CN109580543B - Method for acquiring thermal emissivity of parallel flat plate under thermal distribution gradient - Google Patents

Method for acquiring thermal emissivity of parallel flat plate under thermal distribution gradient Download PDF

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CN109580543B
CN109580543B CN201811419763.4A CN201811419763A CN109580543B CN 109580543 B CN109580543 B CN 109580543B CN 201811419763 A CN201811419763 A CN 201811419763A CN 109580543 B CN109580543 B CN 109580543B
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CN109580543A (en
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刘华松
孙鹏
李士达
季一勤
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Tianjin Jinhang Institute of Technical Physics
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Abstract

The invention belongs to the technical field of optics, and particularly relates to a method for acquiring the thermal emissivity of a parallel flat plate under a thermal distribution gradient. When the parallel flat plate is in the condition of having a thermal distribution gradient, the refractive index and the extinction coefficient of the material are changed due to the thermal effect. The method is a calculation method for calculating the thermal emissivity of the parallel flat plate by discretizing the continuous temperature gradient in the parallel flat plate, performing plane slicing on the material in the axial vertical direction, and linearly superposing the radiation light wave intensity of the multilayer slices. The spectral emissivity characteristic of the material under the thermal distribution gradient can be calculated by the method. The method has universality for the heat radiation of the semitransparent parallel flat optical material.

Description

Method for acquiring thermal emissivity of parallel flat plate under thermal distribution gradient
Technical Field
The invention belongs to the technical field of optics, and particularly relates to a method for acquiring the thermal emissivity of a parallel flat plate under a thermal distribution gradient.
Background
The infrared window (Ge, Si and ZnS) is a key component of the infrared imaging detection system, is positioned at the forefront end of the infrared imaging detection system and is an important structure/function integrated component.
In recent years, with the rapid development of infrared imaging detection technology, the service environment of an infrared window is increasingly harsh. The infrared optical window of the infrared imaging detection system of the supersonic infrared end-guided missile is tested seriously to bear thermal shock. Under the action of pneumatic heating during high-speed flight, the temperature of the optical window can be rapidly increased (when the optical window flies in Mach 3, the temperature of the surface of the window can reach 523K). At this time, the thermal emissivity of the infrared window may increase significantly with the increase of temperature, and when the temperature is increased to make the radiation wavelength of the window itself close to the detection wavelength of the detector, the imaging quality of the system may be deteriorated, and in severe cases, the radiation signal of the detected object may be drowned. Therefore, theoretical calculation analysis must be performed on the high temperature emissivity of the infrared window.
The time of the infrared end-guidance process is generally short, and the temperature of the short-time pneumatically-heated infrared window is generally in an unsteady state and shows a gradient change in the direction perpendicular to the axial direction from the outer surface to the inner surface. Currently, studies on high temperature emissivity of the infrared window are based on steady state. The analytical methods involved in these studies are not suitable for calculating the high temperature emissivity of the infrared window that characterizes temperature gradient changes at non-steady state.
In summary, under the requirement of controlling the emissivity of the optical element of the infrared optical system in a complex thermal environment, how to solve the problem of evaluating and characterizing the emissivity of the optical window material under temperature gradient distribution becomes one of the important problems in the field of the current infrared optical system manufacturing technology.
Disclosure of Invention
Technical problem to be solved
The technical problem to be solved by the invention is as follows: how to solve the problem of calculating and analyzing the emissivity of the parallel flat optical material under the thermal temperature gradient distribution.
(II) technical scheme
In order to solve the technical problem, the invention provides a method for acquiring the thermal emissivity of a parallel flat plate under a thermal distribution gradient, which comprises the following steps:
step 1: firstly, the surface of the optical material of the parallel flat plate is assumed to be smooth, and the surface roughness is far smaller than the working wavelength;
step 2: determining a temperature gradient equation according to a specific application;
the thickness of the optical material of the parallel flat plate is dsNoting the temperature of the upper surface as TmaxTemperature of the lower surface is TminThe linear temperature gradient equation represents the temperature distribution at the x position within the material:
Figure BDA0001880304560000021
wherein T (x) is the temperature of any planar position x within the material;
and step 3: parallel flat platesThe optical material is subjected to plane slicing, the number of the layers of the section is N, and the thickness of each layer of the slice is dsN, thickness of planar slice not more than 1 times lambda0，λ0Is the operating wavelength or the center wavelength of the operating spectrum; the temperature of the slice at layer j is then:
Tj＝Tmax-j×(Tmax-Tmin) (2)
and 4, step 4: respectively calculating the temperatures of two surfaces of the optical material according to the formula, and obtaining the refractive index N of the upper surface according to the thermo-optic coefficient of the materiala(λ,Tmax)＝na(λ)-i×ka(lambda), refractive index of lower surface Nb(λ,Tmax)＝nb(λ)-i×kb(λ)；na(lambda) and nb(λ) is the real part of the refractive index, ka(lambda) and kb(λ) is the imaginary refractive index;
and 5: at an incident angle theta0In the case of (2), the refractive index of the incident medium is N0Then, the equivalent refractive index of the two surfaces of the incident medium and the material is calculated as follows:
equivalent refractive index N of incident medium0,s,pComprises the following steps:
Figure BDA0001880304560000022
equivalent refractive index N of the upper surface of the materiala,s,p(λ,Tmax) Comprises the following steps:
Figure BDA0001880304560000031
wherein, thetaaIs the angle of refraction of the upper surface;
equivalent refractive index N of the lower surface of the materialb,s,p(λ,Tmin) Comprises the following steps:
Figure BDA0001880304560000032
wherein,θban angle of refraction for the lower surface;
the refraction angle is determined using fresnel's law:
N0sinθ0＝Na(λ,Tmax)sin[θa(λ,Tmax)]＝Nb(λ,Tmin)sin[θb(λ,Tmin)]
(6)
step 6: at an incident angle theta0In the case of (2), the reflectance of the upper surface is calculated, where the variables (λ, T) are omittedmax) Obtaining:
Figure BDA0001880304560000033
and 7: at an incident angle theta0In the case of (2), the reflectance of the lower surface is calculated, where the variables (λ, T) are omittedmin) Obtaining:
Figure BDA0001880304560000034
and 8: and calculating the equivalent refractive index and the equivalent extinction coefficient of the j-th slice. The light wave is transmitted in a non-uniform wave mode in the absorption medium, the equal breadth and the equal phase surface are separated and not superposed, the equal breadth and the equal phase surface respectively have respective normal directions, and the two normal directions are superposed only when the light wave is in normal incidence; therefore, the transmission of light waves is characterized by the normal directions of the isosurface and the isosurface, and the equivalent refractive index is used in the absorption medium
Figure BDA0001880304560000041
Equivalent extinction coefficient K and real propagation angle of light
Figure BDA0001880304560000049
Characterizing the transmission behavior of the light wave;
angle of light propagation in slice of layer j
Figure BDA00018803045600000410
The Fresnel refraction law is satisfied:
Figure BDA0001880304560000042
wherein N isj(λ,Tj) Is the complex refractive index of the slice of the j-th layer, thetajIs the angle of refraction;
angle of refraction theta in layer jjThe sine and cosine of (c) are expressed as follows:
sinθj＝s'+js" cosθj＝c'+jc" (10)
equivalent refractive index of j-th slice
Figure BDA0001880304560000043
The following can be written:
Figure BDA0001880304560000044
equivalent extinction coefficient K and equivalent refractive index of jth layer of sliced sheet
Figure BDA0001880304560000045
The following relation is satisfied:
Figure BDA0001880304560000046
wherein the variables in equation (12) are all functions of (λ, Tj); n isjAnd kjIs Nj(λ，Tj) The real and imaginary parts of (c);
and step 9: since the equivalent refractive index and extinction coefficient of the substrate can be calculated by the equations (9) to (12), the angle θ can be arbitrarily set0Direction incidence, internal transmission u of jth layer slicejThe expression is as follows:
Figure BDA0001880304560000047
in the formula (13), dsIs the geometric thickness of the substrate, alpha is the coefficient of thermal expansion of the material, TRTRoom temperature, λ wavelength, N number of slices; the internal transmittance u of the j-th slice can be obtained by the equations (9) to (13)j；
Step 10: the calculated expression of the transmittance U in the optical material under the temperature gradient distribution is as follows:
Figure BDA0001880304560000048
step 11: based on the principle of linear superposition, the incidence angle θ of the optical material can be calculated from the equations (6), (7) and (14)0The following spectral characteristics were respectively as follows:
reflectivity R (lambda, theta)0) Comprises the following steps:
Figure BDA0001880304560000051
transmittance T (λ, θ)0) Comprises the following steps:
Figure BDA0001880304560000052
step 12: obtaining the temperature gradient T of the optical material from the formula (15) and the formula (16) according to kirchhoff's lawmin～TmaxSpectral directional emissivity of epsilon (lambda, theta)0) Comprises the following steps:
Figure BDA0001880304560000053
(III) advantageous effects
Compared with the prior art, the method has the advantages that the continuous temperature gradient is subjected to plane slicing treatment, the thermo-optic coefficient of the slices is applied to the calculation of the internal transmittance of the plane slices, and meanwhile, the spectral directional emissivity characteristic of the parallel flat optical material is obtained on the basis of the linear superposition principle of light waves by utilizing the reflection spectral characteristics of the two surfaces at different temperatures. The method overcomes the defect that the traditional calculation method can only be suitable for calculating the emissivity of the optical material in a stable temperature state, provides a spectral directional emissivity calculation and analysis method of the optical material under the temperature gradient of an unstable state, and has universality for transparent substrates and semitransparent substrates.
Drawings
FIG. 1 is a graph of refractive index versus temperature for a zinc sulfide material.
FIG. 2 is a plot of extinction coefficient versus temperature for a zinc sulfide material.
FIG. 3 is a temperature gradient profile of a parallel flat sheet material.
FIG. 4 is a graph of the reflection spectrum characteristics of a zinc sulfide material (thickness 6mm, 0 degree incident angle).
FIG. 5 is a graph of the transmission spectral characteristics of a zinc sulfide material (thickness 6mm, 0 degree angle of incidence).
FIG. 6 is a graph of the emissivity spectral characteristics of a zinc sulfide material (thickness 6mm, 0 degree angle of incidence).
FIG. 7 is a graph of the reflection spectrum characteristics of a zinc sulfide material (thickness 6mm, 45 degree incident angle).
FIG. 8 is a graph of the transmission spectral characteristics of a zinc sulfide material (thickness 6mm, 45 degree angle of incidence).
FIG. 9 is a graph of the emissivity spectral characteristics of a zinc sulfide material (thickness 6mm, 45 degree angle of incidence).
Fig. 10 is a schematic diagram of the technical solution of the present invention.
Detailed Description
In order to make the objects, contents, and advantages of the present invention clearer, the following detailed description of the embodiments of the present invention will be made in conjunction with the accompanying drawings and examples.
In order to solve the problems of the prior art, the invention provides a method for acquiring the thermal emissivity of a parallel flat plate under a thermal distribution gradient, which comprises the following steps:
step 1: firstly, the surface of the optical material of the parallel flat plate is assumed to be smooth, and the surface roughness is far smaller than the working wavelength;
step 2: determining a temperature gradient equation according to a specific application;
the thickness of the optical material of the parallel flat plate is dsNoting the temperature of the upper surface as TmaxTemperature of the lower surface is TminThe linear temperature gradient equation represents the temperature distribution at the x position within the material:
Figure BDA0001880304560000061
wherein T (x) is the temperature of any planar position x within the material;
and step 3: planar slicing the optical material of the parallel flat plate, wherein the number of the layers of the section is N, and the thickness of each layer of slice is dsN, thickness of planar slice not more than 1 times lambda0，λ0Is the operating wavelength or the center wavelength of the operating spectrum; the temperature of the slice at layer j is then:
Tj＝Tmax-j×(Tmax-Tmin) (2)
and 4, step 4: respectively calculating the temperatures of two surfaces of the optical material according to the formula, and obtaining the refractive index N of the upper surface according to the thermo-optic coefficient of the materiala(λ,Tmax)＝na(λ)-i×ka(lambda), refractive index of lower surface Nb(λ,Tmax)＝nb(λ)-i×kb(λ)；na(lambda) and nb(λ) is the real part of the refractive index, ka(lambda) and kb(λ) is the imaginary refractive index;
and 5: at an incident angle theta0In the case of (2), the refractive index of the incident medium is N0Then, the equivalent refractive index of the two surfaces of the incident medium and the material is calculated as follows:
equivalent refractive index N of incident medium0,s,pComprises the following steps:
Figure BDA0001880304560000071
equivalent refractive index N of the upper surface of the materiala,s,p(λ,Tmax) Comprises the following steps:
Figure BDA0001880304560000072
wherein, thetaaIs the angle of refraction of the upper surface;
equivalent refractive index N of the lower surface of the materialb,s,p(λ,Tmin) Comprises the following steps:
Figure BDA0001880304560000073
wherein, thetabAn angle of refraction for the lower surface;
the refraction angle is determined using fresnel's law:
N0sinθ0＝Na(λ,Tmax)sin[θa(λ,Tmax)]＝Nb(λ,Tmin)sin[θb(λ,Tmin)]
(6)
step 6: at an incident angle theta0In the case of (2), the reflectance of the upper surface is calculated, where the variables (λ, T) are omittedmax) Obtaining:
Figure BDA0001880304560000074
and 7: at an incident angle theta0In the case of (2), the reflectance of the lower surface is calculated, where the variables (λ, T) are omittedmin) Obtaining:
Figure BDA0001880304560000081
and 8: and calculating the equivalent refractive index and the equivalent extinction coefficient of the j-th slice. The light waves propagate in the absorption medium in a non-uniform wave manner, the isosurface and the isophase surface are separated and do not coincide, and the isosurface and the isophase surface respectively have respective normal directions, and only when the light waves are in normal incidence, the two normal directionsThe directions are coincident; therefore, the transmission of light waves is characterized by the normal directions of the isosurface and the isosurface, and the equivalent refractive index is used in the absorption medium
Figure BDA0001880304560000082
The (mode of isoplanar normal), the equivalent extinction coefficient K (mode of isoplanar normal) and the true propagation angle of light
Figure BDA0001880304560000089
Characterizing the transmission behavior of the light wave;
angle of light propagation in slice of layer j
Figure BDA00018803045600000810
The Fresnel refraction law is satisfied:
Figure BDA0001880304560000083
wherein N isj(λ,Tj) Is the complex refractive index of the slice of the j-th layer, thetajIs the angle of refraction;
angle of refraction theta in layer jjThe sine and cosine of (c) are expressed as follows:
sinθj＝s'+js" cosθj＝c'+jc" (10)
equivalent refractive index of j-th slice
Figure BDA0001880304560000084
The following can be written:
Figure BDA0001880304560000085
equivalent extinction coefficient K and equivalent refractive index of jth layer of sliced sheet
Figure BDA0001880304560000086
The following relation is satisfied:
Figure BDA0001880304560000087
wherein the variables in equation (12) are all functions of (λ, Tj); n isjAnd kjIs Nj(λ，Tj) The real and imaginary parts of (c);
and step 9: since the equivalent refractive index and extinction coefficient of the substrate can be calculated by the equations (9) to (12), the angle θ can be arbitrarily set0Direction incidence, internal transmission u of jth layer slicejThe expression is as follows:
Figure BDA0001880304560000088
in the formula (13), dsIs the geometric thickness of the substrate, alpha is the coefficient of thermal expansion of the material, TRTRoom temperature, λ wavelength, N number of slices; the internal transmittance u of the j-th slice can be obtained by the equations (9) to (13)j；
Step 10: the calculated expression of the transmittance U in the optical material under the temperature gradient distribution is as follows:
Figure BDA0001880304560000091
step 11: based on the principle of linear superposition, the incidence angle θ of the optical material can be calculated from the equations (6), (7) and (14)0The following spectral characteristics were respectively as follows:
reflectivity R (lambda, theta)0) Comprises the following steps:
Figure BDA0001880304560000092
transmittance T (λ, θ)0) Comprises the following steps:
Figure BDA0001880304560000093
step 12: according to kirschner HuoFreund's Law, the temperature gradient T of the optical material obtained from the formula (15) and the formula (16)min～TmaxSpectral directional emissivity of epsilon (lambda, theta)0) Comprises the following steps:
Figure BDA0001880304560000094
example 1
Example of the embodiment: spectral radiance characteristic calculation of 6mm zinc sulfide material at 7-10 μm
1) Setting the temperature range of the upper and lower surfaces of the parallel flat plate to be T max623K and T min273K, thickness d of materials＝6mm；
2) The refractive index-temperature curve of the zinc sulfide material is shown in figure 1, the extinction coefficient-temperature curve is shown in figure 2, and the data are from Applied optics,2005,44(32): 6913;
3) the temperature gradient from the upper surface to the lower surface of the zinc sulfide material is in linear distribution, and the axial temperature distribution of the material is;
Figure BDA0001880304560000101
4) the temperature distribution of the zinc sulfide material is calculated and obtained and is shown in figure 3;
5) carrying out planar slicing and layering on the parallel flat-plate zinc sulfide material, wherein the number of layers is 1000;
6) when the incident angle is 0 degrees, the reflection spectrum of the zinc sulfide material under the temperature gradient is calculated as shown in fig. 4, the average reflectivity is 0.2473, the average reflectivity of the material at room temperature is 0.2467, the average reflectivity is increased by 0.0006 compared with the reflectivity of the material at room temperature, and the reflectivity is not greatly changed as a whole.
7) The transmission spectrum of the zinc sulfide material under the temperature gradient is calculated as shown in figure 5 when the incident angle is 0 degrees, the average transmission is 0.7309, the average transmission of the material at room temperature is 0.7367, the average transmission is reduced by 0.0068 compared with the transmission of the material at room temperature, and the overall transmission in the spectral region is reduced.
8) When the incident angle is 0 degree, calculating to obtain the emission spectrum of the zinc sulfide material under the temperature gradient as shown in figure 6, wherein the average emissivity is 0.0219, the average emissivity of the material at room temperature is 0.0167, and the average emissivity is increased by 0.0068 compared with the emissivity of the material at room temperature; the position emissivity of the long wavelength is increased greatly, and the maximum increase reaches more than 1%.
9) When the incident angle is 45 degrees, the reflection spectrum of the zinc sulfide material under the temperature gradient is calculated as shown in figure 7, the average reflectivity is 0.2516, the average reflectivity of the material at room temperature is 0.2512, the average reflectivity is increased by 0.0004 compared with the reflectivity of the material at room temperature, and the reflectivity is not greatly changed as a whole.
10) The transmission spectrum of the zinc sulfide material at an incident angle of 45 degrees was calculated as shown in fig. 8, and the average transmission was 0.7254, the average transmission of the material at room temperature was 0.7313, the average transmission was 0.0059 lower than the transmission of the material at room temperature, and the overall transmission in the spectral region was lower.
11) When the incident angle is 0 degree, calculating to obtain the emission spectrum of the zinc sulfide material under the temperature gradient as shown in figure 9, wherein the average emissivity is 0.0230, the average emissivity of the material at room temperature is 0.0176, and the average emissivity is increased by 0.0054 compared with the emissivity of the material at room temperature; the position emissivity of the long wavelength is increased greatly, and the maximum increase reaches more than 1%.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.

Claims (4)

1. A method for acquiring the thermal emissivity of a parallel flat plate under a thermal distribution gradient is characterized by comprising the following steps:
step 1: firstly, the surface of the optical material of the parallel flat plate is assumed to be smooth, and the surface roughness is far smaller than the working wavelength;
step 2: determining a temperature gradient equation according to a specific application;
the thickness of the optical material of the parallel flat plate is dsNoting the temperature of the upper surface as TmaxTemperature of the lower surface is TminThe linear temperature gradient equation represents the temperature distribution at the x position within the material:
Figure FDA0002814285710000011
wherein T (x) is the temperature of any planar position x within the material;
and step 3: planar slicing the optical material of the parallel flat plate, wherein the number of the layers of the section is N, and the thickness of each layer of slice is dsN, thickness of planar slice not more than 1 times lambda0，λ0Is the operating wavelength or the center wavelength of the operating spectrum; the temperature of the slice at layer j is then:
Tj＝Tmax-j×(Tmax-Tmin) (2)
and 4, step 4: respectively calculating the temperatures of two surfaces of the optical material according to the formula, and obtaining the refractive index N of the upper surface according to the thermo-optic coefficient of the materiala(λ,Tmax)＝na(λ)-i×ka(lambda), refractive index of lower surface Nb(λ,Tmax)＝nb(λ)-i×kb(λ)；na(lambda) and nb(λ) is the real part of the refractive index, ka(lambda) and kb(λ) is the imaginary refractive index;
and 5: at an incident angle theta0In the case of (2), the refractive index of the incident medium is N0Then, the equivalent refractive index of the two surfaces of the incident medium and the material is calculated as follows:
equivalent refractive index N of incident medium0,s,pComprises the following steps:
Figure FDA0002814285710000012
equivalent refractive index N of the upper surface of the materiala,s,p(λ,Tmax) Comprises the following steps:
Figure FDA0002814285710000021
wherein, thetaaIs the angle of refraction of the upper surface;
equivalent refractive index N of the lower surface of the materialb,s,p(λ,Tmin) Comprises the following steps:
Figure FDA0002814285710000022
wherein, thetabAn angle of refraction for the lower surface;
the refraction angle is determined using fresnel's law:
N0sinθ0＝Na(λ,Tmax)sin[θa(λ,Tmax)]＝Nb(λ,Tmin)sin[θb(λ,Tmin)]
(6)
step 6: at an incident angle theta0In the case of (2), the reflectance of the upper surface is calculated, where the variables (λ, T) are omittedmax) Obtaining:
Figure FDA0002814285710000023
and 7: at an incident angle theta0In the case of (2), the reflectance of the lower surface is calculated, where the variables (λ, T) are omittedmin) Obtaining:
Figure FDA0002814285710000024
and 8: calculating the equivalent refractive index and the equivalent extinction coefficient of the j layer slice; the light waves propagate in the absorption medium in a non-uniform wave manner, with the isosurface and the isophase surface being separated and not superposed, each of which hasFrom the normal direction, only when the normal incidence is carried out, the two normal directions are coincident; therefore, the transmission of light waves is characterized by the normal directions of the isosurface and the isosurface, and the equivalent refractive index is used in the absorption medium
Figure FDA0002814285710000031
Equivalent extinction coefficient K and real propagation angle of light
Figure FDA0002814285710000032
Characterizing the transmission behavior of the light wave;
angle of light propagation in slice of layer j
Figure FDA0002814285710000033
The Fresnel refraction law is satisfied:
Figure FDA0002814285710000034
wherein N isj(λ,Tj) Is the complex refractive index of the slice of the j-th layer, thetajIs the angle of refraction;
angle of refraction theta in layer jjThe sine and cosine of (c) are expressed as follows:
sinθj＝s'+js" cosθj＝c'+jc" (10)
equivalent refractive index of j-th slice
Figure FDA0002814285710000035
The following can be written:
Figure FDA0002814285710000036
equivalent extinction coefficient K and equivalent refractive index of jth layer of sliced sheet
Figure FDA0002814285710000037
The following relation is satisfied:
Figure FDA0002814285710000038
wherein the variables in equation (12) are all functions of (λ, Tj); n isjAnd kjIs Nj(λ，Tj) The real and imaginary parts of (c);
and step 9: since the equivalent refractive index and extinction coefficient of the substrate can be calculated by the equations (9) to (12), the angle θ can be arbitrarily set0Direction incidence, internal transmission u of jth layer slicejThe expression is as follows:
Figure FDA0002814285710000039
in the formula (13), dsIs the geometric thickness of the substrate, alpha is the coefficient of thermal expansion of the material, TRTRoom temperature, λ wavelength, N number of slices; the internal transmittance u of the j-th slice can be obtained by the equations (9) to (13)j；
Step 10: the calculated expression of the transmittance U in the optical material under the temperature gradient distribution is as follows:
Figure FDA00028142857100000310
step 11: based on the principle of linear superposition, the incidence angle θ of the optical material can be calculated from the equations (6), (7) and (14)0The following spectral characteristics were respectively as follows:
reflectivity R (lambda, theta)0) Comprises the following steps:
Figure FDA0002814285710000041
transmittance T (λ, θ)0) Comprises the following steps:
Figure FDA0002814285710000042
step 12: obtaining the temperature gradient T of the optical material from the formula (15) and the formula (16) according to kirchhoff's lawmin～TmaxSpectral directional emissivity of epsilon (lambda, theta)0) Comprises the following steps:
Figure FDA0002814285710000043
2. the method of claim 1, wherein the equivalent refractive index is a refractive index equivalent index
Figure FDA0002814285710000044
Is the mode of the equiphase surface normal.
3. The method for obtaining the thermal emissivity of a parallel plate under a thermal profile gradient as claimed in claim 1, wherein the equivalent extinction coefficient K is a mode of the isoplanar normal.
4. The method of claim 1, wherein d is the thermal emissivity of the parallel plate under the gradient of thermal distributionsIs the geometric thickness of the substrate.
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