TWI709078B - Method of designing a free-form surface lens for light collimation - Google Patents

Abstract

The present invention discloses a method of designing a free-form surface lens for light collimation, and the method includes the steps of: inputting a default value, wherein a LED source is positioned at the left side of a lens, a +z axis is defined as the central axis of the LED source, a distance between the LED source and the apex of the lens is defined as a D ₀ value, and a ξ value ranges between -0.5 and 50; determining a first free-form surface of the lens, wherein the first free-form surface is formulated with an equation: r=r ₁ (θ); and determining a second free-form surface of the lens, wherein the second free-form surface is formulated with r=r ₂ (α). As such, after the light emitted from the LED source is received by the lens, the light is parallel with the +z axis.

Description

Free-form lens design method applied to light source collimation

The invention relates to a free-form surface lens design method applied to light source collimation, in particular to a free-form surface lens lens design applied to light-emitting diode light source collimation and combined parallel light source.

Because the LED light source has a certain size of light-emitting area, and the light diffusion angle is quite large, the design of the traditional collimating lens is not easy, and its optical effect is not ideal, or the collimated light still has a large half-angle of divergence , Or else the energy extraction efficiency is not high, or the light source is partitioned, resulting in a more disordered light pattern and energy distribution. Facing an LED light source with a non-point light source and a large divergence angle, the design of the collimating lens must adopt a free-form surface with maximum design freedom, and cooperate with a more precise analytical solution, in order to take into account the performance and requirements of multiple optics.

The purpose of the present invention is to provide a new free lens design method that can target a given LED light source through a set of systematic and theoretically based design steps and methods to obtain a free curve with both sides The surface lens can effectively convert the LED light source into a collimated light source with continuous energy distribution in space.

Another object of the present invention is based on the collimation and continuous energy distribution characteristics of the above-mentioned light source. The method of arranging a large number of collimated light sources can be further used to obtain a collimated light source with a larger area. Finally, with appropriate mechanical movement, It meets the current specifications of the traditional UV flat uniform exposure light source, and replaces the existing mercury lamp-based UV exposure light source module with many advantages such as low price, long life, power saving, environmental protection, simple structure, and easy use.

，起始條件 r ₁(0 ^o )=D _o ，其中，α是虛擬光源發出的光線與+z軸的夾角，n _o 與n分別是空氣與透鏡材料的光學折射係數；以及決定該第二自由曲面，該第二自由曲面為數學方程式r=r ₂ (α)，將所有的入射光線，經折射與+z軸平行，r ₂ (α)滿足下列 的微分方程式

，其中，T _o 為所選 定之透鏡厚度。 In order to achieve the above objective, the first embodiment of the present invention discloses a free-form surface lens design method applied to light source collimation, including the following steps: input a preset value, an LED light source on the left side of a lens, +z axis is the light source The central axis of the lens has a first free-form surface and a second free-form surface. The distance from the LED light source to the apex of the lens is preset to be D _o . A ξ value is selected, and the selected range of the ξ value is between -0.5 and 50 ; Determine the first free-form surface, the mathematical equation of the first free-form surface r = r ₁ ( θ ), satisfy the following differential equations:

, The initial condition r ₁ (0 ^o ) = D _o , where α is the angle between the light emitted by the virtual light source and the +z axis, n _o and n are the optical refractive index of air and the lens material respectively; and determine the second Free-form surface, the second free-form surface is the mathematical equation r = r ₂ ( α ), all incident light rays are refracted and parallel to the +z axis, r ₂ ( α ) satisfies the following differential equation

, Where T _o is the selected lens thickness.

，起始條件 r ₁(0 ^o )=D _o ，其中，α ₁為該第一虛擬光源發出的光線與+z軸的夾角，n _o 與n分別是空氣與透鏡材料的光學折射係數(optical refraction index)；決定該第二自由曲面，距離該第一虛擬光源左邊ξ ₂ D _o 位置的點為一第二虛擬光源的出發點，該第二自由曲面為數學方程式r=r ₂ (α ₁ )，滿足下列 的微分方程式

，起始條件 r ₂(0 ^o )=(ξ ₁+1)D _o +T _o ，其中，α ₂為該第二虛擬光源發出的光線與+z軸的夾角，T _o 為該第一自由曲面和該第二自由曲面所組成之透鏡厚度；決定該第三自由曲面，距離該第二虛擬光源左邊ξ ₃ D _o 位置的點為一第三虛擬光源的出發點，該第三自由曲面為數學方程式r=r ₃ (α ₂ )，滿足下列的微分方程 式

，起始條件r ₃(0 ^o )=(ξ ₂+ξ ₁+1)D _o +D ₁+T _o ，其中， D ₁ 為該第二自由曲面在光軸上離該第三自由曲面的距離，α ₃為該第三虛擬光源發出的光線與+z軸的夾角；以及決定該第四自由曲面，該第四自由曲面為數學方程式r=r ₄ (α ₃ )，將所有的入射光線，經折射與+z軸平行，r ₄ (α ₃ )滿足下列的微分方程式

，其中，T ₁ 為該第 三自由曲面和該第四自由曲面所組成之透鏡厚度。 In order to achieve the above objective, the second embodiment of the present invention discloses a free-form surface lens design method applied to light source collimation, including the following steps: input a preset value, an LED light source is on the left side of the two lenses, and the +z axis is the light source The two sets of lenses are respectively a first lens and a second lens. The first lens has a first free-form surface and a second free-form surface, and the second lens has a third free-form surface and a second lens. The fourth free-form surface, the distance from the LED light source to the lens vertex is preset to be D _o , three ξ values are selected, namely ξ ₁ , ξ ₂ , and ξ ₃ , where the selected range of the ξ ₁ value is -0.5 to 50 Ξ ₂ and ξ ₃ are incremental variables greater than zero; determine the first free-form surface, and the point ξ ₁ D _{o to the} left of the LED light source is the starting point of a first virtual light source, the first free-form surface The mathematical equation r = r ₁ ( θ ), satisfies the following differential equation as

, The initial condition r ₁ (0 ^o ) = D _o , where α _{1 is} the angle between the light emitted by the first virtual light source and the +z axis, and n _o and n are the optical refraction coefficients of the air and the lens material (optical refraction index); determine the second free-form surface, the point at the left ξ ₂ D _{o of} the first virtual light source is the starting point of a second virtual light source, and the second free-form surface is the mathematical equation r = r ₂ (α ₁ ) , Satisfies the following differential equation

, The initial condition r ₂ (0 ^o )=( ξ ₁ +1) D _o + T _o , where α _{2 is} the angle between the light emitted by the second virtual light source and the +z axis, and T _{o is} the first free The thickness of the lens formed by the curved surface and the second free-form surface; determining the third free-form surface, the point at the left ξ ₃ D _{o of} the second virtual light source is the starting point of a third virtual light source, and the third free-form surface is mathematical The equation r = r ₃ (α ₂ ) satisfies the following differential equation

, The initial condition r ₃ (0 ^o )=( ξ ₂ + ξ ₁ +1) D _o + D ₁ + T _o , where D ₁ is the distance of the second free-form surface from the third free-form surface on the optical axis Distance, α _{3 is} the angle between the light emitted by the third virtual light source and the +z axis; and determines the fourth free-form surface, which is the mathematical equation r = r ₄ ( α ₃ ), and all incident light , After refraction and parallel to +z axis, r ₄ ( α ₃ ) satisfies the following differential equation

, Where T ₁ is the lens thickness formed by the third free-form surface and the fourth free-form surface.

In order to achieve the above objective, the third embodiment of the present invention discloses that a free-form surface lens manufactured according to the above design method is combined with a UV-LED to form a collimating lens module, and a plurality of the collimating lens modules are arrayed Sorting, the array has N rows, and the distance between the centers of any two adjacent free-form surface lenses in any row is defined as a period D , where the period is equally divided by N , and the second row to the Nth row at the same position The center of the free-form lens projected onto the adjacent points on the periodic line are the same, and the distance is D/N .

In order to achieve the above objective, the third embodiment of the present invention discloses that a free-form surface lens manufactured according to the above design method is combined with a UV-LED to form a collimating lens module, and a plurality of the collimating lens modules are arrayed For sequencing, each collimating lens module completes large-area exposure in a circular motion, defining the distance between the free-form surface lens and the center of the adjacent free-form surface lens as a period, and the radius of the circular motion is smaller than the period.

The beneficial effect of the present invention is that the use of the above free-form surface lens design method has the following advantages: 1. Smaller half angle of light divergence, closer to a standard parallel collimated light source; 2. Lower production cost; 3. Energy-saving and electricity-saving, long service life, low use cost; 4. Small size, light weight, easy to install; 5. Meet environmental protection requirements.

11~13: Steps

21~25: Step

30: Collimating lens module

32: Free-form lens

34: UV-LED

A: Lens vertex

D: Period

D ₀ : distance

D/5: distance

FS ₁ : First free-form surface

FS ₂ : Second free-form surface

FS ₃ : Third free-form surface

FS ₄ : Fourth free-form surface

r: distance

r ₁ : distance

r ₂ : distance

r ₃ : distance

r ₄ : distance

S: LED light source

S’: Virtual light source or first virtual light source

S": Second virtual light source

S''': third virtual light source

T _o : lens thickness

T ₁ : lens thickness

θ : angle

α : angle

α ₁ : angle

α ₂ : angle

α ₃ : angle

Fig. 1 is a schematic diagram illustrating the first preferred embodiment of the free-form lens design method applied to light source collimation according to the present invention; Fig. 2 is a schematic diagram illustrating the first preferred embodiment of the free-form surface lens design method applied to light source collimation according to the present invention Two preferred embodiments; Figure 3 is a schematic diagram illustrating that the left side of the first preferred embodiment is an LED light source, with a certain light-emitting area and a certain light-emitting angle, and the +z axis is the central axis of the light source; Figure 4 -1 is a schematic diagram illustrating the design of the first free-form surface of the first preferred embodiment; Fig. 4-2 is a schematic diagram illustrating the design of the second free-form surface of the first preferred embodiment; Figure 5 is a Schematic diagram, a cross-sectional view of a free-form surface lens simulated according to the first preferred embodiment; Figure 6 is a schematic diagram illustrating that the left side of the second preferred embodiment is an LED light source with a certain size of light-emitting area and a certain amount of light Angle, +z axis is the central axis of the light source; Figure 7-1 is a schematic diagram illustrating the design of the first free-form surface of the second preferred embodiment; Figure 7-2 is a schematic diagram illustrating the design of the second free-form surface of the second preferred embodiment; Figure 7 -3 is a schematic diagram illustrating the design of the third free-form surface of the second preferred embodiment; Figure 7-4 is a schematic diagram illustrating the design of the fourth free-form surface of the second preferred embodiment; Figure 8 is a A schematic diagram illustrating the two lenses simulated by the second preferred embodiment and the corresponding four free-form surface lenses; FIG. 9 is a schematic diagram illustrating the other two lenses simulated by the second preferred embodiment and Corresponding four free-form surface lens cross-sections; Figures 10-1 and 10-2 are schematic diagrams illustrating the third embodiment of the present invention, a free-form surface lens manufactured according to the design method of the first embodiment or the second embodiment Combined with a UV-LED to form a collimating lens module; and Figures 10-1 and 10-3 are schematic diagrams illustrating the fourth embodiment of the present invention, which is manufactured according to the design method of the first embodiment or the second embodiment A free-form surface lens is combined with a UV-LED to form a collimating lens module.

This patent proposes a new free-form lens design method The method can collimate the light emitted by the light emitting diode (LED) to achieve the goal of being close to the parallel light source. The lens design principle is based on the principle of refraction of light on the curved interface of two media in geometric optics and the mathematical analysis method of differential geometry to derive the differential equation and analytical solution of the lens surface; this patent is the most important The invention of using a "virtual light source asymptotic method" design method, combined with the above differential equations and analytical solutions, the free-form surface lens designed can take into account the parallelism of the LED light source after collimation and the energy collection efficiency of the LED light source . The designed free-form surface lens can be matched with its LED light source to form a single collimated light source; if a large number of collimated light sources are arranged into a large area distributed collimated light source, the final coordinated mechanical movement, such as linear scanning or Circular perturbation can achieve large-area collimated and uniform plane illumination. This LED combined collimated and uniform plane light source can be used to replace the traditional ultraviolet plane light source that uses mercury lamps and complex optical systems. It is used in the industrial manufacturing process of photolithography.

Referring to FIG. 1, the first embodiment of the present invention discloses a free-form surface lens design method applied to light source collimation, which includes the following steps: inputting a preset value 11, determining a first free-form surface 12, and determining a second free-form surface Surface 13.

Enter a preset value of 11, an LED light source is on the left side of a lens, the +z axis is the central axis of the light source, the lens has two left and right free-form surfaces that are axisymmetric to the +z axis, and the lens has a first free-form surface and a second free-form surface, the LED light source to a predetermined apex of the lens is the distance D _o, ξ a selected value, the selected value of ξ ranges between -0.5 to 50. Among them, with the LED light source as the origin, the ξ value moves to the right as a negative value, and moves to the left as a positive value.

， 起始條件r ₁(0 ^o )=D _o ，其中，D _o 是LED光源到透鏡頂點的距離，α是虛擬光源發出的光線與+z軸的夾角，n _o 與n分別是空氣與透鏡材料的光學折射係數(optical refraction index)，ξ值選定的範圍在-0.5到50之間。 Determine the first free-form surface 12, the point at the left ξD _{o of} the LED light source is the starting point of a virtual light source, and the first free-form surface is used to allow all the light rays originating from the LED light source to meet on the first free-form surface When refraction occurs, the refracted light can be regarded as the light emitted by the virtual light source. The mathematical equation of the first free-form surface is r = r ₁ ( θ ), which satisfies the following differential equation:

, The initial condition r ₁ (0 ^o ) = D _o , where D _o is the distance from the LED light source to the lens vertex, α is the angle between the light emitted by the virtual light source and the +z axis, n _o and n are the air and the lens, respectively The material's optical refraction index (optical refraction index), the selected range of ξ value is between -0.5 and 50.

，其中，D _o 是LED光源到透鏡頂點的距離，T _o 為所選定之透鏡厚度，α是虛擬光源發出的光線與+z軸的夾角，n _o 與n分別是空氣與透鏡材料的光學折射係數，ξ值選定的範圍在-0.5到50之間。 The second free-form surface 13 is determined, and all light entering from the left side is regarded as emitted by the virtual light source and in the lens material with an optical refraction coefficient of n . The second free-form surface refracts all incident light to a refractive index of n In the air of n _o , the second free-form surface is the mathematical equation r = r ₂ (α) , all incident light rays are refracted and parallel to the +z axis, r ₂ ( α ) satisfies the following differential equation

, Where D _o is the distance from the LED light source to the apex of the lens, T _o is the selected lens thickness, α is the angle between the light emitted by the virtual light source and the +z axis, n _o and n are the optical refraction of the air and the lens material, respectively Coefficient, the selected range of ξ value is between -0.5 and 50.

Referring to FIG. 2, the second embodiment of the present invention discloses a free-form lens design method applied to light source collimation, which includes the following steps: input a preset value 21, determine the first free-form surface 22, determine a second free-form surface The curved surface 23, a third free curved surface 24 and a fourth free curved surface 25 are determined.

Enter a preset value of 21, an LED light source is on the left side of the two sets of lenses, the +z axis is the central axis of the light source, the lens has two free-form surfaces that are axisymmetric to the +z axis, and the two sets of lenses are respectively a first A lens and a second lens, the first lens has a first free-form surface and a second free-form surface, and the second lens has a third free-form surface and a fourth free-form surface, preset the LED light source to the lens The distance between the vertices is D _o , three ξ values are selected, namely ξ ₁ , ξ ₂ , ξ ₃ , where the selected range of the ξ ₁ value is between -0.5 and 50, and ξ ₂ and ξ ₃ are greater than zero The incremental variable. Among them, with the LED light source as the origin, the ξ ₁ value moves to the right as a negative value, and moves to the left as a positive value. Then, the left ξ ₁ D _{o of} the LED light source is taken as the origin or the first virtual light source, and the ξ ₂ value moves to the right as a negative value, and moves to the left as a positive value. Then, the left ξ ₂ D _{o of the} first virtual light source is taken as the origin or the second virtual light source, the value of ξ ₃ moves to the right as a negative value, and moves to the left as a positive value. Since ξ ₂ and ξ ₃ are incremental variables greater than zero, both ξ ₂ D _o and ξ ₃ D _o move to the left, which is called the virtual light source asymmetry method.

，起始條件r ₁(0 ^o )=D _o ，其中，D _o 是LED 光源到透鏡頂點的距離，α ₁為該第一虛擬光源發出的光線與+z軸的夾角，n _o 與n分別是空氣與透鏡材料的光學折射係數(optical refraction index)，ξ ₁ 值選定的範圍在-0.5到50之間。 Determine the first free-form surface 22, and the point at the left ξ ₁ D _{o of} the LED light source is the starting point of a first virtual light source. When the free-form surfaces meet and refract, the refracted light can be regarded as the light emitted by the first virtual light source. The mathematical equation of the first free-form surface is r = r ₁ ( θ ), which satisfies the following differential equation:

, The initial condition r ₁ (0 ^o ) = D _o , where D _o is the distance from the LED light source to the apex of the lens, α _{1 is} the angle between the light emitted by the first virtual light source and the +z axis, n _o and n respectively It is the optical refraction index of air and lens material. The selected range of ξ ₁ value is between -0.5 and 50.

，起始條件r ₂(0 ^o )=(ξ ₁+1)D _o +T _o ，其中，D _o 是 LED光源到透鏡頂點的距離，T _o 為該第一自由曲面和該第二自由曲面所組成之透鏡厚度，α ₁為該第一虛擬光源發出的光線與+z軸的夾角，α ₂為該第二虛擬光源發出的光線與+z軸的夾角，n _o 與n分別是空氣與透鏡材料的光學折射係數，ξ ₁ 值選定的範圍在-0.5到50之間，ξ ₂ 為大於零的增量變數。 Determine the second free-form surface 23, and the point at the left ξ ₂ D _{o of} the first virtual light source is the starting point of a second virtual light source, and the second free-form surface is such that all light rays originating from the first virtual light source , When the second free-form surface meets and is refracted, the refracted light can be regarded as the light emitted by the second virtual light source. The second free-form surface is the mathematical equation r = r ₂ (α ₁ ) , which satisfies The following differential equation

, The initial condition r ₂ (0 ^o )=( ξ ₁ +1) D _o + T _o , where D _o is the distance from the LED light source to the lens vertex, and T _{o is} the first free-form surface and the second free-form surface The thickness of the lens is composed, α _{1 is} the angle between the light emitted by the first virtual light source and the +z axis, α _{2 is} the angle between the light emitted by the second virtual light source and the +z axis, n _o and n are air and For the optical refractive index of the lens material, the selected range of ξ ₁ value is between -0.5 and 50, and ξ ₂ is an incremental variable greater than zero.

，起始條件r ₃(0 ^o )=(ξ ₂+ξ ₁+1)D _o +D ₁+T _o ，其中， D _o 是LED光源到透鏡頂點的距離，D ₁ 為該第二自由曲面在光軸上離該第三自由曲面的距離，T _o 為該第一自由曲面和該第二自由曲面所組成之透鏡厚度，α ₂為該第二虛擬光源發出的光線與+z軸的夾角，α ₃為該第三虛擬光源發出的光線與+z軸的夾角，n _o 與n分別是空氣與透鏡材料的光學折射係數，ξ ₁ 值選定的範圍在-0.5到50之間，ξ ₂ 為大於零的增量變數。 Determine the third free-form surface 24, and the point at the left ξ ₃ D _{o of} the second virtual light source is the starting point of a third virtual light source, and the third free-form surface is such that all light rays originating from the second virtual light source When the third free-form surface meets and is refracted, the refracted light can be regarded as the light emitted by the third virtual light source. The third free-form surface is the mathematical equation r = r ₃ ( α ₂ ), which satisfies The following differential equation

, The initial condition r ₃ (0 ^o )=( ξ ₂ + ξ ₁ +1) D _o + D ₁ + T _o , where D _o is the distance from the LED light source to the apex of the lens, and D _{1 is} the second free-form surface The distance from the third free-form surface on the optical axis, T _{o is} the thickness of the lens formed by the first free-form surface and the second free-form surface, and α ₂ is the angle between the light emitted by the second virtual light source and the +z axis , Α _{3 is} the angle between the light emitted by the third virtual light source and the +z axis, n _o and n are the optical refraction coefficients of air and the lens material respectively, the selected range of ξ ₁ is between -0.5 and 50, ξ ₂ Is an incremental variable greater than zero.

，其中，D _o 是LED 光源到透鏡頂點的距離，D ₁ 為該第二自由曲面在光軸上離該第三自由曲面的距離，T _o 為該第一自由曲面和該第二自由曲面所組成之透鏡厚度，T ₁ 為該第三自由曲面和該第四 自由曲面所組成之透鏡厚度，α ₃為該第三虛擬光源發出的光線與+z軸的夾角，n _o 與n分別是空氣與透鏡材料的光學折射係數，ξ ₁ 值選定的範圍在-0.5到50之間，ξ ₂ 為大於零的增量變數，ξ ₃ 為大於零的增量變數。 The fourth free-form surface 25 is determined, and all light entering from the left side is regarded as being emitted by the third virtual light source, and in the lens material with an optical refraction coefficient of n , the fourth free-form surface refracts all incident light rays to the refracted In the air with a coefficient of n _o , and the refracted light is parallel to the +z axis, the fourth free-form surface is the mathematical equation r = r ₄ ( α ₃ ), which is parallel to the +z axis after refraction, r ₄ ( α ₃ ) Satisfy the following differential equations

, Where D _o is the distance from the LED light source to the apex of the lens, D _{1 is} the distance between the second free-form surface and the third free-form surface on the optical axis, and T _{o is} the distance between the first free-form surface and the second free-form surface. The lens thickness of the composition, T _{1 is} the lens thickness of the third free-form surface and the fourth free-form surface, α _{3 is} the angle between the light emitted by the third virtual light source and the +z axis, n _o and n are air respectively With respect to the optical refractive index of the lens material, the selected range of ξ ₁ value is between -0.5 and 50, ξ ₂ is an incremental variable greater than zero, and ξ ₃ is an incremental variable greater than zero.

Refer to Figure 3, the first preferred example of the present invention. The left side of the figure is an LED light source with a certain light-emitting area and a certain light-emitting angle. The +z axis is the central axis of the light source; the right side of the LED light source is a lens. The lens has two left and right free-form surfaces that are axisymmetric to the +z axis. They are the first free-form surface (FS ₁ ) and the second free-form surface (FS ₂ ). The light emitted by the LED can pass through the FS ₁ and FS ₂ surfaces. After the double refraction, it becomes a collimated light source that is as parallel to the +z axis as possible. The two curved surfaces take the origin of the LED light source ( S ) as the coordinate origin, and use polar coordinates (r, θ ) to describe the curved surfaces FS ₁ and FS ₂ .

There are two design principles of the present invention: (1) the design modification of "virtual light source gradually moving away"; (2) the design principle of free-form surface with analytical solutions of mathematical equations.

，並配合一起始條件r ₁(0 ^o )=D _o ；其中， 是虛擬射線與+z軸的夾角，n _o 與n分別是空氣與鏡片材料的光學折射係數。 The design of "virtual light source fade away" is as follows: Assume that the distance from the light source ( S ) to the lens vertex ( A ) is D _o , as shown in Figure 4-1, the first preferred example of the present invention, the first freedom on the left side of the lens The design principle of the curved surface (FS ₁ ) is to first select a ξ value by the designer. The selected range of the ξ value is between -0.5 and 50, and then the position of the left ξ D _o from the light source ( S ) in Figure 4-1 The point ( S' ) is the starting point of a virtual light source, and the first free-form surface (FS ₁ ) is designed so that all light rays starting from the S light point will be refracted when they intersect and refract the surface FS ₁ The back light can be regarded as the light emitted by the virtual light source point ( S' ); or as shown in Figure 4-1, the light that has been refracted by the curved surface FS ₁ and has entered the lens material (indicated by the solid line). The left side is extended in a straight line (indicated by the dashed line), and will intersect the optical axis (+z) at the virtual light source point ( S' ). In addition, the mathematical equation r = r ₁ (θ) of the curved surface FS ₁ should satisfy the following differential equations according to the basic principles of geometric optics:

, And cooperate with an initial condition r ₁ (0 ^o ) = D _o ; where is the angle between the virtual ray and the +z axis, and n _o and n are the optical refraction coefficients of air and the lens material, respectively.

，其中，T _o 為所選定之鏡片厚度。 The design method of the second free-form surface (FS ₂ ) is to consider all light entering from the left as emitted by the virtual light source ( S' ), and it is a lens material with an optical refraction coefficient of n , so the mathematical equation r = r ₂ (α) defines the curved surface FS ₂ , all incident light needs to be refracted into the air with a refractive index of n _o , and the refracted light needs to be parallel to the +z axis, as shown in Figure 4-2 . According to the basic theory of geometric optics, r ₂ ( α ) should satisfy the following differential equations:

, Where T _o is the selected lens thickness.

Referring to Figure 5, a cross-sectional view of a free-form surface lens simulated according to the first preferred example, wherein the ξ values are respectively 0.2, 0.4, 0.6, 0.8 and 1.0. According to the above-mentioned design method of the first free-form surface and the second free-form surface, Draw a cross-sectional view of the free-form surface. From the figure, it can be seen that when the value of ξ is larger, the radius and thickness of the lens become larger.

Referring to Fig. 6, the second preferred example of the present invention, where the left side is an LED light source with a certain light-emitting area and a certain light-emitting angle, and the +z axis is the central axis of the light source. In this example, two sets of lenses are designed. This lens group has two groups of left and right free-form surfaces that are axisymmetric to the +z axis, namely the first free-form surface (FS ₁ ), the second free-form surface (FS ₂ ), the third free-form surface (FS ₃ ) and the Four free-form surfaces (FS ₄ ), the light emitted by the LED can be refracted four times by the FS ₁ , FS ₂ , FS ₃ and FS ₄ surfaces to become a collimated light source that is as parallel to the +z axis as possible. Design the best FS ₁ , FS ₂ , FS ₃ and FS ₄ curved surfaces to avoid hot spots caused by interface reflection of LED light in the lens. These four curved surfaces are based on the original light source of the LED. The point (S) is the origin of the coordinates, and the polar coordinates (r, θ ) are used to describe the FS ₁ , FS ₂ , FS ₃ and FS ₄ surfaces.

The design principles of the present invention: (1) the design modification of "triple virtual light source gradually away"; (2) the curved surface design principle with the analytical solution of mathematical equations.

The design of the "triple virtual light source fade away" is as follows: Assume that the distance from the light source ( S ) to the lens vertex (A) is D _o , as shown in Figure 7-1, Figure 7-2 and Figure 7-3, the first of the present invention 2. A better example, the design principle of the first free-form surface (FS ₁ ) on the left side of the lens is that the designer first selects three ξ values, namely ξ ₁ , ξ ₂ , and ξ ₃ , where the selected range of the ξ ₁ value is -Between 0.5 and 50. ξ ₂ and ξ ₃ are incremental variables greater than zero, and the point ( S' ) at the left ξ ₁ D _{o of the} light source ( S ) in Figure 7-1 is the starting point of a virtual light source, and the first free-form surface The design of (FS ₁ ) is to allow all the light rays starting from the light point ( S ) to intersect with the curved surface FS ₁ and be refracted. The refracted light can be regarded as emitted by the virtual light source point ( S' ) In other words, the light that has been refracted by the curved surface FS ₁ and entered the lens material, if it extends straight to the left, or intersects the optical axis (+z) at the virtual light source point ( S' ), as shown in the figure Shown in 7-1. Based on this concept, the light from the light source ( S ) is refracted by the first free-form surface (FS ₁ ), and the light extends straight to the left, intersecting the optical axis (+z) at the first virtual light source point ( S' ), the distance ξ ₁ D _o between the light source ( S ) and the first virtual light source point ( S' ), this is the first virtual light source gradually moving away; as shown in Figure 7-2, next, from the first virtual light source point ( S' ) The light from the second free-form surface (FS ₂ ) is refracted, and the light extends straight to the left, intersecting the optical axis (+z) at the second virtual light source point ( S” ), the first virtual The distance between the light source point ( S' ) and the second virtual light source point ( S” ) is ξ ₂ D _o , which is the second virtual light source gradually moving away; as shown in Figure 7-3, again, from the second virtual light source point ( S” ) The starting light is refracted by the third free-form surface (FS ₃ ), and the light extends straight to the left, intersecting the optical axis (+z) at the third virtual light source point ( S''' ), the second virtual light source The distance ξ ₃ D _o between the point ( S" ) and the third virtual light source point ( S''' ), which is the third virtual light source gradually moving away; the mathematical equations of the curved surfaces FS1, FS2 and FS3 are r = r ₁ (θ ), r = r ₂ (α ₁ ), r = r ₃ (α ₂ ) , according to the basic principles of geometric optics, the differential equations in Table 1 should be satisfied:

，其中，D _o 為光源 在光軸上離曲面FS₁的距離，D ₁ 為曲面FS₂在光軸上離曲面FS₃的距離，T _o 為曲面FS₁和曲面FS₂組成之透鏡鏡片厚度，T ₁ 為曲面FS₃和曲面FS₄組成之透鏡鏡片厚度，如圖7-4所示。 As shown in Figure 7-4, the design method of curved surface FS ₄ is to treat all light entering from the left as emitted by a virtual light source ( S''' ), and it is a lens material with an optical refractive index of n Therefore, the curved surface FS ₄ defined by the mathematical equation r = r ₄ (α ₃ ) needs to refract all incident light into the air with a refractive index of n _o , and the refracted light needs to be parallel to the +z axis, As shown in Figure 7-4. According to the basic theory of geometric optics r ₄ (α ₃ ) , the following differential equations should be satisfied:

, Where D _o is the distance between the light source and the curved surface FS ₁ on the optical axis, D ₁ is the distance between the curved surface FS ₂ and the curved surface FS ₃ on the optical axis, and T _o is the lens thickness of the curved surface FS ₁ and the curved surface FS ₂ , T ₁ is the thickness of the lens made up of curved FS ₃ and curved FS ₄ , as shown in Figure 7-4.

Refer to Figure 8 for the simulated cross-sectional view of the two lenses and the corresponding four free-form surface lenses of the second preferred example. There are three groups of two lenses in total, the first group ξ ₁ =0.5, ξ ₂ =0.5, ξ ₃ =0.5 ; The second group ξ ₁ =4, ξ ₂ =0.5, ξ ₃ =0.5; the third group ξ ₁ =8, ξ ₂ =0.5, ξ ₃ =0.5, change the value of ξ ₁ and maintain the increments of ξ ₂ and ξ ₃ Numerical value. From the lens change, it can be seen that the shape of the left lens is obviously different, while the right lens has the same shape because of the same increment of ξ ₂ and ξ ₃ .

Refer to Figure 9 for the other two lenses and the corresponding four free-form surface lens profiles simulated by the second preferred example. There are three groups of two lenses in total, the first group ξ ₁ =0.5, ξ ₂ =0.5, ξ ₃ = 0.5; the second group ξ ₁ =0.5, ξ ₂ =0.5, ξ ₃ =4; the third group ξ ₁ =0.5, ξ ₂ =0.5, ξ ₃ =8, change the value of ξ ₃ , maintain the increase of ξ ₁ and ξ ₂ From the lens change, it can be seen that there is a significant difference in the shape of the right lens, while the left lens has the same shape due to the same increment of ξ ₁ and ξ ₂ . Furthermore, it can be based on the lens and free-form surface designed in this patent, plus a plurality of point light sources not on the optical axis, and use Ray Tracing to perform off-axis light source (Off-Axis Source) lenses Surface optimization design.

In summary, this patent provides a lens or lens system design method, which can collimate the light emitted by the LED light source through the refraction of the free-form surfaces of each lens into parallel to the optical axis. Light; among them, each free-form surface of each lens is composed of a series of "virtual focus" "gradually away" from the LED light source and a set of corresponding analytical solutions of equations. This design can be accomplished by only a single lens (two free-form surfaces) or multiple lenses.

10-1 and 10-2, in the third embodiment of the present invention, a free-form surface lens 32 and a UV-LED 34 are combined to form a collimating lens according to the design method of the first embodiment or the second embodiment. Module 30. Since the light intensity of the central area of the single UV-LED 34 is stronger than the light intensity of the surrounding areas, no matter whether the single collimating lens module 30 is used in an independent setting or array sequence, the light intensity received by the light receiving area cannot be evenly distributed. . To this end, under the condition that the plurality of collimating lens modules 30 are arranged in an array, the array has N rows, and the distance between the centers of any two adjacent free-form surface lenses in any row is defined as a period D, where the period D divides the distance equally by N, and the projections from the center of the free-form lens at the same position in the second row to the Nth row to the adjacent points on the periodic line are the same, and the distances are all D/N. In this way, the light intensity received by a single block in the light-receiving area is the accumulated light intensity obtained by irradiating the plurality of UV-LEDs 34 at the same position in the first row to the Nth row to the single block, so that the light-receiving area The light intensity received by each block is the same to achieve the effect of uniform light intensity distribution. Referring to Fig. 10-2, for example, the array has 5 rows, and the distances between the centers of the free-form lenses of the second row and the fifth row onto the periodic line are all D/5.

10-1 and 10-3, the fourth embodiment of the present invention according to the first embodiment or the second embodiment of the design method to produce a free-form surface lens 32 and a UV-LED 34 combined to form a collimating lens mold Group 30, a plurality of the collimating lens modules 30 are arranged in an array, each collimating lens module 30 completes large-area exposure in a circular motion, defining the free-form lens 32 and the adjacent free-form lens 32 The center distance is one cycle, The radius of the circular motion is smaller than this period.

However, the foregoing are only preferred embodiments of the present invention, and should not be used to limit the scope of implementation of the present invention, that is, simple equivalent changes and modifications made in accordance with the scope of the patent application of the present invention and the description of the invention, All are still within the scope of the invention patent.

11~13‧‧‧Step

Claims (12)

A free-form surface lens design method for light source collimation, including the following steps: (A) Input a preset value, an LED light source S is on the left side of a lens, the +z axis is the central axis of the light source, and the lens has a first Free-form surface and a second free-form surface, preset the distance from the LED light source S to the lens vertex to be D _o , select a ξ value, and the selected range of the ξ value is between -0.5 and 50; (B) determine the first Free-form surface, the mathematical equation of the first free-form surface r = r ₁ ( θ ), satisfies the following differential equation:

, The initial condition r ₁ (0 ^o ) = D _o , where α is the angle between the light emitted by a virtual light source S'and the +z axis, n _o and n are the optical refractive index of the air and the lens material, r ₁ Is the distance from the LED light source S to the first free-form surface, θ is the angle between the light emitted by the LED light source S and the +z axis, the virtual light source S'is located on the +z axis, at the position ξD _{o to the} left of the LED light source S And (C) determine the second free-form surface, the second free-form surface is the mathematical equation r = r ₂ ( α ), all incident light rays are refracted and parallel to the +z axis, r ₂ ( α ) satisfies The following differential equation

, Where T _o is the selected lens thickness, and r _{2 is} the distance from the virtual light source S'to the second free-form surface. According to the free-form lens design method for light source collimation described in item 1 of the scope of patent application, the lens has two free-form surfaces that are axisymmetric to the +z axis. According to the free-form lens design method for light source collimation described in the scope of the patent application, in step (B), the point at the left ξD _{o of} the LED light source S is the starting point of the virtual light source S', and the The first free-form surface is used to allow all light rays emitted from the LED light source S to be refracted when the first free-form surface intersects, and the refracted light rays can be regarded as the light rays emitted by the virtual light source S′. According to the free-form lens design method for light source collimation described in the scope of patent application, in step (C), all light entering from the left side is regarded as emitted by the virtual light source S', and the optical refraction coefficient It is a lens material of n , the second free-form surface refracts all incident light into the air with a refractive index of n _o , and the refracted light is parallel to the +z axis. A free-form surface lens design method applied to light source collimation, including the following steps: (A) Input a preset value, an LED light source S is on the left side of the two sets of lenses, the +z axis is the central axis of the light source, and the two sets of lenses are respectively Is a first lens and a second lens, the first lens has a first free-form surface and a second free-form surface, and the second lens has a third free-form surface and a fourth free-form surface, and the LED is preset The distance from the light source to the lens vertex is D _o , three ξ values are selected, namely ξ ₁ , ξ ₂ , and ξ ₃ , where the selected range of the ξ ₁ value is between -0.5 and 50, and ξ ₂ and ξ ₃ Is an incremental variable greater than zero; (B) determines the first free-form surface, and the point at the left ξ ₁ D _{o of} the LED light source S is the starting point of a first virtual light source S', the mathematical equation of the first free-form surface r = r ₁ ( θ ), the following differential equation is satisfied

, The initial condition r ₁ (0 ^o ) = D _o , where α _{1 is} the angle between the light emitted by the first virtual light source S'and the +z axis, and n _o and n are the optical refractive index of the air and the lens material, respectively (optical refraction index), r _{1 is} the distance from the LED light source S to the first free-form surface, θ is the angle between the light emitted by the LED light source S and the +z axis, and the first virtual light source S'is located on the +z axis , The point on the left ξ ₁ D _{o of} the LED light source S; (C) Determine the second free-form surface, and the point on the left ξ ₂ D _{o of} the first virtual light source S'is a second virtual light source S" Starting point, the second free-form surface is the mathematical equation r = r ₂ (α ₁ ) , which satisfies the following differential equation

, The initial condition r ₂ (0 ^o )=( ξ ₁ +1) D _o + T _o , where α _{2 is} the angle between the light emitted by the second virtual light source S" and the +z axis, and T _{o is} the The thickness of the lens formed by a free-form surface and the second free-form surface, r _{2 is} the distance from the first virtual light source S'to the second free-form surface, the second virtual light source S" is located on the +z axis, A point on the left ξ ₂ D _{o of} a virtual light source S'; (D) determines the third free-form surface, and a point on the left ξ ₃ D _{o of} the second virtual light source S" is a third virtual light source S''' The starting point for the third free-form surface is the mathematical equation r = r ₃ (α ₂ ) , which satisfies the following differential equation

, The initial condition r ₃ (0 ^o )=( ξ ₂ + ξ ₁ +1) D _o + D ₁ + T _o , where D ₁ is the distance of the second free-form surface from the third free-form surface on the optical axis Distance, α _{3 is} the angle between the light emitted by the third virtual light source S''' and the +z axis, r _{3 is} the distance from the second virtual light source S” to the third free-form surface, and the third virtual light source S''' is located on the +z axis, at the point ξ ₃ D _o on the left side of the second virtual light source S'; and (E) determines the fourth free surface, which is the mathematical equation r = r ₄ ( α ₃ ), all incident light rays are refracted and parallel to the +z axis, r ₄ ( α ₃ ) satisfies the following differential equation

, Where T ₁ is the lens thickness formed by the third free-form surface and the fourth free-form surface, and r _{4 is} the distance from the third virtual light source S"' to the fourth free-form surface. According to the free-form lens design method for light source collimation described in item 5 of the scope of patent application, the two sets of lenses have two pairs of left and right The +z axis is an axisymmetric free-form surface. According to the free-form lens design method for light source collimation described in item 5 of the scope of patent application, in step (B), the first free-form surface is such that all the light rays emitted from the LED light source S are in the first When the free-form surfaces meet and refract, the refracted light can be regarded as the light emitted by the first virtual light source S′. According to the free-form lens design method for light source collimation described in the scope of the patent application, in step (C), the second free-form surface is such that all the light rays emitted from the first virtual light source S' When the second free-form surface meets and is refracted, the refracted light can be regarded as the light emitted by the second virtual light source S". According to the free-form lens design method for light source collimation described in item 5 of the scope of patent application, in step (D), the third free-form surface is such that all the light rays emitted from the second virtual light source S" When the third free-form surface meets and is refracted, the refracted light can be regarded as the light emitted by the third virtual light source S"'. According to the free-form surface lens design method for light source collimation described in item 5 of the scope of patent application, in step (E), all light entering from the left side is regarded as emitted by the third virtual light source S''', and In a lens material with an optical refractive index of n , the fourth free-form surface refracts all incident light into the air with a refractive index of n _o , and the refracted light is parallel to the +z axis. A free-form surface lens is combined with a UV-LED to form a collimating lens module according to the design method of item 1 or 5 of the scope of patent application. A plurality of the collimating lens modules are arranged in an array, and the array has N Row, define the distance between the centers of any two adjacent free-form surface lenses in any row as a period D , where the period is equally divided by N , and the center of the free-form surface lens at the same position in the second row to the Nth row is projected to The adjacent points on the periodic line are the same with each other, and the distance is D/N . A free-form surface lens and a UV-LED are combined to form a collimating lens module according to the design method No. 1 or 5 of the scope of patent application. A plurality of the collimating lens modules are arranged in an array, and each collimator The lens module completes large-area exposure in a circular motion. The distance between the free-form surface lens and the center of the adjacent free-form surface lens is defined as a period, and the radius of the circular motion is smaller than the period.

Images