CN117075329B - Double-layer diffraction optical element optimization method and system and electronic equipment - Google Patents
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Abstract
本申请公开了一种双层衍射光学元件优化方法、系统及电子设备，包括：根据微结构高度、波长范围、入射角度最大值和周期宽度计算第一层衍射光学元件的主衍射级次和衍射角；根据主衍射级次和衍射角确定双层衍射光学元件的遮挡长度和倾斜因子；结合确定出的遮挡长度和倾斜因子建立二维分析模型以计算双层衍射光学元件在给定波长下的带宽积分效率。克服了传统的标量衍射理论在分析有限周期宽度的双层衍射光学元件的局限性，尤其是在斜入射时双层衍射光学元件的衍射效率计算问题。可实现有限周期宽度下的任意波长范围和斜入射下的双层衍射光学元件的带宽积分衍射效率最大化，用于双层衍射光学元件的优化，解决了衍射光学元件设计中对设计波长的依赖。
The present application discloses a method, system and electronic device for optimizing a double-layer diffractive optical element, including: calculating the main diffraction order and diffraction angle of the first layer of diffractive optical element according to the microstructure height, wavelength range, maximum incident angle and period width; determining the blocking length and tilt factor of the double-layer diffractive optical element according to the main diffraction order and diffraction angle; establishing a two-dimensional analysis model in combination with the determined blocking length and tilt factor to calculate the bandwidth integral efficiency of the double-layer diffractive optical element at a given wavelength. It overcomes the limitations of the traditional scalar diffraction theory in analyzing double-layer diffractive optical elements with a finite period width, especially the problem of calculating the diffraction efficiency of double-layer diffractive optical elements at oblique incidence. It can maximize the bandwidth integral diffraction efficiency of double-layer diffractive optical elements in any wavelength range and oblique incidence under a finite period width, and is used for the optimization of double-layer diffractive optical elements, solving the dependence on the design wavelength in the design of diffractive optical elements.
Description
Technical Field
The application relates to the technical field of optical elements, in particular to a double-layer diffraction optical element optimization method, a double-layer diffraction optical element optimization system and electronic equipment.
Background
In the field of optical imaging, double-layer diffractive optical elements have been widely used, which mainly serve to improve resolution and sharpness of optical imaging. While conventional single-layer diffractive optical elements can achieve only limited resolution and sharpness, double-layer diffractive optical elements can improve imaging quality by alternately using two diffractive optical elements, thereby achieving more accurate imaging effects. The double-layer diffraction optical element has the advantages that the aberration problem of the single-layer diffraction optical element can be overcome, and the imaging quality and the imaging precision are improved.
Currently, double-layer diffractive optical elements are mainly analyzed and optimally designed by scalar diffraction theory, but these schemes have some problems. The most important of these problems is that conventional scalar diffraction theory is not suitable for designing and optimizing a double-layer diffractive optical element when the period width of the double-layer diffractive optical element is limited and the incident angle is large. Moreover, the design of the diffractive optical element needs to consider a plurality of parameters, such as the thickness, period, incident angle, material and the like of the diffractive optical element, and complex interaction relation exists between the parameters, so that an optimal design scheme is difficult to determine.
Therefore, how to achieve accurate analysis and optimization of diffraction efficiency of a double-layer diffractive optical element is a technical problem to be solved in the art.
Disclosure of Invention
In order to solve the technical problems, the application provides the following technical scheme:
in a first aspect, embodiments of the present application provide a method for optimizing a dual-layer diffractive optical element, including:
calculating a main diffraction order and a diffraction angle of the first layer diffraction optical element according to the microstructure height, the wavelength range, the maximum value of the incident angle and the period width;
determining the shielding length and the tilting factor of the double-layer diffraction optical element through the main diffraction order and the diffraction angle;
the determined occlusion length and tilt factor are combined to determine the band diffraction efficiency of the two-layer diffractive optical element at a given wavelength, which is used to analyze the optical performance of the diffractive optical element.
In one possible implementation, the first and second layer diffractive optical elements are transparent films or media of finite period width.
In one possible implementation, the diffraction efficiency of the diffractive optical element at each operating wavelength and angle of incidence is calculated as:
wherein phi is the phase delay of the diffractive optical element at each working wavelength and incident angle, m is the main diffraction order of the double-layer diffractive optical element, t 1 ,t 2 ,t 3 ,t 4 K is the shielding distance of four corners of the diffraction optical element in the same period 1 And K 2 Is the tilt factor of the diffractive optical element at each operating wavelength.
In one possible implementation, the tilt factor of the diffractive optical element at each operating wavelength is:
wherein θ is 1 ，θ 2 Indicating the principal diffraction angle at which light leaves the first layer diffractive optical element and the second layer diffractive optical element.
In one possible implementation, the phase retardation calculation formula of the diffractive optical element at each operating wavelength and at any incident angle is:
wherein h is the phase retardation of the diffractive optical element at each operating wavelength and angle of incidence 1 And h 2 Representing the effective microstructure height of the first layer and the second layer diffraction elements. θ 0 Represents the incident angle, theta 1 Representing the principal diffraction angle, θ, of light leaving the first layer diffraction element 2 Indicating the principal diffraction angle at which light leaves the second layer diffraction element. n is n 1 And n 2 The refractive index of the first layer and the second layer of diffraction element material is shown, and λ is the wavelength of incident light.
In one possible implementation, the calculation formula of the shielding length of the diffractive optical element at each working wavelength is: when theta is as 1 ≥θ 0 In the time-course of which the first and second contact surfaces,when theta is as 1 ＜θ 0 When (I)>Wherein the method comprises the steps ofH 1 And H 2 Representing the microstructure heights of the first layer diffractive optical element and the second layer diffractive optical element, T being the period width of the diffractive optical element, α 1 ，α 2 Representing the blaze angles of the first and second layer diffractive optical elements,
wherein when theta is 1 When the number of the groups is less than 0,the equivalent microstructure height of the first and second layer diffractive optical elements is calculated by the following formula:
wherein t is 1 ,t 2 ,t 3 ,t 4 Is the shielding distance alpha of four angles of the diffraction optical element in the same period 1 And alpha 2 For the blaze angles of the first layer and the second layer diffraction elements, T is the period width of the diffraction elements.
In one possible implementation, the dual layer diffractive optical element is formed by stacking two adjacent and vertically transparent films or media.
In one possible implementation, the wavelength range is any wavelength within the spectral range.
In a second aspect, embodiments of the present application provide a dual layer diffractive optical element optimization system comprising:
the calculation module is used for calculating the main diffraction order and diffraction angle of the first layer of diffraction optical element according to the microstructure height, the wavelength range, the maximum incidence angle and the period width;
a first determining module for determining a blocking length and a tilting factor of the double layer diffractive optical element by the main diffraction order and the diffraction angle;
and a second determination module for determining the band diffraction efficiency of the double-layer diffraction optical element at a given wavelength by combining the determined shielding length and the inclination factor, wherein the diffraction efficiency is used for analyzing the optical performance of the diffraction optical element.
In a third aspect, an embodiment of the present application provides an electronic device, including:
a processor;
a memory;
and a computer program, wherein the computer program is stored in the memory, the computer program comprising instructions which, when executed by the processor, cause the electronic device to perform the method of any one of the possible implementations of the first aspect.
In the embodiment of the application, the limitation of the traditional scalar diffraction theory in analyzing the double-layer diffraction optical element with the limited period width is overcome, and particularly, the problem of calculating the diffraction efficiency of the double-layer diffraction optical element in oblique incidence is solved. The bandwidth integral diffraction efficiency maximization of the double-layer diffraction optical element under any wavelength range with a limited period width and oblique incidence can be realized, the method is used for optimizing the double-layer diffraction optical element, and the dependence on design wavelength in the design of the diffraction optical element is solved.
Drawings
FIG. 1 is a schematic flow chart of a method for optimizing a dual-layer diffractive optical element according to an embodiment of the present application;
FIG. 2 is a schematic diagram of light provided by an embodiment of the present application as blocked by a first layer diffractive optical element;
FIG. 3 is a schematic diagram of light provided by an embodiment of the present application when it is blocked by a second layer diffractive optical element;
FIG. 4 is a schematic diagram showing the variation of diffraction efficiency with wavelength of incident light when the incident angle is-20 ° according to the embodiment of the present application;
fig. 5 is a schematic diagram of a change rule of bandwidth integral diffraction efficiency with an incident angle according to an embodiment of the present application;
FIG. 6 is a schematic diagram of a dual layer diffractive optical element optimization system according to an embodiment of the present application;
fig. 7 is a schematic diagram of an electronic device according to an embodiment of the present application.
Detailed Description
The present invention is described below with reference to the drawings and the detailed description.
Referring to fig. 1, the method for optimizing a dual-layer diffractive optical element according to the present embodiment includes:
s101, calculating the main diffraction order and diffraction angle of the first layer diffraction optical element according to the microstructure height, the wavelength range, the incidence angle maximum value and the period width.
Determining requirements and characteristics of the element, including wavelength, maximum incidence angle, period, material; wherein the angle of incidence is negative to the left and positive to the right of the normal of the diffractive optical element. Diffraction angles follow the same sign convention.
The diffraction angle of the light after leaving the first layer diffractive optical element and the second layer diffractive optical element is calculated.
Diffraction angle θ at which light leaves the first layer diffractive optical element 1 From the refraction angle close to the diffraction primary order: θ 1 ＝α 1 -asin(n 1 ·sin(α 1 -θ 0 )). Diffraction angle θ at which light leaves the second layer diffractive optical element 2 Determination by diffraction equation
S102, determining the shielding length and the tilting factor of the double-layer diffraction optical element through the main diffraction order and the diffraction angle.
The tilt factor of the light passing through the first layer of diffractive optical element isThe tilt factor through the second layer is
The case where light is blocked can be classified into two cases, the first is that light is mainly blocked by the first layer diffraction optical element and the second is that light is mainly blocked by the second layer diffraction optical element.
Light is mainly blocked by the first layer diffractive optical element, and the relationship between the light and the double layer diffractive optical element is as shown in fig. 2, and at this time, light is mainly blocked by the first layer diffractive optical element, so that it is necessary to trace the light from the second layer diffractive optical element. The diffraction angle is now greater than the angle of incidence, and the length of the occlusion is determined by the following equation:
at this time theta 1 ≥θ 0 ，
Light is mainly blocked by the second layer diffractive optical element, where the relationship between the light and the double layer diffractive optical element is shown on the right side of fig. 3, where the diffraction angle is smaller than the incident angle, and light is mainly blocked by the second layer diffractive optical element, so it is necessary to trace the light from the lower right corner.
At this time theta 1 ＜θ 0 ，Wherein->H 1 And H 2 Representing the microstructure heights of the first layer diffractive optical element and the second layer diffractive optical element, T being the period width of the diffractive optical element, α 1 ，α 2 The blaze angles of the first and second layer diffractive optical elements are indicated. In this case, the sizes of t2 and t4 are divided into two cases, the first case is that the diffraction angle is larger than zero, and at this time, the calculation methods of t2 and t4 are identical to the first case. When the diffraction angle is less than zero, as shown on the left side of figure 3,
the corresponding equivalent microstructure height can be expressed as
S103, determining the diffraction efficiency of the band of the double-layer diffraction optical element at a given wavelength by combining the determined shielding length and the determined inclination factor, wherein the diffraction efficiency is used for analyzing the optical performance of the diffraction optical element.
The retardation of a dual layer diffractive optical element can be expressed as:
the diffraction efficiency is as follows:
according to the diffraction efficiency calculation formula, the polychromatic light integral diffraction efficiency under a broadband and the average diffraction efficiency under a large visual field can be obtained, and the optical performance of the double-layer diffraction optical element is comprehensively analyzed.
As a preference for the above technical solution, PC and PMMA are selected as the base materials, the visible light wave band of 400nm-700nm is selected as the working wave band, and the incident angle range is-20 DEG to 20 deg. The period width of the double-layer diffraction optical element is 20 μm, and the microstructure height H of the first layer diffraction optical element 1 Microstructure height H of second layer diffractive optical element = 4.475 μm 2 Taking this as an example, the diffraction efficiency of the double-layer diffractive optical element is calculated and compared with the existing scalar diffraction theory calculation method and vector diffraction theory calculation method to illustrate the effectiveness and advancement of the analytical model of the present invention.
Fig. 4 shows a variation rule of diffraction efficiency with wavelength of incident light when the incident angle is-20 °, wherein the analysis model proposed by the present patent is closer to the analysis result of the vector diffraction theory, which is far better than the analysis result of the existing scalar diffraction theory. The analysis model gives consideration to the efficiency of scalar diffraction theory and the accuracy of vector diffraction theory, and plays an important role in the diffraction efficiency analysis of the double-layer diffraction optical element.
Fig. 5 shows a law of variation of bandwidth integral diffraction efficiency with incident angle, wherein the variation of integral diffraction efficiency with incident angle predicted by the analysis model proposed by the present patent is consistent with the analysis result of vector diffraction theory, and the error is far smaller than that of scalar diffraction theory. As the period width increases, the error of the analytical model results and the time-domain finite difference method also decrease, which suggests that the analytical model can be used to analyze the diffraction efficiency of a multilayer diffractive optical element of finite period width. For a double-layer diffraction optical element with a period width of more than 20 μm, the time and resources far greater than those of a scalar diffraction theory are also required for analysis by using the vector diffraction theory, and when the period width continues to increase, the convergence and numerical stability of the vector diffraction theory are both reduced, and the time and memory resources required for numerical solution are greatly increased. The analysis model based on the double-layer diffraction optical element can effectively make up the limitation of scalar diffraction theory, guide the optimal design of the double-layer diffraction optical element and improve the imaging quality of the refraction-diffraction mixed optical system under a large visual field.
After a portion of the parameters are determined, the bandwidth integration efficiency of the dual-layer diffractive optical element for a given wavelength and angle of incidence can be maximized by changing the parameters of the microstructure height, period width, etc., thereby achieving an optimal design of the dual-layer diffractive optical element.
In the actual production process, the difference between the product performance index and the target value obtained in the actual production process is predicted and evaluated according to the model, and the corresponding adjustment is carried out to improve the product quality.
Corresponding to the method for optimizing the double-layer diffraction optical element provided by the embodiment, the application also provides an embodiment of a double-layer diffraction optical element optimizing system.
Referring to fig. 6, the dual layer diffractive optical element optimizing system 20 in the present embodiment includes:
a calculation module 201 for calculating a main diffraction order and a diffraction angle of the first layer diffraction optical element according to the microstructure height, the wavelength range, the maximum value of the incident angle, and the period width;
a first determination module 202 for determining the occlusion length and the tilt factor of the double layer diffractive optical element from the primary diffraction order and the diffraction angle;
the second determination module 203 determines the band diffraction efficiency of the two-layer diffractive optical element at a given wavelength in combination with the determined occlusion length and the tilt factor, which diffraction efficiency is used to analyze the optical performance of the diffractive optical element.
The embodiment of the application also provides electronic equipment which is used for optimizing the double-layer diffraction optical element.
Referring to fig. 7, a schematic structural diagram of an electronic device according to an embodiment of the present application is provided. As shown in fig. 7, the electronic device 300 may include: a processor 301, a memory 302 and a communication unit 303. The components may communicate via one or more buses, and those skilled in the art will appreciate that the electronic device structure shown in FIG. 7 is not limiting of the embodiments herein, and that it may be a bus-like structure, a star-like structure, or include more or fewer components than shown, or may combine some components, or a different arrangement of components.
Wherein the communication unit 303 is configured to establish a communication channel, so that the electronic device can communicate with other electronic devices.
The processor 301, which is a control center of the electronic device, connects various parts of the entire electronic device using various interfaces and lines, performs various functions of the electronic device and/or processes data by running or executing software programs and/or modules stored in the memory 302, and invoking data stored in the memory. The processor may be comprised of integrated circuits (integrated circuit, ICs), such as a single packaged IC, or may be comprised of packaged ICs that connect multiple identical or different functions. For example, the processor 301 may include only a central processing unit (central processing unit, CPU). In the embodiment of the application, the CPU may be a single operation core or may include multiple operation cores.
Memory 302 for storing instructions for execution by processor 301, memory 302 may be implemented by any type of volatile or nonvolatile memory electronics or combination thereof, such as Static Random Access Memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic memory, flash memory, magnetic disk, or optical disk.
The execution of the instructions in memory 302, when executed by processor 301, enables electronic device 300 to perform some or all of the steps of the method embodiments described above.
Corresponding to the above embodiment, the embodiment of the present application further provides a computer readable storage medium, where the computer readable storage medium may store a program, where when the program runs, the electronic device where the computer readable storage medium is located may be controlled to execute some or all of the steps in the above method embodiment. In particular, the computer readable storage medium may be a magnetic disk, an optical disk, a read-only memory (ROM), a random access memory (random access memory, RAM), or the like.
Corresponding to the above embodiments, the present application also provides a computer program product comprising executable instructions which, when executed on a computer, cause the computer to perform some or all of the steps of the above method embodiments.
In the embodiments of the present application, "at least one" means one or more, and "a plurality" means two or more. "and/or", describes an association relation of association objects, and indicates that there may be three kinds of relations, for example, a and/or B, and may indicate that a alone exists, a and B together, and B alone exists. Wherein A, B may be singular or plural. The character "/" generally indicates that the context-dependent object is an "or" relationship. "at least one of the following" and the like means any combination of these items, including any combination of single or plural items. For example, at least one of a, b and c may represent: a, b, c, a-b, a-c, b-c, or a-b-c, wherein a, b, c may be single or plural.
In several embodiments provided herein, any of the functions, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a computer-readable storage medium. Based on such understanding, the technical solution of the present application may be embodied essentially or in a part contributing to the prior art or in a part of the technical solution, in the form of a software product stored in a storage medium, including several instructions for causing a computer electronic device (which may be a personal computer, a server, or a network electronic device, etc.) to perform all or part of the steps of the methods described in the embodiments of the present application. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a read-only memory (ROM), a random access memory (random access memory, RAM), a magnetic disk, or an optical disk, or other various media capable of storing program codes.
The foregoing is merely specific embodiments of the present application, and any person skilled in the art may easily conceive of changes or substitutions within the technical scope of the present application, which should be covered by the protection scope of the present application. The protection scope of the present application shall be subject to the protection scope of the claims.
Claims (6)
1. A method of optimizing a bilayer diffractive optical element, comprising:
calculating a main diffraction order and a diffraction angle of the first layer diffraction optical element according to the microstructure height, the wavelength range, the maximum value of the incident angle and the period width;
determining the shielding length and the tilting factor of the double-layer diffraction optical element through the main diffraction order and the diffraction angle;
determining diffraction efficiency of the double-layer diffraction optical element at a given wavelength by combining the determined shielding length and the determined inclination factor, wherein the diffraction efficiency is used for analyzing the optical performance of the diffraction optical element;
the diffraction efficiency calculation formula of the diffraction optical element at each working wavelength and incidence angle is as follows:
the tilt factor of the diffractive optical element at each operating wavelength is:
，/>；
the phase delay calculation formula of the diffraction optical element under each working wavelength and any incidence angle is as follows:
，
the calculation formula of the shielding length of the diffraction optical element at each working wavelength is as follows:
when (when)When (I)>
When (when)When (I)>Wherein->，
Wherein whenWhen (I)>
The equivalent microstructure height of the first and second layer diffractive optical elements is calculated by the following formula:
，
wherein:for the retardation of the diffractive optical element at each working wavelength and angle of incidence, m is the principal diffraction order of the double layer diffractive optical element, +.>Is the shielding distance of four angles of the diffraction optical element in the same period, T is the period width of the diffraction optical element, < ->And->A tilt factor for the diffractive optical element at each operating wavelength; />Indicating the angle of incidence +.>Indicating the principal diffraction angle of light leaving the first layer diffraction element,/>Representing the principal diffraction angle of light leaving the second layer diffraction element +.>And->Representing the effective microstructure height of the first layer and the second layer diffraction element, +.>And->The refractive index of the first layer and the second layer of diffraction element material, λ being the wavelength of incident light; />And->Representing the microstructure height of the first layer diffractive optical element and the second layer diffractive optical element +.>The blaze angles of the first and second layer diffractive optical elements are indicated.
2. The method of optimizing a dual layer diffractive optical element according to claim 1, wherein the first and second layer diffractive optical elements are transparent films or media of finite period width.
3. The method of optimizing a bilayer diffractive optical element according to claim 1, wherein the bilayer diffractive optical element is formed by stacking two adjacent and vertically transparent films or media.
4. The method of optimizing a bilayer diffractive optical element according to claim 1, wherein the wavelength range is any wavelength in the spectral range.
5. A dual layer diffractive optical element optimization system for implementing the dual layer diffractive optical element optimization method of claim 1, comprising:
the calculation module is used for calculating the main diffraction order and diffraction angle of the first layer of diffraction optical element according to the microstructure height, the wavelength range, the maximum incidence angle and the period width;
a first determining module for determining a blocking length and a tilting factor of the double layer diffractive optical element by the main diffraction order and the diffraction angle;
a second determining module, configured to determine a band diffraction efficiency of the two-layer diffractive optical element at a given wavelength in combination with the determined occlusion length and the tilt factor, where the diffraction efficiency is used to analyze an optical performance of the diffractive optical element;
the diffraction efficiency calculation formula of the diffraction optical element at each working wavelength and incidence angle is as follows:
the tilt factor of the diffractive optical element at each operating wavelength is:
，/>；
the phase delay calculation formula of the diffraction optical element under each working wavelength and any incidence angle is as follows:
，
the calculation formula of the shielding length of the diffraction optical element at each working wavelength is as follows:
when (when)When (I)>
When (when)When (I)>Wherein->，
Wherein whenWhen (I)>
The equivalent microstructure height of the first and second layer diffractive optical elements is calculated by the following formula:
，
wherein:for the retardation of the diffractive optical element at each working wavelength and angle of incidence, m is the principal diffraction order of the double layer diffractive optical element, +.>Is the shielding distance of four angles of the diffraction optical element in the same period, T is the period width of the diffraction optical element, < ->And->A tilt factor for the diffractive optical element at each operating wavelength; />Indicating the angle of incidence +.>Indicating the principal diffraction angle of light leaving the first layer diffraction element,/>Representing the principal diffraction angle of light leaving the second layer diffraction element +.>And->Representing the effective microstructure height of the first layer and the second layer diffraction element, +.>And->The refractive index of the first layer and the second layer of diffraction element material, λ being the wavelength of incident light; />And->Representing the microstructure height of the first layer diffractive optical element and the second layer diffractive optical element +.>The blaze angles of the first and second layer diffractive optical elements are indicated.
6. An electronic device, comprising:
a processor;
a memory;
and a computer program, wherein the computer program is stored in the memory, the computer program comprising instructions that, when executed by the processor, cause the electronic device to perform the method of any one of claims 1 to 4.
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| CN101813797A (en) * | 2010-03-03 | 2010-08-25 | 长春理工大学 | Optimal design method of multilayer diffraction optical element |
| CN110806641A (en) * | 2019-11-21 | 2020-02-18 | 西北工业大学 | Optimization method of dual-band infrared multi-layer diffractive element at oblique incidence |
| CN111736336A (en) * | 2020-07-03 | 2020-10-02 | 杭州驭光光电科技有限公司 | Method for optimizing period of diffractive optical element |
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| CN110806641A (en) * | 2019-11-21 | 2020-02-18 | 西北工业大学 | Optimization method of dual-band infrared multi-layer diffractive element at oblique incidence |
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