CN114019666A - Total reflection type LED (light emitting diode) micro-lighting light distribution element - Google Patents

Total reflection type LED (light emitting diode) micro-lighting light distribution element Download PDF

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CN114019666A
CN114019666A CN202111238990.9A CN202111238990A CN114019666A CN 114019666 A CN114019666 A CN 114019666A CN 202111238990 A CN202111238990 A CN 202111238990A CN 114019666 A CN114019666 A CN 114019666A
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light
total reflection
incident
distribution element
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CN114019666B (en
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王尧
何锋赟
包兴臻
胡玥
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Changchun Institute of Optics Fine Mechanics and Physics of CAS
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Changchun Institute of Optics Fine Mechanics and Physics of CAS
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    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B21/00—Microscopes
    • G02B21/06—Means for illuminating specimens
    • G02B21/08—Condensers
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
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Abstract

The invention provides a total reflection type LED (light emitting diode) micro-lighting light distribution element, which comprises a collimation structure and a light condensation structure; the collimating structure is used for collimating light rays emitted by the LED light source, and the light condensing structure is used for focusing the collimated light rays on a sample to be measured; the collimating structure comprises a first cylindrical surface, a second cylindrical surface, a first transmission surface and a total reflection surface, wherein the first cylindrical surface and the first transmission surface form a bottom cavity; the second cylindrical surface is used for transition between the collimation structure and the light condensation structure; the light-concentrating structure includes a reflective surface and a second transmissive surface. According to the invention, by carrying out sectional design on the LED micro-illumination light distribution element, all light rays emitted by the LED light source are effectively controlled, the energy utilization rate is improved, and uniform illumination of the LED light source on the sample surface is realized; and the integrated processing is adopted, the difficulty in assembly and adjustment is reduced, and the microscope illumination can be realized by only adopting one light distribution element.

Description

Total reflection type LED (light emitting diode) micro-lighting light distribution element
Technical Field
The invention belongs to the technical field of LED illumination, and particularly relates to a total reflection type LED microscopic illumination light distribution element based on non-imaging optics.
Background
The LED light source has the advantages of energy conservation, environmental protection, high reliability, long service life, no infrared radiation and the like, does not generate heat basically, is considered as an excellent cold light source, and gradually becomes a preferred light source for micro-illumination. However, there are two major drawbacks to existing LED micro-illumination systems: firstly, the overall structure of a microscope system is larger due to the fact that lenses of the illumination system have multiple optical paths, the portability of the microscope cannot be realized, and the further expansion of the microscope market is limited; secondly, the traditional lens can only control the central light beam emitted by the light source, the LED light source has a large light emitting angle, the large-angle light beam is wasted due to the fact that the large-angle light beam cannot be collected, and the energy utilization rate of the lighting system is reduced.
Disclosure of Invention
In order to solve the problems, the invention provides a total reflection type LED micro-illumination light distribution element based on non-imaging optics.
In order to achieve the purpose, the invention adopts the following specific technical scheme:
the invention provides a total reflection type LED (light emitting diode) micro-lighting light distribution element which is characterized by comprising a collimation structure and a light condensation structure;
the collimating structure is used for collimating light rays emitted by the LED light source, and the light condensing structure is used for focusing the collimated light rays on a sample to be measured;
the collimating structure comprises a first cylindrical surface, a second cylindrical surface, a first transmission surface and a total reflection surface, wherein the first cylindrical surface and the transmission surface form a bottom cavity;
the second cylindrical surface is used for transition between the collimation structure and the light condensation structure;
the light-concentrating structure includes a reflective surface and a second transmissive surface.
Preferably, the first transmission surface and the total reflection surface are both rotationally symmetric free-form surfaces and are both designed by a non-imaging method.
Preferably, the non-imaging method design of the first transmission surface comprises the following steps:
s0, optionally selecting the diameter of the bottom surface of one first cylindrical surface as an x axis, selecting a rotation symmetry axis as a y axis, and taking the intersection point of the rotation symmetry axis and the plane where the cavity opening of the bottom cavity is located as a coordinate origin; the refractive index of the material of the light distribution element is n, assuming that
Figure BDA0003318531030000021
And
Figure BDA0003318531030000022
expressing the vector forms of the incident light and the emergent light, respectively, Snell's law expresses as shown in equation (1):
Figure BDA0003318531030000023
wherein ,n1 and n2Respectively representing the refractive indexes of materials where incident rays and emergent rays are located;
s1, dividing a first incident light ray emitted from the LED light source and incident on the first transmission surface into M parts according to an incident angle, wherein the first incident angle of the first incident light ray is represented by formula (2):
Figure BDA0003318531030000024
wherein ,
Figure BDA0003318531030000025
a unit vector representing the x-axis direction,
Figure BDA0003318531030000026
a unit vector representing the y-axis direction; thetacThe maximum included angle between the first incident ray and the rotational symmetry axis is defined;
s2, writing the first incident light and the first emergent light into vector form, as shown in formula (3):
Figure BDA0003318531030000027
s3, connecting any point P on the first transmission surface1jIs set as (x)1j,y1j) Obtaining the point P according to the formula (3) and the formula (1)1jNormal vector of
Figure BDA0003318531030000028
Obtain a point P1jA tangent line of (c);
point P on the curve of the first transmission surface1jTaking a point P1j+1(x1j+1,y1j+1) Point P1j+1At P1jOn the tangent of (C), point P1j+1Is a point P1j+1At the first incident ray
Figure BDA0003318531030000029
And point P1jThe intersection point of the tangent lines is located;
giving a starting point P for the first incident ray and the first emergent ray divided by the formula (3)10(x10,y10) Calculating the normal vector of the first transmission surface according to the formula (1), and obtaining coordinates of each point on the first transmission surface through repeated iterative calculation, wherein the coordinate of the end point is marked as P1end(x1end,y1end)。
Preferably, the non-imaging method design of the total reflection surface comprises the following steps:
s11, dividing a second incident light beam emitted from the LED light source and incident on the total reflection surface into M parts according to the incident angle, wherein the second incident angle of the second incident light beam is represented as formula (5):
Figure BDA0003318531030000031
after the first incident light is refracted by the first cylindrical surface, the second incident light is obtained to be incident on the total reflection surface, and the refraction angle is expressed as a formula (6):
Figure BDA0003318531030000032
s22, writing the second incident light and the second emergent light into vector form, as shown in equation (7):
Figure BDA0003318531030000033
s33, connecting any point P on the total reflection surface2jIs set as (x)2j,y2j) The point P is obtained from the formula (7) and the formula (1)2jNormal vector of
Figure BDA0003318531030000034
Obtain a point P2jA tangent line of (c);
point P on the curve of said total reflection surface2jTaking a point P2j+1(x2j+1,y2j+1) Point P2j+1At P2jOn the tangent of (C), point P2j+1Is a point P2j+1At the second incident ray
Figure BDA0003318531030000035
And point P2jThe intersection point of the tangent lines is located;
for the second incident ray and the second emergent ray divided by the formula (7), a starting point P is given20(x20,y20)，x20>x1end，y 200; calculating the normal vector of the total reflection surface according to the formula (1), and obtaining the coordinates of each point on the total reflection surface through repeated iterative calculation, wherein the coordinate of the end point is marked as P2end(x2end,y2end)。
Preferably, the reflecting surface is a paraboloid and the second transmitting surface is a sphere.
Preferably, the collimated light beam is incident on the reflecting surface and then converged at a focus, and the coordinate of the focus is (-x)2end-r,y2end+ h); the rotational symmetry axes of the reflecting surface and the second transmission surface are both y ═ x2end-r; the equation of the paraboloid of the reflecting surface is shown in the formula (8):
(x+(r+x2end))2＝-4f(y-(y2end+h+f)) (8)
wherein the focal length of the reflecting surface is f, the radius of the second transmitting surface is r, and the diameter of the second cylindrical surface is 2x2endThe height of the second cylindrical surface is h; the coordinate of the intersection point of the reflecting surface and the second cylindrical surface is (x)2end,y2end+h)。
Preferably, the focal length f of the reflecting surface is expressed by the following formula (9):
Figure BDA0003318531030000041
preferably, the equation of the paraboloid of the reflecting surface is shown in formula (10):
Figure BDA0003318531030000042
preferably, the equation of the second transmission plane is as shown in equation (11):
Figure BDA0003318531030000043
preferably, the material of the light distribution element is polymethyl methacrylate; the refractive index of the material of the light distribution element is 1.49 at a wavelength of 546.1 nm.
The total reflection type LED micro-illumination light distribution element based on non-imaging optics is designed in a segmented manner by adopting the law of energy conservation and the Snell's law, so that all light rays emitted by an LED light source are effectively controlled, the energy utilization rate is improved, and the uniform illumination of the LED light source on a sample surface is realized; the microscope can be illuminated by only one light distribution element, so that the volume and the weight of an illumination system are effectively reduced, and the microscope is convenient to carry and use. Meanwhile, the light distribution element can be integrally processed after being designed in a segmented mode, and the difficulty in assembly and adjustment is effectively reduced.
Drawings
Fig. 1 is a schematic diagram of a total reflection type LED micro-illumination light distribution element in an embodiment of the present invention.
Fig. 2 is a schematic structural diagram of a total reflection type LED micro-illumination light distribution element in an embodiment of the present invention.
Fig. 3 is a schematic diagram of the design principle of the first transmission surface in one embodiment of the present invention.
Fig. 4 is a schematic diagram of the design principle of the total reflection surface in one embodiment of the present invention.
FIG. 5 is a schematic diagram of the design of the reflective surface and the second transmissive surface in one embodiment of the invention.
FIG. 6 is a sample surface illuminance distribution plot in an embodiment of the present invention.
Reference numerals
The device comprises an LED light source 1, a light distribution element 2, a sample surface 3 to be measured, a collimation structure 21, a light condensation structure 22, a first cylindrical surface 31, a first transmission surface 32, a total reflection surface 33, a second cylindrical surface 34, a reflection surface 41 and a second transmission surface 42.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not to be construed as limiting the invention.
As shown in fig. 1 and fig. 2, fig. 1 is a schematic diagram of a total reflection type LED micro-illumination light distribution element in an embodiment of the present invention, and fig. 2 is a schematic diagram of a structure of the total reflection type LED micro-illumination light distribution element in an embodiment of the present invention.
As can be seen from fig. 1, light emitted from the LED light source 1 passes through the light distribution element 2 of this embodiment and is focused on the sample surface 3.
In this specific embodiment, the total reflection type LED micro-illumination light distribution element 2 includes a collimating structure 21 and a light condensing structure 22; the collimating structure 21 is configured to collimate light emitted by the LED light source 1, and the light-focusing structure 22 is configured to focus the collimated light on a sample to be measured, specifically, on the sample surface 3 to be measured.
Specifically, the collimating structure 21 includes a first cylindrical surface 31, a second cylindrical surface 34, a first transmission surface 32 and a total reflection surface 33, where the first cylindrical surface 31 and the first transmission surface 32 form a bottom cavity for placing an LED light source; the second cylindrical surface 34 is used for transition between the collimating structure 21 and the light-concentrating structure 22; the first cylindrical surface 31 and the second cylindrical surface 34 are both straight cylindrical surfaces, a straight surface in the first cylindrical surface 31 is parallel to a straight surface in the second cylindrical surface 34, and a side surface of the second cylindrical surface 34 is perpendicular to the bottom edge of the total reflection surface 33; specifically, the light-gathering structure 22 includes a reflective surface 41 and a second transmissive surface 42; the reflecting surface 41 is directly connected with the second cylindrical surface, and the second transmitting surface 42 is directly connected with the second cylindrical surface 34 by a spherical surface and a cylindrical surface.
In a specific embodiment, the first transmission surface 32 and the total reflection surface 33 are both rotationally symmetric free curved surfaces, and are designed by a non-imaging method, specifically, by finding the relationship between the tangent plane direction of a point on the curved surface and the outgoing ray and the incoming ray at the point, the point on the curved surface can be iteratively solved.
As shown in fig. 3, which is a schematic diagram of the design principle of the first transmission plane 32, the first transmission plane 32 is obtained by only considering its 2D structure and finally rotating the 3D entity around its central symmetry axis. Specifically, the non-imaging method design of the first transmission surface 32 includes the steps of:
s0, taking a rotational symmetry axis as a y axis, wherein an intersection point of the rotational symmetry axis and a plane where a cavity opening of the bottom cavity is located is a coordinate origin point O; the cavity opening of the bottom cavity is the cavity opening of the LED light source cavity, and the point O of the origin of coordinates is the position of the LED light source; at the mouth of LED light source appearance chamberThe diameter of the bottom surface of one optional first cylindrical surface 31 in the plane is taken as an x axis, and the refractive index of the material of the light distribution element 2 is n, provided that
Figure BDA0003318531030000061
And
Figure BDA0003318531030000062
expressing the vector forms of the incident light and the emergent light, respectively, Snell's law expresses as shown in equation (1):
Figure BDA0003318531030000063
wherein ,n1 and n2Respectively representing the refractive indexes of materials where incident rays and emergent rays are located;
s1, dividing a first incident light ray emitted from the LED light source 1 and incident on the first transmission surface 32 into M parts according to an incident angle, where M may be any value, and then the first incident angle of the first incident light ray is expressed as shown in formula (2):
Figure BDA0003318531030000071
wherein ,
Figure BDA0003318531030000072
a unit vector representing the x-axis direction,
Figure BDA0003318531030000073
a unit vector representing the y-axis direction; thetacThe maximum included angle between the first incident light ray emitted by the LED light source and incident on the first transmission surface 32 and the rotational symmetry axis;
after the first incident light is incident on the first transmission surface 32, the first emergent light emitted from the first transmission surface 32 is collimated light.
S2, writing the first incident light and the first emergent light into vector form, as shown in formula (3):
Figure BDA0003318531030000074
s3, connecting any point P on the first transmission surface 321jIs set as (x)1j,y1j) Obtaining the point P according to the formula (3) and the formula (1)1jNormal vector of
Figure BDA0003318531030000075
Obtain a point P1jA tangent line of (c);
point P on the curve of the first transmission surface 321jTaking a point P1j+1(x1j+1,y1j+1) Point P1j+1At P1jOn the tangent of (C), point P1j+1Is the point P1j+1At the first incident ray
Figure BDA0003318531030000076
And point P1jThe intersection point of the tangent lines is located;
giving a starting point P for the first incident ray and the first emergent ray divided by the formula (3)10(x10,y10) Calculating the normal vector of the first transmission surface 32 according to the formula (1), and obtaining coordinates of each point on the first transmission surface 32 through repeated iterative calculation, wherein the coordinates of the end point are marked as P1end(x1end,y1end)。
As shown in fig. 4, a schematic diagram of a design principle of the total reflection surface 33, specifically, a non-imaging method design of the total reflection surface 33 includes the steps of:
s11, dividing the second incident light emitted from the LED light source 1 and incident on the total reflection surface 33 into M parts according to the incident angle, where M may be any value, and then the second incident angle of the second incident light is expressed as shown in formula (5):
Figure BDA0003318531030000081
specifically, M is only used for representing the number of parts, and no other additional limitation is provided; the number of the second incident light rays uniformly divided according to the incident angle can be the same as or different from the number of the first incident light rays uniformly divided according to the incident angle;
after the first incident light is refracted by the first cylindrical surface 31, the second incident light is obtained to be incident on the total reflection surface 33, and the refraction angle is expressed as formula (6):
Figure BDA0003318531030000082
s22, writing the second incident light and the second emergent light into vector form, as shown in equation (7):
Figure BDA0003318531030000083
s33, connecting any point P on the total reflection surface 332jIs set as (x)2j,y2j) The point P is obtained from the formula (7) and the formula (1)2jNormal vector of
Figure BDA0003318531030000084
Obtain a point P2jA tangent line of (c);
point P on the curve of said total reflection surface 332jTaking a point P2j+1(x2j+1,y2j+1) Point P2j+1At P2jOn the tangent of (C), point P2j+1Is the point P2j+1At the second incident ray
Figure BDA0003318531030000085
And point P2jThe intersection point of the tangent lines is located;
for the second incident ray and the second emergent ray divided by the formula (7), a starting point P is given20(x20,y20)，x20>x1end，y 200; calculating saidThe normal vector of the total reflection surface 33 is repeatedly calculated to obtain the coordinates of each point on the total reflection surface 33, and the coordinate of the end point is marked as P2end(x2end,y2end)。
In a specific embodiment, the diameter of the bottom surface of the second cylindrical surface 34 in the collimating structure 21 is 2 ×2endAnd the height h mainly plays a role in the transition from the collimating structure 21 to the condensing structure 22.
In a specific embodiment, in the light collecting structure 22, the reflecting surface 41 is a paraboloid, and the second transmitting surface 42 is a spherical surface.
As shown in fig. 5, which is a schematic diagram of the design principle of the reflection surface 41 and the second transmission surface 42, it can be seen from the diagram that parallel light rays passing through the collimating structure, i.e. collimated light rays enter the reflection surface 41 and then converge at the focus Q; the spherical center of the second transmission surface 42 coincides with the focal point of the reflection surface 41, and the light rays do not deviate after passing through the second transmission surface 42 and still converge at the focal point Q of the reflection surface 41, so that the coordinate of the focal point Q is (-x)2end-r,y2end+ h); meanwhile, the focus Q of the reflecting surface 41 is also the sample surface 3 to be measured; the rotational symmetry axes of the reflective surface 41 and the second transmissive surface 42 are y-x2end-r; the vertex S of the reflecting surface 41 has a coordinate (-x)2end-r,y2end+h+f)，y2end+h+f>r; the equation of the paraboloid of the reflecting surface 41 is shown in formula (8):
(x+(r+x2end))2＝-4f(y-(y2end+h+f)) (8)
wherein the focal length of the reflecting surface 41 is f, the second transmitting surface 42 is a spherical surface with a radius of r, and the diameter of the second cylindrical surface is 2 ×2endAnd the height of the second cylindrical surface is h.
P4Is the intersection of the reflecting surface 41 and the second cylindrical surface 34 and has the coordinate of (x)2end,y2end+ h) and the focal length f of the reflecting surface 41 obtained by substituting the formula (8) is expressed by the formula (9):
Figure BDA0003318531030000091
further, the equation of the paraboloid of the reflecting surface 41 is shown in the formula (10):
Figure BDA0003318531030000092
the equation for the second transmission surface 42 is shown in equation (11):
Figure BDA0003318531030000093
in the present embodiment, the material of the light distribution element 2 can be applied to various optical materials; in one embodiment, the material polymethyl methacrylate PMMA of the light distribution element 2 may have different refractive indices when irradiated with light of different wavelengths.
By the non-imaging optical design method, the first transmission surface 32, the total reflection surface 33, the reflection surface 41, the second transmission surface 42 and the like are respectively and specifically designed, namely, the LED micro-illumination light distribution element 2 is designed in a segmented manner, and the light distribution element 2 formed by combining the specific designs can effectively control all light rays emitted by the LED light source, so that the energy utilization rate is improved, and the uniform illumination of the LED light source on a sample surface is realized; moreover, the microscope can be illuminated by only one light distribution element 2, so that the volume and the weight of an illumination system are effectively reduced, and the microscope is convenient to carry and use. Meanwhile, the light distribution element 2 can be integrally processed after being designed in a segmented mode, and the difficulty in assembly and adjustment is effectively reduced.
The following is further illustrated by specific examples.
Example 1
In this embodiment, as shown in fig. 2, the light distribution element 2 includes a collimating structure 21 and a light condensing structure 22; the collimating structure 21 is used for collimating light emitted by the LED light source, and the light-focusing structure 22 is used for focusing the collimated light on the sample 3 to be measured. The collimating structure 21 comprises a first cylindrical surface 31, a second cylindrical surface 34, a first transmission surface 32 and a total reflection surface 33, wherein the first cylindrical surface 31 and the first transmission surface 31 form a bottom cavity; the second cylindrical surface 34 is used for the transition between the collimating structure 21 and the light-concentrating structure 22; the light concentrating structure 22 includes a reflective surface 41 and a second transmissive surface 42.
The light distribution element 2 is made of polymethyl methacrylate (PMMA), and the refractive index of the material of the light distribution element 2 is 1.49 at a wavelength of 546.1 nm. The maximum angle that can be controlled by the first transmission surface 32 is 30 °, and according to the non-imaging design method, the diameter of the collimation structure 21 of the light distribution element is 14mm, and the height is 7.9 mm; the first cylindrical surface 31 of the collimating structure 21 has a diameter of 5.4mm and a height of 4.7 mm. The height of the second cylindrical surface 34 of the transition portion is 5 mm. The reflecting surface 41 of the light-gathering structure 22 is a paraboloid, and the focal length of the paraboloid is 11 mm; the second transmission surface of the light-gathering structure 22 is a spherical surface, and the radius of the spherical surface is 8 mm. That is, the equation of the paraboloid of the reflecting surface 41 is shown in equation (12):
(x+15)2＝-44(y-23.9) (12)
specifically, the illuminance distribution of the light distribution element 2 on the sample surface 3 is as shown in fig. 6, and it can be seen from the figure that the illuminance has high uniformity.
According to the total reflection type LED micro-illumination light distribution element based on non-imaging optics, the LED micro-illumination light distribution element is designed in a segmented mode according to the law of conservation of energy and the Snell's law, all light rays emitted by an LED light source are effectively controlled, the energy utilization rate is improved, and uniform illumination of the LED light source on a sample surface is achieved. The microscope can be illuminated by only one light distribution element, so that the volume and the weight of an illumination system are effectively reduced, and the microscope is convenient to carry and use. Meanwhile, the light distribution element can be integrally processed, so that the difficulty in assembly and adjustment is reduced.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
While embodiments of the present invention have been shown and described above, it should be understood that the above embodiments are exemplary and should not be taken as limiting the invention. Variations, modifications, substitutions and alterations of the above-described embodiments may be made by those of ordinary skill in the art without departing from the scope of the present invention.
The above embodiments of the present invention should not be construed as limiting the scope of the present invention. Any other corresponding changes and modifications made according to the technical idea of the present invention should be included in the protection scope of the claims of the present invention.

Claims (10)

1. A total reflection type LED (light emitting diode) micro-illumination light distribution element is characterized by comprising a collimation structure and a light condensation structure;
the collimating structure is used for collimating light rays emitted by the LED light source, and the light condensing structure is used for focusing the collimated light rays on a sample to be measured;
the collimating structure comprises a first cylindrical surface, a second cylindrical surface, a first transmission surface and a total reflection surface, wherein the first cylindrical surface and the transmission surface form a bottom cavity;
the second cylindrical surface is used for transition between the collimation structure and the light condensation structure;
the light-concentrating structure includes a reflective surface and a second transmissive surface.
2. The total reflection type LED micro-illumination light distribution element according to claim 1, wherein the first transmission surface and the total reflection surface are both rotationally symmetric free-form surfaces, and are designed by a non-imaging method.
3. A total reflection LED micro-illumination light distribution element as claimed in claim 2, wherein the non-imaging design of the first transmissive surface comprises the steps of:
s0, optionally selecting the diameter of the bottom surface of one first cylindrical surface as an x axis, selecting a rotation symmetry axis as a y axis, and taking the intersection point of the rotation symmetry axis and the plane where the cavity opening of the bottom cavity is located as a coordinate origin; the refractive index of the material of the light distribution element is n, assuming that
Figure FDA0003318531020000011
And
Figure FDA0003318531020000012
expressing the vector forms of the incident light and the emergent light, respectively, Snell's law expresses as shown in equation (1):
Figure FDA0003318531020000013
wherein ,n1 and n2Respectively representing the refractive indexes of materials where incident rays and emergent rays are located;
s1, dividing a first incident light ray emitted from the LED light source and incident on the first transmission surface into M parts according to an incident angle, wherein the first incident angle of the first incident light ray is represented by formula (2):
Figure FDA0003318531020000014
wherein ,
Figure FDA0003318531020000015
a unit vector representing the x-axis direction,
Figure FDA0003318531020000016
a unit vector representing the y-axis direction; thetacThe maximum included angle between the first incident ray and the rotational symmetry axis is defined;
s2, writing the first incident light and the first emergent light into vector form, as shown in formula (3):
Figure FDA0003318531020000021
s3, connecting any point P on the first transmission surface1jIs set as (x)1j,y1j) Obtaining the point P according to the formula (3) and the formula (1)1jNormal vector of
Figure FDA0003318531020000022
Obtain a point P1jA tangent line of (c);
point P on the curve of the first transmission surface1jTaking a point P1j+1(x1j+1,y1j+1) Point P1j+1At P1jOn the tangent of (C), point P1j+1Is a point P1j+1At the first incident ray
Figure FDA0003318531020000023
And point P1jThe intersection point of the tangent lines is located;
giving a starting point P for the first incident ray and the first emergent ray divided by the formula (3)10(x10,y10) Calculating the normal vector of the first transmission surface according to the formula (1), and obtaining coordinates of each point on the first transmission surface through repeated iterative calculation, wherein the coordinate of the end point is marked as P1end(x1end,y1end)。
4. The total reflection type LED micro-illumination light distribution element according to claim 3, wherein the non-imaging design method of the total reflection surface comprises the following steps:
s11, dividing a second incident light beam emitted from the LED light source and incident on the total reflection surface into M parts according to the incident angle, wherein the second incident angle of the second incident light beam is represented as formula (5):
Figure FDA0003318531020000024
after the first incident light is refracted by the first cylindrical surface, the second incident light is obtained to be incident on the total reflection surface, and the refraction angle is expressed as a formula (6):
Figure FDA0003318531020000025
s22, writing the second incident light and the second emergent light into vector form, as shown in equation (7):
Figure FDA0003318531020000031
s33, connecting any point P on the total reflection surface2jIs set as (x)2j,y2j) The point P is obtained from the formula (7) and the formula (1)2jNormal vector of
Figure FDA0003318531020000032
Obtain a point P2jA tangent line of (c);
point P on the curve of said total reflection surface2jTaking a point P2j+1(x2j+1,y2j+1) Point P2j+1At P2jOn the tangent of (C), point P2j+1Is a point P2j+1At the second incident ray
Figure FDA0003318531020000033
And point P2jThe intersection point of the tangent lines is located;
for the second incident ray and the second emergent ray divided by the formula (7), a starting point P is given20(x20,y20)，x20>x1end，y200; calculating the normal vector of the total reflection surface according to the formula (1), and obtaining the coordinates of each point on the total reflection surface through repeated iterative calculation, wherein the coordinate of the end point is marked as P2end(x2end,y2end)。
5. The fully reflective LED micro-lighting light distribution element of claim 4, wherein the reflective surface is a paraboloid and the second transmissive surface is a sphere.
6. The total reflection type LED micro-illumination light distribution element according to claim 5, wherein the collimated light is incident on the reflection surface and then converged at a focus point, and the coordinate of the focus point is (-x)2end-r,y2end+ h); the rotational symmetry axes of the reflecting surface and the second transmission surface are both y ═ x2end-r; the vertex of the reflecting surface has a coordinate (-x)2end-r,y2end+h+f)，y2end+h+f>r; the equation of the paraboloid of the reflecting surface is shown in the formula (8):
(x+(r+x2end))2＝-4f(y-(y2end+h+f)) (8)
wherein the focal length of the reflecting surface is f, the radius of the second transmitting surface is r, and the diameter of the second cylindrical surface is 2x2endThe height of the second cylindrical surface is h; the coordinate of the intersection point of the reflecting surface and the second cylindrical surface is (x)2end,y2end+h)。
7. A total reflection type LED micro-illumination light distribution element according to claim 6, wherein the focal length f of the reflecting surface is expressed by the following formula (9):
Figure FDA0003318531020000034
8. a total reflection LED micro-illumination light distribution element according to claim 7, wherein the equation of the paraboloid of the reflection surface is as shown in the formula (10):
Figure FDA0003318531020000041
9. a total reflection type LED micro-illumination light distribution element according to claim 6, wherein the equation of the second transmission surface is as shown in formula (11):
Figure FDA0003318531020000042
10. a total reflection type LED micro-illumination light distribution element according to claim 1, wherein the light distribution element is made of polymethyl methacrylate; the refractive index of the material of the light distribution element is 1.49 at a wavelength of 546.1 nm.
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