Smoothly faceted hybrid wraparound edge reflective surface and method of construction thereof

Abstract

The application provides a mixed winding edge reflecting surface with smooth mouth surface and a construction method thereof, wherein the method comprises the following steps: determining a projection profile edge line expression of the reflecting surface corresponding to the smooth mouth surface; constructing a local coordinate system based on the projection profile edge line expression; generating a strict parameter equation of the mixed winding edge in a global coordinate system with gamma as the independent variable based on the transformation relationship between the local coordinate system and the global coordinate system; wherein gamma is the y e axis negative direction towards x e angle corresponding to the radian of the positive direction rotation of the axis; constructing a curvature radius residual expression with continuous curvature in two dimensions according to the strict parameter equation; and generating the mixed winding edge reflecting surface with smooth mouth surface by using the residual expression. According to the scheme, the measurement accuracy of electromagnetic characteristic parameters of the reflecting surface in the process of tight field measurement can be improved.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic measurement technology, and in particular to a smooth-surfaced hybrid wound edge reflective surface and its construction method. Background Technology

[0002] Compact field measurement is a primary method for measuring the electromagnetic properties of various scatterers and radiators. It offers advantages such as being unaffected by weather and interference clutter, requiring limited testing space, and providing good measurement consistency. The core component of a compact field is the reflecting surface. To reduce the influence of the diffraction field at the edge of the reflecting surface on the amplitude and phase of the still zone, targeted treatment of its edges is usually necessary. Common treatment methods include, but are not limited to, adding edge teeth and edge winding.

[0003] Please refer to Figure 1 This refers to a hybrid wound edge reflective surface constructed in the prior art. The aperture of this hybrid wound edge reflective surface has discontinuous regions, and the reflected waves from these discontinuous regions can affect the accuracy of measurement results when measuring electromagnetic characteristic parameters. Summary of the Invention

[0004] This invention provides a smooth-aperture hybrid wound edge reflective surface and its construction method, which can improve the accuracy of electromagnetic characteristic parameter measurement during the compaction field measurement process of the reflective surface.

[0005] In a first aspect, embodiments of the present invention provide a method for constructing a smooth, hybrid-wound edge reflective surface, comprising:

[0006] Determine the expression for the projection profile edge line of the reflecting surface corresponding to the smooth aperture;

[0007] A local coordinate system is constructed based on the projection contour edge line expression;

[0008] Based on the transformation relationship between the local and global coordinate systems, a rigorous parametric equation for the hybrid wrapping edge in the global coordinate system is generated, with γ as the independent variable; where γ is the equation of the edge in the local coordinate system from y e negative x-axis e The radians corresponding to the angle of positive rotation of the axis;

[0009] Based on the rigorous parametric equations, construct a two-dimensional curvature radius residual expression;

[0010] The residual expression is used to generate a smooth, hybrid, wound-edge reflective surface.

[0011] In one possible implementation, the expression for the projected profile edge line of the reflecting surface corresponding to the smooth aperture is:

[0012] Top right corner area:

[0013] x ax =Rsinθ+(x max -R), θ∈[0°,90°]

[0014] y ax =Rcosθ+(y max -R), θ∈[0°,90°]

[0015] Bottom right corner area:

[0016] x ax =Rcosθ+(x max -R), θ∈[0°,-90°]

[0017] y ax =Rsinθ+(y max +R),θ∈[0°,-90°]

[0018] Among them, the upper left and upper right regions are symmetrical, and the lower left and lower right regions are symmetrical.

[0019] Where, x ax y ax This represents the projection components of the reflected surface's projection contour edge line on the x and y axes in the global coordinate system; x max y max R represents the maximum value of the projection components of the reflected surface's projection outline edge line on the x and y axes in the global coordinate system; R represents the fillet radius; θ represents the rotation angle corresponding to the fillet position.

[0020] In one possible implementation, the transformation relationship between the local coordinate system and the global coordinate system is as follows:

[0021]

[0022] Where x, y, and z represent the coordinates of a point in the global coordinate system; x e y e p represents the coordinates of the corresponding point in the global coordinate system within the local coordinate system; x j y j z j This represents the coordinates of the connection point between the main reflecting surface region and the winding edge region in the global coordinate system; x p1 x p2 x p3 Represents the local coordinate system x e The projection components of the unit vector on the x, y, and z axes of the global coordinate system; y p1 y p2 y p3 Represents the local coordinate system y eThe projection components of the p-axis unit vector onto the x, y, and z axes of the global coordinate system; p1 and p2 represent the projection components of the p-axis unit vector of the local coordinate system onto the x and y axes of the global coordinate system.

[0023] In one possible implementation, the strictly parametric equation of the hybrid winding edge in the global coordinate system with γ as the independent variable is:

[0024]

[0025]

[0026]

[0027] Where C represents the fractional factor in the transformation relationship between the local and global coordinate systems; f c Indicates the focal length of the primary reflecting surface; γ m This represents the maximum radian value that γ can take; x m Indicates with γ m The maximum length of the extension line of the corresponding main reflective surface region; a e Indicates the semi-major axis of the ellipse used for mixed winding; b e Let denote the semi-minor axis of the ellipse used for hybrid winding; b(γ) denotes the transition function of hybrid winding, and when γ = 0, b(γ) = 0, γ = γ m When b(γ) = 1.

[0028] In one possible implementation, the residual expression is:

[0029]

[0030] Where ε represents the radius of curvature residual; x (n) y (n) z (n) This represents the nth derivative of each component of the rigorous parametric equation of the hybrid winding edge in the global coordinate system with γ as the independent variable, where n is a positive integer.

[0031] In one possible implementation, generating a smooth, hybrid-wound edge reflective surface using the residual expression includes:

[0032] With the projection center of the reflecting surface (x) avg y avg ) as the center of rotation, with (x) ax y ax ) and (x avg y avgThe plane determined by the line vector connecting the z-axis and the z-axis vector is used as the cutting plane. The contour lines with a set rotation angle interval are solved sequentially. Based on the continuity of the contour lines on the same side of the reflective surface, the contour lines on the same side are lofted to obtain a smooth mixed-wound edge reflective surface.

[0033] Secondly, embodiments of the present invention also provide a smooth-surfaced hybrid wound edge reflective surface, which is constructed using any of the above-described construction methods.

[0034] This invention provides a smooth hybrid coiled edge reflective surface and its construction method. By smoothing the four corners of the reflective surface corresponding to the aperture, the rectangular corners at the four corners are rounded. By constructing a local coordinate system and using the transformation relationship between the local and global coordinate systems, a strict parametric equation for the hybrid coiled edge in the global coordinate system is generated. Based on this strict parametric equation, a two-dimensional curvature continuous radius of curvature residual expression is constructed to optimize the continuity condition of the radius of curvature, thereby eliminating the edge lines of the hybrid coiled edge region. Thus, the edge of the aperture becomes smooth, which can improve the accuracy of electromagnetic characteristic parameter measurement during the compaction field measurement of the reflective surface. Attached Figure Description

[0035] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0036] Figure 1 It is a hybrid wound edge reflective surface constructed in existing technologies;

[0037] Figure 2 This is a flowchart of a method for constructing a smooth hybrid wound edge reflective surface according to an embodiment of the present invention;

[0038] Figure 3 This is a schematic diagram of a smooth, hybrid, wound edge reflective surface according to an embodiment of the present invention;

[0039] Figure 4 This is a schematic diagram illustrating the position of a local coordinate system in a global coordinate system according to an embodiment of the present invention;

[0040] Figures 5-16 This is a schematic diagram of the amplitude-phase curve of the static zone of a smooth hybrid wound edge reflective surface provided in an embodiment of the present invention. Detailed Implementation

[0041] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0042] As mentioned above, Figure 1 The mixed-wound edge reflective surface in the middle has a discontinuous region on its aperture, that is, there is an edge line at the edge of the rectangular aperture. The existence of this edge line will inevitably affect the measurement results of electromagnetic characteristic parameters.

[0043] Based on the above problems, the inventive concept of this invention is to smooth the mixed-wound edge reflective surface of the rectangular aperture and eliminate the ridges at the edge position to improve the accuracy of electromagnetic characteristic parameter measurement results.

[0044] The following describes the specific implementation of the above concept.

[0045] Please refer to Figure 2 This invention provides a method for constructing a smooth, hybrid, wound edge reflective surface, the method comprising:

[0046] Step 200: Determine the expression for the projection contour edge line of the reflecting surface corresponding to the smooth aperture.

[0047] Step 202: Construct a local coordinate system based on the projection contour edge line expression;

[0048] Step 204: Based on the transformation relationship between the local coordinate system and the global coordinate system, generate a rigorous parametric equation for the hybrid wrapping edge in the global coordinate system with γ as the independent variable; where γ is the equation of the edge in the local coordinate system from y e negative x-axis e The radians corresponding to the angle of positive rotation of the axis;

[0049] Step 206: Construct a two-dimensional curvature radius residual expression based on the strict parametric equation;

[0050] Step 208: Generate a smooth hybrid wound edge reflective surface using the residual expression.

[0051] In this embodiment of the invention, the four corners of the reflecting surface corresponding to the aperture are smoothed, so that the rectangular corners at the four corners are rounded. By constructing a local coordinate system, the transformation relationship between the local coordinate system and the global coordinate system is used to generate a strict parametric equation for the hybrid winding edge in the global coordinate system. Based on this strict parametric equation, a two-dimensional curvature continuous radius of curvature residual expression is constructed to optimize the continuity condition of the radius of curvature, so that the edge lines of the hybrid winding edge region are eliminated. Thus, the edge of the aperture becomes smooth, thereby improving the accuracy of electromagnetic characteristic parameter measurement during the compaction field measurement of the reflecting surface.

[0052] The following description Figure 2 The execution method of each step is shown.

[0053] First, for step 200, determine the expression of the projection contour edge line of the reflecting surface corresponding to the smooth opening.

[0054] In this embodiment of the invention, the radius of the rounded corner of the rectangular opening needs to be used to determine the area of ​​the projection of the reflecting surface at the rounded corner position that requires smoothing. Please refer to [reference needed]. Figure 3 This is a schematic diagram of the desired smooth, hybrid, wound-edge reflective surface, based on... Figure 3 The expression needed to form the projection contour edge line is as follows:

[0055] Top right corner area:

[0056] x ax =Rsinθ+(x max -R), θ∈[0°,90°]

[0057] y ax =Rcosθ+(y max -R), θ∈[0°,90°]

[0058] Bottom right corner area:

[0059] x ax =Rcosθ+(x max -R), θ∈[0°,-90°]

[0060] y ax =Rsinθ+(y max +R),θ∈[0°,-90°]

[0061] The upper left and upper right regions are symmetrical, as are the lower left and lower right regions. The expression for the upper left region can be derived from the expression for the upper right region, and similarly, the expression for the lower left region can be derived from the expression for the lower right region.

[0062] Where, xax y ax This represents the projection components of the reflected surface's projection contour edge line on the x and y axes in the global coordinate system; x max y max R represents the maximum value of the projection components of the reflected surface's projection outline edge line on the x and y axes in the global coordinate system; R represents the fillet radius; θ represents the rotation angle corresponding to the fillet position.

[0063] Then, for step 202 "Constructing a local coordinate system based on the projection contour edge line expression" and step 204 "Generating a rigorous parametric equation for the hybrid wrapping edge in the global coordinate system with γ as the independent variable based on the transformation relationship between the local coordinate system and the global coordinate system; where γ is the equation of the local coordinate system from y e negative x-axis e The radians corresponding to the angle of rotation in the positive direction of the axis.

[0064] Because the four corners of the main reflector area are smoothed and rounded, the aperture of the main reflector area changes. Therefore, it is necessary to reconstruct the local coordinate system. Please refer to [reference needed]. Figure 4 The figure shows the position of the local coordinate system in the global coordinate system. The shaded area in the figure is the main reflective surface area, and the area surrounding the main reflective surface area is the mixed winding edge area. The main reflective surface area and the mixed winding edge area together constitute the main reflective surface.

[0065] In this embodiment of the invention, the transformation relationship between the local coordinate system and the global coordinate system is as follows:

[0066]

[0067] Where x, y, and z represent the coordinates of a point in the global coordinate system; x e y e p represents the coordinates of the corresponding point in the global coordinate system within the local coordinate system; x j y j z j This represents the coordinates of the connection point between the main reflecting surface region and the winding edge region in the global coordinate system; x p1 x p2 x p3 Represents the local coordinate system x e The projection components of the unit vector on the x, y, and z axes of the global coordinate system; y p1 y p2 y p3 Represents the local coordinate system y e The projection components of the p-axis unit vector onto the x, y, and z axes of the global coordinate system; p1 and p2 represent the projection components of the p-axis unit vector of the local coordinate system onto the x and y axes of the global coordinate system.

[0068] To construct the reflective surface, the outline of the hybrid winding region needs to be drawn in the local coordinate system and then placed in the global coordinate system for construction. Therefore, it is necessary to generate a strict parametric equation of the hybrid winding edge in the global coordinate system with γ as the independent variable based on the above transformation relationship.

[0069] In this embodiment of the invention, the strict parametric equation of the hybrid winding edge in the global coordinate system with γ as the independent variable is:

[0070]

[0071]

[0072]

[0073] Where C represents the fractional factor in the transformation relationship between the local and global coordinate systems; f c Indicates the focal length of the primary reflecting surface; γ m This represents the maximum radian value that γ can take; x m Indicates with γ m The maximum length of the extension line of the corresponding main reflective surface region; a e Indicates the semi-major axis of the ellipse used for mixed winding; b e Let denote the semi-minor axis of the ellipse used for hybrid winding; b(γ) denotes the transition function of hybrid winding, and when γ = 0, b(γ) = 0, γ = γ m When b(γ) = 1.

[0074] Next, for step 206, a curvature radius residual expression for two-dimensional curvature continuity is constructed based on the strict parametric equation.

[0075] After determining the strict parametric equations, it is necessary to ensure sufficient continuity between the form of the strict parametric equations and the equations truncated by the paraboloid of revolution, ensuring that the spliced ​​lines are smooth, i.e., the continuity of the formed mixed-wound edge region, and eliminating the edges within the region. This requires minimizing the curvature radius residual to optimize the continuity condition of the curvature radius. In this embodiment of the invention, the expression for the curvature radius residual of two-dimensional curvature continuity constructed based on the strict parametric equations is as follows:

[0076]

[0077] Where ε represents the radius of curvature residual; x (n) y (n) z (n) This represents the nth derivative of each component of the rigorous parametric equation of the hybrid winding edge in the global coordinate system with γ as the independent variable, where n is a positive integer.

[0078] In this embodiment, the radius of curvature residual must be less than a preset value, such as 0.0001.

[0079] Finally, for step 208, a smooth hybrid wound edge reflective surface is generated using the residual expression.

[0080] After the above conditions are set, when generating a smooth hybrid coiled edge reflective surface, a smooth hybrid coiled edge reflective surface can be obtained by sweep lofting according to the continuity and density of the contour lines. Specifically:

[0081] With the projection center of the reflecting surface (x) avg y avg ) as the center of rotation, with (x) ax y ax ) and (x avg y avg The plane determined by the line vector connecting the z-axis and the z-axis vector is used as the cutting plane. The contour lines with a set rotation angle interval are solved sequentially. Based on the continuity of the contour lines on the same side of the reflective surface, the contour lines on the same side are lofted to obtain a smooth mixed-wound edge reflective surface.

[0082] This invention also provides a smooth-surfaced hybrid wound edge reflective surface, which is constructed using any of the above-described construction methods.

[0083] To verify the measurement performance of the smooth-aperture hybrid-wound edge reflector, this embodiment performs measurement simulations on a smooth-aperture hybrid-wound edge reflector with a minimum operating frequency of 0.8 GHz. A schematic diagram of the static region amplitude-phase curve of the smooth-aperture hybrid-wound edge reflector is obtained; please refer to [the diagram]. Figures 5-16 ,in, Figures 5-7 This is a schematic diagram of the amplitude-phase curve of the horizontal cross section in the static region corresponding to horizontal polarization. Figures 8-10 This is a schematic diagram of the amplitude-phase curve of the vertical cross section in the static region corresponding to horizontal polarization. Figures 11-13 This is a schematic diagram of the amplitude-phase curve of the horizontal cross section in the static region corresponding to vertical polarization. Figures 14-16 This is a schematic diagram of the amplitude-phase curve of the vertical cross section in the static region corresponding to vertical polarization. The results show that its static region amplitude taper, amplitude ripple, phase fluctuation, and cross-polarization are all superior to conventional design specifications.

[0084] It is evident that by modifying the traditional edge formula, a smooth-aperture hybrid-wound edge reflective surface can be constructed. Compared with the traditional hybrid-wound edge reflective surface, the smooth-aperture hybrid-wound edge reflective surface has superior static phase characteristics.

[0085] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0086] Those skilled in the art will understand that all or part of the steps of the above method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps of the above method embodiments. The aforementioned storage medium includes various media that can store program code, such as ROM, RAM, magnetic disk, or optical disk.

[0087] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method of constructing a hybrid wraparound edge reflector face with a smooth oral surface, characterized by, The application relates to a method for constructing a mixed winding edge reflector with a smooth aperture surface. The four-corner positions of a reflection surface corresponding to the aperture surface are smoothed, so that the rectangular corners of the four-corner positions are processed into rounded corners, and a projection contour edge line expression of the smooth reflection surface corresponding to the aperture surface is determined; A local coordinate system is constructed based on the projection contour edge line expression; Based on the transformation relationship between the local coordinate system and the global coordinate system, a strict parametric equation of the hybrid winding edge in the global coordinate system is generated with γ as the independent variable; wherein γ is the arc corresponding to the angle of the rotation of the axis positive direction in the local coordinate system. y e axis negative direction x e axis positive direction rotation A curvature radius residual expression with two-dimensional curvature continuity is constructed according to the strict parameter equation; The mixed winding edge reflector with a smooth aperture surface is generated by using the residual expression; The projection contour edge line expression of the smooth reflection surface corresponding to the aperture surface is as follows: The upper-right corner region is Rsintheta + theta = Rcostheta x ax The upper-left corner region is Rcostheta + theta = Rsintheta ( x max -R ), The lower-right corner region is Rcostheta + theta = Rsintheta ∈[0°,90°] y ax The lower-left corner region is Rsintheta + theta = Rcostheta +( y max -R ) , Wherein, the upper-left corner region is symmetrical to the upper-right corner region, and the lower-left corner region is symmetrical to the lower-right corner region; ∈[0°,90°] The transformation relationship between the local coordinate system and the global coordinate system is as follows: x ax The strict parameter equation of the mixed winding edge in the global coordinate system with gamma as the independent variable is as follows: ( x max -R ), The residual expression is as follows: ∈[0°,-90°] y ax The method for generating the mixed winding edge reflector with a smooth aperture surface by using the residual expression comprises the following steps: +( y max +R ) , The method is constructed by using the construction method in any one of claims 1-4. ∈[0°,-90°] ​ wherein x ax , y ax denotes the projection of the edge line of the projection profile of the reflective surface in the global coordinate system x , y on the axis; x max , y max denotes the maximum value of the projection of the edge line of the projection profile of the reflective surface in the global coordinate system x , y on the axis; R denotes the rounding radius; ​ denotes the rotation angle corresponding to the rounding position.

2. The method of claim 1, wherein, ​ wherein x , y , z denotes the point coordinate value in the global coordinate system; x e , y e , p denotes the point coordinate value in the local coordinate system of the corresponding point in the global coordinate system; x j , y j , z j denotes the coordinate value in the global coordinate system of the connection point of the main reflection surface region and the winding edge region; x p1 , x p2 , x p3 denotes the local coordinate system x e the projection component of the axis unit vector on the global coordinate system x , y , z axis; y p1 , y p2 , y p3 denotes the local coordinate system y e the projection component of the axis unit vector on the global coordinate system x , y , z axis; p 1, p 2 denotes the local coordinate system p the projection component of the axis unit vector on the global coordinate system x , y axis.

3. The method of claim 2, wherein, ​ wherein, C denotes a fractional factor in the transformation relationship between the local coordinate system and the global coordinate system; f c denotes the focal length of the main reflecting surface; ​ m denotes the maximum radian value that γ can take; x m denotes the maximum radian value that γ can take; ​ m denotes the maximum length of the corresponding main reflecting surface region extension line; a e denotes the semi-major axis of the ellipse for hybrid winding; b e denotes the semi-minor axis of the ellipse for hybrid winding; ​ denotes the transition function for hybrid winding, and when γ = 0, ​ = 0, γ = 0, ​ m when, ​ = 1.

4. The method of claim 3, wherein, ​ wherein denotes the curvature radius residual; x (n) , y (n) , z (n) denotes the partial derivative of the components of the strict parametric equation of the hybrid winding edge in the global coordinate system with respect to the self variable γ, n the partial derivative of the components of the strict parametric equation of the hybrid winding edge in the global coordinate system with respect to the self variable γ, n is a positive integer.

5. The method according to any one of claims 1 to 4, characterized in that, ​ With the center of the reflection surface as the projection center ( x avg , y avg ) as the center of rotation, with ( x ax , y ax )and( x avg , y avg The connecting vector of ) and z The plane determined by the axis vector is used as the cutting plane, and the contour lines with a set rotation angle interval are obtained by solving them sequentially. Based on the continuity of the contour lines on the same side of the reflective surface, the contour lines on the same side are lofted to obtain a smooth mixed-wound edge reflective surface.

6. A hybrid wraparound edge-mirrored surface with a smooth mouth, characterized by ​

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