A method for characterizing non-uniform thermal emission of an infrared window

Abstract

This application provides a method for characterizing the non-uniform thermal radiation characteristics of an infrared window. The infrared window includes a double-spherical substrate, which includes a first surface L1 and a second surface L2. The characterization method includes: establishing an emissivity calculation model for points on the second surface L2 at a preset direction and a preset wavelength; the emissivity calculation model is: ε=(1-e ‑βD )T L2 Where ε is the actual emissivity, and T L2 Let β be the transmittance within the second curved surface L2, β be the material absorption coefficient, and D be the cumulative distance of material radiation in a predetermined direction within the substrate. Different points are selected on the second curved surface L2, and the emissivity at each point in a predetermined direction and at a predetermined wavelength is calculated using an emissivity calculation model, thereby characterizing the thermal radiation characteristics of the infrared window. This method achieves the calculation of emissivity distribution at different positions and in different directions on the surface of an infrared window containing a double-spherical substrate, solving the problem of emissivity characterization for infrared windows with non-uniform surface thermal radiation.

Description

Technical Field

[0001] This application relates to infrared window thermal radiation characterization technology, specifically to a method for characterizing the non-uniform thermal radiation characteristics of an infrared window. Background Technology

[0002] Emissivity is defined as the ratio of radiation emitted by an object's surface to radiation emitted by a blackbody at the same temperature. In different applications, depending on the specific focus of the radiating object, the integral average emissivity for a particular wavelength and direction, or across all wavelengths and directions, may be artificially defined. This typically includes spectral directional emissivity at a specific temperature (i.e., the ratio of emission intensity at a given wavelength and direction to the emission intensity of a blackbody at the same temperature and wavelength), full-wavelength directional emissivity, spectral hemispherical emissivity, and full-wavelength hemispherical emissivity. Treating a flat infrared window with a uniform temperature distribution as a point mass and characterizing its radiation characteristics using the above emissivity definition can effectively explain and predict the impact of window thermal radiation on the imaging system.

[0003] However, when the window substrate is spherical, the shape characteristics of the two surfaces of the window modulate its own radiation distribution. Although the total spatial radiation intensity of the window as a whole does not change significantly due to its surface shape, it causes local variations in the radiation intensity distribution in various directions, forming a non-uniform distribution. Currently, this non-uniform distribution characteristic has not been considered in practical optical system design applications, and it has not been characterized. Summary of the Invention

[0004] In view of the above-mentioned defects or deficiencies in the prior art, it is desirable to provide a method for characterizing the non-uniform thermal radiation characteristics of an infrared window, wherein the infrared window includes a double spherical substrate, the double spherical substrate includes a first surface L1 and a second surface L2, and the characterization method includes:

[0005] Establish an emissivity calculation model for points on the second surface L2 in a preset direction and at a preset wavelength;

[0006] The calculation model for the emissivity is as follows:

[0007] ε=(1-e -βD )T L2 ;

[0008] Where ε is the actual emissivity, T L2 β is the transmittance within the surface of the second curved surface L2, β is the material absorption coefficient, and D is the cumulative distance of material radiation in a predetermined direction within the substrate;

[0009] Different points are selected on the second surface L2, and the emissivity of each point in a preset direction and at a preset wavelength is calculated using the emissivity calculation model, thereby characterizing the thermal radiation characteristics of the infrared window.

[0010] According to the technical solution provided in the embodiments of this application, the process of establishing the emissivity calculation model includes:

[0011] Establish a calculation model for the directional cumulative distance;

[0012] A calculation model for the transmittance within the second curved surface L2 is established.

[0013] According to the technical solution provided in the embodiments of this application, the process of establishing the calculation model for the directional cumulative distance includes:

[0014] A spatial rectangular coordinate system is established with the vertex of the first surface L1 as the origin;

[0015] Select a first fixed point A on the second surface L2, and determine the first coordinates of the first fixed point A as (x0, y0, z0);

[0016] An incident ray pointing towards the first fixed point A is established in the double spherical substrate;

[0017] Based on the incident ray, a second fixed point B is determined on the first curved surface L1. The second fixed point B is the intersection of the incident ray and the first curved surface L1, and then the second coordinates of the second fixed point B are determined.

[0018] Based on the first coordinate and the second coordinate, the calculation model for the directional cumulative distance is obtained according to the distance formula between two points.

[0019] According to the technical solution provided in the embodiments of this application, the establishment of the incident light includes:

[0020] Determine the center of the second surface L2, and connect the center of the second surface L2 with the first fixed point A to obtain the normal line;

[0021] A refracted ray passing through the first fixed point A is selected, and the angle between the refracted ray and the normal is the angle of refraction.

[0022] According to Fresnel's law of refraction, the angle of incidence between the incident ray and the normal is established by the angle of refraction.

[0023] The incident ray is obtained based on the incident angle.

[0024] According to the technical solutions provided in the embodiments of this application,

[0025] The expression for the angle of refraction is established by:

[0026] In the spatial rectangular coordinate system, determine the direction vector m of the normal;

[0027] In the spatial rectangular coordinate system, determine the direction vector n of the refracted ray;

[0028] Based on the direction vector of the refracted ray and the direction vector of the normal, the expression for the angle of refraction is obtained:

[0029] Where a is the angle of refraction;

[0030] The expression for the incident angle is established by:

[0031] According to Snell's law of refraction, we get:

[0032]

[0033] Therefore, the expression for the angle of refraction is obtained:

[0034]

[0035] Where b is the angle of incidence.

[0036] The complex refractive index of the substrate.

[0037] According to the technical solution provided in the embodiments of this application, the establishment of the expression for the first surface L1 includes:

[0038] Based on the radius of curvature of the first surface L1, the coordinates of the center of the first surface L1 in the spatial rectangular coordinate system are determined to be (0,0,R1).

[0039] Based on the coordinates of the center of the first surface L1, the expression for the first surface L1 is as follows:

[0040] x 2 +y 2 +(z-R1) 2 =R1 2 ,

[0041] Wherein, R1 is the radius of curvature of the first surface L1.

[0042] According to the technical solution provided in the embodiments of this application, the establishment of the expression for the incident ray includes:

[0043] Based on the incident angle, determine the direction vector of the incident ray in the spatial rectangular coordinate system:

[0044]

[0045] in,

[0046] Let be the direction vector of the incident ray.

[0047] w = k × m,

[0048] Where k is a unit vector;

[0049] The expression for the incident ray, based on its direction vector, is as follows:

[0050]

[0051] in,

[0052]

[0053] According to the technical solution provided in the embodiments of this application, the process of establishing the expression of the calculation model for the directional cumulative distance includes:

[0054] Combining the expression for the first surface L1 and the expression for the incident ray, we obtain the second coordinates of the second fixed point B in the spatial rectangular coordinate system as follows:

[0055] (x0+x P t,y0+y P t,z0+z P t);

[0056] Based on the first coordinate and the second coordinate, the expression for the calculation model of the directional cumulative distance is as follows:

[0057]

[0058] According to the technical solution provided in the embodiments of this application, the process of establishing a calculation model for the transmittance within the second curved surface L2 includes:

[0059] T is calculated using the complex refractive index and the incident angle. L2 =1-R L2 ;

[0060] Among them, R L2 Let L2 be the reflectivity of the second surface.

[0061] According to the technical solution provided in the embodiments of this application, the calculation process of the reflectivity of the second curved surface L2 includes:

[0062] According to Fresnel's law of reflection:

[0063]

[0064]

[0065]

[0066] Among them, RL2，s R is the reflectivity of transverse wave polarization. L2，s Let N be the reflectivity of transverse wave polarization, and N0 be the complex refractive index of air.

[0067] The beneficial effects are as follows: Based on the concept of "spectral orientation and fixed-point emissivity", this application establishes an emissivity calculation model ε=(1-e) for a point on a double-spherical substrate surface at a preset direction and preset wavelength. -βD )T L2 By introducing parameters such as the radiation position, direction, and wavelength of a bispherical substrate surface, and analyzing the path of radiated light rays at a specific point on the surface of the bispherical substrate in a certain direction and at a specific wavelength within the substrate, the spectral orientation and localized emissivity of an infrared window with bispherical structural characteristics were obtained. By changing the localized position on the bispherical substrate surface, the radiation distribution of the bispherical surface in a specific direction and at a specific wavelength was obtained. The calculation of emissivity distribution at different positions and directions on the surface of an infrared window containing a bispherical substrate was achieved, solving the problem of characterizing the emissivity of infrared windows with non-uniform surface thermal radiation. Attached Figure Description

[0068] Other features, objects, and advantages of this application will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0069] Figure 1 This is a schematic diagram of the transmission of radiated light on a double-spherical substrate.

[0070] Figure 2 The emissivity of the radiated light at each point on the surface of the double-spherical zinc sulfide substrate L2 at θ0 = 45° and wavelength of 10 μm is given. Detailed Implementation

[0071] The present application will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0072] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0073] Please refer to Figures 1-2 A method for characterizing the non-uniform thermal radiation characteristics of an infrared window, wherein the infrared window comprises a double-spherical substrate, the double-spherical substrate comprising a first surface L1 and a second surface L2, and the characterization method comprising:

[0074] Establish an emissivity calculation model for points on the second surface L2 in a preset direction and at a preset wavelength;

[0075] The calculation model for the emissivity is as follows:

[0076] ε=(1-e -βD )T L2 ;

[0077] Where ε is the actual emissivity, T L2 β is the transmittance within the surface of the second curved surface L2, β is the material absorption coefficient, and D is the cumulative distance of material radiation in a predetermined direction within the substrate;

[0078] Different points are selected on the second surface L2, and the emissivity of each point in a preset direction and at a preset wavelength is calculated using the emissivity calculation model, thereby characterizing the thermal radiation characteristics of the infrared window.

[0079] Specifically, after light passes through a material of thickness D, the absorption rate A is: A = 1 - e -βD .

[0080] Furthermore, according to Kirchhoff's laws, the emissivity ε0 of a material with thickness D is also ε0 = 1 - e -βD .

[0081] Furthermore, considering the internal reflection of radiated light as it passes through the polished surface of the material, the actual emissivity ε is: ε=(1-e -βD )T L2 .

[0082] Specifically, the material absorption coefficient β = 4πk / λ;

[0083] Where π is the mathematical constant pi, k is the extinction coefficient, and λ is the wavelength.

[0084] Specifically, the material of the double-spherical substrate is zinc sulfide, and the wavelength of the radiated light is 10μm.

[0085] Furthermore, the absorption coefficient β of zinc sulfide is 4 * 3.14 * 6.707 × 10⁻⁶. -6 / (10×10 -6 ).

[0086] Specifically, such as Figure 1 As shown, the emissivity calculation model is used to calculate the emissivity of each point in a preset direction and at a preset wavelength.

[0087] Working principle: Based on the concept of "spectral orientation and fixed-point emissivity", this application establishes an emissivity calculation model ε=(1-e) at a point on a double-spherical substrate surface in a preset direction and at a preset wavelength. -βD )T L2By introducing parameters such as the radiation position, direction, and wavelength of a bispherical substrate surface, and analyzing the path of radiated light rays at a specific point on the surface of the bispherical substrate in a certain direction and at a specific wavelength within the substrate, the spectral orientation and localized emissivity of an infrared window with bispherical structural features is obtained. By changing the localized position on the bispherical substrate surface, the radiation distribution of the bispherical surface in a specific direction and at a specific wavelength is obtained. This method enables the calculation of emissivity distribution at different locations on the surface of an infrared window containing a bispherical substrate, solving the problem of characterizing the emissivity of infrared windows with non-uniform surface thermal radiation.

[0088] In a preferred embodiment, the process of establishing the emissivity calculation model includes:

[0089] Establish a calculation model for the directional cumulative distance;

[0090] A calculation model for the transmittance within the second curved surface L2 is established.

[0091] Specifically, the calculation model for the directional cumulative distance is as follows:

[0092] Specifically, the calculation model for the transmittance within the second curved surface L2 is: ε=(1-e -βD )T L2 .

[0093] In a preferred embodiment, the process of establishing the calculation model for the directional cumulative distance includes:

[0094] A spatial rectangular coordinate system is established with the vertex of the first surface L1 as the origin;

[0095] Select a first fixed point A on the second surface L2, and determine the first coordinates of the first fixed point A as (x0, y0, z0);

[0096] An incident ray pointing towards the first fixed point A is established in the double spherical substrate;

[0097] Based on the incident ray, a second fixed point B is determined on the first curved surface L1. The second fixed point B is the intersection of the incident ray and the first curved surface L1, and then the second coordinates of the second fixed point B are determined.

[0098] Based on the first coordinate and the second coordinate, the calculation model for the directional cumulative distance is obtained according to the distance formula between two points.

[0099] Specifically, such as Figure 1 As shown, the vertex of the first surface L1 is O, which is the origin of the spatial rectangular coordinate system.

[0100] In a preferred embodiment, the establishment of the incident light includes:

[0101] Determine the center of the second surface L2, and connect the center of the second surface L2 with the first fixed point A to obtain the normal line;

[0102] A refracted ray passing through the first fixed point A is selected, and the angle between the refracted ray and the normal is the angle of refraction.

[0103] According to Fresnel's law of refraction, the angle of incidence between the incident ray and the normal is established by the angle of refraction.

[0104] The incident ray is obtained based on the incident angle.

[0105] In a preferred embodiment, the establishment of the expression for the first surface L1 includes:

[0106] Based on the radius of curvature of the first surface L1, the coordinates of the center of the first surface L1 in the spatial rectangular coordinate system are determined to be (0,0,R1).

[0107] Based on the coordinates of the center of the first surface L1, the expression for the first surface L1 is as follows:

[0108] x 2 +y 2 +(z-R1) 2 =R1 2 ,

[0109] Wherein, R1 is the radius of curvature of the first surface L1.

[0110] Specifically, let the radii of curvature of the first surface L1 and the second surface L2 of the double spherical base be R1 = 300 mm and R2 = 280 mm, respectively. Figure 1 As shown, the angle between the refracted ray and the Z-axis of the spatial rectangular coordinate system is θ0 = 45°, the incident angle in the substrate is b, and the refraction angle in space is a.

[0111] Furthermore, let the center coordinates of the first surface L1 be (0,0,300), the expression is: x 2 +y 2 +(z-300) 2 =300 2 .

[0112] Furthermore, the coordinates of the center of the L2 surface are (0,0,R2+h), and the expression is: x 2 +y 2 +(z-280-h) 2 =280 2 ;

[0113] The thickness of the substrate at x=0 is h=6mm, and the diameter of the substrate is d=50mm.

[0114] In a preferred embodiment,

[0115] The expression for the angle of refraction is established by:

[0116] In the spatial rectangular coordinate system, determine the direction vector m of the normal;

[0117] In the spatial rectangular coordinate system, determine the direction vector n of the refracted ray;

[0118] Based on the direction vector of the refracted ray and the direction vector of the normal, the expression for the angle of refraction is obtained:

[0119] Where a is the angle of refraction;

[0120] The expression for the incident angle is established by:

[0121] According to Snell's law of refraction, we get:

[0122]

[0123] Therefore, the expression for the angle of refraction is obtained:

[0124]

[0125] Where b is the angle of incidence.

[0126] The complex refractive index of the substrate.

[0127] Specifically, the direction vector m of the normal is the tangent normal vector of the second surface L2 passing through point A;

[0128] Furthermore, the direction vector of the normal is m = (-x0, -y0, R2 + h - z0);

[0129] Furthermore, if m = (-x0, -y0, 286-z0), then the equation of the tangent plane of the second surface L2 passing through point A is: -x0(x-x0)-y0(y-y0)+(286-z0)(z-z0)=0.

[0130] Specifically, since the angle θ0 = 45° between the refracted ray and the Z-axis of the spatial rectangular coordinate system, the direction vector of the refracted ray is n = (0, sinθ0, cosθ0) = (0, sin45°, cos45°).

[0131] Furthermore, the equation of the refracted ray is:

[0132] Specifically, the optical constants and complex refractive index of the double spherical substrate at a temperature of 500℃ and a wavelength of 10μm are... To express.

[0133] In a preferred embodiment, establishing the expression for the incident ray includes:

[0134] Based on the incident angle, determine the direction vector of the incident ray in the spatial rectangular coordinate system:

[0135]

[0136] in,

[0137] Let be the direction vector of the incident ray.

[0138] w = k × m,

[0139] Where k is a unit vector;

[0140] The expression for the incident ray, based on its direction vector, is as follows:

[0141]

[0142] in,

[0143]

[0144] Specifically, unit vector

[0145] In a preferred embodiment, the process of establishing the expression for the calculation model of the directional cumulative distance includes:

[0146] Combining the expression for the first surface L1 and the expression for the incident ray, we obtain the second coordinates of the second fixed point B in the spatial rectangular coordinate system as follows:

[0147] (x0+x P t,y0+y P t,z0+z P t);

[0148] Based on the first coordinate and the second coordinate, the expression for the calculation model of the directional cumulative distance is as follows:

[0149]

[0150] In a preferred embodiment, the process of establishing a calculation model for the transmittance within the second curved surface L2 includes:

[0151] T is calculated using the complex refractive index and the incident angle.L2 =1-R L2 ;

[0152] Among them, R L2 Let L2 be the reflectivity of the second surface.

[0153] Specifically, the process of repeated reflection, propagation, and superposition of radiated light from the internally transmissive double spherical substrate only considers the first transmission and reflection of light on the inner surface of the window.

[0154] In a preferred embodiment, the calculation process for the reflectivity of the second curved surface L2 includes:

[0155] According to Fresnel's law of reflection:

[0156]

[0157]

[0158]

[0159] Among them, R L2，s R is the reflectivity of transverse wave polarization. L2，s Let N be the reflectivity of transverse wave polarization, and N0 be the complex refractive index of air.

[0160] Specifically, N0 = 1.

[0161] The above description is merely a preferred embodiment of this application and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in this application is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the inventive concept. For example, technical solutions formed by substituting the above features with (but not limited to) technical features with similar functions disclosed in this application.

Claims

1. A method for characterizing the non-uniform thermal radiation features of an infrared window, wherein the infrared window comprises a double-spherical substrate, and the double-spherical substrate comprises a first curved surface. L 1 and Second Surface L 2, characterized in that, The characterization method includes: Establish the second surface L The point on point 2 is in a preset direction, and the emissivity calculation model is based on a preset wavelength. The calculation model for the emissivity is as follows: ； in ε For the actual emission rate, T L2 For the second surface L 2. In-surface transmittance β The material absorption coefficient, D The cumulative distance of material radiation in a predetermined direction within the substrate; On the second curved surface L 2. Select different points on the infrared window and use the emissivity calculation model to calculate the emissivity of each point in a preset direction and at a preset wavelength, thereby characterizing the thermal radiation characteristics of the infrared window. The process of establishing the emissivity calculation model includes: Establish a calculation model for directional cumulative distance; Establish the second surface L 2. Calculation model for in-surface transmittance; The process of establishing the calculation model for the directional cumulative distance includes: With the first curved surface L Establish a spatial rectangular coordinate system with the vertex of 1 as the origin; On the second curved surface L 2. Select a first fixed point A, and determine the first coordinate of the first fixed point A as: ( x 0, y 0, z 0); An incident ray pointing towards the first fixed point A is established in the double spherical substrate; Based on the incident light ray, on the first curved surface L 1. A second fixed point B is determined on the surface, wherein the second fixed point B is the incident ray and the first curved surface. L The intersection of point 1 and point B is used to determine the second coordinates of the second fixed point B. Based on the first coordinate and the second coordinate, the calculation model for the directional cumulative distance is obtained according to the distance formula between two points; The calculation model for the directional cumulative distance is as follows: .

2. The method for characterizing the non-uniform thermal radiation features of an infrared window according to claim 1, characterized in that, The establishment of the incident light ray includes: Determine the second surface L The center of circle 2 is connected to the second surface. L The normal line is obtained by finding the center of circle 2 and the first fixed point A; A refracted ray passing through the first fixed point A is selected, and the angle between the refracted ray and the normal is the angle of refraction. According to Fresnel's law of refraction, the angle of incidence between the incident ray and the normal is established by the angle of refraction. The incident ray is obtained based on the incident angle.

3. The method for characterizing the non-uniform thermal radiation features of an infrared window according to claim 2, characterized in that, The expression for the angle of refraction is established by: In the spatial rectangular coordinate system, determine the direction vector of the normal. m ; In the spatial rectangular coordinate system, determine the direction vector of the refracted ray. n ; Based on the direction vector of the refracted ray and the direction vector of the normal, the expression for the angle of refraction is obtained: , in a The angle of refraction; The expression for the incident angle is established by: According to Snell's law of refraction, we get: Therefore, the expression for the angle of refraction is obtained: in b Angle of incidence The complex refractive index of the substrate.

4. The method for characterizing the non-uniform thermal radiation features of an infrared window according to claim 3, characterized in that, The first surface L The creation of an expression includes: Based on the first curved surface L The radius of curvature of 1 is used to determine the first surface. L 1. The center coordinates of the circle in the spatial rectangular coordinate system are (0, 0, ...). R 1); Based on the first curved surface L The first surface is obtained by finding the center coordinates of the circle. L The expression is: ， in, R1 For the first curved surface L1 The radius of curvature.

5. The method for characterizing the non-uniform thermal radiation features of an infrared window according to claim 4, characterized in that, The establishment of the expression for the incident ray includes: Based on the incident angle, determine the direction vector of the incident ray in the spatial rectangular coordinate system: ， in, Let be the direction vector of the incident ray. ， in, k It is a unit vector; The expression for the incident ray, based on its direction vector, is as follows: ， in, 。 6. The method for characterizing the non-uniform thermal radiation features of an infrared window according to claim 5, characterized in that, The expression of the calculation model for the directional cumulative distance includes the following: The first curved surface L1 Combining the expression and the incident ray expression, we obtain the second coordinates of the second fixed point B in the spatial rectangular coordinate system as follows: ； Based on the first coordinate and the second coordinate, the expression for the calculation model of the directional cumulative distance is as follows: 。 7. The method for characterizing the non-uniform thermal radiation features of an infrared window according to claim 3, characterized in that, Establish the second surface L The process of calculating the surface transmittance includes: Calculated using the complex refractive index and the incident angle. ; Wherein, RL2 is the second surface. L2 The reflectivity.

8. The method for characterizing the non-uniform thermal radiation features of an infrared window according to claim 7, characterized in that, Second surface L The calculation process for the reflectivity of a surface includes: According to Fresnel's law of reflection: in, R L2，s The reflectivity is for transverse wave polarization. N 0 represents the complex refractive index of air.

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