Refractive linear condenser lens

Abstract

The invention provides a refractive linear condensing lens model which is characterized in various elliptical shapes including a plane, a semicircle and an ellipse. The process of forming the grooves begins with dividing the edge angle of the lens into smaller angles. By applying the Snell equation and considering the refractive index of the material, the size of the groove is defined by each angle division, so that the light is accurately refracted to the focal point of the mathematical origin. The saw-toothed surface of the lens faces the receiver, and the smooth surface of the lens faces the sun. The substrate supporting the linear grooves increases the thickness of the lens, providing basic structural integrity. In addition, the invention also includes a pitch angle to accommodate potential errors during processing and manufacturing. According to the invention, the problems of aggravated achromatism caused by loss of an original internal light path and damage to an expected calculation focus due to removal of an optical section of a traditional Fresnel lens are solved, and the light condensation efficiency is remarkably improved.

Description

Technical Field

[0001] The present invention relates to the technical fields of solar thermal utilization and solar concentration technology, involving comprehensive optical and thermal utilization and high-power concentration, and particularly relates to a preparation method for a refractive linear concentrating lens for an optical module and an optical imaging device. Background Art

[0002] Solar concentrators, as optical elements in a concentrating system, have an important impact on the overall efficiency of the concentrating system. They mainly change the path of light through reflection or refraction. For example, reflective concentrators include dish concentrators, parabolic trough concentrators, etc., while Fresnel lenses are examples of refractive concentrators.

[0003] Fresnel lenses are the cornerstone of the modern refractive concentrator market. This type of lens was initially developed by Augustin-Jean Fresnel in the 19th century. It adapted the concept of a concentrating aspherical lens into a planar form, using a small part of the curved surface on a plane made of the same material. By dividing the aspherical lens into equal-length parts to produce grooves of uniform length, or into equal-height parts to produce grooves of the same height. Essentially, a Fresnel lens consists of a series of linear prism grooves related to an aspherical lens, designed to direct incident light to a common focus. These lenses are thin, light, usually have a high aperture, and contain many small grooves. Today, Fresnel lenses are widely used in concentrators, illuminators, magnifying glasses, and other fields.

[0004] However, the modeling process of traditional Fresnel lenses involves partial slicing of an aspherical lens, resulting in the loss of the original internal light path. Due to the removal of the small-piece geometry and light path in the aspherical lens, each wavelength reaches a different focus, thus deteriorating the achromatic effect. In addition, the removal of these optical segments disrupts the expected calculated focus, making it difficult for Fresnel lenses to achieve the precise focal length of the highest focal spot. Summary of the Invention

[0005] The object of the present invention: Design a refractory linear concentrating lens that refracts all incident light to a common focus. Different from Fresnel lenses, this design does not rely on the segmentation of an aspherical lens, nor does it eliminate any key light paths to achieve this effect. Instead, it only applies Snell's law of refraction on a section of the elliptical surface to simulate each refraction groove, directing all light paths to a unified mathematical focus. This method ensures that all refracted light paths converge precisely to the focus position with minimal achromatism, significantly improving the concentrating efficiency. In addition, compared with traditional Fresnel lenses, the innovative modeling process requires fewer grooves to achieve the same or higher energy density. This type of lens has been proven to be able to effectively solve or alleviate some problems related to traditional Fresnel lenses.

[0006] Technical solution: To achieve the above object, the present invention provides a new method for modeling a refractive linear concentrating lens system. This lens is formed by connecting a series of linear grooves in series on a mathematically calculated elliptical contour. The lens can be modeled as a linear planar lens, very similar to a linear Fresnel lens or a linear arch Fresnel lens. The linear grooves face downward towards the receiver, and the smooth surface faces the sun. Through the calculation of Snell's law of refraction, each individual linear groove can refract light to a common focus.

[0007] The method for obtaining the groove position parameters is as follows:

[0008] Define the physical parameters of the refractive linear concentrating lens model: radius (r), focal length (h f ), lens height (h l ), lens thickness (d t ), including the tilt angle (θ p ) considering manufacturing errors, and define the sub-angle (δω n ) of each groove. The sum of all angles of all sub-angles cannot be greater than or equal to the lens edge angle (ω 0 ).

[0009] Consider the general elliptic equation, where a is the major axis length and b is the minor axis length.

[0010] The shape of the lens is involved in the calculation of the major axis and minor axis through and b = h f + h l .

[0011] When the value of h l is large enough, the shape of the lens can be arched, and when the value of h l is close enough to zero, the shape of the lens can be flat.

[0012] The input surface of the groove is a chain-like contour of an elliptical arch, and the input surface faces the sun. The number (N) of prisms or grooves is defined by the number of sub-angles (δω 0 ) within the lens edge angle (ω n ), where the sum of δω n must be less than ω 0 , expressed as

[0013] The generation process of the groove starts from the outermost side of the lens, point A n＝0 = (r, h f ). Therefore, the distance from point A n＝0 to the origin is called AO n＝0 . The distance between the origin and point B n＝0 can be calculated through the elliptic equation for the projection angle ωn＝1 is obtained from the intercept of the projection line at the origin, i.e., The projection angle conforms to the formula

[0014] Point A n and point B n The coordinates on the ellipse can both be expressed as: A n =(AO n sinω n , AO n cosω n ), B n =(BO n sinω n+1 , BO n cosω n+1 ).

[0015] The size of the input surface is described as

[0016] At the input angle of any given nth groove This angle is the displacement angle from the normal of the input surface AB n and is also the inclination angle of the groove relative to the horizontal line of point A n .

[0017] Taking n λ as the refractive index of the material, the Snell equation is separated into The optical displacement angle γ in the medium is obtained n .

[0018] The output angle β from inside the medium to the outside n can be calculated by the Snell equation

[0019] By knowing α n and β n and θ p , the remaining points for prism modeling can be found by finding the intersection points of point A n and point B n at the relevant angles.

[0020] Considering point A o,n as the new origin and point B o,n as the extension of AB n on the x-axis. Then the inclination of each point is described as and

[0021] The intercept point on this pseudo-triangle is set as point The size of the output surface

[0022]

[0023] In the case where the known output surface is AC o,n , then C n = (x A,n - AC o,n cosβ n , y A,n - AC o,n sinβ n ).

[0024] A series of grooves can be represented as a sequence of points, in the following order: A 1 , C 1 , A 2 (or B 1 ), C 2 , A 3 (or B 2 ), …, A N (or B N-1 ), C N .

[0025] The physical thickness of the lens is included above the groove chain on the input surface, which represents the substrate thickness of the lens and is defined as follows: D n = (x A,n , y A,n + d t ).

[0026] Having determined the coordinates of each point, the lens can be actually produced. This can be achieved through a two-step process: first, machining is used to create the mold, and then injection molding is used to produce a common PMMA plastic linear lens, or precision diamond cutting of fused silica or other materials is used to manufacture the linear lens.

[0027] Compared with the prior art, the improvements of the present invention are as follows:

[0028] 1. This solution adopts a total refraction optical system based on Snell's law, where each groove is generated separately with the aim of guiding light to a single focus, thus improving the focusing efficiency. In contrast, the focusing mechanism of a Fresnel lens is entirely based on applying Snell's law to a "larger" aspherical lens.

[0029] 2. This model provides a wider range of shape options, supporting linear planar and linear arched configurations. In contrast, traditional Fresnel lenses require different calculation methods for similar designs.

[0030] 3. This model provides a higher degree of groove division / formation, which is based on a small angular division (δω n ) of the total edge angle. δω can be adjustedn To achieve the same segmentation method as the traditional Fresnel lens.

[0031] 4. This model ensures an accurate optical path for light to reach the expected focal point. In contrast, the traditional Fresnel lens truncates the expected light propagation distance within the aspherical lens, resulting in a missing optical path. This difference is a key factor contributing to a significant shift in the focal spot position and a broader achromatism.

[0032] 5. Compared with the traditional Fresnel lens, this model is significantly simpler in conceptual design. It can create a lens with just a few known parameters, while the traditional method requires an aspherical lens as a reference.

[0033] 6. The groove generation process of this model is sensitive to materials, i.e., the refractive indices of different materials will affect the formation of grooves. This enables the system to automatically adapt and ensure that light is precisely focused on the correct focal point. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 Schematic diagram of the existing modeling method of the Fresnel lens involved in an embodiment of the present invention. Left: Equi - distance segmentation. Right: Equi - height segmentation.

[0035] Figure 2 Schematic diagram of the shape of the refractive linear concentrator lens based on the ellipse equation involved in an embodiment of the present invention. Where 1 is the refractive linear concentrator lens and 2 is the ellipse.

[0036] Figure 3 Schematic diagram of various models of the refractive linear concentrator lens designed according to their respective ellipse shapes. High h l value lenses have a more obvious curvature, and low h l value lenses have a flatter profile. Where 3 is the planar refractive linear concentrator lens and 4 is the curved refractive linear concentrator lens.

[0037] Figure 4 Schematic diagram of the input surface from ω n to ω n -δω n truncation A n to B n in an embodiment of the present invention.

[0038] Figure 5 Detailed model of the nth groove involved in an embodiment of the present invention.

[0039] Figure 6 Schematic diagram involved in an embodiment of the present invention. Left figure: From point A o,n (serving as the virtual origin) and B o,nCalculate point C at the intersection of the straight line projected by length on the x-axis with AB n and output plane AC o,n 。 Right figure: From AC o,n to C o,n completion of the edge / groove. n

[0040] Figure 7 This is the refracting linear concentrator lens model involved in an embodiment of the present invention. The grooved chain process starts from each point. For physical integrity, the lens should have a certain thickness.

[0041] Figure 8 This is the front and side views of the refracting linear concentrator lens involved in an embodiment of the present invention.

[0042] Figure 9 This is the overview diagram of the refracting linear concentrator lens involved in an embodiment of the present invention. Detailed implementation mode

[0043] As Figure 1 shown, the traditional lens modeling process involves segmenting parts of the aspherical lens, which inherently leads to the loss of the original internal optical path. This loss changes the optical path of the Fresnel lens for different wavelengths, exacerbating the achromatic aberration problem caused by the refractive characteristics of the material and its geometry. In addition, the removal of this optical segment disrupts the expected calculated focus, making it difficult for the Fresnel lens to accurately determine the correct distance of the highest focal spot. Traditional Fresnel lenses often replace the optimal transmission curve with a parabolic or circular arc curve, which often leads to a reduction in the concentration efficiency.

[0044] The present invention will alleviate most of the problems currently existing in traditional Fresnel lenses. First, it does not depend on the geometry of the aspherical lens, and the present invention allows the lens to be formed in a planar or curved mode according to the inserted parameters. The optical path reaching the focus is directly calculated by Snell's equation.

[0045] Referring to the accompanying drawings, the present invention is further elaborated in detail as follows:

[0046] Figure 2 Shows a curved refracting linear concentrator lens designed based on an elliptical shape. The lens is located in the upper half of the ellipse, and its effective collection area is determined by the radius r, the focal length h f , the lens height h l . The center of the ellipse serves as the focus of the lens. ω 0 angle represents the lens edge angle, and δω n represents the small angular division that determines the size of the nth groove.

[0047] Considering the general ellipse equation, where a is the length of the major axis and b is the length of the minor axis. ​

[0048] The shape of the lens is determined by and b = h f +h l which are involved in the calculation of the major and minor axes.

[0049] Figure 3 Several possible refractive linear concentrator lens models are illustrated by adjusting specific variables. When the value of h l is large enough, the lens can be arched, and when h l is close to zero, the lens can be planar.

[0050] Figure 4 The process of modeling the input surface of the groove is shown. The size of the groove is the intercept of the projection lines of the origin through ω n and ω n+1 with the elliptical line.

[0051] The refractive linear concentrator lens model first models the outermost groove. The first point is at A n＝0 =(r, h f ), and the distance between the origin and A is AO n＝0 .

[0052] The second point on the input surface B n＝0 is located at the intersection of the elliptical curve and the projection of the straight line starting from ω n＝1 . The projection angle conforms to the formula The focal point equation is

[0053] The coordinates of point A n and point B n on the elliptical line can both be expressed as: A n =(AO n sinω n , AO n cosω n ), B n =(BO n sinω n+1 , BO n cosω n+1 ).

[0054] The size of the input surface is described as

[0055] At any given input angle of the nth groove This angle is the displacement angle from the normal of the input surface AB n , and it is also the inclination angle of the groove with respect to the horizontal line of point A n .

[0056] Taking n λLet \(n\) be the refractive index of the material. Snell's equation is separated into The optical displacement angle \(\gamma\) in the medium is obtained n .

[0057] Figure 5 The fully generated groove form is shown. Since the refractive index of the material is well - defined and the target position through \(\omega\) n is also known, then the value of the output angle \(\beta\) n can be determined by Snell's formula as:

[0058] Figure 6 A method for determining the third point required to define the shaped groove is demonstrated. Using the output angle \(\beta\) n at point A n , point C n is determined as the intersection of the projection line of point A n at angle \(\beta\) n and the vertical projection line of point B n . To simplify the calculation, A n is regarded as the pseudo - origin \(A'\) o,n , and the new point B o,n is located on the x - axis, with a distance equivalent to \(AB\) n .

[0059] Define the projection slope of point A o,n as The projection slope of point B o,n is

[0060] Using the input angle \(\alpha\) n , the output angle \(\beta\) n and the pitch angle \(\theta\) p , the intersection of this pseudo - triangle can be determined, and thus the final vertex C o,n is defined by the following formula: The output surface size is

[0061] Given the known output surface \(AC\) o,n , the point C n =(x A,n -AC o,n \(\cos\beta\) n ,y A,n -AC o,n \(\sin\beta\) n ) in the original Cartesian space, thus completing Figure 5 the groove shown.

[0062] Figure 7 The formation process of the groove chain is illustrated. The linear groove is similar to a saw - tooth and can be represented as a series of points. In this case, the sequence follows the order: A1 , C 1 , A 2 (or B 1 ), C 2 , A 3 (or B 2 ), …, A N (or B N-1 ), C N .

[0063] The physical thickness of the lens is above the chain of grooves on the input surface, which represents the substrate thickness of the lens and is defined as follows: D n = (x A,n , y A,n + d t ).

[0064] Figure 8 And Figure 9 illustrate the present invention in three - dimensional views. Since the coordinates of each point are precisely defined, the physical form can be easily manufactured. First, a mold is created by machining, and then a common PMMA plastic is injection - molded to complete the linear lens. Alternatively, a precision diamond cutting of fused silica or other materials is used to manufacture the linear lens.

[0065] The above is only one embodiment of the present invention. For common knowledge such as specific technical solutions or features known in the implementation scheme, no excessive description is made here. It should be noted that for those skilled in the art, several deformations and improvements can be made without departing from the technical scheme of the present invention, which should also be regarded as the protection scope of the present invention and will not affect the implementation effect of the present invention and the practicality of the patent. The protection scope claimed in this application should be based on the content of its claims, and the specific implementation methods and other records in the specification can be used to interpret the content of the claims.

Claims

1. A refractive linear focusing lens, which consists of a mathematical design of a lens with a high degree of input variables. The lens model uses a mathematical ellipse equation to outline its physical shape, so it can be a flat narrow lens or an arched narrow lens, with concentric grooves facing downward toward the receiver and a smooth surface facing the direction of the sun. Through Snell's law of refraction, it is calculated that each individual linear groove refracts light to a common focus.

2. The refractive linear focusing lens according to claim 1, wherein the lens material is characterized by light transmission capability and can be made of any light transmitting material, such as PMMA or silicon dioxide.

3. The refractive linear focusing lens according to claim 1, characterized in that The grooves are arranged symmetrically around the central axis.

4. The refractive linear condenser lens according to claim 1, wherein the shape is composed of a radius (r), a focal length (h f ), lens height (h l ), these variables define the shape of the lens model according to the ellipse equation; each linear circular groove is determined by its corresponding index angle (δω n ), which determines the size and spacing of the grooves; the shape of each linear groove is determined by the refractive index of the material (n λ ) definition; manufacturing error is included including pitch angle (θ p ) of the groove shape; lens thickness (d t ) should be presented to achieve structural integrity.

5. The refractive linear focusing lens according to claim 1, characterized in that: The incident surface and the working surface (groove) meet the optimal transmission condition, and the incident angle of parallel light incident on the incident surface is equal to the exit angle of the working surface.

6. The design method of the refractive linear focusing lens according to claims 1-5 comprises the following steps: S1. Determine the physical parameters of the lens, radius (r), focal length (h f ), lens height (h l ), then according to the ellipse equation The overall outline of the lens is segmented from a portion of the ellipse, where b=h f +h l , when h l When the value is large enough, the shape of the lens can be arched, and when h l When the value is close enough to zero, the shape of the lens can be flat. S2. Determine the indexing angle of the nth slot (δω n ), the sum of all indexing angles cannot be greater than the lens edge angle (ω0), giving a tilt angle error (θ p ) to account for possible manufacturing errors. S3. The groove modeling process starts from the outermost side of the lens, and a vertex of the input surface is precisely defined as A n＝0 =(r,h f ), the second point of the input surface is obtained by It is determined by calculating the intersection of a known ellipse and a projection line from the focus (origin), where Then B n The coordinates of the point are (BO n sinω n+1 ,BO n cosω n+1 ). S4. Input the length of the surface AB n＝0 pass The incident angle α is calculated to be n＝0 pass Calculated. S5. Determine the material used for the lens and thus determine the refractive index (n λ ), and calculate the refraction angle in the medium using the Snell equation When the target position (origin) is known, the output angle is calculated using the Snell refraction equation S6. Then the geometry of the slot can be calculated using all the associated angles. First, point A o,n As the new origin, point B o,n As AB n The spread on the x-axis, then the tendency of each point is described as and Then set the intercept point on the pseudo triangle to point The size of the output surface At the known output AC o,n In the case of point C in the original Cartesian space n =(x A,n -AC o,n cosβ n ,y A,n -AC o,n sinβ n ), thus completing the construction of the slot. S7. The continuous sequence of all slots is in a jagged shape and can be represented as a sequence of points. In this case, the order is as follows: A1, C1, A2 (or B1), C2, A3 (or B2), ..., A N (or B N-1 ), C N , N is the total number of slots. S8. The thickness of the lens is the thickness of the lens substrate, defined as D n =(x A,n ,y A,n +d t ).

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