CN115047618A - Design method of compact double-free-form-surface dodging lens for extended light source - Google Patents
Design method of compact double-free-form-surface dodging lens for extended light source Download PDFInfo
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Abstract
A design method of a compact type double-free-form-surface lens for an extended light source belongs to the technical field of optical design and aims to solve the problem that the existing light intensity design method can only be used for far-field illumination and cannot be applied to near-field and far-field illumination, and the method comprises the following steps: determining the illumination distribution of a target surface according to design target parameters; designing initial contour curves of the inner free-form surface and the outer free-form surface; step three, iteratively calculating the remaining part of the free-form surface according to the initial contour curve and the angle difference formed on the target surface after the edge light of the extended light source passes through the lens; and step four, obtaining two-dimensional free-form surface discrete points of the double-free-form surface optical element according to the method, guiding the discrete points into three-dimensional modeling software, fitting an inner free-form surface curve and an outer free-form surface curve, and rotating the curves around an optical axis to obtain a free-form surface element entity. The design method is not limited to the illumination distance, has universality, and can be simultaneously used for near-field and far-field illumination.
Description
The technical field is as follows:
the invention relates to a design method of a compact double-free-form-surface dodging lens for an extended light source, and belongs to the technical field of optical design.
The background art comprises the following steps:
with the development of new energy lighting technology, LEDs have been widely used in the lighting field as a new generation of green lighting devices, having the advantages of small size, high luminous efficiency, low cost, and the like. Compared with the traditional spherical optical system, the free-form surface optical system has the advantages of small volume, high energy utilization rate and the like, and can effectively reduce the length and the volume of the whole optical system. With the progress of modern optical processing technology, such as injection molding technology, the application of the optical free-form surface in an optical system is promoted. Today, multi-chips and large LEDs dominate the lighting market of the developing country. However, to date, there is no general optical design method suitable for an extended light source that can achieve the illuminance distribution of far-field, near-field illumination simultaneously.
An article of 'Ultra-compact LED lens with double free form surfaces for uniform illumination' published in 2015 by Hu S.Hu, K.Du, T.Mei and the like in Optics Express journal utilizes a genetic algorithm and a light intensity design method to design a double free-form surface dodging lens, and based on the assumption that light rays of an extended light source are parallel light emergent after passing through the lens, the initial structure of a free-form surface is solved by restricting the height of the free-form surface and the emergent angle of the light rays. The finally designed compact double-free-form-surface lens can realize the illumination effect with the illuminance uniformity of more than 90% on a target surface with the distance of 1m, but is not suitable for near-field illumination. The double free-form surfaces designed by the existing light intensity design method can realize the preset light intensity distribution on the target surface, but are only suitable for the condition of long illumination distance, and are not verified to be suitable for near-field illumination.
The Chinese patent publication number is CN212391665U, the patent name is 'double free-form surface lens for LED surface light source short-distance illumination', the initial lens inner and outer contour curve of the incident surface and the emergent surface are fitted by parabola; and iterating to obtain other parts of the double free-form surfaces, fitting discrete points of the free-form surfaces by utilizing even high-order polynomials, and deriving the discrete points to obtain the lens model. Design examples, while enabling short-range lighting, do not verify suitability for far-field lighting.
The invention content is as follows:
the invention provides a design method of a compact double-free-form-surface dodging lens for an extended light source, which aims to solve the problem that the existing light intensity design method can only be used for far-field illumination and cannot be applied to near-field and far-field illumination, and simultaneously enables a designed optical element to have optical performances of high energy utilization rate and high uniformity.
The technical scheme for solving the technical problem is as follows:
a design method of a compact double-free-form-surface dodging lens for an extended light source comprises the following steps: designing the element height of a double-free-form-surface lens; step two, calculating a quadratic polynomial curve coefficient of the initial contour curve of the inner free-form surface and the outer free-form surface; step three, an initial contour curve is divided evenly, and the remaining free-form surface discrete points are solved in an iterative manner by utilizing the angle difference value of the left and right edge light rays after passing through the initial contour curve and the vector form of the refraction law; and step four, obtaining two-dimensional free-form surface discrete points of the double-free-form surface optical element according to the method, guiding the discrete points into three-dimensional modeling software, fitting an inner free-form surface curve and an outer free-form surface curve, and rotating the curves around an optical axis to obtain a free-form surface element entity.
Step one, the target parameter determines the illuminance distribution of the target surface, and the illuminance of the target surface is determined by the following formula:
in the formula: e 2D Is the illuminance of the target surface, sin θ Left side of 、sinθ Right side The sine value is formed on the target surface after the edge light passes through the lens; omega 2D Is the projection plane angle, and L is the luminance brightness of the LED; setting an included angle formed by a point on a target surface and a z axis after light rays emitted from a light source are refracted by a lens and sin theta Left side of When they coincide, are positive, and sin θ Right side Negative when consistent; the upper and lower integral limits of the projection plane angle are respectively determined by the included angle formed by the two edge light rays of the light source reaching the target surface and the vertical direction.
In the illumination distribution formula of the target surface in the step one, the illumination of the target surface is made to be equal everywhere, and omega formed by the light after passing through the lens is controlled 2D Equal to each other; at omega 2D Given the coordinates of the initial point, the height of the center of the outer free-form surface can be determined, given known conditions.
In the second step, the initial contour curves of the inner free-form surface and the outer free-form surface are determined by the following formula:
z＝a i x 2 +b i ，
wherein i-1, 2 represents the inner and outer lens profiles, and requires a i Less than 0.
The third step is specifically as follows: averaging the initial curve obtained in the step two, obtaining an angle difference value formed by the edge light of the extended light source on the target surface after passing through the lens according to the illumination distribution formula in the step one, and iteratively calculating the rest part of the free-form surface, wherein the discrete point calculation of the free-form surface can be determined by a normal vector of a known initial contour curve:
in the formula: n is the normal vector of the discrete points of the free-form surface, e in ，e out Is the unit normal vector of the incident light and the emergent light; n is I And n O Refractive indices of the incident and refractive index media, respectively; the free-form surface discrete point is obtained from the intersection point of the tangent vector of the previous point and the incident vector.
The invention has the beneficial effects that: the invention provides a design method of a compact double-free-form-surface dodging lens for an extended light source, and solves the problem of illumination of the extended light source at near and far distances. Under the condition of not considering Fresnel loss, under the condition that the ratio of the illumination distance to the lens height is less than 5 near-field illumination, the energy utilization rate of the designed optical system is more than 99%, and the illumination uniformity is more than 93%; in a far-field illumination system with an illumination distance of more than 250mm, the energy utilization rate of the designed optical system is more than 97%, and the illumination uniformity is more than 92%.
The design method provided by the invention directly utilizes the angle difference formed by the fact that the left and right edge light rays of the extended light source reach the target surface after being refracted by the lens to control the illumination distribution of the target surface, and simultaneously considers the size of the light source, the light emitting characteristic of the light source and the illumination distance in the design, so that the design method is not limited to the illumination distance, has universality and can be simultaneously used for near-field and far-field illumination.
Description of the drawings:
FIG. 1 is a parameter diagram of an illumination distribution and an extended light source for a two-dimensional object plane.
Fig. 2 is a schematic diagram of dual free-form lens height and initial curve determination.
FIG. 3 is a schematic diagram of iteratively solving the remainder of the free-form surface.
Fig. 4 is a two-dimensional profile curve of a near-field dual-free-form surface lens.
Fig. 5 is a far field dual-free-form surface lens two-dimensional profile curve.
Fig. 6 is a near-field dual-free-form lens illumination profile.
Fig. 7 is a far field dual-free-form lens illumination profile.
The specific implementation mode is as follows:
the present invention will be described in further detail with reference to the accompanying drawings.
The specific implementation and design examples of the invention are as follows:
the design parameters are given as follows: light source diameter S 1 S 2 2mm, the lens material n is 1.59102, the distance from the illumination surface to the LED surface light source is 15mm, and the illumination surface is perpendicular to the optical axis Z axis, and the aim of the embodiment is to realize uniform illumination with the illumination radius of the target surface being 15 mm. In the XOZ plane, preset I 1 Point coordinates of (0.37,0.97), O 1 The Z-coordinate value of the point is set to 3.9mm,
the point coordinates can be found by triangulating R, and H.
A design method of a compact double-free-form-surface dodging lens for an extended light source comprises the following steps:
step one, under the two-dimensional condition, an LED light source with a certain length is provided, after edge light rays of the LED light source pass through a free-form surface lens, the luminous flux in a two-dimensional target plane area is as follows:
in the formula: omega 2D For projected plane angle, sin θ Left side of 、sinθ Right side The sine value of the edge ray on the target surface after passing through the lens is formed. Omega 2D To project the plane angle, L is the luminance of the LED. The upper and lower limits of the integral of the projection plane angle are respectively determined by the included angle between the vertical direction and the target plane reached by the two marginal rays of the light source, as shown in fig. 1.
And determining the illumination distribution of the target surface according to the design target parameters. When the free-form surface dodging lens is designed, the showroom distribution formula of light in the target plane area can be deduced, and when the illumination intensity at each point of the target plane is equal, the omega formed by the light after passing through the lens is controlled 2D Are equal.
And step two, designing initial contour curves of the inner free-form surface and the outer free-form surface. Calculating the initial contour curves of the inner free-form surface and the outer free-form surface, wherein the initial curve of the lens is determined by the following formula:
z＝a i x 2 +b i (2)
wherein i is 1,2 represents the inner and outer lens profiles, and requires a i Less than 0.
The calculation of the initial curve is shown in fig. 2. I is 1 I 2 And O 1 O 2 Is an initial curve, and I 1 And I 2 、O 1 And O 2 The points are symmetrical about the Z axis. Two marginal rays S 1 I 1 And S 2 I 2 Respectively reach O after being refracted by the first free-form surface 1 Point and O 2 The point, the emergent rays 1 and 2 reach the center point R of the illumination surface 0 And (4) point. At the moment, the included angle formed by the light rays 1 and 2 and the Z axis is theta l(0) 、θ r(0) And theta r(0) ＝-θ l(0) 。
The curve I is calculated by using the formula (2) 1 I 2 And O 1 O 2 In I 1 Dot and O 1 After the first derivative of the point, two parabolas are usedAnd fitting the initial contour of the inner free-form surface and the initial contour of the outer free-form surface by a line. One parabola acts as the inlet profile and the other parabola represents the initial curve of the outlet profile. To ensure that all light is injected into the lens, I 1 Coordinates of the points should ensure the curve I 1 I 2 Is open downwards, i.e. I 1 Is negative. O is 1 Is dependent on omega 2D (0) Is determined at R 0 Illumination of a spot while O 1 Should meet the preset lens aperture size requirement.
And step three, iteratively calculating the remaining part of the free-form surface according to the initial contour curve and the angle difference formed on the target surface after the edge light of the extended light source passes through the lens. The remaining part of the free-form surface is calculated by iteration on the basis of the calculation of the initial parabolic curve, as shown in fig. 3. Along the x-axis, divide the initial curve O equally 1 O 2 To obtain a series of data points P i (i ═ 1, 2., N), light ray S 1 Q i Through Q i Enters the lens and then reaches P i Point, and the parabolic curve expression of the inner free-form surface is known, so Q i The point coordinates can be calculated by the fermat principle. From S 1 、S 2 The light emitted by the point is refracted by the optical system and then is positioned on the target surface R i The points form angles theta with the Z axis l(i) 、θ r(i) (i＝1,...,N)。
As shown in FIG. 3(a), for marginal ray S 1 Q 1 In other words, its emergent ray 3 finally reaches R on the target plane 1 Points according to point P 1 And R 1 Can be found to be the angle theta l(1) A value of (a) is l(1) Then substituting the formula (1) to solve the problem of theta r(1) . From R by reverse tracing 1 The emitted light 4 and the included angle formed by the light 4 and the z axis is theta r(1) Then substituted into R 1 The coordinates of the points can be used to obtain a linear expression of the ray 4. Point P N+1 Is the light ray 4 and the previous point P N At the intersection of tangent lines, i.e. tangent vector
With light 4The point of intersection is P N+1 ，P N+1 The coordinates of the points can be found.
Through the refraction of the backward tracing ray 4 to S 2 To calculate the point P N+1 The normal vector of (a). The discrete point calculation of the free-form surface can be determined by the normal vector of the discrete points of the free-form surface:
in the formula: n is the normal vector of the discrete points of the free-form surface, e in ，e out Is the unit normal vector of the incident light and the emergent light; n is I And n O The refractive indices of the incident and refractive index media, respectively.
While keeping the original curve parameter a 1 ，b 1 While not changing, the inner free-form surface is subject to cubic spline fitting, so that the inner free-form surface point Q 0 …Q N+i Coordinates and tangent vector of point
As is known, the solving process is shown in fig. 3 (b). P is N+1 ，Q N+1 The coordinates of the points are known, the refracted ray P N+1 Q N+1 Vector can be found, P N+1 The incident vector at a point is R 1 P N+1 Then P is N+1 The normal vector of the point can be obtained by the formula (3). Repeating the iterative calculation process until R max To (3).
And step four, importing the discrete points obtained by calculation into three-dimensional modeling software, fitting all the discrete points into a curve by utilizing a spline curve construction function built in the software, and rotating the fitted curve around the Z axis to obtain the three-dimensional solid model of the free-form surface lens.
The center height h of the outer curved surface of the near-field double-free-form-surface lens is 4mm and the diameter d of the lens is 8.23mm, which are calculated by the method, and shown in fig. 4.
The obtained lens is led into optical simulation software, and 1000 ten thousand ray traces are carried out to obtain an illumination distribution diagram, and a near-field target surface illumination distribution curve is shown in fig. 6. Simulation results show that the illuminance uniformity in a target area with the radius of 15mm reaches 0.931, and the light energy utilization rate is 0.991 under the condition that Fresnel loss is not considered. High-energy utilization rate and compact structure of high-uniformity illumination are realized.
In order to prove the universality of the design method, the double-free-form-surface dodging lens for far-field illumination is designed and is implemented as follows.
The design parameters are given as follows: diameter S of LED area light source 1 S 2 The lens material n is set to be 1.59102 mm, the distance from the illumination surface to the LED surface light source is 10m, and the illumination surface is perpendicular to the optical axis z axis, and the aim of the embodiment is to realize uniform illumination with the illumination radius of 10 m. Initial design parameter initial point I of far-field dual-free-form-surface lens on XOZ plane in the design example 1 The coordinates are (8, 6), O 1 Point z coordinate 18.9mm, O 1 The x-coordinate of the point can be found by trigonometric relations.
A design method of a compact double-free-form-surface dodging lens for an extended light source comprises the following steps:
firstly, in a two-dimensional situation, after an edge light of an LED light source with a certain length passes through a free-form surface lens, the luminous flux in a two-dimensional target plane area is:
in the formula: omega 2D For projected plane angle, sin θ Left side of 、sinθ Right side The sine value of the edge ray on the target surface after passing through the lens is formed. Omega 2D To project the plane angle, L is the luminance of the LED. The upper and lower limits of the integral of the projection plane angle are respectively determined by the included angle formed by the two edge light rays of the light source reaching the target surface and the vertical direction, as shown in fig. 1.
Step one, determining the illumination distribution of a target surface according to design target parameters. When the free-form surface dodging lens is designed, the formula of luminous flux in the target plane area can be deduced, and when the illuminance of the target plane is everywhereWhen equal, only the omega formed by the light after passing through the lens needs to be controlled 2D Equal to each other.
And step two, designing initial contour curves of the inner free-form surface and the outer free-form surface. Calculating the initial contour curve of the inner free-form surface and the outer free-form surface, wherein the initial curve of the lens is determined by the following formula:
z＝a i x 2 +b i (5)
where i is 1 and 2 represents the inner and outer lens profiles. And requires a i Less than 0.
As shown in fig. 2. I.C. A 1 I 2 And O 1 O 2 Is an initial curve, and I 1 And I 2 、O 1 And O 2 The points are symmetrical about the Z axis. Two marginal rays S 1 I 1 And S 2 I 2 Respectively reach O after being refracted by the first free-form surface 1 Point and O 2 The point, the emergent rays 1 and 2 reach the center point R of the illumination surface 0 And (4) point. At the moment, the included angle formed by the light rays 1 and 2 and the Z axis is theta l(0) 、θ r(0) And theta r(0) ＝-θ l(0) 。
After calculating curve I 1 I 2 And O 1 O 2 In I 1 Dot and O 1 After the first derivative of the points, the inner and outer free-form surface initial contours are fitted using the two parabolas of equation (5). One parabola acts as the inlet profile and the other parabola represents the initial curve of the outlet profile. To ensure that all light is injected into the lens, I 1 Coordinates of the points should ensure the curve I 1 I 2 Is open downwards, i.e. secured at I 1 The first derivative of the point is negative. O is 1 Is dependent on omega 2D (0) Is determined at R 0 Illumination of a spot while O 1 Should meet the preset lens aperture size requirement.
And step three, iteratively calculating the remaining part of the free-form surface according to the initial contour curve and the angle difference formed on the target surface after the edge light of the extended light source passes through the lens. Calculating the rest of the free-form surface, and equally dividing the initial curve O along the x-axis 1 O 2 Obtaining a series of data points P i (i＝1,2, N), light S 1 Q i Through Q i Enters the lens and then reaches P i Point, and the parabolic curve expression of the inner free-form surface is known, so Q i The point coordinates can be calculated by the fermat principle. From S 1 、S 2 The light emitted by the point is refracted by the optical system and then is positioned on the target surface R i The points form angles theta with the Z axis l(i) 、θ r(i) (i＝1,...,N)。
As shown in FIG. 3(a), for marginal ray S 1 Q 1 In other words, its emergent ray 3 finally reaches R on the target plane 1 Points according to point P 1 And R 1 Can be found to be the angle theta l(1) A value of (a) is l(1) Then substituting into formula (4) to solve formula to obtain theta r(1) . From R by reverse tracing 1 The emitted light 4 and the included angle formed by the light 4 and the z axis is theta r(1) Then substituted into R 1 The coordinates of the points can be used to obtain a linear expression of the ray 4. Point P N+1 Is the light ray 4 and the previous point P N At the intersection of tangent lines, i.e. tangent vector
The intersection point with the ray 4 is P N+1 ，P N+1 The coordinates of the points can be found.
Through the refraction of the backward tracing ray 4 to S 2 To calculate the point P N+1 The normal vector of (c). The discrete point calculation of the free-form surface can be determined by the normal vector of the discrete points of the free-form surface:
in the formula: n is the normal vector of the discrete points of the free-form surface, e in ，e out Is the unit normal vector of the incident light and the emergent light; n is I And n O The refractive indices of the incident and refractive index media, respectively.
While maintaining the original curve parameter a 1 ，b 1 While not changing, the inner free-form surface is processedCubic spline fitting such that the inner free curve point Q 0 …Q N+i Coordinates and tangent vector of point
As is known, the solving process is shown in fig. 3 (b). P N+1 ，Q N+1 The coordinates of the points are known, the refracted ray P N+1 Q N+1 Vector can be found, P N+1 The incident vector at a point is R 1 P N+1 Then P is N+1 The normal vector of the point can be obtained by equation (6). Repeating the iterative calculation process until R max To (3).
And step four, importing the discrete points obtained by calculation into three-dimensional modeling software, fitting all the discrete points into a curve by utilizing a spline curve construction function built in the software, and rotating the fitted curve around the Z axis to obtain the three-dimensional solid model of the free-form surface lens.
The initial curve of the lens was calculated by the above method, the height h of the center of the outer curved surface was 20mm, and the diameter d of the lens was 45.1mm, as shown in FIG. 5.
The far-field target surface illuminance distribution curve is shown in fig. 7, the uniformity of the illuminance in the target surface with the radius of 10m is 92.4%, and the light energy utilization rate of the system is 99% without considering fresnel loss.
According to the design method of the double-free-form-surface dodging lens for the extended light source, the near field and far field can be uniformly illuminated by adjusting the initial parameters according to different design targets. The initial surface shape and the parameters of the inner surface and the outer surface are different, but the method flows are completely the same, which explains the universality of the design method.
Claims (5)
1. A design method of a compact double-free-form surface lens for an extended light source is characterized by comprising the following steps:
determining the illumination distribution of a target surface according to design target parameters;
designing initial contour curves of the inner free-form surface and the outer free-form surface;
step three, iteratively calculating the remaining part of the free-form surface according to the initial contour curve and the angle difference formed on the target surface after the edge light of the extended light source passes through the lens;
and step four, obtaining two-dimensional free-form surface discrete points of the double-free-form surface optical element according to the method, guiding the discrete points into three-dimensional modeling software, fitting an inner free-form surface curve and an outer free-form surface curve, and rotating the curves around an optical axis to obtain a free-form surface element entity.
2. The method as claimed in claim 1, wherein the step of determining the illuminance of the target surface with the target parameter is determined by the following formula:
in the formula: e 2D Is the illuminance, sin θ, of the target surface Left side of 、sinθ Right side The sine value is formed on the target surface after the edge light passes through the lens; omega 2D Is the projection plane angle, L is the luminance brightness of the LED; setting an included angle formed by a point on a target surface and a z axis after light rays emitted from a light source are refracted by a lens and sin theta Left side of When they coincide, are positive, and sin θ Right side Negative when consistent; the upper and lower integral limits of the projection plane angle are respectively determined by the included angle formed by the two edge light rays of the light source reaching the target surface and the vertical direction.
3. The method as claimed in claim 2, wherein the illuminance distribution formula of the target surface in the first step is such that the illuminance of the target surface is equal everywhere, and the omega formed by the light passing through the lens is controlled 2D Equal to each other; at omega 2D Given the coordinates of the initial point, the center height of the outer free-form surface can be determined, given the known conditions.
4. The method as claimed in claim 3, wherein the initial contour curves of the inner and outer free-form surfaces in step two are determined by the following formula:
z＝a i x 2 +b i ，
wherein i is 1,2 represents the inner and outer lens profiles, and requires a i Less than 0.
5. The method as claimed in claim 4, wherein the step three is specifically as follows: averaging the initial curve obtained in the step two, obtaining an angle difference value formed by the edge light of the extended light source on the target surface after passing through the lens according to the illumination distribution formula in the step one, and iteratively calculating the rest part of the free-form surface, wherein the discrete point calculation of the free-form surface can be determined by a normal vector of a known initial contour curve:
in the formula: n is the normal vector of discrete points of the free-form surface, e in ，e out Is the unit normal vector of the incident light and the emergent light; n is I And n O Refractive indices of the incident and refractive index media, respectively; the free-form surface discrete point is obtained from the intersection point of the tangent vector of the previous point and the incident vector.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN107678152A (en) * | 2017-09-04 | 2018-02-09 | 华南理工大学 | LED free-form surface lens for optical microphotograph mirror reflection illuminator |
| US20180348523A1 (en) * | 2017-06-01 | 2018-12-06 | Seiko Epson Corporation | Display apparatus |
| CN110543014A (en) * | 2019-08-15 | 2019-12-06 | 中山市华南理工大学现代产业技术研究院 | Design method of double-free-form-surface lens for short-distance illumination of LED (light emitting diode) surface light source |
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Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20180348523A1 (en) * | 2017-06-01 | 2018-12-06 | Seiko Epson Corporation | Display apparatus |
| CN107678152A (en) * | 2017-09-04 | 2018-02-09 | 华南理工大学 | LED free-form surface lens for optical microphotograph mirror reflection illuminator |
| CN110543014A (en) * | 2019-08-15 | 2019-12-06 | 中山市华南理工大学现代产业技术研究院 | Design method of double-free-form-surface lens for short-distance illumination of LED (light emitting diode) surface light source |
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Application publication date: 20220913 |