CN108956534B - Refractive index measurement method based on open cavity Fabry-Perot interferometer - Google Patents
Refractive index measurement method based on open cavity Fabry-Perot interferometer Download PDFInfo
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- G01N21/41—Refractivity; Phase-affecting properties, e.g. optical path length
- G01N21/45—Refractivity; Phase-affecting properties, e.g. optical path length using interferometric methods; using Schlieren methods
Abstract
The invention discloses a refractive index measuring method based on an open cavity Fabry-Perot interferometer. The invention tracks the wavelength drift position of the target interference valley of the appointed order according to the relation between the size and the order of the target free spectrum range at the reference wavelength position in the output spectrum of the interferometer and the measured refractive index, and calculates the refractive index of the medium in the open cavity by using the relation between the wavelength of the target interference valley and the refractive index. The invention overcomes the defect of small measurement range of the existing method and can realize the measurement of large refractive index range. Furthermore, since the wavelength range observed by the present invention can exhibit multiple interference valleys, the FSR of the interferometer can be smaller in the case of achieving a large refractive index measurement range, resulting in: the interference wave trough becomes sharp, and the accuracy of the wave trough position judgment is improved; and a larger-size open cavity is allowed, so that the manufacturing difficulty of the sensor is reduced.
Description
Technical Field
The invention relates to the technical field of optical fiber refractive index sensors, in particular to a refractive index measuring method based on an open cavity Fabry-Perot interferometer.
Background
The optical fiber refractive index sensor has the advantages of low cost, acid and alkali corrosion resistance, low transmission loss, high response speed, strong repeatability, electromagnetic interference resistance and the like, so that the optical fiber refractive index sensor is widely applied to the fields of physics, chemistry, biomedicine and the like, and the research on the optical fiber refractive index sensor is increasingly active in recent years. The open Fabry-Perot interferometer sensor has ultrahigh refractive index sensitivity, good linearity and low temperature cross sensitivity, and has high application value in the field of micro refractive index change measurement.
The current commonly used wavelength demodulation methods are Fourier transform method (Pevec S, et al. high resolution, all-fiber, micro-machined sensor for spatial light source) of active index and temporal optics Express, absolute optical path difference measurement method (L i X, et al. A high sensitivity and optical fiber-refractive index for refractive index measurement accuracy for refractive index measurement, sensor, 2016) of active index and temporal index measurement, which can be measured by a free-wavelength spectrum-based refractive index shift method, which can measure the refractive index by a free-wavelength-dependent refractive index shift method, which can measure the refractive index of a measured object through a free-wavelength spectrum-observation method, but has a smaller wavelength-dependent refractive index shift, which can be measured by a free-wavelength-dependent refractive index shift method, which can measure the refractive index of a measured object through a free-wavelength spectrum-optical spectrum-induced refractive index shift method, which can measure the refractive index of a measured object through a free-wavelength shift method, a free-wavelength-dependent refractive index shift method, a free-measured object, a free-induced refractive index shift method, a free-measured spectrum, a wavelength-induced refractive index shift method, a free-induced refractive index, a wavelength, a free-induced refractive index, a wavelength, a wavelength.
For an open cavity Fabry-Perot interferometer sensor, when the refractive index of a medium in a Fabry-Perot cavity changes, a comb-shaped interference spectrum drifts, the wavelength change of interference valleys and the change of the refractive index in the Fabry-Perot cavity present a linear relation, and the intra-cavity refractive index information can be obtained by detecting the drift of the interference valleys in a certain wavelength range. The traditional open cavity Fabry-Perot interferometer refractive index measurement usually adopts a wavelength tracking method, and only one interference valley appears in a wavelength observation range when the refractive index in a cavity is changed, and the order corresponding to the interference valley cannot be changed. The wavelength viewing range is approximately equal to the free spectral range of the observed interference valley at the initial refractive index. Because the refractive index sensitivity of the open cavity Fabry-Perot interferometer is very high, and the FSR is relatively small, the traditional wavelength tracking method causes the refractive index measurement range to be very small, and the application range of the refractive index is limited.
Disclosure of Invention
Aiming at the problems, the invention provides a novel method for measuring the refractive index of an open cavity Fabry-Perot interferometer aiming at double-beam interference according to the change rule of the size and the order of the FSR of an interference peak at any wavelength when the refractive index in a cavity changes, and the method can track the change of a target interference valley in a large wavelength range, thereby greatly expanding the measurement range of the refractive index.
The invention relates to a refractive index measurement method based on an open cavity Fabry-Perot interferometer, which is characterized in that the wavelength drift position of a target interference valley of a specified order is tracked according to the relation between the size and the order of a target free spectral range at a reference wavelength position in an output spectrum of the interferometer and a measured refractive index, and the refractive index of a medium in an open cavity is calculated by using the relation between the wavelength and the refractive index of the target interference valley; the method comprises the following specific steps: firstly, calibrating the open cavity Fabry-Perot interferometer by using a series of matching fluids with known refractive indexes in a measurement range to obtain the following refractive indexes: the relation between the size of the target free spectral range and the order, and the relation between the wavelength of the target interference valley and the measured refractive index; and then the open-cavity Fabry-Perot interferometer is used for actual measurement, the order of the target FSR is determined according to the size of the target FSR in the actual measurement interference spectrum, so that the position of the target interference valley is deduced, and finally the value of the measured refractive index is calculated by using the calibrated relation between the wavelength of the target interference valley and the refractive index.
The Fabry-Perot interferometer is an open cavity structure with double-beam interference.
The reference wavelength can be assigned as the wavelength of any interference valley in the interference spectrum of the Fabry-Perot interferometer when the measured refractive index reaches the measured minimum value.
The target free spectral range at the reference wavelength position refers to a free spectral range with the same order as the adjacent wave trough in the short wave direction of the reference wavelength.
And the target interference valley of the specified order is defined as the interference valley adjacent to the reference wavelength short wave direction in the interference spectrum when the measured refractive index reaches the measurement minimum value.
The invention has the following beneficial effects:
(1) the refractive index measuring range of the open cavity Fabry-Perot interferometer sensor is greatly expanded.
(2) Because the size of the target FSR of the same order and the measured refractive index present a linear relationship, at least two points are sampled in the refractive index range corresponding to the target FSR of the same order in the calibration process to complete the fitting of the partial relational expression, thereby greatly reducing the number of sampling points in the calibration process.
(3) Since multiple interference valleys may occur over the observed wavelength range, the FSR of the interferometer may be smaller in the case of achieving a large refractive index measurement range, resulting in: the interference wave trough becomes sharp, and the accuracy of the wave trough position judgment is improved; and a larger-size open cavity is allowed, so that the manufacturing difficulty of the sensor is reduced.
Drawings
FIG. 1 is a schematic diagram of a double-beam interference open cavity fiber Fabry-Perot interferometer;
FIG. 2a is a schematic diagram of the correspondence of a reference wavelength to a target FSR (the reference wavelength is between two interference valleys);
FIG. 2b is a diagram illustrating the correspondence between the reference wavelength and the target FSR (the reference wavelength is equal to a certain interference valley);
FIG. 3 is a graph of the target FSR size, order and SRI correspondence;
FIG. 4 is a graphical illustration of the relationship of target FSR size and its corresponding order;
FIG. 5 is a photomicrograph of an actual sensor fabricated;
FIG. 6 shows the interference spectrum of an actually fabricated sensor in deionized water, and the selection of a reference wavelength and a target trough;
FIG. 7a is a calibration curve (target FSR vs. SRI) for an actual fabricated sensor;
FIG. 7b is a calibration curve (target interference trough wavelength versus SRI) for an actual fabricated sensor.
Detailed Description
The refractive index measurement method related to the present invention is explained as follows:
first, basic theory
The structure of an open cavity fiber Fabry-Perot interferometer is shown in figure 1. The open cavity interferometer in fig. 1 is formed by core-shifting and welding a single-mode fiber 1, a single-mode fiber 2 and another fiber 3, wherein the single-mode fiber 1, the single-mode fiber 2 and the fiber 3 play a connecting role and cannot shield fiber cores of the single-mode fiber 1 and the single-mode fiber 2. The part 4 which is not welded between the single-mode fiber I1 and the single-mode fiber II 2 is an open Fabry-Perot cavity, which is called an open cavity for short. The interface of the single-mode fiber I1 and the open cavity medium forms a first reflecting mirror 5, and the interface of the open cavity medium and the single-mode fiber II 2 forms a second reflecting mirror 6. When one beam of light is transmitted to the first reflector 5 through the first single-mode fiber 1, a part of light is reflected and recorded as reflected light I, and the rest of light reaches the second reflector 6 through the open cavity and is reflected again. The reflected light from the second mirror 6 is denoted as reflected light II, which is again reflectedAnd the secondary light is coupled into the fiber core of the single-mode fiber I1 through the open cavity and generates Fabry-Perot interference with the reflected light I. Because the reflectivity of the two mirrors is low, the interferometer generates double-beam interference, and the interference spectrum of the interferometer is comb-shaped. According to the theory of two-beam interference, the mth order interference valley wavelength dipmThe expression of (a) is:
where n is the index of refraction of the medium in the open cavity, i.e., the ambient index of refraction (SRI), L is the length of the open cavity, it can be seen that the interference valley wavelength of the lower order is larger, and in the case of L being constant, the dip of the same ordermLinear with SRI. Thus, by tracking dipmCan be used to perform SRI measurements.
The wavelength range between two adjacent interference valleys is called the Free Spectral Range (FSR), the mth order free spectral range FSRmThe expression of (a) is:
it can be seen that the FSRs of different orders are slightly different, and under the condition of L being unchanged, the FSRs of the same ordermAlso linear with SRI. Experiments have found that in the C-band range, dipmComparison with FSRmIs more sensitive to SRI.
Second, the scheme design of the invention
In the application of the open cavity fabry-perot interferometer sensor, in order to obtain higher refractive index sensitivity, a scheme of tracking the wavelength change of the interference valley is generally adopted. To extend the refractive index measurement range, it is necessary to extend the wavelength viewing range, but this will result in multiple interference valleys within the wavelength viewing range. Therefore, how to identify the target interference valley to be tracked is a difficult point for this type of sensor to extend the refractive index measurement range.
The scheme design of the invention is as follows: the order information of the FSR is obtained by measuring the size of the FSR at a certain designated wavelength, the position of a target interference valley is determined according to the relation between the order of the FSR and the order of the target interference valley, and the SRI is calculated by using the relational expression between the target interference valley and the SRI. The method allows for multiple interference valleys within the wavelength viewing range, so that theoretically the wavelength viewing range can be extended to infinity (limited in practice by the wavelength range of the light source output), thereby enabling a wide range of refractive index measurements.
Third, the basic principle of the invention
The basic principle of the invention is essentially the magnitude of the FSR at a given wavelength and the law of its order as a function of SRI. For ease of description, the specified wavelength is referred to as the reference wavelength; the FSR at the reference wavelength is referred to as the target FSR. There are two cases when determining the target FSR from the reference wavelength: one is that the reference wavelength is located between two interference valleys; one is that the reference wavelength is equal to some interference valley wavelength. In both cases, the FSR of the same order as the interference trough adjacent to the left side (short wave direction) of the reference wavelength is used as the target FSR. As shown in fig. 2a and 2b, the dotted line is the reference wavelength and the dashed line is the target FSR.
Because the interference spectrum is red-shifted with increasing SRI, the minimum value of the measured refractive index is taken as the initial refractive index and is marked as n0At this time, the corresponding interference spectrum is the initial interference spectrum. Taking the wavelength corresponding to any interference valley in the initial interference spectrum as a reference wavelength, taking the adjacent interference valley in the short wave direction of the reference wavelength as a target interference valley, wherein the order of the target interference valley is defined as m and is expressed as dipm(n), wherein n is the corresponding SRI of the interference spectrum. Target interference valley wavelength in initial state is dipm(n0) Target FSR is m-th order and size is FSRm(n0). According to theoretical derivation, the size and order of the target FSR and the SRI are shown in FIG. 3, where n isi＝[2m+(2i-1)]n0/(2m-1)，i＝0,1,2,3…。
It can be seen that as SRI increases, the following rules exist: (1) the order corresponding to the target FSR is gradually increased; (2) the size of the target FSR of the same order is linearly increased; (3) the lower order target FSR is larger in size and higher in refractive index sensitivity than the higher order target FSR; (4) the maximum value of a certain order target FSR is equal to the minimum value of a lower order target FSR; (5) the size of the target FSR is one-to-one with the SRI. The relationship between the size of the target FSR and the corresponding order can be obtained by using the rule, as shown in FIG. 4.
In actual measurement, the order of the target FSR under the current SRI can be determined according to the relationship between the size of the target FSR and the corresponding order thereof as shown in fig. 4, so as to determine the target interference dipmThe position of (a). For example, if the order of the target FSR is m + i (i is 0,1,2 …), i troughs in the long-wave direction are the target interference troughs dip from adjacent troughs in the short-wave direction of the reference wavelength as the starting pointm。
According to the principle, when a plurality of interference valleys appear in the wavelength observation range, the target interference valleys can be continuously tracked, and therefore the open cavity refractive index measurement range is expanded.
Fourthly, the concrete steps of the invention
The method for measuring the refractive index of the open cavity Fabry-Perot interferometer provided by the invention comprises the following two steps: and (5) calibrating and actually measuring. The calibration aims at obtaining a relational expression of the target FSR size and the order of the open cavity Fabry-Perot interferometer and a relational expression of the target interference valley wavelength and the measured refractive index. In actual measurement, the order of the target FSR is obtained by obtaining the size of the target FSR, then the position of the target interference valley is determined, and finally the numerical value of the measured refractive index is calculated according to the relational expression of the target interference valley wavelength and the SRI.
Example (b):
according to the measurement method described above, an open-cavity Fabry-Perot interferometer sensor having a cavity length of about 68 μm was fabricated, and an object micrograph thereof is shown in FIG. 5.
Taking the interference spectrum in the deionized water as an initial interference spectrum, selecting an interference valley at 1518.84nm as a reference wavelength, and determining a target interference valley dipmAnd target FSR (in this case FSR)m) As shown in fig. 6.
And calibrating the refractive index within the range of 1.333-1.4 RIU. The sensor is used for measuring 21 groups of refractive index matching fluids with the refractive index range of 1.333-1.4 RIU, each matching fluid is measured for 3 times respectively, and target FSR and target interference trough dip under different SRI are obtainedmThe change rules of (a) are shown in fig. 7(a) and fig. 7(b), respectively. The mesh in FIG. 7(a) is drawnThe average value of the three measurements of the target FSR is fit with a relation curve of the target FSR and the SRI, and the target FSR in the same order monotonically increases along with the increase of the SRI, and the target FSR in different orders gradually decreases along with the increase of the order to present a step-shaped curve, which is identical with theoretical derivation. Similarly, the target interference trough dip in FIG. 7(b) is takenmThe average of three measurements was fitted to the target interference trough versus SRI. The experimental result shows that the refractive index sensitivity of the sensor can reach 1260.282nm/RIU, the linear fitting degree reaches 0.99992, and a good linear relation is kept in the measured refractive index range, which is consistent with the theoretical derivation.
Using the calibration curve to carry out actual measurement, respectively immersing the sensing head into 3 matching fluids with different refractive indexes, firstly measuring the size of the target FSR to determine the position of the target interference valley, and then calculating the refractive index of the matching fluid to be measured according to the relation function of the central wavelength of the target interference valley and the SRI, wherein the table 1 shows the actual measurement result and the relative error, and the average relative error is only 9.73 × 10-5Percent, has higher accuracy. The above measurements verify the effectiveness of the method of the invention. TABLE 1 measurement results and errors of actual sensor fabrication
| Measuring group | Actual value | Measured value | Relative error |
| First group | 1.3414 | 1.3414013 | 9.69×10-5％ |
| Second group | 1.3645 | 1.364501 | 7.33×10-5％ |
| Third group | 1.3983 | 1.3983017 | 12.16×10-5％ |
Claims (2)
1. A refractive index measurement method based on an open cavity Fabry-Perot interferometer is characterized in that: tracking the wavelength drift position of a target interference valley of a specified order according to the relationship between the size and the order of a target free spectral range at a reference wavelength position in an output spectrum of the interferometer and the measured refractive index, and calculating the refractive index of a medium in the open cavity by using a relational expression between the wavelength and the refractive index of the target interference valley; the method comprises the following specific steps: firstly, calibrating the open cavity Fabry-Perot interferometer by using a series of matching fluids with known refractive indexes in a measurement range to obtain the following refractive indexes: the relation between the size of the target free spectral range and the order, and the relation between the target interference valley wavelength and the measured refractive index are as follows:
taking the minimum value of the measured refractive index as an initial refractive index and marking as n0The corresponding interference spectrum is an initial interference spectrum, the wavelength corresponding to any interference valley in the initial interference spectrum is taken as a reference wavelength, the adjacent interference valley in the short wave direction of the reference wavelength is taken as a target interference valley, the order of the target interference valley is defined as m and is expressed as dipm(n), wherein n is the ambient refractive index SRI corresponding to the interference spectrum; target interference valley wavelength in initial state is dipm(n0) The FSR range of the target free spectrum is m-order,
according to the theory of two-beam interference, the mth order interference valley wavelength dipmThe expression of (a) is:
wherein n is the refractive index of the medium in the open cavity, namely the ambient refractive index SRI, L is the length of the open cavity, and when L is not changed, dip of the same ordermIn linear relationship with SRI, by tracing dipmCan implement the measurement of SRI;
the target FSR has the following relationship with refractive index: (1) the order corresponding to the target FSR is gradually increased; (2) the size of the target FSR of the same order is linearly increased; (3) the lower order target FSR is larger in size and higher in refractive index sensitivity than the higher order target FSR; (4) the maximum value of a certain order target FSR is equal to the minimum value of a lower order target FSR; (5) the size of the target FSR corresponds to the SRI one by one;
then the open cavity Fabry-Perot interferometer is used for actual measurement, the order of the target free spectral range is determined according to the size of the target free spectral range in the actual measurement interference spectrum, so as to deduce the position of the target interference valley,
finally, calculating the value of the measured refractive index by using a calibrated relation between the wavelength of the target interference valley and the refractive index;
the reference wavelength is specified as the wavelength of any interference valley in the interference spectrum of the Fabry-Perot interferometer when the measured refractive index reaches the measurement minimum value;
the target free spectral range at the reference wavelength position refers to a free spectral range with the same order as the adjacent wave trough in the reference wavelength short wave direction;
and the target interference valley of the specified order is defined as the interference valley adjacent to the reference wavelength short wave direction in the interference spectrum when the measured refractive index reaches the measurement minimum value.
2. The method for measuring the refractive index based on the open cavity Fabry-Perot interferometer according to claim 1, characterized in that: the Fabry-Perot interferometer is an open cavity structure with double-beam interference.
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| CN113607688B (en) * | 2021-06-03 | 2024-03-19 | 天津工业大学 | Microfluidic refractive index sensor based on double-hole microstructure optical fiber |
| CN114739285B (en) * | 2022-04-01 | 2023-06-06 | 厦门大学 | Fabry-Perot cavity length accurate measurement method based on digital virtual reference cavity and vernier effect |
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