CN114166253B - Method and system for improving Mach-Zehnder sensor measurement range based on nonlinear regression data processing - Google Patents

Method and system for improving Mach-Zehnder sensor measurement range based on nonlinear regression data processing Download PDF

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CN114166253B
CN114166253B CN202111488431.3A CN202111488431A CN114166253B CN 114166253 B CN114166253 B CN 114166253B CN 202111488431 A CN202111488431 A CN 202111488431A CN 114166253 B CN114166253 B CN 114166253B
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transfer function
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zehnder
measurement range
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CN114166253A (en
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尹锐
曹令鑫
黄庆捷
杨洪亮
吕琳
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Shanghai Haina Xinda Data Technology Co ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01D—MEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
    • G01D5/00—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable
    • G01D5/26—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable characterised by optical transfer means, i.e. using infrared, visible, or ultraviolet light
    • G01D5/266—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable characterised by optical transfer means, i.e. using infrared, visible, or ultraviolet light by interferometric means
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01K—MEASURING TEMPERATURE; MEASURING QUANTITY OF HEAT; THERMALLY-SENSITIVE ELEMENTS NOT OTHERWISE PROVIDED FOR
    • G01K11/00—Measuring temperature based upon physical or chemical changes not covered by groups G01K3/00, G01K5/00, G01K7/00 or G01K9/00
    • G01K11/006—Measuring temperature based upon physical or chemical changes not covered by groups G01K3/00, G01K5/00, G01K7/00 or G01K9/00 using measurement of the effect of a material on microwaves or longer electromagnetic waves, e.g. measuring temperature via microwaves emitted by the object
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
    • G01L1/00—Measuring force or stress, in general
    • G01L1/24—Measuring force or stress, in general by measuring variations of optical properties of material when it is stressed, e.g. by photoelastic stress analysis using infrared, visible light, ultraviolet
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis

Abstract

The invention relates to a method and a system for improving the measurement range of a Mach-Zehnder sensor based on nonlinear regression data processing, which are as follows: (1) obtaining discrete data by measurement with an optical measurement device; (2) Processing discrete data by adopting a fitting algorithm, and restoring a transfer function, wherein the transfer function refers to the shape rule of the real output spectrum of the optical device when the input light is flat white light; thereby expanding the measurement range of the Mach-Zehnder optical sensor and making the Mach-Zehnder optical sensor break through the limitation of FSR and spectral width of the light source. The measurement range can be extended to infinity in theory, in practice, to a new measurement range after modification as long as the waveguide is able to maintain single mode operating conditions.

Description

Method and system for improving Mach-Zehnder sensor measurement range based on nonlinear regression data processing
Technical Field
The invention relates to a method and a system for improving the measurement range of a Mach-Zehnder sensor based on nonlinear regression data processing, and belongs to the technical field of optical measurement.
Background
Currently, in the method of optical measurement by means of spectrum, the peak value or valley value position of the spectrum is used to represent the physical quantity to be measured. Many optical devices are based on interference principles, with a Free Spectral Range (FSR) present. The measurement can only be completed when the peak or valley of the spectrum is within the FSR. As shown in fig. 1. Assuming that fig. 1 is a temperature sensor, the solid curve is the reflection or transmission spectrum of the sensor at 10 degrees, the reflection or transmission spectrum of the device at 20 degrees stretches to be moved to the shape of the broken line, and the meaning of the black broken line arrow in fig. 1 is that the peak value of the same diffraction order is moved from about 222nm to 253nm, the measurement range of the sensor is basically 10 degrees to 20 degrees, and when the temperature is below 10 degrees and above 20 degrees, the spectrum also has a peak value in the range of 222-253nm, but we cannot determine the diffraction order of the peak value, and cannot reversely deduce the value of the temperature to be measured. In other words, when we measure a peak at 240nm, if we determine that the current temperature is between 10 degrees and 20 degrees, we can back-infer that the current temperature is 18 degrees; when we do not know whether the current temperature is between 10 degrees and 20 degrees, we cannot determine whether the temperature of the reverse-derived is 18 degrees, 8 degrees, or 38 degrees.
Beyond the FSR of the device, the peak value is not in a one-to-one relationship with the physical quantity to be measured. This is a problem commonly faced by current sensors based on spectroscopic measurements. Solving this problem can be aided by a lower sensitivity but larger range sensor, which in addition to increasing cost, has the following problems: as the research level of the sensor is improved, the sensitivity of the device is also higher, and obviously, the measurement range of the device is smaller and smaller along with the improvement of the sensitivity. Therefore, besides the limitation of FSR, the spectrum width of the broad spectrum light source is limited, the spectrum width of the common C-band ASE broad spectrum light source is 40nm-70nm, and the spectrum width of the visible light plus near infrared light source is slightly larger, but can only reach 800nm-1000nm. For many sensors with ultra-high sensitivity, such as ultra-high sensitivity temperature sensors, the sensitivity reaches more than 50nm/K, and even if a 1000nm light source is used, the measuring range can only reach 20 degrees; for example, the ultra-high sensitivity liquid refractive index sensor has many researches exceeding 20000nm/RIU by 2021 in the last half year, and the individual researches reach 100000nm/RIU, and the measurement range can only reach 0.05 at most under the existing measurement method. This problem, independent of the FSR, is a difficulty caused by the limited linewidth of the broad spectrum light sources used in the test system.
Therefore, there is currently no solution with an ultra-wide range, especially for ultra-high sensitivity optical sensors.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method for expanding the measuring range of a Mach-Zehnder sensor based on nonlinear regression data processing;
the invention also provides a system for expanding the measuring range of the Mach-Zehnder sensor based on nonlinear regression data processing;
the invention can expand the measuring range of the Mach-Zehnder sensor to infinite under the condition of not changing the spectrum width of the light source.
The technical scheme of the invention is as follows:
a method for expanding the measurement range of a Mach-Zehnder sensor based on nonlinear regression data processing comprises the following steps:
(1) Measuring and obtaining discrete data of the Mach-Zehnder sensor;
(2) Processing discrete data by adopting a fitting algorithm, and restoring a transfer function, wherein the transfer function is an acquired high-resolution spectrum image;
if the input is flat white light, i.e. the power at each wavelength is all equal, the output spectrum of the Mach-Zehnder sensor is a transfer function, as shown in formula (I):
Figure GDA0003454845050000021
in the formula (I), y i For outputting light intensity; x is x i Parameters related to waveguide effective refractive index change caused by physical quantity to be measured; a and b are variables determined according to different measurement scene initial conditions and device parameters; c and d are parameters related to the maximum and minimum of the actual transfer function; lambda is the wavelength of light;
if the input is not flat white light, the transfer function is the output spectrum divided by the input spectrum.
(3) And (3) obtaining a physical quantity to be measured according to the transfer function restored in the step (2), wherein the physical quantity to be measured is a measurement target of the Mach-Zehnder sensor.
According to a preferred embodiment of the invention, a, b, c, d, λ in formula (I) are five parameters to be determined;
the specific fitting method of formula (I) is as follows:
a. calculating the measured dispersion point, i.e. the discrete data of the Mach-Zehnder sensor, is expressed as n sets of data points (x 1 ,y 1 )，(x 2 ,y 2 )，…，(x n ,y n ) To transfer functionThe sum of squares, x of the distances of (2) 1 ……x n Refers to the parameters related to the effective refractive index of the waveguide, y, determined by the physical quantity to be measured 1 ……y n Refers to optical power;
the square of the distance from the scattered point to the transfer function is measured as
Figure GDA0003454845050000022
i=1, 2, …, n, the sum of squares of the distances of the individual scattered points to the transfer function is +.>
Figure GDA0003454845050000023
b. Respectively solving partial derivatives of the five undetermined parameters of a, b, c, d and lambda, wherein the position where the partial derivatives are zero is the function with the minimum distance to each measuring scattered point; the square term is expanded and a, b, c, d, λ is biased to obtain equation set (II):
Figure GDA0003454845050000024
Figure GDA0003454845050000031
Figure GDA0003454845050000032
Figure GDA0003454845050000033
Figure GDA0003454845050000034
/>
wherein A is cos ＝cos[(a+b·x i )·2π/λ]，A sin ＝sin[(a+b·x i )·2π/λ]And solving the equation (II) by a computer program through a numerical method to obtain the values of a, b, c, d and lambda.
According to the present invention, preferably, in the step (3), when the physical quantity to be measured is a wavelength of light, the transfer function is represented by formula (iii):
Figure GDA0003454845050000035
in formula (iii), a=n 1 ·(L 1 -L 2 )，
Figure GDA0003454845050000036
P out Is the optical power, V is the applied voltage, P out V is y and x in the formula (I) respectively; n is n 1 Is the effective refractive index of the waveguide, d g The length of a notch at the outer side of the short interference arm electrode of the Mach-Zehnder sensor; l (L) 1 、L 2 The length of the long interference arm and the length of the short interference arm of the Mach-Zehnder sensor are respectively referred to; n is n e Is the refractive index of the extraordinary ray of the lithium niobate material, gamma 33 =31.2pm/V, which is the electro-optic coefficient of the lithium niobate material in the z direction, Γ is the integral coefficient of the electric field between the optical field and the electrode;
and (3) obtaining the value of the light wavelength lambda by iterating the numerical value of the equation set (II).
According to the invention, preferably, in the step (3), when the physical quantity to be measured is pressure, the input light is broad spectrum light, and the transfer function is shown as formula (IV):
Figure GDA0003454845050000037
wherein b=m1·l p ，a＝n 1 ·(L 1 -L 2 )，I out To output light intensity, L p The length of the short interference arm bearing the pressure; p is the pressure; m1 refers to the photoelastic coefficient of the material;
at this time, the input is broad spectrum light, and the photoelastic coefficient and the compression length of the material are known, thus, I out 、λ i A, p, c, d are functions and variables, and are undetermined coefficients;
at this time, the measured scattered point to transfer functionIs the square of the distance of (2)
Figure GDA0003454845050000038
i=1, 2, …, n, the sum of squares of the distances of the individual scattered points to the transfer function is +.>
Figure GDA0003454845050000039
For a, p, c, d, the system of partial derivatives is shown in formula (V):
Figure GDA0003454845050000041
Figure GDA0003454845050000042
Figure GDA0003454845050000043
Figure GDA0003454845050000044
in the formula (V), A cos ＝cos[(a+b·p)·2π/λ i ]，A sin ＝sin[(a+b·p)·2π/λ i ]And solving equation (V) by a computer program through a numerical method to obtain values of a, p, c and d, wherein p is the value of the pressure to be measured.
A system for expanding the measurement range of Mach-Zehnder sensor based on nonlinear regression data processing comprises a discrete data acquisition module, a transfer function calculation module and a physical quantity calculation module to be measured;
the discrete data acquisition module is used for: measuring and acquiring discrete data by an optical measuring device;
the transmission function solving module is used for: processing discrete data by adopting a fitting algorithm, and restoring a transfer function, wherein the transfer function is an acquired high-resolution spectrum image;
the module for obtaining the physical quantity to be measured is used for: and solving the physical quantity to be measured according to the restored transfer function.
A computer device comprising a memory storing a computer program and a processor implementing the steps of a method of expanding a mach-zehnder type sensor measurement range based on nonlinear regression data processing when executing the computer program.
A computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the steps of a method of expanding a measurement range of a mach-zehnder type sensor based on nonlinear regression data processing.
The beneficial effects of the invention are as follows:
the existing ultra-high sensitivity optical sensor in the market cannot expand the range infinitely, when the invention performs optical measurement, under the condition of not increasing the spectrum width of a light source (namely, the cost of the light source is not increased), the measurement range of the Mach-Zehnder sensor can be expanded to be theoretically infinite by virtue of scientific data processing, and the invention is limited only by the normal interference range of the device and is not limited by FSR and the spectrum width of the light source in practice; the invention is also suitable for optical detection of all transmission spectrum or reflection spectrum to be detected, and the method can be applied only if the transmission function can be analyzed, and the application range and the meaning are huge.
Drawings
FIG. 1 is a schematic diagram of a temperature sensor at 10 degrees, 20 degrees reflection or transmission spectrum;
FIG. 2 is a schematic diagram of the Mach-Zehnder sensor;
FIG. 3 is a schematic diagram of measurement results of a Mach-Zehnder sensor;
FIG. 4 is a schematic diagram of a system for expanding the measurement range of Mach-Zehnder sensors based on nonlinear regression data processing according to the present invention.
Detailed Description
The invention is further defined by, but is not limited to, the following drawings and examples in conjunction with the specification.
Example 1
A method for expanding the measurement range of a Mach-Zehnder sensor based on nonlinear regression data processing comprises the following steps:
(1) Obtaining discrete data of the Mach-Zehnder sensor by measuring with an optical measuring device (a spectrometer or an optical power meter);
(2) Processing discrete data by adopting a fitting algorithm, and restoring a transfer function, wherein the transfer function is an acquired high-resolution spectrum image;
if the input is flat white light, i.e. the power at each wavelength is all equal, the output spectrum of the Mach-Zehnder sensor is a transfer function, as shown in formula (I):
Figure GDA0003454845050000051
in the formula (I), y i For outputting light intensity; x is x i Parameters related to waveguide effective refractive index change caused by physical quantity to be measured; a and b are variables determined according to different measurement scene initial conditions and device parameters; c and d are parameters related to the maximum and minimum of the actual transfer function; theoretically c=d=0.5, but the actual device is not necessarily equal to 0.5 due to manufacturing errors; lambda is the wavelength of light;
the transfer function represents the entire operating characteristics and the entire information of the optical device.
If the input is not flat white light, the transfer function is the output spectrum divided by the input spectrum (power division at the same wavelength). The output spectrum divided by the input spectrum operates as: the input spectrum, namely the power value under the specific wavelength, can be measured by a spectrometer, the different power values under a group of specific wavelengths are input spectrum data, the output spectrum data is measured by the spectrometer, the output power under the same wavelength is divided by the input power, the power ratio under a group of different wavelengths is obtained by dividing the output spectrum by the input spectrum, and the result is obtained according to different optical devices.
In actual measurement, the method does not depend on the position of a certain peak value or valley value to determine the physical quantity to be measured, but depends on nonlinear regression, and the physical quantity to be measured is calculated by a mathematical formula and is irrelevant to the certain peak value or valley value, so that the physical quantity to be measured can be reversely deduced as long as a group of scattered point measurement results exist. Therefore, as long as the device can work normally, the physical quantity to be measured can be calculated regardless of the FSR of the device and the spectral width of the light source.
(3) And (3) obtaining a physical quantity to be measured according to the transfer function restored in the step (2), wherein the physical quantity to be measured is a measurement target of the Mach-Zehnder sensor. The measurement target of the temperature sensor is temperature, and the effective refractive index of the waveguide of the integrated Mach-Zehnder interferometer is different at different temperatures. At different temperatures, the output spectral shape of the sensor will change. The temperature at which the sensor is located can be extrapolated back from the transfer function of the sensor.
Example 2
A method for expanding a measurement range of a mach-zehnder sensor based on nonlinear regression data processing according to embodiment 1, which is different in that:
in the formula (I), a, b, c, d and lambda are five undetermined parameters;
the specific fitting method of formula (I) is as follows:
a. calculating the measured dispersion point, i.e. the discrete data of the Mach-Zehnder sensor, is expressed as n sets of data points (x 1 ,y 1 )，(x 2 ,y 2 )，…，(x n ,y n ) Sum of squares, x of distance to transfer function 1 ……x n Refers to the parameters related to the effective refractive index of the waveguide, y, determined by the physical quantity to be measured 1 ……y n Refers to optical power;
the square of the distance from the scattered point to the transfer function is measured as
Figure GDA0003454845050000061
i=1, 2, …, n, the sum of squares of the distances of the individual scattered points to the transfer function is +.>
Figure GDA0003454845050000062
b. Respectively solving partial derivatives of the five undetermined parameters of a, b, c, d and lambda, wherein the position where the partial derivatives are zero is the function with the minimum distance to each measuring scattered point; the square terms are expanded and the a, b, c, d, λ are biased to obtain equation set (II) (the following equations are combined to form equation set):
Figure GDA0003454845050000063
Figure GDA0003454845050000064
Figure GDA0003454845050000065
Figure GDA0003454845050000066
/>
Figure GDA0003454845050000067
wherein A is cos ＝cos[(a+b·x i )·2π/λ]，A sin ＝sin[(a+b·x i )·2π/λ]And solving the equation (II) by a computer program through a numerical method to obtain the values of a, b, c, d and lambda.
The values of c and d, if the operation of dividing the output spectrum by the input spectrum, have no dimension and are between 0 and 1. If the input spectrum is ideal flat white light, the input spectrum is not needed to be divided by the output spectrum, and the dimension is the power dimension such as milliwatt, microwatt and the like which are commonly used for optical power. Lambda is the wavelength of light and varies depending on the difference in light source used. The values of the 2 unknowns a and b vary from sensor to sensor.
Example 3
A method of expanding a measurement range of a mach-zehnder type sensor based on nonlinear regression data processing according to embodiment 1 or 2, which is different in that:
in the step (3), when the physical quantity to be measured is the wavelength of light, fig. 2 is a device structure diagram, and the transfer function is shown in formula (iii):
Figure GDA0003454845050000071
in the formula (III), P out Is the optical power, V is the applied voltage, P out V is y and x in the formula (I) respectively; n is n 1 Is the effective refractive index of the waveguide, d g The length of a notch at the outer side of the short interference arm electrode of the Mach-Zehnder sensor; l (L) 1 、L 2 The length of the long interference arm and the length of the short interference arm of the Mach-Zehnder sensor are respectively referred to;
the material used in the device is bulk material lithium niobate transferred by X-cut y, in figure 2, gray curve is electrode, black curve is optical waveguide made by lithium niobate proton exchange process, its effective refractive index is n 1 The proton exchange process increases the extraordinary rays of the lithium niobate material and decreases the ordinary rays, so that only the extraordinary rays are in the waveguide. The electrode structure is push-pull type adopted by lithium niobate devices frequently, and the electrode spacing is d e The outside of the short-arm electrode has a length d g For the purpose of allowing the inner electrode to be drawn out.
The expressions for a and b at this time are: a=n 1 ·(L 1 -L 2 )，
Figure GDA0003454845050000072
Wherein n is e Is the refractive index of the extraordinary ray of the lithium niobate material, gamma 33 =31.2pm/V is the electro-optic coefficient of the lithium niobate material in the z-direction, Γ is the integral coefficient of the electric field between the optical field and the electrode. For lithium niobate materials, the y-direction waveguide has a change in its electro-optic coefficient and refractive index when turning in the z-direction, and the two equations above for a and b are only approximate schematic expressions. But for a device that has been fabricated, a and b are fixed for a stable temperature. Therefore, the value can be determined by fitting in actual operation without knowing a very accurate theoretical calculation method.
And (3) through numerical iteration of the equation set, the wavelength lambda of the physical quantity to be measured is further obtained.
The measurement results of the device are shown in fig. 3.
It is obvious that with the traditional method, only the light wavelength between 1530-1564nm can be received by the sensor to be correctly detected, and beyond the range, the detection result can be obtained, but the result is that the pair is wrong, and the result is completely unknown.
The fitting method comprises the following steps:
Figure GDA0003454845050000073
Figure GDA0003454845050000074
Figure GDA0003454845050000075
/>
Figure GDA0003454845050000076
Figure GDA0003454845050000077
wherein A is cos ＝cos[(a+b·V i )·2π/λ]，A sin ＝sin[(a+b·V i )·2π/λ]。
The values of a, b, c, d and lambda can be solved by numerical solution by combining the above five equations into a system of equations. The result of fitting the resulting wavelengths of light is shown in Table 1.
TABLE 1
Figure GDA0003454845050000081
As can be seen from the data in Table 1, for the same data, we can recover the wavelength values by scientific calculations with an average measurement error of 13.9pm for wavelengths less than 1530nm and greater than 1564 nm.
Example 4
A method of expanding a measurement range of a mach-zehnder type sensor based on nonlinear regression data processing according to embodiment 1 or 2, which is different in that:
when the physical quantity to be measured is pressure, the input light is broad spectrum light, and the transfer function is shown as formula (IV):
Figure GDA0003454845050000082
wherein b=m1·l p ，a＝n 1 ·(L 1 -L 2 )，I out To output light intensity, L p The length of the short interference arm bearing the pressure; p is the pressure; m1 refers to the photoelastic coefficient of the material;
at this time, the input is broad spectrum light, and the photoelastic coefficient and the compression length of the material are known, thus, I out 、λ i A, p, c, d are functions and variables, and are undetermined coefficients;
at this time, the square of the distance from the scattered point to the transfer function is
Figure GDA0003454845050000091
i=1, 2, …, n, the sum of squares of the distances of the individual scattered points to the transfer function is +.>
Figure GDA0003454845050000092
For a, p, c, d, the system of partial derivatives is shown in formula (V):
Figure GDA0003454845050000093
Figure GDA0003454845050000094
Figure GDA0003454845050000095
Figure GDA0003454845050000096
in the formula (V), A cos ＝cos[(a+b·p)·2π/λ i ]，A sin ＝sin[(a+b·p)·2π/λ i ]And solving equation (V) by a computer program through a numerical method to obtain values of a, p, c and d, wherein p is the value of the pressure to be measured.
Example 5
A system for expanding the measurement range of Mach-Zehnder sensor based on nonlinear regression data processing, as shown in figure 4, comprises a discrete data acquisition module, a transfer function calculation module and a physical quantity to be measured calculation module;
the discrete data acquisition module is used for: measuring and acquiring discrete data by an optical measuring device; the transmission function solving module is used for: processing discrete data by adopting a fitting algorithm, and restoring a transfer function, wherein the transfer function is an acquired high-resolution spectrum image; the physical quantity to be measured solving module is used for: and solving the physical quantity to be measured according to the restored transfer function.
Example 6
A computer device comprising a memory storing a computer program, and a processor implementing the steps of the method of expanding a mach-zehnder type sensor measurement range based on nonlinear regression data processing of any one of embodiments 1-4 when the computer program is executed.
Example 7
A computer readable storage medium having stored thereon a computer program which, when executed by a processor, performs the steps of the method of expanding the measurement range of a mach-zehnder type sensor based on nonlinear regression data processing of any one of embodiments 1-4.

Claims (6)

1. A method for expanding the measurement range of a mach-zehnder sensor based on nonlinear regression data processing, comprising the steps of:
(1) Measuring and obtaining discrete data of the Mach-Zehnder sensor;
(2) Processing discrete data by adopting a fitting algorithm, and restoring a transfer function, wherein the transfer function is an acquired high-resolution spectrum image;
if the input is flat white light, i.e. the power at each wavelength is all equal, the output spectrum of the Mach-Zehnder sensor is a transfer function, as shown in formula (I):
Figure FDA0003979981720000011
in the formula (I), y i For outputting light intensity; x is x i Parameters related to waveguide effective refractive index change caused by physical quantity to be measured; a and b are variables determined according to different measurement scene initial conditions and device parameters; c and d are parameters related to the maximum and minimum of the actual transfer function; lambda is the wavelength of light;
if the input is not flat white light, the transfer function is the output spectrum divided by the input spectrum;
(3) Obtaining a physical quantity to be measured according to the transfer function restored in the step (2), wherein the physical quantity to be measured is a measurement target of the Mach-Zehnder sensor;
in the formula (I), a, b, c, d and lambda are five undetermined parameters;
the specific fitting method of formula (I) is as follows:
a. calculating the measured dispersion point, i.e. the discrete data of the Mach-Zehnder sensor, is expressed as n sets of data points (x 1 ,y 1 )，(x 2 ,y 2 )，…，(x n ,y n ) Sum of squares, x of distance to transfer function 1 ……x n Refers to the parameters related to the effective refractive index of the waveguide, y, determined by the physical quantity to be measured 1 ……y n Refers to optical power;
the square of the distance from the scattered point to the transfer function is measured as
Figure FDA0003979981720000012
The sum of squares of the distances of the scattered points to the transfer function is +.>
Figure FDA0003979981720000013
b. Respectively solving partial derivatives of the five undetermined parameters of a, b, c, d and lambda, wherein the position where the partial derivatives are zero is the function with the minimum distance to each measuring scattered point; the square term is expanded and a, b, c, d, λ is biased to obtain equation set (II):
Figure FDA0003979981720000014
Figure FDA0003979981720000015
Figure FDA0003979981720000016
Figure FDA0003979981720000021
Figure FDA0003979981720000022
wherein A is cos ＝cos[(a+b·x i )·2π/λ]，A sin ＝sin[(a+b·x i )·2π/λ]And solving the equation (II) by a computer program through a numerical method to obtain the values of a, b, c, d and lambda.
2. The method for expanding the measurement range of a mach-zehnder sensor based on nonlinear regression data processing according to claim 1, wherein in step (3), when the physical quantity to be measured is a wavelength of light, the transfer function is as shown in formula (iii):
Figure FDA0003979981720000023
in formula (iii), a=n 1 ·(L 1 -L 2 )，
Figure FDA0003979981720000024
P out Is the optical power, V is the applied voltage, P out V is y and x in the formula (I) respectively; n is n 1 Is the effective refractive index of the waveguide, d g The length of a notch at the outer side of the short interference arm electrode of the Mach-Zehnder sensor; l (L) 1 、L 2 The length of the long interference arm and the length of the short interference arm of the Mach-Zehnder sensor are respectively referred to; n is n e Is the refractive index of the extraordinary ray of the lithium niobate material, gamma 33 =31.2pm/V, which is the electro-optic coefficient of the lithium niobate material in the z direction, Γ is the integral coefficient of the electric field between the optical field and the electrode;
and (3) obtaining the value of the light wavelength lambda by iterating the numerical value of the equation set (II).
3. The method for expanding a measurement range of a mach-zehnder sensor based on nonlinear regression data processing according to claim 1, wherein in the step (3), when the physical quantity to be measured is pressure, the input light is broad spectrum light, and the transfer function is represented by formula (iv):
Figure FDA0003979981720000025
wherein b=m1·l p ，a＝n 1 ·(L 1 -L 2 )，I out To output light intensity, L p The length of the short interference arm bearing the pressure; p is the pressure; m1 refers to the photoelastic coefficient of the material;
the square of the distance from the scattered point to the transfer function is measured as
Figure FDA0003979981720000026
The sum of squares of the distances of the scattered points to the transfer function is +.>
Figure FDA0003979981720000027
For a, p, c, d, the system of partial derivatives is shown in formula (V):
Figure FDA0003979981720000028
Figure FDA0003979981720000031
Figure FDA0003979981720000032
Figure FDA0003979981720000033
in the formula (V), A cos ＝cos[(a+b·p)·2π/λ i ]，A sin ＝sin[(a+b·p)·2π/λ i ]And solving equation (V) by a computer program through a numerical method to obtain values of a, p, c and d, wherein p is the value of the pressure to be measured.
4. A system for expanding the measurement range of a mach-zehnder type sensor based on nonlinear regression data processing, which is characterized in that the method for expanding the measurement range of the mach-zehnder type sensor based on nonlinear regression data processing as set forth in any one of claims 1 to 3 comprises a discrete data acquisition module, a transfer function calculation module and a physical quantity to be measured calculation module;
the discrete data acquisition module is used for: measuring and acquiring discrete data by an optical measuring device; the transmission function solving module is used for: processing discrete data by adopting a fitting algorithm, and restoring a transfer function, wherein the transfer function is an acquired high-resolution spectrum image; the module for obtaining the physical quantity to be measured is used for: and solving the physical quantity to be measured according to the restored transfer function.
5. A computer device comprising a memory and a processor, the memory storing a computer program, characterized in that the processor, when executing the computer program, implements the steps of the method of expanding the measurement range of a mach-zehnder type sensor based on nonlinear regression data processing as claimed in any one of claims 1 to 3.
6. A computer readable storage medium having stored thereon a computer program, which when executed by a processor, implements the steps of the method of expanding the measurement range of a mach-zehnder type sensor based on nonlinear regression data processing as claimed in any one of claims 1 to 3.
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