, the value of Δλ( t ) is determined by the change in the output signal U , in the general case, using the calibration dependence Δλ( U ). It is advisable to use the output voltage ( UR ) at the output of the photodetector module of the radiation reflected by the fiber Bragg grating, but _it is possible to use the output voltage at the output of the photodetector module of the radiation that has passed through the fiber with the Bragg grating. For the Gaussian spectral dependence of the reflection of a fiber Bragg grating with a resonant wavelength λ _FBG in the state fixed to the sample and half-width σ _FBG, the value Δλ can be calculated using the formula:

(3),

where U _R0 is the voltage at the output of the photodetector module of reflected radiation at the initial position of the fiber with the Bragg grating on the sample. The dependence maintains a one-to-one correspondence between Δλ and the output voltage until equality of the resonant wavelength of the Bragg grating and the wavelength of the semiconductor laser is achieved, assuming the choice of the resonant wavelength of the Bragg grating in accordance with the claims.

The crack width l during the opening process is determined similarly to the change in crack width over time (using formulas (2) and (3)), but taking into account the initial value of the crack width l ₀ - before pulsed mechanical action, if the crack already existed:

,(4)

Speed the increase in crack width is determined by the formula:

,(5)

where Δτ ₀₁ is the time interval from the beginning of the change in the output signal t ₀ to the selected moment in time t ₁ , at which the value of the output signal U ( t ₁ ) is reached.

The principle of thermal compensation when performing measurements is based on the simultaneous use of two photodetector modules - radiation reflected and transmitted through a fiber Bragg grating. As the temperature changes, both the power and wavelength of the semiconductor laser radiation and the resonant wavelength of the Bragg grating change. Let both modules have the same sensitivity. Then the expression describing the voltage at the output of the modules can be represented as:

, (6)

, (7)

where U _R and U _T are the voltage at the output of the photodetector modules of the radiation reflected and transmitted through the fiber Bragg grating, respectively, p ₀ is the radiation power of the semiconductor laser, k _R is the reflection coefficient of the fiber Bragg grating at the resonant wavelength, k _λ is the coefficient depending, first everything from the emission spectrum of a semiconductor laser and the reflection spectrum of a fiber Bragg grating. From expressions (6) and (7) it follows that:

, (8)

So the attitude independent of power , which is a consequence of the fact that the fiber Bragg grating divides the radiation incident on it into reflected and transmitted radiation, regardless of the power of the semiconductor laser. Then, having experimentally measured the ratio (8) at the initial moment of time, i.e. having actually specified the relative position of the operating wavelength of the semiconductor laser and the reflection spectrum of the fiber Bragg grating, then, during the measurement process, it is sufficient to maintain the measured value of the ratio (8) by changing the temperature of the semiconductor laser, carried out by adjusting the current flowing through the Peltier element or manually mode, or automatically using existing automatic control systems.

Time interval between the synchronizer pulse and the moment of interruption of the passage of light through the optical fiber in the event of its break due to exceeding the permissible value of fiber stretching, allows you to determine the speed propagation of a crack leading to fiber rupture according to the formula:

, (9)

The claimed device was tested on an experimental model. The study was carried out on a polymethyl methacrylate sample with a thickness of 5 mm and dimensions of 200x200 mm. A slot was made in the middle of the side of a square 50 mm long and 2 mm wide. The parameters of the pulse generator were as follows: maximum pulse current - 100 kA, voltage - up to 30 kV, pulse duration - from 1 to 5 μs. A current pulse passing through a flat conductor created a crack in the sample under study. Next, an optical fiber with a Bragg grating was glued onto the surface of the sample, the middle of which was installed approximately above the crack. The half-width of the semiconductor laser radiation spectrum is 0.015 nm, the central wavelength of the radiation at room temperature is 1551.3 nm. The fiber Bragg grating was manufactured on a piece of single-mode optical fiber, the grating length was 10 mm, the half-width of the reflection spectrum was 0.07 nm, the resonant wavelength was 1150.6 nm, and the reflectance at the resonant wavelength was 0.8. That is, the parameters of the laser and fiber Bragg grating corresponded to the claims.

Crack opening rates were measured under normal mechanical loading of the sample material. An oscillogram of the output voltage at the output of the photodetector module of reflected radiation by a Bragg grating is shown in Fig. 2. From the oscillogram it follows that before the start of loading the signal was approximately 0.04 V, after 0.1 V, i.e. there was expansion of the crack. There was also elastic deformation of the material - after the maximum value of the signal, there was a partial decrease in the elongation of the crack. The presence of a minimum in the U ( t ) dependence is due to the fact that the maximum stretching of the Bragg grating was such that its resonant wavelength turned out to be greater than the wavelength of the semiconductor laser radiation.

Thus, the inventive device makes it possible to determine all the necessary parameters of crack opening, but is insensitive to strong pulsed magnetic fields due to the use of optical fibers. The inventive device makes it possible to control the working length of a semiconductor laser relative to the reflection spectrum of a fiber Bragg grating, which makes it possible to adjust the device either manually or using standard automatic control systems, using the measured ratio of the transmitted and reflected signals of the fiber Bragg grating. That is, the inventive device allows for thermal compensation during measurements.

Claims (5)

A device for measuring the speed of crack opening, consisting of a source of optical radiation, fiber Bragg gratings, photodetector modules, characterized in that the device contains one or more optical fibers with Bragg gratings with a reflectance at the resonant wavelength from 10 to 90%, the optical fibers are fixed on the surface of the material under study perpendicular to the slot on the material sample, the attachment points of the optical fibers are located at a distance from 10 mm to 20 mm, the output end of each of the optical fibers with Bragg gratings is connected to its photodetector, one or more semiconductor lasers are connected to one or more optical fibers with Bragg gratings through fiber circulators, one more port of each of the circulators is connected to its own photodetector, half-width of the spectrum $$\sigma$$ _LD radiation of a semiconductor laser is chosen significantly less than the half-width of the spectrum $$\sigma$$ _FBG reflection fiber Bragg grating, The operating wavelength of the semiconductor laser is set in the range from $$\lambda$$ _FBG +0.4 $$\sigma$$ _FBG before $$\lambda$$ _FBG +1.3 $$\sigma$$ _FBG , where $$\lambda$$ _FBG resonant reflection wavelength of fiber Bragg grating, photodetectors and a pulse synchronizer of the current generator are connected to the outputs of a multichannel analog-to-digital converter, by the delay time between the signal of the pulse synchronizer and the signal of the reflected radiation by the Bragg grating, the speed of crack opening in the direction parallel to the slot of the material sample is determined; by the magnitude of the signal - the width of the crack in the process of opening; by the duration of the pulse reflected by the Bragg grating - the speed of crack expansion; by the delay between the pulse synchronizer and interruption of the passage of light through the optical fiber - the time until the fiber is destroyed due to exceeding the permissible value of fiber stretching, the relative position of the operating wavelength of the semiconductor laser and the reflection spectrum of the Bragg grating is determined by the ratio of the power passed through the fiber with the Bragg grating and the reflected power.