Design method of monomer corner reflector dihedral error
By constructing a far-field diffraction model and considering the laser polarization characteristics, the corner reflector design was optimized, solving the problem of poor universality of existing corner reflectors and improving the accuracy of laser ranging.
Patent Information
- Application Number
- CN202410936898.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-07-12
- Publication Date
- 2026-02-13
- Estimated Expiration
- 2044-07-12
AI Technical Summary
Existing corner reflectors are designed for relatively limited applications and have poor versatility, resulting in large ranging errors when using laser ranging.
By constructing a far-field diffraction model, using Fraunhofer's formula and Jones matrix, the far-field energy distribution within the velocity difference angle range is calculated, the optimal dihedral angle error of the corner reflector is designed, and the design of the corner reflector is optimized by considering the laser polarization characteristics and the structural characteristics of the corner reflector.
It improves the versatility of corner reflectors, reduces ranging errors, and enhances the accuracy of laser ranging.
Smart Images
Figure CN119001681B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the field of laser ranging, in particular to a design method of dihedral angle error of single cube corner reflector. BACKGROUND
[0002] The cube corner reflector is a tetrahedral prism, in which three surfaces are perpendicular to each other, called reflecting surfaces, and the fourth surface can be divided into a circular bottom surface and a triangular bottom surface according to whether it is cut. When laser light enters the interior of the cube corner reflector through the bottom surface, it will undergo three total reflections on the three reflecting surfaces and then exit through the bottom surface. The direction of the exiting laser light is exactly opposite to that of the incident laser light. This backward reflection characteristic is independent of the incident direction of the laser light.
[0003] When laser light is obliquely incident on the array of cube corner reflectors, it will cause laser pulse broadening and thus introduce ranging error, because it is unknown which cube corner reflector reflects the echo pulse back. Therefore, the single cube corner reflector has become the main object of consideration for the cube corner reflector.
[0004] The 100mm aperture solid cube corner reflector developed by the University of Maryland in the United States has been completed and has completed optical testing. The current design of the cube corner reflector is mainly aimed at lunar laser ranging and considers the cube corner reflector as a solid cube corner reflector, and the design method lacks universality, because the laser light is assumed to have polarization characteristics. SUMMARY
[0005] To solve the technical problem of the single object and poor universality of the existing cube corner reflector design, the present application provides a design method of dihedral angle error of single cube corner reflector, which comprises:
[0006] calculating the range of the velocity difference angle according to the orbital elements of the ranging target;
[0007] constructing a far-field diffraction model based on the dihedral angle error compensating the velocity difference effect;
[0008] inputting the parameters of the cube corner reflector and the ranging laser and the range of the velocity difference angle as input conditions into the far-field diffraction model, performing far-field diffraction simulation on the cube corner reflector with dihedral angle error by Fresnel formula in the far-field diffraction model, and obtaining the corresponding far-field energy distribution;
[0009] calculating the optimal dihedral angle error of the cube corner reflector according to the far-field energy distribution.
[0010] As a preferred scheme, the method for calculating the range of the velocity difference angle according to the orbital elements of the ranging target comprises:
[0011] The linear velocity vector of the ranging target is calculated according to the orbit elements of the ranging target, and the velocity difference angle is calculated by projecting the difference between the linear velocity vector of the station rotation and the linear velocity vector of the ranging target onto the direction perpendicular to the ranging target-station vector.
[0012] As a preferred solution, the size of the velocity difference angle is calculated by the following formula:
[0013]
[0014] wherein v r is the projection of the satellite motion velocity relative to the station in the direction perpendicular to the ranging target-station vector, and c is the speed of light; the satellite motion velocity satisfies the energy formula:
[0015]
[0016] wherein v is the linear velocity of the satellite revolving around the earth, G is the earth gravitational constant, r is the distance from the satellite to the earth center of mass, and a is the semi-major axis of the satellite orbit; similarly, the station also has a linear velocity of rotation on the earth, which satisfies:
[0017]
[0018] wherein ω is the angular velocity of the earth rotation, RE is the earth radius, is the latitude of the station.
[0019] As a preferred solution, the method for constructing the far-field diffraction model comprises:
[0020] The far-field diffraction is calculated by the Fraunhofer formula, and the specific formula is:
[0021]
[0022] wherein z1 represents the distance from the diffraction plane to the observation plane, x1 and y1 are the horizontal coordinate and vertical coordinate of the diffraction plane respectively, x and y are the horizontal coordinate and vertical coordinate of the observation plane respectively, the second term in the formula is a quadratic phase factor, which has no effect on the intensity of light, is a spherical wave with an amplitude of 1, is a complex amplitude on the diffraction aperture, is the wave number, and thus The Fraunhofer formula is simplified as:
[0023]
[0024] is a quadratic phase factor, which has no effect on the calculation of the far-field diffraction spot energy distribution, and thus is ignored; finally, the Fraunhofer formula is obtained as follows:
[0025]
[0026] As a preferred solution, the method for constructing the far-field diffraction model further comprises: calculating the far-field diffraction image of the corner reflector through the wave front distribution of the diffraction plane; the wave front distribution of the diffraction plane is quantitatively described by establishing two coordinate systems, specifically:
[0027] A corner coordinate system o-xyz is established through the three straight edges of the corner reflector, o being the vertex of the corner reflector; a bottom surface coordinate system o'-x'y'z' is established on the bottom surface of the corner reflector, o' being the projection of the vertex on the bottom surface and also the center of the bottom surface of the corner reflector, the z' axis being the normal direction of the bottom surface, and the y' axis direction being the projection of the y axis on the bottom surface, o'-x'y'z' forming a right-hand system; since the incident light vector and the reflected light vector are symmetrical about the reflection surface, the calculation can be performed through the method of mirror transformation; the Household matrix of the mirror transformation is related to the normal vector of the reflection surface; in the corner coordinate system, the normal vectors of the three reflection surfaces are the x axis, the y axis and the z axis.
[0028] As a preferred solution, the conversion matrix of the bottom surface coordinate system and the corner coordinate system is as follows:
[0029]
[0030] wherein is the vector in the corner coordinate system, is the vector in the bottom surface coordinate system.
[0031] As a preferred solution, the method for constructing the far-field diffraction model further comprises:
[0032] The far-field diffraction simulation considering the polarization characteristics of the laser is specifically:
[0033] For the calculation of polarized light, the Jones vector is used to describe linearly polarized light or circularly polarized light; for linearly polarized light, it is represented as: θ being the polarization angle of the linearly polarized light, the size of which is the included angle between the polarization direction of the linearly polarized light and the x axis of the coordinate system, and for circularly polarized light, it is represented as ± respectively corresponding to left-handed and right-handed circularly polarized light; the total reflection process only changes the phase of s wave and p wave, therefore, the process is represented by a Jones matrix: δ s ,δ p respectively representing the phase change of s wave and p wave in the process of one total reflection;
[0034] The Jones vector and the Jones matrix are extended to three dimensions;
[0035] The laser is decomposed into s wave and p wave which are perpendicular and parallel to the incident plane, and the laser is transmitted in the corner reflector to establish a coordinate system to quantitatively describe the change of the direction and phase of s wave and p wave in the transmission process of the laser in the corner reflector;
[0036] For polarized light, p, s, and k constitute a right-handed system, and according to the physical meaning of s wave, the following can be obtained:
[0037]
[0038] Where N represents the normal of the incident surface of the corner reflector;
[0039] In the ray tracing process, the light vector is defined in the corner coordinate system;
[0040] Before the phase superposition of s wave and p wave by the Jones matrix, a matrix is introduced to realize the conversion of the coordinate system; the Fresnel formula of each refraction or reflection process is represented by a matrix, and the change of the light vector on the qth surface is represented by matrix P q
[0041]
[0042] Since p, s, and k constitute a right-handed system, the matrices are all orthogonal matrices, that is, the inverse matrix is equal to the transpose matrix; J q That is, the three-dimensional Jones matrix of the qth surface; a s,q And a p,q are the transmission or reflection coefficients of s wave and p wave, which are calculated by the Fresnel formula according to the optical process; The matrix is used to convert the light vector in the corner coordinate system to the (s q , p q , k q-1 ) coordinate system; O out,q The matrix is used to convert the light vector in the (s q , p q ', k q ) coordinate system to the corner coordinate system; s q represents the s wave component of the refraction or reflection process on the qth surface; p q represents the p wave component before the refraction or reflection process on the qth surface, which is obtained by the cross product of s q and k q-0 ; k q-1 represents the exit light vector of the q-1th surface in the corner coordinate system, and k q is the same; p q ' represents the p wave component of the exit light after the refraction or reflection process on the qth surface;
[0043] The polarization state change of the laser after passing through the corner reflector is described by 5 matrix multiplications; the 5 matrices correspond to 5 refraction or reflection processes, and the 5 matrices are respectively referred to as a first matrix, a second matrix, a third matrix, a fourth matrix and a fifth matrix, and specifically are as follows:
[0044] The process corresponding to the first matrix is that the laser is refracted when being incident on the bottom surface of the corner reflector;
[0045] The processes corresponding to the second matrix, the third matrix and the fourth matrix are that the laser is totally reflected at the three reflecting surfaces;
[0046] The process corresponding to the fifth matrix is that the laser is refracted through the bottom surface and then exits from the inside of the corner reflector to the outside space; the whole calculation process is an iterative process, and the initial s0, p0 and p0' are defined as follows:
[0047]
[0048] p0 = s0 * k0
[0049] p'0 = s'0 * k'0
[0050] k'0 represents the light vector of k0 after refraction or reflection, the P matrix of the 5 processes is calculated based on s0, p0 and p0', and finally the final exit vector is obtained by multiplying the incident polarization vector on the left by the multiplication of the 5 P matrices.
[0051] As a preferred scheme, the changes of the directions and phases of s waves and p waves during the transmission of the laser in the corner reflector are as follows:
[0052] During the transmission of the laser in the corner reflector, a total of two refractions and three total reflections are experienced; among them, the refraction only changes the amplitude of the s wave and the p wave, but does not change the phase of the s wave and the p wave; in the three total reflection processes, the amplitudes of the s wave and the p wave are unchanged, and the phases are changed; in each total reflection process, the incident surface of the laser is different, so the phase and direction of the s wave and the p wave are changed.
[0053] As a preferred scheme, the corner reflector includes a solid corner reflector and a hollow corner reflector.
[0054] As a preferred scheme, the method for calculating the optimal corner reflector dihedral angle error according to the far-field energy distribution in the variation range of the speed difference angle includes:
[0055] The normalized energy mean of the far-field energy distribution in the variation range of the speed difference angle is taken as an evaluation index to obtain the optimal corner reflector dihedral angle error design.
[0056] Compared with the prior art, the present application has the beneficial effects that:
[0057] The application can obtain corresponding orbit root numbers according to different ranging targets, and then design optimal dihedral angle errors of different aperture angle reflectors by using a far-field diffraction model.
[0058] The application can calculate the relative echo photon number by considering the aperture of the angle reflector, the dihedral angle error, the speed difference angle range, the laser incidence angle and other factors. BRIEF DESCRIPTION OF DRAWINGS
[0059] Figure 1 A flow chart of a design method of a dihedral angle error of a single angle reflector is provided for the embodiment.
[0060] Figure 2 A coordinate system diagram is provided for the embodiment. DETAILED DESCRIPTION
[0061] The accompanying drawings are only used for illustrative description, and cannot be understood as a limitation on the application;
[0062] It should be clear that the described embodiments are only some of the embodiments of the application, not all the embodiments. Based on the embodiments in the application, all other embodiments obtained by those of ordinary skill in the art without creative labor fall within the scope of protection of the application.
[0063] The terms used in the application are only for the purpose of describing specific embodiments, and are not intended to limit the application. The singular forms "a", "said" and "the" used in the application and the appended claims are also intended to include the plural forms, unless the context clearly indicates otherwise. It should also be understood that the term "and / or" used herein means and includes any or all possible combinations of one or more associated listed items.
[0064] The following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The implementations described in the following exemplary embodiments do not represent all implementations consistent with the present application. Instead, they are merely examples of apparatuses and methods consistent with some aspects of the present application, as detailed in the appended claims. In the description of the application, it should be understood that the terms "first", "second", "third", etc. are only used to distinguish similar objects, and do not necessarily describe a specific order or sequence, nor can they be understood as indicating or implying relative importance. For those of ordinary skill in the art, the specific meaning of the above terms in the application can be understood according to the specific circumstances.
[0065] Further, in the description of the present application, "a plurality of" means two or more, unless otherwise specified. The association relationship of "and / or" describes the association relationship of the associated objects, which means that there can be three relationships, for example, A and / or B can represent the following three cases: A exists alone, A and B exist together, and B exists alone. The character " / " generally represents an "or" relationship between the associated objects before and after it. The present application is further described below in conjunction with the accompanying drawings and embodiments.
[0066] The present application is further described below in conjunction with the accompanying drawings and embodiments.
[0067] Embodiment 1
[0068] Please refer to Figure 1 The embodiment provides a design method for dihedral angle error of a single monomer corner reflector, and the method comprises the following steps:
[0069] S1: calculating the variation range of the speed difference angle according to the orbital elements of the ranging target;
[0070] S2: compensating the speed difference effect based on the dihedral angle error, and constructing a far-field diffraction model;
[0071] S3: inputting the parameters of the corner reflector and the ranging laser and the variation range of the speed difference angle into the far-field diffraction model, performing far-field diffraction simulation on the corner reflector with dihedral angle error in the far-field diffraction model through the Fraunhofer formula, and obtaining the corresponding far-field energy distribution;
[0072] Specifically, the input conditions of the far-field diffraction model further include the bottom aperture of the corner reflector and the wavelength of the ranging laser.
[0073] S4: calculating the optimal dihedral angle error of the corner reflector according to the far-field energy distribution.
[0074] In a specific embodiment, the method for calculating the speed difference angle range according to the orbital elements of the ranging target comprises:
[0075] The line velocity vector of the ranging target is calculated according to the orbital elements of the ranging target, and the variation range of the speed difference angle of the ranging target is calculated after the line velocity vector is subtracted from the line velocity vector of the station rotation and then projected onto the direction perpendicular to the ranging target-station vector.
[0076] In a specific embodiment, the size of the speed difference angle is calculated by the following formula:
[0077]
[0078] Wherein v ris the projection of the satellite's motion velocity on the direction perpendicular to the range-target-station vector, c is the speed of light; the satellite's motion velocity satisfies the virial theorem:
[0079]
[0080] where v is the linear velocity of the satellite revolving around the earth, G is the earth's gravitational constant, r is the distance from the satellite to the earth's center of mass, and a is the semi-major axis of the satellite's orbit; similarly, the station also has a linear velocity of rotation on the earth, which satisfies:
[0081]
[0082] where ω is the angular velocity of the earth's rotation, RE is the radius of the earth, is the latitude of the station.
[0083] In a specific embodiment, the method for constructing a far-field diffraction model comprises:
[0084] The far-field diffraction is calculated by the Fraunhofer formula, and the specific formula is:
[0085]
[0086] where z1 represents the distance from the diffraction plane to the observation plane, x1 and y1 are the horizontal coordinate and vertical coordinate of the diffraction plane, respectively, and x and y are the horizontal coordinate and vertical coordinate of the observation plane, respectively; the second term is a quadratic phase factor, which has no effect on the intensity of light, is a spherical wave with an amplitude of 1, is a complex amplitude on the diffraction aperture, is the wave number, so let The Fraunhofer formula is simplified as:
[0087]
[0088] is a quadratic phase factor, which has no effect on the calculation of the far-field diffraction spot energy distribution, so it is ignored; finally, the Fraunhofer formula is obtained as follows:
[0089]
[0090] In a specific embodiment, the method for constructing a far-field diffraction model further comprises: calculating the far-field diffraction image of the corner reflector by the wavefront distribution of the diffraction plane; the wavefront distribution of the diffraction plane is quantitatively described by establishing two coordinate systems, specifically:
[0091] Please refer to Figure 2, a corner cube coordinate system o-xyz is established by three straight edges of the corner reflector, o is the vertex of the corner reflector; a bottom surface coordinate system o'-x'y'z' is established on the bottom surface of the corner reflector, o' is the projection of the vertex on the bottom surface and also the center of the bottom surface of the corner reflector, the z' axis is the normal direction of the bottom surface, the y' axis direction is the projection of the y axis on the bottom surface, and o'-x'y'z' forms a right-hand system; since the incident light vector and the reflected light vector are symmetrical about the reflecting surface, the calculation can be performed by the mirror image transformation method; the Household matrix of the mirror image transformation is related to the normal vector of the reflecting surface; in the corner cube coordinate system, the normal vectors of the three reflecting surfaces are the x axis, the y axis and the z axis.
[0092] In a specific embodiment, the conversion matrix of the bottom surface coordinate system and the corner cube coordinate system is as follows:
[0093]
[0094] wherein is a vector in the corner cube coordinate system, is a vector in the bottom surface coordinate system.
[0095] In a specific embodiment, the corner reflector includes a solid corner reflector and a hollow corner reflector.
[0096] In a specific embodiment, the method for calculating the optimal dihedral angle error of the corner reflector according to the far-field energy distribution in the variation range of the speed difference angle includes:
[0097] The normalized energy mean of the far-field energy distribution in the variation range of the speed difference angle is taken as an evaluation index to obtain the optimal dihedral angle error design of the corner reflector.
[0098] Embodiment 2
[0099] For reference Figure 1 , the present embodiment can be regarded as an improved or extended embodiment of embodiment 1, specifically:
[0100] A design method of dihedral angle error of a single corner reflector, the method includes:
[0101] S1: calculating the variation range of the speed difference angle according to the orbital elements of the ranging target;
[0102] S2: based on the dihedral angle error compensating the speed difference effect, a far-field diffraction model is constructed;
[0103] S3: inputting the parameters of the corner reflector and the ranging laser and the variation range of the speed difference angle into the far-field diffraction model, performing far-field diffraction simulation on the corner reflector with dihedral angle error by the Fraunhofer formula in the far-field diffraction model, and obtaining the corresponding far-field energy distribution;
[0104] Specifically, the input conditions of the far-field diffraction model further include the bottom surface aperture of the corner reflector and the ranging laser wavelength.
[0105] S4: calculating the optimal corner reflector dihedral angle error according to the far-field energy distribution.
[0106] In a specific embodiment, the method for calculating the range rate angle range according to the orbit elements of the ranging target comprises:
[0107] According to the orbit elements of the ranging target, the line velocity vector of the ranging target is calculated, and after the line velocity vector of the station rotation is subtracted, the ranging target's range rate angle range is calculated by projecting it onto the direction perpendicular to the ranging target-station vector.
[0108] In a specific embodiment, the magnitude of the range rate angle is calculated by the following formula:
[0109]
[0110] where v r is the projection of the satellite's motion speed relative to the station in the direction perpendicular to the ranging target-station vector, and c is the speed of light; the satellite's motion speed satisfies the energy formula:
[0111]
[0112] where v is the line speed of the satellite revolving around the earth, G is the earth's gravitational constant, r is the distance from the satellite to the earth's center of mass, and a is the semi-major axis of the satellite's orbit; similarly, the station also has a line speed of rotation on the earth, which satisfies:
[0113]
[0114] where ω is the angular speed of the earth's rotation, RE is the earth's radius, is the latitude of the station.
[0115] In a specific embodiment, the method for constructing the far-field diffraction model comprises:
[0116] The far-field diffraction is calculated by the Fraunhofer formula, and the specific formula is:
[0117]
[0118] where z1 represents the distance from the diffraction plane to the observation plane, x1 and y1 are the horizontal and vertical coordinates of the diffraction plane, respectively, and x and y are the horizontal and vertical coordinates of the observation plane, respectively; the second term is a quadratic phase factor, which has no effect on the intensity of light, is a spherical wave with an amplitude of 1, The complex amplitude on the diffraction aperture, is the wave number, so that The Fraunhofer formula is simplified as:
[0119]
[0120] is a quadratic phase factor, which has no effect on the calculation of the energy distribution of the far-field diffraction spot, so it is ignored; finally, the Fraunhofer formula is as follows:
[0121]
[0122] It should be noted that if only the relative distribution of energy is considered, the constant term outside the integral can be ignored, and the above formula is the same as the form of two-dimensional Fourier transform, so the calculation of Fraunhofer diffraction can be regarded as the Fourier transform of the complex amplitude on the diffraction aperture.
[0123] In a specific embodiment, the method for constructing a far-field diffraction model further comprises: calculating a far-field diffraction image of the corner reflector through a wavefront distribution of a diffraction plane; the wavefront distribution of the diffraction plane is quantitatively described by establishing two coordinate systems, specifically:
[0124] Please refer to Figure 2 , a corner coordinate system o-xyz is established through three straight edges of the corner reflector, o is the vertex of the corner reflector; a bottom surface coordinate system o'-x'y'z' is established on the bottom surface of the corner reflector, o' is the projection of the vertex on the bottom surface, which is also the center of the bottom surface, the z' axis is the normal direction of the bottom surface, and the y' axis direction is the projection of the y axis on the bottom surface, o'-x'y'z' forms a right-handed system; since the incident light vector and the reflected light vector are symmetrical about the reflection surface, the calculation can be performed by mirror transformation; the Household matrix of mirror transformation is related to the normal vector of the reflection surface; in the corner coordinate system, the normal vectors of the three reflection surfaces are x axis, y axis and z axis.
[0125] In a specific embodiment, the conversion matrix of the bottom surface coordinate system and the corner coordinate system is as follows:
[0126]
[0127] wherein is a vector in the corner coordinate system, is a vector in the bottom surface coordinate system;
[0128] It should be noted that the specific principle is that the three reflecting surfaces of the corner reflector are artificially controlled to be no longer strictly perpendicular. When a plane wave is incident on such a corner reflector, the reflected light spot will be split to a certain extent, thereby greatly increasing the number of echo photons at the velocity difference angle. This method is particularly effective for compensating large-aperture corner reflectors.
[0129] In one specific embodiment, the method of constructing a far-field diffraction model further comprises:
[0130] Considering the far-field diffraction simulation of the polarization characteristics of the laser, specifically:
[0131] For the calculation of polarized light, the Jones vector is used to describe linearly polarized light or circularly polarized light; for linearly polarized light, it is represented as: θ is the polarization angle of linearly polarized light, which is the angle between the polarization direction of linearly polarized light and the x-axis of the coordinate system; for circularly polarized light, it is represented as ± correspond to left-handed and right-handed circularly polarized light, respectively; the total reflection process only changes the phase of s and p waves, therefore, this process is represented by a Jones matrix: δ s ,δ p represent the phase changes of s and p waves in one total reflection process, respectively;
[0132] The Jones vector and the Jones matrix are extended to three dimensions;
[0133] The laser is decomposed into s and p waves perpendicular and parallel to the incident plane, and the laser propagates inside the corner reflector, and a coordinate system is established to quantitatively describe the changes in direction and phase of s and p waves during the laser propagation inside the corner reflector;
[0134] For polarized light, p, s, and k form a right-handed system, and according to the physical meaning of s wave, we can get:
[0135]
[0136] where N represents the normal to the incident surface of the corner reflector;
[0137] Specifically, for the incident light vector k of the qth surface q is actually the refracted\reflected light vector k q-1 of the q-1th surface. Therefore, the ray tracing problem of polarized light is essentially an iterative process, and the output of the last refraction\reflection process is the input of the next refraction\reflection process.
[0138] To facilitate the calculation of the reflected light vector, the light vector is defined in the corner coordinate system during the ray tracing process;
[0139] Because the direction and phase of s and p wave will change with each reflection process, the phase change of three total reflections cannot be simply added as the total phase change;
[0140] Before applying the Jones matrix to add the phase of s and p wave, a matrix is introduced to realize the coordinate transformation; the Fresnel formula of each refraction or reflection process is represented by a matrix, and the change of light vector at the qth surface is represented by matrix P q :
[0141]
[0142]
[0143] Because p, s, k form a right-handed system, the matrix is an orthogonal matrix, that is, the inverse matrix is equal to the transpose matrix; J q is the three-dimensional Jones matrix of the qth surface; a s,q and a p,q are the transmission or reflection coefficients of s and p wave respectively, which are calculated by the Fresnel formula according to the optical process; The matrix is used to convert the light vector in the corner coordinate system to the (s q , p q , k q-1 ) coordinate system; O out,q The function of the matrix is to convert the light vector in the (s q , p q ', k q ) coordinate system to the corner coordinate system; s q represents the s wave component of the qth surface after refraction or reflection; p q represents the p wave component before the qth surface refraction or reflection, which is obtained by the cross product of s q and k q-1 ; k q-1 represents the outgoing light vector of the q-1th surface in the corner coordinate system, k q is the same; p q ' represents the p wave component of the outgoing light after the qth surface refraction or reflection;
[0144] The polarization state change of laser after the corner reflector is described by multiplying five matrices; the five matrices correspond to five refraction or reflection processes, and the five matrices are respectively referred to as the first matrix, the second matrix, the third matrix, the fourth matrix and the fifth matrix, which are specifically:
[0145] The process corresponding to the first matrix is that the laser is incident on the bottom surface of the corner reflector and is refracted;
[0146] The processes corresponding to the second matrix, the third matrix and the fourth matrix are that the laser light is totally reflected at the three reflecting surfaces;
[0147] The process corresponding to the fifth matrix is that the laser light is refracted through the bottom surface and then exits from the corner reflector to the outside space; the whole calculation process is an iterative process, and the initial s0, p0 and p0' are defined as:
[0148]
[0149] p0 = s0 x k0
[0150] p'0 = s'0 x k'0
[0151] k'0 represents the light vector of k0 after refraction or reflection, the P matrix of the five processes is calculated based on s0, p0 and p0', and finally the five P matrices are multiplied by the incident polarization vector on the left to obtain the final exit vector.
[0152] In a specific embodiment, the changes of the directions and phases of s waves and p waves during the transmission of the laser light in the corner reflector are as follows:
[0153] During the transmission of the laser light in the corner reflector, a total of two refractions and three total reflections are experienced; among them, the refraction only changes the amplitude of the s wave and the p wave, but does not change the phase of the s wave and the p wave; in the three total reflection processes, the amplitudes of the s wave and the p wave remain unchanged, and the phases change; in each total reflection process, the incident surface of the laser light is different, so the phases and directions of the s wave and the p wave change.
[0154] In a specific embodiment, the corner reflector includes a solid corner reflector and a hollow corner reflector.
[0155] In a specific embodiment, the method for calculating the optimal corner reflector dihedral angle error according to the far-field energy distribution in the range of the variation of the velocity difference angle includes:
[0156] The normalized energy mean of the far-field energy distribution in the range of the variation of the velocity difference angle is taken as an evaluation index to obtain the optimal corner reflector dihedral angle error design.
[0157] Obviously, the above embodiments of the present application are only examples for clearly illustrating the present application, and are not intended to limit the implementation modes of the present application. For those skilled in the art, other different forms of changes or variations can be made on the basis of the above description. Here, it is not necessary and impossible to exhaust all the implementation modes. Any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the claims of the present application.
Claims
1. A design method for the dihedral angle error of a single-unit corner reflector, characterized in that, The method comprises: The range of the velocity difference angle is calculated according to the orbital elements of the ranging target; The velocity difference effect is compensated based on the dihedral angle error, and a far-field diffraction model is constructed; The parameters of the corner reflector and the ranging laser and the range of the velocity difference angle are input into the far-field diffraction model, far-field diffraction simulation of the corner reflector with the dihedral angle error is performed by using the Fraunhofer formula in the far-field diffraction model, and corresponding far-field energy distribution is obtained; The optimal dihedral angle error of the corner reflector is calculated according to the far-field energy distribution. The method for constructing the far-field diffraction model further comprises: The far-field diffraction simulation considering the polarization characteristics of the laser is specifically as follows: For the calculation of polarized light, the Jones vector is used to describe linearly or circularly polarized light; for linearly polarized light, it is denoted as , is the polarization angle of linearly polarized light, whose magnitude is the angle between the polarization direction of linearly polarized light and the coordinate system axis, and for circularly polarized light, it is denoted as , correspond to left-handed and right-handed circularly polarized light, respectively; the total reflection process only changes the phase of and waves, so this process is represented by a Jones matrix: , , represent the phase changes of and waves in the process of total reflection, respectively; The Jones vector and the Jones matrix are extended to three dimensions; The laser is decomposed into the direction perpendicular to the incident plane and the direction parallel to the incident plane, that is The wave and The wave, the laser transmits inside the corner reflector, establishes a coordinate system to quantitatively describe the transmission process of the laser inside the corner reflector The wave and The change of the direction and phase of the wave For polarized light, constitute a right-handed system, and according to The physical meaning of the wave can be obtained: wherein represents a normal to the corner reflector's incident surface; In the ray tracing process, the light vector is defined in the corner coordinate system; In applying the Jones matrix pair Waves and Before the waves undergo phase superposition, a matrix is introduced to achieve coordinate system transformation; the Fresnel formula for each refraction or reflection process is represented by a matrix, the nth... The change in the surface light vector is represented by a matrix. express: because They form a right-handed system, therefore all the matrices are orthogonal matrices, that is, the inverse matrix is equal to the transpose matrix; That is to say, the first The three-dimensional Jones matrix of each surface; and They are respectively Waves and The transmission or reflection coefficient of a wave is calculated using Fresnel's formula. The matrix is used to transform the light vector in the pyramidal coordinate system to ( ). In coordinate system; The function of a matrix is to ( Transform the light vector from the ) coordinate system to the pyramidal coordinate system; Indicates the first A surface undergoes refraction or reflection. wave component; Indicates the first Before the refraction or reflection process occurs on a surface wave components, through and We obtain it through cross product; This means that in the pyramidal coordinate system, the first... The emitted light vector of each surface, Similarly; Indicates the first The emitted light is produced after refraction or reflection occurs on each surface. wave component; The polarization state change of the laser after passing through the corner reflector is described by multiplying five matrices, and the five matrices correspond to five refraction or reflection processes, and the five matrices are respectively referred to as a first matrix, a second matrix, a third matrix, a fourth matrix and a fifth matrix, and specifically as follows: The process corresponding to the first matrix is that the laser is incident on the bottom surface of the corner reflector and is refracted; The processes corresponding to the second matrix, the third matrix and the fourth matrix are that the laser is totally reflected at the three reflecting surfaces; The process corresponding to the fifth matrix is that the laser is refracted through the bottom surface and exits from the inside of the corner reflector to the outside space; The entire calculation process is an iterative process, initially , and are defined as: representing light vectors after refraction or reflection, based on , and calculating 5 process matrices, finally multiplying 5 matrices with incident polarization vector to get final exit vector The method for calculating the range of the velocity difference angle according to the orbital elements of the ranging target comprises: The line velocity vector of the ranging target is calculated according to the orbital elements of the ranging target, and the range of the velocity difference angle is calculated after the line velocity vector is subtracted from the line velocity vector of the station rotation and then projected onto the direction perpendicular to the ranging target-station vector.
2. The design method for the dihedral angle error of a single-unit corner reflector according to claim 1, characterized in that, The size of the velocity difference angle is calculated by the following formula: wherein is the projection of the velocity of the satellite relative to the station in the direction perpendicular to the range target-station vector, is the speed of light; the velocity of the satellite satisfies the virial theorem: wherein is the linear velocity of the satellite around the Earth, G is the Earth gravitational constant, r is the distance of the satellite to the Earth's center, is the semi-major axis of the satellite orbit; similarly the station on the Earth also has a linear velocity of rotation satisfying: wherein is the angular velocity of the earth rotation, is the radius of the earth, is the latitude of the station.
3. The method of claim 2, wherein the method further comprises: The method for constructing the far-field diffraction model comprises: The far-field diffraction is calculated by using the Fraunhofer formula, and the specific formula is as follows: where denotes the distance from the diffraction plane to the observation plane, , are the transverse and longitudinal coordinates of the diffraction plane, respectively, , are the transverse and longitudinal coordinates of the observation plane, respectively, where the second term is a quadratic phase factor which has no effect on the intensity of the light, is a spherical wave of unit amplitude, is the complex amplitude on the diffraction aperture, is the wave number, so that the Fraunhofer formula simplifies to: The second phase factor has no effect on the calculation of the far-field diffraction spot energy distribution, so it is ignored; finally, the Fraunhofer formula is as follows: 。 4. The design method for the dihedral angle error of a single-unit corner reflector according to claim 3, characterized in that, The method for constructing the far-field diffraction model further comprises: the far-field diffraction image of the corner reflector is calculated by using the wavefront distribution of the diffraction plane; and the wavefront distribution of the diffraction plane is quantitatively described by establishing two coordinate systems, and specifically as follows: Establish a pyramidal coordinate system using the three right-angled sides of the corner reflector. , Let the vertex of the corner reflector be a coordinate system on the bottom surface of the corner reflector. , This is the projection of the vertex onto the bottom surface, which is also the center of the bottom surface of the corner reflector. The axis is the direction of the normal to the base. axial direction The projection of the axis onto the bottom surface. This forms a right-handed system; since the incident and reflected light vectors are symmetrical about the reflecting plane, they can be calculated using the mirror transformation method; the mirror transformation... Household The matrix is related to the normal vector of the reflecting surface; in the pyramidal coordinate system, the normal vectors of the three reflecting surfaces are respectively... axis, shaft and axis.
5. The method of claim 4, wherein the method further comprises: The conversion matrix of the bottom surface coordinate system and the corner coordinate system is as follows: wherein is a vector in the base coordinate system, is a vector in the base coordinate system.
6. The method of claim 5, wherein the method further comprises: Laser transmission inside corner reflector Wave and The changes in direction and phase of the wave are specifically: During the transmission of laser light inside the corner reflector, it undergoes two refractions and three total internal reflections; among them, refraction only changes the... Waves and The amplitude of the wave remains unchanged. Waves and The phase of the wave; during the three total internal reflections, Waves and The amplitude of the wave remains constant, but the phase changes; the incident surface of the laser is different in each total internal reflection process, therefore... Waves and Both the wave phase and direction change.
7. The method of claim 1, wherein: The corner reflector comprises a solid corner reflector and a hollow corner reflector.
8. The method of claim 1, wherein: The method for calculating the optimal dihedral angle error of the corner reflector according to the far-field energy distribution in the range of the velocity difference angle comprises: The normalized energy mean of the far-field energy distribution in the range of the velocity difference angle is taken as an evaluation index to obtain the optimal dihedral angle error design of the corner reflector.