CN104317053A - Free-form surface lens construction method based on lighting of LED desk lamp - Google Patents

Abstract

The invention claims to protect a method for constructing a free-form surface lens for LED desk lamp lighting. The method simplifies the calculation of the free-form surface lens of the LED desk lamp from three-dimensional space to the calculation of the generatrix l of the free-form surface of the lens in two-dimensional space, with the light source of the LED desk lamp as the origin Establish coordinates, establish an equation according to the relationship between the incident and outgoing light vectors and normal vectors according to Snell's law; the radiant flux of the LED desk light source is equal to the luminous flux received by the target lighting surface, and the equation can be listed, and the target lighting surface in the calculation The formed spot is a uniform circular spot, so the illuminance E is equal, so that the relationship between the known coordinates on the target illumination surface and the coordinates of the free-form surface of the lens can be established. According to the coordinates on the known target surface, the numerical method iteratively solves the generatrix l of the free-form surface of the lens, and then fits its data and rotates around the axis to obtain the free-form surface, which is closed and solidified into a lens. The invention improves the effective utilization rate of light and the uniformity of illuminance.

Description

Construction Method of Freeform Surface Lens Based on LED Desk Lamp Illumination

technical field

The invention relates to a free-form surface lens for LED desk lamp lighting. The light source used in the LED desk lamp is a high-power LED. The free-form surface lens can improve the effective utilization rate and illuminance uniformity of the light emitted by the light source, and belongs to the technical field of LED lighting applications.

Background technique

LED desk lamp is exactly the desk lamp using LED (Light Emitting Diode) as light source. LED desk lamp is suitable for reading, writing, reviewing and other office or study lighting places, to ensure a good visual environment in the work area, so as to improve the efficiency of office and study. If the illuminance and uniformity of the lighting area are poor, people's vision will be easily fatigued, which will affect work efficiency and vision, so special attention should be paid to the quality of lighting. Compared with traditional light sources, LED lighting has significant advantages such as energy saving, environmental protection, long life, safety, and small size. With the improvement of the luminous efficiency of high-power LEDs, the luminous efficacy of power LEDs has reached 100lm/W to 161lm/W, and it is possible to use LEDs as the lighting source of desk lamps.

LEDs have great potential as a light source for table lamps because they use direct current without flickering and are highly efficient lighting sources. However, if the LED does not have a reasonable light distribution, the light spot irradiated on the target surface will be too bright in the middle, and the surrounding area will become dark and uneven lighting. This requires the design of optical devices to match the light source of the LED desk lamp. Design optical devices including lenses and reflectors, because the former is beneficial to the installation of LED light source and the design of heat dissipation structure, and if the latter is used, the LED light source itself and its heat dissipation structure will block the reflected light and affect the distribution of light in the lighting area . Therefore, a high-efficiency free-form surface lens is designed to have a better control of the angle of the outgoing light and a better level of illumination and uniformity.

Contents of the invention

Aiming at the deficiencies in the prior art above, the object of the present invention is to provide a light utilization rate high, and the illuminated illuminance is uniform. The technical solution of the present invention is as follows: a free-form surface lens construction method based on LED desk lamp lighting, which Include the following steps:

101. Take the LED light source as the coordinate origin of the three-dimensional coordinate system, establish a three-dimensional coordinate system, and measure the vertical distance from the LED light source to the target lighting surface as h. The LED light source is surrounded by a free-form surface lens. Assume that the coordinates on the free-form surface of the lens are Where θ is the angle between the projection of the light on the xoy surface and the positive direction of the x-axis, is the angle between the ray and the positive direction of the z-axis, is when the angle is , the distance from point a to the origin; point b(x, y, z) on the target lighting surface, the unit vectors of the outgoing light and the incident light are Out, In, and the normal vector of the tangent plane is N, and the free-form surface lens refracts The rate is set to n, and the refractive index of air is set to 1;

102. Set the free-form surface bus l of the lens of the LED table lamp, simplify the three-dimensional space to the two-dimensional space xoz or yoz, and solve the lens bus l on the two-dimensional space xoz or yoz plane, at this time θ is k is 0,1,2...;

103. Take k as 0, θ as 0, and the two-dimensional space as xoz, establish the vector relationship, and list the vector relationship equation by Snell's law of refraction;

104. List the equations according to the radiant flux of the LED light source and the luminous flux received by the target light, and then according to the uniform illuminance of the circular spot with a radius of d on the target lighting surface, that is, E is equal, the LED light source is selected as a Lambertian body, and its exist The light intensity in the angular direction is The following equation can be obtained,

Therefore we can see,

get the equation,

105. Use the numerical method to solve the differential equation in step 104 A series of values ρ ₁ , ρ ₂ ,...ρ _N obtained by discrete solution using the Runge-Kutta method;

106. The series of numerical values ρ ₁ , ρ ₂ ,...ρ _N obtained by solving in step 105 are the distance from the point on the bus line l of the free-form surface of the lens to the origin, and the points on the bus line l are converted into Cartesian coordinates,

107. Import the free-form surface generatrix l data of the lens into the modeling software, and then rotate it around the central axis to obtain the free-form surface of the lens, which is the free-form surface lens of the LED desk lamp.

Further, the Runge-Kutta method in step 105 is in the interval The weighted average of the slopes of the four points is used as the approximate value of the average slope, which constitutes the fourth-order classic Runge-Kutta formula,

Where n=0,1,2,...N-1, ρ(0)=ρ ₀ , ρ ₁ , ρ ₂ ,...ρ _N can be obtained.

Advantage of the present invention and beneficial effect are as follows:

In the present invention, the light source of the LED desk lamp is located at the coordinate origin, followed by the lens. The illumination target surface forms a circular spot with uniform illumination, so the lens can be considered to be rotationally symmetric, and its symmetry axis passes through the center point of the LED light source and the circular spot. Because the lens is rotationally symmetric, solving the free-form surface in three-dimensional space can be simplified as finding the free-form surface generatrix of the lens in two-dimensional space, which simplifies the design method.

In the present invention, the free-form surface lens is applied to the LED desk lamp lighting, which can improve the effective utilization rate of the light of the LED desk lamp, solve the curved surface through the equation, can more accurately control the distribution of the light in the lighting target area, and can improve the illumination and uniformity of the lighting target area Spend.

Description of drawings

Figure 1 is a three-dimensional schematic diagram of the LED desk lamp light source, the free-form surface of the lens, and the target lighting surface;

Figure 2 is a schematic diagram of the relationship between incident and outgoing light rays and normal lines;

Figure 3 is the data fitting of the free-form surface lens busbar of the LED desk lamp;

Fig. 4 is the rotating body of the free-form surface lens generatrix of the LED desk lamp;

Fig. 5 is the free-form surface lens entity of the LED desk lamp;

Fig. 6 is embodiment LED desk lamp free-form surface lens;

Fig. 7 is the free-form surface lens entity of the LED desk lamp of the embodiment;

Fig. 8 is an illuminance distribution diagram on the target lighting surface of the LED desk lamp;

Fig. 9 is a graph showing the distribution of illuminance on the target lighting surface of the LED desk lamp.

Figure 10 is a flowchart of a preferred embodiment of the present invention.

Detailed ways

A non-limiting embodiment is given below in conjunction with the accompanying drawings to further illustrate the present invention. It should be understood, however, that these descriptions are exemplary only, and are not intended to limit the scope of the invention. Also, in the following description, descriptions of well-known structures and techniques are omitted to avoid unnecessarily obscuring the concept of the present invention.

The present invention realizes the LED desk lamp free-form surface lens of the circular light spot of uniform illumination by solving the equation, and its specific design points are as follows:

(1) The LED desk lamp forms a uniform circular spot on the target irradiation surface, which is rotationally symmetric. The luminous characteristics of the LED light source are rotational symmetry around the luminous axis. The free-form surface lens of the LED table lamp is also rotationally symmetric, so find the equation of the generatrix of the free-form surface of the lens.

(2) Establish a three-dimensional coordinate system, the LED light source coincides with the origin, and the coordinates on the free-form surface of the lens are set to Where θ is the angle between the projection of the light on the xoy surface and the positive direction of the x-axis, is the angle between the ray and the positive direction of the z-axis, is when the angle is , the distance from point a to the origin. Point b(x, y, z) on the target illumination surface, the unit vectors of the outgoing light and the incident light are Out, In, and the normal vector of the tangent plane is N. The refractive index of the free-form surface lens is set to n, and the refractive index of air is set to 1.

(3) In order to obtain the busbar l of the lens free-form surface of the LED table lamp, and the lens is rotationally symmetric, the three-dimensional space can be simplified into a two-dimensional space, which can be simplified to xoz or yoz two-dimensional plane to solve the lens busbar l, at this time θ for k is 0, 1, 2....

(4) Take k to be 0, θ to be 0, and the two-dimensional space to be xoz to establish a vector relationship. According to Snell's law,

[1+n ² -2n(Out·In)] ^1/2 ·N＝Out-nIn (1)

in,

Out＝(ob-oa)/|ob-oa| (3)

ob＝(x,z) (4)

When the free-form surface is rotationally symmetric, when When it is a certain value, the value of ρ(θ) is the same in the range of 0≤θ≤2π, that is, it does not change with θ, ρ _θ =0.

[1+n ² -2n(Out·In)] ^1/2 ·N _x ＝Out _x -nIn _x (7)

[1+n ² -2n(Out·In)] ^1/2 ·N _z ＝Out _z -nIn _z (8)

N _x /N _z ＝(Out _x -nIn _x )/(Out _z -nIn _z ) (9)

(5) List the equations according to the fact that the radiant flux of the LED light source is equal to the luminous flux received by the target light, and the illuminance of the circular spot with a radius of d on the target illumination surface is uniform, that is, E is equal. The LED light source is generally a Lambertian body, and its The light intensity in the angular direction is So the following equation can be obtained,

Therefore we can see,

So by (11), (14) get the equation,

(6) For solving the differential equation numerically, the Runge-Kutta method is used for discretization. First put into many discrete points and corresponds to (ρ ₀ , ρ ₁ , ρ ₂ , . . . ρ _N ). n=0, 1, 2, . . . N. When n=0, , ρ(0)=ρ ₀ , that is, the central height dimension of the free-form surface lens is ρ ₀ . Consider using the linear relationship combination of function values at several points of the function to construct an approximate formula, which not only avoids partial derivatives, but also improves the calculation accuracy. This is the basic idea of the Runge-Kutta method. In order to meet the needs of improving accuracy, you can use the interval The weighted average of the slopes of the four points is used as the approximate value of the average slope, which constitutes the fourth-order classic Runge-Kutta formula,

Where n=0,1,2,...N-1, ρ(0)=ρ ₀ , ρ ₁ , ρ ₂ ,...ρ _N can be obtained.

(7) The obtained series of values ρ ₁ , ρ ₂ ,...ρ _N are the distance from the point on the bus line l of the free-form surface of the lens to the origin, and the points on the bus line l are converted into Cartesian coordinates as,

(8) Import the free-form surface bus l data of the obtained lens into the modeling software, and then rotate it around the central axis to obtain the free-form surface of the lens, and then materialize the curved surface into a free-form surface lens, which is the free-form surface of the LED desk lamp lens.

The invention adopts a numerical method to solve the free-form surface equation of the LED desk lamp lens, and has the characteristics of flexible design, short period and accuracy. In one embodiment of the present invention, the light source of the LED table lamp adopts a Lambertian LED with a luminous area of 1 mm×1 mm, which is a commodity with a single LED of 1 W and a light effect of 100 lm/W common in the market. In the design, the vertical distance from the LED desk light source to the target lighting surface is 400mm, the target irradiation range is a circular area with a radius of 500mm, and the lens is PMMA. Since the LED light-emitting part is encapsulated with a raised hemisphere, in order to install the free-form surface lens on the LED light source well, a hemisphere with a radius of 3mm is dug out at the center of the bottom of the lens, and the center of the sphere coincides with the center of the bottom of the lens. From Figure 8 and Figure 9, it can be seen that because the LED free-form surface lens redistributes the light, the light is distributed on the target lighting surface as much as possible, and the illuminance uniformity is greatly improved, forming a bright and uniform circular spot, so that people have A more comfortable visual environment and good uniformity make it less likely to cause visual fatigue when people use LED desk lamps, thereby protecting eye health and improving work efficiency.

The above embodiments should be understood as only for illustrating the present invention but not for limiting the protection scope of the present invention. After reading the contents of the present invention, skilled persons can make various changes or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the claims of the present invention.

Claims (2)

1. A free-form surface lens construction method based on LED desk lamp illumination, is characterized in that: comprise the following steps: 101. Take the LED light source as the coordinate origin of the three-dimensional coordinate system, establish a three-dimensional coordinate system, and measure the vertical distance from the LED light source to the target lighting surface as h. The LED light source is surrounded by a free-form surface lens. Assume that the coordinates on the free-form surface of the lens are Where θ is the angle between the projection of the light on the xoy surface and the positive direction of the x-axis, is the angle between the ray and the positive direction of the z-axis, is when the angle is , the distance from point a to the origin; point b(x, y, z) on the target lighting surface, the unit vectors of the outgoing light and the incident light are Out, In, and the normal vector of the tangent plane is N, and the free-form surface lens refracts The rate is set to n, and the refractive index of air is set to 1; 102. Set the free-form surface bus l of the lens of the LED table lamp, simplify the three-dimensional space to the two-dimensional space xoz or yoz, and solve the lens bus l on the two-dimensional space xoz or yoz plane, at this time θ is k is 0,1,2...; 103. Take k as 0, θ as 0, and the two-dimensional space as xoz, establish the vector relationship, and list the vector relationship equation by Snell's law of refraction; 104. List the equations according to the radiant flux of the LED light source and the luminous flux received by the target light, and then according to the uniform illuminance of the circular spot with a radius of d on the target lighting surface, that is, E is equal, the LED light source is selected as a Lambertian body, and its exist The light intensity in the angular direction is The following equation can be obtained, Therefore we can see, get the equation, 105. Use the numerical method to solve the differential equation in step 104 A series of values ρ ₁ , ρ ₂ ,...ρ _N obtained by discrete solution using the Runge-Kutta method; 106. The series of numerical values ρ ₁ , ρ ₂ ,...ρ _N obtained by solving in step 105 are the distance from the point on the bus line l of the free-form surface of the lens to the origin, and the points on the bus line l are converted into Cartesian coordinates, 107. Import the free-form surface generatrix l data of the lens into the modeling software, and then rotate it around the central axis to obtain the free-form surface of the lens, which is the free-form surface lens of the LED desk lamp. 2. The free-form surface lens construction method based on LED desk lamp lighting according to claim 1, characterized in that: the Runge-Kutta method in step 105 is in the interval The weighted average of the slopes of the four points is used as the approximate value of the average slope, which constitutes the fourth-order classic Runge-Kutta formula, Where n=0,1,2,...N-1, ρ(0)=ρ ₀ , ρ ₁ , ρ ₂ ,...ρ _N can be obtained.