Element manufacturing tolerance determination method based on light deviation allowance index

Abstract

The invention relates to the technical field of optical processing, in particular to an element manufacturing tolerance determination method based on a light deviation allowance index, which comprises the following steps of: adding a form error to an ideal optical element to obtain an actual form optical element; determining an incidence vector of light rays entering the ideal optical element or the optical element in the actual form; determining a light deviation allowance value, and determining an ideal emergent vector when the ideal optical element emits light and an actual form emergent vector when the actual form optical element emits light based on the incident vector; calculating an included angle between an ideal emergent vector and an actual emergent vector, and determining a constraint condition of the vector included angle by combining the determined light deviation allowance value; based on the constraint condition, a constraint formula of the form error is obtained, and the constraint formula is the manufacturing tolerance index. Ray optics is directly used for obtaining a one-hand conclusion, error transmission is avoided, and the method is used for errors of various scales and curved surfaces.

Description

Technical Field

[0001] The present invention belongs to the technical field of optical processing, and particularly relates to a method for determining the manufacturing tolerance of components based on the ray deviation tolerance index. Background Art

[0002] Nowadays, there are many models for the influence of manufacturing errors on the imaging of optical systems. If the errors are classified according to the spatial frequency of the errors, they can be divided into low-frequency errors, medium-frequency errors, and high-frequency errors. For low-frequency errors, the small aberration theory can be used to calculate their influence on the imaging of optical systems; for random high-frequency errors, the scattering theory can be used to calculate their influence on the imaging of optical systems; for periodic high-frequency errors, the diffraction theory can be used for processing; and for medium-frequency errors whose error scales are far from the wavelength and the element aperture and are not applicable to the above theoretical analysis, the analysis means are relatively limited, but there are still relevant studies. The paper "Use of pupil-difference moments for predicting optical performance impacts of generalized mid-spatial frequency surface errors" published in "Optics Express" proposes a PDPD method for estimating the MTF degradation range, and "Effects on the OTF of MSF structures with random variations" published in "Optics Express" gives a method for analyzing the OTF of turning manufacturing errors. These methods all establish a positive relationship between errors and image quality. If a large number of numerical statistics are made, it is expected to be able to perform reverse error tolerance constraints.

[0003] For many large-aperture optical components, the characteristic manufacturing errors generated by the manufacturing means such as small grinding heads, air bags, stress discs, and magnetorheological technologies are all in the millimeter range, and the above theories are not applicable. Therefore, a general formula for millimeter-scale error tolerance needs to be developed urgently. Summary of the Invention

[0004] In view of this, the present invention aims to provide a method for determining the manufacturing tolerance of components based on the ray deviation tolerance index, directly obtaining first-hand conclusions using ray optics without error transfer, and being applicable to errors and surfaces of various scales.

[0005] To achieve the above object, the technical solution of the present invention is realized as follows: A method for determining the manufacturing tolerance of components based on the ray deviation tolerance index, comprising: S1: Add form errors to the ideal optical element to obtain the actual form optical element; determine the incident vector of the light ray incident on the ideal optical element or the actual form optical element. S2: Determine the deviation of the light ray from the tolerance value, and based on the incident vector obtained in step S1, determine the ideal exit vector when the light ray exits the ideal optical element and the actual form exit vector when the light ray exits the actual form optical element. S3: Calculate the angle between the ideal exit vector and the actual form exit vector obtained in step S2, and determine the constraint condition of the vector angle in combination with the deviation tolerance value of the light ray determined in step S2. S4: Based on the constraint condition obtained in step S3, obtain the constraint formula of the form error, and the constraint formula is the manufacturing tolerance index.

[0006] Furthermore, the process of determining the ideal exit vector based on the incident vector in step S2 includes: Calculate the normalized surface normal of the ideal optical element. ; Wherein, represents the normalized surface normal of the ideal optical element, and g x represents the partial derivative of the surface equation of the ideal optical element with respect to x, and g y represents the partial derivative of the surface equation of the ideal optical element with respect to y. Based on the normalized surface normal of the ideal optical element, determine the ideal reflection action matrix through the following formula: ; Wherein, R represents the ideal reflection action matrix, I represents the identity matrix, represents the outer product of vectors; Based on the ideal reflection action matrix, determine the ideal exit vector through the following formula: ; Wherein, represents the ideal exit vector, represents the normalized incident vector.

[0007] Furthermore, the process of determining the actual form exit vector based on the incident vector in step S2 includes: Calculate the normalized surface normal of the actual form optical element through the following formula: ; Wherein, represents the normalized surface normal of the actual form optical element, and E x represents the partial derivative of the surface equation of the actual form optical element with respect to x, and E y represents the partial derivative of the surface equation of the actual form optical element with respect to y. Based on the normalized surface normal of the actual form optical element, the actual reflection action matrix is determined by the following formula: ; where M represents the actual reflection action matrix and I represents the identity matrix; Based on the actual reflection action matrix, the actual form outgoing vector is determined by the following formula: ; where, represents the actual form outgoing vector.

[0008] Furthermore, in step S3, the included angle is obtained by the following formula: ; The constraint condition is: cosθ(x,y)≥cosΔ(x,y); where θ(x,y) represents the included angle and Δ(x,y) represents the allowable deviation of the light ray deviation.

[0009] Furthermore, in step S4, the constraint condition is further: ; The constraint condition is solved to obtain the constraint range of the form error, and the constraint range is the constraint formula.

[0010] Compared with the prior art, the present invention can achieve the following beneficial effects: In the method for determining the component manufacturing tolerance based on the light ray deviation tolerance index described in the present invention, only relying on the form topography and its differential of the light ray deviation tolerance and the manufacturing error, the tolerance requirement of the manufacturing error for the light ray deviation requirement can be calculated. It has strong application prospects for the tolerance allocation of manufacturing errors in optical design. The method provided by the present invention uses ray optics more directly to obtain first-hand conclusions without error transmission, effectively improving the confirmation accuracy of the component manufacturing tolerance and expanding the applicable range of optical components. And the previous manufacturing tolerance was given by statistical indexes such as RMS, SlopeRMS, PSD, etc. The present invention provides a point-by-point tolerance calculation method. Relatively speaking, the constraint of manufacturing error is more compact. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] The drawings constituting a part of the present invention are used to provide a further understanding of the present invention. The schematic embodiments and descriptions thereof of the present invention are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings: Figure 1 is a schematic flow chart of the method for determining the component manufacturing tolerance based on the light ray deviation tolerance index described in the embodiment of the present invention. Detailed implementation manners

[0012] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not constitute a limitation to the present invention.

[0013] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.

[0014] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by the terms "center", "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. is based on the orientation or positional relationship shown in the accompanying drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation to the present invention. In addition, the terms "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the quantity of the indicated technical features. Thus, the features defined with "first", "second", etc. may explicitly or implicitly include one or more of such features. In the description of the present invention, unless otherwise specified, the meaning of "a plurality" is two or more.

[0015] In the description of the present invention, it should be noted that unless otherwise clearly defined and limited, the terms "installed", "connected", "connected" should be understood in a broad sense. For example, it may be a fixed connection, a detachable connection, or an integral connection; it may be a mechanical connection or an electrical connection; it may be directly connected, or indirectly connected through an intermediate medium, and it may be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood through specific situations.

[0016] The present invention will be described in detail below with reference to the accompanying drawings and in conjunction with embodiments.

[0017] As Figure 1 shown, the method for determining the manufacturing tolerance of an element based on the light deviation tolerance index described in the embodiment of the present invention includes: S1: Adding a form error to an ideal optical element to obtain an actual form optical element; determining the incident vector of the light incident on the ideal optical element or the actual form optical element.

[0018] The form error is determined according to the analysis scenario in the optical design software. Based on the form error, a corresponding error map is designed. For example, in the magnetorheological polishing element, medium-frequency errors will remain on its surface, and the error map is superimposed on the surface of the ideal optical element to obtain the actual form optical element. The side of the actual form optical element on which the manufacturing error map is superimposed is the error surface. The process of obtaining the actual form optical element can be automatically realized according to actual needs in the existing optical design software, and the present invention does not limit this. The incident vector is determined by the usage mode of the element. For example, if the manufacturing tolerance under different fields of view needs to be calculated, then the incident vector corresponding to each typical field of view is required.

[0019] S2: Determine the ray deviation tolerance value, and based on the incident vector obtained in step S1, determine the ideal exit vector when the ideal optical element emits light, and the actual form exit vector when the actual form optical element emits light.

[0020] The ray deviation tolerance value is given according to actual needs, and the present invention does not limit this. In some embodiments, the process of determining the ideal exit vector based on the incident vector includes: Calculate the normalized surface normal of the ideal optical element; ; Among them, represents the normalized surface normal of the ideal optical element, and g x represents the x partial derivative of the surface equation of the ideal optical element, and g y represents the y partial derivative of the surface equation of the ideal optical element; Based on the normalized surface normal of the ideal optical element, determine the ideal reflection action matrix through the following formula: ; Among them, R represents the ideal reflection action matrix, I represents the identity matrix, represents the outer product of vectors; Based on the ideal reflection action matrix, determine the ideal exit vector through the following formula: ; Among them, represents the ideal exit vector, represents the normalized incident vector.

[0021] In some embodiments, the process of determining the actual form exit vector based on the incident vector includes: Calculate the normalized surface normal of the actual form optical element through the following formula; ; Among them, represents the normalized surface normal of the actual form optical element, and E xThe x partial derivative of the surface equation representing the actual form of the optical element, E y The y partial derivative of the surface equation representing the actual form of the optical element; Based on the normalized surface normal of the actual form optical element, the actual reflection action matrix is determined by the following formula: ; where M represents the actual reflection action matrix and I represents the identity matrix; Based on the actual reflection action matrix, the actual form outgoing vector is determined by the following formula: ; where, represents the actual form outgoing vector.

[0022] S3; Calculate the included angle between the ideal outgoing vector obtained in step S2 and the actual form outgoing vector, and determine the constraint condition of the vector included angle in combination with the ray deviation tolerance value.

[0023] In some embodiments, the included angle is obtained by the following formula: ; The constraint condition is: cosθ(x,y)≥cosΔ(x,y); where θ(x,y) represents the included angle and Δ(x,y) represents the ray deviation tolerance value.

[0024] S4: Based on the constraint condition obtained in step S3, obtain the constraint formula of the form error, and the constraint formula is the manufacturing tolerance index.

[0025] In some embodiments, the constraint condition is further: ; Solve the constraint condition to obtain the constraint range of the form error, and the constraint range is the constraint formula.

[0026] To clearly illustrate the method for determining the manufacturing tolerance of components based on the ray deviation tolerance index described in the embodiments of the present invention, an embodiment is provided.

[0027] Embodiment: S1: Add form error to the ideal optical element to obtain the actual form optical element; determine the incident vector of the ray incident on the ideal optical element or the actual form optical element.

[0028] In this embodiment, the confirmed ideal optical element is a parabolic mirror optical element in an ideal state, and the surface equation of this ideal optical element is expressed as: ; Among them, f represents the focal length of the parabolic mirror optical element, specifically 500 mm, and the aperture of the parabolic mirror optical element is 200 mm. Correspondingly, the surface equation of the actual form optical element is expressed as: ; where E(x, y) represents the form error.

[0029] In this embodiment, the normalized incident vector V In is set to V In (x, y, z) = [0, 0, 1] T , that is, the incident light rays are all incident on the ideal optical element or the actual form optical element along the direction of [0, 0, 1] T .

[0030] S2: Determine the allowable deviation value of the light ray, and based on the incident vector obtained in step S1, determine the ideal outgoing vector when the ideal optical element emits light, and the actual form outgoing vector when the actual form optical element emits light.

[0031] In this embodiment, it is set that the allowable deviation value of the light ray Δ(x, y) = 0.02 rad, that is, the deviation between the outgoing light rays at all positions on the actual form optical element and the outgoing light rays at all positions on the ideal optical element does not exceed 0.02 rad.

[0032] In this embodiment, the process of determining the ideal outgoing vector based on the incident vector includes: Calculate the normalized surface normal of the ideal optical element ; ; In this embodiment, taking the tolerance calculation of a light ray with the incident point (x, y) = (8, 6) as an example to give the specific calculation process, where (8, 6) is the position with coordinates (8, 6) inside the aperture of the parabolic mirror optical element. At this time, in the above formula, , , and then the corresponding normalized surface normal is obtained.

[0033] Based on the normalized surface normal , determine the ideal reflection action matrix R through the following formula: .

[0034] Based on the ideal reflection action matrix R, determine the ideal outgoing vector through the following formula : .

[0035] In this embodiment, the process of determining the actual form of the outgoing vector based on the incident vector includes: Calculate the normalized surface normal of the actual form optical element by the following formula ; .

[0036] Based on the normalized surface normal , determine the actual reflection action matrix M by the following formula: ; At the incident point (x, y) = (8, 6), based on the actual reflection action matrix M, determine the actual form of the outgoing vector by the following formula : .

[0037] S3; Calculate the angle between the ideal outgoing vector obtained in step S2 and the actual form of the outgoing vector, and determine the constraint condition of the vector angle in combination with the ray deviation tolerance.

[0038] Since the normalized incident vector V In has a vector modulus of 1, and both the actual reflection action matrix M and the ideal reflection action matrix R are orthogonal matrices, the modulus of the transformed vector is 1. At this time, there is: ; In some embodiments, the angle is obtained by the following formula: ; The ray deviation tolerance Δ ∈ [0, π / 2], so the constraint condition is equivalent to: cosθ(x, y) ≥ cosΔ(x, y); The ray deviation tolerance Δ(x, y) = 0.02 rad, cosΔ(x, y) = 0.9998, and further the constraint condition is: cosθ(x, y) ≥ 0.9998.

[0039] S4: Based on the constraint condition obtained in step S3, obtain the constraint formula of the form error, and the constraint formula is the manufacturing tolerance index.

[0040] In some embodiments, the constraint condition is further: ; Solve the constraint condition to obtain the constraint range of the form error. This process is specifically: ; Substitute the above formula into the constraint condition and further transform to get: ; Furthermore, it is obtained that: ; Furthermore, it is obtained that: ; Furthermore, when the incident point is (x, y) = (8, 6), there is a constraint range: ; wherein, grad represents obtaining the gradient, represents calculating the modulus of the vector.

[0041] This constraint range indicates that for the applied light ray (0, 0, 1), which is modulated by this ideal optical element, if it is desired that the deviation angle θ of the light ray emerging at (8, 6) is less than 0.02 rad, then the squared modulus of the gradient of the error at (8, 6) needs to be less than 2.0004×10 -4 . The above-mentioned constraint range is the constraint equation, and this constraint equation is the manufacturing tolerance index at this point of this element for this application, that is, it indicates that the manufacturing tolerance index obtained by the method provided by the present invention is that if this ideal optical element is manufactured according to the requirement of the applied light ray (0, 0, 1) and θ < 0.02 rad, then the squared modulus of the gradient of the error of the actual optical element at (8, 6) needs to be less than 2.0004×10 -4 .

[0042] It should be understood that various forms of the processes shown above can be used, reordering, adding or deleting steps. For example, the steps recorded in the disclosure of the present invention can be executed in parallel, sequentially or in a different order, as long as the desired results of the technical solutions disclosed by the present invention can be achieved, and no limitations are imposed herein.

[0043] The above specific embodiments do not constitute a limitation to the protection scope of the present invention. Those skilled in the art should understand that various modifications, combinations, sub - combinations and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for determining the manufacturing tolerance of a component based on the light deviation tolerance index, characterized in that Including: S1: Add form errors to the ideal optical element to obtain the actual form optical element; Determine the incident vector of the light ray incident on the ideal optical element or the actual form optical element; S2: Determine the deviation of the light ray from the tolerance value, and based on the incident vector obtained in step S1, determine the ideal exit vector when the ideal optical element emits light, and the actual form exit vector when the actual form optical element emits light; S3； Calculate the included angle between the ideal exit vector and the actual form exit vector obtained in step S2, and combine with the deviation tolerance value of the light ray determined in step S2 to determine the constraint condition of the vector included angle; S4: Based on the constraint condition obtained in step S3, obtain the constraint formula of the form error, and the constraint formula is the manufacturing tolerance index.

2. The method for determining the manufacturing tolerance of components based on the light deviation tolerance index according to claim 1, wherein The process of determining the ideal exit vector based on the incident vector in step S2 includes: Calculate the normalized surface normal of the ideal optical element; ； wherein, represents the normalized surface normal of the ideal optical element, g x represents the x partial derivative of the surface equation of the ideal optical element, g y represents the y partial derivative of the surface equation of the ideal optical element; Based on the normalized surface normal of the ideal optical element, determine the ideal reflection action matrix through the following formula: ； wherein, R represents the ideal reflection action matrix, and I represents the identity matrix, represents the outer product of vectors; Based on the ideal reflection action matrix, determine the ideal exit vector through the following formula: ； Among them, represents the ideal exit vector, represents the normalized incident vector.

3. The method for determining the manufacturing tolerance of components based on the light deviation tolerance index according to claim 2, characterized in that, The process of determining the actual form exit vector based on the incident vector in step S2 includes: Calculate the normalized surface normal of the actual form optical element through the following formula; ； Among them, represents the normalized surface normal of the actual-form optical element, E x represents the x partial derivative of the surface equation of the actual-form optical element, E y represents the y partial derivative of the surface equation of the actual-form optical element; Based on the normalized surface normal of the actual form optical element, determine the actual form reflection action matrix through the following formula: ； Where, M represents the actual form reflection action matrix, and I represents the identity matrix; Based on the actual form reflection action matrix, determine the actual form exit vector through the following formula: ； Among them, represents the actual form outgoing vector.

4. The method for determining the manufacturing tolerance of a component based on the light deviation tolerance index according to claim 3, characterized in that In step S3, the included angle is obtained through the following formula: ； The constraint condition is: cosθ(x,y)≥cosΔ(x,y); Where, θ(x,y) represents the included angle, and Δ(x,y) represents the deviation tolerance value of the light ray.

5. The method for determining the manufacturing tolerance of a component based on the light deviation tolerance index according to claim 4, wherein In step S4, the constraint condition is further: ； Solve the constraint condition to obtain the constraint range of the form error, and the constraint range is the constraint formula.

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