A method for calculating the scattering distribution of the curved mirror of a gravitational wave telescope

Abstract

The present invention provides a method for calculating the mirror scattering distribution of a curved mirror of a gravitational wave telescope, which is used to solve the technical problems that the existing methods for analyzing the backscattered light distribution of a gravitational wave telescope have a large gap between the analysis results and the actual mirror scattering distribution data of the curved mirror, or cannot truly reflect the actual scattering distribution of the curved mirror. The method for calculating the mirror scattering distribution of a curved mirror of a gravitational wave telescope provided by the present invention uses a microelement method to divide the curved mirror into a plurality of plane mirror microelements, and solves the normal vector of each plane mirror microelement, and then combines the model analysis method or the actual measurement method to obtain the scattering distribution function of each plane mirror microelement on the curved mirror to be measured. ， Then, the scattering distribution of the curved reflector to be measured in the entire plane is obtained; this method is simple and easy to operate, and effectively solves the problem that the scattering distribution of the curved reflector is difficult to accurately calculate, and provides further technical support for the stray light suppression of the optical system.

Description

Technical Field

[0001] The invention relates to a method for calculating the mirror scattering distribution of a curved reflector, and in particular to a method for calculating the mirror scattering distribution of a curved reflector of a gravitational wave telescope. Background Art

[0002] As an important medium in gravitational wave detectors, gravitational wave telescopes not only need to transmit watt-level laser signals from local satellite base stations to satellite base stations millions of kilometers away, but also need to receive picowatt-level weak laser signals sent from satellite base stations millions of kilometers away. Therefore, a stable two-way laser detection link needs to be formed between the two satellite base stations. Taking the off-axis quadruple reflector gravitational wave telescope as an example, Figure 1 As shown, it includes an aperture stop 1, a primary mirror 2, a secondary mirror 3, a third mirror 4, a fourth mirror 5, and an exit pupil 6; wherein the primary mirror 2 is a parabolic reflector, the secondary mirror 3 is a hyperbolic reflector, and the third mirror 4 and the fourth mirror 5 are spherical reflectors. In the process of emitting energy, after the laser signal passes through the exit pupil 6, it is reflected by the fourth mirror 5, the third mirror 4, the secondary mirror 3, and the primary mirror 2 in sequence, and finally emitted from the aperture stop 1 to the distant satellite base station; in the process of receiving energy, after the laser signal that has traveled millions of kilometers passes through the aperture stop 1, it is reflected by the primary mirror 2, the secondary mirror 3, the third mirror 4, and the fourth mirror 5 in sequence, and then enters the exit pupil 6.

[0003] For a gravitational wave telescope, stray light from the sun, terrestrial light sources, etc., has no coherence with the laser light beam, so it has little effect on laser heterodyne interferometry detection. However, in the process of emitting energy, the gravitational wave telescope will produce backscattered light due to the uneven mirror surface of the gravitational wave telescope, such as roughness, particle scattering, etc. If the backscattered light suppression conditions of the gravitational wave telescope are insufficient, the weak laser signal of the picowatt level sent by the satellite base station millions of kilometers away will be overwhelmed by noise at any time, which will have a fatal impact on energy reception. In order to improve the signal-to-noise ratio of the gravitational wave detector, it is usually necessary to make the backscattered light energy of the gravitational wave telescope less than 10 of the laser emission light power. -10 This is a very strict stray light indicator, but the scattering distribution data of the actual curved mirror surface is difficult to obtain. In order to obtain the backscattered light energy of the gravitational wave telescope, it is necessary to accurately analyze and effectively suppress the backscattered light distribution of the gravitational wave telescope.

[0004] At present, there are two methods to analyze the backscattered light distribution of gravitational wave telescopes: one is to directly set the mirror scattering distribution under the corresponding roughness level through the built-in theoretical model of the relevant stray light software, thereby analyzing the scattered light of the curved mirror surface; the other is to analyze the scattered light of the curved mirror surface by bringing in the measured scattering distribution data of the plane mirror under the corresponding roughness level. However, the first analysis method is only the simulation result of the roughness theoretical model, which is quite different from the actual scattering distribution data of the curved mirror surface. The second analysis method uses the measured data of the scattering distribution data of the plane mirror under the corresponding roughness level, which cannot truly reflect the actual scattering distribution of the curved mirror. Summary of the invention

[0005] The purpose of the present invention is to solve the technical problems that the existing methods for analyzing the backscattered light distribution of a gravitational wave telescope have a large gap between the analysis results and the actual surface scattering distribution data of the curved reflector, or cannot truly reflect the actual scattering distribution of the curved reflector, and to provide a method for calculating the surface scattering distribution of the curved reflector of a gravitational wave telescope.

[0006] In order to achieve the above purpose, the technical solution provided by the present invention is as follows:

[0007] A method for calculating the mirror scattering distribution of a curved reflector of a gravitational wave telescope is special in that it comprises the following steps:

[0008] Step 1: Divide the mirror surface of the curved reflector to be measured of the gravitational wave telescope into k plane mirror elements by using the element method, where k>1;

[0009] Step 2: Establish the mirror curve equation of the curved reflector to be measured, and solve the normal vector of each plane mirror element according to the mirror curve equation of the curved reflector to be measured.

[0010] Step 3: Make the incident light I0 incident on the surface of the curved reflector to be measured, and determine the corresponding reflected light I according to the incident light I0. r ;

[0011] Step 4: Use model analysis or actual measurement to obtain the scattering distribution function BSDF of each plane mirror element on the curved reflector to be measured i ;

[0012] Step 5, calculating the scattering distribution of the mirror surface of the curved reflector to be measured at a single spatial point;

[0013] Step 5.1, select any spatial point P in the reflection space of the curved reflector to be measured, and define the center point of any plane mirror microelement as O i , i = 1, 2, 3 ... k, the center point O of the plane mirror microelement iConnected to the space point P, O i P is the direction of the scattered light of the plane mirror element passing through the space point P; calculate the direction O of the scattered light of the plane mirror element passing through the space point P i P and the normal vector of the plane mirror element The angle between the reflected light I r The normal vector of the plane mirror element Then, combined with the scattering distribution function BSDF of each plane mirror element on the curved reflector to be measured obtained in step 4, i , determine the BSDF value of the plane mirror element at the spatial point P;

[0014] Step 5.2, traverse the other plane mirror elements of the curved reflector to be measured according to the method of step 5.1, and obtain the BSDF values ​​of all plane mirror elements at the spatial point P;

[0015] Step 5.3, sum up the BSDF values ​​of all plane mirror elements at the spatial point P to obtain the scattering distribution of the surface of the curved reflector to be measured at the spatial point P;

[0016] Step 5.4, taking the position of spatial point P as 0 degrees, rotate around the central axis of the curved reflector to be measured under the premise of a fixed azimuth angle, record its position as the next spatial point after each rotation of a fixed angle, repeat steps 5.1 to 5.3 until it rotates to 180 degrees around the center of the curved reflector to be measured, and obtain the scattering distribution of the curved reflector surface to be measured in the entire plane.

[0017] Furthermore, in step 4, the scattering distribution function BSDF of each plane mirror element on the curved reflector to be measured is obtained by using a model analysis method. i Specifically:

[0018] Step 4.1, use the Harvey-Shack model to analyze the roughness σ of the surface of different plane mirror micro-element rms The scattering distribution caused by the plane mirror is calculated according to the following formula: roughness :

[0019]

[0020] Among them, β S is the scattered light I s The projection of the unit vector of on the plane mirror element, β0 is the reflected light I r The projection of the unit vector on the plane mirror element, s is the tilt factor, l is the flip angle, the value range is 0.0001-0.01, and b0 is a constant to be determined;

[0021] Step 4.2: Use the MIE spherical scattering model to analyze the scattering distribution caused by the contamination particles on the surface of different plane mirror micro-elements, and calculate the scattering distribution function BSDF of each plane mirror micro-element under different contamination particles according to the following formula: pollution :

[0022]

[0023] Among them, D i is the distribution function of contamination particles on the microelement surface of the plane mirror, i1 is the horizontal component of the scattering intensity function, and λ is the wavelength of the incident light I0;

[0024] Step 4.3, calculate the scattering distribution function BSDF of each plane mirror element on the curved reflector to be tested according to the following formula: i :

[0025] BSDF i =BSDF roughness +BSDF pollution .

[0026] Furthermore, in step 4.1, the undetermined constant b0 is obtained by the following method:

[0027] Step a1, calculate the total integrated scattering TIS of the Harvey-Shack model by the following formula:

[0028]

[0029] Where Δn is the difference between the spatial refractive index of the incident light and the spatial refractive index of the reflected light;

[0030] Step a2, combining the total integrated scattering TIS and the roughness σ of the plane mirror element rms The value is obtained by solving the unknown constant b0 through the following formula:

[0031]

[0032]

[0033] Furthermore, in step 4.2, i1 is obtained by the following method:

[0034] Step b1, calculate the Mie scattering coefficient a according to the following formula: n With b n :

[0035]

[0036]

[0037] where j n (z), h n(1) (z) are spherical Bessel function and Hankel function of given parameters of order n, z = x or mx; m is the complex refractive index of the pollution particle at the incident wavelength, x is the dimensionless diameter value, a is the radius of the pollution particle;

[0038] Step b2, calculate the Mie scattering angle function π according to the following formula n (cosθ) and τ n (cosθ):

[0039]

[0040]

[0041] Where θ is the incident angle of the incident light ray I0, P n (1) is a first-order Legendre polynomial;

[0042] Step b3, calculating the horizontal component i1 of the scattering intensity function according to the following formula:

[0043]

[0044] Among them, S1 is the amplitude of the scattered light in the horizontal direction, and n is the loop variable.

[0045] Furthermore, in step b3, the maximum value of n is n max Determined by the following formula:

[0046]

[0047] Among them, round is the rounding function.

[0048] Furthermore, in step 4, the scattering distribution function BSDF of each plane mirror element on the curved reflector to be measured is obtained by actual measurement method: i Specifically:

[0049] Prepare a plane reflector with the same processing flow and mirror roughness as the curved reflector to be tested, and use it as a test sample. Place the test sample and the curved reflector to be tested in the same test environment. Measure the angle-resolved scattering distribution ARS of the test sample by an angular resolution scatterometer, obtain the BSDF data of the test sample at the angle of each plane mirror microelement, and use it as the scattering distribution function BSDF of each plane mirror microelement on the curved reflector to be tested. i .

[0050] Furthermore, in step 5.4, each time the fixed angle is rotated, its position is recorded as the next spatial point, specifically:

[0051] After each rotation of 1 degree, its position is recorded as the next spatial point.

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] 1. The present invention provides a method for calculating the scattering distribution of a curved reflector of a gravitational wave telescope. The method adopts a microelement method to divide the curved reflector into a plurality of plane mirror microelements, and solves the normal vector of each plane mirror microelement. The scattering distribution function of each plane mirror microelement on the curved reflector to be measured is obtained by combining a model analysis method or an actual measurement method, and then the scattering distribution of the mirror surface of the curved reflector to be measured in the entire plane is obtained. The method for calculating the scattering distribution of the curved reflector of the present invention has high accuracy and is simple and easy to operate. It effectively solves the problem that the scattering distribution of the curved reflector is difficult to accurately calculate, and provides further technical support for the stray light suppression of the optical system.

[0054] 2. Based on the strict requirements of the backscattered light of the gravitational wave telescope, the results of the actual measurement method are more realistic than the theoretical model analysis method. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 This is a schematic diagram of the principle of an existing off-axis quadruple reflector gravitational wave telescope;

[0056] Figure 2 The scattering distribution curves of each plane mirror element at different roughness in step 4.1 of Example 1 of the present invention;

[0057] Figure 3 The scattering distribution curve of each plane mirror element under different pollution particles in step 4.2 of the first embodiment of the present invention;

[0058] Figure 4 This is a schematic diagram of the scattering distribution of the curved reflector to be measured at a spatial point P in step 5.1 of the first embodiment of the present invention;

[0059] Figure 5 This is a schematic diagram of the backscattered light energy absorbed by the gravitational wave detector obtained by calculating the scattering distribution of the curved reflector surface to be measured in the entire plane obtained by Example 1 of the present invention.

[0060] Figure 1 The reference numerals in the figures are as follows:

[0061] 1-Aperture stop; 2-Primary mirror; 3-Secondary mirror; 4-Third mirror; 5-Quadrature mirror; 6-Exit pupil. DETAILED DESCRIPTION

[0062] The technical solution of the present invention will be clearly and completely described below in combination with the embodiments of the present invention and the accompanying drawings. Obviously, the described embodiments are not limitations of the present invention.

[0063] Embodiment 1

[0064] A method for calculating the mirror scattering distribution of a curved reflector of a gravitational wave telescope comprises the following steps:

[0065] Step 1: First, divide the curved mirror of the gravitational wave telescope into k extremely small plane mirror elements by the element method, where k>1. The number of elements to be divided is determined according to the accuracy of the system stray light index. The more elements there are, the more accurate the calculation results will be, but the longer the calculation time will be. The curved mirrors of the gravitational wave telescope usually include aspherical mirrors and spherical mirrors. Aspherical mirrors include parabolic mirrors and hyperbolic mirrors.

[0066] Step 2: Establish the mirror curve equation of the curved reflector to be measured, and solve the normal vector of each plane mirror element according to the mirror curve equation of the curved reflector to be measured. Normal vector of the plane mirror element For a spherical reflector, the direction points to the center of the sphere; for a parabolic reflector and a hyperbolic reflector, the direction points to the focus of the surface.

[0067] Step 3: Make the incident light I0 incident on the reflector of the curved surface to be measured. According to the law of reflection, the corresponding reflected light I0 can be obtained by determining the incident light I0. r At the same time, since the surface of the curved reflector to be tested is not completely smooth, it will reflect the light. I There are multiple reflected rays I in various propagation directions distributed around r. r .

[0068] Step 4: Use the theoretical model analysis method to obtain the scattering distribution function BSDF of each plane mirror element on the curved reflector to be tested i .

[0069] From the perspective of theoretical model analysis,

[0070] The scattering distribution characteristics of each plane mirror microelement surface on the measured curved reflector include the following two cases: rms The scattering distribution caused by and the scattering distribution caused by particle contamination on the surface of the plane mirror microelement.

[0071] Step 4.1, use the Harvey-Shack model to analyze the roughness σ of the surface of different plane mirror micro-element rms The scattering distribution caused by the plane mirror is obtained under different roughness. Figure 2 As shown, RMS = = 0.2nm ~ RMS = = 0.5nm represents the roughness σ of the surface of different plane mirror microelement rmsThe scattering distribution function BSDF of each plane mirror element at different roughness is calculated according to the following formula: roughness :

[0072]

[0073] Among them, β S is the scattered light I s The projection of the unit vector of onto the plane mirror element, β S = sinθ s ,θ s is the scattered light I s The normal vector to the plane mirror element The angle between them; β0 is the reflected light I r The projection of the unit vector of the plane mirror on the infinitesimal element, β0 = sinθ r ,θ r For reflected light I r The normal vector to the plane mirror element ; S is the slope of the scattering distribution function, also known as the tilt factor, which expresses the degree to which the scattering distribution is concentrated in the reflection direction; l is the flip angle, with a value range of 0.0001-0.01; b0 is an undetermined constant, which indicates that the curve is in |β s -The value when β0|=0.

[0074] b0 Total integrated scattering TIS combined with roughness σ via the Harvey-Shack model rms Calculate and solve.

[0075] According to the total integral scattering theory, when the roughness σ rms When it is much smaller than the wavelength λ of the incident light I0, the calculation formula of TIS is as follows: for the reflection plane, the difference between the spatial refractive index of the incident light and the spatial refractive index of the reflected light is Δn=2.

[0076]

[0077] Substituting the solved TIS into the following equation, we can solve for b0:

[0078]

[0079]

[0080] Step 4.2, the MIE sphere scattering model is used to analyze the scattering distribution caused by particle contamination on the surface of different plane mirror micro-elements. The scattering distribution curves of each plane mirror micro-element under different particle contamination are as follows: Figure 3 As shown, CL100~CL500 represent the cleanliness levels of different plane mirror microelement surfaces.

[0081] The specific process of using the MIE sphere scattering model analysis is as follows:

[0082] (a) Calculate the Mie scattering coefficient a according to the following formula n With b n :

[0083]

[0084] where j n (z), h n (1) (z) are spherical Bessel functions and Hankel functions of given parameters of order n, respectively. The coefficients of different orders can be calculated through the recursive formula of the function; z = x or mx; m is the complex refractive index of the pollution particle at the incident wavelength, a is the radius of the pollution particle, and x is the dimensionless diameter value.

[0085] (b) Calculate the Mie scattering angle function π according to the following formula n (cosθ) and τ n (cosθ):

[0086]

[0087]

[0088] Where θ is the incident angle of the incident light ray I0, P n (1) is a first-order Legendre polynomial.

[0089] (c) Calculate the horizontal component i1 and vertical component i2 of the scattering intensity function according to the following formula:

[0090]

[0091]

[0092] Among them, S1 is the amplitude of the scattered light in the horizontal direction, S2 is the amplitude of the scattered light in the vertical direction, and n is a loop variable, whose maximum value is round is the rounding function.

[0093] (d) Calculate the scattering distribution function BSDF of each plane mirror element under different pollution particles by the following formula pollution :

[0094]

[0095] Among them, D i is the distribution function of contamination particles on the surface of the plane mirror microelement.

[0096] Step 4.3, calculate the scattering distribution function BSDF of each plane mirror element on the curved reflector to be measured according to the following formula: i :

[0097] BSDF i =BSDF roughness +BSDF pollution .

[0098] Step 5, calculating the scattering distribution of the curved reflector to be measured at a single spatial point.

[0099] Step 5.1, such as Figure 4 As shown, select any spatial point P in the reflection space of the curved reflector to be measured, and define the center point of any plane mirror microelement as Q i (i=1,2,3……k), the center point Q of the plane mirror microelement i Connected to the space point P, O i P is the direction of the scattered light of the plane mirror element passing through the space point P; calculate the direction O of the scattered light of the plane mirror element passing through the space point P i P and the normal vector of the plane mirror element The angle θ between s And the reflected light I r The normal vector of the plane mirror element The angle θ between r (According to the law of reflection, θ r With the incident angle θ i Then, combined with the scattering distribution function BSDF of each plane mirror element on the curved reflector to be measured obtained in step 4, i , determine the BSDF value of the plane mirror element at the spatial point P.

[0100] Step 5.2, traverse the other plane mirror elements of the curved reflector to be measured according to the method of step 5.1, and obtain the BSDF values ​​of all plane mirror elements at the spatial point P.

[0101] Step 5.3, sum up the BSDF values ​​of all plane mirror elements at the spatial point P to obtain the scattering distribution of the surface of the curved reflector to be tested at the spatial point P.

[0102] Step 5.4, taking the position of the spatial point P as 0 degrees, rotate around the central axis of the curved surface reflector to be measured under the premise of a fixed azimuth angle, and record its position as the next spatial point after each rotation of a fixed angle. In this embodiment, each rotation is 1 degree; repeat steps 5.1 to 5.3 until it is rotated to 180 degrees around the center of the curved surface reflector to be measured, and obtain the scattering distribution of the curved surface reflector to be measured in the entire plane.

[0103] like Figure 5As shown, when subsequently calculating the backscattered light energy absorbed by the gravitational wave detector D, the position of the gravitational wave detector D is first determined, and the corresponding solid angle dΩ of each plane mirror microelement in the gravitational wave detector D is calculated. i The integral value of the BSDF scattering distribution is the sum of the corresponding solid angle dΩ of all plane mirror elements in the gravitational wave detector D. i The integral value of the BSDF scattering distribution is obtained, that is, the backscattered light energy absorbed by the gravitational wave detector D is obtained.

[0104] Embodiment 2

[0105] The difference between this embodiment and the first embodiment is only the difference in step 4. In this embodiment, step 4 adopts the actual measurement method to obtain the scattering distribution function BSDF of the mirror surface of the curved reflector, which is specifically:

[0106] Prepare a plane reflector with the same processing flow and mirror roughness as the curved reflector to be tested, and use it as a test sample. Place the test sample and the curved reflector to be tested in the same test environment. Measure the angle-resolved scattering distribution ARS of the test sample by an angular resolution scatterometer, obtain the BSDF data of the test sample at the angle of each plane mirror microelement, and use it as the scattering distribution function BSDF of each plane mirror microelement on the curved reflector to be tested. i Based on the stringent requirements of the backscattered light of the gravitational wave telescope, the results of the actual measurement method provided in this embodiment are more authentic than the theoretical model analysis method.

[0107] The above description is only used to illustrate the technical solution of the present invention rather than to limit it. For ordinary professional and technical personnel in the field, the specific technical solution recorded in the above embodiment can be modified, or some of the technical features therein can be replaced by equivalents, and these modifications or replacements do not make the essence of the corresponding technical solution deviate from the scope of the technical solution protected by the present invention.

Claims

1. A method for calculating the mirror scattering distribution of a curved reflector of a gravitational wave telescope, characterized in that: The following steps are involved: Step 1: Divide the mirror surface of the curved reflector to be measured of the gravitational wave telescope into k plane mirror elements by using the element method, where k>1; Step 2: Establish the mirror curve equation of the curved reflector to be measured, and solve the normal vector of each plane mirror element according to the mirror curve equation of the curved reflector to be measured. Step 3: Make the incident light I0 incident on the surface of the curved reflector to be measured, and determine the corresponding reflected light I according to the incident light I0. r ; Step 4: Use model analysis or actual measurement to obtain the scattering distribution function BSDF of each plane mirror element on the curved reflector to be measured i ; Step 5, calculating the scattering distribution of the mirror surface of the curved reflector to be measured at a single spatial point; Step 5.1, select any spatial point P in the reflection space of the curved reflector to be measured, and define the center point of any plane mirror microelement as O i , i = 1, 2, 3 ... k, the center point O of the plane mirror microelement i Connected to the space point P, O i P is the direction of the scattered light of the plane mirror microelement passing through the space point P; Calculate the direction O of the scattered light from the plane mirror element passing through the space point P i P and the normal vector of the plane mirror element The angle between the reflected light I r The normal vector of the plane mirror element Then, combined with the scattering distribution function BSDF of each plane mirror element on the curved reflector to be measured obtained in step 4, i , determine the BSDF value of the plane mirror element at the spatial point P; Step 5.2, traverse the other plane mirror elements of the curved reflector to be measured according to the method of step 5.1, and obtain the BSDF values ​​of all plane mirror elements at the spatial point P; Step 5.3, sum up the BSDF values ​​of all plane mirror elements at the spatial point P to obtain the scattering distribution of the surface of the curved reflector to be measured at the spatial point P; Step 5.4, taking the position of spatial point P as 0 degrees, rotate around the central axis of the curved reflector to be measured under the premise of a fixed azimuth angle, record its position as the next spatial point after each rotation of a fixed angle, repeat steps 5.1 to 5.3 until it rotates to 180 degrees around the center of the curved reflector to be measured, and obtain the scattering distribution of the curved reflector surface to be measured in the entire plane.

2. The method for calculating the mirror scattering distribution of a curved reflector of a gravitational wave telescope according to claim 1, characterized in that: In step 4, the scattering distribution function BSDF of each plane mirror element on the curved reflector to be measured is obtained by using the model analysis method. i Specifically: Step 4.1, use the Harvey-Shack model to analyze the roughness σ of the surface of different plane mirror micro-element rms The scattering distribution caused by the plane mirror is calculated according to the following formula: roughness : Among them, β S is the scattered light I s The projection of the unit vector of on the plane mirror element, β0 is the reflected light I r The projection of the unit vector on the plane mirror element, s is the tilt factor, l is the flip angle, the value range is 0.0001-0.01, and b0 is a constant to be determined; Step 4.2: Use the MIE spherical scattering model to analyze the scattering distribution caused by the contamination particles on the surface of different plane mirror micro-elements, and calculate the scattering distribution function BSDF of each plane mirror micro-element under different contamination particles according to the following formula: pollution : Among them, D i is the distribution function of contamination particles on the microelement surface of the plane mirror, i1 is the horizontal component of the scattering intensity function, and λ is the wavelength of the incident light I0; Step 4.3, calculate the scattering distribution function BSDF of each plane mirror element on the curved reflector to be tested according to the following formula: i : BSDF i =BSDF roughness +BSDF pollution 。 3. The method for calculating the mirror scattering distribution of a curved reflector of a gravitational wave telescope according to claim 2, characterized in that: In step 4.1, the undetermined constant b0 is obtained by the following method: Step a1, calculate the total integrated scattering TIS of the Harvey-Shack model by the following formula: Where Δn is the difference between the spatial refractive index of the incident light and the spatial refractive index of the reflected light; Step a2, combining the total integrated scattering TIS and the roughness σ of the plane mirror element rms The value is obtained by solving the unknown constant b0 through the following formula:

4. The method for calculating the mirror scattering distribution of a curved reflector of a gravitational wave telescope according to claim 2, characterized in that: In step 4.2, i1 is obtained by the following method: Step b1, calculate the Mie scattering coefficient a according to the following formula: n With b n : where j n (z), h n (1) (z) are spherical Bessel function and Hankel function of given parameters of order n, z = x or mx; m is the complex refractive index of the pollution particle at the incident wavelength, x is the dimensionless diameter value, a is the radius of the pollution particle; Step b2, calculate the Mie scattering angle function π according to the following formula n (cosθ) and τ n (cosθ): Where θ is the incident angle of the incident light ray I0, P n (1) is a first-order Legendre polynomial; Step b3, calculating the horizontal component i1 of the scattering intensity function according to the following formula: Among them, S1 is the amplitude of the scattered light in the horizontal direction, and n is the loop variable.

5. The method for calculating the mirror scattering distribution of a curved reflector of a gravitational wave telescope according to claim 4, characterized in that: In step b3, the maximum value of n is n max Determined by the following formula: Among them, round is the rounding function.

6. The method for calculating the mirror scattering distribution of a curved reflector of a gravitational wave telescope according to claim 1, characterized in that: In step 4, the scattering distribution function BSDF of each plane mirror element on the curved reflector to be measured is obtained by actual measurement method. i Specifically: Prepare a plane reflector with the same processing flow and mirror roughness as the curved reflector to be tested, and use it as a test sample. Place the test sample and the curved reflector to be tested in the same test environment. Measure the angle-resolved scattering distribution ARS of the test sample by an angular resolution scatterometer, obtain the BSDF data of the test sample at the angle of each plane mirror microelement, and use it as the scattering distribution function BSDF of each plane mirror microelement on the curved reflector to be tested. i .

7. The method for calculating the mirror scattering distribution of a curved reflector of a gravitational wave telescope according to claim 1, characterized in that: In step 5.4, each time the fixed angle is rotated, its position is recorded as the next spatial point: After each rotation of 1 degree, its position is recorded as the next spatial point.

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