Microstructure optical imaging element design method and microstructure optical imaging element

Abstract

The invention belongs to the technical field of eye vision optics, and relates to a microstructure optical imaging element design method and a microstructure optical imaging element, and the method comprises the steps: building a microstructure lens three-dimensional model under different rise variations based on the structure parameters of a mother lens and the structure parameters of a negative microlens array under different rise variations; acquiring modulation transfer function curves of the optical system containing the three-dimensional models of the microstructural lenses and spatial frequencies of first minimum value points on the modulation transfer function curves; fitting the spatial frequencies of all the first minimum value points and the corresponding rise variations to obtain a relation equation of the spatial frequencies of the minimum value points and the rise variations; based on the relation equation of the spatial frequency of the minimum value point and the rise variation, the spatial frequency limit value when the imaging contrast of the microstructure lens is lower than the preset minimum contrast when the rise variation is infinite is obtained, so that the threshold value range of the rise variation is obtained, and a theoretical basis is provided for the design of the microstructure lens based on negative refractive power.

Description

Technical Field

[0001] The present invention relates to the technical field of ophthalmic optics, and in particular to a design method of a microstructured optical imaging element and a microstructured optical imaging element. Background Art

[0002] Based on the contrast principle, myopia control frame glasses can effectively slow down the deepening of myopia and enable wearers to obtain good visual effects by designing special microstructures on the lenses to change the contrast during retinal imaging. In the prior art, the Diffusion Optics Technology (DOT) is mostly adopted, that is, the incident light is slightly scattered by a semi-transparent dot-like blurring microstructure to reduce the contrast of the retina. However, this semi-transparent dot-like structure is obvious on the lens surface and can be observed by the naked eye. This appearance defect does not meet the expectations of some wearers for the high-quality appearance of spectacle lenses. Recently, clinical studies have shown that adding a microstructured lens with negative refractive power can also reduce the contrast of retinal imaging, which can not only achieve the effect of myopia management but also maintain the high-quality appearance of the lens.

[0003] As Figure 1 shown in the schematic diagram of several layout patterns of microstructured lenses based on negative refractive power, Figure 2 shown in the schematic diagram of the structure of a microstructured lens based on negative refractive power. The microstructured lens based on negative refractive power is composed of a mother lens 10 and a plurality of negative microlens arrays 20. Each negative microlens array 20 contains a plurality of microlenses 200. The distance from the vertex of the arc surface of the mother lens to the vertex of the arc surface of the microlens in the negative microlens array is called the sagittal height change amount of the microstructured lens. By changing the sagittal height change amount of the microstructured lens, the imaging contrast of the lens on the retina can be changed. Since there is little research on the microstructured lens based on negative refractive power at present, there is a lack of theoretical guidance for the selection of the sagittal height change amount parameter of the microstructured lens based on negative refractive power. How to find the value range of the sagittal height change amount that has an inhibitory effect on the imaging contrast while taking into account the lens appearance and processing cost, so as to provide theoretical guidance for the selection of the sagittal height change amount during the design of the microstructured lens based on negative refractive power, and then design a microstructured lens that can meet the requirements of imaging contrast, appearance, and processing cost is the problem to be solved at present.

[0004] When changing the sagittal height variation of the microstructure lens, structural parameters such as the curvature radius and the position of the curvature center of the microlenses in the negative microlens array will also change. Therefore, to find the sagittal height variation value that has an inhibitory effect on the imaging contrast while taking into account the appearance and processing cost, it is necessary to continuously change the sagittal height variation, calculate the structural parameters of the microlenses based on different values of the sagittal height variation, and construct a three-dimensional model of the microstructure lens. By obtaining the modulation transfer function values of the three-dimensional model of the microstructure lens under different sagittal height variations, it is determined whether the microstructure lens under the current sagittal height variation meets the imaging contrast requirements. At the same time, the appearance and processing cost of the microstructure lens under different sagittal height variations are compared to find the range of sagittal height variation values that can effectively inhibit the imaging contrast. However, this process requires continuous modeling and trial calculations, consuming a large amount of time and computing power, and having low efficiency; moreover, since the sagittal height variation cannot cover all values, this method of a large number of modeling and trial calculations cannot effectively obtain the appropriate range of sagittal height variation values.

[0005] In summary, how to obtain the range of sagittal height variation values that have an inhibitory effect on the imaging contrast of the microstructure lens based on negative refractive power and take into account the appearance and processing cost of the lens, so as to provide theoretical guidance for parameter selection in the design of the microstructure lens based on negative refractive power, is a problem that needs to be solved currently. Summary of the Invention

[0006] For this reason, the technical problem to be solved by the present invention is how to obtain the range of sagittal height variation values that have an inhibitory effect on the imaging contrast of the microstructure lens based on negative refractive power and take into account the appearance and processing cost of the lens, so as to provide theoretical guidance for parameter selection in the design of the microstructure lens based on negative refractive power, which is a problem that needs to be solved currently.

[0007] To solve the above technical problem, the present invention provides a design method for a microstructure optical imaging element, including: Constructing three-dimensional models of microstructure lenses under different sagittal height variations based on the structural parameters of the master lens and the structural parameters of the negative microlens array under different sagittal height variations; Obtaining the modulation transfer function curves of the optical systems containing the three-dimensional models of the respective microstructure lenses, and the spatial frequencies of the first minimum points on the respective modulation transfer function curves; Fitting the spatial frequencies of the first minimum points on the respective modulation transfer function curves and their corresponding sagittal height variations to obtain a relationship equation between the spatial frequency of the minimum point and the sagittal height variation; Based on the relationship equation between the spatial frequency of the minimum point and the sagittal height variation, obtaining the spatial frequency limit value when the imaging contrast of the microstructure lens is lower than the preset minimum contrast when the sagittal height variation is infinite; Taking the spatial frequency of the minimum value point being greater than or equal to the spatial frequency limit value as the target, solve the relationship equation between the spatial frequency of the minimum value point and the sagittal height change amount, and obtain the value range of the sagittal height change amount threshold of the microstructure lens based on negative refractive power.

[0008] Preferably, after obtaining the value range of the sagittal height change amount threshold of the microstructure lens based on negative refractive power, it further includes: Among the modulation transfer function curves of each three-dimensional model of the microstructure lens, take the modulation transfer function curve with the largest fluctuation frequency as the target modulation transfer function curve, and take the sagittal height change amount corresponding to the target modulation transfer function curve as the target sagittal height change amount; Perform a one-dimensional fitting of the spatial frequency on the target modulation transfer function curve to obtain a polynomial equation of the modulation transfer function with respect to the normalized spatial frequency; Based on the target sagittal height change amount and the relationship equation between the spatial frequency of the minimum value point and the sagittal height change amount, obtain the spatial frequency scaling ratio equation; normalize the spatial frequency based on the spatial frequency scaling ratio equation to obtain the normalized spatial frequency equation; Substitute the normalized spatial frequency equation into the polynomial equation of the modulation transfer function with respect to the spatial frequency, and then fit it with the modulation transfer function curves of the three-dimensional models of the microstructure lens under different sagittal height change amounts to obtain a quantization model of the modulation transfer function with respect to the sagittal height change amount and the spatial frequency; Based on the value range of the sagittal height change amount threshold, obtain the value range of the sagittal height change amount, and use the quantization model to calculate the modulation transfer function values at each value within the value range of the sagittal height change amount of the microstructure lens based on negative refractive power; take the sagittal height change amount with the smallest modulation transfer function value as the optimal sagittal height change amount of the microstructure lens based on negative refractive power.

[0009] Preferably, after the optimal sagittal height change amount of the microstructure lens based on negative refractive power, it further includes: Obtain the optimal structural parameters of the negative microlens array at the optimal sagittal height change amount; Based on the structural parameters of the master lens, the optimal structural parameters of the negative microlens array, and the microstructure arrangement type, design and obtain the microstructure lens based on negative refractive power.

[0010] Preferably, obtaining the spatial frequency scaling ratio equation based on the target sagittal height change amount and the relationship equation between the spatial frequency of the minimum value point and the sagittal height change amount includes: Input the target sagittal height change amount into the relationship equation between the spatial frequency of the minimum value point and the sagittal height change amount, and calculate the spatial frequency of the minimum value point corresponding to the target sagittal height change amount; Based on the ratio of the spatial frequency of the minimum value point corresponding to the target sagittal height change amount to the relationship equation between the spatial frequency of the minimum value point and the sagittal height change amount, obtain the spatial frequency scaling ratio equation.

[0011] Preferably, the relationship equation between the spatial frequency of the minimum point and the change in sagitta height is expressed as: , where, represents the relationship equation between the spatial frequency of the minimum point and the change in sagitta height; represents the change in sagitta height; represents the correlation coefficient between the spatial frequency of the minimum point and the change in sagitta height; The calculation formula for the spatial frequency limit value is: , , where, represents the spatial frequency limit value.

[0012] Preferably, the polynomial equation of the modulation transfer function with respect to the normalized spatial frequency is expressed as: , where, represents the polynomial equation of the modulation transfer function with respect to the spatial frequency; represents the normalized spatial frequency; represents the first correlation coefficient; represents the second correlation coefficient; represents the third correlation coefficient; represents the fourth correlation coefficient; represents the fifth correlation coefficient; represents the sixth correlation coefficient; The normalized spatial frequency equation is expressed as: , where, represents the normalized spatial frequency; represents the spatial frequency; represents the spatial frequency scaling ratio; represents the target change in sagitta height corresponding to the spatial frequency of the minimum point.

[0013] Preferably, the quantization model is expressed as: , , where, represents the modulation transfer function value.

[0014] Preferably, the process of obtaining the structural parameters of the master mirror includes: Based on the spherical power and the preset front surface optical power of the master mirror, calculate the rear surface optical power of the master mirror; Based on the refractive index of the mother mirror material, the optical power of the front surface of the mother mirror, and the optical power of the rear surface of the mother mirror, the curvature radius of the front surface of the mother mirror and the curvature radius of the rear surface of the mother mirror are calculated.

[0015] Preferably, the process of obtaining the structural parameters of the negative microlens array under different sag variation amounts includes: Based on the sag variation amount and the sag of the mother mirror, the sag of the microlenses in the negative microlens array is calculated, and the curvature radius of the microlenses is calculated based on the sag of the microlenses; Based on the preset micro-structure arrangement type, the mother mirror and the negative microlens array are arranged to obtain the position parameters of the center point of the negative microlens array; Based on the position parameters of the curvature center of the mother mirror and the center point of the negative microlens array, the position of the curvature center and the tilt angle of the microlenses in the negative microlens array are calculated.

[0016] The present invention also provides a micro-structured optical imaging element, which is designed by the above-mentioned design method of the micro-structured optical imaging element based on negative refractive power.

[0017] The design method of the micro-structured optical imaging element based on negative refractive power provided by the present application has the following beneficial effects: 1. First, use the three-dimensional models of microstructure lenses with different sagittal height variations to reflect the actual shapes and optical characteristics of microstructure lenses based on negative refractive power at different sagittal height variations; obtain the modulation transfer function curves of the optical systems containing the three-dimensional models of each microstructure lens. Since the first minimum point on the curve represents the position where the performance of the microstructure lens begins to change significantly in the spatial frequency domain, therefore, in this application, by fitting the spatial frequency corresponding to the first minimum point on each modulation transfer function and the sagittal height variation, the relationship equation between the spatial frequency of the minimum point and the sagittal height variation can be constructed, thereby obtaining the internal relationship between the spatial frequency and the sagittal height variation. Since when the sagittal height variation approaches infinity, under the action of the sagittal height variation, the modulation transfer function value will reduce the contrast to the theoretical limit value of the spatial frequency at the low imaging level, therefore, based on the relationship equation between the sagittal height variation and the spatial frequency, this application can obtain the spatial frequency limit value when the imaging contrast of the microstructure lens is lower than the preset minimum contrast when the sagittal height variation approaches infinity. This spatial frequency limit value defines the limit performance that the microstructure lens can achieve under the given imaging resolution requirements; finally, with the goal that the spatial frequency of the minimum point is greater than this limit value, solving the relationship equation can obtain the feasible interval of the sagittal height variation threshold when the imaging contrast requirement is met, so as to select the sagittal height variation within the range less than this feasible interval to design a microstructure lens based on negative refractive power that has an inhibitory effect on imaging contrast. Since when the sagittal height variation is greater than this threshold feasible interval, the effect of reducing the imaging contrast of the microstructure lens is not significant, and it will also increase the processing difficulty and affect the appearance of the lens, therefore, through limited modeling and data simulation, this application has obtained the value range of the sagittal height variation threshold that can effectively reduce the imaging contrast and take into account the lens appearance and processing cost. When designing the lens, only need to select the sagittal height variation within the range less than this feasible interval, which provides a theoretical basis for the selection of the sagittal height variation when designing the microstructure lens based on negative refractive power.

[0018] 2. Since the modulation transfer function curve of the lens based on negative refractive power shows a downward trend with fluctuations as the spatial frequency increases, it is difficult to directly fit the relationship between the modulation transfer function, spatial frequency, and the change in sagittal height. However, the present application discovers that there is an approximate horizontal scaling relationship between the modulation transfer function curves corresponding to different changes in sagittal height, and there is no scaling relationship longitudinally. Therefore, the modulation transfer function curve with a larger fluctuation frequency can better reflect the changes in the optical characteristics of the microstructure lens at different spatial frequencies. Based on this, the present application uses the modulation transfer function curve with the largest fluctuation frequency as the target modulation transfer function curve and the corresponding change in sagittal height as the target change in sagittal height. By performing a one-variable fit of the spatial frequency on the target modulation transfer function curve, a polynomial equation of the modulation transfer function with respect to the normalized spatial frequency is obtained. At the same time, considering the horizontal scaling relationship between the modulation transfer function curves, a spatial frequency scaling ratio equation is constructed using the relationship equation between the target change in sagittal height and the spatial frequency of the minimum point and the change in sagittal height to normalize the spatial frequency and obtain a normalized spatial frequency equation, eliminating the influence of the change in sagittal height on the spatial frequency scale, enabling the modulation transfer functions corresponding to different changes in sagittal height to be compared under a unified spatial frequency scale. After fitting the normalized spatial frequency equation with the modulation transfer function curves corresponding to different changes in sagittal height, a quantization model of the modulation transfer function with respect to the change in sagittal height and spatial frequency can be obtained, thereby using this quantization model to evaluate the imaging contrast of the microstructure lens based on negative refractive power when the change in sagittal height takes different values, and thus optimizing the microstructure lens based on negative refractive power, further improving the design efficiency of the microstructure lens based on negative refractive power. Moreover, the quantization model constructed in the present application can be used as a theoretical guidance and a general evaluation index for designing myopia prevention and control lenses, which can not only compare the effects of different types of myopia prevention and control lenses horizontally but also compare the full-frequency band effects of spatial frequencies. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to make the content of the present invention easier to be clearly understood, the following further describes the present invention in detail according to specific embodiments of the present invention in conjunction with the accompanying drawings, where: Figure 1 It is a schematic diagram of the layout style of the microstructure lens provided by the present application; where Figure 1 (a) in is a schematic diagram of the first layout style, Figure 1 (b) in is a schematic diagram of the second layout style, Figure 1 (c) in is a schematic diagram of the third layout style, Figure 1 (d) in is a schematic diagram of the fourth layout style; Figure 2 It is a schematic diagram of the structure type on the surface of a microstructure lens provided by the present application and the division of each structure area; Figure 3Flowchart of the microstructured lens design method based on negative refractive power provided by this application; Figure 4 Position projection of the vertices of the hexagonal grid negative microlens array provided by an embodiment of this application on the vertex section of the master mirror; Figure 5 Schematic diagram of the calculation principle of the curvature center of the microlenses in the negative microlens array provided by an embodiment of this application; Figure 6 Schematic diagram of the calculation principle of the curvature center of the microlenses in the positive microlens array provided by an embodiment of this application; Figure 7 Schematic diagram of the optical path formed by the master mirror and the myopic model eye provided by an embodiment of this application; Figure 8 Partial schematic diagram of the solid model of the microstructured lens constructed by an embodiment of this application; Figure 9 Schematic diagram for comparing modulation transfer function curves corresponding to different sag height change amounts provided by an embodiment of this application; Figure 10 Schematic diagram for comparing the modulation transfer function curve with the fitting result when the sag height change amount is 10 μm provided by an embodiment of this application; Figure 11 Schematic diagram for obtaining the spatial frequency of the first minimum point on the modulation transfer function curve and fitting the spatial frequency of the minimum point with the sag height change amount provided by an embodiment of this application; wherein, Figure 11 in (a) is the schematic diagram for obtaining the spatial frequency of the first minimum point on the modulation transfer function curve, Figure 11 in (b) is the schematic diagram for fitting the spatial frequency of the minimum point with the sag height change amount; Figure 12 Schematic diagram for comparing the actual data of the modulation transfer function with respect to the sag height change amount and spatial frequency with the binary fitting result provided by an embodiment of this application; Figure 13 Schematic diagram for comparing the actual modulation transfer function value with the modulation transfer function value obtained from the quantization model when the sag height change amount is 15 μm provided by an embodiment of this application; Figure 14 Schematic diagram of the arrangement of a microlens array with a combination of positive and negative microlenses provided by an embodiment of this application; Figure 15 Schematic diagram of another arrangement of a microlens array with a combination of positive and negative microlenses provided by an embodiment of this application; Figure 16 Schematic diagram for comparing the modulation transfer function curves of the microstructured lens based on positive refractive power and the microstructured lens based on negative refractive power provided by an embodiment of this application; Description of the reference numerals in the drawings: 1. Central foveal region; 10. Mother lens; 2. Regulation region; 20. Negative microlens array; 200. Microlens. Detailed implementation manners

[0020] The present invention will be further described below in conjunction with the drawings and specific embodiments, so that those skilled in the art can better understand the present invention and be able to implement it, but the specific embodiments cited are not intended to limit the present invention.

[0021] As Figure 1 shown in the schematic diagrams of the layout styles of several microstructured lenses provided by the present application; among them, Figure 1 (a) in is the schematic diagram of the first layout style, Figure 1 (b) in is the schematic diagram of the second layout style, Figure 1 (c) in is the schematic diagram of the third layout style, Figure 1 (d) in is the schematic diagram of the fourth layout style. It should be noted that when designing a microstructured lens based on negative refractive power, the layout style can be selected from Figure 1 any one of them, or other styles can also be selected.

[0022] Figure 2 For Figure 1 shown in (a) of, it is the schematic diagram of the structure type on the surface of the microstructured lens and the division of each structure region. It can be seen that the microstructured lens structurally includes a central foveal region 1 and a regulation region 2. Among them, the central foveal region 1 includes a mother lens 10, and the regulation region 2 includes a plurality of negative microlens arrays 20 and a part of the mother lens 10 located in the central region of the negative microlens array 20. Each negative microlens array 20 is composed of a plurality of microlenses 200. It should be noted that at least half of the microlenses 200 in the negative microlens array 20 are negative microlenses. The change amount of the sagittal height of the microstructured lens refers to the distance from the vertex of the arc surface of the mother lens 10 to the vertex of the arc surface of the microlens 200 in the negative microlens array 20. When the change amount of the sagittal height of the microstructured lens changes, the structural parameters of the microlenses 200 in the negative microlens array 20 will change, and the imaging contrast of the microstructured lens will also change. Therefore, if you want to obtain a range of sagittal height change amounts that can have an inhibitory effect on the imaging contrast and at the same time take into account the lens processing cost and appearance, it is necessary to determine the structural parameters of the microlenses 200 in the negative microlens array 20 based on different sagittal height change amount values, so as to model the microstructured lenses under different sagittal height change amounts, and judge whether the microstructured lens under the current sagittal height change amount has an imaging contrast inhibitory effect through this model, and compare the appearance and processing cost of the lenses under different sagittal height change amounts. However, this method of continuous modeling and trial calculation takes a lot of time and cannot enumerate all values. Therefore, it is impossible to find a range of sagittal height change amounts that makes the microstructured lens based on negative refractive power have an inhibitory contrast effect and meet the requirements of appearance and processing cost.

[0023] In order to more effectively and efficiently obtain the sagittal height change threshold that enables the negative refractive power-based microstructured lens to have an anti-contrast effect, without affecting the appearance of the lens and taking into account the lens processing cost, the present application proposes the following method to provide theoretical guidance for the design of the negative refractive power-based microstructured lens.

[0024] Please refer to Figure 3 , Figure 3 which is a flowchart of the microstructured optical imaging element design method provided by the present application. The method specifically includes: S1: Based on the structural parameters of the master mirror and the structural parameters of the negative microlens array at different sagittal height changes, construct a three-dimensional model of the microstructured lens at different sagittal height changes.

[0025] Specifically, the sagittal height change refers to the distance from the vertex of the arc surface of the master mirror to the vertex of the arc surface of the microlens in the negative microlens array.

[0026] Optionally, in some embodiments of the present application, a three-dimensional model of the microstructured lens at each sagittal height change can be constructed based on the structural parameters of the master mirror and the structural parameters of the negative microlens array when the sagittal height change takes different values in the range of 1 to 10 μm.

[0027] S2: Obtain the modulation transfer function curve of the optical system containing each three-dimensional model of the microstructured lens, and the spatial frequency of the first minimum point on each modulation transfer function curve.

[0028] S3: Fit the spatial frequency of the first minimum point on each modulation transfer function curve and its corresponding sagittal height change to obtain the relationship equation between the spatial frequency of the minimum point and the sagittal height change.

[0029] S4: Based on the relationship equation between the spatial frequency of the minimum point and the sagittal height change, obtain the spatial frequency limit value when the imaging contrast of the microstructured lens is lower than the preset minimum contrast when the sagittal height change is infinite.

[0030] S5: With the goal that the spatial frequency of the minimum point is greater than or equal to the spatial frequency limit value, solve the relationship equation between the spatial frequency of the minimum point and the sagittal height change to obtain the value range of the sagittal height change threshold of the negative refractive power-based microstructured lens.

[0031] Furthermore, the relationship equation between the spatial frequency of the minimum point and the sagittal height change is expressed as: , where represents the relationship equation between the spatial frequency of the minimum point and the sagittal height change; represents the sagittal height change; It represents the correlation coefficient between the spatial frequency at the minimum point and the change in sagittal height; The calculation formula for the spatial frequency limit value is: , , where, represents the spatial frequency limit value.

[0032] In this application, three-dimensional models of microstructure lenses with different changes in sagittal height are used to reflect the actual shape and optical characteristics of the microstructure lenses based on negative refractive power at different changes in sagittal height; the modulation transfer function curves of the optical system containing the three-dimensional models of each microstructure lens are obtained. Since the first minimum point on the curve represents the position where the performance of the microstructure lens begins to change significantly in the spatial frequency domain, therefore, in this application, by fitting the spatial frequency corresponding to the first minimum point on each modulation transfer function and the change in sagittal height, the relationship equation between the spatial frequency at the minimum point and the change in sagittal height can be constructed, so as to obtain the internal relationship between the spatial frequency and the change in sagittal height. Since when the change in sagittal height approaches infinity, the modulation transfer function value will, under the action of the change in sagittal height, reduce the contrast to the spatial frequency limit value at the low imaging level, therefore, based on the relationship equation between the change in sagittal height and the spatial frequency, this application can obtain the spatial frequency limit value when the imaging contrast of the microstructure lens is lower than the preset minimum contrast when the change in sagittal height approaches infinity. This spatial frequency limit value defines the limit performance that the microstructure lens can achieve under the given imaging contrast requirements; finally, with the goal that the spatial frequency at the minimum point is greater than this limit value, solving the relationship equation can obtain the feasible interval of the change in sagittal height when the imaging contrast requirements are met, so as to select the change in sagittal height within this feasible interval to design a microstructure lens based on negative refractive power that has an inhibitory effect on the imaging contrast. Through limited modeling and data simulation, this application obtains the value range of the sagittal height change threshold, providing a theoretical basis for the selection of the sagittal height change when designing a microstructure lens based on negative refractive power.

[0033] Since a higher change in sagittal height has little effect on reducing the imaging contrast of the microstructure lens, and it will also increase the processing difficulty and affect the appearance of the lens, therefore, there is no need to select a larger change in sagittal height outside this feasible interval during design. This application obtains the value range of the sagittal height change threshold that takes into account the inhibitory effect on the imaging contrast, processing cost, and appearance. When designing a microstructure lens based on negative refractive power, even if it is necessary to design a lens with the best inhibitory effect on the imaging contrast, the maximum value of the change in sagittal height only needs to be within this range, improving the design efficiency of the microstructure lens. It should be noted that the design method provided by this application can also be extended to the design of microstructure parameters other than the change in sagittal height, such as diameter, filling rate, and surface shape, etc.

[0034] Furthermore, in the prior art, the modulation transfer function value is usually used to evaluate the contrast of the microstructure lens. At the same time, the parameters of the microstructure lens are regulated by the relationship between the modulation transfer function, the change in sagittal height, and the spatial frequency, so as to optimize the imaging contrast of the microstructure lens on the retina. However, to obtain a regression relationship with a good fitting degree and independent spatial frequency and change in sagittal height, the modulation transfer function value needs to show a monotonically decreasing trend with the changes in sagittal height and spatial frequency. Since the microstructure lens often has a complex arrangement and a variable surface shape, the modulation transfer function value may show a fluctuating decreasing trend as the spatial frequency increases. This makes it difficult to construct a model that can accurately fit the relationship among the three. In the existing designs of microstructure lenses based on negative refractive power, there is no contrast analysis for the change in sagittal height, nor a quantitative method and model with high precision for controlling the contrast by regulating the change in sagittal height.

[0035] Based on the above problems, the embodiment of the present application also establishes a multiple regression model with high precision for controlling the retinal contrast (modulation transfer function, MTF) by the change in sagittal height, thereby providing a theoretical model for the regulation of the change in sagittal height and further improving the design efficiency of the microstructure lens based on negative refractive power.

[0036] Specifically, after step S5, it further includes: S6: Using the modulation transfer function curve with the largest fluctuation frequency as the target modulation transfer function curve, and using the change in sagittal height corresponding to the target modulation transfer function curve as the target change in sagittal height.

[0037] S7: Performing a one-dimensional fitting of the spatial frequency on the target modulation transfer function curve to obtain a polynomial equation of the modulation transfer function with respect to the normalized spatial frequency.

[0038] Specifically, the polynomial equation of the modulation transfer function with respect to the normalized spatial frequency is expressed as: , where, represents the polynomial equation of the modulation transfer function with respect to the spatial frequency; represents the normalized spatial frequency; represents the first correlation coefficient; represents the second correlation coefficient; represents the third correlation coefficient; represents the fourth correlation coefficient; represents the fifth correlation coefficient; represents the sixth correlation coefficient.

[0039] S8: Based on the relationship equation between the target sagittal height variation and the spatial frequency of the minimum point and the sagittal height variation, obtain the spatial frequency scaling ratio equation; normalize the spatial frequency based on the spatial frequency scaling ratio equation to obtain the normalized spatial frequency equation.

[0040] Specifically, in some embodiments of the present application, obtaining the spatial frequency scaling ratio equation based on the relationship equation between the target sagittal height variation and the spatial frequency of the minimum point and the sagittal height variation includes: Input the target sagittal height variation into the relationship equation between the spatial frequency of the minimum point and the sagittal height variation, and calculate the spatial frequency of the minimum point corresponding to the target sagittal height variation; Based on the ratio of the spatial frequency of the minimum point corresponding to the target sagittal height variation to the relationship equation between the spatial frequency of the minimum point and the sagittal height variation, obtain the spatial frequency scaling ratio equation.

[0041] Specifically, the normalized spatial frequency equation is expressed as: , where, represents the normalized spatial frequency; represents the spatial frequency; represents the spatial frequency scaling ratio; represents the target sagittal height variation corresponding to the spatial frequency of the minimum point.

[0042] S9: After substituting the normalized spatial frequency equation into the polynomial equation of the modulation transfer function with respect to the spatial frequency, fit it with the modulation transfer function curve of the three-dimensional model of the microstructure lens under different sagittal height variations to obtain the quantization model of the modulation transfer function with respect to the sagittal height variation and the spatial frequency.

[0043] Specifically, the quantization model is expressed as: , , where, represents the modulation transfer function value.

[0044] S10: Based on the value range of the sagittal height variation threshold, obtain the value range of the sagittal height variation, and use the quantization model to calculate the modulation transfer function values at each value within the value range of the sagittal height variation of the microstructure lens based on negative refractive power; take the sagittal height variation with the minimum modulation transfer function value as the optimal sagittal height variation of the microstructure lens based on negative refractive power.

[0045] Furthermore, after the optimal sagittal height variation of the microstructure lens based on negative refractive power, it further includes: Obtain the optimal structural parameters of the negative microlens array under the optimal sagittal height variation; Based on the structural parameters of the mother lens, the optimal structural parameters of the negative microlens array, and the type of microstructure arrangement, a microstructure lens based on negative refractive power is designed.

[0046] Since the modulation transfer function curve of the lens based on negative refractive power shows a trend of fluctuating downward as the spatial frequency increases, it is difficult to directly fit the relationship between the modulation transfer function, the spatial frequency, and the change in sagittal height. However, this application discovers that there is an approximate horizontal scaling relationship between the modulation transfer function curves corresponding to different changes in sagittal height, and there is no scaling relationship longitudinally. Therefore, the modulation transfer function curve with a larger fluctuation frequency can better reflect the changes in the optical characteristics of the microstructure lens at different spatial frequencies. Based on this, this application uses the modulation transfer function curve with the largest fluctuation frequency as the target modulation transfer function curve, and the corresponding change in sagittal height as the target change in sagittal height; by performing a univariate fit of the spatial frequency on the target modulation transfer function curve, a polynomial equation of the modulation transfer function with respect to the normalized spatial frequency is obtained; considering the horizontal scaling relationship between the modulation transfer function curves, a spatial frequency scaling ratio equation is constructed using the relationship equation between the target change in sagittal height and the spatial frequency and sagittal height at the minimum point to normalize the spatial frequency to obtain a normalized spatial frequency equation, eliminating the influence of the change in sagittal height on the spatial frequency scale, enabling the modulation transfer functions corresponding to different changes in sagittal height to be compared on a unified spatial frequency scale. Fitting the normalized spatial frequency equation with the modulation transfer function curves corresponding to different changes in sagittal height can obtain a quantization model of the modulation transfer function with respect to the change in sagittal height and the spatial frequency, thereby using this quantization model to evaluate the imaging contrast of the microstructure lens when the change in sagittal height takes different values, and thus optimizing the microstructure lens. The method provided in this application obtains a high-precision quantization model using the modulation transfer function curves of the microstructure lens with a small number of changes in sagittal height, avoiding more modeling and experiments, and further improving the design efficiency of the microstructure lens. In addition, the quantization model constructed in this application can be used as a theoretical guidance and a general evaluation index for designing myopia prevention and control lenses, which can not only compare the effects of different types of myopia prevention and control lenses horizontally, but also compare the effects of the entire frequency band of the spatial frequency.

[0047] Furthermore, the process of obtaining the structural parameters of the mother lens in step S1 includes: Based on the spherical power and the preset front surface optical power of the mother lens, the back surface optical power of the mother lens is calculated; Based on the refractive index of the mother lens material, the front surface optical power of the mother lens, and the back surface optical power of the mother lens, the front surface curvature radius and the back surface curvature radius of the mother lens are calculated.

[0048] The process of obtaining the structural parameters of the negative microlens array under different changes in sagittal height includes: Calculate the sagittal height of the microlenses in the negative microlens array based on the change in sagittal height and the sagittal height of the master mirror, and calculate the radius of curvature of the microlenses based on the sagittal height of the microlenses; Arrange the master mirror and the negative microlens array based on a preset type of microstructure arrangement to obtain the position parameters of the center point of the negative microlens array; Calculate the position of the center of curvature and the tilt angle of the microlenses in the negative microlens array based on the position parameters of the center of curvature of the master mirror and the center point of the negative microlens array.

[0049] Based on the method for designing a microstructure lens based on negative refractive power provided in the above embodiments, an embodiment of the present application also provides a microstructure lens, which is designed by the method for designing a microstructure lens based on negative refractive power described above.

[0050] The method for designing a microstructure lens based on negative refractive power provided by the present application will be further explained and illustrated below through specific examples.

[0051] The microstructure lens of this embodiment selects Figure 1 the layout style shown in (a) in, and the structure type of the surface of the microstructure lens and the division of the regions to which each structure belongs are as shown in Figure 2 It can be seen that the microstructure lens in this embodiment structurally includes a central clear vision area 1 and a regulation area 2. Among them, the central clear vision area 1 includes a master mirror 10, and the regulation area 2 includes a plurality of negative microlens arrays 20 and a master mirror 10 located in the central area of the negative microlens array 20. Each negative microlens array 20 is composed of a plurality of microlenses 200.

[0052] The method for designing a microstructure lens based on negative refractive power provided in this embodiment specifically includes the following steps: S10: Calculate the structural parameters of the master mirror 10 according to the spherical power of the spectacle wearer, which specifically includes: S100: Given that the spherical power of a certain myopic eye is -3D and the front surface optical power F1 of the preset master mirror 10 is 2D, calculate the back surface optical power F2 of the master mirror 10. The specific calculation formula is: .

[0053] S101: Calculate the front and back surface radii of curvature of the master mirror 10 based on the refractive index n of the material of the master mirror 10, the front surface optical power of the master mirror 10, and the back surface optical power of the master mirror 10. The specific calculation formula is: , , Among them, represents the front surface radius of curvature of the master mirror 10; Represents the curvature radius of the rear surface of the master mirror 10. It should be noted that the curvature radius is a signed parameter. The curvature radius of a spherical surface bent to the left is positive, and the curvature radius of a spherical surface bent to the right is negative.

[0054] As shown in Table 1, the structural parameters of the master mirror 10 provided in this embodiment are as follows: Table 1

[0055] S20: Obtain the structural parameters of the negative microlens array 20 under different sagitta variation amounts (in this embodiment, taking the example of obtaining the structural parameters of the negative microlens array 20 when the sagitta variation amount is 6 μm), which specifically includes: S200: Based on the preset diameter of 6 mm of the central fovea 1 and the full aperture D1 = 6 mm of the central fovea 1, determine that the regulation area 2 is the area outside 3 mm from the principal optical axis.

[0056] S201: With the diameter value range of the microlenses 200 in the negative microlens array 20 being 0.1 mm to 2 mm as a constraint, determine that the diameter D200 of the microlenses 200 is 1 mm; with the value range of the sagitta variation amount of the negative microlens array 20 caused by the excision of the microlenses 200 being 1 μm to 10 μm as a constraint, determine that the sagitta variation amount H of the negative microlens array 20 is 6 μm.

[0057] Specifically, for the negative microlens array 20, the sagitta variation amount H refers to the distance from the arc vertex of the master mirror 10 in the negative microlens array 20 to the arc vertex of the microlenses 200 in the negative microlens array 20. Therefore , where represents the sagitta of the master mirror 10, represents the sagitta of the microlenses 200. It should be noted that for the positive microlens array, .

[0058] For spherical microlenses, the relationship between their curvature c, radial distance r, and the sagitta z at this radial distance r is as follows: , , where , represents the spherical curvature radius; represents the microlens semi-aperture, .

[0059] S202: Obtain the sagitta of the master mirror 10 based on the curvature radius R1 of the master mirror 10 , and obtain the curvature radius of the microlenses 200 based on the sagitta of the microlenses 200 , as shown in Table 2, when the sagittal height change amount H = 6 μm, the optical structure parameters of the master mirror 10 and the microlens 200 are as follows: Table 2

[0060] In addition, in order to compare the effects of microstructure lenses with negative refractive power and microstructure lenses with positive refractive power on suppressing retinal contrast, this embodiment also gives the optical structure parameters of the master mirror and the microlens when the microlens array is a positive microlens array, as shown in Table 3: Table 3

[0061] S203: Select the layout style of the microstructure lens to be used, and then determine the grid type and the position parameters of the grid center point, which specifically include: Based on Figure 1 the layout style shown in (a) therein, select to use a hexagonal grid, and the distance d between adjacent grid center points = D200 = 1 mm.

[0062] Further, taking the principal optical axis of the master mirror 10 as the Z-axis, the horizontal direction perpendicular to the Z-axis as the X-axis, and the vertical direction as the Y-axis, establish a three-dimensional XYZ rectangular coordinate system. Make a section z = 0 with the vertex (0, 0, 0) of the master mirror 10. The positions of the center points of each hexagonal grid in this section and the central macular area 1 are as Figure 4 shown. In the figure, the hexagonal grid is represented by an inscribed circle, the radius of the inscribed circle is D200 / 2, and the center point of the hexagonal grid is the center of the inscribed circle.

[0063] Let the center coordinates of the inscribed circle be (x0, y0, 0). The distances from each center point along the X and Y axes to the principal optical axis are hx = x0 and hy = y0 respectively. Thus, more center point coordinates can be obtained by drawing a grid in Figure 4 . If the inscribed circle of the grid is not within the central macular area 1, the center point of this grid is used as the layout position of the negative microlens array, as in Figure 4 1 to 12 therein. The coordinate calculation and optical modeling analysis can be carried out through the negative microlens array unit directly above the central macular area 1.

[0064] It should be noted that the grid layout position of the planar image obtained in this embodiment will be used as the position of the grid of the microlenses 200 on the surface of the master mirror 10. In the above calculation method, if the diameter of the microlenses 200 on the microstructure lens remains unchanged all the time, there will be a certain gap between the microlenses 200 on the curved surface, and the closer to the edge of the microstructure lens, the larger the gap between the microlenses 200, and the greater the error of the calculated position parameters. In other embodiments, another calculation method can also be used: calculate based on the angles occupied by the respective microlenses 200 on the surface of the master mirror 10. However, since there is a certain overlap at the edges of the respective microlenses 200 on the curved surface, and the overlapping area between the microlenses 200 is larger closer to the edge of the microstructure lens.

[0065] S204: According to the position of the grid center points on the tangent plane, calculate the position of the curvature center of the microlens 200, and its calculation principle is as Figure 5 shown. Let the curvature center of the master mirror 10 be P, and use the movement process from A to B to C in Figure 5 to represent the calculation steps. The position of A in the figure is the center of a certain inscribed circle in Figure 4 . The specific calculation process includes: Project the grid along the principal optical axis onto the front surface of the master mirror 10, that is, translate each vertex of the grid along z = 0 to the front surface of the master mirror 10. For example, the coordinates of the center of the inscribed circle of the grid are A(x0, y0, 0). Suppose the translation distance along the Z axis is z, then the coordinates of the center of the inscribed circle of the grid on the front surface of the master mirror 10 after translation are B(x0, y0, z), as shown in Figure 5 step1 in.

[0066] Let the curvature center of the microlens 200 corresponding to this grid be C(x0 ’ , y0 ’ , z ’ ). Since the curvature center C of the microlens 200, the vertex B of the center of the inscribed circle of the grid on the front surface of the master mirror 10, and the curvature center P of the master mirror 10 are collinear, then the vertex B can be translated outward along the extension line of BP to obtain C, and the translation distance is the absolute value of the curvature radius r1 of the microlens 200 minus the sagittal height change H, as shown in Figure 5 step2 in.

[0067] Draw perpendicular lines from the curvature center C of the microlens 200 and the vertex B of the center of the inscribed circle of the grid on the front surface of the master mirror 10 to the principal optical axis respectively to obtain a set of similar triangles , then there is: , where, , .

[0068] It is known that , r1, H, and the coordinates of the in-circle center of the grid (x0, y0, 0), the coordinates of the curvature center of the microlens 200 can be calculated as (x0 ’ , y0 ’ , z ’ ). It should be noted that the calculation process of the coordinates of the curvature center of the microlens in the microstructured lens with positive refractive power is the same as the above process, but point C is located on the BP connection line, and , and its calculation principle is as Figure 6 shown.

[0069] As shown in Table 4 are the coordinate data of points A, B, and C related to vertices 1 to 6 in the negative microlens array 20 directly above the central fixation area 1: Figure 4 in Table 4

[0070] S205: Calculate the tilt angle of the microlens 200 in the negative microlens array 20 based on the position of the in-circle center A of the grid (the angle between the principal optical axis of the microlens 200 and the principal optical axis of the parent lens 10 in different coordinate directions is the tilt angle of the microlens 200), which specifically includes: Denote the angle between the principal optical axis of the microlens 200 and the y = 0 plane (X tilt) as α, with the positive direction being the direction of increasing y coordinate, and denote the angle between the principal optical axis of the microlens 200 and the x = 0 plane (Y tilt) as β, with the positive direction being the direction of decreasing x coordinate. The magnitudes of both are equivalent to the components of the angle between the BP connection line and the principal optical axis of the parent lens 10 on the X-axis and Y-axis. Since the surface shape of the microlens 200 is rotationally symmetric, there is no need to calculate the Z tilt. The calculation formulas for the X tilt and Y tilt are: , , Based on the above calculation process, in this embodiment, all the structural parameters of the microlens 200 corresponding to vertices 1 to 6 in the negative microlens array 20 directly above the central fixation area 1 are obtained, as shown in Table 5: Figure 4 in Table 5

[0071] S30: Based on the above structural parameters of the parent lens 10 and the negative microlens array 20, use the optical software Zemax to construct an optical system of a three-dimensional model of the microstructured lens with different sag height variation amounts, which specifically includes: S300: Model the myopia model and the master mirror 10: Use the sequential mode of Zemax software to establish the Liou eye model. The data of the Liou eye model is shown in Table 6. Set the wavelength of the optical system to 0.55 μm, and the fields of view to 0°, 8°, and 16°. Model the master mirror 10 based on the parameters in Table 1 in the non-sequential mode to obtain the model P1 of the master mirror 10. Among them, the distance from the back surface of the microstructure lens to the front surface of the cornea is 12 mm. With the value range of the pupil radius from 1 mm to 3 mm as the constraint, determine the pupil radius to be 1.5 mm. Focus and optimize the vitreous body thickness of the Liou eye model in the sequential mode to make it a myopia model corresponding to -3D spherical diopter, as Figure 7 shown is the schematic optical path diagram composed of the master mirror 10 and the myopia model eye.

[0072] Table 6

[0073] S301: Model the negative microlens array 20 based on different sagittal height variations (H = 1 μm, 2 μm, 4 μm, 6 μm, 8 μm, 10 μm), which specifically includes: Input the structural parameters of the six microlenses 200 in the single negative microlens array 20 obtained in step S20 in the non-sequential mode. Among them, the microlens is a plano-convex lens, as Figure 5 shown in MNKDJ. The coordinates of the curvature center C of each microlens 200 are used as the positioning point coordinates of the front surface center, the curvature radius r1 is used as the thickness CD and the back surface curvature radius, input the tilt angle data. The semi-aperture CM of the microlens 200 is slightly larger than the semi-aperture used in the calculation, that is, EF / 2 = D200 / 2 = 0.5 mm, and take CM = 0.6 mm, so as to obtain the models P2 - P7 of the six microlenses 200 in the negative microlens array 20 that can be used for structural resection.

[0074] Use the Boolean object to perform subtraction to obtain the lens obtained by resection of P2 - P7 on P1. Its Boolean object expression is: , It should be noted that the back surface of the microlens of the microstructure lens based on positive refractive power for comparison is a plane, so use the Boolean object addition to combine P1 - P7.

[0075] Hide the master mirror and the microlens except the Boolean object to complete the optical modeling, as Figure 8The figure shows a partial schematic diagram of the physical model of a microstructured lens with a built-in negative microlens array 20. To better analyze the influence of the negative microlens array 20, the maximum field of view range in the system is adjusted to -16.5°, and the pupil radius is 1.4 mm. At this time, the light rays in the maximum field of view can just completely cover six microlenses 200 in the negative microlens array 20, and the vitreous body thickness of the Liou eye model is refocused and optimized again.

[0076] S40: Select the maximum field of view that completely covers the microlenses in the 3D model of the microstructured lens under different sagittal height variations, and record the modulation transfer function values on the retina of the myopia model for the microstructured lenses with H = 1μm, 2μm, 4μm, 6μm, 8μm, and 10μm respectively (the modulation transfer function values in this embodiment are the means of the modulation transfer function values in the meridional and sagittal directions), as shown in Table 7 for the modulation transfer function values corresponding to some spatial frequencies under different sagittal height variations: Table 7

[0077] S50: Analyze the variation trend between the modulation transfer function values and the sagittal height variation to obtain a quantitative model of the modulation transfer function with respect to the sagittal height variation and spatial frequency; analyze the spatial frequency limit value at which the negative microlens array 20 reduces the modulation transfer function value; compare the reduction effects of the microstructured lenses based on positive refractive power and those based on negative refractive power on the modulation transfer function value under the same sagittal height variation, which specifically includes: S500: Use Matlab software to fit the quantitative model of the modulation transfer function value with respect to the sagittal height variation and spatial frequency, which specifically includes: As Figure 9 shown is a schematic diagram of the modulation transfer function curves for spatial frequencies from 0 to 35 lp / mm when the sagittal height variation is 1μm, 2μm, 4μm, 6μm, 8μm, and 10μm. It can be seen from the figure that as the sagittal height variation increases, the decline rate of the modulation transfer function value accelerates, and the modulation transfer function curves when H = 6μm, 8μm, and 10μm tend to be close.

[0078] Since the spatial frequencies at which the obtained modulation transfer function values are used are at intervals, the intervals are small and the data volume is large. Using traditional exponential or logarithmic forms and a binary equation with independent sagittal height variation and spatial frequency cannot effectively fit the undulating characteristics of the curve. For example: using or such curve types to obtain the regression relationship, the corresponding correlation coefficients are all lower than 0.76; even after adding some correlation terms it is still lower than 0.9.

[0079] From Figure 9 it can be observed that: 1. There is an approximate horizontal scaling relationship between the curves, that is, the curves with the sag height change from 1 to 8 μm can all be obtained by intercepting a section of the curve with a sag height change of 10 μm and stretching it horizontally. 2. The modulation transfer function values at the first minimum point of the curves all approach 0.2, and it can be approximately considered that there is no scaling relationship longitudinally. Based on the above observations, in order to obtain a regression relationship that more conforms to the actual situation, the following steps are adopted in this embodiment to fit the relationship between the modulation transfer function value, the sag height change, and the spatial frequency.

[0080] Step 1: Use the curve with the most features (i.e., the highest fluctuation frequency) to establish a polynomial equation of the modulation transfer function without the scaling ratio with respect to the normalized spatial frequency: Perform a univariate fitting of the spatial frequency on the curve with a sag height change of 10 μm, which has the largest horizontal compression degree and retains the most features, to obtain a polynomial equation of the modulation transfer function with respect to the normalized spatial frequency. In this embodiment, it is found that a high-order fraction can best retain the first oscillation of the curve with a small number of parameters and fit the subsequent small fluctuations as much as possible. The polynomial equation is: , where, represents the polynomial equation of the modulation transfer function with respect to the normalized spatial frequency; represents the normalized spatial frequency; represents the first correlation coefficient; represents the second correlation coefficient; represents the third correlation coefficient; represents the fourth correlation coefficient; represents the fifth correlation coefficient; represents the sixth correlation coefficient.

[0081] Specifically, after performing a univariate fitting on the curve with a sag height change of 10 μm in this embodiment, the obtained polynomial equation is , and the correlation coefficient = 0.994 between the modulation transfer function and the normalized spatial frequency. It can be seen that the polynomial equation provided in this embodiment can well fit the modulation transfer function curve and be further extended to a bivariate fitting. As Figure 10 shown in the schematic diagram of the comparison between the modulation transfer function curve and the fitting result when the sag height change is 10 μm, the solid line in the figure is the fitting data, and the dotted line is the actual data.

[0082] Step 2: Use the ratio between the spatial frequencies at the minimum points on the curve with the most features (i.e., the highest fluctuation frequency) to determine the scaling ratio and normalize the spatial frequency. Specifically, it includes: From Figure 9It can be found that as the change in sagittal height increases, the spatial frequency of the first minimum point on the modulation transfer function curve decreases accordingly. Figure 11 In (a) of Figure 11 , the first minimum points with sagittal height changes of H = 1μm, 2μm, and 10μm are marked. Based on this, the ratio between the spatial frequencies of the first minimum points on the curve is used for the calculation of the horizontal scaling ratio. To improve the accuracy of the scaling ratio calculation, in this embodiment, the steps in S20 to S40 are used to add some negative microstructure arrays with changes in sagittal height for modeling. The modeling of the microstructure lens is completed for sagittal height changes of 1μm to 10μm (at intervals of 1μm) and 12μm, 15μm, and 20μm, and the spatial frequencies of the first minimum points on the corresponding modulation transfer function curves are recorded, obtaining the results shown in (a) of Figure 11 ; by analyzing and fitting the spatial frequencies of the first minimum points on each curve with the change in sagittal height, the fitting results shown in (b) of Figure 11 are obtained. It can be seen from the figure that the spatial frequency of the first minimum point on the curve shows a decreasing trend with a decreasing rate of decrease with the change in sagittal height. After fitting, it is confirmed that the fitting degree is high, and in this embodiment, it is found that the form of relatively gradual change is a power function curve, and the correlation coefficient between the spatial frequency of the minimum point and the change in sagittal height is greater than 0.999.

[0083] Specifically, the relationship equation between the spatial frequency of the minimum point of the modulation transfer function curve fitted in this embodiment and the change in sagittal height is expressed as: , where represents the relationship equation between the spatial frequency of the minimum point and the change in sagittal height; represents the change in sagittal height; represents the correlation coefficient between the spatial frequency of the minimum point and the change in sagittal height.

[0084] The sagittal height change of 10μm corresponding to the curve with the most features is input into the relationship equation between the spatial frequency of the minimum point and the change in sagittal height to calculate the spatial frequency of the minimum point corresponding to a sagittal height change of 10μm. Based on the ratio between the spatial frequency of the minimum point corresponding to a sagittal height change of 10μm and the relationship equation between the spatial frequency of the minimum point and the change in sagittal height, the spatial frequency scaling ratio equation is obtained.

[0085] The spatial frequency is normalized using the spatial frequency scaling ratio equation to obtain the following normalized spatial frequency equation: .

[0086] Step 3: Substitute the normalized spatial frequency equation into the polynomial equation of the modulation transfer function with respect to the normalized spatial frequency as the independent variable, and obtain the following fitting objective formula: , Perform a binary fit on the above fitting objective formula and the modulation transfer function curves (taking values at intervals of 0.5 lp / mm) of the 0 - 35 lp / mm spatial frequency at H = 1μm, 2μm, 4μm, 6μm, 8μm, and 10μm. After simplification, obtain the quantization model of the modulation transfer function with respect to the change in sagittal height and spatial frequency: , , where, represents the modulation transfer function value.

[0087] The fitting effect of this quantization model is good, and the correlation coefficient = 0.9722. Using this quantization model, the modulation transfer function values in the visible segment range with the change in sagittal height from 0 to 10μm and the modulation transfer function values in the core feature frequency band with the change in sagittal height above 10μm can be determined with relatively high precision (taking values at intervals of 0.5 lp / mm). As Figure 12 shown is a comparison schematic diagram of the actual data of the modulation transfer function with respect to the change in sagittal height and spatial frequency and the binary fitting result. The surface in the figure is the fitting result, and the points represent the actual data.

[0088] Step 4: Verify the quantization model, which specifically includes: Obtain the modulation transfer function curve of the optical system of the microstructured lens three-dimensional model with the change in sagittal height H being 15μm. Then substitute the change in sagittal height H = 15μm into the quantization model, and based on the output of the quantization model, obtain the predicted modulation transfer function curve when the change in sagittal height H = 15μm. As Figure 13 shown is a comparison schematic diagram of the actual modulation transfer function value and the modulation transfer function value obtained from the quantization model when the change in sagittal height is 15μm. The curve in the figure represents the predicted modulation transfer function curve, and the dotted line represents the actual modulation transfer function curve.

[0089] S501: Analyze the reduction effect threshold of the modulation transfer function value of the negative microlens array 20 on the microstructured lens at different changes in sagittal height from the perspective of spatial frequency, which specifically includes: It can be seen from Figure 11 that the modulation transfer function curves corresponding to different changes in sagittal height all drop to about 0.2 at the spatial frequency of the first minimum point. At this time, the imaging effect has dropped to a relatively poor level. Therefore, the effect of different changes in sagittal height on reducing contrast is manifested as the spatial frequency size at which the modulation transfer function value drops to the minimum value of 0.2. It should be noted that through Figure 11Through analysis, the present application discovers that the spatial frequency of the first minimum point on the modulation transfer function curve can also be used as an evaluation index for the imaging contrast suppression effect of the lens.

[0090] Therefore, when the sagittal height change amount H approaches positive infinity, the theoretical limit value of the spatial frequency at which the modulation transfer function value reduces the contrast to a low imaging level under the action of the sagittal height change amount can be obtained, and its calculation formula is: , , Therefore, it can be considered that under the action of the sagittal height change amount H, the theoretical spatial frequency threshold for the reduction effect of the imaging contrast is approximately When, the spatial modulation transfer function drops to 0.2; while at H = 2μm, 5μm, 10μm, 15μm, and 20μm, calculated by the above quantitative model, the spatial frequencies of the minimum points are 12.807 , 5.826 , 3.696 , 3.028 and , it can be seen that starting from H = 10μm, the change in the spatial frequency of the minimum point tends to be gentle and is already very close to the theoretical threshold of the spatial frequency of the minimum point. The effect of choosing a sagittal height change amount higher than H = 20μm to reduce the contrast is not significant, and there are also problems such as increasing the processing difficulty and affecting the lens aesthetics. Therefore, H = 10μm - 20μm is the appropriate value range for the sagittal height change amount threshold.

[0091] In summary, according to the relationship between the spatial frequency of the minimum point and the sagittal height change amount in the quantitative model, after obtaining the theoretical threshold of the spatial frequency at which the contrast reduces to a low imaging level under the limit sagittal height change amount, by comparing with the spatial frequency of the minimum point under any sagittal height change amount, the appropriate sagittal height change amount threshold, that is, the appropriate structural parameter value of the microstructured lens, can be conveniently determined.

[0092] S502: Compare the reduction effects of the negative microlens array and the positive microlens array on the MTF under the same sagittal height change amount: Take the sagittal height change amount H = 6μm, calculate the parameters required for modeling using the structural parameters of the positive microlens array shown in Table 3, and establish a three-dimensional model of the microstructured lens as shown in Figure 8 . Optionally, three arrangement methods can be adopted. The first is that all six microlenses in the microlens array are positive microlenses. The second is that half of the six microlenses in the microlens array are positive microlenses and half are negative microlenses, and the positive microlenses and negative microlenses are arranged in sequence. The third is that the six microlenses in the microlens array are arranged with positive and negative microlenses staggered. The second and third arrangement methods are as shown in Figure 14 and Figure 15As shown in the figure, the hatched part in the figure represents negative microlenses, and the unhatched part is positive microlenses.

[0093] Combined with the modulation transfer function values of the all-negative microlens array arrangement with the sagittal height change amount H = 6μm obtained in step S40, analyze the modulation transfer function values of the maximum field of view under the four arrangements: when the sagittal height change amount H = 6μm, as Figure 16 shown are the modulation transfer function curves of all-negative microlenses, all-positive microlenses, half-positive and half-negative, and positive and negative staggered microstructures with the same diameter. Table 8 shows the modulation transfer function values of all-positive lenses and all-negative lenses at six spatial frequencies, and the reduction rate of the modulation transfer function value of all-negative microlenses relative to all-positive microlenses.

[0094] Table 8

[0095] From Figure 16 it can be seen that the effect of all-negative microlenses in suppressing retinal contrast in the visible segment is much greater than that of all-positive microlenses; moreover, by calculating the data shown in Table 8, it is found that: the average reduction rate of the modulation transfer function value of all-negative microlenses relative to all-positive microlenses at six spatial frequencies is about 55%. In addition, the effect of the half-positive and half-negative and positive and negative staggered microlens arrangements in suppressing retinal contrast is also much better than that of the all-positive microlens form, and the effect of all-negative microlenses in suppressing retinal contrast is significantly better than that of the half-positive and half-negative and positive and negative staggered arrangements. Therefore, the following conclusion is drawn in this embodiment: adding half or more negative microlenses to the microstructure can obtain an effect of reducing retinal contrast that is much greater than that of all-positive microlenses.

[0096] Obviously, the above embodiments are only examples clearly described and are not limitations on the implementation manners. For those of ordinary skill in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation manners here. And the obvious changes or modifications derived therefrom are still within the protection scope of the present invention.

Claims

1. A method for designing a microstructure optical imaging element, characterized in that: include: Based on the structural parameters of the mother lens and the structural parameters of the negative microlens array under different sag changes, a three-dimensional model of the microstructure lens under different sag changes is constructed. Obtaining a modulation transfer function curve of an optical system including each three-dimensional model of a microstructure lens, and a spatial frequency of the first minimum point on each modulation transfer function curve; Fit the spatial frequency of the first minimum point on each modulation transfer function curve and its corresponding vector height change to obtain the relationship equation between the spatial frequency of the minimum point and the vector height change; Based on the relationship equation between the spatial frequency and the change in vector height at the minimum point, the spatial frequency limit value when the image contrast of the microstructure lens is lower than the preset minimum contrast when the change in vector height is infinite is obtained; With the goal of making the spatial frequency of the minimum point greater than or equal to the spatial frequency limit value, the equation of the relationship between the spatial frequency of the minimum point and the vector height change is solved, and the value range of the vector height change threshold of the microstructure lens based on negative refractive power is obtained.

2. The method for designing a microstructure optical imaging element according to claim 1, characterized in that: After obtaining the value range of the vector height change threshold value of the microstructure lens based on negative refractive power, it also includes: The modulation transfer function curve with the largest fluctuation frequency among the modulation transfer function curves of the three-dimensional models of the microstructure lens is used as the target modulation transfer function curve, and the vector height change amount corresponding to the target modulation transfer function curve is used as the target vector height change amount; Performing a spatial frequency univariate fitting on the target modulation transfer function curve to obtain a polynomial equation of the modulation transfer function with respect to the normalized spatial frequency; Based on the target vector height variation and the relationship equation between the spatial frequency of the minimum point and the vector height variation, a spatial frequency scaling ratio equation is obtained; based on the spatial frequency scaling ratio equation, the spatial frequency is normalized to obtain a normalized spatial frequency equation; After substituting the normalized spatial frequency equation into the polynomial equation of the modulation transfer function with respect to the spatial frequency, the modulation transfer function curve of the three-dimensional model of the microstructure lens under different vector height changes is fitted to obtain the quantitative model of the modulation transfer function with respect to the vector height change and the spatial frequency; Based on the value range of the vector height change threshold, the value range of the vector height change is obtained, and the modulation transfer function value of the vector height change of the micro-structure lens based on negative refractive power at each value within the value range is calculated using a quantitative model; the vector height change with the smallest modulation transfer function value is taken as the optimal vector height change of the micro-structure lens based on negative refractive power.

3. The method for designing a microstructure optical imaging element according to claim 2, characterized in that: The optimal sagittal height change of the microstructure lens based on negative refractive power also includes: Obtain the optimal structural parameters of the negative microlens array under the optimal vector height variation; Based on the structural parameters of the mother lens, the optimal structural parameters of the negative microlens array and the microstructure arrangement type, a microstructure lens with negative refractive power is designed.

4. The method for designing a microstructure optical imaging element according to claim 2, characterized in that: Based on the relationship equation between the target vector height change and the spatial frequency of the minimum point and the vector height change, the spatial frequency scaling ratio equation is obtained, including: Input the target vector height variation into the relationship equation between the spatial frequency of the minimum point and the vector height variation, and calculate the spatial frequency of the minimum point corresponding to the target vector height variation; Based on the ratio of the spatial frequency of the minimum point corresponding to the target vector height change and the relationship equation between the spatial frequency of the minimum point and the vector height change, the spatial frequency scaling ratio equation is obtained.

5. The method for designing a microstructure optical imaging element according to claim 1, characterized in that: The relationship between the spatial frequency of the minimum point and the change in vector height is expressed as: ， in, The equation that represents the relationship between the spatial frequency of the minimum point and the change in vector height; Indicates the change in vector height; Represents the correlation coefficient between the spatial frequency of the minimum point and the change in vector height; The calculation formula for the spatial frequency limit is: ， ， in, Indicates the spatial frequency limit.

6. The method for designing a microstructure optical imaging element according to claim 4, characterized in that: The polynomial equation for the modulation transfer function with respect to normalized spatial frequency is expressed as: ， in, A polynomial equation representing the modulation transfer function with respect to spatial frequency; represents the normalized spatial frequency; represents the first correlation coefficient; represents the second correlation coefficient; represents the third correlation coefficient; represents the fourth correlation coefficient; represents the fifth correlation coefficient; represents the sixth correlation coefficient; The normalized spatial frequency equation is expressed as: ， in, represents the normalized spatial frequency; represents the spatial frequency; represents the spatial frequency scaling ratio; Indicates the target height change The spatial frequency of the corresponding minimum point.

7. The method for designing a microstructure optical imaging element according to claim 6, characterized in that: The quantitative model is expressed as: ， ， in, Represents the modulation transfer function value.

8. The method for designing a microstructure optical imaging element according to claim 1, characterized in that: The process of obtaining the structural parameters of the mother mirror includes: Based on the spherical power and the preset front surface power of the mother lens, the rear surface power of the mother lens is calculated; Based on the refractive index of the mother mirror material, the optical focal length of the front surface of the mother mirror and the optical focal length of the back surface of the mother mirror, the curvature radius of the front surface of the mother mirror and the curvature radius of the back surface of the mother mirror are calculated.

9. The method for designing a microstructure optical imaging element according to claim 8, characterized in that: The process of obtaining the structural parameters of the negative microlens array under different vector height changes includes: Based on the sagittal height variation and the sagittal height of the mother lens, the sagittal height of the microlens in the negative microlens array is calculated, and based on the sagittal height of the microlens, the radius of curvature of the microlens is calculated; Arrange the mother lens and the negative microlens array based on a preset microstructure arrangement type to obtain the position parameters of the center point of the negative microlens array; Based on the position parameters of the center of curvature of the mother lens and the center point of the negative microlens array, the center of curvature position and the tilt angle of the microlens in the negative microlens array are calculated.

10. A microstructure optical imaging element, characterized in that: The microstructure optical imaging element is designed by the microstructure optical imaging element design method according to any one of claims 1 to 9.

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