Low-sidelobe shaped reflector antenna optimization method suitable for terahertz FOD radar

Abstract

The invention discloses a low-sidelobe shaped reflector antenna optimization method suitable for a terahertz FOD radar, and belongs to the technical field of airfield runway foreign matter detection, and the method comprises the steps: setting a reflector horizontal aperture, a reflector vertical aperture and a reflector shape based on the ground side sidelobe performance demand and the vertical plane antenna beam width demand; generating a first type of reflecting surface according to the set reflecting surface horizontal aperture, the reflecting surface vertical aperture and the reflecting surface shape; performing shaping processing on the first type reflecting surface to directly generate an unfolded curved surface; and controlling and adjusting the unfolded curved surface according to a preset strategy to obtain a second type of reflecting surface. According to the low-sidelobe shaped reflector antenna optimization method suitable for the terahertz FOD radar, the ground side sidelobe performance of the antenna is remarkably improved, the characteristic of low sidelobe is achieved, the characteristic of high gain is kept, the beam width of the antenna is not affected, and the overall airfield runway foreign matter detection performance of the radar is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of airport runway foreign object detection, and in particular to an optimization method for a low-sidelobe shaped reflector antenna suitable for a terahertz FOD radar. Background Art

[0002] During takeoff and landing, aircraft engines exert tremendous suction, easily sucking small debris from the runway into the engines. This can damage the aircraft and affect the proper functioning of the wings, landing gear, and other equipment. This not only causes direct economic losses but also potentially endangers the lives of the crew and passengers. Therefore, clearing foreign debris from airport runways is essential. Most domestic airports rely on manual runway inspections and cleaning, which is time-consuming, labor-intensive, and inefficient. Using airport debris detection radars can improve runway inspection efficiency, reduce single inspection times, and enable 24-hour continuous operation. The antenna portion of an airport debris detection radar requires high antenna gain to ensure that the electromagnetic wave energy is transmitted far enough to strike the object being detected, where it is reflected and transmitted back to the receiver with sufficient energy to generate an effective signal. Secondly, while maintaining high gain, the antenna also needs to have low sidelobes. This is because the antenna's sidelobe beams can point toward the ground outside the runway. Reflecting off the ground, these reflections can also create clutter that returns to the radar's receiving end and interferes with the actual signal being detected. Therefore, optimizing the antenna's sidelobe performance while maintaining antenna gain to improve the radar's overall detection performance is a pressing technical challenge. Summary of the Invention

[0003] The purpose of the present invention is to provide a low sidelobe shaped reflector antenna optimization method suitable for terahertz FOD radar to solve the problems existing in the background technology.

[0004] To achieve the above object, the present invention provides a method for optimizing a low sidelobe shaped reflector antenna suitable for terahertz FOD radar, comprising the following steps: S1. Setting the horizontal aperture, vertical aperture, and shape of the reflector based on the sidelobe performance requirements and vertical antenna beamwidth requirements on the ground side. The reflector shape includes but is not limited to a rectangle, a polygon, and an ellipse. S2. Generate a first type of reflecting surface according to the set horizontal aperture, vertical aperture, and shape of the reflecting surface; S3, performing a shaping process on the first type of reflective surface to directly generate an unfolded surface; S4. Control and adjust the unfolded surface according to a preset strategy to obtain a second type of reflective surface.

[0005] Preferably, step S1 specifically includes: Obtain antenna beam width requirements and, based on the relationship between antenna beam angular width and antenna reflector aperture, obtain the vertical aperture of the reflector. The horizontal aperture of the reflector is calculated based on the sidelobe performance requirements on the ground side and the antenna beamwidth requirements. The sidelobe performance requirements on the ground side are specifically the antenna main beam gain requirements G. The shape of the reflecting surface is specifically an ellipse.

[0006] Preferably, obtaining the antenna beam width requirement and obtaining the vertical aperture of the reflector based on the relationship between the antenna beam angular width and the aperture of the antenna reflector specifically includes: The relationship between the antenna beam angle width and the antenna reflector aperture is as follows: ; in, is the antenna beam width; is the wavelength corresponding to the frequency band; D is the vertical aperture of the antenna's reflecting surface.

[0007] Preferably, the horizontal aperture of the reflecting surface is calculated based on the sidelobe performance requirement on the ground side and the beam width requirement of the antenna. The sidelobe performance requirement on the ground side is specifically the main beam gain requirement G of the antenna, which specifically includes: The relationship between the antenna's main beam gain requirement G and the horizontal aperture of the reflecting surface is as follows: ; in, is the wavelength corresponding to the frequency band; D is the vertical aperture of the antenna's reflecting surface; H is the horizontal aperture of the antenna's reflecting surface.

[0008] Preferably, step S2 specifically includes: The ratio of the parabola focal length to the horizontal aperture of the reflector is determined based on the horizontal aperture of the reflector and the main beam gain requirement G of the antenna to obtain the parabola focal length; Generate a parabola based on the horizontal aperture of the reflecting surface and the focal length of the parabola, and use the generated parabola as the first type of reflecting surface; The parabola equation corresponding to the parabola is: ; in, is the focal length of the parabola; is the horizontal aperture of the reflecting surface; Indicates the coordinate of a spatial point in the x-axis direction; Indicates the coordinate of a spatial point in the y-axis direction.

[0009] Preferably, step S3 specifically includes: The first type of reflective surface is shaped by non-uniform rational B-spline technology to generate a non-uniform rational B-spline surface with a degree in u direction and b degree in v direction. , the non-uniform rational B-spline surface As an unfolded surface.

[0010] Preferably, non-uniform rational B-spline surface The expression is: ; in, is a piecewise rational basis function, A control network with two directions, that is, control points, is formed.

[0011] Preferably, piecewise rational basis functions The specific expression is: ; in, is the weighted value of the control point; are the non-rational B-spline basis functions defined on the knot vectors U and V respectively; is a non-rational B-spline basis function defined on the node vector U, corresponding to the node p and the feature a, is a non-rational B-spline basis function defined on the node vector V, corresponding to the node q and the feature b, It is the product term of the basis function and the corresponding weight, which is used to participate in the calculation of the rational basis function; Non-uniform rational B-spline surfaces The specific expression is: ; in, A control network with two directions, that is, control points, is formed; is the weighted value of the control point; are the non-rational B-spline basis functions defined on the knot vectors U and V respectively.

[0012] Preferably, the preset strategy specifically includes: When the control point The weighted value When it is equal to 1, the control point The controlled surface area remains in its original state; When the control point The weighted value When greater than 1, the control point The controlled surface area moves toward the control point Close to generate control point The controlled surface area bulges outwards; When the control point The weighted value When it is less than 1, the control point The controlled surface area moves toward the control point Move away to create a control point The controlled surface area has an inward concave effect; By controlling each control point The weighted value Adjustments are made to change the shape of the unfolded surface to obtain a corresponding second type of reflective surface.

[0013] Therefore, the present invention adopts the above-mentioned low sidelobe shaped reflector antenna optimization method suitable for terahertz FOD radar. By using NURBS surface generation technology to shape the reflector, and optimize the control points of the reflector, the antenna's ground side sidelobe performance is significantly improved, achieving the characteristics of low sidelobe while still having the characteristics of high gain, and without affecting the antenna beam width, thereby improving the radar's overall performance in detecting foreign objects on airport runways.

[0014] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 is an overall flow chart of an embodiment of the present invention; Figure 2 Schematic diagram of the structure of an embodiment of the present invention; Figure 3 The aperture size and outline shape of the reflecting surface of an embodiment of the present invention; Figure 4 is a shaped antenna beam pattern according to an embodiment of the present invention; Figure 5 A comparison diagram of the shaped reflective surface of an embodiment of the present invention and a common parabola in direction five; Figure 6 This is an example of a NURBS surface with a control point weight of 1; Figure 7 An example of a NURBS surface with a control point weight of 5. DETAILED DESCRIPTION

[0016] The following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort shall fall within the scope of protection of the present invention.

[0017] See also Figure 1-7A method for optimizing a low sidelobe shaped reflector antenna suitable for terahertz FOD radar comprises the following steps: S1. Set the horizontal aperture, vertical aperture and shape of the reflector based on the sidelobe performance requirements on the ground side and the antenna beam width requirements on the vertical plane. The shape of the reflector includes but is not limited to rectangle, polygon and ellipse.

[0018] In this embodiment, if Figure 2 As shown, a horn antenna is used as a feed source, and an offset position relationship is formed between the horn antenna and the reflecting surface, so as to reduce the influence of the shielding effect on the antenna gain.

[0019] In this embodiment, step S1 specifically includes: Obtain the antenna beam width requirement and, based on the relationship between the antenna beam angular width and the antenna reflector aperture, obtain the vertical aperture of the reflector.

[0020] In this embodiment, the relationship between the antenna beam angle width and the antenna reflector aperture is as follows: ; in, is the antenna beam width; is the wavelength corresponding to the frequency band; D is the vertical aperture of the antenna's reflecting surface.

[0021] In this embodiment, after conducting a field investigation and research on the actual scenario of the airport, it is expected that the radar antenna will be located approximately one hundred meters away from the runway. Geometric calculations are performed on the radar installation position and the actual layout of the airport. It is found that the antenna's elevation beam width needs to reach approximately 0.4°. This ensures that the scanning beam covers the airport runway while minimizing the coverage of areas outside the runway into the radar scanning area, thereby reducing clutter interference.

[0022] In this embodiment, in the application of the airport foreign object detection radar, emphasis is placed on the sidelobe performance on the ground side and the antenna beam width in the vertical plane.

[0023] In this embodiment, the antenna beam width requirement is specifically the antenna surface beam angle width at a frequency of 240 GHz. It needs to reach 0.392. At this time, the vertical aperture D of the antenna's reflecting surface is 220mm.

[0024] The horizontal aperture of the reflecting surface is calculated based on the sidelobe performance requirements on the ground side and the beam width requirements of the antenna. The sidelobe performance requirements on the ground side are specifically the main beam gain requirements G of the antenna.

[0025] In this embodiment, the relationship between the antenna's main beam gain requirement G and the horizontal aperture of the reflecting surface is as follows: ; in, is the wavelength corresponding to the frequency band; D is the vertical aperture of the antenna's reflecting surface; H is the horizontal aperture of the antenna's reflecting surface.

[0026] In this embodiment, in order to make the antenna gain sufficiently large, a sufficiently large horizontal reflector aperture should be set to meet the gain requirement. The gain requirement is obtained according to the radar equation, which is as follows: ; in, P is the radar transmission power; is the receiving antenna gain; is the transmitting antenna gain; is the wavelength corresponding to the frequency band; is the radar pulse time; The RCS of the target to be measured; F is the system noise factor; is the Boltzmann constant term, 4×10 -21 W / Hz; is the minimum signal-to-noise ratio of the system; L is the system loss.

[0027] In this embodiment, the receiving antenna gain = Transmitting antenna gain = Antenna's main beam gain requirement G.

[0028] The antenna beamwidth requirement is specifically based on the radar equation. Substituting all physical quantities except antenna gain into the equation at a frequency of 240 GHz, the antenna gain G is determined to be 56.1 dB. The antenna wavelength λ is 1.25 mm. Based on the relationship between the antenna's main beam gain requirement G and the horizontal aperture of the reflector, the horizontal aperture of the reflector is determined to be 500 mm.

[0029] The simulation verification was carried out on the reflector with a horizontal aperture of 500mm and a vertical aperture of 220mm. The final gain of the designed elliptical reflector was 56.904dB>56.1dB, meeting the gain requirement.

[0030] In this embodiment, the shape of the reflective surface is specifically an ellipse.

[0031] In this embodiment, after determining the aperture of the reflector, the edge shape of the reflector will affect the antenna's directional pattern performance. Through comparative experiments, reflectors with the same aperture but different edge shapes are set, and simulations are performed under the condition that only the edge shapes are different. The rectangular reflector has the largest main beam gain at the same aperture, but its side lobe performance is also the worst among the three edge shapes. The main beam gain of the elliptical reflector will decrease slightly, but its side lobe performance is the best among the three edge shapes. In order to have better side lobe performance, the elliptical reflector is selected as the design of the reflector for this antenna. The shape of the reflector in the final design is as follows: Figure 3 shown.

[0032] S2. Generate a first type of reflecting surface according to the set horizontal aperture, vertical aperture, and shape of the reflecting surface.

[0033] In this embodiment, step S2 specifically includes: The ratio of the parabola focal length to the horizontal aperture of the reflector is determined based on the horizontal aperture of the reflector and the main beam gain requirement G of the antenna to obtain the parabola focal length; Generate a parabola based on the horizontal aperture of the reflecting surface and the focal length of the parabola, and use the generated parabola as the first type of reflecting surface; The parabola equation corresponding to the parabola is: ; in, is the focal length of the parabola; is the horizontal aperture of the reflecting surface; Indicates the coordinate of a spatial point in the x-axis direction; Indicates the coordinate of a spatial point in the y-axis direction.

[0034] In this embodiment, conventional reflector antennas mostly use parabolic surfaces as reflective surfaces. Conventional parabolic surfaces are expressed by the parabolic surface equation: Once the focal length and aperture of the parabola are determined, the corresponding regular parabola can be generated by substituting parameters a and b into the parabola equation.

[0035] In antenna design, the optimal ratio of focal length to parabola aperture, f / D ≤ 2.6, was determined. Simulation optimization was performed based on this ratio. Taking a beamwidth of 0.392° into consideration, a focal length setting was selected that maximized the antenna's pattern gain. After comparing antenna gains at different focal lengths, a focal length of 248.5mm was chosen for this antenna. A conventional parabola was generated based on the aforementioned aperture and focal length. The sidelobes of a conventional parabola are symmetrical, and there is room for optimization of the ground-facing sidelobes.

[0036] S3. Perform shaping processing on the first type of reflective surface to directly generate an unfolded surface.

[0037] In this embodiment, step S3 specifically includes: The first type of reflective surface is shaped by non-uniform rational B-spline technology to generate a non-uniform rational B-spline surface with a degree in u direction and b degree in v direction. , the non-uniform rational B-spline surface As an unfolded surface.

[0038] In this embodiment, the non-uniform rational B-spline surface The expression is: ; in, is a piecewise rational basis function, A control network with two directions, that is, control points, is formed.

[0039] In this embodiment, the piecewise rational basis function The specific expression is: ; in, is the weighted value of the control point; are the non-rational B-spline basis functions defined on the knot vectors U and V respectively; is a non-rational B-spline basis function defined on the node vector U, corresponding to the node p and the feature a, is a non-rational B-spline basis function defined on the node vector V, corresponding to the node q and the feature b, It is the product term of the basis function and the corresponding weight, and is used to participate in the calculation of rational basis functions.

[0040] In this embodiment, the piecewise rational basis function The main properties are as follows: Normative: .

[0041] Non-negativity: , for all Both are established.

[0042] Local support: When In the rectangular area Other than that, .

[0043] If a>0, b>0, then The maximum value is reached exactly once.

[0044] Differentiability: The node lines in the u and v directions form a rectangle. Any order partial derivative exists, and at the node in the u direction (v direction), yes subdifferentiable, where p is the degree of repetition of the node.

[0045] According to the third property of local support, we know that the moving control point Or change the weight of the control point , affecting only rectangular space The shape of the surface inside the area will not affect the shape outside the area.

[0046] In this embodiment, the non-uniform rational B-spline surface The specific expression is: ; in, A control network with two directions, that is, control points, is formed; is the weighted value of the control point; are the non-rational B-spline basis functions defined on the knot vectors U and V respectively.

[0047] In this embodiment, the aperture of the reflecting surface and the focal length of the parabola are determined, and the parabola equation is: It is expressed by NURBS surface expression, that is, using NURBS surface to form a regular paraboloid. In the NURBS surface expression, by setting each control point By using the equation for the parabola and the NURBS surface expression to establish an equation, the resulting NURBS surface is almost completely similar to a conventional parabola. Furthermore, the surface is formed in one step, without relying on splicing, resulting in a smooth surface that can effectively reflect electromagnetic waves.

[0048] In this embodiment, the control points are used to express the NURBS surface of the conventional parabola, where the elliptical circle is the 500mm×220mm fan-shaped beam reflector that needs to be cut out from the rotationally symmetric reflector. After the conventional parabola is formed by the NURBS surface, it is necessary to change the shape of the conventional parabola to achieve the effect of improving the side lobe performance on the ground side. From the properties of the NURBS surface mentioned above, we know that changing the control points of the NURBS surface The weighted value , will change the shape of the NURBS surface. The specific weighted values ​​are as follows: Different weighted values Affect the shape of the surface by controlling the points The weighted value Adjust the curved surface shape of the reflector to change the reflection effect of the reflector on the feed electromagnetic wave, so as to reduce the side lobe of the ground. Because we need to optimize the performance of the ground-facing sidelobes, we focus on changing the weights of the control points in the area of ​​the reflector that produces the ground-facing sidelobes. By adjusting the weights from 1 to other values, we obtain a new reflector shape.

[0049] The simulation performance of the shaped reflector antenna is as follows: Figure 4 and Figure 5 As shown in the figure, the gain of the shaped antenna is 56.904dB, which is only 0.02dB lower than that of the ordinary parabolic antenna. However, the sidelobe performance of the shaped antenna on the ground side is significantly improved. Because the sidelobe on the air side is emitted toward the sky, it will not cause reflected echo interference to the radar system. Therefore, by sacrificing the sidelobe performance on the air side, the sidelobe performance on the ground side is improved. The sidelobe performance of the shaped antenna on the ground side is improved from the original -25.72dB to -30.93dB, which is a significant improvement on the ground side side. At the same time, the vertical beamwidth of the antenna is still 0.392°. Through analysis of the simulation results, the shaped reflector antenna has a significant improvement on the sidelobe performance on the ground side, reaching more than -30dB while maintaining high gain and the beamwidth of a fan-shaped narrow beam, and has good sidelobe performance.

[0050] S4. Control and adjust the unfolded surface according to a preset strategy to obtain a second type of reflective surface.

[0051] In this embodiment, the preset strategy specifically includes: When the control point The weighted value When it is equal to 1, the control point The controlled surface area remains in its original state; When the control point The weighted value When greater than 1, the control point The controlled surface area moves toward the control point Close to generate control point The controlled surface area bulges outwards; When the control point The weighted value When it is less than 1, the control point The controlled surface area moves toward the control point Move away to create a control point The controlled surface area has an inward concave effect; By controlling each control point The weighted value Adjustments are made to change the shape of the unfolded surface to obtain a corresponding second type of reflective surface.

[0052] In this embodiment, when the selected control point The weighted value When is 1, the shape of the surface is Figure 6 As shown in the figure; when the weight value of the control point of the surface is set to be greater than 1, the surface will be closer to the control point, so when the weight value changes from 1 to 5, the surface area controlled by this control point will bulge outward and be closer to the control point; when the weight value of the control point of the surface is less than 1, the surface will be farther away from the control point, so when the weight value changes from 1 to 0.1, the surface area controlled by this control point will be concave inward and away from the control point, as shown in the figure; Figure 7 shown.

[0053] Therefore, the present invention adopts the above-mentioned low sidelobe shaped reflector antenna optimization method suitable for terahertz FOD radar, which significantly improves the ground side lobe performance of the antenna, realizes the low sidelobe characteristics and maintains the high gain characteristics, and does not affect the antenna beam width, thereby improving the radar's overall performance in detecting foreign objects on airport runways.

[0054] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for optimizing a low sidelobe shaped reflector antenna suitable for terahertz FOD radar, characterized in that: The following steps are involved: S1. Set the horizontal aperture, vertical aperture, and shape of the reflector based on the sidelobe performance requirements on the ground side and the antenna beamwidth requirements on the vertical plane. The reflector shapes include rectangular, polygonal, and elliptical. S2. Generate a first type of reflecting surface according to the set horizontal aperture, vertical aperture, and shape of the reflecting surface; S3, performing a shaping process on the first type of reflective surface to directly generate an unfolded surface; S4. Control and adjust the unfolded surface according to a preset strategy to obtain a second type of reflective surface.

2. The method for optimizing a low sidelobe shaped reflector antenna for a terahertz FOD radar according to claim 1, wherein: Step S1 specifically includes: Obtain antenna beam width requirements and, based on the relationship between antenna beam angular width and antenna reflector aperture, obtain the vertical aperture of the reflector. The horizontal aperture of the reflector is calculated based on the sidelobe performance requirements on the ground side and the antenna beamwidth requirements. The sidelobe performance requirements on the ground side are specifically the antenna main beam gain requirements G. The shape of the reflecting surface is specifically an ellipse.

3. The method for optimizing a low sidelobe shaped reflector antenna for a terahertz FOD radar according to claim 2, wherein: The relationship between the antenna beam angle width and the antenna reflector aperture is as follows: ； in, is the antenna beam width; is the wavelength corresponding to the frequency band; D is the vertical aperture of the antenna's reflecting surface.

4. The method for optimizing a low sidelobe shaped reflector antenna for a terahertz FOD radar according to claim 3, wherein: The horizontal aperture of the reflector is calculated based on the sidelobe performance requirements on the ground side and the antenna beamwidth requirements. The sidelobe performance requirements on the ground side are specifically the antenna main beam gain requirements G, which include: The relationship between the antenna's main beam gain requirement G and the horizontal aperture of the reflecting surface is as follows: ； in, is the wavelength corresponding to the frequency band; D is the vertical aperture of the antenna's reflecting surface; H is the horizontal aperture of the antenna's reflecting surface.

5. The method for optimizing a low sidelobe shaped reflector antenna for a terahertz FOD radar according to claim 1, wherein: Step S2 specifically includes: The ratio of the parabola focal length to the horizontal aperture of the reflector is determined based on the horizontal aperture of the reflector and the main beam gain requirement G of the antenna to obtain the parabola focal length. Generate a parabola based on the horizontal aperture of the reflecting surface and the focal length of the parabola, and use the generated parabola as the first type of reflecting surface; The parabola equation corresponding to the parabola is: ； in, is the focal length of the parabola; is the horizontal aperture of the reflecting surface; Represents the coordinate of a spatial point in the x-axis direction; Indicates the coordinate of a spatial point in the y-axis direction.

6. The method for optimizing a low sidelobe shaped reflector antenna for terahertz FOD radar according to claim 1, wherein: Step S3 specifically includes: The first type of reflective surface is shaped by the non-uniform rational B-spline method to generate a non-uniform rational B-spline surface with a degree in the u direction and b degree in the v direction. , the non-uniform rational B-spline surface As an unfolded surface.

7. The method for optimizing a low sidelobe shaped reflector antenna for terahertz FOD radar according to claim 6, wherein: Non-uniform rational B-spline surfaces The expression is: ； in, is a piecewise rational basis function, A control network with two directions is formed, which is a control point.

8. The method for optimizing a low sidelobe shaped reflector antenna for terahertz FOD radar according to claim 7, wherein: Piecewise rational basis functions The specific expression is: ； in, is the weighted value of the control point; are the non-rational B-spline basis functions defined on the knot vectors U and V respectively; is a non-rational B-spline basis function defined on the node vector U, corresponding to the node p and the feature a, is a non-rational B-spline basis function defined on the node vector V, corresponding to the node q and the feature b, It is the product term of the basis function and the corresponding weight, which is used to participate in the calculation of the rational basis function; Non-uniform rational B-spline surfaces The specific expression is: ； in, A control network with two directions, that is, control points, is formed; is the weighted value of the control point; are the non-rational B-spline basis functions defined on the knot vectors U and V respectively.

9. The method for optimizing a low sidelobe shaped reflector antenna for terahertz FOD radar according to claim 8, wherein: The preset strategies include: When the control point The weighted value When it is equal to 1, the control point The controlled surface area remains in its original state; When the control point The weighted value When it is greater than 1, the control point The controlled surface area moves toward the control point Close to generate control point The controlled surface area bulges outwards; When the control point The weighted value When it is less than 1, the control point The controlled surface area moves toward the control point Move away to create a control point The controlled surface area has an inward concave effect; By controlling each control point The weighted value Adjustments are made to change the shape of the unfolded surface to obtain a corresponding second type of reflective surface.

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