An economic tolerance analysis method, device and equipment of an optical system and a storage medium

Abstract

The economic tolerance analysis method, device, equipment and storage medium of the optical system provided by the embodiment of the application first determine the parameter tolerance of the structure to be analyzed, then determine the distortion function based on the parameter tolerance and use the Taylor formula to determine the change of the distortion when the parameter tolerance changes; then determine the sensitivity coefficient based on the object side of the optical system to solve the sensitivity coefficient in the Taylor formula expansion, so as to determine the parameters that have a great influence on the distortion according to the size of the sensitivity coefficient; finally, determine the best economic tolerance according to the tolerance cost function corresponding to each parameter tolerance, the sensitivity coefficient and the distortion function determined according to the preset processing parameter information, so as to solve the distortion expression and the tolerance cost function determined in the above steps, and determine the size of the parameter tolerance, so that the tolerance value can meet the distortion requirement and the processing cost is the lowest, and the purpose of balancing the economic tolerance is achieved.

Description

[Technical Field]

[0001] This invention relates to the field of optical design technology, and more specifically to an economic tolerance analysis method for optical systems. [Background Technology]

[0002] Currently, optical system design often requires tolerance analysis, primarily focusing on the impact of tolerances on image quality. However, for mass-produced lenses, such as automotive lenses and mobile phone lenses, the cost factor of tolerances also needs to be considered. The relationship between tolerance size and tolerance cost is often non-linear; as tolerance increases, tolerance cost decreases significantly, but image quality deteriorates at the same time. Therefore, the tolerance must not only meet image quality requirements but also ensure the lowest possible cost. This type of tolerance is called economic tolerance, but currently, there is no precise and rigorous method for balancing economic tolerances in optical design systems. [Summary of the Invention]

[0003] In view of this, the present invention provides an economic tolerance analysis method, apparatus, device and storage medium for optical systems. By solving the tolerance value by simultaneously solving the distortion expression and the tolerance cost function, the distortion requirements can be met while the processing cost can be minimized, thus providing a solution for the economic tolerance trade-off.

[0004] In a first aspect, embodiments of the present invention provide a method for economic tolerance analysis of an optical system, comprising:

[0005] Determine the parametric tolerances of the structure to be analyzed, wherein the parametric tolerances include radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance;

[0006] The distortion function is determined using Taylor's formula based on the aforementioned radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance.

[0007] The sensitivity coefficient is determined based on the object plane using an optical system;

[0008] Based on the pre-defined processing parameter information corresponding to the radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance, determine the tolerance cost function corresponding to each of the radius tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance;

[0009] The economic tolerances corresponding to the radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance are determined based on the sensitivity coefficient, tolerance cost function, and distortion function.

[0010] Optionally, the step of determining the distortion function using Taylor's formula based on the radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance includes:

[0011] The relationship between five structural parameters—radius of curvature, thickness, refractive index, eccentricity, and tilt—and distortion is defined as δy'=δy'(t1,t2,...t). n Expand according to Taylor's formula, omitting third-order terms and terms of higher order:

[0012]

[0013] Where δy' represents distortion, y' z t represents the height of the principal ray at the image plane, and t represents the ideal image height. i ,t j The standard structural parameters include: radius of curvature, thickness, refractive index, eccentricity, tilt, and Δt. i ,Δt j They represent the structural parameter t respectively. i ,t j The size of the tolerance, These represent the first-order sensitivity coefficient and the second-order sensitivity coefficient, respectively.

[0014] Optionally, the step of determining the sensitivity coefficient based on the object space using an optical system includes:

[0015] In an optical system, the intersection points and propagation directions of the principal ray with each lens are traced. Based on the intersection point coordinates and propagation direction of the ray on the previous lens, the intersection point coordinates and propagation direction of the ray on the next lens are obtained by tracing the ray until the image plane is reached.

[0016] The sensitivity coefficient is calculated based on the coordinates and direction obtained from tracking the principal ray.

[0017] Optionally, in an optical system, the steps of tracing the intersection points and propagation directions of the principal ray with each lens include:

[0018] Based on the known coordinates P of the intersection point between the ray and the previous lens i (x i ,y i ,z i The direction of light propagation is

[0019] Using the standard spherical equation, the vector expression of the law of refraction, and related vector geometric relationships, the coordinates P of the intersection point of the light rays on the next lens are obtained. i+1 (x i+1 ,y i+1 ,z i+1 ), and the direction of the light's subsequent propagation. Where (x, y, z) represent the coordinates when a coordinate system is established with the lens sphere as the vertex, and (α, β, γ) represent the three direction cosines. The equation of the sphere is expressed as follows:

[0020] x 2 +y 2 +z 2 -2rx=0

[0021] Where r represents the radius of the sphere, the vector expression of the law of refraction is as follows:

[0022]

[0023] n and n' represent the object-side refractive index and the image-side refractive index, respectively; It represents the normal direction vector, which is a unit vector.

[0024] Optionally, the step of calculating the sensitivity coefficient based on the coordinates and direction obtained from tracking the principal ray includes:

[0025] Obtain the principal ray coordinates, propagation direction vector, and principal ray tracing equations;

[0026] By differentiating the relevant structural parameters, the sensitivity coefficients between adjacent surfaces are obtained. The system of equations includes coordinates y, z and directions β, γ, and is expressed as follows:

[0027]

[0028] Where y i ,z i ,β i ,γ i It is a composite function; y i-1 ,z i-1 ,β i-1 ,γ i-1 ,y i ,z i For relevant intermediate variables; t i The five structural parameters—radius of curvature, thickness, refractive index, tilt, and eccentricity—are represented as independent variables.

[0029] By combining the law of refraction and the equations of eccentric and tilted spherical coordinates, the structural parameters are differentiated.

[0030] The coordinate equation of the eccentric and tilted sphere in the XOY plane is expressed as follows:

[0031] (x-rcos(θ)) 2 +(y-rsin(θ)-p) 2 +z 2 =r 2

[0032] Where θ represents the tilt in the XOY plane, p represents the eccentricity in the y direction, and the structural parameter t i Find the first derivative to obtain the matrix:

[0033]

[0034] The matrix is ​​defined as follows:

[0035]

[0036] Furthermore, it can be expressed as follows:

[0037]

[0038]

[0039] The expression for the first derivative of the coordinate y is as follows:

[0040]

[0041] Obtain the first-order sensitivity coefficient between two adjacent surfaces. For structural parameter t j Find the second-order partial derivative, expressed as follows:

[0042]

[0043] Where t i =t j ,t i ≠t j Both are acceptable, and when the structural parameter t i ,t j When both participate in the propagation of light between adjacent surfaces i-1 and i, there exists a coefficient.

[0044] in It can be expressed as the following formula:

[0045]

[0046]

[0047]

[0048]

[0049] Where, when the structural parameter t j When light propagates between adjacent surfaces i-1 and i, there exists a coefficient.

[0050] Obtain the cross sensitivity coefficient between two adjacent surfaces. Iterative propagation continues until the image plane m is reached. At this point, the first-order sensitivity coefficients of the five structural parameters (radius of curvature, thickness, refractive index, tilt, and eccentricity) to distortion are obtained. Right now First-order sensitivity coefficient Expressed as follows:

[0051]

[0052] Similarly, the sensitivity coefficient is obtained by iterating sequentially. and the correlation coefficient between the image plane and the final mirror of the optical system. Second-order sensitivity coefficients were obtained

[0053] Second-order sensitivity coefficient Expressed as follows:

[0054]

[0055] in It can be expressed as the following formula:

[0056]

[0057]

[0058]

[0059]

[0060] Optionally, the step of determining the tolerance cost function corresponding to each of the radius tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance based on the preset processing parameter information for each of these tolerances includes:

[0061] The tolerance cost function ω is set based on the preset tolerances for radius of curvature, thickness, refractive index, eccentricity, and tilt. i (Δt i ), where Δt i The tolerance cost function expression is as follows: This represents any one of the following: radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance.

[0062] ω i (Δt i )=k i (Δt i )v i (Δt i )

[0063] Where ki (Δt i ) represents the tolerance Δt i Cost weight; v i (Δt i ) represents the tolerance Δt i Processing parameter information.

[0064] Optionally, the formula for determining the economic tolerances corresponding to the radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance based on the sensitivity coefficient, tolerance cost function, and distortion function is as follows:

[0065]

[0066] Where M represents the system's distortion range after tolerance analysis; E can represent the cost budget in the tolerance processing parameter information or the minimum sum of all tolerance cost functions under the premise that the tolerance meets the distortion range requirements.

[0067] Solving the system of equations yields the economic tolerances corresponding to the radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance.

[0068] Secondly, embodiments of the present invention also provide an economic tolerance analysis device for an optical system, comprising:

[0069] The first determining module is used to determine the parameter tolerances of the structure to be analyzed, wherein the parameter tolerances include radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance;

[0070] The second determining module is used to determine the distortion function based on the radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance using the Taylor formula;

[0071] The third determination module is used to determine the sensitivity coefficient based on the object space using the optical system;

[0072] The fourth determining module is used to determine the tolerance cost function corresponding to each of the radius tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance and tilt tolerance based on the preset processing parameter information corresponding to each of the radius tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance and tilt tolerance.

[0073] The fifth determining module is used to determine the economic tolerances corresponding to the radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance based on the sensitivity coefficient, tolerance cost function, and distortion function.

[0074] Thirdly, embodiments of the present invention also provide an economic tolerance analysis device for an optical system, including a memory and a processor. The memory is used to store information including program instructions, and the processor is used to control the execution of the program instructions. When the program instructions are loaded and executed by the processor, the economic tolerance analysis method for the optical system described in any one of the first aspects is implemented.

[0075] Fourthly, embodiments of the present invention also provide a storage medium, the storage medium including a stored program, wherein, when the program is executed, the device where the storage medium is located is controlled to perform the economic tolerance analysis method of the optical system according to any one of the first aspects.

[0076] In the technical solution provided by this invention embodiment, the parameter tolerances of the structure to be analyzed are first determined. These parameter tolerances include radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance. Then, based on the radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance, the Taylor formula is used to determine the distortion function, thereby determining how the distortion changes when the above five structural parameter tolerances change. Next, the sensitivity coefficient is determined based on the object side using an optical system, and the sensitivity coefficient in the Taylor formula expansion is solved to determine the parameters that have a significant impact on distortion based on the magnitude of the sensitivity coefficient. Finally, according to... The pre-defined processing parameters for radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance are used to determine the tolerance cost function, sensitivity coefficient, and distortion function for each tolerance. This determines the optimal economic tolerance. The distortion expression and tolerance cost function determined in the above steps are then solved simultaneously to find the magnitude of the tolerances for the five structural parameters: radius of curvature, thickness, refractive index, eccentricity, and tilt. These tolerance values ​​ensure that the distortion requirements are met while minimizing processing costs, thus achieving a balance between economic tolerances and tolerances. [Attached Image Description]

[0077] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0078] Figure 1 This is a flowchart of an economic tolerance analysis method for an optical system provided by an embodiment of the present invention;

[0079] Figure 2 This is a distortion diagram provided for an embodiment of the present invention;

[0080] Figure 3A flowchart of step S103 is provided for an embodiment of the present invention;

[0081] Figure 4 This is a schematic diagram of relevant quantities when light passes through a single refracting spherical surface, provided in an embodiment of the present invention.

[0082] Figure 5 This is a schematic diagram illustrating the calculation of the second paraxial ray and the principal ray provided in an embodiment of the present invention;

[0083] Figure 6 This is a schematic diagram of ray tracing provided for an embodiment of the present invention.

[0084] Figure 7 This is a schematic diagram of the eccentricity and tilt of a spherical mirror provided in an embodiment of the present invention.

[0085] Figure 8 This is a schematic diagram of an economic tolerance analysis device for an optical system provided in an embodiment of the present invention.

[0086] Figure 9 This is a schematic diagram of an economic tolerance analysis device for an optical system provided in an embodiment of the present invention.

Detailed Implementation Methods

[0087] To better understand the technical solution of the present invention, the embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0088] It should be understood that 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.

[0089] The terminology used in the embodiments of this invention is for the purpose of describing particular embodiments only and is not intended to limit the invention. The singular forms “a,” “the,” and “the” as used in the embodiments of this invention and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise.

[0090] It should be understood that the term "and / or" used in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.

[0091] Currently, optical system design often requires tolerance analysis, primarily focusing on the impact of tolerances on image quality. However, for mass-produced lenses, such as automotive lenses and mobile phone lenses, the cost factor of tolerances also needs to be considered. The relationship between tolerance size and tolerance cost is often non-linear; as tolerance increases, tolerance cost decreases significantly, but image quality deteriorates at the same time. Therefore, the tolerance must not only meet image quality requirements but also ensure the lowest possible cost; this type of tolerance is called economic tolerance.

[0092] However, current optical design software lacks economic tolerance analysis capabilities. Distortion, caused by spherical aberration, occurs when the principal ray, passing through the optical system, is positioned at a height on the image plane that differs from the ideal image height. Distortion reflects the degree of distortion in the image formed by the optical system relative to the object itself. Generally, distortion increases with the object-side field of view. Therefore, distortion correction is necessary in the design of wide-angle lenses, visual lenses, and camera lenses, while the requirements for distortion correction are even more stringent for some industrial inspection lenses.

[0093] In summary, the embodiments of the present invention provide an economic tolerance analysis method, apparatus, device, and storage medium for an optical system. By solving the tolerance value by simultaneously solving the distortion expression and the tolerance cost function, the distortion requirements can be met while minimizing the processing cost, thus providing a solution for the economic tolerance trade-off.

[0094] like Figure 1 As shown, this embodiment of the invention first provides a method for economic tolerance analysis of an optical system, including:

[0095] Step S101: Determine the parameter tolerances of the structure to be analyzed, wherein the parameter tolerances include radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance;

[0096] Currently, an economic tolerance determination method using MTF as an image quality evaluation standard has been proposed in existing technologies. However, this method cannot analyze distortion, and its analysis of the impact of tolerance on image quality is not precise enough. Furthermore, the structural parameter types analyzed in this paper do not include eccentricity and tilt, but only three structural parameters: radius of curvature, thickness, and refractive index. Therefore, in practical applications, parameter tolerances including radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance, which are combined with the above five structural parameters, can improve the accuracy of economic tolerances.

[0097] Step S102: Based on the curvature radius tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance, the distortion function is determined using the Taylor formula;

[0098] In this step, Taylor's formula is used to represent distortion, which can clearly show how the distortion changes when the tolerances of the five structural parameters—radius of curvature, thickness, refractive index, eccentricity, and tilt—change. The expression includes the above five variables, which facilitates subsequent solutions.

[0099] Further, step S102, the step of determining the distortion function using Taylor's formula based on the curvature radius tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance, includes:

[0100] like Figure 2 As shown, the relationship between five structural parameters—radius of curvature, thickness, refractive index, eccentricity, and tilt—and distortion is δy'=δy'(t1,t2,...t n Expand according to Taylor's formula, omitting third-order terms and terms of higher order:

[0101]

[0102] Where δy' represents distortion, y' z t represents the height of the principal ray at the image plane, and t represents the ideal image height. i ,t j The standard structural parameters include: radius of curvature, thickness, refractive index, eccentricity, tilt, and Δt. i ,Δt j They represent the structural parameter t respectively. i ,t j The size of the tolerance, These represent the first-order sensitivity coefficient and the second-order sensitivity coefficient, respectively.

[0103] It can be observed that the distortion expression involves two constant terms: the height of the principal ray at the image plane and the ideal image height. Therefore, for a certain field of view in the object side, it is necessary to calculate the ideal image height of the object side after passing through the optical system and the height of the principal ray at the image plane after passing through the optical system. Furthermore, the principal ray needs to be traced to determine the coordinates of its intersection with each surface and its propagation direction vector. This provides the necessary data for calculating the tolerance sensitivity coefficient in subsequent steps. Based on this, in step S103, the sensitivity coefficient is determined based on the object side using the optical system, such as... Figure 3 As shown, it includes:

[0104] Step S1031: In the optical system, the intersection point and propagation direction of the main ray with each lens are traced. Based on the intersection point coordinates and propagation direction of the ray on the previous lens, the ray is traced to obtain the intersection point coordinates and propagation direction of the ray on the next lens, until the image plane is reached.

[0105] Step S1032: Calculate the sensitivity coefficient based on the coordinates and direction obtained from tracking the main ray.

[0106] Specifically, this embodiment of the invention provides a practical use case:

[0107] Calculate the second paraxial ray path using the paraxial ray path calculation formula to obtain the ideal image height. Figure 4 , Figure 5 The parameters are: object aperture angle u, image aperture angle u', incident angle i, refraction angle i', object distance l, image distance l', and distance l from the entrance pupil to the first surface. z Principal ray object aperture angle u z The distance from the exit pupil to the last surface of the optical system is l' z The principal ray image aperture angle u' z The relationship formula is as follows:

[0108]

[0109] Where n is the object-side refractive index, n' is the image-side refractive index, and r is the radius of the spherical lens.

[0110] Similarly, based on the actual ray path calculation formula, the principal ray path is calculated to obtain the principal ray's height on the image plane. Figure 4 , Figure 5 The parameters are: object aperture angle U, image aperture angle U', incident angle I, refraction angle I', object distance L, image distance L', and distance L from the entrance pupil to the first surface. Z Principal ray object aperture angle U Z The distance L' from the exit pupil to the last surface of the optical system Z The principal ray image aperture angle U' Z The relationship is as follows:

[0111]

[0112] According to the ray tracing diagram in Figure 6, trace the principal ray, and find the intersection points and propagation directions of the ray with each lens. First, the coordinates P of the intersection point of the ray with the previous lens are known. i (x i ,y i ,z i The direction of light propagation is Using the standard spherical equation, the vector expression of the law of refraction, and related vector geometric relationships, the coordinates P of the intersection point of the light rays on the next lens are obtained. i+1 (x i+1 ,y i+1 ,z i+1 ), and the direction of the light's subsequent propagation.

[0113] Where (x,y,z) represents the coordinates when a coordinate system is established with the lens sphere as the vertex, and (α,β,γ) represents the three direction cosines.

[0114] The equation for the sphere is expressed as follows:

[0115] x 2 +y 2 +z 2 -2rx=0

[0116] Where r represents the radius of the sphere.

[0117] The vector expression for the law of refraction is as follows:

[0118]

[0119] n and n' represent the object-side refractive index and the image-side refractive index, respectively; It represents the normal direction vector, which is a unit vector.

[0120] In this embodiment of the invention, based on the ray tracing results of the principal ray, the coordinates and propagation direction vector of the principal ray are obtained. Simultaneously, the principal ray tracing equations are obtained, and the sensitivity coefficients between adjacent surfaces are obtained by differentiating the relevant structural parameters. The structural parameters include: radius of curvature, thickness, refractive index, tilt, and eccentricity. The equations only require coordinates y, z and directions β, γ, and can be expressed as follows:

[0121]

[0122] Where y i ,z i ,β i ,γ i It is a composite function; y i-1 ,z i-1 ,β i-1 ,γ i-1 ,y i ,z i For relevant intermediate variables; t i The five structural parameters—radius of curvature, thickness, refractive index, tilt, and eccentricity—are represented as independent variables.

[0123] The structural parameters are differentiated by combining the law of refraction and the equations of eccentric and tilted spherical coordinates.

[0124] The spherical surface with eccentricity and tilt within the XOY plane, such as... Figure 7 As shown, its coordinate equation is expressed as follows:

[0125] (x-rcos(θ)) 2 +(y-rsin(θ)-p) 2 +z 2 =r 2

[0126] Where θ represents the inclination in the XOY plane, and p represents the eccentricity in the y direction.

[0127] Furthermore, regarding the structural parameter t i Find the first derivative to obtain the matrix:

[0128]

[0129] The matrix is ​​defined as follows:

[0130]

[0131] Furthermore, it can be expressed as follows:

[0132]

[0133]

[0134] The expression for the first derivative of the coordinate y is as follows:

[0135]

[0136] Furthermore, the first-order sensitivity coefficients between two adjacent surfaces are obtained. It includes five structural parameter types: radius of curvature, thickness, refractive index, tilt, and eccentricity;

[0137] Furthermore, regarding the structural parameter t j Find the second-order partial derivatives for five structural parameter types: radius of curvature, thickness, refractive index, tilt, and eccentricity. The expression is as follows:

[0138]

[0139] Where t i =t j ,t i ≠t j Both are acceptable, and when the structural parameter t i ,t j When both participate in the propagation of light between adjacent surfaces i-1 and i, there exists a coefficient. Otherwise, all four coefficients mentioned above are 0.

[0140] in It can be expressed as the following formula:

[0141]

[0142]

[0143]

[0144]

[0145] Where, when the structural parameter t j When light propagates between adjacent surfaces i-1 and i, there exists a coefficient. Otherwise, all four coefficients mentioned above are 0.

[0146] Furthermore, the cross sensitivity coefficient between two adjacent surfaces is obtained. It includes cross terms of five structural parameter types: radius of curvature, thickness, refractive index, tilt, and eccentricity.

[0147] Furthermore, the iteration continues until the image plane m is reached. At this point, the first-order sensitivity coefficients of the five structural parameters (radius of curvature, thickness, refractive index, tilt, and eccentricity) to distortion are obtained. Right now First-order sensitivity coefficient Expressed as follows:

[0148]

[0149] Similarly, the sensitivity coefficient is obtained by iterating sequentially. and the correlation coefficient between the image plane and the final mirror of the optical system. This allows us to obtain the second-order sensitivity coefficients of the five structural parameters—radius of curvature, thickness, refractive index, tilt, and eccentricity—to distortion.

[0150] Furthermore, the second-order sensitivity coefficient Expressed as follows:

[0151]

[0152] in It can be expressed as the following formula:

[0153]

[0154]

[0155]

[0156]

[0157] In this embodiment of the invention, the sensitivity coefficient takes into account the combined effect of different tolerances on distortion, so the cross term is not ignored. At the same time, when calculating the sensitivity coefficient, it is not necessary to track too many rays. For different fields of view, different principal rays are tracked, and the data such as the intersection coordinates of each surface and the propagation vector obtained by tracking the principal rays are used to solve the problem. Specifically, the distortion expression with five tolerance types as variables, namely radius of curvature, thickness, refractive index, eccentricity, and tilt, can be determined. Based on the magnitude of the sensitivity coefficient, it can also be determined which parameter tolerance has a greater impact on distortion, which facilitates the adjustment of the tolerance.

[0158] Step S104: Determine the tolerance cost function corresponding to each of the radius tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance based on the preset processing parameter information.

[0159] In this embodiment of the invention, the processing parameter information refers to the processing information provided by the optical processing factory regarding the tolerances of five structural parameters: radius of curvature, thickness, refractive index, eccentricity, and tilt. Specifically, the processing information may refer to processing cost information. Furthermore, it should be noted that the processing information provided by the optical processing factory for the tolerances of these five structural parameters includes the processing cost and upper and lower limits of the tolerances. Using this raw data, the factory's tolerance processing situation can be understood, allowing for the establishment of a tolerance cost function in subsequent steps. The more detailed and accurate the data provided, the more reliable the established tolerance cost function will be.

[0160] In this step, for the structural parameters to be subjected to tolerance analysis, including the tolerances of five structural parameters—radius of curvature, thickness, refractive index, eccentricity, and tilt—the upper and lower limits of processing and processing costs are determined through the optical processing factory. Furthermore, based on the tolerance information provided in this step, a tolerance cost function ω is set for the tolerances of the five structural parameters: radius of curvature, thickness, refractive index, eccentricity, and tilt. i (Δt i This leads to the determination of the tolerance cost function ω, which reflects the relationship between processing costs and tolerance size. i (Δt i ).

[0161] Specifically, step S104, which involves determining the tolerance cost function corresponding to each of the radius tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance based on the preset processing parameter information, includes:

[0162] The tolerance cost function ω is set based on the preset tolerances for radius of curvature, thickness, refractive index, eccentricity, and tilt. i (Δti ), where Δt i The tolerance cost function expression is as follows: This represents any one of the following: radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance.

[0163] ω i (Δt i )=k i (Δt i )v i (Δt i )

[0164] Where k i (Δt i ) represents the tolerance Δt i Cost weight; v i (Δt i ) represents the tolerance Δt i The processing parameter information, specifically the processing capacity, is used in this step, where the tolerance cost function ω... i (Δt i The composition can be divided into two parts: one part reflects the tolerance cost of five structural parameters, namely radius of curvature, thickness, refractive index, eccentricity, and tilt; the other part combines the processing capability of the above five structural parameters, namely the upper and lower limits of tolerance.

[0165] Step S105: Determine the economic tolerances corresponding to the radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance based on the sensitivity coefficient, tolerance cost function, and distortion function.

[0166] In this embodiment of the invention, by combining the sensitivity coefficients of five structural parameter tolerances (radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance) to distortion, as well as the cost function of the tolerance, and solving the distortion function together, the tolerance can be constrained from both the aspects of image quality and cost.

[0167] Specifically, in step S105, the economic tolerances corresponding to the radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance are determined based on the sensitivity coefficient, tolerance cost function, and distortion function. The formula for this step is as follows:

[0168]

[0169] Where M represents the system's distortion range after tolerance analysis; E can represent the cost budget in the tolerance processing parameter information or the minimum sum of all tolerance cost functions under the premise that the tolerance meets the distortion range requirements.

[0170] Solve the system of equations to obtain the economic tolerances corresponding to the radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance. Solve the distortion expression and tolerance cost function determined in the above steps to find the magnitude of the tolerances of the five structural parameters: radius of curvature, thickness, refractive index, eccentricity, and tilt. Finally, these tolerance values ​​can ensure that the distortion requirements are met while minimizing the processing cost.

[0171] In summary, the economic tolerance analysis method provided by this invention, which uses distortion as an image quality evaluation standard, calculates the sensitivity coefficient by tracing the principal ray and then determines the economic tolerance by combining it with the tolerance cost function. Applying this method to tolerance analysis on mass-produced lenses not only satisfies distortion requirements but also effectively reduces processing costs. Furthermore, the sensitivity coefficient takes into account the combined effects of different tolerances on distortion, thus not ignoring cross-terms. Simultaneously, calculating the sensitivity coefficient does not require tracing too many rays; different principal rays are traced for different fields of view. Finally, the tolerance cost function can be designed and allocated according to the different processing capabilities of different factories and at different times, offering strong flexibility.

[0172] In another embodiment of the present invention, an economic tolerance analysis device for an optical system is also provided, such as... Figure 8 As shown, it includes:

[0173] The first determining module 01 is used to determine the parameter tolerances of the structure to be analyzed, wherein the parameter tolerances include radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance;

[0174] The second determining module 02 is used to determine the distortion function based on the radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance using the Taylor formula;

[0175] The third determining module 03 is used to determine the sensitivity coefficient based on the object using the optical system;

[0176] The fourth determining module 04 is used to determine the tolerance cost function corresponding to each of the radius tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance and tilt tolerance based on the preset processing parameter information corresponding to each of the radius tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance and tilt tolerance.

[0177] The fifth determining module 05 is used to determine the economic tolerances corresponding to the radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance based on the sensitivity coefficient, tolerance cost function, and distortion function.

[0178] This invention first determines the parameter tolerances of the structure to be analyzed, including radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance. Then, based on these tolerances, a Taylor series is used to determine the distortion function, thus determining how the distortion changes when the five structural parameter tolerances change. Next, an optical system is used to determine the sensitivity coefficient based on the object side, solving for the sensitivity coefficient in the Taylor series expansion. The magnitude of this sensitivity coefficient is used to identify parameters that have a significant impact on distortion. Finally, based on preset tolerances for radius of curvature, thickness, refractive index, and eccentricity tolerances, the distortion function is determined. The processing parameter information corresponding to the radius tolerance, eccentricity tolerance, and tilt tolerance is used to determine the tolerance cost function, sensitivity coefficient, and distortion function corresponding to the radius tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance, respectively. The optimal economic tolerance is then determined by simultaneously solving the distortion expression and tolerance cost function determined in the above steps to find the magnitude of the tolerances for the five structural parameters: radius of curvature, thickness, refractive index, eccentricity, and tilt. These tolerance values ​​can ensure that the distortion requirements are met while minimizing the processing cost, thus achieving the goal of balancing economic tolerances. The specific implementation process can be referred to the above embodiment, and will not be repeated here.

[0179] This invention provides a storage medium that includes a stored program. When the program runs, it controls the device where the storage medium is located to execute the steps of the above-described information sharing method. For a detailed description, please refer to the embodiments of the above-described information sharing method.

[0180] This invention provides an economic tolerance analysis device for an optical system, including a memory and a processor. The memory stores information including program instructions, and the processor controls the execution of the program instructions. When the program instructions are loaded and executed by the processor, they implement the steps of the information sharing method described above. For a detailed description, please refer to the embodiments of the information sharing method described above.

[0181] Figure 9 This is a schematic diagram of an economic tolerance analysis device for an optical system provided in an embodiment of the present invention. Figure 6 As shown, the information sharing device 6 in this embodiment includes a processor 61, a memory 62, and a computer program 63 stored in the memory 62 and executable on the processor 61. When the processor 61 executes the computer program 63, it implements the information sharing method described in the embodiment; to avoid repetition, these details are not elaborated here. Alternatively, when the processor 61 executes the computer program, it implements the functions of each model / unit in the information sharing device described in the embodiment; to avoid repetition, these details are not elaborated here.

[0182] The information sharing device 6 includes, but is not limited to, a processor 61 and a memory 62. Those skilled in the art will understand that... Figure 6 This is merely an example of information sharing device 6 and does not constitute a limitation on information sharing device 6. It may include more or fewer components than shown, or combine certain components, or different components. For example, information sharing device 6 may also include input / output devices, network access devices, buses, etc.

[0183] The processor 61 may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0184] The memory 62 can be an internal storage unit of the information sharing device 6, such as a hard disk or RAM of the information sharing device 6. The memory 62 can also be an external storage device of the information sharing device 6, such as a plug-in hard disk, Smart Media Card (SMC), Secure Digital (SD) card, or Flash Card equipped on the information sharing device 6. Furthermore, the memory 62 can include both internal storage units and external storage devices of the information sharing device 6. The memory 62 is used to store computer programs and other programs and data required by the information sharing device 6. The memory 62 can also be used to temporarily store data that has been output or will be output.

[0185] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0186] In the embodiments provided by this invention, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces, indirect coupling or communication connection between apparatuses or units, and may be electrical, mechanical, or other forms.

[0187] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0188] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or in the form of hardware plus software functional units.

[0189] The integrated units implemented as software functional units described above can be stored in a computer-readable storage medium. These software functional units, stored in a storage medium, include several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute some steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0190] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for analyzing the economic tolerances of an optical system, characterized in that, include: Determine the parametric tolerances of the structure to be analyzed, wherein the parametric tolerances include radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance; The distortion function is determined using Taylor's formula based on the aforementioned radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance. The sensitivity coefficient is determined based on the object plane using an optical system; Based on the pre-defined processing parameter information corresponding to the radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance, determine the tolerance cost function corresponding to each of the following: The economic tolerances corresponding to the radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance are determined based on the sensitivity coefficient, tolerance cost function, and distortion function.

2. The method for economic tolerance analysis of an optical system according to claim 1, characterized in that, The steps for determining the distortion function using Taylor's formula based on the aforementioned radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance include: The relationship between five structural parameters—radius of curvature, thickness, refractive index, eccentricity, tilt, and distortion—is investigated. Expanding according to Taylor's formula, and neglecting third-order terms and terms of higher order: ； in Indicates distortion. This indicates the height of the principal ray at the image plane, and represents the ideal image height. The standard structural parameters include: radius of curvature, thickness, refractive index, eccentricity, and tilt. Representing structural parameters respectively The size of the tolerance, ; represent the first-order sensitivity coefficient and the second-order sensitivity coefficient, respectively.

3. The method for economic tolerance analysis of an optical system according to claim 1, characterized in that, The steps for determining the sensitivity coefficient based on the object side using an optical system include: In an optical system, the intersection points and propagation directions of the principal ray with each lens are traced. Based on the intersection point coordinates and propagation direction of the ray on the previous lens, the intersection point coordinates and propagation direction of the ray on the next lens are obtained by tracing the ray until the image plane is reached. The sensitivity coefficient is calculated based on the coordinates and direction obtained from tracking the principal ray.

4. The method for economic tolerance analysis of an optical system according to claim 3, characterized in that, In an optical system, the steps for tracing the intersections and propagation directions of the principal ray with each lens include: Based on the known coordinates of the intersection point between the ray and the previous lens The direction of light propagation is ; Using the standard equation of the sphere, the vector expression of the law of refraction, and related vector geometric relationships, the coordinates of the intersection point of the light rays on the next lens are obtained. And the direction of light propagation thereafter. ,in This represents the coordinates when a coordinate system is established with the lens sphere as the vertex. The equation of the sphere, representing the three direction cosines, is as follows: ； in Representing the radius of the sphere, the vector expression of the law of refraction is as follows: ； These represent the object-side refractive index and the image-side refractive index, respectively. It represents the normal direction vector, which is a unit vector.

5. The method for economic tolerance analysis of an optical system according to claim 4, characterized in that, The step of calculating the sensitivity coefficient based on the coordinates and direction obtained from tracking the principal ray includes: Obtain the principal ray coordinates, propagation direction vector, and principal ray tracing equations; Differentiating the relevant structural parameters yields the sensitivity coefficients between adjacent surfaces. The system of equations includes coordinates. and direction The expression is as follows: ； in It is a composite function; For relevant intermediate variables; The five structural parameters—radius of curvature, thickness, refractive index, tilt, and eccentricity—are represented as independent variables. By combining the law of refraction and the equations of eccentric and tilted spherical coordinates, the structural parameters are differentiated. Among them, The coordinate equation of a sphere with eccentricity and tilt is expressed as follows: ； in, Indicates in In-plane tilt, Indicates in Directional eccentricity affects structural parameters Find the first derivative to obtain the matrix: ； ； The matrix is ​​defined as follows: ； ； Furthermore, it can be expressed as follows: ； ； Regarding coordinates The first derivative is expressed as follows: ； ； Obtain the first-order sensitivity coefficient between two adjacent surfaces. For structural parameters Find the second-order partial derivative, expressed as follows: ； ； in Both are acceptable, and when the structural parameters All participate in adjacent faces and When light propagates between them, there exists a coefficient. ; in It can be expressed as the following formula: ； ； ； ； Among them, when structural parameters Participating adjacent faces and When light propagates between them, there exists a coefficient. ; Obtain the cross sensitivity coefficient between two adjacent surfaces. Iterative propagation until the image plane is reached. Up to this point, the first-order sensitivity coefficients of the five structural parameters (radius of curvature, thickness, refractive index, tilt, and eccentricity) to distortion are obtained. ,Right now First-order sensitivity coefficient Expressed as follows: ； ； Similarly, the sensitivity coefficient is obtained by iterating sequentially. and the correlation coefficient between the image plane and the final mirror of the optical system. The second-order sensitivity coefficients were obtained. ; Second-order sensitivity coefficient Expressed as follows: ； ； in It can be expressed as the following formula: ； ； ； 。 6. The method for economic tolerance analysis of an optical system according to claim 1, characterized in that, The steps for determining the tolerance cost functions corresponding to the respective curvature radius tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance based on the pre-defined machining parameter information include: Set the tolerance cost function based on the preset radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance. ,in, The tolerance cost function expression is as follows: This represents any one of the following: radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance. ； in Indicates tolerance Cost weighting; Indicates tolerance Processing parameter information.

7. The method for economic tolerance analysis of an optical system according to claim 1, characterized in that, The formulas for determining the economic tolerances corresponding to the radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance based on the sensitivity coefficient, tolerance cost function, and distortion function are as follows: ； in, This indicates the range of distortion that the system can withstand after tolerance analysis; It can represent the cost budget in the tolerance processing parameter information or the minimum value of the sum of all tolerance cost functions under the premise that the tolerance meets the distortion range requirements; Solving the system of equations yields the economic tolerances corresponding to the radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance.

8. An economic tolerance analysis device for an optical system, characterized in that, include: The first determining module is used to determine the parameter tolerances of the structure to be analyzed, wherein the parameter tolerances include radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance; The second determining module is used to determine the distortion function based on the radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance using the Taylor formula; The third determination module is used to determine the sensitivity coefficient based on the object space using the optical system; The fourth determining module is used to determine the tolerance cost function corresponding to each of the preset curvature radius tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance based on the corresponding processing parameter information. The fifth determining module is used to determine the economic tolerances corresponding to the radius of curvature tolerance, thickness tolerance, refractive index tolerance, eccentricity tolerance, and tilt tolerance based on the sensitivity coefficient, tolerance cost function, and distortion function.

9. An economic tolerance analysis device for an optical system, comprising a memory and a processor, wherein the memory is used to store information including program instructions, and the processor is used to control the execution of the program instructions, characterized in that: When the program instructions are loaded and executed by the processor, the economic tolerance analysis method for the optical system according to any one of claims 1 to 7 is implemented.

10. A storage medium comprising a stored program, characterized in that, When the program is running, it controls the device containing the storage medium to perform the economic tolerance analysis method for the optical system according to any one of claims 1 to 7.

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