CN101813797A - Optimal design method of multilayer diffraction optical element - Google Patents
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Abstract
The invention relates to an optimal design method of a multilayer diffraction optical element, which belongs to the technical field of optical design. The optimal design is not realized in the prior art. The method comprises the following steps of: (1) optimally selecting an optical material of the multilayer diffraction optical element according to a surface microstructure height formula of the multilayer diffraction optical element; (2) determining the bandwidth integration average diffraction efficiency distribution by using different design wavelength combinations in the entire working waveband; (3) determining the greatest bandwidth integration average diffraction efficiency and the relative design wavelength in the entire working waveband; and (4) substituting the design wavelength corresponding to the greatest bandwidth integration average diffraction efficiency into the surface microstructure height formula of the multilayer diffraction optical element, and calculating out the optimal surface microstructure height and the optimal design wavelength of the multilayer diffraction optical element. The method is used for designing the multilayer diffraction optical element used for a wide-waveband imaging optical system, and maximizes the bandwidth integration average diffraction efficiency of the multilayer diffraction optical element.
Description
Technical Field
The invention relates to an optimal design method of a multilayer diffraction optical element, which is used for designing the multilayer diffraction optical element of a broadband imaging optical system, can realize the maximization of the bandwidth integral average diffraction efficiency and the quantitative optimal design of the multilayer diffraction optical element, can improve the imaging quality of a refraction/diffraction mixed optical system containing the multilayer diffraction optical element, and belongs to the technical field of optical design.
Background
With the development of optical manufacturing technology, the diffractive optical element creates an independent branch in modern optics, and revolutionizes traditional optical design theory and manufacturing process. The diffractive optical element can be used for correcting various imaging defects such as chromatic aberration, aberration and the like, and brings more design freedom and wide material selectivity to optical design, thereby realizing special optical functions. In the design process of the refraction/diffraction mixed optical system, the diffraction efficiency of the single-layer diffraction optical element is sharply reduced along with the deviation of the central wavelength, so that the imaging quality is influenced. Therefore, the single-layer diffractive optical element can be used only for an optical system of a limited band width. In recent years, multilayer diffractive optical elements have been developed to overcome this disadvantage and achieve an improvement in the diffraction efficiency of a wide band.
At present, the diffraction efficiency of the diffractive optical element of the refraction/diffraction mixed optical system is generally analyzed by adopting a scalar diffraction theory method, and the imaging quality of the refraction/diffraction mixed optical system is pre-evaluated by adopting a method of bandwidth integration average diffraction efficiency and the product of the optical transfer function of the optical system. In the design process of the refraction/diffraction hybrid optical system, two-step design is generally adopted, wherein the first step adopts common optical design software such as zemax, codev and the like to design the optical system, and the second step designs the diffraction efficiency of the diffraction optical element. In the design process of the single-layer diffractive optical element, the design wavelength of the single-layer diffractive optical element is consistent with the central wavelength of the optical system, and then the bandwidth integration average diffraction efficiency is a definite value, but in the design process of the multilayer diffractive optical element, the central wavelength of the multilayer diffractive optical element is the central wavelength of the optical system, and meanwhile, a plurality of groups of design wavelengths exist, so that the bandwidth integration average diffraction efficiencies of the corresponding multilayer diffractive optical elements are different, and the influence on the folding/diffracting mixed optical system is also different.
Regarding the optimal design of the multilayer diffraction optical element, no scientific and reliable design method exists at present. The design wavelength of the multilayer diffraction optical element in the visible light band reported in the prior art is selected to be F light and C light, or the two ends of the band, the height calculation of the surface microstructure of the multilayer diffraction optical element is carried out through the design wavelength and the selected optical material, and whether the bandwidth integral average diffraction efficiency is maximum or not is not considered.
Disclosure of Invention
The invention aims to maximize the bandwidth integral average diffraction efficiency of the multilayer diffraction optical design, and provides an optimal design method of a multilayer diffraction optical element.
Since the structure of the multilayer diffractive optical element has various forms, the multilayer diffractive optical element can be equivalent to a separate type multilayer diffractive optical element regardless of the change of the structural form.
The method of the invention specifically comprises the following steps:
1. optimally selecting optical materials for forming the multilayer diffraction optical element according to a surface microstructure height formula of the multilayer diffraction optical element;
2. in the whole working waveband, different design wavelength combinations are adopted to determine the bandwidth integral average diffraction efficiency distribution;
3. determining the maximum bandwidth integral average diffraction efficiency and the corresponding design wavelength in the whole working waveband;
4. and substituting the determined design wavelength corresponding to the maximum bandwidth integral average diffraction efficiency into a surface microstructure height formula of the multilayer diffraction optical element, and calculating to obtain the optimized surface microstructure height and the optimized diffraction efficiency of the multilayer diffraction optical element.
By utilizing the bandwidth integral average diffraction efficiency of the multilayer diffraction optical element, when the visible light waveband is 0.4-0.7 mu m, polymethacrylate and polycarbonate are used as base materials, and the design wavelengths are 0.4 mu m and 0.7 mu m, the microstructure heights of the harmonic diffraction elements of all layers are 17.372 mu m and 13.476 mu m respectively, so that the obtained bandwidth integral average diffraction efficiency is 95.319%; when the F spectral line and the C spectral line are used as design wavelengths, the heights of the microstructures of the harmonic diffraction elements are 24.171 micrometers and 19.261 micrometers respectively, and the obtained bandwidth integral average diffraction efficiency is 96.832%. The method has the technical effects that the maximum bandwidth integral average diffraction efficiency obtained by the method is 99.253%, the corresponding design wavelength is 0.435 μm and 0.598 μm, the microstructure height of each harmonic diffraction element is 16.460 μm and 12.813 μm respectively, the obtained bandwidth integral average diffraction efficiency is higher than 0.4 μm and 0.7 μm, and the bandwidth integral average diffraction efficiency of 0.435 μm and 0.598 μm are 3.934% and 2.241% respectively when the design wavelength is set, the surface microstructure height of each harmonic diffraction element is small, the optimal design of the multilayer diffraction optical element is realized, the bandwidth integral average diffraction efficiency design of the multilayer diffraction optical element can be realized, and the problem of optimal selection of the design wavelength in the design is solved.
Drawings
Fig. 1 is a schematic structural view of a multilayer diffractive optical element.
FIG. 2 is a graph showing the relationship between diffraction efficiency and wavelength for the designed wavelengths of 0.4 μm and 0.7 μm for the multilayer diffractive optical element.
FIG. 3 is a graph showing the relationship between diffraction efficiency and wavelength for the designed wavelengths of 0.486 μm and 0.656 μm of the multilayer diffractive optical element.
FIG. 4 is a graph showing a relationship between the maximum bandwidth integrated average diffraction efficiency of the multilayer diffractive optical element and the variation of the first design wavelength when the second design wavelength is an arbitrary value from 0.4 μm to 0.7 μm.
FIG. 5 is a graph showing a relationship between the maximum bandwidth integrated average diffraction efficiency of the multilayer diffractive optical element and the variation of the second design wavelength when the first design wavelength is an arbitrary value from 0.4 μm to 0.7 μm.
Fig. 6 is a graph showing a relationship between diffraction efficiency and wavelength when the bandwidth integration efficiency of the multilayer diffractive optical element is maximum.
Fig. 7 is a graph showing the relationship between diffraction efficiency and wavelength for three cases where the design wavelengths of the multilayer diffractive optical element are different, and this graph is also referred to as an abstract drawing.
Detailed Description
The method of the present invention is further described below, and the structure of the multilayer diffractive optical element is shown in FIG. 1, in which the number of layers is two.
The first step is to optimally select optical materials for forming the multilayer diffraction optical element according to a surface microstructure height formula of the multilayer diffraction optical element. According to the expression of the phase delay phi (lambda) of the diffractive optical element in scalar diffraction theory:
φ(λ)＝k[n1(λ)-1]H1+k[n2(λ)-1]H2 (1)
in the formula: λ is the operating wavelength, k is the wavenumber and k is 2 π/λ, n1(lambda) and n2(λ) is a refractive index of the optical material of the multilayer diffractive optical element at a wavelength of λ, H1And H2The heights of the surface microstructures of the layers of the multilayer diffractive optical element are respectively. When the optical material and design wavelength of the multilayer diffraction optical element are lambda1、λ2After determination, the phase delays of the multilayer diffractive optical element form a system of linear equations:
the multilayer diffractive optical element is obtained by solving the system of linear equations (2) with the diffraction order m being 1, and the design wavelength λ of the multilayer diffractive optical element is obtained1、λ2Surface microstructure height H1、H2：
When the design wavelength of the multilayer diffractive optical element is determined and one of the selected materials is a high refractive index, low dispersion optical material and the other is a low refractive index, high dispersion optical material, the denominator in the surface microstructure height formulas (3) and (4) of the multilayer diffractive optical element is the maximum, and then the surface microstructure height of the multilayer diffractive optical element is the minimum.
And secondly, determining the bandwidth integral average diffraction efficiency distribution by adopting different design wavelength combinations in the whole working waveband. When the optical material and the design wavelength of the multilayer diffractive optical element are determined, the height of the surface microstructure of the multilayer diffractive optical element is also determined, and the diffraction efficiency eta of the m-th diffraction order of the multilayer diffractive optical element is determinedm(λ) is:
wherein, <math><mrow><mi>sin</mi><mi>c</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><mi>sin</mi><mrow><mo>(</mo><mi>πx</mi><mo>)</mo></mrow></mrow><mi>πx</mi></mfrac></mrow></math>
at a design wavelength of λ in the multilayer diffractive optical element1、λ2The bandwidth-integrated average diffraction efficiency eta of the m-th diffraction ordermint(λ1，λ2) Comprises the following steps:
in the formula: lambda [ alpha ]min、λmaxRespectively representing the minimum and maximum wavelengths of the operating band.
And thirdly, determining the maximum bandwidth integral average diffraction efficiency and the corresponding design wavelength in the whole working waveband. After the materials constituting the multilayer diffractive optical element are determined, when the wavelength λ is designed1、λ2In the case of a pair of different variation amounts, it is found from equation (6) that the bandwidth-integrated average diffraction efficiency of the multilayer diffractive optical element also varies. When the design wavelength lambda1Is a fixed wavelength, λ2Is a wavelength from the minimum λminTo a maximum wavelength lambdamaxAny value in between, there is a maximum bandwidth integrated mean diffraction efficiency ηmint(λ1)maxThen, based on the principle, different design wavelengths λ can be drawn1The maximum bandwidth at time integrates the change in diffraction. Similarly, when the design wavelength λ2Is a fixed wavelength, λ1Is a wavelength from the minimum λminTo a maximum wavelength lambdamaxAny value in between, there is a maximum bandwidth integrated mean diffraction efficiency ηmint(λ2)maxThen, according to the principle, different design wavelengths λ are drawn2The maximum bandwidth at time integrates the change in diffraction. According to the definition of the bandwidth integral average diffraction efficiency, the maximum bandwidth integral average diffraction efficiency and the first design wavelength lambda1The maximum bandwidth integral average diffraction efficiency distribution graph, and the maximum bandwidth integral average diffraction efficiency and the second design wavelength lambda2The distribution diagram of the maximum bandwidth integral average diffraction efficiency shows that the design wavelength corresponding to the maximum bandwidth integral average diffraction efficiency of the multilayer diffractive optical element is a pair of symmetrical points, and the bandwidth integral average diffraction efficiency of the multilayer diffractive optical element can be maximized, namely (lambda)1，λ2，ηmmax) And (lambda)2，λ1，ηmmax) The corresponding design wavelength is the design wavelength of the multilayer diffractive optical element with the maximized bandwidth-integrated average diffraction efficiency.
And fourthly, substituting the determined design wavelength corresponding to the maximum bandwidth integral average diffraction efficiency into a surface microstructure height formula of the multilayer diffraction optical element, and calculating to obtain the optimized surface microstructure height and the optimized diffraction efficiency of the multilayer diffraction optical element. Determining a design wavelength according to the maximum bandwidth integral average diffraction efficiency, substituting the design wavelength into surface microstructure height formulas (3) and (4) of the multilayer diffraction optical element to obtain the surface microstructure height of the multilayer diffraction optical element, substituting the optimized surface microstructure height of the multilayer diffraction optical element into a phase delay expression (1) of the multilayer diffraction optical element, and obtaining the diffraction efficiency of the m diffraction order of the optimized multilayer diffraction optical element according to a diffraction efficiency formula (5) of the m diffraction order of the multilayer diffraction optical element.
The method of the present invention is further illustrated by the example of a multilayer diffractive optical element using the high refractive index, low dispersion optical material N-FK51A and the low refractive index, high dispersion material P-SF67 from Schottky, Germany.
When the design wavelength selection waveband of the multilayer diffractive optical element is 0.4 μm and 0.7 μm at two ends, the height of the surface microstructure of the multilayer diffractive optical element is 8.674 μm and 3.934 μm respectively, the bandwidth integration average diffraction efficiency is 95.524%, and the diffraction efficiency distribution is shown in figure 2. When the design wavelength of the multilayer diffractive optical element is selected from an F (0.4861 μm) line and a C (0.6563 μm) line, the surface microstructure height of the multilayer diffractive optical element is 11.700 μm and 5.606 μm, respectively, the bandwidth integral average diffraction efficiency is 97.032%, and the diffraction efficiency distribution is shown in FIG. 3.
When the multilayer diffractive optical element is designed according to the above maximization of the bandwidth-integrated average diffraction efficiency, the relationship between the bandwidth-integrated average diffraction efficiency of the multilayer diffractive optical element and the first design wavelength is shown in fig. 4, and the relationship between the bandwidth-integrated average diffraction efficiency and the second design wavelength is shown in fig. 5. From fig. 4 and 5, it can be seen that the design wavelength corresponding to the maximum bandwidth integrated average diffraction efficiency of the multilayer diffractive optical element is a pair of symmetric points, and the maximum bandwidth integrated average diffraction efficiency of the multilayer diffractive optical element is maximized, that is, when the design wavelength is usedIs λ1＝0.435μm，λ2＝0.598μm，ηmmax99.288% when λ1＝0.598μm，λ2＝0.435μm，ηmmax99.288%, the corresponding design wavelength is the design wavelength of the multilayer diffractive optical element with the maximum bandwidth-integrated average diffraction efficiency.
When the design wavelengths of the multilayer diffractive optical element were 0.435 μm and 0.598 μm, the surface microstructure heights of the multilayer diffractive optical element were 8.186 μm and 3.739 μm, respectively, and the bandwidth-integrated average diffraction efficiency was 99.288%, and the diffraction efficiency distribution is shown in fig. 6.
According to the formula (5), the diffraction efficiencies of different methods are obtained
And the diffraction efficiency at the design wavelength determined according to the method of the present invention
Distribution, as shown in FIG. 7.
Claims (3)
1. An optimal design method of a multilayer diffraction optical element is characterized in that (1) optical materials forming the multilayer diffraction optical element are optimally selected according to a surface microstructure height formula of the multilayer diffraction optical element; (2) in the whole working waveband, different design wavelength combinations are adopted to determine the bandwidth integral average diffraction efficiency distribution; (3) determining the maximum bandwidth integral average diffraction efficiency and the corresponding design wavelength in the whole working waveband; (4) and substituting the determined design wavelength corresponding to the maximum bandwidth integral average diffraction efficiency into a surface microstructure height formula of the multilayer diffraction optical element, and calculating to obtain the optimized surface microstructure height and the optimized diffraction efficiency of the multilayer diffraction optical element.
2. The method of claim 1, wherein the surface microstructure height formula of the multilayer diffractive optical element is as follows:
in the formula: h1And H2Respectively the height of the surface microstructure of each layer of the multi-layer diffraction optical element, m is the diffraction order, lambda1、λ2For the design wavelength, n, of the multilayer diffractive optical element1(λ1)、n1(λ2)、n2(λ1) And n2(λ2) Respectively the refractive index of the optical material of the multilayer diffractive optical element to the design wavelength.
3. The method of claim 1, wherein the bandwidth-integrated average diffraction efficiency is determined by the following equation:
in the formula: etam int(λ 1, λ 2) is the bandwidth-integrated average diffraction efficiency of the m-th diffraction order, λmin，λmaxRespectively representing the minimum and maximum wavelengths, η, of the operating bandm(λ) is the diffraction efficiency of the m-th diffraction order.
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Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104237992A (en) * | 2014-10-13 | 2014-12-24 | 长春理工大学 | Method for analyzing eccentricity errors of multilayer diffractive optical elements |
| CN112188065A (en) * | 2020-09-30 | 2021-01-05 | 维沃移动通信有限公司 | Imaging device and electronic apparatus |
| WO2021057651A1 (en) * | 2019-09-24 | 2021-04-01 | 杭州驭光光电科技有限公司 | Design method of diffractive optical assembly, and diffractive optical assembly |
| CN112859328A (en) * | 2021-01-13 | 2021-05-28 | 吉林大学 | Optical flow integrated broadband and high-efficiency multilayer diffraction optical element and preparation method thereof |
| CN113970844A (en) * | 2021-10-30 | 2022-01-25 | 西北工业大学 | Optimization design method of free-form surface substrate multilayer diffraction element |
| CN117075329A (en) * | 2023-07-26 | 2023-11-17 | 泰山学院 | Double-layer diffraction optical element optimization method and system and electronic equipment |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN101231357A (en) * | 2007-01-22 | 2008-07-30 | 佳能株式会社 | Laminated diffraction optical element |
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| CN101231357A (en) * | 2007-01-22 | 2008-07-30 | 佳能株式会社 | Laminated diffraction optical element |
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Cited By (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104237992A (en) * | 2014-10-13 | 2014-12-24 | 长春理工大学 | Method for analyzing eccentricity errors of multilayer diffractive optical elements |
| WO2021057651A1 (en) * | 2019-09-24 | 2021-04-01 | 杭州驭光光电科技有限公司 | Design method of diffractive optical assembly, and diffractive optical assembly |
| US11740483B2 (en) | 2019-09-24 | 2023-08-29 | Hangzhou Uphoton Optoelectronics Technology Co., Ltd. | Method of diffractive optical assembly, and diffractive optical assembly |
| CN112188065A (en) * | 2020-09-30 | 2021-01-05 | 维沃移动通信有限公司 | Imaging device and electronic apparatus |
| CN112188065B (en) * | 2020-09-30 | 2022-02-15 | 维沃移动通信有限公司 | Imaging device and electronic apparatus |
| CN112859328A (en) * | 2021-01-13 | 2021-05-28 | 吉林大学 | Optical flow integrated broadband and high-efficiency multilayer diffraction optical element and preparation method thereof |
| CN113970844A (en) * | 2021-10-30 | 2022-01-25 | 西北工业大学 | Optimization design method of free-form surface substrate multilayer diffraction element |
| CN117075329A (en) * | 2023-07-26 | 2023-11-17 | 泰山学院 | Double-layer diffraction optical element optimization method and system and electronic equipment |
| CN117075329B (en) * | 2023-07-26 | 2024-04-12 | 泰山学院 | Double-layer diffraction optical element optimization method and system and electronic equipment |
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