WO2012025019A1 - 聚光透镜、复眼式透镜聚光器及复眼式聚光太阳电池组件 - Google Patents

聚光透镜、复眼式透镜聚光器及复眼式聚光太阳电池组件 Download PDF

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Publication number
WO2012025019A1
WO2012025019A1 PCT/CN2011/078396 CN2011078396W WO2012025019A1 WO 2012025019 A1 WO2012025019 A1 WO 2012025019A1 CN 2011078396 W CN2011078396 W CN 2011078396W WO 2012025019 A1 WO2012025019 A1 WO 2012025019A1
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WIPO (PCT)
Prior art keywords
lens
optical axis
concentrating
spot
receiving surface
Prior art date
Application number
PCT/CN2011/078396
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English (en)
French (fr)
Inventor
黄忠
刘汉
李少春
Original Assignee
成都钟顺科技发展有限公司
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Filing date
Publication date
Application filed by 成都钟顺科技发展有限公司 filed Critical 成都钟顺科技发展有限公司
Priority to US13/582,829 priority Critical patent/US9279914B2/en
Priority to EP11819394.5A priority patent/EP2610649A4/en
Priority to AU2011295603A priority patent/AU2011295603B2/en
Publication of WO2012025019A1 publication Critical patent/WO2012025019A1/zh

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Classifications

    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B3/00—Simple or compound lenses
    • G02B3/0006—Arrays
    • G02B3/0037—Arrays characterized by the distribution or form of lenses
    • G02B3/0056—Arrays characterized by the distribution or form of lenses arranged along two different directions in a plane, e.g. honeycomb arrangement of lenses
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B3/00—Simple or compound lenses
    • G02B3/0006—Arrays
    • G02B3/0037—Arrays characterized by the distribution or form of lenses
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F24—HEATING; RANGES; VENTILATING
    • F24S—SOLAR HEAT COLLECTORS; SOLAR HEAT SYSTEMS
    • F24S23/00—Arrangements for concentrating solar-rays for solar heat collectors
    • F24S23/30—Arrangements for concentrating solar-rays for solar heat collectors with lenses
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B19/00—Condensers, e.g. light collectors or similar non-imaging optics
    • G02B19/0004—Condensers, e.g. light collectors or similar non-imaging optics characterised by the optical means employed
    • G02B19/0009—Condensers, e.g. light collectors or similar non-imaging optics characterised by the optical means employed having refractive surfaces only
    • G02B19/0014—Condensers, e.g. light collectors or similar non-imaging optics characterised by the optical means employed having refractive surfaces only at least one surface having optical power
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B19/00—Condensers, e.g. light collectors or similar non-imaging optics
    • G02B19/0033—Condensers, e.g. light collectors or similar non-imaging optics characterised by the use
    • G02B19/0038—Condensers, e.g. light collectors or similar non-imaging optics characterised by the use for use with ambient light
    • G02B19/0042—Condensers, e.g. light collectors or similar non-imaging optics characterised by the use for use with ambient light for use with direct solar radiation
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B19/00—Condensers, e.g. light collectors or similar non-imaging optics
    • G02B19/0033—Condensers, e.g. light collectors or similar non-imaging optics characterised by the use
    • G02B19/0076—Condensers, e.g. light collectors or similar non-imaging optics characterised by the use for use with a detector
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/09—Beam shaping, e.g. changing the cross-sectional area, not otherwise provided for
    • G02B27/0938—Using specific optical elements
    • G02B27/095—Refractive optical elements
    • G02B27/0955—Lenses
    • G02B27/0961—Lens arrays
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B3/00—Simple or compound lenses
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B3/00—Simple or compound lenses
    • G02B3/02—Simple or compound lenses with non-spherical faces
    • G02B3/06—Simple or compound lenses with non-spherical faces with cylindrical or toric faces
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01L—SEMICONDUCTOR DEVICES NOT COVERED BY CLASS H10
    • H01L31/00—Semiconductor devices sensitive to infrared radiation, light, electromagnetic radiation of shorter wavelength or corpuscular radiation and specially adapted either for the conversion of the energy of such radiation into electrical energy or for the control of electrical energy by such radiation; Processes or apparatus specially adapted for the manufacture or treatment thereof or of parts thereof; Details thereof
    • H01L31/04—Semiconductor devices sensitive to infrared radiation, light, electromagnetic radiation of shorter wavelength or corpuscular radiation and specially adapted either for the conversion of the energy of such radiation into electrical energy or for the control of electrical energy by such radiation; Processes or apparatus specially adapted for the manufacture or treatment thereof or of parts thereof; Details thereof adapted as photovoltaic [PV] conversion devices
    • H01L31/054—Optical elements directly associated or integrated with the PV cell, e.g. light-reflecting means or light-concentrating means
    • H01L31/0543—Optical elements directly associated or integrated with the PV cell, e.g. light-reflecting means or light-concentrating means comprising light concentrating means of the refractive type, e.g. lenses
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00—Energy generation through renewable energy sources
    • Y02E10/40—Solar thermal energy, e.g. solar towers
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00—Energy generation through renewable energy sources
    • Y02E10/50—Photovoltaic [PV] energy
    • Y02E10/52—PV systems with concentrators

Definitions

  • the invention relates to a collecting lens and a compound eye lens concentrator for collecting and projecting sunlight onto a photovoltaic cell in the field of concentrating photovoltaic power generation technology; the invention also relates to a concentrating lens and a compound eye lens based on the above concentrating lens and the compound eye lens A compound eye concentrating solar cell module for an optical device.
  • Concentrated photovoltaic power generation technology is recognized as an effective way to reduce the cost of photovoltaic power generation.
  • a complete concentrating photovoltaic power generation system mainly includes a compound eye concentrating solar cell module, a solar tracker, an electric energy storage or an inverter device.
  • the compound-eye concentrating solar cell module is a photoelectric conversion component mainly composed of a compound-eye lens concentrator and a circuit board on which a photovoltaic cell wafer is mounted.
  • the compound eye lens concentrator comprises a plurality of planar array concentrating lenses.
  • the concentrating lens is substantially facing the direction of sunlight through the sun tracker, and then the sunlight is respectively collected by the concentrating lens and projected onto the receiving surface of the photovoltaic cell wafer corresponding to each concentrating lens on the circuit board. Thereby, current is generated in each photovoltaic cell wafer, and these currents are output through the lines on the circuit board.
  • the concentrating solar cell module disclosed in the invention patent application of the publication No. CN101640502A is highly representative.
  • the point-concentrating Fresnel lens used in the battery assembly has become an industry-recognized best choice for concentrating lenses.
  • Fresnel lenses are not without drawbacks.
  • the Fresnel lens can be regarded as a combination of a plurality of convex lenses with the same optical axis, so that the light spot energy distribution after the light collection is not uniform enough.
  • the use of a commonly used spherical convex lens instead of a Fresnel lens solves the problem of low light transmittance.
  • the spherical convex lens can only concentrate the light at the focus of the lens, so whether the photovoltaic cell wafer is mounted at a position slightly ahead or behind the focus of the lens will cause uneven distribution of the spot energy of the center and the periphery of the receiving surface of the battery wafer. , causing a potential difference inside the battery, thereby forming an internal current, which is consumed inside the battery, reducing the output power of the battery; in addition, the internal current is also an important cause of the temperature rise inside the battery, and the internal temperature of the battery The increase in efficiency causes the efficiency of the concentrating solar cell module to decrease.
  • the technical problem to be solved by the present invention is to provide a collecting lens which has a high transmittance and can ensure a relatively uniform light spot energy distribution after collecting light, and provides a compound eye lens collecting light using the collecting lens.
  • a collecting lens which has a high transmittance and can ensure a relatively uniform light spot energy distribution after collecting light, and provides a compound eye lens collecting light using the collecting lens.
  • the technical solution adopted by the present invention to solve the technical problem thereof is: a collecting lens which is a convex lens which can refract mutually parallel incident light to a receiving surface located outside the lens to form a spot.
  • the vertical distance between the contact point of any incident light and the lens and the optical axis of the lens is X
  • the vertical distance between the projection point formed by the incident light refracted by the lens to the receiving surface and the center of the spot is m
  • the radius of the lens is a
  • the radius of the spot is b
  • the lens has a rotating convex surface whose optical axis is an axis of rotation and an end plane opposite to the rotating convex surface, and the intersection of the rotating convex surface and any longitudinal section passing through the optical axis of the lens is a
  • the incident light rays distributed along the radial direction of the lens and parallel to the optical axis thereof may be refracted to a curve forming a projection line on the receiving surface, and the curve is reflected on the longitudinal section thereof and at the center of the end plane
  • the curve equation in the plane coordinate system whose point is the coordinate origin is:
  • the coefficient h is a linear distance between the end plane and the receiving surface; the coefficient a is the radius of the lens; the coefficient b is the length of the projection line; the coefficient n is the refractive index of the lens; and the variable X is the curve The lateral distance between any point above and the optical axis of the lens, the variable y is the longitudinal distance between the point and the end plane.
  • the curve equation is obtained without the applicant's limited experimentation with the prior art.
  • the curve equation is obtained based on the applicant's creative recognition that a better way to make the spot energy distribution uniform after concentrating is to compress the light into the receiving surface by the rotating convex surface of the lens. That is, after the incident ray is refracted to the receiving surface by any point on the curve, the point is between the abscissa X on the curve equation and the lateral distance m between the projection point on the receiving surface and the optical axis of the lens.
  • the shape of the rotating convex surface determined by the curve equation can be fully realized industrially. Since the existing lens is usually molded by molding, the shape of the rotating convex surface after molding is controlled by a molding die. In the mold design process, as long as the above curve equation is input into the mold design software, the theoretical model that can generate the curve and then rotate to form the rotating convex surface can be processed; in the mold manufacturing process, the corresponding mold cavity can be processed by the numerical control machine tool.
  • the concentrating lens disclosed above having the special curve equation is only one example of the concentrating lens to be protected by the present invention.
  • the concentrating lens having the special curve equation is a plano-convex lens, so that the incident ray parallel to the optical axis of the lens is refracted only once by the rotating convex surface of the lens, so that any incident ray and the lens are
  • the vertical distance between the contact point and the optical axis is the abscissa X of the incident ray passing through one of the points on the curve on the curve equation; the parallel incident rays are refracted by the lens to the receiving surface
  • the spot radius is the projection line half length b; and the vertical distance between the projection point of the incident light ray refracted from the contact point to the receiving surface and the center of the spot is the lateral distance m of the projection point from the optical axis of the lens.
  • plano-convex lens has a simple structure, which is advantageous for lens design and manufacture, an equivalent alternative to the concentrating lens of the above special curve equation can be employed in the teaching of the present invention.
  • the lens can also be designed as a convex lens with a convex surface on both sides.
  • the compound eye lens concentrator of the present invention comprises a plurality of planar array concentrating lenses, wherein each lens is a convex lens which can refract mutually parallel incident light to a receiving surface located outside the lens to form a spot.
  • the vertical distance between the contact point of any one of the incident light rays and the lens and the optical axis of the lens is x, and the projection point formed by the incident light refracted by the lens to the receiving surface is perpendicular to the center of the spot
  • the distance is m
  • the radius of the lens is a
  • the radius of the spot is b
  • the concentrating lens of the plurality of planar arrays on the compound eye lens concentrator can be pasted on a transparent glass plate A compound-eye concentrating solar cell module with a box structure for packaging with a circuit board.
  • these concentrating lenses can also be integrally formed with the glass plate.
  • each of the collecting lenses has a rotating convex surface with a rotating optical axis of the lens and an end plane opposite to the rotating convex surface, and the intersecting line of the rotating convex surface and any longitudinal section passing through the optical axis of the lens is Incident light rays distributed along the longitudinal direction of the lens and parallel to the optical axis thereof are refracted to a curve forming a linear spot on the receiving surface, and the curve is reflected on the longitudinal section thereof and at the center of the end plane
  • the point in the plane coordinate system of the coordinate origin :
  • the coefficient h is a linear distance between the end plane and the receiving surface; the coefficient a is the radius of the lens; the coefficient b is half length of the projection line; the coefficient n is the refractive index of the lens; the variable X is the curve The lateral distance between any point above and the optical axis of the lens, the variable y is the longitudinal distance between the point and the end plane.
  • each concentrating lens is cut into a polygonal structure having at least three cylinder faces; and any adjacent condensing lens in the compound eye concentrator is bonded by the opposite cylindrical faces of the two lenses.
  • the purpose of cutting the periphery of each collecting lens into a polygonal structure having at least three cylinders is to conveniently bond the adjacent collecting lenses to each other in the compound eye lens concentrator.
  • the lenses are in a planar array.
  • each concentrating lens is cut into a quadrilateral structure having four cylinder faces, wherein adjacent cylinder faces are perpendicular to each other; and any adjacent condensing lens in the compound eye lens concentrator passes through two lenses
  • the opposite cylindrical bonding further causes each of the collecting lenses in the fly-eye lens concentrator to have a rectangular array.
  • the periphery of each concentrating lens is cut into a quadrilateral structure having four cylinders, and the purpose of the adjacent cylinders being perpendicular to each other is to make the condensing lenses in the compound-eye lens concentrator have a rectangular array. .
  • the advantage of cutting the periphery of the concentrating lens into a quadrangular structure is that the shape of the spot after concentrating is also a quadrangular structure, so that each photovoltaic cell wafer can also be formed into a quadrangular structure, so that when performing battery cutting, It saves material and is easy to process.
  • the present invention also provides a compound eye concentrating solar cell module using the above-described compound eye lens concentrator.
  • the beneficial effects of the invention are as follows: the optical simulation experiment shows that the transmittance of the concentrating lens is as high as 90% ⁇ 93%, and the spot energy distribution curve is approximated by the saddle shape after concentrating through the concentrating lens, that is, the spot is displayed. The energy distribution is even.
  • the concentrating lens of the invention can be used not only in the field of concentrating photovoltaic power generation technology, but also for other uniform concentrating light. Required on the optical device.
  • FIG. 1 is an exploded perspective view of a compound eye lens concentrator of the present invention.
  • Figure 1 (a) is a schematic view of the overall structure of a compound eye lens concentrator.
  • Figure 1 (b) is a schematic view showing the structure of a single collecting lens in a compound eye lens concentrator.
  • Figure 2 is an enlarged view of Figure 1 (b).
  • Fig. 3 is a full cross-sectional view taken along line A of Fig. 2 (with a longitudinal section 2 as a section).
  • Figure 4 is a diagram showing the energy distribution of the spot after using a conventional spherical convex lens as a collecting lens.
  • the brightness of the spot indicates the level of energy, and the higher the brightness, the higher the energy.
  • Fig. 5 is a light spot energy distribution curve after a conventional spherical convex lens is used as a collecting lens.
  • Fig. 5 The abscissa of Fig. 5 is the spot width, and the ordinate is the energy intensity. Therefore, Fig. 5 can be regarded as observing the spot energy distribution on the cross section or the longitudinal section of Fig. 4.
  • Fig. 6 is a view showing the light spot energy distribution after the condensing lens of the present invention is used.
  • the brightness of the spot indicates the level of energy, and the higher the brightness, the higher the energy.
  • Fig. 7 is a light spot energy distribution curve after the condensing lens of the present invention is used.
  • Fig. 7 The abscissa of Fig. 7 is the spot width, and the ordinate is the energy intensity. Therefore, Fig. 5 can be regarded as observing the spot energy distribution on the cross section or the longitudinal section of Fig. 4.
  • Fig. 8 is a schematic view showing another embodiment of the concentrating lens of the present invention.
  • FIG. 9 is a schematic structural view of a compound eye concentrating solar cell module of the present invention.
  • the compound eye concentrating solar cell assembly shown in FIG. 9 is a box-type structure which is packaged by a compound eye lens concentrator 5 and a circuit board 6 on which a plurality of photovoltaic cell wafers 7 are mounted; ⁇ 3, wherein the compound eye lens concentrator 5 has a plurality of planar array concentrating lenses 1 , each of which refracts incident light 3 parallel to its optical axis 103 to a convex lens on the receiving surface 4 of the photovoltaic cell wafer 7 corresponding to the collecting lens 1; wherein, as shown in FIGS.
  • each of the collecting lenses 1 has a rotating convex surface 101 with the lens optical axis 103 as a rotating axis and
  • the opposite end plane 102 of the rotating convex surface 101, the intersection of the rotating convex surface 101 and any one of the longitudinal cross sections 2 passing through the optical axis 103 of the lens is a refracting incident light ray 3 distributed along the radial direction of the lens in the longitudinal section 2 to
  • a curve 104 of a projection straight line is formed on the receiving surface 4, and the curve equation in the plane coordinate system of the longitudinal section 2 on which the curve 104 is located and whose center point of the end plane 102 is the coordinate origin A is:
  • the coefficient h is a linear distance between the end plane 102 and the receiving surface 4;
  • the coefficient a is the radius of the collecting lens 1;
  • the coefficient b is the half length of the projection straight line;
  • the coefficient n is the refractive index of the lens;
  • the variable X is the lateral distance between any point B on the curve 104 and the optical axis 103 of the lens, and the variable y is the longitudinal distance between the point B and the end plane 102.
  • the curve equation is obtained based on the applicant's creative recognition that a better way to make the spot energy distribution uniform after concentrating is to compress the light proportionally onto the receiving surface 4 by the rotating convex surface 101 of the lens. That is, after the incident ray 3 is refracted to the receiving surface 4 through any point B on the curve 104, the abscissa X of the point B on the curve equation and the projection point on the corresponding receiving surface are from the lens optical axis 103.
  • Tan ( 6 ) ⁇ (4)
  • the variables " ⁇ " and “ ⁇ " represent the magnitude of the incident angle and the angle of refraction, respectively, as the ray passes through the curve. The remaining coefficients and the meaning of the variables have been explained above. Based on the equations, the above curve equation can be derived mathematically.
  • each concentrating lens 1 is cut into a polygonal structure having at least three cylinders 105; between the adjacent condensing lenses 1 of the fly-eye lens concentrator, the opposite columns are passed through the two lenses.
  • the face 105 is bonded.
  • the purpose of cutting the periphery of each concentrating lens 1 into a polygonal structure having at least three cylinders 105 is to facilitate bonding of the adjacent concentrating lenses 1 to each other in the fly-eye lens concentrator.
  • Each of the collecting lenses 1 is in a planar array.
  • each concentrating lens 1 is cut into a quadrangular structure having four cylindrical faces 105, wherein adjacent cylindrical faces 105 are perpendicular to each other; and any adjacent condensing lens 1 of the compound eye lens concentrator
  • Each of the collecting lenses 1 in the fly-eye lens concentrator is in a rectangular array by being bonded by the opposing cylindrical faces 105 of the two lenses.
  • each will be condensed
  • the periphery of the mirror 1 is cut into a quadrangular structure having four cylindrical faces 105, and the purpose of the adjacent cylindrical faces 105 being perpendicular to each other is such that each of the collecting lenses 1 in the compound-eye lens concentrator has a rectangular array.
  • each of the collecting lenses 1 in the fly-eye lens concentrator has a rectangular array is that the spot refracted by these collecting lenses 1 is also rectangular, so that the shape of the photovoltaic cell wafer 7 can be designed to be rectangular. Since these photovoltaic cell wafers 7 are cut by a large cell sheet, when the photovoltaic cell wafer 7 is rectangular, it is easy to cut while saving material.
  • the concentrating lens 1 used in the compound-eye lens concentrator in the compound-eye concentrating solar cell module of the present invention is compared with the uniformity of the spot energy distribution after concentrating the ordinary spherical lenticular lens.
  • the spot energy distribution of the ordinary spherical convex lens after concentrating as shown in Fig. 4, the brightness of the center of the spot is the highest, and the brightness of the periphery is suddenly lowered; reflected on the graph shown in Fig. 5 is a steeply rising wave shape.
  • Figures 4 to 5 show that the energy is concentrated in the center of the spot, and the energy distribution is extremely uneven.
  • the spot energy distribution after concentrating the concentrating lens 1 used in the present invention as shown in FIG.
  • the brightness of the rectangular spot is uniform; reflected on the graph shown in FIG. 7 is approximately a "saddle" shape, indicating that the spot is on the spot.
  • the energy of each point is located at the peak position of the "saddle” curve, and the energy distribution is relatively uniform.
  • the transmittance of the concentrating lens of the present invention is as high as 90% to 93%, and the transmittance of the Fresnel lens is about 75%, which proves that the concentrating lens of the present invention also has Good transmission rate.
  • the condensing lens 1 of the present invention can also be realized in the manner shown in FIG.
  • the both side faces of the collecting lens shown in Fig. 8 are respectively rotating convex surfaces.
  • the intersection of the two rotating convex surfaces and any one of the longitudinal sections 2 passing through the optical axis 103 of the lens is the curve 106 and the curve 107 shown in Fig. 8, respectively. If the point F shown in FIG. 8 is taken as the coordinate origin (ie, the lens optical center), the lens radius is a, and the projection point formed by the incident light passing through the lens edge and refracted to the receiving surface 4 is perpendicular to the optical axis 103.
  • the distance is b
  • the point C (x, y) is the intersection of any incident ray 3 and the curve 106
  • the point D (xl, yl) is the intersection of the ray refracted by the incident ray 3 through the curve 106 and the curve 107, the incident
  • the projection point of the ray 3 on the receiving surface 4 after being twice refracted by the lens is the point E (m, h), and the incident angle ⁇ of the angle Y and C at the point D on the curve 107 and the optical axis 103
  • the angles of incidence ⁇ and the angle of refraction ⁇ of the refraction angle ⁇ and the point D are unknown
  • the lens radius is a
  • the incident light is formed by the lens edge and refracted onto the receiving surface 4
  • the vertical distance b between the projection point and the optical axis 103 and the refractive index of the lens are both known numbers, and the following set of equations can be obtained
  • curve equations of curve 106 and curve 107 can be derived.

Description

聚光透镜、 复眼式透镜聚光器及复眼式聚光太阳电池组件 技术领域
本发明涉及聚光光伏发电技术领域中用于将太阳光汇聚并投射到光伏电池上的聚光 透镜及复眼式透镜聚光器；本发明还涉及一种基于上述聚光透镜和复眼式透镜聚光器的复 眼式聚光太阳电池组件。
背景技术
聚光光伏发电技术是公认的可降低光伏发电成本的有效途径。 目前， 一个完整的聚光 光伏发电系统主要包括复眼式聚光太阳电池组件、太阳跟踪器、 电能存储或逆变设备等几 部分。 复眼式聚光太阳电池组件作为光电转换部件， 主要由复眼式透镜聚光器和安装有光 伏电池晶片的电路板所组成。
其中， 复眼式透镜聚光器包括多块平面阵列的聚光透镜。使用时通过太阳跟踪器使聚 光透镜基本正对阳光照射方向，然后通过这些聚光透镜分别将太阳光汇聚并投射到电路板 上与各个聚光透镜相对应的光伏电池晶片的接收面上，从而使各个光伏电池晶片中产生电 流， 这些电流通过电路板上的线路输出。
公开号为 CN101640502A的发明专利申请文件所公开的聚光太阳电池组件极具代表 性。该电池组件中采用的点聚光菲涅尔透镜已成为业界公认的聚光透镜的最佳选折。仍有 许多公开了采用聚光菲涅尔透镜作聚光透镜的聚光光伏发电技术的参考文献，在此不再赘 述。
实际上，采用菲涅尔透镜并非没有缺憾。比如， 由于菲涅尔透镜表面纹路的加工缺陷， 会造成一部分入射光线的损失， 导致光线透过率仅处于 75 %左右的较低水平上； 而且这 种加工缺陷又是以目前的加工技术所难以克服的。又如， 菲涅尔透镜可看成由多个同光轴 凸透镜的组合， 故其聚光后光斑能量分布不够均匀。
采用普遍使用的球面凸透镜替代菲涅尔透镜可解决光线透过率较低的问题。然而， 球 面凸透镜只能将光线集中于该透镜的焦点， 因此无论将光伏电池晶片安装在其焦点略靠前 或靠后的位置， 都会造成电池晶片接收面的中心与周边的光斑能量分布不均， 致使电池内 部产生电势差， 进而形成内部电流， 这一部分电流会在电池内部消耗掉， 减小了电池输出 功率； 另外， 内部电流的产生也是电池内部的温度升高的重要原因， 而电池内部温度升高 又使得聚光太阳电池组件的效率下降。
发明内容 本发明所解决的技术问题是提供一种既具有较高的透过率又能够保证聚光后光斑能 量分布较为均匀的聚光透镜， 并提供一种使用该聚光透镜的复眼式透镜聚光器。
本发明解决其技术问题所采用的技术方案是： 一种聚光透镜， 该透镜为一块可将相互 平行的入射光线折射到一个位于该透镜外侧的接收面上进而形成光斑的凸透镜，若设其中 任意一条入射光线和所述透镜的接触点与该透镜光轴之间的垂直距离为 X， 该入射光线经 透镜折射到所述接收面上后形成的投影点与所述光斑中心的垂直距离为 m， 并且该透镜的 半径为 a， 所述光斑的半径为 b， 则该透镜满足以下条件， 即： x/m=a/b。
作为上述技术方案的优选方案，该透镜具有以其光轴为旋转轴的旋转凸面以及与该旋 转凸面相对的端平面，该旋转凸面与任意一个通过该透镜光轴的纵截面的交线为一条可使 该纵截面上沿透镜径向分布并与其光轴平行的入射光线折射到所述接收面上形成投影直 线的曲线，将该曲线反映在其所在纵截面上并以所述端平面的中心点为坐标原点的平面坐 标系中的曲线方程为：
Figure imgf000004_0001
其中， 系数 h为所述端平面与接收面之间的直线距离； 系数 a为所述透镜的半径； 系数 b为所述投影直线的长； 系数 n为透镜折射率； 变量 X为所述曲线上任意一点与透镜光轴之 间的横向距离， 变量 y为该点与端平面之间的纵向距离。
必须指出，该曲线方程的获得并不是申请人在现有技术的启示下进行有限次实验就能 够得到的。 实际上， 该曲线方程的获得是基于申请人创造性的认识到， 要使聚光后光斑能 量分布均匀的一个较好办法， 是通过透镜的旋转凸面将光线等比例压缩到接收面上。 也就 是说， 当入射光线经过所述曲线上的任意一点折射到接收面上以后， 该点在曲线方程上的 横坐标 X与接收面上的投影点距透镜光轴的横向间距 m之间的比值，应该等于所述透镜的半 径 a与所述投影直线半长 b之间的比值， gPx/m=a/b。 根据已知的透镜折射规律并结合上面 的等式， 可得到下面一组方程：
x/m=a/b ( 1 )
sin ( Θ ) =nsin ( β ) ( 2 )
x-m= (h-y) tan ( β - θ ) ( 3 ) tan ( 6 ) =牟 （4) 其中， 变量 " θ "和 " β "分别表示光线经过所述曲线时的入射角大小和折射角大小。 其余系数及变量的含义均已在上面进行了解释。在上述方程组的基础上， 经数学推导可得 到上述曲线方程。
该曲线方程所决定的旋转凸面的形状完全能够在产业上得以实现。由于现有透镜通常 采用模压的方式成型， 成型后旋转凸面的形状通过成型模具来控制。 在模具设计过程中， 只要将上述曲线方程输入模具设计软件， 即能够生成曲线再旋转形成旋转凸面的理论数 模； 在模具制造过程中通过数控机床就能够加工出相应的模具型腔。
申请人还需要指出的是，上面所公开的具有所述特殊曲线方程的聚光透镜仅仅是本发 明所要保护的聚光透镜中的一个实例而已。 实际上， 这个具有所述特殊曲线方程的聚光透 镜是一个平凸透镜， 因此与该透镜光轴平行的入射光线仅由该透镜的旋转凸面进行一次折 射，故任意一条入射光线和所述透镜的接触点与光轴之间的垂直距离就是该入射光线经过 所述曲线上的其中一点在曲线方程上的横坐标 X； 这些平行的入射光线经该透镜折射到所 述接收面上后所形成的光斑半径就是所述投影直线半长 b; 并且入射光线从该接触点经透 镜折射到接收面上的投影点与光斑中心的垂直距离就是该投影点距透镜光轴的横向间距 m。
虽然平凸透镜具有结构简单， 利于透镜设计和制造等优点， 但是在本发明的技术启示 下， 还可采用与上述特殊曲线方程的聚光透镜的等同替代方案。 比如也可以将透镜设计为 两面均为旋转凸面的凸透镜。 这时， 只要遵循 x/m=a/b (其中， 设入射光线和所述透镜的 接触点与该透镜光轴之间的垂直距离为 x， 该入射光线经透镜折射到所述接收面上后形成 的投影点与所述光斑中心的垂直距离为 m， 并且该透镜的半径为 a， 所述光斑的半径为 b ) 的条件， 并结合已知的镜折射规律， 就可以推导出这两个旋转凸面的方程， 并最终获得这 两个旋转凸面的理论数模。
本发明的复眼式透镜聚光器包括多块平面阵列的聚光透镜，所述各透镜为一块可将相 互平行的入射光线折射到一个位于该透镜外侧的接收面上进而形成光斑的凸透镜，若设其 中任意一条入射光线和所述透镜的接触点与该透镜光轴之间的垂直距离为 x， 该入射光线 经透镜折射到所述接收面上后形成的投影点与所述光斑中心的垂直距离为 m， 并且该透镜 的半径为 a， 所述光斑的半径为 b， 则该透镜满足以下条件， 即： x/m=a/b。
其中，该复眼式透镜聚光器上的多块平面阵列的聚光透镜可粘贴在一块透明的玻璃板 上以便与电路板封装成的一个箱型结构的复眼式聚光太阳电池组件。 当然， 这些聚光透镜 也可以与该玻璃板一体成型。
具体的，所述各聚光透镜具有以透镜光轴为旋转轴的旋转凸面以及与该旋转凸面相对 的端平面，该旋转凸面与任意一个通过该透镜光轴的纵截面的交线为一条可使该纵截面上 沿透镜径向分布并与其光轴平行的入射光线折射到一个所述接收面上形成直线光斑的曲 线，将该曲线反映在其所在纵截面上并以所述端平面的中心点为坐标原点的平面坐标系中 的曲 ：
Figure imgf000006_0001
其中， 系数 h为所述端平面与接收面之间的直线距离； 系数 a为所述透镜的半径； 系数 b为所述投影直线半长； 系数 n为透镜折射率； 变量 X为所述曲线上任意一点与透镜光轴之 间的横向距离， 变量 y为该点与端平面之间的纵向距离。
进一步的， 各聚光透镜的周边被截成具有至少三个柱面的多边形结构； 该复眼式透镜 聚光器中任意相邻聚光透镜之间通过两透镜相对的柱面粘接。显然， 将各聚光透镜的周边 截成具有至少三个柱面的多边形结构的目的，是为了方便的将相邻聚光透镜之间粘接起来 使复眼式透镜聚光器中的各聚光透镜呈平面阵列。
具体的， 各聚光透镜的周边被截成具有四个柱面的四边形结构， 其中相邻柱面之间相 互垂直；该复眼式透镜聚光器中任意相邻聚光透镜之间通过两透镜相对的柱面粘接进而使 该复眼式透镜聚光器中的各聚光透镜呈矩形阵列。显然， 将各聚光透镜的周边截成具有四 个柱面的四边形结构， 且相邻柱面之间相互垂直的目的， 是使该复眼式透镜聚光器中的各 聚光透镜呈矩形阵列。 并且， 将聚光透镜的周边截成四边形结构的好处还在于， 聚光后光 斑的形状也为四边形结构， 因此相应的可将各光伏电池晶片也制成四边形结构， 这样在进 行电池切割时既能够节省材料又可以便于加工。
本发明还提供了一种采用了上述复眼式透镜聚光器的复眼式聚光太阳电池组件。 本发明的有益效果是： 通过光学模拟实验发现， 该聚光透镜的透过率高达 90 %〜93 % , 并且通过该聚光透镜聚光后光斑能量分布曲线近似 "马鞍"形， 即表明光斑能量分布 均匀。本发明的聚光透镜不仅可用于聚光光伏发电技术领域， 也可用于其他具有均匀聚光 要求的光学设备上。
附图说明
图 1 为本发明复眼式透镜聚光器的分解示意图。
图 1 ( a) 为复眼式透镜聚光器的整体结构示意图。
图 1 (b ) 为构成复眼式透镜聚光器中单个聚光透镜的结构示意图。
图 2为图 1 (b ) 的放大图。
图 3为图 2的 A向全剖视图 （以纵截面 2为剖面）。
图 4为采用传统球面凸透镜作为聚光透镜后光斑能量分布图。
图 4中光斑亮度表示能量高低， 亮度越高表示能量越高。
图 5为采用传统球面凸透镜作为聚光透镜后光斑能量分布曲线。
图 5的横坐标为光斑宽度， 纵坐标为能量强度。 因此， 图 5可以看作在图 4的横截面 或纵截面上观察光斑能量分布。
图 6为采用本发明的聚光透镜后光斑能量分布图。
图 6中光斑亮度表示能量高低， 亮度越高表示能量越高。
图 7为采用本发明的聚光透镜后光斑能量分布曲线。
图 7的横坐标为光斑宽度， 纵坐标为能量强度。 因此， 图 5可以看作在图 4的横截面 或纵截面上观察光斑能量分布。
图 8为本发明聚光透镜另一种实施方式的示意图。
图 9为本发明复眼式聚光太阳电池组件的结构示意图。
具体实施方式
下面结合附图对本发明做进一步的说明。
如图 9所示的复眼式聚光太阳电池组件，该组件是由复眼式透镜聚光器 5和安装有多 片光伏电池晶片 7的电路板 6封装而成的一个箱型结构； 如图 1〜3所示， 其中的复眼式 透镜聚光器 5具有多块平面阵列的聚光透镜 1， 这些聚光透镜 1均为一块可将平行于其光 轴 103的入射光线 3折射到一个与该聚光透镜 1对应的光伏电池晶片 7的接收面 4上的凸 透镜； 其中， 如图 2〜3所示， 所述各聚光透镜 1具有以透镜光轴 103为旋转轴的旋转凸 面 101以及与该旋转凸面 101相对的端平面 102， 该旋转凸面 101与任意一个通过该透镜 光轴 103的纵截面 2的交线为一条可使该纵截面 2上沿透镜径向分布的入射光线 3折射到 所述接收面 4上形成投影直线的曲线 104， 将该曲线 104反映在其所在纵截面 2上并以所 述端平面 102的中心点为坐标原点 A的平面坐标系中的曲线方程为：
Figure imgf000008_0001
其中， 系数 h为所述端平面 102与接收面 4之间的直线距离； 系数 a为所述聚光透镜 1的半径； 系数 b为所述投影直线的半长； 系数 n为透镜折射率； 变量 X为所述曲线 104 上任意一点 B与透镜光轴 103之间的横向距离，变量 y为该点 B与端平面 102之间的纵向 距离。
该曲线方程的获得是基于申请人创造性的认识到，要使聚光后光斑能量分布均匀的一 个较好办法， 是通过透镜的旋转凸面 101将光线等比例压缩到接收面 4上。 也就是说， 当入 射光线 3经过所述曲线 104上的任意一点 B折射到接收面 4上以后， 该点 B在曲线方程上的横 坐标 X与对应接收面上的投影点距透镜光轴 103的横向间距 m之间的比值， 应该等于所述聚 光透镜 1的半径 a与所述投影直线半长 b之间的比值， gPx/m=a/b。根据已知的镜折射规律并 结合上面的等式， 可得到下面一组方程：
x/m=a/b ( 1 )
sin ( Θ ) =nsin ( β ) ( 2 )
x-m= (h-y) tan ( β - θ ) ( 3 )
tan ( 6 ) =牟 （4) 其中， 变量 " θ "和 " β "分别表示光线经过所述曲线时的入射角大小和折射角大小。 其余系数及变量的含义已在上面进行了解释。在该方程组的基础上， 可数学推导得到上述 曲线方程。
如图 2所示， 各聚光透镜 1的周边被截成具有至少三个柱面 105的多边形结构； 该复 眼式透镜聚光器中任意相邻聚光透镜 1之间通过两透镜相对的柱面 105粘接。显然， 将各 聚光透镜 1的周边截成具有至少三个柱面 105的多边形结构的目的，是为了方便的将相邻 聚光透镜 1之间粘接起来使复眼式透镜聚光器中的各聚光透镜 1呈平面阵列。
具体的， 各聚光透镜 1的周边被截成具有四个柱面 105的四边形结构， 其中相邻柱面 105之间相互垂直； 该复眼式透镜聚光器中任意相邻聚光透镜 1之间通过两透镜相对的柱 面 105粘接进而使该复眼式透镜聚光器中的各聚光透镜 1呈矩形阵列。显然， 将各聚光透 镜 1的周边截成具有四个柱面 105的四边形结构， 且相邻柱面 105之间相互垂直的目的， 是使该复眼式透镜聚光器中的各聚光透镜 1呈矩形阵列。
使该复眼式透镜聚光器中的各聚光透镜 1呈矩形阵列的好处在于， 经这些聚光透镜 1 折射的光斑也为矩形， 因此可将光伏电池晶片 7的形状设计为矩形。 由于这些光伏电池晶 片 7是通过一块较大的电池片切割而成的， 当光伏电池晶片 7为矩形时， 即能够便于切割 同时又可以节省材料。
现对本发明复眼式聚光太阳电池组件中的复眼式透镜聚光器所使用的聚光透镜 1 与 普通球面凸透镜聚光后光斑能量分布均匀性进行对比。对于普通球面凸透镜聚光后光斑能 量分布， 如图 4所示， 光斑中心的亮度最高， 其周边亮度骤然降低； 反映在图 5所示的曲 线图上为一陡然升降的波浪形。 图 4〜5说明能量集中在光斑的中心部位， 可见能量分布 极不均匀。 对于本发明所使用的聚光透镜 1聚光后光斑能量分布， 如图 6所示， 矩形光斑 的亮度一致； 反映在图 7所示的曲线图上近似为一 "马鞍"形， 说明光斑上各点能量均位 于 "马鞍"形曲线的波峰位置， 可见能量分布比较均匀。
此外， 通过光线透过率测试， 发现本发明的聚光透镜的透过率高达 90 %〜93 %， 而 菲涅尔透镜的透过率为 75 %左右， 证明本发明的聚光透镜还具有良好的透过率。
申请人还需要说明的是， 在进行上述对比时， 已将两个试验的光线的入射总能量调整 一致， 并保证了接收面上的光斑大小基本相等。 对于图 7所示的曲线图， 其波峰位置并不 是十分平滑， 在一定范围内具有上下波动， 主要由于本试验模拟的是太阳光谱， 光线能量 本身就不是十分均匀造成 。
本发明的聚光透镜 1也可以采用图 8所示的方式得以实现。图 8所示的聚光透镜的两 侧面分别为旋转凸面。这两个旋转凸面与任意一个通过该透镜光轴 103的纵截面 2的交线 分别为图 8中所示的曲线 106和曲线 107。 若以图 8中所示的 F点为坐标原点 （即透镜光 心）， 设透镜半径为 a， 入射光线经该透镜边缘并折射到接收面 4上后形成的投影点与光 轴 103的垂直距离为 b， 点 C ( x, y) 为任意一入射光线 3与曲线 106的交点， 点 D ( xl， yl )为该入射光线 3经过曲线 106折射后的光线与曲线 107的交点， 该入射光线 3经透镜 两次折射后在接收面 4上的投影点为点 E (m， h)， 曲线 107上点 D处的法线与光轴 103 的夹角 Y、 C点的入射角 Θ和折射角 β以及 D点的入射角 ε和折射角 α均为未知数， 透镜 半径为 a、 坐标原点 F与接收面 4的垂直距离 h、 入射光线经该透镜边缘并折射到接收面 4上后形成的投影点与光轴 103的垂直距离 b以及透镜的折射率均为已知数， 可得到下面 的一组方程： x/m=a/b ( 1 )
sin ( Θ ) =nsin ( β ) (2)
tan(6)= 牟 (3)
tan ( θ - β ) = (x-xl) I (y+yl) (4)
sin ( a ) =nsin[ y + ( θ - β ) ] (5)
tan ( a -y ) = (xl- m) / (h- yl) (6)
tan Y (7)
dxl
并且， 由于该聚光透镜的两侧面分别为旋转凸面， 因此还具有如下边界条件， 即： 当 X =0时， tan Θ =0
当 xl = 0时， tan y =0
这样， 就能够推导出曲线 106和曲线 107的曲线方程。
通过上面两个具体实施方式， 总结出本发明的关键是运用了以下思路： 若设其中任意 一条入射光线 3和所述透镜的接触点与该透镜光轴 103之间的垂直距离为 x， 该入射光线 3经透镜折射到所述接收面 4上后形成的投影点与所述光斑中心的垂直距离为 m， 并且该 透镜的半径为 a， 所述光斑的半径为 b， 则该透镜应满足以下条件， 即： x/m=a/b。

Claims

权利要求书
1、 一种聚光透镜， 该透镜为一块可将相互平行的入射光线 （3)折射到一个位于该透 镜外侧的接收面 （4) 上进而形成光斑的凸透镜， 其特征在于： 若设其中任意一条入射光 线 （3) 和所述透镜的接触点与该透镜光轴 （103) 之间的垂直距离为 x， 该入射光线 （3) 经透镜折射到所述接收面 （4) 上后形成的投影点与所述光斑中心的垂直距离为 m， 并且 该透镜的半径为 a， 所述光斑的半径为 b， 则该透镜满足以下条件， 即： x/m=a/b。
2、 如权利要求 1所述的聚光透镜， 其特征在于： 该透镜具有以其光轴 （103) 为旋转 轴的旋转凸面 （101) 以及与该旋转凸面 （101)相对的端平面 （102)， 该旋转凸面 （101) 与任意一个通过该透镜光轴 （103) 的纵截面 （2) 的交线为一条可使该纵截面 （2) 上沿 透镜径向分布并与其光轴 （103) 平行的入射光线 （3) 折射到所述接收面 （4) 上形成投 影直线的曲线 （104)， 将该曲线 （104) 反映在其所在纵截面 （2) 上以所述端平面 （102) 的中
Figure imgf000011_0001
其中， 系数 h为所述端平面 （102) 与接收面 （4)之间的直线距离； 系数 a为所述透 镜的半径;系数 b为所述投影直线的半长;系数 n为透镜折射率;变量 X为所述曲线上（ 104) 任意一点 （B) 与透镜光轴 （103) 之间的横向距离， 变量 y为该点 （B) 与端平面 （102) 之间的纵向距离。
3、 如权利要求 2所述的聚光透镜， 其特征在于： 该透镜的周边被截成具有至少三个 柱面 （105) 的多边形结构。
4、 如权利要求 3所述的聚光透镜， 其特征在于： 该透镜的周边被截成具有四个柱面 (105) 的四边形结构， 其中相邻柱面 （105) 之间相互垂直。
5、 复眼式透镜聚光器， 包括多块平面阵列的聚光透镜 （1)， 所述各透镜为一块可将 相互平行的入射光线 （3)折射到一个位于该透镜外侧的接收面 （4)上进而形成光斑的凸 透镜， 其特征在于： 若设其中任意一条入射光线 （3) 和所述透镜的接触点与该透镜光轴
(103) 之间的垂直距离为 x， 该入射光线 （3) 经透镜折射到所述接收面 （4) 上后形成 的投影点与所述光斑中心的垂直距离为 m， 并且该透镜的半径为 a， 所述光斑的半径为 b， 则该透镜满足以下条件， 即： x/m=a/b。
6、 如权利要求 5所述的复眼式透镜聚光器， 其特征在于： 所述各聚光透镜 （1)具有 以透镜光轴 （103) 为旋转轴的旋转凸面 （101) 以及与该旋转凸面 （101) 相对的端平面
(102)， 该旋转凸面 （101) 与任意一个通过该透镜光轴 （103) 的纵截面 （2) 的交线为 一条可使该纵截面 （2) 上沿透镜径向分布并与其光轴 （103) 平行的入射光线 （3) 折射 到所述接收面 （4) 上形成投影直线的曲线 （104)， 将该曲线 （104) 反映在其所在纵截面
(2)上并以所述端平面 （102) 的中心点为坐标原点 （A) 的平面坐标系中的曲线方程为：
Figure imgf000012_0001
其中， 系数 h为所述端平面 （102) 与接收面 （4)之间的直线距离； 系数 a为所述透 镜的半径;系数 b为所述投影直线的半长;系数 n为透镜折射率;变量 X为所述曲线上（ 104) 任意一点 （B) 与透镜光轴 （103) 之间的横向距离， 变量 y为该点 （B) 与端平面 （102) 之间的纵向距离。
7、 如权利要求 6所述的复眼式透镜聚光器， 其特征在于： 各聚光透镜 （1) 的周边被 截成具有至少三个柱面 （105) 的多边形结构； 该复眼式透镜聚光器中任意相邻聚光透镜 (1) 之间通过两透镜相对的柱面 （105) 粘接。
8、 如权利要求 7所述的复眼式透镜聚光器， 其特征在于： 各聚光透镜 （1) 的周边被 截成具有四个柱面 （105) 的四边形结构， 其中相邻柱面 （105)之间相互垂直； 该复眼式 透镜聚光器中任意相邻聚光透镜 （1)之间通过两透镜相对的柱面 （105)粘接进而使该复 眼式透镜聚光器中的各聚光透镜 （1) 呈矩形阵列。
9、 复眼式聚光太阳电池组件， 该组件是由复眼式透镜聚光器（5)和安装有多片光伏 电池晶片 （7) 的电路板 （6) 封装而成的一个箱型结构， 所述复眼式透镜聚光器 （5) 具 有多块平面阵列的聚光透镜 （1)， 这些聚光透镜 （1) 均为一块可将相互平行的入射光线 (3) 折射到一个位于该透镜外侧的接收面 （4) 上进而形成光斑的凸透镜， 其特征在于： 若设其中任意一条入射光线 （3)和所述透镜的接触点与该透镜光轴 （103)之间的垂直距 离为 x， 该入射光线 （3) 经透镜折射到所述接收面 （4) 上后形成的投影点与所述光斑中 心的垂直距离为 m， 并且该透镜的半径为 a， 所述光斑的半径为 b， 则该透镜满足以下条 件， BP : x/m=a/b。
10、如权利要求 9所述的复眼式聚光太阳电池组件，其特征在于：所述各聚光透镜（1 ) 具有以透镜光轴 （103) 为旋转轴的旋转凸面 （101 ) 以及与该旋转凸面 （101 ) 相对的端 平面 （102 )， 该旋转凸面 （101 ) 与任意一个通过该透镜光轴 （103) 的纵截面 （2) 的交 线为一条可使该纵截面 （2) 上沿透镜径向分布并与其光轴 （103 ) 平行的入射光线 （3) 折射到所述接收面 （4) 上形成投影直线的曲线 （104)， 将该曲线 （104) 反映在其所在纵 截面 （2 ) 上并以所述端平面 （102) 的中心点为坐标原点 （A) 的平面坐标系中的曲线方 程为：
Figure imgf000013_0001
其中， 系数 h为所述端平面 （102) 与接收面 （4)之间的直线距离； 系数 a为所述透 镜的半径;系数 b为所述投影直线的半长;系数 n为透镜折射率;变量 X为所述曲线上（ 104) 任意一点 （B) 与透镜光轴 （103) 之间的横向距离， 变量 y为该点 （B) 与端平面 （102) 之间的纵向距离。
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