CN-121995621-A - Design method of double-free-form surface uniform illumination lens

Abstract

The invention discloses a design method of a double-free-surface uniform illumination lens, which is characterized in that a lambertian characteristic extension source with half width of D max is assumed to be a set of infinite multiple small point sources, an inner free-surface is designed by utilizing the illumination square law in combination with the luminous characteristic of the lambertian light source, an outer free-surface is designed according to the energy conservation principle and the light intensity energy mapping method, a free-surface point cloud set is calculated through a point-by-point construction and tangent line iteration method, and a polynomial curve expression of the double free-surface is obtained by performing linear polynomial fitting on point clouds. The polynomial coefficients are input into lighttools software to obtain the three-dimensional solid model of the lens. Optical simulation was performed by setting the light emission data of the light source, the illumination distance H, and the illumination radius R max . With a pitch-height ratio of 1, the preliminary simulation resulted in an illuminance uniformity of 88.8%. Through optimizing the polynomial coefficient of the curved surface expression, the illuminance uniformity of 97.7% can be obtained after a plurality of optimization iterations.

Inventors

• XUE CHANGXI
• LI ZIHENG

Assignees

• 长春理工大学

Dates

Publication Date

20260508

Application Date

20241102

Claims (2)

1. 1. A method for designing a double free-form surface uniform illumination lens, comprising the following steps: step one, establishing a point-to-point light intensity energy mapping method mathematical model; step two, calculating the point light source in Intensity of luminescence in the direction, and the distance to Is a luminance of a certain point of (a); Thirdly, selecting a light source irradiation normal direction with a horizontal direction to the right as an x-axis positive direction and a vertical direction to the vertical direction as a y-axis positive direction, establishing a rectangular coordinate system xOy, establishing a refraction model of light rays entering a medium from air, wherein R max is a target plane, N 0 is an air refractive index, N 1 is a medium refractive index, an included angle between the incident light rays and the normal direction after passing through the refraction plane is O, T is a tangential vector of a refraction point, and N is a normal vector; step four, establishing a light source numerical expression for generating constant illumination on a target plane according to a light intensity mapping method; The O obtained in the fifth step and the fourth step is the included angle between the emergent light and the normal direction, which is called a second divergence angle, according to the formula (4), The divergence angle O can be selected as an ideal refraction angle; Step six, establishing a light source-target surface energy mapping mathematical model, and calculating a departure divergence angle as The total luminous flux emitted and the total energy received by Rmax at the maximum illumination radius of the target surface; Establishing an extended source light intensity target surface energy mapping method mathematical model; step eight, using formulas (2) and (7), in order to obtain a curved surface with equal target illuminance as a secondary light source, it is necessary to satisfy The illumination distance r 0 and the illumination distance r 0 can be obtained Is a numerical relationship of (2); Step nine, assuming that an LED light source with half-width D max is considered as a set of n point sources Di, and the maximum divergence half-angle of the light source Equally divided into n parts, on the x-axis where the light source is placed, it is assumed that the ith light source has the ith divergence half-angle limit corresponding thereto, i.e. D i has the corresponding divergence half-angle limit Assuming that the light emitted by Di does not exceed its half-angle limit Step ten, according to the formula (7), an inner free-form surface P i with the initial height of h1 and equal illuminance distribution can be found, and the point cloud coordinate under the two-dimensional plane is; step eleven, according to equation (8), calculating from the initial divergence angle to the maximum divergence half angle And the half width D max of the light source, all the inner free-form surface discrete points can be obtained; Step twelve, setting each discrete point of the free-form surface P i as a secondary light-emitting source, establishing a two-dimensional coordinate system in the horizontal and vertical directions of P i , and establishing a refraction model that light rays emitted from P i reach a point Q i of the outer free-form surface through a medium; Step thirteen, obtaining the light intensity I Pi at the point P i and the light intensity I Di at the point D i according to the formula (1), and if the lens is axisymmetric, obtaining according to the energy conservation law and the formula (3); fourteen, according to the formula (9), the sine value and the cosine value of O i can be obtained through calculation; fifteen, calculating the tangent value of the Oi for subsequent calculation through formulas (10) and (11), wherein the Oi is assumed to be the specific emergent direction of the refracted ray; Sixteenth, setting each discrete point of the free-form surface Q i as a secondary light-emitting source, establishing a two-dimensional coordinate system in the horizontal and vertical directions of Q i , and establishing a refraction model that light emitted from Q i reaches the R i point of the illumination plane; Seventeenth, according to formula (6), the total luminous flux received at the Ri point at this time is obtained as follows; Eighteen, according to the formula (1), the formula (6) and the formula (12), numerical relational expressions of R i and R max can be obtained; Nineteenth, according to formula 13, the coordinates Ri (Ri, H) of each expected target point can be calculated, combining the coordinates of each point P i of the inner free-form surface and the outgoing direction angle O i of P i , and calculating the coordinates of the point Q i of the outer free-form surface point by utilizing the refraction law and tangential line iteration method; Twenty, all discrete points are imported into modeling software soildworks, fitted into two sample curves, and the curves are rotated around a Z axis to obtain a three-dimensional solid model of the double free-form surface lens, the solid model is imported into lighttools for initial optical simulation, and the calculated uniformity is 88%; and twenty-one, fitting the double free-form surfaces into polynomial curves, setting polynomial coefficients as optimization variables, and performing iterative optimization, wherein the final optimization result is that the illuminance uniformity of 97.7% is obtained.
2. 2. The method of claim 1, wherein in the step ten, the inner free Qu Miandian cloud coordinates are obtained by using an illuminance square law, in the step fourteen, sine values and cosine values of the emergent ray angles are obtained by using a formula (3) and a formula (9) and used for subsequent calculation, and in the step eighteen, the expected target point coordinates are obtained according to a formula (6) and a formula (12) and used for subsequent calculation.

Description

Design method of double-free-form surface uniform illumination lens Technical Field The invention relates to a design method of a double-free-form surface uniform-illumination lens, and belongs to the field of illumination design. Background As an emerging light source technology, LED (light emitting diode) light sources have significant advantages of high efficiency, environmental protection, and the like, and have become mainstream light sources of various manufacturers. Conventional LED light sources typically produce an uneven distribution along the optical axis in the illumination plane. However, uniformity is critical in the fields of human eyes, indoor and medical lighting, etc. Achieving illumination uniformity is also an important issue in the field of illumination optical design. However, the existing research method has certain defects, solving differential equations is complicated, the design of an extended source is mainly based on the assumption of a point source, in addition, the design structure of some systems is complex, and some methods cannot consider near-field illumination and far-field illumination at the same time. Disclosure of Invention To solve the limitations of the existing design methods, we propose a new approach. Firstly, regarding an LED extended light source as a set of a plurality of point sources, we consider that the method is more accurate than the traditional method of treating the LED light source as a single point, then a uniform secondary luminous inner free-form surface is designed by applying the illuminance square law, and finally a double free-form surface lens is designed according to a source-target mapping method and combining the luminous characteristics of the LED light source. We refer to this approach as the hypothetical point source set (HPE) approach. As shown in fig. 1, the invention provides a single-point measuring method for performance parameters of laser beams, which comprises the following steps: step one, establishing a point-to-point light intensity energy mapping method mathematical model; step two, calculating the point light source in The luminous intensity in the direction is calculated to calculate the point light source inThe opposite distance in the direction isIs a luminance of a certain point of (a); Thirdly, selecting a horizontal rightward direction as an x-axis positive direction, and a vertical upward direction as a y-axis positive direction and a normal direction of light source irradiation to establish a rectangular coordinate system xOy, establishing a refraction model of basic light rays entering a medium from air, wherein R max is a target plane, N 0 is an air refractive index, N 1 is a medium refractive index, and an included angle between the incident light rays and the normal direction after passing through a refraction surface is O; step four, establishing a light source numerical expression for generating constant illumination on a target plane according to a light intensity mapping method; The O obtained in the fifth step and the fourth step is the included angle between the emergent light and the normal direction, which is called a second divergence angle, according to the formula (4), The divergence angle O can be selected as an ideal refraction angle; Step six, establishing a light source-target surface energy mapping mathematical model, and calculating a departure divergence angle as Total luminous flux emitted and total energy received by R max at the maximum illumination radius of the target surface; Establishing an extended source light intensity target surface energy mapping method mathematical model; step eight, using formulas (2) and (7), in order to obtain a curved surface with equal target illuminance as a secondary light source, it is necessary to satisfy The illumination distance r 0 and the illumination distance r 0 can be obtainedIs a numerical relationship of (2); Step nine, assuming that an LED light source with half-width D max is considered as a set of an infinite number of point sources D i, assuming a total number of n, and assuming the maximum divergence half-angle of the light source Equally divided into n parts, assuming that the ith light source has its corresponding ith divergence half angle limit in the x-axis direction of the plane in which the light source is placed, i.e., each light source D i has its corresponding divergence half angle limitProvided that the light emitted by the light source D i does not exceed its half-angle limit Step ten, according to the formula (7), an inner free-form surface P i with an initial height of h 1 and equal illuminance distribution can be found, and the point cloud coordinate under the two-dimensional plane is; step eleven, according to equation (8), calculating from the initial divergence angle to the maximum divergence half angle And the half width D max of the light source, all the inner free-form surface discrete points can be obtained; Step twelve, se