CN107623189B - A kind of manufacturing method of hemispheric Lumberg lens antenna - Google Patents

Abstract

The invention discloses a manufacturing method of a hemispherical Luneberg lens antenna, wherein the hemispherical Luneberg lens antenna is distributed with a cavity, and has a hemispherical surface and a bottom plane passing through the center plane of the sphere; wherein, the method comprises the steps of: selecting an antenna for materials for manufacturing the hemispherical Luneberg lens antenna; determining the structural parameters of the hemispherical Luneberg lens antenna; making a three-dimensional digital model of the hemispherical Luneberg lens antenna with the structural parameters; using an additive manufacturing method to manufacture the said three-dimensional digital model A hemispherical Lumberg lens antenna; a metal foil layer is applied to the bottom plane. The shape, size and distribution of the cavity structure in the hemispherical Lumberg lens antenna made by the invention can be adjusted and controllable, the precise control of the average dielectric constant of the concentric layers can be realized, and different design requirements can be met; and the manufacturing materials are widely used. , The production process is simple, the yield is high, and there is no gap between layers, so that the product quality is more stable and reliable.

Description

A kind of manufacturing method of hemispheric Lumberg lens antenna

This application is a divisional application for an invention patent application with an application date of "February 16, 2015", an application number of "201510084764.8", and an invention title of "A method for manufacturing a hemispherical Lumberg lens antenna".

technical field

The present invention relates to the field of communications, and more particularly, to a manufacturing method of a hemispherical Lumberg lens antenna.

Background technique

The Lumber lens antenna takes a sphere as its basic shape (sometimes also called Lumber sphere in this article), which is a concept proposed by RK Lumber in 1944 based on the geometrical optics method. A Lumberg lens antenna is a lens antenna that focuses electromagnetic waves to a focal point through a dielectric. It is a sphere made of dielectric material that can focus electromagnetic waves from all directions to a corresponding point on the surface of the lens. In the part that is infinitely close to the surface of the sphere, the dielectric constant of the material is 1 (that is, the same as that of air), and the dielectric constant at the center of the sphere is 2. The dielectric constant of the sphere from the surface to the center of the material is gradual, and its change rule is ε _r (r)=2-(r/R) ² (0≤r≤R), where r is the distance from the current position to the center of the sphere. distance, R is the radius of the Lumberg lens antenna.

Lumberg lens antennas are generally designed for specific target incident electromagnetic waves. The incident electromagnetic wave of the target penetrates the surface of the sphere, and is then refracted and focused on the focal point on the other side of the sphere. Different electromagnetic wave signals have different incident directions and different focal positions on the spherical surface. Therefore, when the Lunberg lens antenna is a complete sphere, the received signal has a wide angle and azimuth. Simply move the feed position along the surface of the lens, or place multiple feeds to receive multiple signals at the same time without changing Location of the lens antenna. Furthermore, unlike other antennas which have a limited applicable frequency band, Lumberg lens antennas can be used, for example, for microwaves with wavelengths from 1 meter to 0.1 cm and all electromagnetic bands with wavelengths greater than microwaves, including radio waves with wavelengths from 3000 meters to ^10-3 meters , so it is suitable for large-capacity bandwidth communication systems.

In addition, because the Luneberg lens antenna has the characteristics of focusing electromagnetic waves, its radar reflection cross-sectional area (that is, the RCS value, which is also a key technical indicator to measure the performance of Luneberg lens antennas) is much larger than its physical cross-sectional area, so it can be used to set lightning protection. Reach false targets, interfere with camouflage, target calibration, rescue, etc.

The spherical symmetry structure and the function of focusing electromagnetic waves of the Lumberg lens antenna as a complete sphere make it widely used in satellite communications, radar antennas, electronic countermeasures and other fields, as satellite ground stations, satellite news broadcast vehicles, radio astronomical telescopes, military fake Antenna components for targets, target drones, target bombs, automotive anti-collision radars, etc.

Theoretically, the dielectric constant of the material used for Lumberg lens antennas should vary continuously from 2 to 1 from the center of the sphere to the outermost layer. However, it is actually impossible to make such an ideal Lunberg lens antenna, and a discrete spherical shell with a layered design is generally used instead.

Initially, materials with different dielectric constants were used to make Lumberg lens antennas. However, the materials that can meet the requirements are very limited, and the gradient of dielectric constant between materials is too large. Therefore, the quality of Lunberg spheres made by material selection is The radiation characteristics of the lens are not optimal, and it has not been widely used.

In 2003, Sébastien R ondineau et al. (Sébastien R ondineau et al. Aslicedspherical luneburg lens. IEEE Antennas Wireless Propagat.lett. 2003, 2: 163-166) layered the Luneburg lens antenna along the spherical radial direction, according to certain punching rules. Holes are drilled in the dielectric layer to achieve the desired dielectric constant. The Lunberg lens with this punching design is very difficult to operate in hole positioning and processing, and due to the large number of holes, there are problems such as deformation and insufficient mechanical strength, and the firmness of each part is low. This design method only achieves the macroscopic dielectric constant equivalent, and the efficiency of the lens antenna is very low, at 26.5GHz, the efficiency is only 30%, and at 32GHz, the efficiency is only 15%.

The foaming method is currently the most commonly used method for making Lumberg lens antennas. In this method, the beads made of resin are generally foamed appropriately, and then screened and grouped according to particle size. Then different groups of foamed materials are mixed according to the designed dielectric constant so that the dielectric constant of the mixed material is equal to the predetermined dielectric constant. Then the adhesive and foam beads are mixed together, and poured into a spherical mold of suitable size. After the volatile components in the adhesive are volatilized, the beads are hardened and bonded to obtain a ball with a predetermined dielectric constant. shell.

The Lunberg lens antennas produced at present are usually wrapped by multiple layers of materials with different dielectric constants, and the change of the dielectric constant is discrete, which approximately simulates the continuous and smooth change of the dielectric constant in the ideal state. Generally speaking, the more layers of material wrapped, the closer the lens antenna is to the ideal state. However, this also increases the probability of the existence of air between layers. In theory, the radial thickness of the air layer is greater than 5% of the incident wavelength. % can significantly degrade Lumberg lens antenna performance.

In addition, increasing the number of layers will correspondingly increase the manufacturing difficulty and material cost, mold cost and manufacturing cycle. Therefore, in the prior art, the number of layers of the sphere is usually limited to about 10 layers, and structures with more than 10 layers are rare, so the degree of simulating the ideal continuous and smooth change of the dielectric constant is limited, especially for large-sized Lumberg lens antennas.

In the prior art, the material used to manufacture the Lunberg lens antenna by the foaming method is usually polystyrene foam. The volume fraction of air within the foam can be controlled by controlling the density of the foam, thereby controlling its macroscopic average dielectric constant to a desired value. However, when the foam density reaches the expected value during foaming, it only means that the macroscopic average dielectric constant of the entire foam reaches the expected value. Due to the characteristics of the foaming process, it is difficult to ensure the uniformity of the material everywhere on the microscopic level. There are a lot of bubbles that are too large or too small, so that the dielectric constant fluctuates on the microscopic level, causing the product performance to deviate from expectations, and the performance deviation of different batches of products is also different. In addition, according to the scattering effect, when the foam is When the diameter of the inner bubble is greater than one-third of the incident wavelength, the performance of the Lunberg lens can also be significantly reduced. At the same time, in the foaming method, the beads may undergo secondary foaming during the molding process, making it difficult to control the dielectric constant and reducing the uniformity. In addition, the foamed material shrinks after the mold is cooled, resulting in an air gap between adjacent spherical shells during assembly, which has a great impact on the performance of the lens. Therefore, the foaming method has problems such as difficulty in controlling the dielectric constant tolerance, and difficulty in uniformity in the interior.

As a dielectric passive device, the Lumberg lens antenna has the advantages of small size, light weight, large radar cross-sectional area, large pattern and spectrum width, but its manufacturing process is difficult, tedious and time-consuming, high cost, and consistent products. Poor performance limits its promotion and application.

In order to reduce the volume of the Luneberg lens antenna and save the cost, sometimes a Lunberg lens antenna with a non-holonomic sphere can be fabricated. A hemispherical Lumberg lens antenna has a hemispherical surface and a bottom plane. The bottom plane is a plane passing through the center of the sphere. The bottom plane is usually covered with a metal foil layer. Based on the principle of geometrical optics, the hemispheric Lumberg lens antenna can simulate the Lumberg lens antenna of a complete sphere to a large extent.

SUMMARY OF THE INVENTION

In view of the above problems, the purpose of the present invention is to provide a manufacturing method of a hemispherical Lumberg lens antenna with simple process, low cost and good use effect.

The purpose of the present invention is achieved through the following technical solutions.

1. A method for making a hemispherical Luneberg lens antenna, the hemispherical Luneberg lens antenna is distributed with a cavity, has a hemispherical surface and a bottom plane, and the bottom plane is a plane passing through the center of the sphere; wherein, the method includes the following step:

(1) Select the material used to manufacture the hemispherical Lumberg lens antenna;

(2) Determine the structural parameters of the hemispherical Lumberg lens antenna;

(3) making a three-dimensional digital model of the hemispherical Lumberg lens antenna with the structural parameters; and

(4) manufacturing the hemispherical Lumberg lens antenna from the three-dimensional digital model using an additive manufacturing method; and

(5) A metal foil layer is applied on the bottom plane of the hemispherical Lumberg lens antenna.

2. The method according to technical solution 1, wherein a complete spherical Luenberger lens antenna is firstly fabricated, and then the complete spherical Luenberger lens antenna is divided into hemispheric Luenberger lens antennas in equal parts as required, and then the hemispheric Luenberger lens antenna is divided into equal parts. A metal foil layer is attached to the bottom plane of the primary lens antenna.

3. The method according to technical solution 1 or 2, wherein the structural parameters are selected from the group consisting of the following parameters: the diameter, radius, number of layers of the hemispherical Lumberg lens antenna, and the shape, size and distributed.

4. The method according to any one of technical solutions 1 to 3, wherein:

In step (1), the material is determined according to the target performance and/or target size of the hemispherical Lumberg lens antenna.

5. The method according to technical solution 4, wherein the target performance is measured by radar scattering cross-sectional area, and the target size is measured by the diameter, radius and/or number of layers of a hemispherical Lumberg lens antenna.

6. The method according to technical solution 4 or 5, wherein, in the step (2), the structural parameter is determined according to the target performance and/or target size and/or the dielectric constant of the material .

7. The method according to any one of technical solutions 4 to 6, wherein, in the step (3), it also includes adjusting the structural parameters by a trial-and-error method through simulation technology to achieve the hemispherical Lumberg lens The target performance of the antenna.

8. The method according to technical solution 7, wherein the number of layers of the hemispherical Lumberg lens antenna, the shape, size and/or distribution of the cavity are adjusted to achieve the target performance of the hemispherical Lunberg lens antenna.

9. The method according to any one of technical solutions 4 to 8, wherein, after the step (5), it further comprises checking whether the manufactured hemispherical Lunberg lens antenna has the target performance and/or target size.

10. The method according to any one of technical solutions 1 to 9, wherein the additive manufacturing method is selected from the group consisting of fusion build-up molding, selective laser sintering molding, and laser light curing molding.

11. The method according to technical solution 10, wherein the additive manufacturing method is melt deposition molding.

12. The method according to technical solution 11, wherein, in the melt deposition molding, the temperature of the showerhead is the melting point of the material + 20°C to 30°C; and/or the speed of the showerhead is 60 to 80 mm/min; and / or the sprinkler positioning accuracy is ± 0.1 mm in the z direction; and/or the sprinkler positioning accuracy is ± 0.2 mm in the x direction; and/or the sprinkler positioning accuracy is ± 0.2 mm in the y direction.

13. The method according to any one of technical solutions 1 to 12, wherein:

The hemispherical Lumberg lens antenna is a hemisphere with a radius of R, and is designed to include n concentric layers with different dielectric constants from each other, the spherical center layer is denoted as the first layer, and the second to nth concentric layers are in accordance with The radius from small to large is expressed as the second concentric layer to the nth concentric layer, where n is an integer not less than 3, r ₁ is the radius of the spherical center layer; rn =R; ri is the _i - _th layer The radius of the concentric layers; 1≤i≤n;

the average dielectric constant ε _i =2-(r _i /R) ² of the i-th concentric layer in the n concentric layers;

the cavities are distributed in at least one of the n concentric layers;

The volume fraction of cavities in each of the n concentric layers having cavities is designed such that the average permittivity of the concentric layer = the permittivity of the material of the concentric layer×(1-in the concentric layer The volume fraction of all cavities) + the dielectric constant of the medium in the concentric layer cavities × the volume fraction of all cavities in the concentric layer.

14. The method according to technical solution 13, wherein _ri is the average value r _Ai of the outer surface radius r _Oi and the inner surface radius r _Ii of the i-th concentric layer;

15. The method according to technical solution 13 or 14, wherein the distance between any two points on the periphery of any section of the cavity is not greater than one third of the wavelength of the target incident electromagnetic wave.

16. The method according to technical solution 15, wherein the distance between any two points on the periphery of any section of the cavity is not greater than one quarter of the wavelength of the target incident electromagnetic wave.

17. The method according to technical solution 16, wherein the distance between any two points on the periphery of any section of the cavity is no greater than one-fifth of the wavelength of the target incident electromagnetic wave.

18. The method according to any one of technical solutions 13 to 17, wherein the number n of the concentric layers is 2 to 100 or more;

19. The method according to any one of technical solutions 13 to 17, wherein the n is an integer between 3 and 100.

20. The method according to technical solution 19, wherein the n is an integer between 5 and 40.

21. The method according to technical solution 19, wherein the n is an integer between 6 and 20.

22. The hemispherical Lumberg lens antenna according to technical solution 19, wherein the n is an integer between 8 and 12.

23. The method according to any one of technical solutions 13 to 17, wherein the n is an integer not less than 15.

24. The method according to technical solution 23, wherein the n is an integer between 15 and 100.

25. The method according to technical solution 24, wherein the n is an integer between 20 and 100.

26. The method according to technical solution 25, wherein the n is an integer between 40 and 100.

27. The method according to any one of technical solutions 13 to 26, wherein at least a part of the cavities independently have a designed three-dimensional structure.

28. The method according to technical solution 27, wherein the designed three-dimensional structure is a regular three-dimensional structure or an irregular three-dimensional structure.

29. The method according to technical solution 28, wherein the regular three-dimensional structure is a point-symmetric three-dimensional structure, an axis-symmetric three-dimensional structure or a plane-symmetric three-dimensional structure.

30. The method according to technical solution 27, wherein the designed three-dimensional structure is any one or more selected from the group consisting of the following three-dimensional structures: polyhedron, sphere, ellipsoid, cylinder, cone, truncated cone body.

31. The method according to technical solution 30, wherein the polyhedron is a polyhedron having 4 to 20 faces.

32. The method according to technical solution 30, wherein the polyhedron is a regular polyhedron.

33. The method according to technical solution 30, wherein the designed three-dimensional structure is a polyhedron.

34. The method according to technical solution 33, wherein the polyhedron is a polyhedron having four or more faces.

35. The method according to technical solution 34, wherein the polyhedron is a regular polyhedron.

36. The method according to technical solution 35, wherein the regular polyhedron is a regular tetrahedron or a regular hexahedron.

37. The method according to any one of technical solutions 30 to 36, wherein the positions of at least a part of the vertex angles of the polyhedron are independently chamfered.

38. The method according to any one of technical solutions 30 to 36, wherein the positions of at least a part of the edges of the polyhedron are independently chamfered.

39. The method according to any one of technical solutions 13 to 38, wherein the dielectric constant of the concentric layer material is less than 5.

40. The method according to technical solution 39, wherein the dielectric constant of the concentric layer material is less than 3.

41. The method according to technical solution 40, wherein the dielectric constant of the concentric layer material is less than 2.5.

42. The method according to any one of technical solutions 13 to 41, wherein the concentric layer material is at least one selected from the group consisting of thermoplastic materials, photosensitive resins and ceramics.

43. The method according to technical solution 42, wherein the thermoplastic material is selected from the group consisting of polylactic acid, polyacrylonitrile, acrylonitrile-butadiene-styrene terpolymer, polyaryl ether ketone, thermoplastic fluoroplastic One or more of the group consisting of thermoplastic benzocyclobutene and DSM Somos GP Plus 14122 photosensitive resin;

44. The method according to technical solution 42, wherein the concentric layer material is selected from the group consisting of polylactic acid, polyacrylonitrile, terpolymer of butadiene and styrene, polyaryl ether ketone, thermoplastic fluoroplastic, thermoplastic A group consisting of benzocyclobutene, DSM SomosGP Plus 14122 photosensitive resin.

45. The method according to technical solution 42, wherein the material of the concentric layer is polylactic acid.

46. The method according to technical solution 45, wherein the layer number n of the concentric layers is seven.

47. The method according to any one of technical solutions 13 to 46, wherein the materials of the respective concentric layers are the same as each other.

48. The method according to any one of technical solutions 13 to 46, wherein the materials of the respective concentric layers are different from each other.

49. The method according to any one of technical solutions 13 to 46, wherein some of the concentric layers in each concentric layer are made of the same material.

50. The method according to any one of technical solutions 13 to 46, wherein the dielectric constant of the material of each concentric layer decreases along the radial direction from the spherical center layer to the outermost nth layer.

51. The method according to any one of technical solutions 13 to 50, wherein, for a hemispherical Luneberg lens antenna with a diameter of 120 mm, the RCS value of the hemispherical Luneberg lens antenna at 9.4 GHz is equal to or greater than -2 dBsm.

52. The method according to technical solution 51, wherein, for a hemispherical Lumberg lens antenna with a diameter of 120 mm, the RCS value of the hemispherical Lumberg lens antenna at 9.4 GHz is greater than 0 dBsm.

53. The method according to any one of technical solutions 13 to 52, wherein the metal of the metal foil layer is selected from the group consisting of copper, aluminum, silver and gold.

54. The method according to any one of technical solutions 13 to 53, wherein the thickness of the metal foil layer is 0.1 mm to 1 mm.

55. The method according to any one of technical solutions 13 to 54, wherein the thicknesses of the concentric layers are different.

56. The method according to any one of technical solutions 13 to 54, wherein the thicknesses of the concentric layers are partially the same.

57. The method according to any one of technical solutions 13 to 54, wherein the thicknesses of the concentric layers are all the same.

58. The method according to any one of technical solutions 13 to 54, wherein the thickness of each concentric layer decreases or increases radially from the spherical core layer to the outermost nth layer.

59. The method according to any one of technical solutions 13 to 58, wherein cavities are distributed in the outer concentric layers among the n concentric layers.

60. The method according to any one of technical solutions 13 to 58, wherein an outermost layer of the n concentric layers is distributed with cavities.

61. The method according to any one of technical solutions 13 to 60, wherein, among the n concentric layers, a concentric layer close to the spherical core layer does not have a cavity.

62. The method according to any one of technical solutions 13 to 60, wherein the distribution of the cavities in the concentric layers is uniform or substantially uniform.

63. The method of any one of claims 13 to 62, wherein at least some of the cavities have a medium.

64. The method of any one of claims 13 to 62, wherein at least some of the cavities are free of media.

65. The method according to item 63, wherein the medium in the cavity is air.

The present invention also provides a hemispherical Luneberg lens antenna, which is a hemisphere with a radius R and is designed to include n concentric layers with different dielectric constants from each other, and the spherical center layer is denoted as the th 1 layer, the second to nth concentric layers are expressed as the second to nth concentric layers in order of radius from small to large, where n is an integer not less than 3, and r ₁ is the center of the sphere layer radius; rn equals R; ri is the radius of the _i - _th concentric layer; preferably, _ri is the average value r _Ai of the outer surface radius r _Oi and the inner surface radius r _Ii of the i-th concentric layer; 1 ≤i≤n; the hemispherical Lumberg lens antenna has a hemispherical surface and a bottom plane, and the bottom plane is a plane passing through the center of the sphere and is covered with a metal foil layer; wherein:

The average dielectric constant of the i-th concentric layer in the n concentric layers is ε _i =2-(r _i /R) ² , and at least one of the n concentric layers is distributed with cavities;

The volume fraction of cavities in each of the n concentric layers having cavities is designed such that the average permittivity of the concentric layer = the permittivity of the material of the concentric layer×(1-in the concentric layer volume fraction of all cavities) + the dielectric constant of the medium in the concentric layer cavities × the volume fraction of all cavities in the concentric layer;

More preferably, the hemispherical Lunberg lens antenna is manufactured by the method described in any one of the above technical solutions 1 to 65.

The present invention also provides the hemispherical Lumberg lens antenna or the hemispheric Lumberg lens antenna described in any one of technical solutions 1 to 65 in satellite communications, radar antennas, radio astronomical telescopes, military false targets, target drones, targets The application on the anti-collision radar of bombs and automobiles; preferably, the application in the satellite communication is selected from the satellite ground station, the satellite news relay vehicle, the communication satellite communication, the mobile satellite ground station, and the near-Earth satellite positioning. at least one of the group consisting of applications.

The present invention has the following effects:

(1) In the hemispherical Lumberg lens antenna of the present invention, the shape, size and distribution of the cavity structure can be precisely controlled based on performance requirements, so the volume fraction occupied by the cavity in each spherical shell can be effectively adjusted, and then Accurate control of the dielectric constant at the macroscopic and microscopic levels is achieved. In the traditional manufacturing process, due to the randomness of foaming, the size and distribution of bubbles in the foam fluctuate, resulting in poor material uniformity, high adjustment cost, unstable product performance between batches, and yield of traditional Longberg balls. low disadvantage.

(2) In the traditional process, the hemispherical Lumberg lens antenna is mostly manufactured by the assembly process, resulting in a gap between the layers. When the gap between the layers is greater than 5% of the incident wavelength, the performance of the product will be significantly reduced. The hemispherical Lumberg lens antenna of the present invention is an integral structure in which cavity structures of different shapes, sizes and distributions are dispersed. When manufactured by, for example, an additive manufacturing method, there is no interlayer gap, so that the product quality is more stable and reliable. .

(3) The hemispherical Lumberg lens antenna of the present invention can meet different performance requirements by changing the number of layers, the radius, the material for making the spherical shell, and the shape, size and distribution of the cavity structure.

(4) The hemispherical Lumberg lens antenna of the present invention has a wide range of materials, simple production process, low cost, short cycle, high yield, stable product quality, and good social and economic benefits. The order period of Luneberg balls manufactured by traditional process is about one month, and the order period of large-sized Luneberg balls is longer. manufacturing process), the production cycle is about one week to two weeks.

Description of drawings

1 is a schematic cross-sectional view of a hemispherical Lumberg lens antenna of the present invention, wherein 1 is a material body (black area), 2 is a cavity structure (white area, this schematic diagram takes a cube cavity as an example), and 3 is a hemispherical Lumberg lens The metal foil layer on the bottom plane of the antenna.

Detailed ways

In a first aspect, the present invention provides a hemispherical Luneburg lens antenna, which can be a hemisphere with a radius R, and can be designed to include n concentric layers with different dielectric constants, the spherical The central layer may be represented as the first layer, and the second to nth concentric layers may be sequentially represented as the second to nth concentric layers in order of radius from small to large. Wherein, n can be an integer not less than 3, r ₁ is the radius of the spherical center layer; rn _is equal to R; ri is the radius of the _ith concentric layer; the average value of the ith concentric layer in the n concentric layers Dielectric constant ε _i =2-( _ri /R) ² . Preferably, ri is the average value r _Ai of the outer surface radius r _Oi and the inner surface radius r _Ii of the i-th concentric layer; 1≤i≤n; the hemispherical _Lumberg lens antenna has a hemispherical surface and a bottom plane, The bottom plane is a plane passing through the center of the sphere and is covered with a metal foil layer; at least one concentric layer in the n concentric layers is distributed with a cavity; in each of the n concentric layers with a cavity in each concentric layer The cavity volume fraction is designed such that the average dielectric constant of the concentric layer is equal to the dielectric constant of the material of the concentric layer × (1-volume fraction of all cavities in the concentric layer)+the dielectric constant in the cavity of the concentric layer Dielectric constant × volume fraction of total cavities in this concentric layer.

The hemispherical Lumberg lens antenna may be formed by dividing the fabricated Lunberg lens antenna in the form of a complete sphere into two hemispheres along the center of the sphere. A hemispherical Lumberg lens antenna has a hemispherical surface and a bottom plane. The bottom plane is a plane passing through the center of the sphere. The bottom plane is usually all covered with a metal foil layer. In the present invention, the metal of the above-mentioned metal foil layer is not particularly limited. In some preferred embodiments, however, the metal of the metal foil layer is selected from the group consisting of copper, aluminum, silver and gold.

In some embodiments, the hemispherical Luneburg lens antenna is divided into two hemispheres through a plane passing through the center of the sphere. As an alternative embodiment, a hemispherical Lumberg lens antenna can be directly formed without a splitting operation.

The thickness of the metal foil layer is not particularly limited, and may be, for example, 0.1, 0.2, 0.5, 1 mm, or the like.

In the present invention, the number of layers n of the concentric layers is not particularly limited, and those skilled in the art can set according to specific needs according to the content disclosed in this application, for example, according to the needs of the target performance of the hemispherical Lunberg lens antenna to be fabricated, such as for 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 25, 30, 35, 40, 45, 50 , 60, 70, 80, 90, 100 or more. Generally speaking, the larger the number of layers n of the concentric layers, the better the performance of the hemispherical Lumberg lens antenna, but with the increase of the number of layers n, the design and production costs of the hemispherical Lumberg lens antenna will increase, and the increase in the number of layers will bring The benefits will gradually decrease. Thus, in some embodiments, the n is an integer between 3 and 100. Preferably, the n is an integer between 5 and 40; more preferably, the n is an integer between 6 and 20; most preferably, the n is an integer between 8 and 12, for example 8, 9, 10, 11 or 12.

In some alternative embodiments, the number n of the concentric layers may be an integer between 20 and 100 according to requirements, such as performance requirements; further preferably, the n is an integer between 40 and 100.

The radial thickness of each concentric layer is related to the radius R of the hemispheric Lumberg lens antenna and the number of layers n, and the thickness of each concentric layer may be the same or different. For example, the thicknesses of the concentric layers may be different, partially the same, or all the same. In some embodiments, the thickness of each concentric layer may decrease or increase radially from the spherical center layer to the outermost nth layer.

Since the dielectric constant of the material for making the hemispherical Lumberg lens antenna is generally greater than 1, at least one concentric layer among the n concentric layers of the hemispherical Luneberg lens antenna of the present invention, especially the concentric layer located on the outer side, especially the outermost layer The layers can generally be distributed with cavities. As long as the materials of the concentric layers allow, that is, as long as the concentric layers meeting the dielectric constant requirements can be fabricated, the concentric layers near the spherical center layer may not have cavities.

For concentric layers with cavities, at least a portion of the cavities may be designed to independently have a designed three-dimensional structure. Optionally, the designed truncated three-dimensional structure is a regular three-dimensional structure, such as a point-symmetric three-dimensional structure, an axis-symmetric three-dimensional structure or a plane-symmetric three-dimensional structure. Alternatively, the designed three-dimensional structure is an irregular three-dimensional structure. For example, the designed three-dimensional structure may be any three-dimensional structure selected from the group consisting of the following three-dimensional structures: polyhedron, sphere, ellipsoid, cylinder, cone, truncated truncated body; the polyhedron may have more than four faces The polyhedron, such as a polyhedron having 4 to 20 faces, such as a polyhedron having 4, 5, 6, 7, 8, 9, 10, 15 or 20 faces; preferably, the polyhedron is a regular polyhedron, such as Regular tetrahedron or regular hexahedron (see Figure 1, where 1 represents the material body (black area), 2 represents the cavity structure (white area), 3 is the metal foil layer of the bottom plane of the hemispherical Lunberg lens antenna) and so on.

When the three-dimensional structure of the cavity is a polyhedron, from the perspective of the physical strength of the hemispherical Lumberg lens antenna, the positions of at least a part of the vertex angles of the polyhedron are independently chamfered, especially when the size of the cavity is relatively small. in large cases. Based on the same consideration, at least a part of the edges of the polyhedron are independently chamfered in position.

In terms of performance, the distribution of the cavities in the concentric layers should be as uniform as possible, for example, the distribution may be uniform or substantially uniform as required. In addition, the size of the cavity should be as small as possible under the condition that the requirements of the dielectric constant design (such as target performance requirements) and the manufacturing conditions (such as the precision conditions of the manufacturing equipment) are satisfied.

In some preferred embodiments, the hemispherical Lumberg lens antenna of the present invention can be formed by an additive manufacturing method. For example, the additive manufacturing method may be fused deposition modeling (FDM), selective laser sintering (SLS), laser light curing (SLA), and the like.

For example, in the case of adopting fused deposition molding, the additive manufacturing method may include the following steps: (1) selecting materials for manufacturing the hemispherical Luneberg lens antenna, and designing the structure of the hemispherical Luneberg lens antenna; (2) determining Structural parameters of the hemispherical Lumberg lens antenna, the parameters include the number of concentric layers n, the shape, size and distribution of the cavity structure in each layer of the spherical shell; (3) Using 3D software to design the hemispherical Lumberg lens antenna The structure is made into a three-dimensional digital model; (4) Using the FDM method, the selected material is made into a hemispherical Lumberg lens antenna and a metal foil layer is applied to the bottom plane.

Regarding the additive manufacturing method, when using the FDM method, the temperature of the nozzle is preferably the melting point of the thermoplastic material + 20°C to 30°C. The inventors have found that the use of such a nozzle temperature results in the best accuracy and quality of the product. Additionally, in some preferred embodiments, the spray head speed is 60 to 80 mm/min. The inventors found that too fast or too slow will cause the printing size to become larger, indirectly cause the cavity volume to become smaller, make the dielectric constant deviate from the predetermined value, and affect the product performance. In addition, the nozzle positioning accuracy is preferably set to ±0.1 mm in the z direction and/or ±0.2 mm in the xy direction. The inventors of the present invention have found that excessively coarse precision will easily cause product deformation, while too fine precision will significantly prolong the printing time, thereby increasing the manufacturing cost.

In some embodiments, step (1) includes determining the structural parameters of the hemispherical Lumberg lens antenna, the parameters including the radius of the hemispherical Lumberg lens antenna, the number of layers n of the concentric layers, the average dielectric constant of each concentric layer, the The cavity volume fraction of the concentric layers, and/or the shape, size and distribution of the cavities.

Due to the use of additive manufacturing technology to manufacture the hemispherical Lumberg lens antenna, the hemispherical Lumberg lens antenna does not have the interlayer gap caused by other splicing methods such as foaming splicing method or punching splicing method, resulting in the performance degradation of the hemispherical Luneberg lens antenna. The problem. It is believed that when the interlayer gap is larger than 5% of the target incident wavelength, the performance of the antenna will degrade significantly. If the hemispherical Lumberg lens antenna of the present invention is manufactured by the additive manufacturing method, although the concept of layers is still used in the design, there is no interlayer gap in the physical structure, so that the products prepared by the additive manufacturing method have a The quality is more stable and reliable.

In the present invention, the dielectric constant of a concentric layer with cavities is adjusted by the volume fraction of the cavities therein to obtain a target dielectric constant. From the perspective of the performance of the hemispherical Lumberg lens antenna, the size of the cavity is preferably as small as possible, so that the radial dielectric constant of the hemispherical Lumberg lens antenna changes more gently.

In some preferred embodiments, the maximum diameter of the cavity section is not greater than one third of the wavelength of the target incident electromagnetic wave, preferably not greater than one quarter of the wavelength of the target incident electromagnetic wave, more preferably not greater than the wavelength of the target incident electromagnetic wave one-fifth to avoid performance degradation of the hemispherical Lumberg lens antenna. The maximum diameter of the cavity section has the meaning understood by those skilled in the art, which represents the maximum diameter of the smallest circumscribed circle in all sections of the cavity. This means that the distance between any two points on the periphery of any section of the cavity may not be greater than one third of the wavelength of the target incident electromagnetic wave, preferably not greater than one quarter of the wavelength of the target incident electromagnetic wave , more preferably not greater than one-fifth of the wavelength of the target incident electromagnetic wave, in order to avoid performance degradation of the hemispherical Lumberg lens antenna.

The hemispherical Luneberg lens antenna is generally designed for the wavelength of the electromagnetic wave to be received by the hemispherical Luneberg lens antenna, so the hemispherical Luneberg lens antenna will have a corresponding target electromagnetic wave wavelength. To avoid performance degradation of the hemispherical Lumberg lens antenna.

The present invention has no particular limitation on the dielectric constant of the concentric layer material used to manufacture the hemispherical Lumberg lens antenna. However, from the viewpoint of reducing the volume fraction of the cavity, the dielectric constant of the material is preferably less than 5, for example, 5, 4, 3, 2.5, 2. Preferably, the dielectric constant of the material is less than 2.5.

In the present invention, there is no particular limitation on the material used for making the hemispherical Luneberg lens antenna, and materials commonly used in the art for making the hemispherical Luneberg lens antenna can be used. In some preferred embodiments, the material for making the hemispherical Lumberg lens antenna is selected from the group consisting of polylactic acid (PLA), polyacrylonitrile, terpolymer of butadiene and styrene (ABS), polyaryletherketone, thermoplastic Group consisting of fluoroplastics, thermoplastic benzocyclobutene, DSM Somos GP Plus 14122 photosensitive resin. More preferably, the material for making the hemispheric Lumberg lens antenna is selected from the group consisting of PLA, ABS, polyaryl ether ketone, thermoplastic fluoroplastic, thermoplastic benzocyclobutene, DSM Somos GP Plus 14122 photosensitive resin. More preferably, the material is PLA. Most preferably, the material is PLA and the number n of concentric layers is seven. The above-mentioned materials are all known materials and can be obtained commercially, for example, PLA material with the grade of 4060D produced by NatureWorks in the United States can be purchased.

In addition, the materials of the respective concentric layers may be the same or different from each other. For example, the concentric layers may be made of the same material or may be partially made of the same material. In some preferred embodiments, the dielectric constants of the materials of each concentric layer may decrease in the radial direction from the spherical center layer to the outermost nth layer.

In some embodiments of the invention, at least some of the cavities may or may not have a medium. From the viewpoint of convenient manufacture, the medium in the cavity may be air. For example, in the case where the hemispherical Lumberg lens antenna is applied to an unmanned aerial vehicle, the medium in the cavity of the hemispherical Lumberg lens antenna is air.

In some embodiments, the hemispherical Lumberg lens antenna with a radius of 60mm of the present invention has an RCS value equal to or greater than -2dBsm at 9.4GHz; more preferably, the RCS value is equal to or greater than 0dBsm.

In another aspect of the present invention, the present invention provides a method for fabricating a hemispherical Lumberg lens antenna with cavities distributed therein, the method comprising the following steps:

(1) Select the material used to manufacture the hemispherical Lumberg lens antenna;

(2) Determine the structural parameters of the hemispherical Lumberg lens antenna;

(3) making a three-dimensional digital model of the hemispherical Lumberg lens antenna with the structural parameters; and

(4) manufacturing the hemispherical Lumberg lens antenna from the three-dimensional digital model using an additive manufacturing method; and

(5) A metal foil layer is applied on the bottom plane of the hemispherical Lumberg lens antenna.

In the method for fabricating a hemispherical Lumberg lens antenna of the present invention, the materials used for fabricating a hemispherical Lumberg lens antenna are as described above.

In some embodiments, the structural parameters are selected from the group consisting of the diameter, radius and number of layers of the hemispherical Lumberg lens antenna, and the shape, size and distribution of the cavity.

In some embodiments, the three-dimensional digital model is created using 3D software.

In the method for fabricating a hemispherical Lumberg lens antenna of the present invention, the additive manufacturing method is as described above.

Where there are specific requirements for the performance and size of the hemispherical Luneberg antenna, the hemispherical Luneberg antenna to be fabricated may have requirements on performance such as RCS or dimensions such as the diameter or radius of the hemispherical Luneberg antenna. In other words, the hemispherical Lumberg lens antenna to be fabricated has target performance and target size. In this case, in some embodiments, in the above steps (1) and/or (2), the selection is based on the target performance such as RCS and/or target size such as the diameter or radius of a hemispherical Lumberg lens antenna materials and/or determining said structural parameters of the hemispherical Lumberg lens antenna. In addition, the manufacturing method may optionally include in the step (3) that the above-mentioned target performance can be achieved by adjusting the structural parameters by means of a simulation technique and a trial-and-error method. As an additional or alternative embodiment, after the step (5), the manufacturing method further includes a step of checking whether the manufactured hemispherical Lumberg lens antenna has the target performance and/or the target size .

In some optional implementations, a hemispherical Luneburg lens antenna can be fabricated in a similar manner to the above, except that a complete spherical Luenberger lens antenna is first fabricated, and then the complete spherical Luenberger lens antenna is cut into equal parts as required. It is divided into a hemispherical Luneberg lens antenna, and then a metal foil layer is applied on the bottom plane of the hemispherical Luneberg lens antenna.

In another aspect, the present invention provides applications of the hemispherical Lumberg lens antenna, such as applications in satellite communications, radar antennas, radio astronomical telescopes, military false targets, target drones, target bombs, and automotive anti-collision radars; In the case of the application in the satellite communication, the application may be selected from the group consisting of applications in satellite ground stations, satellite news relay vehicles, broadcast satellite communications, mobile satellite ground stations, and near-Earth satellite positioning. at least one.

Example

The present invention will be further described in detail below in conjunction with the examples, the materials used therein can be purchased from the PLA material of the grade 4060D produced by NatureWorks of the United States, and no special equipment is used.

Example 1

The hemispherical Lumberg lens antenna fabricated in this example is a hemisphere with cavities distributed therein. The radius R of the sphere is 60mm, the target RCS value is greater than or equal to 0dBsm, the target incident electromagnetic wave is 9.4GHz, the wavelength is 32mm, and the cavity is A regular hexahedron with a side length of 3.5mm and a metal foil layer thickness of 0.2mm.

In this embodiment, PLA is selected as the material for making the hemispherical Lumberg lens antenna, and its dielectric constant is 2.5. Then use the formula ε _i =2-(r _i /R) ² to calculate the dielectric constant of each concentric layer; then calculate the cavity volume fraction of each concentric layer according to the following formula: Average dielectric constant of each concentric layer = [the concentric layer The dielectric constant of the layer material × (1 - the volume fraction of all cavities in the concentric layer in the concentric layer) + the dielectric constant of the cavity medium × the volume of all the cavities in the concentric layer in the concentric layer Fraction], and then determine the volume and number of cavities in each concentric layer according to the volume fraction of each concentric layer. In this embodiment, the shape of the cavity is a cube, and the maximum diameter of the cavity section (that is, the body diagonal of the cube) is 6mm, and the cavities are evenly distributed in each concentric layer. Using 3D software (Unigraphics NX, Siemens PLM Software), the designed hemispherical Lumberg lens antenna structure was made into a 3D digital model; by FDM method, PLA was fabricated into a hemispherical Lunberg lens antenna and metal foil was applied to the bottom plane. Floor.

The test results show that the average RCS value of the hemispherical Lumberg lens antenna is ≥0dBsm at 9.4GHz. The performance requirements are met.

The hemispherical Lumberg lens antennas of Examples 2-5 were fabricated in a similar manner to Example 1, except for the parameters shown in Table 1.

Table 1 (continued) Diameter (mm)/average dielectric constant/cavity volume fraction (Ri/εi/Vi) of each concentric layer of the hemispherical Lumberg lens antenna fabricated in each example

Layer number Example 1, 2, 3 Example 4 Example 5 1 17.14/1.98/0.35 14.55/1.99/0.48 13.33/2/0.59 2 34.29/1.92/0.39 29.09/1.97/0.49 26.67/1.98/0.59 3 51.43/1.82/0.46 43.64/1.93/0.51 40/1.96/0.6 4 68.57/1.67/0.55 58.18/1.87/0.54 53.33/1.93/0.61 5 85.71/1.49/0.67 72.73/1.79/0.58 66.67/1.89/0.63 6 102.86/1.27/0.82 87.27/1.7/0.63 80/1.84/0.65 7 120/1.05/0.97 101.82/1.6/0.69 93.33/1.78/0.67 8 116.36/1.47/0.75 106.67/1.72/0.7 9 130.91/1.33/0.83 120/1.64/0.73 10 145.45/1.17/0.91 133.33/1.56/0.77 11 160/1.05/0.97 146.67/1.46/0.81 12 160/1.36/0.85 13 173.33/1.25/0.9 14 186.67/1.13/0.95 15 200/1.05/0.98

The above embodiments are only to describe the preferred embodiments of the present invention, and do not limit the scope of the present invention. On the premise of not departing from the actual spirit of the present invention, various modifications and improvements made by those of ordinary skill in the art to the technical solutions of the present invention , shall fall within the protection scope determined by the technical solution of the present invention.

Claims (55)

1. A method for manufacturing a hemispherical Luneberg lens antenna is disclosed, wherein a cavity is distributed on the hemispherical Luneberg lens antenna, the cavity is provided with a hemispherical surface and a bottom plane, and the bottom plane is a plane passing through the center of a sphere; the method is characterized in that:

the hemispherical luneberg lens antenna is a hemisphere with a radius of R and is designed to include n concentric layers with different dielectric constants, the spherical layer is represented as a 1 st layer, and 2 nd to nth concentric layers are sequentially represented as 2 nd to nth concentric layers in order of increasing radius, wherein n is an integer not less than 3, R is₁Is the radius of the spherical center layer; r is_n＝R；r_iRadius of the ith concentric layer; i is more than or equal to 1 and less than or equal to n;

an average dielectric constant of an ith concentric layer of the n concentric layers_i＝2-(r_i/R)²；

The cavities are distributed in at least one of the n concentric layers; the distance between any two points on the periphery of any one section of the cavity is not more than one third of the wavelength of the incident electromagnetic wave of the target;

the volume fraction of the cavities in each of the n concentric layers having cavities is designed such that the average dielectric constant of the concentric layer is the dielectric constant of the material of the concentric layer x (1-volume fraction of all cavities in the concentric layer) + the dielectric constant of the medium in the cavities of the concentric layer x the volume fraction of all cavities in the concentric layer;

at least some of the cavities independently have a designed three-dimensional structure; the designed three-dimensional structure is a polyhedron; the positions of at least one part of the vertex angles of the polyhedron are independently designed to be chamfers; the positions of at least one part of edges of the polyhedron are independently designed to be chamfers;

the method comprises the following steps:

(1) selecting a material for manufacturing a hemispherical luneberg lens antenna;

(2) determining the structural parameters of the hemispherical luneberg lens antenna;

(3) making a three-dimensional digital model of the hemispherical luneberg lens antenna with the structural parameters; and

(4) manufacturing the hemispherical luneberg lens antenna according to the three-dimensional digital model by adopting an additive manufacturing method; the hemispherical luneberg lens antenna is fabricated by an additive manufacturing method such that there is no interlayer gap between each of the n concentric layers; and

(5) a metal foil layer is pasted on the bottom plane of the hemispherical luneberg lens antenna;

the additive manufacturing method is melt stacking molding; in the melt accumulation molding, the temperature of a spray head is the melting point of the material plus 20 ℃ to 30 ℃; and/or a showerhead speed of 60 to 80 mm/min; and/or the positioning precision of the spray head is +/-0.1 millimeter in the z direction; and/or the positioning precision of the spray head is +/-0.2 mm in the x direction; and/or the accuracy of the positioning of the spray head in the y direction is + -0.2 mm.

2. The method of claim 1, wherein the luneberg lens antenna of the complete sphere is fabricated, then split into equal parts as required, and then the metal foil layer is attached to the bottom plane of the hemispherical luneberg lens antenna.

3. The method according to claim 1 or 2, wherein the structural parameter is selected from the group consisting of: the diameter, radius, number of layers of the hemispherical luneberg lens antenna, and the shape, size and distribution of the cavity.

4. The method of claim 1, wherein:

in step (1), the material is determined according to a target performance and/or a target size of the hemispherical luneberg lens antenna.

5. The method of claim 4, wherein the target performance is measured in terms of radar scattering cross-sectional area and the target size is measured in terms of diameter, radius and/or number of layers of a hemispherical luneberg lens antenna.

6. A method according to claim 4 or 5, characterized in that in step (2) the structural parameters are determined according to the target properties and/or target dimensions and/or dielectric constant of the material.

7. The method of claim 4, wherein in step (3), further comprising adjusting the structural parameters by a simulation technique using a trial and error method to achieve a target performance of the hemispherical luneberg lens antenna.

8. The method of claim 7, wherein the number of layers of the hemispherical luneberg lens antenna, the shape, size and/or distribution of the cavities are adjusted to achieve a target performance of the hemispherical luneberg lens antenna.

9. The method of claim 4, wherein after step (5), further comprising verifying whether the hemispherical luneberg lens antenna produced has the target performance and/or target size.

10. The method of claim 1, wherein r is_iIs the outer surface radius r of the ith concentric layer_OiAnd inner surface radius r_IiAverage value of r_Ai。

11. The method of claim 1, wherein the distance between any two points on the perimeter of any one cross section of the cavity is no more than one-quarter of the wavelength of the target incident electromagnetic wave.

12. The method of claim 11, wherein the distance between any two points on the perimeter of any one cross section of the cavity is no more than one fifth of the wavelength of the targeted incident electromagnetic wave.

13. The method according to any one of claims 1, 10, 11 or 12, wherein the number of concentric layers, n, is from 2 to 100 or more than 100.

14. The method of any one of claims 1, 10, 11 or 12, wherein n is an integer between 3 and 100.

15. The method of claim 14, wherein n is an integer between 5 and 40.

16. The method of claim 14, wherein n is an integer between 6 and 20.

17. The method of claim 14, wherein n is an integer between 8 and 12.

18. The method according to any one of claims 1, 10, 11 or 12, wherein n is an integer of not less than 15.

19. The method of claim 18, wherein n is an integer between 15 and 100.

20. The method of claim 19, wherein n is an integer between 20 and 100.

21. The method of claim 20, wherein n is an integer between 40 and 100.

22. The method of claim 1, wherein the designed spatial structure is a regular spatial structure or an irregular spatial structure.

23. The method of claim 22, wherein the regular spatial structure is a point-symmetric spatial structure, an axisymmetric spatial structure, or a plane-symmetric spatial structure.

24. The method of claim 1, wherein the polyhedron is a polyhedron having 4 to 20 faces.

25. The method of claim 1, wherein the polyhedron is a regular polyhedron.

26. The method of claim 1, wherein the polyhedron is a polyhedron having four or more faces.

27. The method of claim 26, wherein the polyhedron is a regular polyhedron.

28. The method according to claim 27, wherein the regular polyhedron is a regular tetrahedron or a regular hexahedron.

29. The method of claim 1, wherein the concentric layer of material has a dielectric constant of less than 5.

30. The method of claim 29, wherein the concentric layer of material has a dielectric constant of less than 3.

31. The method of claim 30, wherein the concentric layer of material has a dielectric constant of less than 2.5.

32. The method according to claim 1, wherein the concentric layers of material are selected from at least one of the group consisting of thermoplastic materials, photosensitive resins, and ceramics.

33. The method of claim 32 wherein the thermoplastic material comprises one or more selected from the group consisting of polylactic acid, polyacrylonitrile, acrylonitrile butadiene styrene terpolymer, polyaryletherketones, thermoplastic fluoroplastics and thermoplastic benzocyclobutene, DSM Somos GP Plus 14122 photosensitive resin.

34. The method as claimed in claim 32, wherein said concentric layers are made of a material selected from the group consisting of polylactic acid, polyacrylonitrile, terpolymers of butadiene and styrene, polyaryletherketones, thermoplastic fluoroplastics, thermoplastic benzocyclobutene, DSM Somos GP Plus 14122 photosensitive resins.

35. The method of claim 32, wherein the concentric layer material is polylactic acid.

36. The method of claim 35, wherein the number n of concentric layers is 7.

37. The method of claim 1, wherein the materials of the respective concentric layers are the same as one another.

38. The method of claim 1, wherein the materials of the respective concentric layers are different from one another.

39. The method of claim 1, wherein some of the concentric layers are made of the same material.

40. A method according to claim 1, wherein the dielectric constant of the material of each concentric layer decreases radially from the centre of sphere layer to the outermost nth layer.

41. The method of claim 1, wherein the RCS value is equal to or greater than-2 dBsm for a hemispherical luneberg lens antenna 120mm in diameter at 9.4 GHz.

42. The method of claim 41, wherein the RCS value is greater than 0dBsm for a hemispherical Luneberg lens antenna 120mm in diameter at 9.4 GHz.

43. The method of claim 1, wherein the metal of the metal foil layer is selected from the group consisting of copper, aluminum, silver, and gold.

44. The method of claim 1, wherein the metal foil layer has a thickness of 0.1mm to 1 mm.

45. The method of claim 1, wherein the thicknesses of the concentric layers are different.

46. The method of claim 1, wherein the thickness of each concentric layer is partially the same.

47. The method of claim 1, wherein the thicknesses of the concentric layers are all the same.

48. The method of claim 1, wherein the thickness of each concentric layer decreases or increases radially from the center layer to the n-th outermost layer.

49. The method of claim 1, wherein the outer one of the n concentric layers is distributed with cavities.

50. The method of claim 1, wherein an outermost layer of the n concentric layers is distributed with cavities.

51. The method of claim 1, wherein a concentric layer of the n concentric layers that is adjacent to the spherical layer does not have a cavity.

52. The method of claim 1, wherein the distribution of the cavities in the concentric layers is uniformly distributed or substantially uniformly distributed.

53. The method of claim 1, wherein at least some of the cavities have a medium.

54. The method of claim 1, wherein at least some of the cavities are devoid of media.

55. The method of claim 54, wherein the medium in the cavity is air.

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