Design method of high-uniformity Fresnel lens of equal-width receiving area

Abstract

The invention discloses a method for designing a high-uniformity Fresnel lens with equal-width receiving areas, which comprises the following steps of: dividing a receiving surface of the Fresnel lens into a plurality of receiving areas with equal width, and establishing an energy equation of each receiving area and the Fresnel lens; based on the energy equation and a preset condensation ratio, determining the number of ring teeth of the Fresnel lens corresponding to each receiving area; determining a critical value of the ring tooth inclination angle of the Fresnel lens, and determining the focal length of the Fresnel lens according to the critical value of the ring tooth inclination angle; and designing a lens generatrix, and obtaining a size parameter of each ring tooth in the Fresnel lens corresponding to each receiving area. According to the invention, equal energy density distribution on the receiving surface is taken as a design idea, and the receiving surface is divided into a plurality of receiving areas with the same width so as to design parameters of each ring tooth of the Fresnel lens, so that high-uniformity distribution of energy density is realized, and the problem of non-uniform energy distribution on the receiving surface after condensation of the Fresnel lens is solved.

Description

Technical Field

[0001] The invention belongs to the technical field of space solar power stations, and in particular relates to a design method for a high-uniformity Fresnel lens with an equal-width receiving area. Background Art

[0002] Once the concept of space solar power station (SSPS) was proposed, it has been widely studied by scholars from all over the world. At present, there are dozens of space solar power station schemes. The concentrating scheme has attracted a lot of attention due to its innovative energy collection mode and structural configuration. In 2012, Mankins proposed the ALPHA scheme, whose overall structure is like a wine glass and adopts a highly modular design, but it is difficult to track the sun, has large energy fluctuations, and has a low collection rate. In 2015, the team of Academician Duan Baoyan of Xidian University proposed an innovative OMEGA scheme. The concentrating system of this scheme uses the spherical concentrating characteristics for energy collection. It is composed of hexagonal thin film units of one-way light-transmitting materials. The system control is simple and the energy collection rate is high. In addition to the reflective concentrating scheme, Ian Cash proposed a CASSIOPeiA scheme similar to the DNA double helix structure in 2017, which uses Fresnel lenses for concentrating. However, after high-power concentrating, there are problems of uneven energy distribution and excessive local energy concentration.

[0003] However, the Fresnel focusing system still has its unique advantages, such as light weight, easy processing, high transmittance, and easy modular production and assembly. The lens formed by the high-transmittance PI film also has the characteristics of high environmental adaptability. Therefore, the Fresnel focusing system still has good application prospects. In 2022, Duc TV and others proposed a cylindrical Fresnel lens concentrator with a receiving angle of 60°, but its spatial configuration is complex, and the energy collection efficiency and energy distribution uniformity on the receiving surface are low. In 2023, Hani B. proposed a two-stage Fresnel concentrator, which has a high energy collection efficiency on the receiving surface, but the use of a secondary reflector increases the quality of the system and the difficulty of designing and manufacturing the solution. Summary of the invention

[0004] In order to solve the above problems existing in the prior art, the present invention provides a method for designing a Fresnel lens with high uniformity in a receiving area of ​​equal width. The technical problem to be solved by the present invention is achieved by the following technical solutions:

[0005] The present invention provides a method for designing a Fresnel lens with high uniformity and equal width receiving area, comprising:

[0006] S1: Divide the receiving surface of the Fresnel lens to be designed into a plurality of receiving areas with equal widths, and establish an energy equation between each receiving area and the Fresnel lens;

[0007] S2: Determine the number of ring teeth on the Fresnel lens corresponding to each receiving area based on the energy equation and a preset light concentration ratio;

[0008] S3: determining a critical value of a ring tooth inclination angle of the Fresnel lens and determining a focal length of the Fresnel lens according to the critical value of the ring tooth inclination angle;

[0009] S4: Obtain the size parameters of each ring tooth on the Fresnel lens corresponding to each receiving area, and complete the busbar design of the Fresnel lens.

[0010] In one embodiment of the present invention, the S1 includes:

[0011] S1.1: The circular receiving surface of the Fresnel lens is divided into m receiving areas of equal width. The width of each receiving area is expressed as:

[0012]

[0013] Where r is the radius of the receiving surface, d i represents the width of the i-th receiving area, i = 1, 2, ..., m;

[0014] S1.2: Obtain the energy equation of each receiving area and the corresponding n ring teeth on the Fresnel lens:

[0015]

[0016] Among them, the light is refracted by n ring teeth on the Fresnel lens to the same receiving area, cr is the focusing ratio, η represents the loss of light transmitted from the Fresnel lens to the receiving surface, and represents the distance from the outer edge of the outermost ring tooth of the Fresnel lens corresponding to the i-1th receiving area and the i-th receiving area to the optical axis z, r i and r i-1 Represents the distance from the outermost sides of the i-1th receiving area and the i-th receiving area to the optical axis z.

[0017] In one embodiment of the present invention, the S2 includes:

[0018] Get the energy of the light refracted by the n ring teeth of the Fresnel lens to the i-th receiving area:

[0019]

[0020] in, represents the distance from the outer edge of the jth ring tooth corresponding to the i-th receiving area to the optical axis z, represents the distance from the outer edge of the j-1th ring tooth corresponding to the i-th receiving area to the optical axis z; I0 represents the energy density of the light incident on the Fresnel lens;

[0021] The expression for obtaining the concentration ratio on the i-th receiving area is:

[0022]

[0023] With the goal of minimizing the distance from the innermost end point R0 of the Fresnel lens to the optical axis z, the number n of ring teeth corresponding to each receiving area is obtained through the expression of the focusing ratio.

[0024] In one embodiment of the present invention, S3 includes:

[0025] S3.1: Based on the influence of total reflection on the lens optical path, determine the critical value of the ring tooth inclination angle:

[0026] n f ·sinα c =1,

[0027] Among them, n f represents the material refractive index of the Fresnel lens, α c represents a critical value of the ring tooth inclination angle of the Fresnel lens;

[0028] S3.2: Obtain an expression for the transmittance of the Fresnel lens;

[0029] S3.3: Obtain the maximum inclination angle α of the ring teeth of the Fresnel lens max :

[0030]

[0031] Wherein, F is the focal length of the Fresnel lens, R is the radius of the Fresnel lens, and r is the radius of the receiving surface;

[0032] S3.4: Obtain the relationship between the transmittance η and the angle of incidence on the exit surface of the Fresnel lens based on the relationship between the transmittance η and the inclination angle of the ring teeth, obtain the relationship between the transmittance and the focal diameter ratio F / R, and then obtain the focal length F based on the preset transmittance η and the radius R of the Fresnel lens, wherein the angle of incidence of the light on the exit surface is equal to the inclination angle of the current ring teeth.

[0033] In one embodiment of the present invention, the transmittance η of the Fresnel lens is expressed as:

[0034]

[0035] Wherein, η1 represents the transmittance on the incident surface of the Fresnel lens, η2 represents the transmittance on the exit surface of the Fresnel lens, the exit surface is the inclined surface of the ring teeth of the Fresnel lens, θ0 represents the incident angle of the light on the exit surface, θ t Represents the refraction angle of the light on the exit surface.

[0036] In one embodiment of the present invention, the S4 includes:

[0037] S4.1: Obtaining the size parameters of each ring tooth on the first receiving area and the corresponding Fresnel lens, wherein the size parameters include the inclination angle, width and height of each ring tooth;

[0038] S4.2: Based on the size parameters obtained in S4.1, size parameters of other acceptance areas except the first acceptance area and each ring tooth on the corresponding Fresnel lens are obtained.

[0039] In one embodiment of the present invention, the S4.1 includes:

[0040] The energy equation of the first receiving area and the corresponding ring teeth on the Fresnel lens is obtained:

[0041]

[0042] Among them, D1 1 、D1 2 , …, D1 n are the widths of the n ring teeth corresponding to the first receiving area, R0 represents the distance from the left end point of the first receiving area of ​​the Fresnel lens to the optical axis z, r0 represents the distance from the left end point of the receiving surface to the optical axis z, and d1 is the width of the first receiving area;

[0043] The width of the light area after the light passes through n ring teeth is made equal to the width of the first receiving area, and the width of each ring tooth corresponding to the first area is obtained:

[0044]

[0045] in, represents the width of the jth ring tooth corresponding to the first receiving area, represents the inclination angle of the jth ring tooth corresponding to the first receiving area, α1 j ' represents the refraction angle of the jth ring tooth corresponding to the first receiving area;

[0046] According to the geometric relationship corresponding to the edge ray theory, the inclination angle α1 of each ring tooth in the first receiving area is obtained. j , and then the width D1 of each ring tooth in the first receiving area is obtained j and height H1 j , the geometric relationship is:

[0047]

[0048] in, represents the distance from the left end point of the j-th ring tooth corresponding to the first receiving area to the optical axis z, that is, the distance from the right end point of the j-1-th ring tooth corresponding to the first receiving area to the optical axis z, represents the height of the jth ring tooth corresponding to the first receiving area, and r1 represents the distance from the right end point of the first receiving area to the optical axis z.

[0049] In one embodiment of the present invention, the S4.2 includes:

[0050] S4.21: The light is refracted from the left end point of the first ring tooth corresponding to the i-th receiving area to the left end point of the i-th receiving area, and the geometric relationship is obtained:

[0051]

[0052] in, represents the height of the first ring tooth corresponding to the i-th receiving area, represents the inclination angle of the first ring tooth corresponding to the i-th receiving area, represents the refraction angle of the first ring tooth corresponding to the i-th receiving area, r i-1 represents the distance from the left endpoint of the i-th receiving area to the optical axis, represents the distance from the left end point of the first ring tooth corresponding to the i-th receiving area to the optical axis; represents the width of the first ring tooth corresponding to the i-th receiving area;

[0053] S4.22: Obtain the inclination angle α of the first ring tooth corresponding to the i-th receiving area according to the geometric relationship in step S4.21 i 1 , and then get the width D of the first ring tooth i 1 , height H i 1 , and the distance R from the right end point of the first ring tooth to the optical axis i 1 ;

[0054] S4.23: Repeat steps S4.21 and S4.22 to obtain the size parameters of the second ring tooth to the n-1th ring tooth corresponding to the i-th receiving area;

[0055] S4.24: Design the generatrix of the nth ring tooth corresponding to the i-th receiving area into a broken line form, so that the exit surface of the nth ring tooth includes a first inclined surface and a second inclined surface, and obtain the width of the nth ring tooth corresponding to the i-th receiving area:

[0056]

[0057] in, represents the ring tooth inclination angle of the first inclined surface of the nth ring tooth corresponding to the i-th receiving area, represents the refraction angle of the first inclined surface, d i1 represents the width of the receiving surface corresponding to the second inclined surface, β i n represents the ring tooth inclination angle of the second inclined surface of the nth ring tooth corresponding to the i-th receiving area, represents the refraction angle of the second inclined surface, d i2 represents the width of the receiving surface corresponding to the first inclined surface;

[0058] S4.25: Obtain two inclination angles of the nth ring tooth and the height of the nth ring tooth corresponding to the ith receiving area.

[0059] Compared with the prior art, the present invention has the following beneficial effects:

[0060] 1. The present invention first divides the receiving surface into several receiving areas of equal width, and then designs the focusing ratio on each receiving area to make the average energy density on each receiving area equal, thereby achieving uniform energy distribution on the entire receiving surface, and finally infers the ring tooth busbar form of the Fresnel lens and the geometric parameters of the ring teeth. The present invention effectively solves the problems of uneven energy distribution on the receiving surface after focusing and excessive energy at the center of the receiving surface, and realizes the design of uniform energy distribution. The Fresnel lens with equal width receiving areas obtained by the present invention can achieve arbitrary focusing to meet the needs of different focusing scenes such as low magnification and high magnification. In addition, the Fresnel lens obtained by the present invention can be directly applied to a single-stage focusing system without the use of a secondary light-homogenizing element, which effectively reduces the control accuracy and quality of the focusing system.

[0061] 2. The present invention adopts a busbar design that combines straight lines and broken lines to establish a relationship between the focusing ratio and the number of ring teeth corresponding to each receiving area, which can achieve a high-uniformity lens design under any multiple of focusing and meet the needs of applications with different multiples of focusing.

[0062] 3. The present invention comprehensively considers the total reflection phenomenon and the influence of the lens ring tooth inclination angle on the overall transmittance of the lens, designs the optimal focal length, and makes the energy collection efficiency on the receiving surface better than 90%, thereby achieving efficient energy collection.

[0063] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 It is a flow chart of a method for designing a high uniformity Fresnel lens with equal width receiving areas provided by an embodiment of the present invention;

[0065] Figure 2 It is a detailed flow chart of a method for designing a high-uniformity Fresnel lens with equal-width receiving areas provided by an embodiment of the present invention;

[0066] Figure 3 is a schematic diagram of an optical path of a Fresnel lens provided by an embodiment of the present invention;

[0067] Figure 4 This is a schematic diagram of a design principle of a lens with equal width receiving area provided by an embodiment of the present invention;

[0068] Figure 5 is a curve showing a change in transmittance versus focal ratio of a Fresnel lens provided by an embodiment of the present invention;

[0069] Figure 6 It is a design principle diagram of the nth ring tooth generatrix of the ith receiving area of ​​a Fresnel lens provided by an embodiment of the present invention;

[0070] Figure 7 The energy distribution cloud diagram and radial variation curve of the 7-fold focusing lens designed by the method of the embodiment of the present invention on the receiving surface;

[0071] Figure 8 The energy distribution cloud diagram and radial variation curve of the 13x condenser lens on the receiving surface designed by the method of the embodiment of the present invention;

[0072] Fig. 9 The energy distribution cloud diagram and radial variation curve of a 143x focusing lens on a receiving surface designed using the method of an embodiment of the present invention are shown. DETAILED DESCRIPTION

[0073] In order to further explain the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the design method of a high uniformity Fresnel lens with equal width receiving area proposed by the present invention is described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0074] The above and other technical contents, features and effects of the present invention are clearly presented in the following detailed description of the specific implementation modes in conjunction with the accompanying drawings. Through the description of the specific implementation modes, the technical means and effects adopted by the present invention to achieve the predetermined purpose can be more deeply and specifically understood. However, the attached drawings are only for reference and explanation purposes and are not used to limit the technical solutions of the present invention.

[0075] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants are intended to cover non-exclusive inclusion, so that an article or device including a series of elements includes not only those elements, but also other elements that are not explicitly listed. In the absence of more restrictions, the elements defined by the statement "including one..." do not exclude the existence of other identical elements in the article or device including the elements.

[0076] The present invention provides a method for designing a Fresnel lens with high uniformity and equal width receiving area. Figure 1 and Figure 2 , the method comprising:

[0077] S1: Design for uniform energy distribution. The receiving surface of the Fresnel lens to be designed is divided into multiple receiving areas with equal widths, and an energy equation between each receiving area and the Fresnel lens is established.

[0078] The Fresnel lens includes a main body and a plurality of ring teeth, which are sequentially arranged on a side surface of the main body, and the upper surface of the main body is the incident surface. The general design method of the Fresnel lens is to design the aperture of the receiving surface according to the aperture and focusing ratio of the required Fresnel lens, and to design the position of the receiving point by the tooth profile geometric parameters of the given lens to achieve focusing and light uniformity. The design method of the high uniformity Fresnel lens of the present invention is to design the aperture of the receiving surface according to the aperture and focusing ratio of the required Fresnel lens, and then divide the receiving surface into a plurality of receiving areas of equal width, and design the generatrix form and tooth profile geometric parameters of the lens according to the edge ray theory.

[0079] Specifically, the circular receiving surface of the Fresnel lens with a radius of r is divided into m receiving areas with equal width and in the shape of a ring, and the width of each receiving area is expressed as:

[0080]

[0081] Among them, d i Represents the width of the i-th receiving area, i = 1, 2, …, m.

[0082] See also Figure 3 , Figure 3 FIG. 1 is a schematic diagram of the optical path of a Fresnel lens provided in an embodiment of the present invention, showing the optical path of sunlight after being refracted by the Fresnel lens. fl The micro-ring is transmitted to the focal plane (i.e., the receiving surface) with a width of dx fpConsidering the energy loss η during the transmission process, the energy equation between the micro-ring on the incident surface and the micro-ring on the receiving surface of the Fresnel lens can be obtained:

[0083] ηI02πx fl dx fl =I(x fp )2πx fp dx fp (2)

[0084] Where I0 represents the energy density of the incident light, which is a solar constant. fl represents the inner radius of the microelement ring on the Fresnel lens, x fp represents the inner ring radius of the microelement ring on the receiving surface, I(x fp ) represents the microelement ring dx on the receiving surface fp The energy density at .

[0085] In order to achieve uniform energy distribution, the energy density on each receiving area is crI0 (cr is the concentration ratio), such as Figure 4 In this embodiment, sunlight is refracted to the same receiving area through n ring teeth on the Fresnel lens, and an energy equation for each receiving area and its corresponding n ring teeth on the Fresnel lens can be established:

[0086]

[0087] in, and represents the distance from the outer edge of the outermost ring tooth of the Fresnel lens corresponding to the i-1th receiving area and the i-th receiving area to the optical axis z, r i and r i-1 represents the distance from the outermost sides of the i-1th receiving area and the i-th receiving area to the optical axis z, η represents the loss of light transmitted from the Fresnel lens to the focal plane, and cr represents the focusing ratio.

[0088] S2: Based on the energy equation and the preset light concentration ratio, the number of ring teeth on the Fresnel lens corresponding to each receiving area is determined.

[0089] Specifically, to achieve the required concentration ratio of the Fresnel lens, that is, the sunlight is refracted by the n ring teeth of the Fresnel lens to the same receiving area, assuming that each receiving area corresponds to the n ring teeth of the Fresnel lens, such as Figure 3 As shown, taking the i-th receiving area as an example, the energy refracted by the n ring teeth of the Fresnel lens to the i-th receiving area is:

[0090]

[0091] in, represents the distance from the outer edge (i.e., the right end point) of the jth ring tooth corresponding to the i-th receiving area to the optical axis z, represents the distance from the outer edge (i.e., the right end point) of the j-1th ring tooth corresponding to the i-th receiving area to the optical axis z, and They respectively represent the distance from the outer edge of the outermost ring tooth of the Fresnel lens corresponding to the i-1th receiving area and the i-th receiving area to the optical axis z, and I0 represents the energy density of the light incident on the Fresnel lens.

[0092] The energy received by the i-th receiving area can be expressed as:

[0093]

[0094] Among them, I i represents the energy density of the i-th receiving area.

[0095] Therefore, the focusing ratio of the Fresnel lens on the i-th receiving area can be expressed as:

[0096]

[0097] It can be seen from formula (6) that when i = 1, that is, for the first receiving area, Figure 4 As shown, the focusing ratio cr is related to the innermost end point R0 of the Fresnel lens and the outermost end point R1 of the ring tooth corresponding to the first receiving area. n , the inner end point r0 of the first receiving area, the outer side r1 of the first receiving area and the energy loss coefficient η. To achieve any multiple of focusing on the first receiving area, it is only necessary to design these five parameters. Similarly, any multiple of focusing on other receiving areas can be achieved.

[0098] According to formula (6), the relationship between the concentration ratio cr and the innermost endpoint R0 of the Fresnel lens can be obtained. In order to reduce the energy concentration area at the center of the receiving surface, it is required that the distance from the innermost endpoint of the Fresnel lens to the optical axis z is the shortest. In the specific design, the innermost endpoint R0 (i.e., the leftmost endpoint) of the Fresnel lens can be minimized, and the distance from the innermost endpoint R0 of the Fresnel lens to the optical axis z can be minimized. The number of ring teeth n corresponding to each receiving area can be obtained through the expression of the concentration ratio.

[0099] S3: Determine a critical value of the ring tooth inclination angle of the Fresnel lens and determine the focal length of the Fresnel lens according to the critical value of the ring tooth inclination angle.

[0100] Step S3 of this embodiment specifically includes:

[0101] S3.1: Determine the critical value of the ring tooth inclination angle based on the effect of total reflection on the lens optical path.

[0102] Specifically, because the sunlight is incident vertically on the mirror surface of the Fresnel lens, the refraction angle of the light after being refracted by each ring tooth is equal to the inclination angle of each ring tooth. If the inclination angle of the ring tooth of the light is too large, the sunlight will only be reflected on the surface of the ring tooth without being refracted, that is, the total reflection phenomenon, causing the actual propagation path of the sunlight to deviate from the design value, resulting in reduced energy collection efficiency.

[0103] According to the law of refraction, the critical value of the ring tooth inclination angle when total reflection occurs satisfies:

[0104] n f ·sinα c =1 (7)

[0105] Among them, n f Represents the material refractive index of the Fresnel lens, α c Indicates the critical value of the ring tooth inclination angle of the Fresnel lens.

[0106] From the above formula (7), it can be obtained that the critical value of the ring tooth inclination angle when total reflection occurs is related to the refractive index n of the Fresnel lens material. f When the lens is made of a certain material, the critical value of its ring tooth inclination angle α can be obtained c .

[0107] S3.2: Consider the effect of the ring tooth inclination angle on the lens transmittance and design the optimal focal length.

[0108] It should be noted that in the Fresnel focusing system, sunlight will be refracted twice through the incident surface and refractive surface of the Fresnel. The first surface (incident surface) is a plane and the incident light is vertically incident, so the incident angle and refraction angle of the first surface are both zero, and the transmittance η1 of the first surface is:

[0109]

[0110] The second surface (the exit surface, i.e. the inclined surface of the ring tooth) is an inclined surface. The incident angle of the light on the second surface is θ0, and the refraction angle is θ t , then the transmittance η2 of the second surface is:

[0111]

[0112] Therefore, for sunlight incident vertically on the Fresnel lens, the overall transmittance η of the Fresnel lens is:

[0113]

[0114] According to the law of refraction, the maximum inclination angle α of the ring teeth of the Fresnel lens max Should meet:

[0115]

[0116] Wherein, F is the focal length of the Fresnel lens, R is the radius of the Fresnel lens, and r is the radius of the receiving surface.

[0117] According to the above formula (11), the relationship between the maximum inclination angle of the ring teeth of the Fresnel lens and the focal diameter ratio F / R can be obtained. The inclination angle of the ring teeth is equal to the incident angle of the second surface of the lens. The relationship between the inclination angle of the ring teeth and the transmittance can be obtained, and then the relationship between the transmittance and the focal diameter ratio F / R can be established, as follows: Figure 5 Considering the need for efficient energy collection of the focusing system, the focal length F is obtained according to the preset transmittance η and the radius R of the Fresnel lens, wherein the incident angle of the light on the exit surface is equal to the inclination angle of the current ring tooth.

[0118] S4: Design the lens generatrix to obtain the size parameters of each ring tooth in the Fresnel lens corresponding to each receiving area.

[0119] Step 4 of this embodiment includes:

[0120] S4.1: Obtaining the size parameters of each ring tooth in the first receiving area and the corresponding Fresnel lens, the size parameters including the inclination angle, width and height of each ring tooth.

[0121] At the beginning of the design, the method of the present invention only gives the width of the receiving area and the distance r0 from the left end point of the receiving area to the central optical axis z. The focusing ratio cr is obtained from step 2 and the focal length F is obtained from step 3.

[0122] For the first receiving area on the receiving surface, the sunlight passing width is D1 1 、D1 2 , …, D1 n The inclination angles are α1 1 , α1 2 , …, α1 n The n ring teeth are transmitted to the receiving area with a width of d1. Formula (3) can be further expressed as:

[0123]

[0124] Wherein, R0 represents the distance from the left end point of the first receiving area of ​​the Fresnel lens to the optical axis z, r0 represents the distance from the left end point of the receiving surface to the optical axis z, and d1 is the width of the first receiving area.

[0125] In order to achieve equal light intensity design, the width of the light area after the sunlight passes through n ring teeth should be equal to the width of the first receiving area. The widths of the ring teeth corresponding to the first area are:

[0126]

[0127] in, represents the width of the jth ring tooth corresponding to the first receiving area, represents the inclination angle of the jth ring tooth corresponding to the first receiving area, α1 j ' represents the refraction angle of the jth ring tooth corresponding to the first receiving area, and the refraction angle can be obtained from the law of refraction.

[0128] Based on formula (13), the width D1 of each ring tooth is j can be regarded as the inclination angle α1 of each ring j And the function of the width d1 of the first receiving area. Since the designed Fresnel lens is a plane Fresnel lens, it is only necessary to design the inclination angle α1 of each ring. j , the height H1 of each ring can be obtained j .

[0129] According to the edge ray theory, sunlight passing through the left end point of each ring tooth should be refracted to the left end point r0 of the first receiving area, and sunlight passing through the right end point of each ring tooth should be refracted to the right end point r1 of the first receiving area. The following geometric relationship can be obtained:

[0130]

[0131] in, represents the distance from the left end point of the j-th ring tooth corresponding to the first receiving area to the optical axis z, that is, the distance from the right end point of the j-1-th ring tooth corresponding to the first receiving area to the optical axis z, represents the height of the jth ring tooth corresponding to the first receiving area, and r1 represents the distance from the right end point of the first receiving area to the optical axis z.

[0132] Combining formulas (14) and (15), the inclination angle α1 of each ring tooth in the first receiving area can be obtained: j , and further obtain the width D1 of each ring tooth in the first receiving area j and height H1 j The first receiving area corresponds to the distances R0 and R1 from the left end point of the first ring tooth and the right end point of the nth ring tooth to the optical axis z. n .

[0133] At this point, the parameter design of the first receiving area and each ring tooth of the lens corresponding thereto is completed.

[0134] S4.2: Based on the size parameters obtained in S4.1, design the size parameters of other acceptance areas except the first acceptance area and each ring tooth in the corresponding Fresnel lens.

[0135] Specifically, in order to achieve efficient energy collection, the ring teeth of the Fresnel lens should be continuous. Now, the outer receiving area and its corresponding ring teeth are designed, taking the i-th (i=2, ..., m) receiving area and its corresponding n ring teeth as an example. Because the Fresnel lens is designed from the inside out, the left end point r of the i-th receiving area is i-1 And the left endpoint R corresponding to n ring teeth i-1 n is a known value.

[0136] The width of sunlight passing through is D i 1 , D i 2 ,…,D i n and the inclination angles are α i 1 , α i 2 , …, α i n The n lens ring teeth transmit to a width d i On the i-th receiving area, equation (3) can be further expressed as:

[0137]

[0138] To achieve equal light intensity design, the width of the light area after the sunlight passes through n ring teeth should be equal to the width of the i-th receiving area, which can be obtained as shown in formula (13): Ring gear inclination Receiving area width d i The relationship between the three.

[0139] The left end point R of the first ring tooth corresponding to the i-th receiving area i-1 n Refraction to the left end point r of the i-th receiving area i-1 The following geometric relationship can be established:

[0140]

[0141] The width of the light area after the sunlight passes through the first ring tooth should be equal to the width of the i-th receiving area, that is:

[0142]

[0143] Combining formulas (17) and (18), we can get the inclination angle α of the first ring tooth corresponding to the i-th receiving area: i 1 , and then the width D of the first ring tooth is obtained i 1 , height H i 1, and the right end point R of the first ring tooth i 1 The second ring tooth to the n-1th ring tooth corresponding to the i-th receiving area can be obtained in sequence according to the above steps. At this time, the right endpoint R of the n-1th ring tooth is solved. i n-1 .

[0144] In the specific design, if the nth ring tooth is also designed according to the steps of the 1st to n-1th ring teeth, it only satisfies formulas (17) and (18), and the energy equation (16) does not hold. To solve the above problem, the generatrix (i.e., the inclined surface) of the nth ring tooth is designed from a straight line to a broken line, so that the exit surface of the nth ring tooth includes a first inclined surface and a second inclined surface, such as Figure 6 As shown. The second ring tooth inclination angle β of the nth ring tooth is introduced i n , and the incident angle θ corresponding to the second ring tooth i2 n The i-th receiving area is also divided into two parts d i1 and d i2 , corresponding to the inclination angles of the two ring teeth respectively.

[0145] By designing the two ring tooth inclination angles corresponding to the nth ring tooth, the width of the light area after the sunlight passes through the nth ring tooth is equal to the width of the i-th receiving area. Formula (18) is transformed into:

[0146]

[0147] in, represents the ring tooth inclination angle of the first inclined surface of the nth ring tooth corresponding to the i-th receiving area, represents the refraction angle of the first inclined surface, d i1 represents the width of the receiving surface corresponding to the second inclined surface, β i n represents the ring tooth inclination angle of the second inclined surface of the nth ring tooth corresponding to the i-th receiving area, represents the refraction angle of the second inclined surface, d i2 Indicates the width of the receiving surface corresponding to the first inclined surface.

[0148] Through the above design, the sunlight passing through the left end point of the nth ring tooth should be refracted to the left end point r of the i-th receiving area. i-1 At the right end point of the i-th ring tooth, the sunlight should be refracted to the right end point r of the i-th receiving area. i Combining formulas (17) and (19), the two inclination angles α of the nth ring tooth can be obtained: i n , β i n , thus obtaining the height H of the nth ring tooth in .

[0149] At this point, the parameter design of the outer receiving area and each ring tooth of the lens corresponding thereto is completed, that is, the generatrix design of the Fresnel lens is completed.

[0150] The design method of a high uniformity Fresnel lens with equal width receiving area proposed in the present invention is further verified by simulation experiments, and an optimal set of lens ring teeth is obtained according to different focusing ratio design requirements.

[0151] (1) Simulation parameters

[0152] Given the relevant parameters of the Fresnel lens: focal length F = 320mm, radius R = 200mm, material is polymethyl methacrylate (PMMA), refractive index n = 1.49, the width of each receiving area is set to d = 5mm, and the distance from the left end point of the first receiving area to the central axis (z axis) is 0mm. Select the concentration ratios of 7, 13 and 143 respectively, design the corresponding Fresnel lenses with equal width receiving areas, and obtain the energy distribution on the receiving surface by ray tracing method.

[0153] (2) Simulation content and results

[0154] Table 1 lists the lens parameters designed with different focusing ratios, as well as the energy collection efficiency and energy distribution uniformity on the receiving surface obtained by simulation calculation; Figure 7 , Figure 8 and Fig. 9 The energy distribution cloud diagram and radial distribution curve of the Fresnel lens designed by the method of the embodiment of the present invention on the receiving surface when the concentration ratio is 7, 13, and 143 are respectively given. Combined with Table 1, it can be seen that the effective energy collection efficiency of the three Fresnel lenses is above 91%, and a high uniformity energy distribution on the receiving surface is achieved. It shows that the Fresnel lens designed by the method of the present invention solves the problem of uneven energy distribution on the receiving surface after concentration, and achieves a high uniformity energy distribution; while ensuring efficient energy collection, any concentration ratio can be achieved to meet different multiples of concentration applications.

[0155] Table 1 Lens parameters designed with different focusing ratios

[0156]

[0157]

[0158] The present invention first divides the receiving surface into a number of receiving areas of equal width, and then makes the average energy density on each receiving area equal by designing the focusing ratio on each receiving area, so as to achieve uniform energy distribution on the entire receiving surface, and finally infers the ring tooth busbar form of the Fresnel lens and the geometric parameters of the ring teeth. The present invention effectively solves the problems of uneven energy distribution on the receiving surface after focusing, excessive energy at the center of the receiving surface, and realizes the design of uniform energy distribution. The Fresnel lens with equal width receiving area obtained by the present invention can achieve arbitrary multiple focusing to meet the needs of different focusing scenes such as low magnification and high magnification. In addition, the Fresnel lens obtained by the present invention can be directly applied to a single-stage focusing system without the use of a secondary light-homogenizing element, which effectively reduces the control accuracy and quality of the focusing system. The present invention adopts a busbar design form combining straight lines and broken lines to establish the relationship between the focusing ratio and the number of ring teeth corresponding to each receiving area, which can realize a high-uniformity lens design under arbitrary multiple focusing to meet the needs of different multiple focusing applications. The present invention comprehensively considers the total reflection phenomenon and the influence of the lens ring tooth inclination angle on the overall transmittance of the lens, designs the optimal focal length, makes the energy collection efficiency on the receiving surface better than 90%, and realizes efficient energy collection.

[0159] Another embodiment of the present invention provides a storage medium, wherein a computer program is stored in the storage medium, and the computer program is used to execute the steps of the method for designing a high uniformity Fresnel lens with equal width receiving areas described in the above embodiment. Another aspect of the present invention provides an electronic device, including a memory and a processor, wherein a computer program is stored in the memory, and when the processor calls the computer program in the memory, the steps of the method for designing a high uniformity Fresnel lens with equal width receiving areas described in the above embodiment are implemented. Specifically, the above integrated module implemented in the form of a software function module can be stored in a computer-readable storage medium. The above software function module is stored in a storage medium, including several instructions for enabling an electronic device (which can be a personal computer, a server, or a network device, etc.) or a processor to execute some steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0160] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. A method for designing a high uniformity Fresnel lens with equal width receiving area, characterized in that: include: S1: Divide the receiving surface of the Fresnel lens to be designed into a plurality of receiving areas with equal widths, and establish an energy equation between each receiving area and the Fresnel lens; S2: Determine the number of ring teeth on the Fresnel lens corresponding to each receiving area based on the energy equation and a preset light concentration ratio; S3: determining a critical value of a ring tooth inclination angle of the Fresnel lens and determining a focal length of the Fresnel lens according to the critical value of the ring tooth inclination angle; S4: Obtain the size parameters of each ring tooth on the Fresnel lens corresponding to each receiving area, and complete the busbar design of the Fresnel lens.

2. The method for designing a high uniformity Fresnel lens with equal width receiving area according to claim 1, characterized in that: The S1 includes: S1.1: The circular receiving surface of the Fresnel lens is divided into m receiving areas of equal width. The width of each receiving area is expressed as: Where r is the radius of the receiving surface, d i represents the width of the i-th receiving area, i = 1, 2, ..., m; S1.2: Obtain the energy equation of each receiving area and the corresponding n ring teeth on the Fresnel lens: Among them, the light is refracted by n ring teeth on the Fresnel lens to the same receiving area, cr is the focusing ratio, η represents the loss of light transmitted from the Fresnel lens to the receiving surface, and They respectively represent the distance from the outer edge of the outermost ring tooth of the Fresnel lens corresponding to the i-1th receiving area and the i-th receiving area to the optical axis z, and ri and ri-1 represent the distance from the outermost side of the i-1th receiving area and the i-th receiving area to the optical axis z.

3. The method for designing a high uniformity Fresnel lens with equal width receiving areas according to claim 2, characterized in that: The S2 includes: Get the energy of the light refracted by the n ring teeth of the Fresnel lens to the i-th receiving area: in, represents the distance from the outer edge of the jth ring tooth corresponding to the i-th receiving area to the optical axis z, represents the distance from the outer edge of the j-1th ring tooth corresponding to the i-th receiving area to the optical axis z; I0 represents the energy density of the light incident on the Fresnel lens; The expression for obtaining the concentration ratio on the i-th receiving area is: With the goal of minimizing the distance from the innermost end point R0 of the Fresnel lens to the optical axis z, the number n of ring teeth corresponding to each receiving area is obtained through the expression of the focusing ratio.

4. The method for designing a high uniformity Fresnel lens with equal width receiving areas according to claim 1, characterized in that: The S3 includes: S3.1: Based on the influence of total reflection on the lens optical path, determine the critical value of the ring tooth inclination angle: nf·sinαc=1, Among them, n f represents the material refractive index of the Fresnel lens, αc represents the critical value of the ring tooth inclination angle of the Fresnel lens; S3.2: Obtain an expression for the transmittance of the Fresnel lens; S3.3: Obtain the maximum inclination angle α of the ring teeth of the Fresnel lens max : Wherein, F is the focal length of the Fresnel lens, R is the radius of the Fresnel lens, and r is the radius of the receiving surface; S3.4: Obtain the relationship between the transmittance η and the angle of incidence on the exit surface of the Fresnel lens based on the relationship between the transmittance η and the inclination angle of the ring teeth, obtain the relationship between the transmittance and the focal diameter ratio F / R, and then obtain the focal length F based on the preset transmittance η and the radius R of the Fresnel lens, wherein the angle of incidence of the light on the exit surface is equal to the inclination angle of the current ring teeth.

5. The method for designing a high uniformity Fresnel lens with equal width receiving areas according to claim 4, characterized in that: The expression of the transmittance η of the Fresnel lens is: Wherein, η1 represents the transmittance on the incident surface of the Fresnel lens, η2 represents the transmittance on the exit surface of the Fresnel lens, the exit surface is the inclined surface of the ring teeth of the Fresnel lens, θ0 represents the incident angle of the light on the exit surface, θ t Represents the refraction angle of the light on the exit surface.

6. The method for designing a high uniformity Fresnel lens with equal width receiving areas according to claim 1, characterized in that: The S4 includes: S4.1: Obtaining the size parameters of each ring tooth on the first receiving area and the corresponding Fresnel lens, wherein the size parameters include the inclination angle, width and height of each ring tooth; S4.2: Based on the size parameters obtained in S4.1, size parameters of other acceptance areas except the first acceptance area and each ring tooth on the corresponding Fresnel lens are obtained.

7. The method for designing a high uniformity Fresnel lens with equal width receiving areas according to claim 6, characterized in that: The S4.1 includes: The energy equation of the first receiving area and the corresponding ring teeth on the Fresnel lens is obtained: Among them, D1 1 、D1 2 , …, D1 n are the widths of the n ring teeth corresponding to the first receiving area, R0 represents the distance from the left end point of the first receiving area of ​​the Fresnel lens to the optical axis z, r0 represents the distance from the left end point of the receiving surface to the optical axis z, and d1 is the width of the first receiving area; The width of the light area after the light passes through n ring teeth is made equal to the width of the first receiving area, and the width of each ring tooth corresponding to the first area is obtained: in, represents the width of the jth ring tooth corresponding to the first receiving area, represents the inclination angle of the jth ring tooth corresponding to the first receiving area, represents the refraction angle of the jth ring tooth corresponding to the first receiving area; The inclination angle of each ring tooth in the first receiving area is obtained according to the geometric relationship corresponding to the edge ray theory Then the width of each ring tooth in the first receiving area is obtained and height The geometric relationship is: in, represents the distance from the left end point of the j-th ring tooth corresponding to the first receiving area to the optical axis z, that is, the distance from the right end point of the j-1-th ring tooth corresponding to the first receiving area to the optical axis z, represents the height of the jth ring tooth corresponding to the first receiving area, and r1 represents the distance from the right end point of the first receiving area to the optical axis z.

8. The method for designing a high uniformity Fresnel lens with equal width receiving areas according to claim 6, characterized in that: The S4.2 includes: S4.21: The light is refracted from the left end point of the first ring tooth corresponding to the i-th receiving area to the left end point of the i-th receiving area, and the geometric relationship is obtained: in, represents the height of the first ring tooth corresponding to the i-th receiving area, represents the inclination angle of the first ring tooth corresponding to the i-th receiving area, represents the refraction angle of the first ring tooth corresponding to the i-th receiving area, ri-1 represents the distance from the left end point of the i-th receiving area to the optical axis, represents the distance from the left end point of the first ring tooth corresponding to the i-th receiving area to the optical axis; represents the width of the first ring tooth corresponding to the i-th receiving area; S4.22: Obtain the inclination angle α of the first ring tooth corresponding to the i-th receiving area according to the geometric relationship in step S4.21 i 1 , and then the width D of the first ring tooth is obtained i 1 , height H i 1 , and the distance R from the right end point of the first ring tooth to the optical axis i 1 ; S4.23: Repeat steps S4.21 and S4.22 to obtain the size parameters of the second ring tooth to the n-1th ring tooth corresponding to the i-th receiving area; S4.24: Design the generatrix of the nth ring tooth corresponding to the i-th receiving area into a broken line form, so that the exit surface of the nth ring tooth includes a first inclined surface and a second inclined surface, and obtain the width of the nth ring tooth corresponding to the i-th receiving area: in, represents the ring tooth inclination angle of the first inclined surface of the nth ring tooth corresponding to the i-th receiving area, represents the refraction angle of the first inclined surface, di1 represents the width of the receiving surface corresponding to the second inclined surface, β i n represents the ring tooth inclination angle of the second inclined surface of the nth ring tooth corresponding to the i-th receiving area, represents the refraction angle of the second inclined surface, and di2 represents the width of the receiving surface corresponding to the first inclined surface; S4.25: Obtain two inclination angles of the nth ring tooth and the height of the nth ring tooth corresponding to the ith receiving area.

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