A free-form surface cylindrical lens design method for realizing uniform light emission of MEMS

Abstract

The application discloses a free surface column lens design method for realizing MEMS uniform light emission, and relates to the field of optical lens design. The method comprises the following steps: a mapping relationship between MEMS light emission energy and a target plane area is established; the vertex coordinates of a free surface generatrix are given, and the coordinates of the rest points on the free surface generatrix are determined according to the mapping relationship; all the points are connected to form the free surface generatrix, and a free surface column lens is constructed based on the free surface generatrix; the lens is arranged between the MEMS and the target plane, and then the light energy reaching each position of the target plane after the exit light beam scanned by the MEMS is refracted by the lens is equal. The MEMS cooperates with the lens to provide a surface structure light with high uniformity and high energy utilization rate for subsequent three-dimensional reconstruction.

Description

Technical Field

[0001] This invention relates to the field of optical lens design, and in particular to a method for designing freeform cylindrical lenses to achieve uniform light output from MEMS. Background Technology

[0002] MEMS micromirrors, with their advantages of small size, low power consumption, high scanning frequency, and long lifespan, are widely used in structured light projection systems. A structured light projection system consists of a semiconductor laser (LD), an optical lens module, and MEMS micromirrors. The laser beam emitted from the LD is shaped by the optical lens module and emitted as a uniform line laser. Then, the line laser is reflected by the high-speed vibrating MEMS micromirrors, scanning the projection area into a rectangular spot. During the scanning process, the brightness of the laser is controlled to achieve alternating bright and dark Gray code fringes or sinusoidal fringes.

[0003] However, the relationship between the MEMS scanning angular velocity ω and time t is:

[0004]

[0005] In the formula, ω0 is the initial angular velocity, and T is the MEMS scanning period. Therefore, as the scanning angular velocity ω increases, the angular velocity of the MEMS decreases, resulting in the emitted light spot appearing dark in the middle and bright at both ends, or the emitted Gray code fringes or sinusoidal fringes appearing sparse in the middle and dense at the edges.

[0006] Therefore, homogenizing the emitted light energy from MEMS scanning is of great significance. Currently, a common method is to filter out edge spots by passing the scanned light through an aperture. However, this method reduces the projection area of ​​the light spot, causing significant light energy loss, and does not fundamentally solve the problem; it also affects the accuracy of subsequent 3D reconstruction. Summary of the Invention

[0007] To address the aforementioned problems and technical requirements, the inventors have proposed a design method for a freeform cylindrical lens that achieves uniform light output from MEMS. This method overcomes the uneven light output caused by the sinusoidal vibration of the MEMS during scanning, eliminates the need for light-blocking structures, improves energy utilization, and provides highly uniform and energy-efficient structured light for subsequent 3D reconstruction. The technical solution of this invention is as follows:

[0008] A method for designing a freeform cylindrical lens to achieve uniform light output in MEMS includes the following steps:

[0009] Establish a mapping relationship between the light-emitting energy of MEMS and the area of ​​the target plane;

[0010] Given the vertex coordinates of the generatrix of a freeform surface, determine the coordinates of the remaining points on the generatrix of the freeform surface based on the mapping relationship;

[0011] Connect all points to form a freeform surface generatrix, and construct a freeform cylindrical lens based on the freeform surface generatrix; the lens is placed between the MEMS and the target plane, so that the light energy of the emitted beam from the MEMS scanning reaches the target plane at each position after being refracted by the lens.

[0012] A further technical solution involves establishing a mapping relationship between the light-emitting energy of the MEMS and the area of ​​the target plane, including:

[0013] The light-emitting energy distribution of the MEMS is divided into M energy units of equal time, and the target plane is divided into M area units of equal area.

[0014] Assuming that the luminous flux of each energy unit illuminates the corresponding area unit, making the average illuminance of each area unit equal, a mapping relationship between energy units and area units is established.

[0015] A further technical solution involves establishing a mapping relationship between energy units and area units, including:

[0016] Let t = T / 4 be the time required for the MEMS to deflect half of its maximum scanning angle. Dividing t into M equal parts, we can express it as follows:

[0017]

[0018] The j-th time t j The scanning angle of the internal MEMS deflection is used as the input to the mapping relationship, and is expressed as:

[0019]

[0020] In the formula, θ=arctan(a / d) represents half of the maximum scanning angle, and a is half of the target plane length, d is the relative distance from the MEMS center point to the target plane, and T is the MEMS scanning period;

[0021] Given that the incident angle after MEMS scanning is θ i After the light rays are refracted by the lens, they reach the corresponding area unit on the target plane. The position of the area unit on the target plane is used as the output of the mapping relationship, represented as:

[0022]

[0023] A further technical solution involves determining the coordinates of the remaining points on the generatrix of the freeform surface based on the mapping relationship, including:

[0024] Let P be the points on the generatrix of the freeform surface. kWhen k = 0, it represents the vertex P0(0,0,z0) of the generatrix of the freeform surface. The vertex P0 is located on the central axis of the light source and is z0 away from the center point of the MEMS.

[0025] Starting from k=1, we successively calculate the incident angle θ. i The light rays passing through point P k-1 The intersection point between the tangent planes is taken as point P. k coordinates (x) k ,0,z k );

[0026] Where: starting from k=1, passing through point P k The tangent plane is determined based on the mapping relationship;

[0027] The incident angle is θ i The light beam is the emitted beam after being scanned by MEMS, θ i It also serves as the input for the mapping relationship.

[0028] Its further technical solution is, after passing point P k The tangent plane is determined based on the mapping relationship, including starting from i = k = 1:

[0029] Based on the mapping relationship, the incident angle is obtained as θ. i The light rays, after being refracted by the lens, reach a position r on the target plane. i , and point P k Determine the direction of the emitted ray, point P k The direction of the incident light is determined by the center point of the MEMS.

[0030] Then, according to Snell's law, we can find point P. k The normal vector is calculated using the following formula:

[0031]

[0032] In the formula, Let be the unit vector of the incident ray. The unit vector of the outgoing ray. Let P be the point k The normal vector, n0 is the air refractive index, and n1 is the lens refractive index;

[0033] The point P is determined by the fact that the tangent plane and the normal vector are perpendicular. k The tangent plane.

[0034] A further technical solution involves constructing a freeform cylindrical lens based on a freeform surface generatrix, including:

[0035] Construct an arc with MEMS center point O as the center. Both the arc and the generatrix of the freeform surface are on the XOZ plane. Extend the arc and the generatrix of the freeform surface along the Y-axis to obtain the two curved surfaces of the lens. Close and connect the two curved surfaces to form a freeform cylindrical lens.

[0036] In the case of MEMS scanning, the emitted light beam does not change direction after passing through the surface of the arc.

[0037] A further technical solution is that the method also includes:

[0038] The inner surface of the surface containing the generatrix of the freeform surface is designed as a non-spherical or cylindrical surface of the freeform surface.

[0039] A further technical solution is that the emitted beam of MEMS scanning first passes through the first curved surface of the lens, and then through the second curved surface of the lens;

[0040] The first curved surface of the lens is the surface containing the arc, and the second curved surface of the lens is the surface containing the generatrix of the freeform surface; or, the first curved surface of the lens is the surface containing the generatrix of the freeform surface, and the second curved surface of the lens is the surface containing the arc.

[0041] A further technical solution is that the method also includes:

[0042] The freeform cylindrical lens constructed based on the freeform surface generatrix can be imported into optical design software for optimization, or the freeform surface generatrix can be optimized based on the particle swarm optimization algorithm to eliminate the accumulated errors in the freeform surface construction process.

[0043] The beneficial technical effects of this invention are:

[0044] This application discloses a design method for a freeform cylindrical lens to achieve uniform light output from MEMS. Based on the established mapping relationship between the light output energy of MEMS and the area of ​​the target plane, a freeform surface of the lens is constructed. Using this lens, the scanning angle of MEMS can be changed. The light energy of the light emitted by MEMS is homogenized by passing through the freeform surface, which can obtain a rectangular light spot or stripe with high energy utilization and high uniformity. This can effectively improve the accuracy and frame rate of subsequent 3D reconstruction. In addition, the lens has the advantages of simple structure and long service life, which is conducive to the high integration and miniaturization of the entire structured light projection system. Attached Figure Description

[0045] Figure 1 This is a flowchart of the design method for a freeform cylindrical lens that achieves uniform light output in MEMS, provided in this application.

[0046] Figure 2 This is a schematic diagram illustrating the design principle of a freeform cylindrical lens for achieving uniform light output in MEMS, as provided in this application.

[0047] Figure 3 This is a schematic diagram of the freeform surface generatrix constructed according to this application.

[0048] Figure 4 This is a schematic diagram of a freeform cylindrical lens structure for achieving uniform light output from a MEMS, provided in this application.

[0049] Figure 5 This is a schematic diagram of the optical path of the beam provided in this application, which passes through MEMS, a freeform cylindrical lens, and finally to the target plane. Detailed Implementation

[0050] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0051] Please refer to Figure 1 As shown, this application provides a design method for a freeform cylindrical lens to achieve uniform light output in MEMS, wherein MEMS referred to in this application is short for MEMS micromirror. The method specifically includes the following steps:

[0052] Step 1: Establish the mapping relationship between the light output energy of MEMS and the target planar area.

[0053] Combination Figure 2 As shown, the light-emitting energy distribution of the MEMS is divided into M equal-time energy units. Equal time means equal energy. Let the luminous flux of each energy unit be... Similarly, the target plane is divided into M equal-area units, each with an area of ​​S0. To establish a one-to-one correspondence between energy units and area units, it is assumed that the luminous flux from each energy unit can illuminate its corresponding area unit, ensuring that the average illuminance of each area unit is equal. Where η is the efficiency of the freeform cylindrical lens to be designed. Therefore, when the number of M is very large, that is, when the area of ​​each area unit is very small compared with the entire target plane, uniform illumination on the target plane can be achieved, thereby establishing the mapping relationship between energy units and area units.

[0054] The target plane is a rectangular surface with a length of 2a. The width is related to the light divergence angle and is not limited here. The relative distance from the MEMS center point O to the target plane is d. Therefore, the maximum scanning angle of the MEMS is θ. total =2arctan(a / d), since the MEMS scan is symmetrical, only one end is considered, θ = arctan(a / d).

[0055] The time-division process of the light-emitting energy distribution of MEMS includes:

[0056] Let the time required for MEMS deflection θ be t = T / 4, where T is the MEMS scanning period. Dividing t into M equal parts, we can express it as follows:

[0057]

[0058] The j-th time t j The scanning angle of the internal MEMS deflection is used as the input to the mapping relationship, and is expressed as:

[0059]

[0060] At this point, the light-emitting energy of the MEMS is divided into M parts according to equal time intervals.

[0061] Given that the incident angle after MEMS scanning is θ i After the light rays are refracted by the lens, they reach the corresponding area unit on the target plane. The position of the area unit on the target plane (considering only one end) is used as the output of the mapping relationship, which is expressed as:

[0062]

[0063] Therefore, the mapping relationship between energy units and area units can be converted into a MEMS scanning angle θ. i The position r of the light ray projected onto the target plane i The correspondence.

[0064] Step 2: Given the vertex coordinates of the freeform surface generatrix, determine the coordinates of the remaining points on the freeform surface generatrix according to the mapping relationship.

[0065] 1) Let P0(0,0,z0) be the vertex of the freeform surface generatrix C0. This vertex P0 is the first point on the freeform surface generatrix C0, located on the light source central axis Z (referred to as the Z-axis), and the distance from the MEMS center point O is z0.

[0066] 2) Calculate the second point P1 on the generatrix C0 of the freeform surface. Point P1 is the intersection point between the ray with an incident angle of θ1 (i.e., the outgoing beam after MEMS scanning) and the tangent plane passing through vertex P0. The normal vector of vertex P0 is known. Along the positive Z-axis, the tangent plane of vertex P0 intersects with... Since the rays are perpendicular to each other, the coordinates of point P1 can be obtained as (x1, 0, z1) using the known geometric vector formula. Based on the mapping relationship established in step 1, the position r1 on the target plane after refraction by the lens for a ray with an incident angle of θ1 can be obtained; let this point be Q1. Therefore, the incident ray... The direction is The emitted ray after passing point P1 The direction is

[0067] Then, according to Snell's law, the normal vector of point P1 can be obtained. The calculation formula is:

[0068]

[0069] In the formula, n0 is the air refractive index, which is approximately 1; n1 is the lens refractive index.

[0070] 3) Calculate the subsequent point P on the generatrix C0 of the freeform surface. k Similarly, by finding the intersection point between the ray of incidence at angle θ2 and the tangent plane passing through point P1, the coordinates of point P2 (x2, 0, z2) can be obtained. And so on, to find the ray of incidence at angle θ... i The light rays passing through point P k-1 The intersection point between the tangent planes is taken as point P. k coordinates (x) k ,0,z k And find point P based on the mapping relationship and Snell's law. k normal vector The point P is determined by the perpendicularity of the tangent plane and the normal vector. k The tangent plane. Thus, the coordinates and normal vectors of all points on the generatrix C0 of the freeform surface can be easily obtained.

[0071] Step 3: Connect all points to form the freeform surface generatrix C0.

[0072] like Figure 3 As shown, it illustrates the distance from vertex P0 to endpoint P. k The curve is half of the generatrix C0 of the freeform surface, which is a curve on the XOZ plane.

[0073] Step 4: Construct a freeform cylindrical lens based on the freeform surface generatrix C0.

[0074] Construct an arc C1 centered at the MEMS center point O. Arc C1 also lies in the XOZ plane. Extend arc C1 and the freeform surface generatrix C0 along the Y-axis to obtain two curved surfaces of the lens. The cross-section of the surface containing arc C1 is circular, and the light beam's output direction remains unchanged after passing through this surface. The cross-section of the surface containing the freeform surface generatrix C0 is a freeform surface. Finally, connect the two curved surfaces to form a freeform cylindrical lens, as shown below. Figure 4 As shown.

[0075] Optionally, the inner surface of the surface containing the generatrix C0 of the freeform surface can be designed as a non-spherical or cylindrical surface of the freeform surface.

[0076] Step 5: Import the freeform cylindrical lens constructed based on the circular arc C1 and the freeform surface generatrix C0 into optical design software for optimization, or optimize the circular arc C1 and the freeform surface generatrix C0 based on optimization algorithms such as particle swarm optimization to eliminate accumulated errors in the freeform surface construction process, thereby giving the freeform cylindrical lens better light uniformity. This application does not limit the optimization algorithm used.

[0077] A freeform cylindrical lens is placed between the MEMS and the target plane. The beam emitted by the MEMS scan first passes through the first curved surface of the lens, and then through the second curved surface of the lens before being projected onto the target plane. For example... Figure 2 As shown in (a), when the first curved surface of the lens is the surface containing the arc C1, and the second curved surface is the surface containing the generatrix C0 of the freeform surface, the optical path is as follows: Figure 5 As shown, after the light beam passes through the MEMS, the emitted beam first passes through the arc surface of the freeform cylindrical lens, and then, along this direction, is refracted by the freeform surface containing the generatrix before reaching the target plane. The light energy at each position is equal. That is, the constructed freeform cylindrical lens can achieve light energy homogenization of the emitted beam from the MEMS, while also possessing high energy utilization efficiency, making it widely applicable in structured light projection systems. For example... Figure 2 As shown in (b), when the first curved surface of the lens is the surface where the generatrix C0 of the freeform surface is located and the second curved surface is the surface where the arc C1 is located, the light beam emitted by the MEMS is first refracted through the freeform surface where the generatrix is ​​located. After the refracted light passes through the surface where the arc is located along the current direction, the light energy at each position on the target plane is equal.

[0078] The above descriptions are merely preferred embodiments of this application, and the present invention is not limited to the above embodiments. It is understood that other improvements and variations directly derived or conceived by those skilled in the art without departing from the spirit and concept of the present invention should be considered to be included within the protection scope of the present invention.

Claims

1. A method for designing a freeform cylindrical lens to achieve uniform light output in MEMS, characterized in that, include: Establish a mapping relationship between the light-emitting energy of MEMS and the area of ​​the target plane; Given the vertex coordinates of the generatrix of the freeform surface, determine the coordinates of the remaining points on the generatrix of the freeform surface according to the mapping relationship; Connect all points to form a freeform surface generatrix, and construct a freeform cylindrical lens based on the freeform surface generatrix; the lens is placed between the MEMS and the target plane, so that the light energy of the outgoing beam scanned by the MEMS is equal at each position on the target plane after being refracted by the lens; Determining the coordinates of the remaining points on the generatrix of the freeform surface based on the mapping relationship includes: Let each point on the generatrix of the freeform surface be... P k , k =0 indicates the vertex of the generatrix of the freeform surface. P 0(0,0, z 0), Vertex P 0 is located on the central axis of the light source, at a distance of [distance missing] from the center point of the MEMS. z 0; from k Starting from 1, the incident angles are calculated sequentially. The light rays and the point of passage P k-1 The intersection point between the tangent planes is taken as the point. P k coordinates ( x k ,0, z k ); Among them: From k Starting from =1, passing through point... P k The tangent plane is determined based on the mapping relationship; The incident angle is The light beam is the emitted beam after being scanned by MEMS. It is also the input to the mapping relationship; Passing Point P k The tangent plane is determined according to the mapping relationship, including, from i = k =1 starts: Based on the mapping relationship, the incident angle is obtained as follows: The light rays, after being refracted by the lens, reach the corresponding position on the target plane as follows: , and point P k Determine the direction of the emitted ray, point P k The direction of the incident light is determined by the center point of the MEMS; Then, according to Snell's law, the point is obtained. P k The normal vector is calculated using the following formula: ； In the formula, Let be the unit vector of the incident ray. Let be the unit vector of the emitted ray. For the point P k The normal vector, The refractive index of air, The refractive index of the lens; The point is obtained by determining that the tangent plane is perpendicular to the normal vector. P k The tangent plane.

2. The method for designing a freeform cylindrical lens to achieve uniform light output in MEMS according to claim 1, characterized in that, Establishing the mapping relationship between MEMS light-emitting energy and target planar area includes: The light-emitting energy distribution of the MEMS is divided into M energy units of equal time, and the target plane is divided into M area units of equal area. Assuming that the luminous flux of each energy unit illuminates the corresponding area unit, such that the average illuminance of each area unit is equal, a mapping relationship between the energy unit and the area unit is established.

3. The method for designing a freeform cylindrical lens to achieve uniform light output in MEMS according to claim 2, characterized in that, Establishing the mapping relationship between the energy unit and the area unit includes: Let the time required for the MEMS to deflect half of the maximum scanning angle be... t = T / 4, will t Dividing into M equal parts is represented as follows: ； The first j Time The scanning angle of the internal MEMS deflection is used as the input to the mapping relationship, and is expressed as: ； In the formula, , representing half of the maximum scanning angle, and a It is half the length of the target plane. d The distance is the relative distance from the center point of the MEMS to the target plane. T MEMS scanning cycle; Given that the incident angle after MEMS scanning is After being refracted by the lens, the light rays reach the corresponding area unit on the target plane. The position of the area unit on the target plane is used as the output of the mapping relationship, expressed as: 。 4. The method for designing a freeform cylindrical lens to achieve uniform light output in MEMS according to claim 1, characterized in that, Constructing a freeform cylindrical lens based on the aforementioned freeform surface generatrix includes: An arc is constructed with the MEMS center point O as the center. Both the arc and the generatrix of the freeform surface are on the XOZ plane. The arc and the generatrix of the freeform surface are extended along the Y-axis to obtain two curved surfaces of the lens. The two curved surfaces are closed and connected to form a freeform cylindrical lens. In this case, the emitted light beam from the MEMS scanning remains unchanged after passing through the surface containing the arc.

5. The method for designing a freeform cylindrical lens to achieve uniform light output in MEMS according to claim 4, characterized in that, The method further includes: The inner surface of the surface containing the generatrix of the freeform surface is designed as a non-spherical or cylindrical surface of the freeform surface.

6. The method for designing a freeform cylindrical lens to achieve uniform light output in MEMS according to claim 4, characterized in that, The emitted beam from the MEMS scan first passes through the first curved surface of the lens, and then through the second curved surface of the lens; The first curved surface of the lens is the surface containing the arc, and the second curved surface of the lens is the surface containing the generatrix of the freeform surface; or, the first curved surface of the lens is the surface containing the generatrix of the freeform surface, and the second curved surface of the lens is the surface containing the arc.

7. The method for designing a freeform cylindrical lens to achieve uniform light output in MEMS according to any one of claims 1-6, characterized in that, The method further includes: The freeform cylindrical lens constructed based on the freeform surface generatrix is ​​imported into optical design software for optimization, or the freeform surface generatrix is ​​optimized based on the particle swarm optimization algorithm to eliminate the accumulated errors in the freeform surface construction process.

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