Method for determining and correcting deformation error amount of main reflecting surface of large antenna for relaxing auxiliary reflecting surface

Abstract

The invention provides a method for determining the relaxation deformation error amount of a main reflecting surface of a large-scale antenna based on compensation of a modified auxiliary reflecting surface. An orthogonal function is utilized to describe an independent error term of the main reflecting surface of the antenna, so that the antenna has universality, and a calculation model of relaxation deformation errors of the main reflecting surface is established by combining the functions of approximate electric field calculation and auxiliary reflecting surface correction. In order to solve the problem of the model containing inner and outer double-layer optimization, an optical path length error iterative compensation method is adopted to quickly design and correct the subreflector. For external optimization, an outer layer solving method for obtaining approximate upper and lower bounds of a relaxed main reflecting surface error term and a convergence result through dichotomy iteration is designed based on a monotonic relationship between a reflecting surface error and an antenna gain.

Description

Technical Field

[0001] This invention relates to the field of high-performance large reflector antenna system design and active adjustment compensation technology. Specifically, it constructs a calculation model to determine the deformation error of the main reflector of the relaxed antenna and designs a fast iterative solution method with inner and outer double-layer optimization, which can obtain excellent convergence results after a small number of iterations. Background Technology

[0002] Large reflector antennas have attracted much attention due to their wide application and increasing demand. Under external loads (such as gravity, wind load, and temperature changes), the antenna structure will deform, leading to a deterioration in electrical performance. Currently, various error compensation methods have been proposed, including array feed compensation, conformal structural design, active surface technology, sub-reflector arrays, and modified sub-reflectors. Among these, modified sub-reflector compensation technology is considered one of the most practical solutions due to its simplicity and cost-effectiveness.

[0003] Numerous scholars have proposed various effective sub-reflector design methods to compensate for primary reflector errors. For example, techniques combining Fourier-Jacobi expansion with GO / PO analysis; iterative field matrix methods based on PO / PO analysis; and the fastest design method combining GO / PO analysis with iterative correction of optical path difference; all these methods can achieve primary reflector error compensation through the design of modified sub-reflectors. Several well-known large-scale reflector antennas, including the Effelsberg 100-meter radio telescope and the Haystack 37-meter radio telescope, have been upgraded using sub-reflector compensation technology after their initial construction. However, the extent to which modified sub-reflector compensation technology can relax the accuracy requirements of the primary reflector remains poorly understood. This gap significantly hinders research progress and engineering applications of correcting primary reflector errors through sub-reflector compensation. Summary of the Invention

[0004] This invention proposes a method for determining the deformation error of the main reflector in a large antenna by adjusting the sub-reflector for deformation. The main reflector error is decomposed into independent orthogonal terms using Zernike polynomials, ensuring the universality of the active surface error relaxation analysis method. A computational model is established to determine the amount of deformation error of the main reflector relaxed by adjusting the sub-reflector for deformation. This computational model is a dual-optimization model, which can be solved in inner and outer layers. The inner optimization uses an iterative compensation method based on optical path difference to quickly design the adjusted sub-reflector; the outer optimization, based on the monotonic relationship between reflector error and antenna gain, designs an approximate upper and lower bound and convergent solution for the main reflector error term using a bisection method iterative solution. Results show that the established model and solution method can effectively determine the relaxation result of the main reflector deformation error, and the adjusted sub-reflector can significantly relax the deformation error of the main reflector, demonstrating the great potential of this technology in antenna structure design and upgrading.

[0005] Step (1) Antenna far-field calculation:

[0006] (1a) To effectively approximate the formula (1) for the far-field integral, the far-field numerical method with relaxed mesh size is adopted. After discretizing the main reflecting surface into a triangular mesh, the far-field integral formula can be simplified to:

[0007] (5)

[0008] in, This represents the area of ​​the triangular facet. The total number of grid cells on the main reflective surface. Integral point pointing to the primary reflector ,like Figure 2 As shown by the pink marker, this integration point has no systematic error and is a node on the actual surface.

[0009] (1b) Antenna far-field calculation method, in the physical optics analysis of the sub-reflector illuminating the main reflector, in reality, point and There is a strict geometric correspondence. When the feed point and the main reflecting surface point When the information is known, the sub-reflector point can be determined using Fermat's principle. This principle states that the total optical path from the feed source to the primary reflector after reflection by the secondary reflector is... To find the extreme value, the optical path can be expressed as:

[0010] (6)

[0011] The coordinates of the sub-reflector node can then be expressed as the solution to the following two nonlinear coupling equations, namely:

[0012] (7)

[0013] The coupling equation (7) can be solved using the Newton-Raphson iterative method. Therefore, the sub-reflector node... can be and Uniquely determined. To simplify the expression of the coupling equations and their solution results, the coordinates of the sub-reflector point can be represented as:

[0014] (8)

[0015] Step (2) Method for determining the relaxation amount of antenna main reflector deformation error. Mathematical description of antenna main reflector deformation: The structural diversity of large reflector antennas leads to significant differences in their deformation error modes. To explore the structural causes of the error in depth and ensure that the study is applicable to any deformation error, large-scale deformation error can usually be decomposed into several low-order independent terms. The most commonly used expansion functions currently include the modified Jacobi polynomial and the Zernike polynomial. In fact, the only difference between these two expansion functions is the index sequence and the normalization constant. Given the wide application of Zernike polynomials in optical equipment and radio telescopes, this paper uses Zernike polynomials to describe the large-scale deformation of reflector antennas.

[0016] Antenna main reflection, deformation error relaxation determination method, main reflection surface deformation amount It can be expressed in Zernike polynomials as follows:

[0017] (9)

[0018] in

[0019] (10)

[0020] in, and represents the coefficients of the even-degree and odd-degree terms of the Zernike polynomial, respectively. The integers n1 and n2 represent the radial wavenumber and circumferential wavenumber, respectively. yes and The comprehensive expression, Includes the remaining constituent terms of the Zernike polynomial. Index n j For functions of n1 and n2, this paper adopts the indexing specifications of Born and Wolf. Represents the polar radius in the normalized unit circle. It is the polar angle, and and These correspond to the actual polar radius and the radius of the antenna's main reflector, respectively. After obtaining the antenna's axial deformation data, the coefficients can be calculated using the least squares method. Therefore, the deformed main reflector can be described as:

[0021] (11)

[0022] Step (3) uses the designed bisection method to calculate the fast iterative solution method for the correction of the sub-reflector relaxation antenna main reflector error. The constructed main reflector error relaxation model REDMRD is a dual optimization model, which includes an inner layer and an outer layer.

[0023] (3a) Through inner layer optimization—rapid design of modified sub-reflectors, the modified sub-reflector is rapidly designed using the optical path difference iterative compensation method. The modified sub-reflector obtained through iterative design... It can be represented as:

[0024] (12)

[0025] in, Indicates an ideal sub-reflecting surface. This is the surface correction amount. This correction amount can be described using a globally orthogonal function, consistent with the method of using Zernike polynomial expansion for the primary reflector, i.e.:

[0026] (13)

[0027] Where parameters , ns1, ns2, , and ns j The definition is consistent with the meaning of the corresponding parameters in equations (9) and (10). This represents the polar radius within the normalized unit circle of the sub-reflector. Its polar angle. According to the phase error iterative compensation method, the sub-reflector node P s The surface correction along the z-direction (which can be solved by equation (8)) can be expressed as:

[0028] (14)

[0029] in, Represents vector The unit normal vector of the sub-reflector node is determined. For incident rays With normal vector The included angle, It is an incident ray The angle between the Z-axis and the Z-axis It is a vector Determined discrete point deformation of the primary reflecting surface After obtaining the correction amount of the sub-reflector node, the coefficients in equation (13) can be calculated by the least squares method.

[0030] (3b) Iterative solution through outer layer optimization—convergence result. Since the feasible boundary for the deformation error amplitude of the antenna's main reflector lacks prior knowledge and reference, a method needs to be established to solve this model with a two-layer optimization structure. The Ruze formula establishes the relationship between the root mean square value of the half-path difference of the deformed antenna surface and the antenna gain loss, and its expression is:

[0031] (15)

[0032] in, Indicates antenna efficiency. and These represent the antenna gain under ideal and deformed conditions, respectively. This is the root mean square value of the half-optical path difference caused by the deformation of the reflecting surface.

[0033] (3c) The outer layer optimization process is executed in two phases. The first iteration mainly determines the... The approximate upper and lower limits of the deformation amplitude A. The second iteration is a continuation of the first iteration, when the performance discrimination condition |G G0| Automatically triggered when g is satisfied. Attached Figure Description

[0034] Figure 1 This is the overall flowchart of the present invention.

[0035] Figure 2 The distribution of the integration surface and integration points for numerical calculations of the antenna far field.

[0036] Figure 3 The flowchart for solving the relaxation model of the main reflector is shown. Detailed Implementation

[0037] The following is in conjunction with the appendix Figure 3 The present invention will be further described below.

[0038] Outer layer optimization—iterative solution of convergence results, the specific steps are as follows:

[0039] (1) Input antenna geometric parameters, initial error amplitude A and ideal gain G0.

[0040] (2) Use equation (5) to calculate the far field of the antenna and obtain the actual gain G.

[0041] (3) Determine whether the convergence condition is met: If it is met, jump to step 8; otherwise, return to step 4 to continue iterating.

[0042] (4) Determine whether the gain loss |G-G0| is greater than the specified gain loss g: If the condition is always met in the initial stage of the first iteration and in the subsequent process, then execute step 5; if the condition is not met in the subsequent iteration, then immediately terminate the current loop and jump to step 9 to start the next iteration calculation.

[0043] (5) Calculate parameter A using the following formula. and A :

[0044] (16)

[0045] Then proceed to step 6.

[0046] (6) Update the deformed main reflector model using equations (8) and (10).

[0047] (7) Design the modified sub-reflector based on equations (12) to (14), and then return to step 2 to continue the iteration.

[0048] (8) Output the deformation amplitude A of the main reflector. The second iteration is a continuation of the first iteration. When the performance discrimination condition |G G0| Automatic triggering occurs when g is satisfied. The core of this stage lies in utilizing the obtained approximate upper and lower bounds to optimize the relaxation amount of the deformation amplitude A using a bisection method. The complete steps following the first iteration are as follows:

[0049] (9) Calculate parameter A using the following formula. (or A ):

[0050] (17)

[0051] (10) Update the deformed main reflective surface using equations (8) and (10).

[0052] (11) Design the modified sub-reflector based on the inner layer optimization equations (12) to (14).

[0053] (12) Use equation (2) to calculate the far-field radiation pattern of the antenna and obtain the actual gain G value.

[0054] (13) Determine whether the convergence condition is met: If it is met, jump to step 8 and output the relaxation amount A; if it is not met, jump to step 14 and continue iterating.

[0055] (14) Determine whether |G-G0| is greater than the specified gain loss g: If it is greater, jump to step 9; otherwise, jump to step 15.

[0056] (15) Calculate parameter A using the following formula. (or A ):

[0057] (18)

Claims

1. A method for determining the deformation error of the main reflector of a large antenna with a corrected sub-reflector relaxation, characterized in that... Includes the following steps: Step (1): Calculate the far-field performance of the large reflector antenna using geometric optics methods. The Zernike polynomial is used to decompose the deformation error of the main reflector into independent terms, thereby enabling a general analysis to determine the deformation error of the relaxed main reflector under arbitrary geometric parameters. Step (2): A computational model was established to relax the deformation error of the main reflector by correcting the sub-reflector for compensation; the model constructs a two-layer optimization problem including inner layer optimization and outer layer optimization; Step (3): The designed bisection method is used to calculate the error of the main reflector of the antenna by fast iterative solution.

2. The method for determining the deformation error of the main reflector of a large antenna with a corrected sub-reflector relaxation according to claim 1, characterized in that, In step (1), the far field of the antenna It can be calculated using the physical optics integral formula, the specific expression of which is as follows: (1) in, This represents the phase constant of the propagating wave. This is the inherent impedance of free space. The surface current of the primary reflecting surface. The calculation was performed using the physical optics approximation method. It is the unit normal vector of the primary reflecting surface, while It is the feed incident field that illuminates the main reflector after being reflected by the secondary reflector.

3. The method for determining the deformation error of the main reflector of a large antenna with a corrected sub-reflector relaxation according to claim 2, characterized in that, In step (1), the physical optical analysis of the illumination of the main reflector by the sub-reflector is performed, and the main reflector is illuminated by the electromagnetic waves emitted by the sub-reflector feed source. According to the principles of physical optics, the electromagnetic wave emitted by the feed source is reflected by the secondary reflector to form the incident wave at the primary reflector, and its expression is: (2) in, Indicates from the feed point Emits and points to the sub-reflector point The direction vector of this point relative to the node of the main reflector. Related. for and The distance between them The divergence factor is calculated using the following formula: (3) in, and Indicates that the ray is in The principal radius of curvature at the point.

4. The method for determining the deformation error of the main reflector of a large antenna with a relaxed sub-reflector according to claim 3, characterized in that, In step (2), a calculation model is established to compensate for the deformation error of the primary reflector by relaxing the deformation of the secondary reflector. First, the deformation of the primary reflector is decomposed into independent error terms. The relaxation of these error terms is applicable to all antennas with the same deformation type. Then, under the condition that a certain loss in antenna performance is allowed, a calculation model for relaxing the deformation error of the primary reflector (REDMRD) can be established by solving for the maximum relaxation amount of the deformation error of the primary reflector. (4) in, This represents the i-th independent error term of the primary reflector. and These represent the gain values ​​of the ideal antenna and the deformable antenna, respectively. GL is the specified gain loss value. This indicates the acceptable gain loss threshold for a specific deformable antenna. It is a corrective sub-reflector designed to compensate for the deformation error of the primary reflector. and These are the first primary reflector surfaces. The upper and lower boundaries of the independent error terms.

5. The method for determining the deformation error of the main reflector of a large antenna with a corrected sub-reflector relaxation according to claim 4, characterized in that, In step (3), a fast iterative solution method for calculating the error of the main reflector of the antenna by using the bisection method is adopted: the constructed main reflector error relaxation model REDMRD is a two-layer optimization model, which includes an inner layer and an outer layer. The inner layer optimization is used to design the corrected sub-reflector to compensate for the deformed main reflector; the outer layer optimization is used to solve the error relaxation problem of the main reflector.

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