CN113218872B - Method for simultaneously identifying multiple parameters of optical characteristics of high-temperature semitransparent material - Google Patents
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Abstract
The invention discloses a method for simultaneously identifying multiple parameters of optical characteristics of a high-temperature translucent material, and belongs to the technical field of thermophysical property measurement of high-temperature materials. The invention solves the problem that the existing spectral transmittance measurement under high temperature condition is influenced by stray light, temperature uniformity and the like and has complexity which is difficult to predict. According to the invention, an inversion model based on an optimized LOA algorithm is established to calculate the apparent emissivity of the translucent material in the high-temperature spectral direction under the high-temperature condition, and the apparent emissivity calculated by the method is well consistent with the measured value of an experiment.
Description
Technical Field
The invention relates to a method for simultaneously identifying multiple parameters of optical characteristics of a high-temperature translucent material, belonging to the technical field of thermophysical property measurement of high-temperature materials.
Background
Translucent materials are widely used in many fields, such as window materials in infrared optical detection. The infrared optical detection has the advantages of high spatial resolution, high sensitivity, strong anti-interference capability, strong working capability under complex background conditions and the like, so that the infrared imaging guidance technology is widely applied. With the flying speed of the aircraft becoming faster and faster, the guidance environment becomes worse and worse, and the traditional guidance technology cannot meet the requirement.
Due to the pneumatic heating influence of high-speed flow field friction on the optical window, the optical window can generate high temperature and deformation, so that optical characteristic parameters such as refractive index, absorption coefficient, scattering coefficient and the like are unevenly distributed, optical path difference is introduced in a view field, and the imaging quality is seriously influenced; the thermal radiation effect of the high-temperature window forms radiation interference, even submerges a target signal and cannot receive target radiation, and the guidance precision is seriously reduced. Therefore, accurate measurement of the spectral properties such as refractive index, absorption coefficient, and scattering coefficient of the semitransparent optical window medium at the same time is required.
The radiation physical property parameter reconstruction based on the inversion technology has the problems of high nonlinearity, inadequacy, low efficiency and the like, no inversion technology and reconstruction model can effectively solve the multi-parameter reconstruction problem at present, and particularly, the problems of morbidity, multivaluence and crosstalk of the multi-parameter field simultaneous reconstruction are not thoroughly solved at present.
Disclosure of Invention
The invention provides a method for simultaneously identifying multiple parameters of optical characteristics of a high-temperature semitransparent material, aiming at solving the problem that the existing spectral transmittance measurement under the high-temperature condition is influenced by stray light, temperature uniformity and the like and has complexity which is difficult to predict.
The technical scheme of the invention is as follows:
a method for simultaneously identifying multiple parameters of optical characteristics of a high-temperature translucent material comprises the following steps:
step 1, obtaining an angle theta through an experimental method1,θ2,θ3,θ4Apparent emissivity measured value epsilon of semitransparent material in spectral directioni(λ,θ),i=1,2,3,4;
if the value of the objective function FobjAnd if the refractive index is greater than the set threshold value xi, returning to the step 2, and updating the spectrum refractive index n 'of the semitransparent test piece according to an inverse problem algorithm'λAnd spectral absorption coefficient κ'λAnd the diffuse reflectance of the spectrum is rho'dλThe set value is recalculated until the objective function value F in step 3objIs less than or equal to the set threshold value xi, the finally updated spectral refractive index n 'of the semitransparent test piece'λAnd spectral absorption coefficient κ'λAnd the diffuse reflectance of the spectrum is rho'dλNamely the true spectral refractive index n of the semitransparent test pieceλSpectral absorption coefficient kappaλAnd spectral diffuse reflectance of ρdλ;
Further, in the one-dimensional condition, when the medium is in a steady state condition and the medium scattering is not considered, the radiation transfer equation in step 2 is:
the boundary conditions are as follows:
in the formula, theta is an included angle between the forward radiation and the backward radiation and a normal line of the inner surface, wherein x is 0, and x is D;
ρdλfor diffuse reflectivity of a surface incident from a medium to a vacuum,
ρsλthe mirror reflectivity of the surface incident from the medium to vacuum, expressed as follows,
further limiting, solving the radiation transfer equation in step 2 can result in:
in the formula, the expression of A, B, C, D is as follows,
the apparent viewing angle has a spectral direction radiation intensity of
Therefore, the apparent emissivity estimated value ε 'in the spectral direction'iThe expression of (lambda) is as follows,
in the formula IbλAnd (T) is the radiation intensity of the black body spectrum with the wavelength of lambda at the experimental measurement temperature.
Further defining, under the one-dimensional condition, when the medium is in a steady state condition and the medium scattering is not considered, the radiation transfer equation in step 5 is:
the boundary conditions are as follows:
in the formula, theta is an included angle between the forward radiation and the backward radiation and a normal line of the inner surface, wherein x is 0, and x is D;
ρdλfor diffuse reflectivity of a surface incident from a medium to a vacuum,
ρsλthe surface mirror reflectivity of the medium incident to the vacuum is expressed by the formula (11),
further defined, solving the radiation transfer equation can result in:
in the formula, A, B, C, D is expressed by the formula (13),
the apparent viewing angle has a spectral direction radiation intensity of
Therefore, the apparent emissivity estimated value ε 'in the spectral direction'iThe expression of (lambda) is as follows,
in the formula IbλAnd (T) is the radiation intensity of the black body spectrum with the wavelength of lambda at the experimental measurement temperature.
The invention has the following beneficial effects: according to the invention, an inverse model based on an optimized LOA algorithm is established to calculate the high-temperature spectral direction apparent emissivity of the translucent material under the high-temperature condition, the apparent direction emissivity calculated by the method is well matched with the measured value of an experiment, and the problem that the spectral transmittance measurement under the high-temperature condition is influenced by stray light, temperature uniformity and the like and has complexity which is difficult to predict is effectively solved.
Drawings
FIG. 1 is a device for measuring apparent emissivity of a semitransparent material in a spectral direction;
FIG. 2 is a heating structure of a device for measuring apparent emissivity of a translucent material in a spectral direction;
FIG. 3 shows the normal emissivity and transmittance of a sapphire sample spectrum obtained by an energy method;
FIG. 4 is the spectral direction emissivity of a sapphire sample obtained by an energy method;
FIG. 5 is a result of inversion of spectral absorption coefficient of a sapphire sample obtained by a specular reflection boundary condition inversion algorithm;
FIG. 6 is a result of inversion of the refractive index of a sapphire sample spectrum obtained by a specular reflection boundary condition inversion algorithm;
FIG. 7 is a calculation of spectral normal emissivity using the method of the present invention in combination with a specular boundary positive problem model;
FIG. 8 is a result of inversion of the spectral absorption coefficient of a sapphire sample obtained by a diffuse reflection boundary condition inversion algorithm;
FIG. 9 is a graph showing an inversion result of a refractive index of a sapphire sample spectrum obtained by a diffuse reflection boundary condition inversion algorithm;
FIG. 10 is a result of the inversion of the spectral direction emissivity by the method of the present invention in combination with a diffuse reflection boundary normal problem model;
FIG. 11 is an inversion result of the emissivity in the 0-degree spectral direction by combining the method of the present invention with a diffuse reflection boundary positive problem model;
FIG. 12 shows the inversion result of the method of the present invention on the emissivity in the 80 ° spectral direction by combining with the diffuse reflection boundary normal problem model.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the invention.
Example 1:
step 1, obtaining an angle θ experimentally using the apparatus shown in FIGS. 1 and 21,θ2,θ3,θ4Apparent emissivity measured value epsilon of semitransparent material in spectral directioni(λ,θ),i=1,2,3,4。
Calculating to obtain an estimated value epsilon 'of the spectral normal apparent emissivity of the semitransparent material by solving a radiation transmission equation'iThe specific method of (lambda, theta) is as follows:
under one-dimensional conditions, when the medium is in steady state conditions and medium scattering is not considered, the radiation transfer equation is:
the boundary conditions are as follows:
in the formula, theta is an included angle between the forward radiation and the backward radiation and a normal line of the inner surface, wherein x is 0, and x is D;
ρdλfor diffuse reflectivity of a surface incident from a medium to a vacuum,
ρsλthe surface mirror reflectivity of the medium incident to the vacuum is expressed by the formula (4),
solving the radiation transfer equation yields:
in the formula, A, B, C, D is expressed by the formula (6),
the apparent viewing angle has a spectral direction radiation intensity of
Therefore, the apparent emissivity estimated value ε 'in the spectral direction'iThe expression of (lambda) is as follows,
in the formula IbλAnd (T) is the radiation intensity of the black body spectrum with the wavelength of lambda at the experimental measurement temperature.
Calculating to obtain the apparent emissivity of the translucent material in the spectral direction by solving a radiation transmission equationThe specific method comprises the following steps:
under one-dimensional conditions, when the medium is in steady state conditions and medium scattering is not considered, the radiation transfer equation is:
the boundary conditions are as follows:
in the formula, theta is an included angle between the forward radiation and the backward radiation and a normal line of the inner surface, wherein x is 0, and x is D;
ρdλfor diffuse reflectivity of a surface incident from a medium to a vacuum,
ρsλthe surface mirror reflectivity of the medium incident to the vacuum is expressed by the formula (11),
solving the radiation transfer equation yields:
in the formula, A, B, C, D is expressed by the formula (13),
the apparent viewing angle has a spectral direction radiation intensity of
Therefore, the apparent emissivity estimate in the spectral direction is ε'iThe expression of (lambda) is as follows,
in the formula IbλAnd (T) is the radiation intensity of the black body spectrum with the wavelength of lambda at the experimental measurement temperature.
And (3) verification test:
(1) when the temperature is 773K, the device shown in the figures 1 and 2 is used, the normal spectral emissivity and the spectral transmittance of the sapphire sample are tested based on an energy method, the thickness of an experimental sample is 0.4mm, and the wavelength range is selected to be 3-6 microns. The data of the spectral normal emissivity and the transmittance of the sample are shown in fig. 3, the experimental data of the apparent direction emissivity of the sample are shown in fig. 4, and the trend of the apparent emissivity along with the change of the wavelength in each direction is calculated by adopting a diffuse reflection boundary condition inversion program, so that the numerical values are different.
(2) The inversion results of the spectral absorption coefficient and refractive index of the material based on the normal emissivity and transmittance measured in (1) using the mirror reflection boundary condition inversion algorithm are shown in fig. 5 and 6.
Combining a mirror reflection boundary positive problem model, calculating the spectral emissivity based on the inversion result of the spectral absorption coefficient and the refractive index, wherein the calculation result is shown in FIG. 7, the line in the graph represents the calculation result, and the point represents the error of the experiment result, as can be seen from FIG. 7, the apparent normal emissivity calculated by using the inversion model based on the optimization LOA algorithm established by the invention is well matched with the measured value of the experiment, and the rationality and reliability of the inversion algorithm provided by the invention are proved.
(3) The results of inversion of the spectral absorption coefficient, the numerical refractive index and the reflectivity of the material based on the experimentally measured 0 °, 60 ° and 80 ° apparent directional emittances using the diffuse reflection boundary condition inversion algorithm are shown in fig. 8 and 9.
Combining a diffuse reflection boundary positive problem model, based on the inversion results of spectral absorption coefficient, refractive index and reflectivity, the calculation results of the emissivity in the spectral direction are shown in figures 10, 11 and 12, the lines in the figures represent the calculation results, and the points represent the errors of the experiment results, as can be seen from figures 10, 11 and 12, the apparent normal emissivity calculated by using the inversion model established based on the optimization LOA algorithm is better matched with the measured value of the experiment, and the rationality and reliability of the inversion algorithm provided by the invention are further proved.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (3)
1. A method for simultaneously identifying multiple parameters of optical characteristics of a high-temperature translucent material is characterized by comprising the following steps:
step 1, obtaining an angle theta through an experimental method1,θ2,θ3,θ4Apparent emissivity measured value epsilon of semitransparent material in spectral directioni(λ,θ),i=1,2,3,4;
Step 2, according to the inverse problem of radiation transmissionSolving algorithm, wherein the spectral refractive index of the semitransparent test piece is assumed to be n'λAnd the spectral absorption coefficient is k'λAnd diffuse reflectance of spectrum is ρ'dλCalculating to obtain an estimated value epsilon 'of apparent emissivity in the spectrum direction of the translucent material by solving a radiation transmission equation'i(λ,θ);
Under one-dimensional conditions, when the medium is in a steady state condition and the scattering of the medium is not considered, the radiation transmission equation in step 2 is as follows:
the boundary conditions are as follows:
in the formula, theta is an included angle between the forward radiation and the backward radiation and a normal line of the inner surface, wherein x is 0, and x is D;
ρdλfor diffuse reflectivity of a surface incident from a medium to a vacuum,
ρsλfor the surface mirror reflectivity of the medium incident to vacuum, the expression is shown below,
step 3, the measured value epsilon of the apparent emissivity in the spectrum direction of the semitransparent material obtained in the step 1i(lambda, theta) and an estimate epsilon 'of the apparent emissivity in the spectral direction of the translucent material obtained in step 1'i(lambda, theta) is substituted into the following objective function calculation formula, and an objective function value F is obtained through calculationobjThe objective function is:
step 4, judging the objective function value F obtained in the step 3objIf it is less than set threshold value xi, if the objective function value FobjIs less than or equal to a set threshold value xi, the spectral refractive index n 'of the semitransparent test piece assumed in the step 2'λAnd spectral absorption coefficient κ'λAnd spectral diffuse reflectance ρ'dλNamely the true spectral refractive index n of the semitransparent test pieceλSpectral absorption coefficient kappaλAnd spectral diffuse reflectance ρdλ;
If the value of the objective function FobjIf the refractive index is larger than the set threshold value xi, returning to the step 2, and updating the spectrum refractive index n 'of the semitransparent test piece according to an inverse problem algorithm'λAnd spectral absorption coefficient κ'λAnd spectral diffuse reflectance ρ'dλThe set value is recalculated until the objective function value F in step 3objIs less than or equal to the set threshold value xi, the finally updated spectral refractive index n 'of the semitransparent test piece'λAnd spectral absorption coefficient κ'λAnd the diffuse reflectance of the spectrum is rho'dλNamely the true spectral refractive index n of the semitransparent test pieceλSpectral absorption coefficient kappaλAnd spectral diffuse reflectance ρdλ;
Step 5, calculating the true spectral refractive index n of the semitransparent test piece according to the step 4λSpectral absorption coefficient kappaλAnd spectral diffuse reflectance of ρdλCalculating to obtain the apparent emissivity of the translucent material in the spectral direction by solving a radiation transmission equationThe measurement of the apparent emissivity of the semitransparent material in the high-temperature spectral direction is completed
Under one-dimensional conditions, when the medium is in a steady state condition and the scattering of the medium is not considered, the radiation transmission equation in step 5 is:
the boundary conditions are as follows:
in the formula, theta is an included angle between the forward radiation and the backward radiation and a normal line of the inner surface, wherein x is 0, and x is D;
ρdλis the diffuse reflectance of the surface from the medium incident to the vacuum;
ρsλthe surface mirror reflectivity of the medium incident to the vacuum is expressed by the formula (11),
2. the method for simultaneously identifying multiple parameters of optical characteristics of a high-temperature translucent material according to claim 1, wherein the solution of the radiation transfer equation in the step 2 can obtain:
in the formula, the expression of A, B, C, D is as follows,
wherein L is a translucent material thickness,. mu. theta. kappa.'λIs the spectral absorption coefficient;
the apparent viewing angle has a spectral direction radiation intensity of
Therefore, the apparent emissivity estimated value ε 'in the spectral direction'iThe expression of (lambda) is as follows,
in the formula IbλAnd (T) is the radiation intensity of the black body spectrum with the wavelength of lambda at the experimental measurement temperature.
3. The method for simultaneously identifying multiple parameters of optical characteristics of high-temperature translucent materials according to claim 1, wherein solving the radiation transfer equation can obtain:
in the formula, A, B, C, D is expressed by the formula (13),
the apparent viewing angle has a spectral direction radiation intensity of
Therefore, the apparent emissivity estimate in the spectral direction is ε'iThe expression of (lambda) is as follows,
in the formula IbλAnd (T) is the radiation intensity of the black body spectrum with the wavelength of lambda at the experimental measurement temperature.
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