A design method for a microstructured optical imaging element and a microstructured optical imaging element

Abstract

The present invention belongs to the technical field of ophthalmic optics, and relates to a design method of a micro-structured optical imaging element and a micro-structured optical imaging element. Based on the structural parameters of the master mirror and the structural parameters of the negative microlens array under different sagittal height variation amounts, a three-dimensional model of the micro-structured lens under different sagittal height variation amounts is constructed; the modulation transfer function curve of the optical system including each three-dimensional model of the micro-structured lens and the spatial frequency of the first minimum point on each modulation transfer function curve are obtained; the spatial frequencies of all the first minimum points and their corresponding sagittal height variation amounts are fitted to obtain the relationship equation between the spatial frequency of the minimum point and the sagittal height variation amount; based on the relationship equation between the spatial frequency of the minimum point and the sagittal height variation amount, the spatial frequency limit value when the imaging contrast of the micro-structured lens is lower than the preset minimum contrast when the sagittal height variation amount is infinite is obtained, thereby obtaining the value range of the sagittal height variation threshold, providing a theoretical basis for the design of the micro-structured 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 method for designing a microstructure optical imaging element and a microstructure optical imaging element. Background Art

[0002] Based on the contrast principle, myopia control frame glasses can effectively slow down the deepening of myopia degree 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 point diffusion myopia control (Diffusion Optics Technology, DOT) technology is mostly used, that is, the incident light is slightly scattered through translucent dot-shaped blurring microstructures to reduce the contrast of the retina. However, this translucent dot-shaped structure is obvious on the lens surface and can be observed with 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 negative refractive power microstructure lens can also reduce the retinal imaging contrast, not only achieving the effect of myopia management but also maintaining the high quality of the lens appearance.

[0003] Such as Figure 1 shows a schematic diagram of several layout styles of negative refractive power microstructure lenses, Figure 2 shows a schematic diagram of the structure of a negative refractive power microstructure lens. The negative refractive power microstructure lens is composed of a mother lens 10 and multiple negative microlens arrays 20. Each negative microlens array 20 contains multiple 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 microstructure lens. By changing the sagittal height change amount of the microstructure lens, the imaging contrast of the lens on the retina can be changed. Since there is currently little research on negative refractive power microstructure lenses, there is a lack of theoretical guidance for the selection of the sagittal height change amount parameter of negative refractive power microstructure lenses. How to find the value range of the sagittal height change amount that has an inhibitory effect on the imaging contrast and takes 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 negative refractive power microstructure lenses, and then design a microstructure lens that can meet the requirements of imaging contrast, appearance, and processing cost is the problem that needs to be solved currently.

[0004] When changing the sagittal height variation of the microstructure lens, structural parameters such as the radius of curvature 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 models of the microstructure lens under different sagittal height variations, it is judged 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 cost and computing power cost, and the efficiency is low; moreover, since the sagittal height variation cannot exhaust 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 the 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 the parameter selection in the design of the microstructure lens based on negative refractive power is a problem that needs to be solved currently.

[0007] To solve the above technical problem, the present invention provides a method for designing a microstructure optical imaging element, including:

[0008] Construct a three-dimensional model of the microstructure lens under different sagittal height variations based on the structural parameters of the master mirror and the structural parameters of the negative microlens array under different sagittal height variations;

[0009] Obtain the modulation transfer function curve of the optical system containing each three-dimensional model of the microstructure lens, and the spatial frequency of the first minimum point on each modulation transfer function curve;

[0010] Fit the spatial frequency of the first minimum point on each modulation transfer function curve and its corresponding sagittal height variation to obtain the relationship equation between the spatial frequency of the minimum point and the sagittal height variation;

[0011] Based on the relationship equation between the spatial frequency of the minimum point and the sagittal height variation, 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 is infinite;

[0012] 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.

[0013] 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:

[0014] 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;

[0015] 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;

[0016] 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;

[0017] 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;

[0018] 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.

[0019] Preferably, after the optimal sagittal height change amount of the microstructure lens based on negative refractive power, it further includes:

[0020] Obtain the optimal structural parameters of the negative microlens array at the optimal sagittal height change amount;

[0021] 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.

[0022] 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:

[0023] Input the spatial frequency corresponding to the minimum value point of the target sag variation into the relationship equation between the spatial frequency and the sag variation, and calculate the spatial frequency corresponding to the minimum value point of the target sag variation;

[0024] Based on the ratio of the spatial frequency corresponding to the minimum value point of the target sag variation to the relationship equation between the spatial frequency of the minimum value point and the sag variation, obtain the spatial frequency scaling ratio equation.

[0025] Preferably, the relationship equation between the spatial frequency of the minimum value point and the sag variation is expressed as:

[0026] ,

[0027] where, represents the relationship equation between the spatial frequency of the minimum value point and the sag variation; represents the sag variation; represents the correlation coefficient between the spatial frequency of the minimum value point and the sag variation;

[0028] The calculation formula for the spatial frequency limit value is:

[0029] ,

[0030] ,

[0031] where, represents the spatial frequency limit value.

[0032] Preferably, the polynomial equation of the modulation transfer function with respect to the normalized spatial frequency is expressed as:

[0033] ,

[0034] 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;

[0035] The normalized spatial frequency equation is expressed as:

[0036] ,

[0037] where, represents the normalized spatial frequency; represents the spatial frequency; represents the spatial frequency scaling ratio; represents the change in the target sagittal height The spatial frequency of the corresponding minimum point.

[0038] Preferably, the quantization model is expressed as:

[0039] ,

[0040] ,

[0041] where, represents the modulation transfer function value.

[0042] Preferably, the process of obtaining the structural parameters of the mother mirror includes:

[0043] Based on the spherical power and the preset front surface optical power of the mother mirror, calculate the rear surface optical power of the mother mirror;

[0044] Based on the refractive index of the mother mirror material, the front surface optical power of the mother mirror, and the rear surface optical power of the mother mirror, calculate the front surface curvature radius and the rear surface curvature radius of the mother mirror.

[0045] Preferably, the process of obtaining the structural parameters of the negative microlens array under different sagittal height changes includes:

[0046] Based on the sagittal height change and the mother mirror sagittal height, calculate the microlens sagittal height in the negative microlens array, and calculate the curvature radius of the microlens based on the microlens sagittal height;

[0047] Arrange the mother mirror and the negative microlens array based on the preset microstructure arrangement type to obtain the position parameters of the center point of the negative microlens array;

[0048] Based on the position parameters of the curvature center of the mother mirror and the center point of the negative microlens array, calculate the curvature center position and tilt angle of the microlens in the negative microlens array.

[0049] The present invention also provides a microstructure optical imaging element, which is designed by the above-mentioned design method of the microstructure optical imaging element based on negative refractive power.

[0050] The design method of the microstructure optical imaging element based on negative refractive power provided by the present application has the following beneficial effects:

[0051] 1. First, use the three-dimensional models of microstructured lenses with different sagittal height variations to reflect the actual shapes and optical characteristics of microstructured 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 microstructured lens. Since the first minimum point on the curve represents the position where the performance of the microstructured 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 microstructured 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 microstructured 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 microstructured 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 on reducing the imaging contrast of the microstructured 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 a microstructured lens based on negative refractive power.

[0052] 2. Since the modulation transfer function curve of a lens with 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, 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 vertically. 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 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 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 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 quantitative model of the modulation transfer function with respect to the change in sagittal height and spatial frequency can be obtained, thereby using this quantitative model to evaluate the imaging contrast of the microstructure lens with negative refractive power when the change in sagittal height takes different values, and thus optimizing the microstructure lens with negative refractive power, further improving the design efficiency of the microstructure lens with negative refractive power. Moreover, the quantitative 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 spatial frequencies. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] In order to make the content of the present invention easier to be clearly understood, the following further details the present invention according to specific embodiments of the present invention in conjunction with the accompanying drawings, where:

[0054] Figure 1 It is a schematic diagram of the layout style of the microstructure lens provided by this application; among them, Figure 1 (a) in it is a schematic diagram of the first layout style, Figure 1 (b) in it is a schematic diagram of the second layout style, Figure 1 (c) in it is a schematic diagram of the third layout style, Figure 1 (d) in it is a schematic diagram of the fourth layout style;

[0055] Figure 2 It is a schematic diagram of the structure type on the surface of a microstructure lens provided by this application and the division of each structure area;

[0056] Figure 3 Flowchart of the microstructure lens design method based on negative refractive power provided for this application;

[0057] Figure 4 Position projection of the vertices of the hexagonal grid negative microlens array provided for an embodiment of this application on the vertex section of the master mirror;

[0058] Figure 5 Schematic diagram of the calculation principle of the curvature center of the microlenses in the negative microlens array provided for an embodiment of this application;

[0059] Figure 6 Schematic diagram of the calculation principle of the curvature center of the microlenses in the positive microlens array provided for an embodiment of this application;

[0060] Figure 7 Schematic diagram of the optical path formed by the master mirror and the myopia model eye provided for an embodiment of this application;

[0061] Figure 8 Partial schematic diagram of the constructed microstructure lens solid model provided for an embodiment of this application;

[0062] Figure 9 Schematic diagram for comparing modulation transfer function curves corresponding to different sagittal height change amounts provided for an embodiment of this application;

[0063] Figure 10 Schematic diagram for comparing the modulation transfer function curve with the fitting result when the sagittal height change amount is 10 μm provided for an embodiment of this application;

[0064] 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 sagittal height change amount provided for an embodiment of this application; where 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 sagittal height change amount;

[0065] Figure 12 Schematic diagram for comparing the actual data of the modulation transfer function with respect to the sagittal height change amount and spatial frequency with the binary fitting result provided for an embodiment of this application;

[0066] 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 sagittal height change amount is 15 μm provided for an embodiment of this application;

[0067] Figure 14 Schematic diagram of the arrangement of a microlens array with a combination of positive and negative microlenses provided for an embodiment of this application;

[0068] Figure 15 This is a schematic diagram of the arrangement of a microlens array of another positive and negative microlens combination provided by the embodiment of the present application;

[0069] Figure 16 This is a schematic diagram for comparing the modulation transfer function curves of a microstructure lens based on positive refractive power and a microstructure lens based on negative refractive power provided by the embodiment of the present application;

[0070] Explanation of the reference numerals in the drawings of the specification: 1, central fovea region; 10, master lens; 2, regulation region; 20, negative microlens array; 200, microlens. Detailed implementation manners

[0071] The present invention will be further described below in conjunction with the accompanying 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 do not limit the present invention.

[0072] As Figure 1 shown is a schematic diagram of the layout styles of several microstructure lenses provided by the present application; among them, Figure 1 in (a) is a schematic diagram of the first layout style, Figure 1 in (b) is a schematic diagram of the second layout style, Figure 1 in (c) is a schematic diagram of the third layout style, Figure 1 in (d) is a schematic diagram of the fourth layout style. It should be noted that when designing a microstructure 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.

[0073] Figure 2 For Figure 1As shown in (a) of [reference], it is a schematic diagram of the structural type of the microstructure lens surface and the division of regions to which each structure belongs. It can be seen that the microstructure lens structurally includes a central clear vision area 1 and a regulation area 2. Among them, the central clear vision area 1 includes a master lens 10, and the regulation area 2 includes a plurality of negative microlens arrays 20 and a part of the master lens 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. It should be noted that at least half of the microlenses 200 in the negative microlens array 20 are negative microlenses. The amount of change in the sagittal height of the microstructure lens refers to the distance from the vertex of the arc surface of the master lens 10 to the vertex of the arc surface of the microlens 200 in the negative microlens array 20. When the amount of change in the sagittal height of the microstructure lens changes, the structural parameters of the microlenses 200 in the negative microlens array 20 will change, and the imaging contrast of the microstructure lens will also change. Therefore, if one wants to obtain a range of values for the amount of change in the sagittal height 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 values of the amount of change in the sagittal height, thereby modeling the microstructure lens under different amounts of change in the sagittal height, and judging whether the microstructure lens under the current amount of change in the sagittal height has an imaging contrast inhibitory effect through this model, and comparing the appearance and processing cost of the lenses under different amounts of change in the sagittal height. 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 values for the amount of change in the sagittal height that makes the microstructure lens based on negative refractive power have an inhibitory effect on contrast and meets the requirements of appearance and processing cost.

[0074] In order to more effectively and efficiently obtain the threshold value of the amount of change in the sagittal height that makes the microstructure lens based on negative refractive power have an inhibitory effect on contrast, does not affect the appearance of the lens, and takes into account the lens processing cost, thereby providing theoretical guidance for the design of the microstructure lens based on negative refractive power, the present application proposes the following method.

[0075] Please refer to Figure 3 , Figure 3 which is a flowchart of the method for designing a microstructure optical imaging element provided by the present application. The method specifically includes:

[0076] S1: Based on the structural parameters of the master lens and the structural parameters of the negative microlens array under different amounts of change in the sagittal height, construct a three-dimensional model of the microstructure lens under different amounts of change in the sagittal height.

[0077] Specifically, the amount of change in the sagittal height refers to the distance from the vertex of the arc surface of the master lens to the vertex of the arc surface of the microlens in the negative microlens array.

[0078] Optionally, in some embodiments of the present application, a three-dimensional model of the microstructure lens under each amount of change in the sagittal height can be constructed based on the structural parameters of the master lens and the structural parameters of the negative microlens array when the amount of change in the sagittal height takes different values in the range of 1 to 10 μm.

[0079] S2: Obtain the modulation transfer function curve of the optical system including the three-dimensional models of each microstructure lens, and the spatial frequency of the first minimum point on each modulation transfer function curve.

[0080] S3: Fit the spatial frequency of the first minimum point on each modulation transfer function curve and its corresponding sag height change amount to obtain the relationship equation between the spatial frequency of the minimum point and the sag height change amount.

[0081] S4: Based on the relationship equation between the spatial frequency of the minimum point and the sag height change amount, obtain the spatial frequency limit value when the imaging contrast of the microstructure lens is lower than the preset minimum contrast when the sag height change amount is infinite.

[0082] S5: Aim at the spatial frequency of the minimum point being greater than or equal to the spatial frequency limit value, solve the relationship equation between the spatial frequency of the minimum point and the sag height change amount to obtain the value range of the sag height change amount threshold of the microstructure lens based on negative refractive power.

[0083] Further, the relationship equation between the spatial frequency of the minimum point and the sag height change amount is expressed as:

[0084] ,

[0085] where, represents the relationship equation between the spatial frequency of the minimum point and the sag height change amount; represents the sag height change amount; represents the correlation coefficient between the spatial frequency of the minimum point and the sag height change amount;

[0086] The calculation formula for the spatial frequency limit value is:

[0087] ,

[0088] ,

[0089] where, represents the spatial frequency limit value.

[0090] This application uses the three-dimensional models of microstructure lenses with different sagittal height variation amounts to reflect the actual shapes and optical characteristics of microstructure lenses based on negative refractive power at different sagittal height variation amounts; obtains the modulation transfer function curves of the optical system containing each three-dimensional model of the microstructure lens. Since the first minimum point on the curve represents the position where the microstructure lens begins to show obvious performance changes 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 amount, the relationship equation between the spatial frequency of the minimum point and the sagittal height variation amount can be constructed, so as to obtain the internal relationship between the spatial frequency and the sagittal height variation amount. Since when the sagittal height variation amount approaches infinity, under the action of the sagittal height variation amount, 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 amount 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 amount approaches infinity. This spatial frequency limit value defines the limit performance that the microstructure lens can achieve under the given imaging contrast requirement; 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 amount when the imaging contrast requirement is met, so as to select the sagittal height variation amount within this feasible interval to design a microstructure lens based on negative refractive power that has an inhibitory effect on imaging contrast. Through limited modeling and data simulation, this application obtains the value range of the sagittal height variation amount threshold, providing a theoretical basis for the selection of the sagittal height variation amount in the design of microstructure lenses based on negative refractive power.

[0091] Since a higher sagittal height variation amount has little effect on reducing the imaging contrast of the microstructure lens, and will also increase the processing difficulty and affect the lens aesthetics, therefore, there is no need to select a larger sagittal height variation amount outside this feasible interval during design. This application obtains the value range of the sagittal height variation amount threshold that takes into account the inhibitory effect on 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 imaging contrast, the maximum value of the sagittal height variation amount only needs to be within this range, improving the design efficiency of the microstructure lens. It is worth noting that the design method provided in this application can also be extended to the design of microstructure parameters other than the sagittal height variation amount, such as diameter, filling rate and surface shape, etc.

[0092] 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 change in sagittal height and spatial frequency. However, the microstructure lens often has a complex arrangement and a variable surface shape. Therefore, the modulation transfer function value may show a fluctuating downward 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.

[0093] 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) through 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.

[0094] Specifically, after step S5, it further includes:

[0095] S6: Use the modulation transfer function curve with the largest fluctuation frequency as the target modulation transfer function curve, and use the change in sagittal height corresponding to the target modulation transfer function curve as the target change in sagittal height.

[0096] S7: Perform a univariate 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.

[0097] Specifically, the polynomial equation of the modulation transfer function with respect to the normalized spatial frequency is expressed as:

[0098] ,

[0099] 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.

[0100] S8: Based on the relationship equation between the target sagittal height change and the spatial frequency of the minimum point and the sagittal height change, 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.

[0101] 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 change and the spatial frequency of the minimum point and the sagittal height change includes:

[0102] Input the target sagittal height change into the relationship equation between the spatial frequency of the minimum point and the sagittal height change, and calculate the spatial frequency of the minimum point corresponding to the target sagittal height change;

[0103] Based on the ratio of the spatial frequency of the minimum point corresponding to the target sagittal height change to the relationship equation between the spatial frequency of the minimum point and the sagittal height change, obtain the spatial frequency scaling ratio equation.

[0104] Specifically, the normalized spatial frequency equation is expressed as:

[0105] ,

[0106] where, represents the normalized spatial frequency; represents the spatial frequency; represents the spatial frequency scaling ratio; represents the target sagittal height change corresponding to the spatial frequency of the minimum point.

[0107] 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 changes to obtain the quantization model of the modulation transfer function with respect to the sagittal height change and the spatial frequency.

[0108] Specifically, the quantization model is expressed as:

[0109] ,

[0110] ,

[0111] where, represents the modulation transfer function value.

[0112] S10: Based on the value range of the sagittal height change threshold, obtain the value range of the sagittal height change, and use the quantization model to calculate the modulation transfer function values at each value within the value range of the sagittal height change of the microstructure lens based on negative refractive power; take the sagittal height change with the minimum modulation transfer function value as the optimal sagittal height change of the microstructure lens based on negative refractive power.

[0113] Furthermore, after the optimal sagittal height variation of the microstructure lens based on negative refractive power, it further includes:

[0114] Obtaining the optimal structural parameters of the negative microlens array under the optimal sagittal height variation;

[0115] Based on the structural parameters of the master mirror, the optimal structural parameters of the negative microlens array, and the microstructure arrangement type, a microstructure lens based on negative refractive power is designed.

[0116] 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 sagittal height variation. However, this application discovers that there is an approximate horizontal scaling relationship between the modulation transfer function curves corresponding to different sagittal height variations, and there is no scaling relationship longitudinally. Therefore, the modulation transfer function curve with a larger fluctuation frequency can better reflect the optical property changes 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 sagittal height variation as the target sagittal height variation; 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; 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 sagittal height variation and the spatial frequency of the minimum value point to normalize the spatial frequency to obtain a normalized spatial frequency equation, eliminating the influence of the sagittal height variation on the spatial frequency scale, enabling the modulation transfer functions corresponding to different sagittal height variations to be compared under a unified spatial frequency scale. Fitting the normalized spatial frequency equation with the modulation transfer function curves corresponding to different sagittal height variations can obtain a quantization model of the modulation transfer function with respect to the sagittal height variation and spatial frequency, thereby using this quantization model to evaluate the imaging contrast of the microstructure lens for different values of the sagittal height variation, and thus optimizing the microstructure lens. The method provided in this application uses the modulation transfer function curves of the microstructure lens with a small number of sagittal height variations to obtain a high-precision quantization model, 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 full-band effects of spatial frequencies.

[0117] Furthermore, the process of obtaining the structural parameters of the master mirror in step S1 includes:

[0118] Based on the spherical power and the preset front surface optical power of the master mirror, the back surface optical power of the master mirror is calculated;

[0119] Based on the refractive index of the mother lens material, the front surface optical power of the mother lens, and the rear surface optical power of the mother lens, the front surface curvature radius of the mother lens and the rear surface curvature radius of the mother lens are calculated.

[0120] The process of obtaining the structural parameters of the negative microlens array under different sagitta change amounts includes:

[0121] Based on the sagitta change amount and the mother lens sagitta, calculate the sagitta of the microlenses in the negative microlens array, and calculate the curvature radius of the microlenses based on the microlens sagitta;

[0122] 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;

[0123] Based on the position parameters of the curvature center of the mother lens and the center point of the negative microlens array, calculate the curvature center position and tilt angle of the microlenses in the negative microlens array.

[0124] Based on the negative refractive power-based microstructure lens design method provided in the above embodiments, an embodiment of the present application also provides a microstructure lens, which is designed by the above negative refractive power-based microstructure lens design method.

[0125] The following further explains the negative refractive power-based microstructure lens design method provided by the present application through specific examples.

[0126] The microstructure lens of this embodiment selects Figure 1 the layout style shown in (a) in, and the structure type on the surface of the microstructure lens and the division of each structure into regions 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 mother lens 10, and the regulation area 2 includes a plurality of negative microlens arrays 20 and a mother lens 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.

[0127] The negative refractive power-based microstructure lens design method provided by this embodiment specifically includes the following steps:

[0128] S10: Calculate the structural parameters of the mother lens 10 according to the spherical power of the spectacle wearer, which specifically includes:

[0129] S100: Given that the spherical power of a certain myopic eye is -3D and the preset front surface optical power F1 of the mother lens 10 is 2D, calculate the rear surface optical power F2 of the mother lens 10. The specific calculation formula is: .

[0130] S101: Calculate the curvature radii of the front and rear surfaces 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 rear surface optical power of the master mirror 10. The specific calculation formula is as follows:

[0131] ,

[0132] ,

[0133] where, represents the curvature radius of the front surface 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 that bends to the left is positive, and the curvature radius of a spherical surface that bends to the right is negative.

[0134] As shown in Table 1, the structural parameters of the master mirror 10 provided in this embodiment are as follows:

[0135] Table 1

[0136]

[0137] S20: Obtain the structural parameters of the negative microlens array 20 under different sagitta variation amounts (taking the case of obtaining the structural parameters of the negative microlens array 20 when the sagitta variation amount is 6 μm in this embodiment). Specifically, it includes:

[0138] S200: Based on the preset diameter 6 mm of the central fovea region 1 and the full aperture D1 = 6 mm of the central fovea region 1, determine that the regulation region 2 is the region 3 mm away from the principal optical axis.

[0139] 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.

[0140] 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, .

[0141] For spherical microlenses, the relationship between the curvature c, the radial distance r, and the sagitta z at the radial distance r is as follows:

[0142] ,

[0143] ,

[0144] in, , represents the radius of curvature of the sphere; represents the semi-aperture of the microlens, .

[0145] S202: Obtaining the sagittal height of the mother mirror 10 based on the curvature radius R1 of the mother mirror 10 , based on the vector height of the microlens 200 Get the curvature radius of the microlens 200 As shown in Table 2, when the vector height variation H=6μm, the optical structure parameters of the mother lens 10 and the microlens 200 are:

[0146] Table 2

[0147]

[0148] In addition, in order to compare the effects of suppressing retinal contrast between a microstructure lens with negative refractive power and a microstructure lens with positive refractive power, this embodiment also provides optical structural parameters of a mother lens and microlenses when the microlens array is a positive microlens array, as shown in Table 3:

[0149] Table 3

[0150]

[0151] S203: Selecting the layout style of the microstructure lens to be used, and then determining the grid type and the position parameters of the grid center point, which specifically includes:

[0152] based on Figure 1 The layout style shown in (a) uses a hexagonal grid, and the spacing between adjacent grid center points is d=D200=1mm.

[0153] Furthermore, a three-dimensional XYZ rectangular coordinate system is established with the main optical axis of the mother 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. The vertex (0, 0, 0) of the mother mirror 10 is taken as the section z=0, and the center points of each hexagonal grid in the section and the positions of the central clear vision area 1 are as follows: Figure 4 As 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.

[0154] Let the coordinates of the center of the inscribed circle be (x0, y0, 0), and the distances from each center point to the principal optical axis along the X and Y axes are hx=x0 and hy=y0, respectively, so thatFigure 4 A grid is drawn in it to obtain more coordinates of the center points of the circles. If the inscribed circle of the grid is not within the central clear vision area 1, the center points of this grid will be used as the layout positions of the negative microlens array. For example, as shown in 1-12 in Figure 4 , the coordinate calculation and optical modeling analysis can be carried out through the negative microlens array unit directly above the central clear vision area 1.

[0155] It should be noted that the layout positions of the plane image grid obtained in this embodiment will be used as the positions of the microlens 200 grid on the surface of the master mirror 10. In the above calculation method, if the diameter of the microlens 200 on the microstructure lens remains unchanged all the time, there will be a certain gap between the microlenses 200 on the 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 each microlens 200 on the surface of the master mirror 10. However, since there is a certain overlap at the edges of each microlens 200 on the surface, and the closer to the edge of the microstructure lens, the larger the overlapping area between the microlenses 200.

[0156] S204: Calculate the curvature center position of the microlens 200 according to the position of the center point of the grid on the tangent plane. The calculation principle is as shown in Figure 5 . Let the curvature center of the master mirror 10 be P. The movement process from A to B to C in Figure 5 represents 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:

[0157] 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 this grid on the front surface of the master mirror 10 after translation are B(x0, y0, z), as shown in step1 in Figure 5 .

[0158] 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 by a certain distance to obtain C. The translation distance is the absolute value of the curvature radius r1 of the microlens 200 minus the change amount H of the sagitta, as shown in step2 in Figure 5 .

[0159] A set of similar triangles can be obtained by drawing perpendicular lines from the curvature center C of the microlens 200 and the vertex B of the in - circle center of the grid on the front surface of the mother mirror 10 to the principal optical axis respectively. Then, we have:

[0160] ,

[0161] Among them, , .

[0162] Given , r1, H and the in - circle center coordinates of the grid (x0, y0, 0) of the microlens 200, the curvature center coordinates (x0 ’ , y0 ’ , z ’ ) of the microlens 200 can be calculated. It should be noted that the calculation process of the curvature center coordinates of the microlens in the micro - structure lens with positive refractive power is the same as the above process, but the C point is located on the BP connection line, and , and its calculation principle is as Figure 6 shown.

[0163] As shown in Table 4, the coordinate data of points A, B, and C related to 1 - 6 vertices in the negative microlens array 20 directly above the central clear vision area 1 are as follows: Figure 4 in

[0164] Table 4

[0165]

[0166] 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 mother mirror 10 in different coordinate directions is the tilt angle of the microlens 200). Specifically, it includes:

[0167] 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 increasing direction of the y - coordinate. 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 decreasing direction of the 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 mother mirror 10 on the X - axis and Y - axis. Since the surface shape of the microlens 200 is a rotationally symmetric structure, there is no need to calculate the Z tilt. The calculation formulas for the X tilt and Y tilt are:

[0168] ,

[0169] ,

[0170] Based on the above calculation process, in this embodiment, the correspondingFigure 4 All the structural parameters of the microlenses 200 corresponding to vertices 1 to 6 in the middle are shown in Table 5 as follows:

[0171] Table 5

[0172]

[0173] S30: Based on the structural parameters of the above-mentioned master mirror 10 and the negative microlens array 20, use the optical software Zemax to construct an optical system of a three-dimensional model of a microstructured lens with different sagittal height variations, which specifically includes:

[0174] 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 are shown in Table 6. Set the wavelength of the optical system to 0.55 μm, 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 rear surface of the microstructured 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 The schematic diagram of the optical path composed of the master mirror 10 and the myopia model eye is shown as follows.

[0175] Table 6

[0176]

[0177] 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:

[0178] 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 by MNKDJ in the figure. 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 rear 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 to P7 of the six microlenses 200 in the negative microlens array 20 that can be used for structural resection.

[0179] Use the Boolean object to perform subtraction to obtain the lens obtained by removing P2 to P7 from P1, and its Boolean object expression is:

[0180] ,

[0181] It should be noted that the back surface of the microlens of the positive refractive power-based microlens structure used for comparison is a plane, so the Boolean object addition is used to combine P1 to P7.

[0182] Hide the master lens and microlenses except for the Boolean object to complete the optical modeling. As Figure 8 shown is a partial schematic diagram of the solid model of the microlens structure including a negative microlens array 20 constructed. 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.

[0183] S40: Select the maximum field of view that completely covers the microlenses in the three-dimensional model of the microlens structure under different sagittal height change amounts, and record the modulation transfer function values on the retina of the myopia model for the microlens structures with H = 1μm, 2μm, 4μm, 6μm, 8μm, and 10μm respectively (the modulation transfer function values in this embodiment are the averages of the modulation transfer function values in the meridian and sagittal directions). As shown in Table 7 are the modulation transfer function values corresponding to some spatial frequencies under different sagittal height change amounts:

[0184] Table 7

[0185]

[0186] S50: Analyze the change trend between the modulation transfer function values and the sagittal height change amount to obtain a quantization model of the modulation transfer function with respect to the sagittal height change amount 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 on the modulation transfer function values of the positive refractive power-based microlens structure and the negative refractive power-based microlens structure under the same sagittal height change amount, which specifically includes:

[0187] S500: Use Matlab software to fit the quantization model of the modulation transfer function value with respect to the sagittal height change amount and spatial frequency, which specifically includes:

[0188] 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 change amounts are 1μm, 2μm, 4μm, 6μm, 8μm, and 10μm. It can be seen from the figure that as the sagittal height change amount 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.

[0189] Since the spatial frequencies used to obtain the modulation transfer function values are For the intervals, where the interval is small and the data volume is large, it is impossible to effectively fit the undulating characteristics of the curve using traditional exponential or logarithmic forms and a binary equation in which the change in sagitta and the spatial frequency are independent of each other. For example, using , or such curve types to obtain the regression relationship, the corresponding correlation coefficient is lower than 0.76 for all; even after adding some relevant terms it is still lower than 0.9.

[0190] From Figure 9 it can be observed that: 1. The curves are approximately in a horizontal scaling relationship, that is, the curves with a sagitta change of 1 to 8 μm can all be obtained by intercepting a section of the curve with a sagitta 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 in the longitudinal direction. Based on the above observations, in order to obtain a regression relationship that is more in line with the actual situation, the following steps are adopted in this embodiment to fit the relationship between the modulation transfer function value, the sagitta change, and the spatial frequency.

[0191] 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 fit of the spatial frequency on the curve with a sagitta change of 10 μm, which has the largest degree of horizontal compression 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:

[0192] ,

[0193] 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.

[0194] Specifically, in this embodiment, after performing a univariate fit on the curve with a sagitta change of 10 μm, the obtained polynomial equation is , and the correlation coefficient = 0.994. It can be seen that the polynomial equation provided in this embodiment can well fit the modulation transfer function curve and can be further extended to binary fitting. As Figure 10 Figure 4 shows a schematic comparison between the modulation transfer function curve and the fitting result when the sagittal height variation is 10 μm. The solid line in the figure is the fitting data, and the dotted line is the actual data.

[0195] Step 2: Determine the scaling ratio using the ratio between the spatial frequencies of the minimum points on the curve with the most features (i.e., the highest fluctuation frequency) to normalize the spatial frequencies. Specifically, it includes:

[0196] From Figure 9 it can be found that as the sagittal height variation increases, the spatial frequency of the first minimum point on the modulation transfer function curve decreases accordingly. Figure 11 In (a) of Figure 5, the first minimum points of the sagittal height variations H = 1 μm, 2 μm, and 10 μm 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 from S20 to S40 are used to add some negative microstructure arrays with sagittal height variations for modeling. The modeling of the microstructure lenses at sagittal height variations of 1 μm to 10 μm (at intervals of 1 μm) and 12 μm, 15 μm, and 20 μm is completed, and the spatial frequencies of the first minimum points on the corresponding modulation transfer function curves are recorded, obtaining the result shown in (a) of Figure 11 Figure 6; through the analysis and fitting of the spatial frequencies of the first minimum points on each curve and the sagittal height variations, the fitting result shown in (b) of Figure 11 Figure 6 is 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 sagittal height variation. 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. The correlation coefficient between the spatial frequency of the minimum point and the sagittal height variation is greater than 0.999.

[0197] Specifically, the relationship equation between the spatial frequency of the minimum point of the modulation transfer function curve fitted in this embodiment and the sagittal height variation is expressed as:

[0198] ,

[0199] where represents the relationship equation between the spatial frequency of the minimum point and the sagittal height variation; represents the sagittal height variation; represents the correlation coefficient between the spatial frequency of the minimum point and the sagittal height variation.

[0200] The vector height change of 10 μm corresponding to the curve with the most features is input into the relationship equation between the spatial frequency of the minimum point and the vector height change, and the spatial frequency of the minimum point corresponding to the vector height change of 10 μm is calculated. Based on the ratio of the spatial frequency of the minimum point corresponding to the vector height change of 10 μm to the relationship equation between the spatial frequency of the minimum point and the vector height change, the spatial frequency scaling ratio equation is obtained.

[0201] The spatial frequency is normalized using the spatial frequency scaling ratio equation to obtain the normalized spatial frequency equation shown below:

[0202] .

[0203] Step 3: Substitute the normalized spatial frequency equation as an independent variable into the polynomial equation of the modulation transfer function with respect to the normalized spatial frequency, and obtain the following fitting target equation:

[0204] ,

[0205] The above fitting target formula is binary fitted with the modulation transfer function curves of 0~35lp / mm spatial frequency under H=1μm, 2μm, 4μm, 6μm, 8μm, and 10μm (with a value interval of 0.5lp / mm), and the quantitative model of the modulation transfer function with respect to the vector height change and spatial frequency is obtained after simplification:

[0206] ,

[0207] ,

[0208] in, Represents the modulation transfer function value.

[0209] The fitting effect of the quantitative model is good, and the correlation coefficient =0.9722. The quantization model can be used to determine the modulation transfer function value of the visible frequency band with a vector height variation of 0~10μm and the modulation transfer function value of the core characteristic frequency band with a vector height variation of more than 10μm with high accuracy (with a value interval of 0.5lp / mm). Figure 12 The figure shows a comparison diagram of the actual data of the modulation transfer function regarding the vector height change and the spatial frequency and the binary fitting result. The surface in the figure is the fitting result and the points represent the actual data.

[0210] Step 4: Verify the quantitative model, which specifically includes:

[0211] Obtain the modulation transfer function curve of the optical system of the microstructure lens when the sagittal height change H is 15 μm, and then substitute the sagittal height change H = 15 μm into the quantization model. Based on the output of the quantization model, obtain the predicted modulation transfer function curve when the sagittal height change H = 15 μm, 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 sagittal height change is 15 μm. In the figure, the curve represents the predicted modulation transfer function curve, and the dotted line represents the actual modulation transfer function curve.

[0212] S501: Analyze the reduction effect threshold of the modulation transfer function value of the negative microlens array 20 on the microstructure lens at different sagittal height changes from the perspective of spatial frequency, which specifically includes:

[0213] From Figure 11 it can be seen that the modulation transfer function curves corresponding to different sagittal height changes are all reduced to about 0.2 at the spatial frequency of the first minimum point. At this time, the imaging effect has been reduced to a relatively poor level. Therefore, the effect of different sagittal height changes on reducing contrast is manifested as the spatial frequency size at which the modulation transfer function value is reduced to the minimum value of 0.2. It should be noted that through the analysis of Figure 11 , this application finds that the spatial frequency size 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.

[0214] Therefore, when the sagittal height change 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 can be obtained, and its calculation formula is:

[0215] ,

[0216] ,

[0217] Therefore, it can be considered that under the action of the sagittal height change H, the theoretical spatial frequency threshold for the reduction effect of imaging contrast is about when the spatial modulation transfer function is reduced to 0.2; and when H = 2 μm, 5 μm, 10 μm, 15 μm, and 20 μm, calculated by the above quantization 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 sag height change larger 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 sag height change threshold.

[0218] In summary, according to the relationship between the spatial frequency of the minimum point and the sag height change in the quantization model, after obtaining the theoretical threshold of the spatial frequency at which the contrast is reduced to a low imaging level under the limit sag height change, by comparing it with the spatial frequency of the minimum point under any sag height change, the appropriate sag height change threshold, that is, the structural parameter value of the appropriate microstructured lens, can be conveniently determined.

[0219] S502: Compare the effect of the negative microlens array and the positive microlens array on the reduction of MTF under the same sag height change:

[0220] Take the sag height change 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 on the master mirror as Figure 8 shown. 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 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 Figure 14 and Figure 15 shown. The hatched part in the figure represents the negative microlens, and the non-hatched part is the positive microlens.

[0221] Combined with the modulation transfer function value of the all-negative microlens array arrangement with a sag height change H = 6μm obtained in step S40, analyze the modulation transfer function values of the maximum field of view under the four arrangements: When the sag height change is H = 6μm, as Figure 16 shown are the modulation transfer function curves of all-negative microlenses and 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, as well as the reduction rate of the modulation transfer function value of all-negative microlenses relative to all-positive microlenses.

[0222] Table 8

[0223]

[0224] From Figure 16It can be seen that the effect of all-negative microlenses in suppressing the retinal contrast within the visible video segment is much greater than that of all-positive microlenses. Moreover, through the calculation of 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 approximately 55%. In addition, the arrangement of half-positive and half-negative and positive-negative alternating microlenses also has a much better effect in suppressing the retinal contrast than the all-positive microlens form, and the effect of all-negative microlenses in suppressing the retinal contrast is significantly better than that of the half-positive and half-negative and positive-negative alternating arrangements. Therefore, the following conclusion is drawn in this embodiment: adding half or more negative microlenses to the microstructure can achieve an effect of reducing the retinal contrast that is much greater than that of all-positive microlenses.

[0225] Obviously, the above embodiments are merely examples given for clear illustration 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 design method for a microstructure optical imaging element, characterized in that, Including: Construct a three-dimensional model of the microstructured lens under different sagittal height change amounts based on the structural parameters of the mother lens and the structural parameters of the negative microlens array under different sagittal height change amounts; 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; Fit the spatial frequency of the first minimum point on each modulation transfer function curve and its corresponding sagittal height change amount to obtain the relationship equation between the spatial frequency of the minimum point and the sagittal height change amount; Based on the relationship equation between the spatial frequency of the minimum point and the sagittal height change amount, 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 amount is infinite; Taking the spatial frequency of the minimum point being greater than or equal to the spatial frequency limit value as the goal, solve the relationship equation between the spatial frequency of the minimum point and the sagittal height change amount to obtain the value range of the sagittal height change amount threshold of the microstructured lens based on negative refractive power; Among the modulation transfer function curves of each three-dimensional model of the microstructured 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 fit 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 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; 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 curves of the three-dimensional models of the microstructured 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 microstructured 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 microstructured lens based on negative refractive power; Obtain the optimal structural parameters of the negative microlens array under the optimal sagittal height change amount; Based on the structural parameters of the mother lens, the optimal structural parameters of the negative microlens array, and the microstructural arrangement type, design and obtain the microstructured lens based on negative refractive power.

2. The design method of the microstructure optical imaging element according to claim 1, characterized in that Based on the target sagittal height change amount and the relationship equation between the spatial frequency of the minimum point and the sagittal height change amount, the obtained spatial frequency scaling ratio equation includes: Input the target sagittal height change amount into the relationship equation between the spatial frequency of the minimum point and the sagittal height change amount, and calculate the spatial frequency of the minimum point corresponding to the target sagittal height change amount; Based on the ratio of the spatial frequency of the minimum point corresponding to the target sagittal height change amount to the relationship equation between the spatial frequency of the minimum point and the sagittal height change amount, obtain the spatial frequency scaling ratio equation.

3. The method for designing a microstructured optical imaging element according to claim 1, wherein The relationship equation between the spatial frequency of the minimum point and the sagittal height change amount is expressed as: ， Among them, 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; The calculation formula for the spatial frequency limit value is: ， ， Among them, represents the spatial frequency limit value.

4. The method for designing a microstructured optical imaging element according to claim 2, characterized in that, The polynomial equation of the modulation transfer function with respect to the normalized spatial frequency is expressed as: ， Among them, 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: ， Among them, represents the normalized spatial frequency; represents the spatial frequency; represents the spatial frequency scaling ratio; represents the change in the target sagittal height The spatial frequency of the corresponding minimum point.

5. The method for designing a microstructured optical imaging element according to claim 4, characterized in that, The quantization model is expressed as: ， ， Among them, represents the modulation transfer function value.

6. 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 primary mirror includes: Based on the spherical power and the preset front surface optical power of the primary mirror, the back surface optical power of the primary mirror is calculated; Based on the refractive index of the primary mirror material, the front surface optical power of the primary mirror, and the back surface optical power of the primary mirror, the front surface curvature radius and the back surface curvature radius of the primary mirror are calculated.

7. The method for designing a microstructured optical imaging element according to claim 6, characterized in that, 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 primary mirror sag, the sag of the microlenses in the negative microlens array is calculated, and the curvature radius of the microlenses is calculated based on the microlens sag; Based on the preset microstructure arrangement type, the primary 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 primary mirror and the center point of the negative microlens array, the curvature center position and tilt angle of the microlenses in the negative microlens array are calculated.

8. A microstructure optical imaging element, characterized in that, The microstructured optical imaging element is designed by the microstructured optical imaging element design method according to any one of claims 1 to 7.

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