NURBS-based high performance three-mirror compact range antenna measurement system

Abstract

The application discloses a high-performance three-mirror compact range antenna measurement system based on NURBS, combines a non-uniform rational B-spline curve surface fitting algorithm with a terahertz three-mirror compact range design, gives a new application of the non-uniform rational B-spline modeling technology according to electromagnetic background and aperture field distribution of a terahertz frequency band, realizes shape conversion of a beam aperture section from a circular shape to a square shape, takes into account the advantages of the B-spline, can realize free distribution of a grid, obtains a shaped surface of a compact range aperture meeting requirements, and solves the adaptation problem of the non-uniform rational B-spline in the shaping surface design process of the three-mirror compact range. In addition, in the process of the three-mirror compact range design, a good energy mapping condition is explored, the energy attenuation relationship function of the edge of a quiet zone is optimized by adjusting light and a propagation path, the energy dispersion problem caused by diffraction of light at the edge of a primary mirror is further solved, and the performance of the whole three-mirror compact range system is improved.

Description

High-performance three-mirror compact field antenna measurement system based on NURBS Technical Field

[0001] This invention relates to the field of high-frequency electromagnetic wave measurement technology, and in particular to a high-performance three-mirror compact field antenna measurement system based on NURBS. Background Technology

[0002] Three-mirror compact field measurement is an antenna measurement method derived from the design of large-aperture mirror antennas. It analyzes from the perspective of ray tracing, by controlling the total optical path of each ray to be equal and the energy distribution to be uniform and proportional, thereby obtaining a uniform plane wave with equal phase and amplitude in the quiet zone of the primary mirror, thus achieving the purpose of antenna measurement.

[0003] Non-uniform rational B-spline (NURBS) is a curve and surface fitting function optimized from the Bessel function. It is now commonly used in 3D surface modeling of ships, artificial arms, etc.

[0004] The P-order NURBS curve is defined as:

[0005]

[0006] Where P i To control the vertices (forming the control polygon), w i N is the weighting factor. i，p (u) is a p-order B-spline basis function defined on a non-uniform control vector.

[0007] The node vector is u = [u0, u1, u2, ..., u... m The node vector is a non-decreasing parameter sequence. There are generally three methods for constructing the node vector: the uniform parameter method, the cumulative chord length method, and the centripetal parameter method. Generally, to map the first and last points of the curve to the first and last data points respectively, the first and last nodes need to be p+1 times. In this case, the elements in the node vector should satisfy 0 = u0 = u1 = ... = u p ≤u p+1 ≤…≤u m-p =u m-p+1 =…=u m =1 (p=3, i.e., cubic B-spline).

[0008] NURBS is the two-dimensional form of B-splines, which extends from curves to surfaces.

[0009] In existing technologies, the establishment of a compact field antenna measurement system with a three-mirror shaped surface commonly employs polynomial techniques for fitting curved surfaces, including cubic B-spline polynomials, Zernike polynomials, and accumulative polynomials, to achieve high-frequency electromagnetic wave measurement. However, accumulative polynomials are more commonly used in curve fitting and cannot perfectly represent curves such as circles. Zernike polynomials employ global optimization, with two basic variables being continuous and orthogonal within a unit circle, making them suitable for synthesizing circular shaped reflectors. Cubic B-spline polynomials ensure curve continuity and differentiability, but are not a complete set of polynomials, thus limiting their application to circular surfaces. Therefore, a new high-performance compact field design method for three-mirror systems is needed. Summary of the Invention

[0010] To address the shortcomings of existing technologies, this invention proposes a high-performance three-mirror compact field antenna measurement system based on NURBS, which solves the adaptation problem of non-uniform rational B-splines in the shaping surface design process of a three-mirror compact field.

[0011] To achieve the above objectives, the present invention provides the following technical solution:

[0012] This invention provides a high-performance three-mirror compact field antenna measurement system based on NURBS, comprising a first shaped mirror, a second shaped mirror, a parabolic primary mirror, and a Gaussian feed, wherein:

[0013] The Gaussian feed source is positioned in the horizontal direction to provide electromagnetic waves;

[0014] The first shaped reflector and the second shaped reflector are surface reflectors obtained by fitting discrete points using non-uniform rational B-spline surface technology;

[0015] The parabolic primary mirror is a curved mirror with a fixed curvature and a specific functional equation.

[0016] The high-performance three-mirror compact field antenna measurement system based on NURBS emits electromagnetic waves from a Gaussian feed, which strike the first shaped mirror. After reflection, convergence, and divergence, the light strikes the second shaped mirror, which then reflects the light again, magnifying its cross-section onto the parabolic primary mirror. Finally, the parabolic primary mirror reflects the light horizontally to obtain a square-shaped quiet zone, which is the effective measurement area of ​​the antenna under test.

[0017] The electromagnetic wave emitted by the Gaussian feed and the light rays that hit the first shaped reflector have a circular cross-section in the vertical direction, which conforms to the radiation characteristics of the Gaussian feed's conical spherical cap beam.

[0018] The light rays reflected by the second shaped mirror to the parabolic primary mirror have a square cross section in the vertical direction, which conforms to the principle of cross section mapping from the focal point of the parabolic primary mirror to the square still area of ​​the primary mirror;

[0019] The optical path lengths from the Gaussian feed to the quiet zone are equal.

[0020] Furthermore, the process of obtaining the first and second shaped mirrors using non-uniform rational B-spline surface technology is as follows:

[0021] By combining the beam distribution with the non-uniform rational B-spline function through the equations of equal optical path and equal energy distribution, the unique solution of the equation is obtained, the location of the solution point is obtained, and the first and second shaping mirror reflecting surfaces are established respectively.

[0022] Furthermore, the specific functional equation of the parabolic primary mirror is:

[0023] -4*4.9*(z-4.042671)=(x 2 +y 2 ).

[0024] Furthermore, the square quiet zone is obtained by selecting a sampling point array based on the energy distribution, and then designing a quiet zone edge taper function to reduce the edge energy.

[0025] Furthermore, the method for selecting the sampling point array based on the energy distribution is as follows: divide the sampling area into equal intervals along the x-axis and y-axis to ensure that the overall sampling area is square.

[0026] Furthermore, the quiet zone edge taper function includes the following three types:

[0027]

[0028]

[0029]

[0030] Where r is the distance from the center of the main mirror, r qz The radius of the still zone in the x-axis or y-axis section of the primary mirror, r all The radius of the reflecting surface of the primary mirror's x-axis or y-axis tangent.

[0031] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0032] This invention provides a high-performance three-mirror compact field antenna measurement system based on NURBS, which is a three-dimensional extension of B-spline polynomials. It combines the curve-surface fitting algorithm of non-uniform rational B-splines with the design of terahertz three-mirror compact fields. Based on the electromagnetic background and aperture field distribution in the terahertz band, it gives non-uniform rational B-spline modeling technology a new application, realizing the transformation of the beam aperture cross-section from circular to square shape, while retaining the advantages of B-splines. Simultaneously, it allows for free mesh allocation, obtaining a shaped surface that meets the required compact field aperture, solving the adaptation problem of non-uniform rational B-splines in the shaped surface design process of three-mirror compact fields. Furthermore, in the process of three-mirror compact field design, a good energy mapping condition is explored. By adjusting the light rays and propagation paths, the energy attenuation relationship function at the edge of the quiet zone is optimized, further solving the energy dispersion problem caused by diffraction of light at the edge of the primary mirror, thereby improving the performance of the entire three-mirror compact field system. Attached Figure Description

[0033] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0034] Figure 1 is a diagram of the high-performance three-mirror compact field antenna measurement system provided in an embodiment of the present invention. Detailed Implementation

[0035] To better understand this technical solution, the technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described examples are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art based on this application are within the scope of protection of the present invention.

[0036] This invention provides a design concept and method for a high-performance compacted field of a three-mirror system. By combining a curve-surface fitting algorithm based on non-uniform rational B-splines, the shape transformation of the beam aperture section is achieved, resulting in a shaped surface that meets our requirements for the compacted field aperture, thereby improving the performance of the entire three-mirror compacted field system.

[0037] As shown in Figure 1, the present invention provides a high-performance three-mirror compact field antenna measurement system, comprising a first shaped mirror 1, a second shaped mirror 2, a parabolic primary mirror, and a Gaussian feed, wherein:

[0038] The Gaussian feed source is positioned in the horizontal direction to provide electromagnetic waves;

[0039] The first shaped reflector 1 and the second shaped reflector 2 are curved surface reflectors obtained by fitting discrete points;

[0040] The parabolic primary mirror is a curved mirror with a fixed curvature and a specific functional equation.

[0041] The high-performance three-mirror compact field antenna measurement system consists of an electromagnetic wave emitted from a feed source, which strikes the first shaped reflector 1. The light is reflected, converged, and diverged before striking the second shaped reflector 2. After further reflection and cross-sectional magnification, the light is projected onto the parabolic primary mirror. Finally, the primary mirror reflects the light horizontally to obtain a quiet zone that meets the required shape, which is the effective measurement area of ​​the antenna under test.

[0042] The application of the non-uniform rational B-spline technique in the compact field system is as follows: by utilizing the characteristics of the non-uniform rational B-spline technique itself, namely local adjustability, continuity, and second-order differentiability, and combining it with the requirement of obtaining a uniform plane wave in a three-mirror compact field system, a non-uniform rational B-spline surface modeling method is adopted in the process of designing the shaped reflector to form a smooth, continuous shaped reflector with more flexible mesh division.

[0043] Section 1 is a circular section located in the vertical direction in front of the shaped reflector 1, which conforms to the radiation characteristics of the Gaussian feed conical spherical cap beam.

[0044] Section 2 is a square section located in the vertical direction in front of the shaped mirror 2, which conforms to the section principle of mapping from the focal point of the primary mirror to the square still area of ​​the primary mirror.

[0045] Section 1 and Section 2 are a point-to-point correspondence obtained by shaping two curved surfaces, which includes specific principles such as the reflection theorem of curved surfaces, the equal optical path length on the path from the feed source to the quiet zone, and the proportionality of corresponding energies.

[0046] The specific technical content is as follows: in the process of designing the first shaped reflector 1 and the second shaped reflector 2, the NURBS method is used to design the curved surface, a suitable sampling point array is selected according to the energy distribution for sampling, and a reasonable quiet zone edge taper function is designed to reduce the edge energy, and finally a square quiet zone with excellent performance is obtained.

[0047] The NURBS method for designing surfaces is as follows:

[0048] The beam exits through the feed source, still forming a circular aperture area. After reflection by the first shaping mirror, the second shaping mirror, and the primary mirror, a rectangular test aperture area is formed for subsequent antenna measurements. The method primarily leverages the smooth and continuous characteristics of the non-uniform rational B-spline function, relying on the final result of a uniform plane wave with equal amplitude and phase. Equations are established based on optical path length and energy distribution, and the weight array of the non-uniform rational B-spline function is solved to calculate the location of the simulation sampling points, thus designing two shaped reflective mirrors.

[0049] Example of surface design:

[0050] The first and second shaping lenses in Figure 1 were both designed using this method.

[0051] The method for selecting a suitable sampling point array based on energy distribution is as follows:

[0052] Divide the sampling area into equal intervals along the x-axis and y-axis to ensure that the overall sampling area is square.

[0053] Example of a sampling point array:

[0054] The x and y coordinate arrays of the sampling points are as follows:

[0055] [(-2, -2) (-2, -1) (-2, 0) (-2, 1) (-2, 2);

[0056] (-1, -2) (-1, -1) (-1, 0) (-1, 1) (-1, 2);

[0057] (0, -2) (0, -1) (0, 0) (0, 1) (0, 2);

[0058] (1, -2) (1, -1) (1, 0) (1, 1) (1, 2);

[0059] (2, -2) (2, -1) (2, 0) (2, 1) (2, 2)]

[0060] The design method for the edge taper function of the quiet zone is to satisfy the following: the center is flat and the edge steep drop is close to 0.

[0061] Example of a taper function at the edge of the quiet zone:

[0062]

[0063]

[0064]

[0065] Where r is the distance from the center of the main mirror, r qz The radius of the still zone in the x-axis (or y-axis) section of the primary mirror, r all The radius of the reflecting surface of the primary mirror's x-axis (or y-axis) section.

[0066] This invention first ensures that the shaped reflective surface is continuous and smooth, while also allowing for free grid division, which facilitates adjusting the number of sampling points in different areas. It enables dense sampling in areas with concentrated energy and sparse sampling in areas with dispersed energy, reducing the overall number of sampling points while achieving the same level of accuracy.

[0067] Secondly, this invention enables the conversion of a circular aperture beam into a square aperture beam, which facilitates obtaining a quiet zone distribution that conforms to the shape of the primary reflector aperture and improves the area utilization rate of the primary reflector.

[0068] In addition, the design of this invention selects an edge energy mapping function that conforms to the edge diffraction and reflection law, which can ensure that the edge energy causes less ripple effect on the center of the quiet zone through diffraction, reflection and other forms, making the quiet zone more uniform and stable as a whole.

[0069] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. A high-performance three-mirror compact field antenna measurement system based on NURBS, characterized in that, The system includes a first shaped reflector, a second shaped reflector, a parabolic primary mirror, and a Gaussian feed. The Gaussian feed is positioned horizontally to provide electromagnetic waves. The first and second shaped reflectors are curved surface mirrors obtained by fitting discrete points using non-uniform rational B-spline surface technology. The parabolic primary mirror is a curved surface mirror with a specific function equation and fixed curvature. The high-performance three-mirror compact field antenna measurement system based on NURBS emits electromagnetic waves from the Gaussian feed, which strike the first shaped reflector. The light rays are reflected, converged, and diverged before striking the second shaped reflector. On the reflector, the light is reflected again, and its cross-section is magnified proportionally onto the parabolic primary mirror. Finally, the parabolic primary mirror reflects the light in the horizontal direction to obtain a square-shaped quiet zone, which is the effective measurement area of ​​the antenna under test. The electromagnetic wave emitted by the Gaussian feed and the light rays hitting the first shaped reflector have a circular cross-section in the vertical direction, which conforms to the radiation characteristics of the conical spherical cap beam of the Gaussian feed. The light rays reflected by the second shaped reflector to the parabolic primary mirror have a square cross-section in the vertical direction, which conforms to the principle of the cross-section mapped from the focal point of the parabolic primary mirror to the square quiet zone of the primary mirror. The optical path lengths from the Gaussian feed to the quiet zone are equal.

2. The high-performance three-mirror compact field antenna measurement system based on NURBS according to claim 1, characterized in that, The process of obtaining the first and second shaped mirrors using non-uniform rational B-spline surface technology is as follows: By combining the beam distribution with the non-uniform rational B-spline function through the equation relationship of equal optical path and equal energy distribution, the unique solution of the equation is obtained, the position of the solution point is obtained, and the first and second shaped mirror reflective surfaces are established respectively.

3. The high-performance three-mirror compact field antenna measurement system based on NURBS according to claim 1, characterized in that, The specific functional equation of the parabolic primary mirror is: -4*4.9*(z-4.042671)=(x 2 +y 2 ).

4. The high-performance three-mirror compact field antenna measurement system based on NURBS according to claim 1, characterized in that, The square quiet zone is obtained by selecting a sampling point array based on the energy distribution, and then designing a reasonable quiet zone edge taper function to reduce the edge energy.

5. The high-performance three-mirror compact field antenna measurement system based on NURBS according to claim 4, characterized in that, The method for selecting the sampling point array based on energy distribution is as follows: divide the sampling area into equal intervals along the x-axis and y-axis, ensuring that the overall sampling area is square.

6. The high-performance three-mirror compact field antenna measurement system based on NURBS according to claim 4, characterized in that, The aforementioned edge taper function for the quiet zone is: Where r is the distance from the center of the main mirror, r qz The radius of the still zone in the x-axis or y-axis section of the primary mirror, r all The radius of the reflecting surface of the primary mirror's x-axis or y-axis tangent.

7. The high-performance three-mirror compact field antenna measurement system based on NURBS according to claim 4, characterized in that, The aforementioned edge taper function for the quiet zone is: Where r is the distance from the center of the main mirror, r qz The radius of the still zone in the x-axis or y-axis section of the primary mirror, r all The radius of the reflecting surface of the primary mirror's x-axis or y-axis tangent.

8. The high-performance three-mirror compact field antenna measurement system based on NURBS according to claim 4, characterized in that, The aforementioned edge taper function for the quiet zone is: Where r is the distance from the center of the main mirror, r qz The radius of the still zone in the x-axis or y-axis section of the primary mirror, r all The radius of the reflecting surface of the primary mirror's x-axis or y-axis tangent.

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