A method for designing a receiving lens of a reflective photoelectric sensor

Abstract

The application belongs to the technical field of optical design, and discloses a design method of a receiving lens of a reflective photoelectric sensor. The receiving lens has a front surface and a rear surface. The front surface of the receiving lens is a free curve which is smoothly connected by multiple curve segments. The contour of the rear surface of the receiving lens is a slope structure with a preset slope. The design method comprises S1, design initialization; S2, construction of the front surface of the receiving lens; S3, construction of the rear surface of the receiving lens; and S4, simulation optimization. Through the synergistic effect of the rotationally symmetric single free surface of the front surface and the slope structure of the rear surface, efficient reception of parallel light axis signals and accurate filtering of small-angle stray light are realized, and the problem of poor filtering of stray light in the system is solved. While improving the reception accuracy of the system, the complexity and manufacturing cost of the system are significantly reduced, and no additional optical elements are needed.

Description

Technical Field

[0001] This invention belongs to the field of optical design technology, specifically relating to a design method for a receiving lens of a reflective photoelectric sensor. Background Technology

[0002] Reflective photoelectric sensors, with their fast response, high precision, high reliability, and ease of installation and maintenance, have become commonly used devices in industrial inspection and automation control. The optical system of this sensor typically consists of a light source, a receiver, and control circuitry, with the receiving lens assembly having a crucial impact on detection performance.

[0003] The receiving lens needs to converge as much of the reflected light from the light source as possible, ensuring it falls onto the receiver surface after passing through the receiving aperture. When the reflection distance is sufficiently far, the reflected target light can be considered parallel. However, stray light from other angles will pass through the receiving lens and fall onto the receiver surface, causing interference. Polarizers are typically used to filter non-parallel light, but even after polarizer filtering, some small-angle stray light remains unfiltered. Using more effective polarizers would further increase costs; therefore, a redesign of the receiving lens structure is needed to further improve the filtering capability for small-angle stray light without significantly increasing costs. Summary of the Invention

[0004] In order to overcome the above-mentioned shortcomings of the prior art, the purpose of this invention is to provide a design method for the receiving lens of a reflective photoelectric sensor, which aims to solve the problems existing in the prior art.

[0005] The technical solution adopted by this invention to solve its technical problem is:

[0006] A design method for a receiving lens of a reflective photoelectric sensor, wherein the receiving lens has a front surface and a rear surface, the contour line of the front surface of the receiving lens is a free curve formed by the smooth connection of multiple curve segments, and the contour of the rear surface of the receiving lens is a slope structure with a preset slope.

[0007] The design method includes the following steps:

[0008] S1. Design Initialization: Establish a simulated light source model by reversing the optical path, and define the parameters of the aperture and the simulated light source;

[0009] S2. Construct the front surface of the receiving lens: Iteratively generate a free curve based on Snell's law to ensure that the light rays emitted from the simulated light source are parallel to the optical axis after being refracted by the front surface of the receiving lens.

[0010] S3. Construct the rear surface of the receiving lens: Calculate the height of the rear surface using a slanted geometric model to ensure that it meets the separation conditions for effective light and stray light.

[0011] S4. Simulation Optimization: Perform data analysis and recalculate the evaluation function value based on the results of the light simulation. If both the evaluation function value and the effective light transmittance meet the preset threshold, the designed receiving lens is obtained.

[0012] Preferably, in step S1, based on the principle of optical path reversibility, the target light spot on the aperture surface is assumed to be a simulated light source, and the size of the target light spot on the aperture surface is determined according to the thickness of the receiving aperture, the aperture, the distance between the aperture and the receiving surface, and the distance between the lens vertex and the aperture.

[0013] Determine the maximum emission angle of the simulated light source and divide it into equal parts, dividing the maximum emission angle of the simulated light source into N unit angles Δθ (Δθ = θ). max / N), to obtain the unit emission angle.

[0014] Preferably, in step S2, the three-dimensional optical path mapping is converted into a two-dimensional planar mapping based on rotational symmetry;

[0015] According to Snell's law, the light vector emitted from the simulated light source is transformed into parallel light parallel to the optical axis after passing through the designed refractive surface: starting from the center of the receiving lens, the free curve of the front surface of the receiving lens is constructed iteratively with a step size of Δθ. According to Snell's law, the normal vector and corresponding tangent of each refractive surface are calculated, and the free curve is formed by connecting the intersections of all tangents and the emitted light rays.

[0016] Rotating the aforementioned free curve around the center of the receiving lens as an axis for one revolution, the resulting free surface is the front surface of the receiving lens.

[0017] Preferably, in step S3, the step of establishing the back surface slope function of the receiving lens includes:

[0018] A bevel angle is set on a cylindrical base of equal radius. The relationship between this angle and the aperture and the axial thickness of the lens is determined by geometric optics analysis. This ensures that the horizontal shift of the parallel incident stray light after refraction by the bevel surface results in a position on the aperture that is more than half the aperture diameter away from the center of the aperture. Similarly, the position of the stray light with an incident angle greater than a preset threshold after refraction results in a position on the aperture that is more than half the aperture diameter away from the center of the aperture.

[0019] The setting of the oblique angle must satisfy the following: after the target light rays parallel to the optical axis are refracted and laterally deflected, the distance from the center of the aperture on the aperture is less than half the aperture diameter; while after the stray light with an incident angle greater than a preset threshold is refracted, the distance from the center of the aperture on the aperture is greater than half the aperture diameter.

[0020] Preferably, an offset equation is established based on Snell's law, the oblique angle is iterated and combined with parameters such as the material refractive index and lens axial thickness to calculate the outgoing ray vector after two refractions, and the distance between the intersection point of the outgoing ray on the aperture surface and the center point of the aperture is obtained.

[0021] Preferably, calculate 0 < θ < θ th The incident ray vector is the unit vector of the outgoing ray after two refractions, where θth is the stray light filtering threshold angle;

[0022] According to the vector form of Snell's law, given the incident unit vector, the unit normal vector of the refracting surface, and the refraction of the medium, the formulas for calculating the outgoing unit vector include:

[0023]

[0024] The unit vector of the interface normal is represented as... The incident unit vector is The outgoing unit vector is The refractive indices of the incident and exit media are n1 and n2, respectively.

[0025] Preferably, in step S4, the optimization objective function is set:

[0026]

[0027] When F=0, the design is deemed to meet the standard, and the output parameter is D, which is the aperture diameter.

[0028] Preferably, in step S4, after the above-mentioned optimization objective function F meets the requirements through numerical calculation, the parameters of the new contour curve are transmitted to the optical simulation software. The front surface contour line of the receiving lens is obtained by rotating symmetry about the y-axis, and the rear surface is obtained by diagonally cutting a cylinder with a bottom surface of R and a height of Δh. The model is created in the optical simulation software and ray tracing is performed. Then, the simulation results are transmitted to the data analysis software for data analysis through DDE technology. Based on the results of the ray simulation, the evaluation function value is calculated again to determine whether the designed receiving lens meets the requirements.

[0029] Preferably, the effective light transmittance is set as follows:

[0030]

[0031] Where E pass To ensure the effective luminous flux passing through the aperture during ray tracing simulation, E total This is to simulate the total emitted luminous flux of the light source.

[0032] Compared with the prior art, the beneficial effects of the present invention include:

[0033] This application presents a design method for the receiving lens of a reflective photoelectric sensor. Addressing the technical shortcomings of existing reflective photoelectric sensors, such as low polarizer stray light filtering efficiency and significant small-angle stray light interference, this method achieves efficient reception of parallel optical axis signals and precise filtering of small-angle stray light through the synergistic effect of a rotationally symmetric freeform surface on the front surface and a sloped structure on the rear surface. This improves system receiving accuracy while significantly reducing system complexity and manufacturing costs, without requiring additional optical components. Attached Figure Description

[0034] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0035] Figure 1 This is a schematic diagram of the steps of the present invention.

[0036] Figure 2 This is a schematic diagram of the front surface design of the receiving lens of the present invention.

[0037] Figure 3 This is a schematic diagram of the rear surface design of the receiving lens of the present invention.

[0038] Figure 4 This is a schematic diagram of the lens model after multiple optimizations of the present invention.

[0039] in:

[0040] 1-Front surface, 2-Rear surface. Detailed Implementation

[0041] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. Many specific details are set forth in the following description to provide a thorough understanding of the present invention; the described embodiments are merely some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0042] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.

[0043] Example:

[0044] See Figures 1-4 A design method for a receiving lens of a reflective photoelectric sensor, wherein the receiving lens has a front surface 1 and a rear surface 2, the contour line of the front surface of the receiving lens is a free curve formed by the smooth connection of multiple curve segments, and the contour of the rear surface of the receiving lens is a slope structure with a preset slope.

[0045] The design methodology includes the following steps:

[0046] S1. Design Initialization: Establish a simulated light source model by reversing the optical path, and define the parameters of the aperture and the simulated light source;

[0047] S2. Construct the front surface of the receiving lens: Iteratively generate a free curve based on Snell's law to ensure that the light rays emitted from the simulated light source are parallel to the optical axis after being refracted by the front surface of the receiving lens.

[0048] S3. Construct the rear surface of the receiving lens: Calculate the height of the rear surface using a slanted geometric model to ensure that it meets the separation conditions for effective light and stray light.

[0049] S4. Simulation Optimization: Perform data analysis and recalculate the evaluation function value based on the results of the light simulation. If both the evaluation function value and the effective light transmittance meet the preset threshold, the designed receiving lens is obtained.

[0050] The design method of this embodiment, through the synergistic effect of the rotationally symmetric freeform surface on the front surface and the slope structure on the rear surface, can expand the distance between the landing points of the target light and stray light on the aperture plane, improve the stray light interference caused by insufficient polarization filtering, thereby achieving efficient reception of parallel optical axis signals and accurate filtering of small-angle stray light, without the need to add additional optical components such as polarization filters, significantly reducing system complexity and manufacturing costs.

[0051] In this embodiment, the details of step S1 are as follows:

[0052] Based on the principle of optical path reversibility, the target light spot on the aperture surface is assumed to be a simulated light source. The size of the target light spot on the aperture surface is determined according to the thickness of the receiving aperture, the aperture, the distance between the aperture and the receiving surface, and the distance between the lens vertex and the aperture.

[0053] Determine the maximum emission angle of the simulated light source and divide it into equal parts, dividing the maximum emission angle of the simulated light source into N unit angles Δθ (Δθ = θ). max / N), to obtain the unit emission angle.

[0054] In step S2, based on rotational symmetry, the three-dimensional optical path mapping is converted into a two-dimensional plane mapping;

[0055] According to Snell's law, the light vector emitted from the simulated light source is transformed into parallel light parallel to the optical axis after passing through the designed refractive surface: starting from the center of the receiving lens, the free curve of the front surface of the receiving lens is constructed iteratively with a step size of Δθ. According to Snell's law, the normal vector and corresponding tangent of each refractive surface are calculated, and the free curve is formed by connecting the intersection points of all tangents and the emitted light rays.

[0056] Rotate the free curve described above around the center of the receiving lens to obtain a free surface, which is the front surface of the receiving lens.

[0057] See Figure 3 The specific steps of S2 include:

[0058] S21. Specifically, starting from (O, A0), assume the light source O is located at the origin, and the normal vector of the receiving lens vertex A0 coincides with the optical axis. The ray OA0 reaches the center of the light spot on the target plane without refraction, at a small angle. The offset generates ray OA1, and point A1 is located in the tangent plane of the surface where A0 is located. Its coordinates can be calculated through geometric relationships.

[0059] S22. According to the principle of reversibility of light paths, after the rays emitted from the virtual light source are refracted by the front surface of the designed lens, all rays should be parallel to the optical axis. Given the incident and exit directions A1x1 of ray OA1, the normal vector N1 at point A1 is calculated using Snell's law. Then... Generate ray OA2 for the angle increment, and repeat the above steps to calculate the coordinates of A2 and the normal vector N2. Iteratively calculate A... n The point coordinates continue until the specified lens radius R is reached.

[0060] In step S3, the step of establishing the back surface slope function of the receiving lens includes:

[0061] A bevel angle is set on a cylindrical base of equal radius. The relationship between this angle and the aperture and the axial thickness of the lens is determined by geometric optics analysis. This ensures that the horizontal shift of the parallel incident stray light after refraction by the bevel surface results in a position on the aperture that is more than half the aperture diameter away from the center of the aperture. Similarly, the position of the stray light with an incident angle greater than a preset threshold after refraction results in a position on the aperture that is more than half the aperture diameter away from the center of the aperture.

[0062] The setting of the oblique angle must meet the following requirements: after the target light rays parallel to the optical axis are refracted and laterally deflected, the position on the aperture is less than half the aperture diameter of the aperture. After the stray light with an incident angle greater than the preset threshold is refracted, the position on the aperture is more than half the aperture diameter of the aperture.

[0063] That is, after iterating the maximum height Δh of the rear surface slope in ascending order of numerical values, the oblique cutting angle is changed to obtain the normal vector of the oblique cut surface, such that: the distance δ(θ between the offset position of effective light parallel to the optical axis on the diaphragm plane and the center of the diaphragm th ) < D / 2, and for stray light with an incident angle θ > θ th , the distance δ(θ between the offset position on the diaphragm plane and the center of the diaphragm th ) ≥ D / 2, where θth is the stray light filtering threshold angle.

[0064] Then, an offset equation is established based on Snell's law, the oblique cutting angle is iterated, and parameters such as the material refractive index and the axial thickness of the lens are combined to calculate the exit ray vector after the light undergoes two refractions, and the distance between the intersection position of the exit ray on the diaphragm plane and the center point of the diaphragm is obtained.

[0065] See further Figure 2 , it is known that after the designed front surface generatrix is rotationally symmetric along the y-axis, the front surface of the designed receiving lens can be obtained. The front surface contour on the two-dimensional coordinate axis is composed of A0, A1, A2...A n . A1', A2'...A n ' are symmetric about the y-axis with A1, A2...A n . According to S3, given that after passing through the normal vector of the refracting surface of A1, A2...A n , the normal vector of the refracting surface of A1', A2'...A n ' can also be obtained.

[0066] See Figure 3 , it is known that the coordinates of A n are (R,y0), let the coordinates of B be (R,y0+Δh), then the connecting line of A n 'B is the rear surface contour of the receiving lens, is the normal vector of the rear surface of the receiving lens. Iteratively calculate the incident ray vectors where 0 < θ < θ th , according to the vector form of Snell's law, given the incident unit vector, the refracting surface unit normal vector and the refractive index of the medium, the formula for obtaining the exit ray unit vector includes:

[0067]

[0068] wherein the interface normal unit vector is expressed as the incident unit vector is the exit unit vector is the refractive indices of the incident medium and the exit medium are n1 and n2, respectively.

[0069] After calculating , ​The x-coordinate of the intersection point with the aperture plane, xθ, can be obtained. Therefore, the distance δ(θ) between the light ray making an angle θ with the optical axis and the center point of the aperture after passing through the designed receiving lens is calculated. th It can be determined that the set optimization objective function is:

[0070]

[0071] When F=0, the design is deemed to meet the standard, and the output parameter is D, which is the aperture diameter.

[0072] In step S4, after the above-mentioned optimization objective function F meets the requirements through numerical calculation, the parameters of the new contour curve are transmitted to the optical simulation software. The front surface contour line of the receiving lens is obtained by rotating symmetry about the y-axis, and the rear surface is obtained by diagonally cutting a cylinder with a bottom surface of R and a height of Δh. The model is created in the optical simulation software and ray tracing is performed. Then, the simulation results are transmitted to the data analysis software for data analysis through DDE technology. Based on the results of the ray simulation, the evaluation function value is calculated again to determine whether the designed receiving lens meets the requirements.

[0073] Set the effective light transmittance:

[0074]

[0075] Where E pass To ensure the effective luminous flux passing through the aperture during ray tracing simulation, E total This is to simulate the total emitted luminous flux of the light source.

[0076] ηeff is used to measure the effective light parallel to the optical axis (θ≤θ). th The proportion of light passing through the aperture after refraction by the lens reflects the lens's transmission efficiency of the effective signal, which requires that the transmittance of parallel light rays from the target be no less than 95%.

[0077] Specifically, if the simulated evaluation function value and effective light transmittance both meet the preset thresholds, then the designed receiving lens is obtained. This process is repeated until the requirements are met, resulting in a lens that meets the specified parameters. Figure 4 A model of a receiving lens that meets the requirements.

[0078] In summary, this invention utilizes a collaborative design approach involving the reverse construction of the optical path on the front surface and the oblique geometric model of the rear surface. The front surface iteratively generates free curves based on the law of refraction and the concept of differential angles, while the rear surface directly correlates the oblique angle with the aperture parameters through geometric optics equations. This avoids complex mathematical derivations, significantly lowers the design threshold, and improves efficiency.

[0079] This invention supports flexible configuration of core parameters such as aperture, lens thickness, and material refractive index. By adjusting the constraints of the oblique angle equation and the threshold of the evaluation function, it can quickly adapt to different scenario requirements.

[0080] In this invention, the front surface curve parameters and the rear surface chamfer angle are transmitted to optical simulation software. Using the aforementioned design method, the returned ray tracing results are used to optimize the parameters. This further reduces manual intervention, ensuring model accuracy and optimization reliability, and is particularly suitable for engineers lacking an optical background to quickly achieve their design goals.

[0081] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Therefore, any modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for designing a receiving lens for a reflective photoelectric sensor, characterized in that, The receiving lens has a front surface and a rear surface. The outline of the front surface of the receiving lens is a free curve formed by the smooth connection of multiple curve segments, and the outline of the rear surface of the receiving lens is a slope structure with a preset slope. The design method includes the following steps: S1. Design Initialization: Establish a simulated light source model by reversing the optical path, and define the parameters of the aperture and the simulated light source; Based on the principle of optical path reversibility, the target light spot on the aperture surface is assumed to be a simulated light source. The size of the target light spot on the aperture surface is determined according to the thickness of the receiving aperture, the aperture, the distance between the aperture and the receiving surface, and the distance between the lens vertex and the aperture. Determine the maximum emission angle of the simulated light source and divide it into N equal units. To obtain the unit emission angle; S2. Construct the front surface of the receiving lens: Iteratively generate a free curve based on Snell's law to ensure that the light rays emitted from the simulated light source are parallel to the optical axis after being refracted by the front surface of the receiving lens. Based on rotational symmetry, the three-dimensional optical path mapping is transformed into a two-dimensional plane mapping; According to Snell's law, the light vector emitted from the simulated light source is transformed into parallel light parallel to the optical axis after passing through the designed refractive surface: starting from the center of the receiving lens, according to... The free curve of the front surface of the receiving lens is constructed by step-size iteration. According to Snell's law, the normal vector of each refractive surface and the corresponding tangent are calculated. The free curve is formed by connecting the intersections of all tangents and the outgoing light rays. Rotate the free curve described above around the center of the receiving lens to obtain a free surface, which is the front surface of the receiving lens. S3. Construct the rear surface of the receiving lens: Calculate the height of the rear surface using a slanted geometric model to ensure that it meets the separation conditions for effective light and stray light. The steps for establishing the back surface slope function of the receiving lens include: A bevel angle is set on a cylindrical base of equal radius. The relationship between this angle and the aperture and the axial thickness of the lens is determined by geometric optics analysis. This ensures that the horizontal shift of the parallel incident stray light after refraction by the bevel surface results in a position on the aperture that is more than half the aperture diameter away from the center of the aperture. Similarly, the position of the stray light with an incident angle greater than a preset threshold after refraction results in a position on the aperture that is more than half the aperture diameter away from the center of the aperture. The setting of the oblique angle must satisfy the following: after the target light rays parallel to the optical axis are refracted and laterally deflected, the position on the aperture is less than half the aperture diameter of the aperture. After the stray light with an incident angle greater than the preset threshold is refracted, the position on the aperture is more than half the aperture diameter of the aperture. S4. Simulation Optimization: Perform data analysis and recalculate the evaluation function value based on the results of the light simulation. If both the evaluation function value and the effective light transmittance meet the preset threshold, the designed receiving lens is obtained.

2. The design method for the receiving lens of the reflective photoelectric sensor according to claim 1, characterized in that, Based on Snell's law, an offset equation is established. The oblique angle is iterated and combined with parameters such as the material refractive index and lens axial thickness to calculate the vector of the outgoing ray after two refractions. The distance between the intersection point of the outgoing ray on the aperture surface and the center point of the aperture is then determined.

3. The design method for the receiving lens of the reflective photoelectric sensor according to claim 2, characterized in that, Calculate 0 < < th The incident ray vector becomes the unit vector of the outgoing ray after two refractions, where... th is the stray light filtering threshold angle; According to the vector form of Snell's law, given the incident unit vector, the unit normal vector of the refracting surface, and the refraction of the medium, the formulas for calculating the outgoing unit vector include: The unit vector of the interface normal is represented as... The incident unit vector is The outgoing unit vector is The refractive indices of the incident and exit media are respectively and .

4. The design method for the receiving lens of the reflective photoelectric sensor according to claim 2, characterized in that, In step S4, the optimization objective function is set: ； When F=0, the design is deemed to meet the standard, and the output parameter is D, which is the aperture diameter.

5. The design method for the receiving lens of the reflective photoelectric sensor according to claim 4, characterized in that, In step S4, after the above-mentioned optimization objective function F meets the requirements through numerical calculation, the parameters of the new contour curve are transmitted to the optical simulation software. The front surface contour line of the receiving lens is obtained by rotating symmetry about the y-axis, and the rear surface is obtained by diagonally cutting a cylinder with a bottom surface of R and a height of Δh. The model is created in the optical simulation software and ray tracing is performed. Then, the simulation results are transmitted to the data analysis software for data analysis through DDE technology. Based on the results of the ray simulation, the evaluation function value is calculated again to determine whether the designed receiving lens meets the requirements.

6. The design method for the receiving lens of the reflective photoelectric sensor according to claim 5, characterized in that, Set the effective light transmittance: ； Where E pass To ensure the effective luminous flux passing through the aperture during ray tracing simulation, E total This is to simulate the total emitted luminous flux of the light source.

Images