CN113866979B - Achromatic method for multi-order diffraction lens and achromatic multi-order diffraction lens - Google Patents
Achromatic method for multi-order diffraction lens and achromatic multi-order diffraction lens Download PDFInfo
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- CN113866979B CN113866979B CN202111043831.3A CN202111043831A CN113866979B CN 113866979 B CN113866979 B CN 113866979B CN 202111043831 A CN202111043831 A CN 202111043831A CN 113866979 B CN113866979 B CN 113866979B
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Abstract
The invention discloses an achromatic method of a multi-order diffraction lens and the achromatic multi-order diffraction lens, firstly, according to the ring number and the gray level of the initial multi-order diffraction lens, designing the constraint optimization problem of the light field intensity at the focus after passing through the multi-order diffraction lens, enabling the focused light field at each wavelength to be consistent, calculating the quasi-global optimal solution of the constraint optimization problem by combining a global optimization algorithm and a search algorithm, and then performing smoothing processing and gradient descent processing to obtain the achromatic multi-order diffraction lens; the maximum value of the depth-to-width ratio of the unit structure of the gray scale order distribution of each ring height of the achromatic multi-order diffraction lens is not more than 2. The invention realizes the parameter design of the large-size wide-spectrum achromatic plane lens, compresses the traditional achromatic system into a plane lens, greatly reduces the volume and the cost of the achromatic imaging system, reduces the processing difficulty, improves the performance of the lens and realizes high-quality achromatic imaging in a wide spectrum range.
Description
Technical Field
The invention relates to an achromatic method of a multi-order diffraction lens and the achromatic multi-order diffraction lens.
Background
In the field of optical imaging, obtaining broad-spectrum achromatic imaging is one of the important targets of optical imaging. In a conventional imaging system, a compound lens made of a plurality of different materials is usually used to eliminate refractive chromatic aberration generated by material dispersion, so as to realize clear imaging in the whole spectrum, or a plurality of refractive lenses are combined into a lens group to realize suppression of chromatic aberration.
Achromatic compound lenses made of various materials are currently roughly classified into three types: achromatic lenses, apochromatic lenses, superachromatic lenses; the achromatic lens is made of at least two materials, so that chromatic aberration at two wavelengths (red light and blue light) can be eliminated; the apochromatic lens adopts at least three materials to eliminate chromatic aberration at three wavelengths; the super-achromatic lens adopts at least four materials, and eliminates chromatic aberration at four wavelengths. Because the achromatic performance of the lens needs to be improved by increasing the types of materials, compared with the common lens, the lens has larger volume, high processing precision requirement and expensive manufacture.
By using different materials and different curvatures of the refraction lenses, different dispersion laws, achromatization can be realized by combining a plurality of refraction lenses into a lens group. The proposal increases the volume and the cost of the whole system in multiples, and simultaneously, the alignment between the lenses is a process with high precision requirement, thereby increasing the difficulty of manufacturing and greatly limiting the popularization and the application of the achromatic imaging device.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide an achromatic method of a multi-order diffraction lens, which can clearly image in a wide spectrum range, and the achromatic multi-order diffraction lens.
The technical scheme is as follows: the achromatization method of the multi-order diffraction lens is characterized by comprising the following steps:
(1) According to the ring number and the gray scale order of the initial multi-order diffraction lens, the constraint optimization problem of the light field intensity I (m, lambda) of the focus of the light passing through the multi-order diffraction lens is designed, so that the focused light field at each wavelength is consistent, wherein m is the gray scale order distribution of the multi-order diffraction lens, and lambda is the wavelength of the light;
(2) Calculating a quasi-global optimal solution m' of the constraint optimization problem by combining a global optimization algorithm and a search algorithm;
(3) Smoothing m ' obtained in the step (2), removing a unit structure with a large depth-width ratio in m ' and obtaining a gray scale order distribution m ' after smoothing;
(4) And (4) performing gradient descending treatment on the m 'obtained in the step (3) to obtain the gray scale order distribution m' of the achromatic multi-order diffraction lens.
Further, the formula of the constraint optimization problem is as follows:
s.t.1≤m i ≤M
i＝1，2...N
wherein m is i The number of gray scale orders of the ith ring height is N, the number of rings of the multi-order diffraction lens is N, and M is the maximum value of the gray scale orders.
The achromatic multi-order diffraction lens consists of annular structures with different heights, and the maximum value of the depth-to-width ratio of unit structures with gray scale order distribution of each annular height is not more than 2:1.
The step (2) is as follows:
(21) Carrying out binarization processing on the gray level order distribution of the initial multi-order diffraction lens;
(22) Calculating a solution of the constraint optimization problem in the step (1) by using a binary genetic algorithm;
(23) And (3) taking the solution obtained in the step (2) as an initial value, and calculating a quasi-global optimal solution m' of the constraint optimization problem in the step (1) by using a pattern search method.
And (4) performing gradient descending treatment on the m' obtained in the step (3) by adopting a steepest descent method.
Has the advantages that: compared with the prior art, the invention has the advantages that: (1) The focal point intensity is used as an achromatic optimization target, so that the calculation complexity is low and the time consumption is short; (2) By combining the global optimization algorithm and the local optimization algorithm, compared with the method only adopting the global optimization algorithm, the optimization speed is higher, the performance of the lens is improved, and high-quality achromatic imaging in a wide spectral range is realized; (3) The design of a large-size wide-spectrum achromatic plane lens is realized, the traditional achromatic system is compressed into a plane lens, and the volume and the cost of the achromatic imaging system are greatly reduced; (4) The structure height distribution is smoothed, so that the processing difficulty is greatly reduced, and the processing of the multi-order diffraction lens with larger thickness becomes feasible;
drawings
FIG. 1 is an initial gray scale order distribution m according to the present invention 0 A schematic diagram of (a);
FIG. 2 is a diagram illustrating a gray scale order distribution m' of a multi-order diffractive lens after a search process according to the present invention;
FIG. 3 is a schematic diagram illustrating gray scale distribution of heights from ring 1341 to ring 1400 in FIG. 2;
FIG. 4 is a schematic diagram of a gray scale order distribution m' of the smoothed multi-order diffraction lens;
FIG. 5 is a schematic illustration of the gray scale order distribution m' "of an achromatic multiple order diffractive lens;
FIG. 6 is a diagram illustrating gray scale distribution of heights from the 1341 th ring to the 1400 th ring in FIG. 5;
FIG. 7 is a schematic diagram of an initial multiple order diffractive lens of the present invention;
FIG. 8 is a schematic diagram of a multi-order diffractive lens after a search process according to the present invention;
FIG. 9 is a schematic view of a smoothed multiple-order diffractive lens of the present invention;
FIG. 10 is a schematic view of an achromatic multiple order diffractive lens of the present invention;
FIG. 11 is a graph showing the results of a focusing experiment for an achromatic multi-order diffractive lens of the present invention;
FIG. 12 is a graph of experimental results of white light imaging with an achromatic multiple order diffractive lens of the present invention;
wherein, the graph (a) is the result of the white light imaging of the resolution plate by the achromatic multi-order diffraction lens;
and (b) is the imaging result of the achromatic multi-order diffraction lens on siemens star white light.
Detailed Description
The achromatization method of the multi-order diffraction lens comprises the following steps:
(1) Achromatic optimization targets for designing multi-order diffractive lenses
The multi-order diffractive lens is composed of a series of ring structures of different heights, and the phase of the lens can be expressed as:
where φ (r) represents the phase at radial coordinate r, λ is the wavelength, n (λ) is the refractive index at the corresponding wavelength, and h (r) is the structure height at r.
In this embodiment, the width of each ring is a fixed value, which can be expressed by Δ r, and the number of rings constituting the lens is N. Because the actual processing needs to adopt a gray level laser photoetching process, the height h is also in a discrete distribution, the height of each order is delta h, m is the gray level order distribution of the multi-order diffraction lens, and m = { m = i }，i＝1，2，3......N，m i The number of gray scale steps, called the height of the ith ring, is between 1 and M, M being the maximum order of the gray scale steps, such that the height at the ith ringh (i Δ r) may be represented as m i Δ h. After introducing the number of rings and the number of gray levels, the optimization objective is expressed as follows:
wherein, I (m, lambda) is the light field intensity converged at the focus after the light with wavelength lambda passes through the lens with the gray scale order distribution of m, and the maxmin optimization means is adopted to ensure the consistency of the focused light field at each wavelength. The focal intensity I is used as the objective function, and the computational complexity, i.e. the number of multiplications to be computed, is O (N), whereas if other objective functions are used, e.g. the optical field intensity of the focal plane as a whole, the computational complexity is O (N) 2 ) The focal intensity I as an objective function is therefore less time consuming. The initial multi-order diffractive lens in this embodiment comprises 2560 rings in total, and the gray scale number is at most 192. Therefore, to realize the achromatic design of the multi-order diffractive lens described above is equivalent to solving the following constrained optimization problem:
(2) Solving a constrained optimization problem for a multi-order diffractive lens
In order to solve the above constraint optimization problem, the optimization design scheme is divided into three parts: search, smoothing and gradient descent.
(21) Search processing
A quasi-global optimal solution is obtained in a short time by combining a global optimization algorithm and a search algorithm, if the global optimization algorithm is only adopted, the search speed is one to two orders of magnitude slower, and the search speed ratio is increased along with the increase of the structure size. In this embodiment, a binary genetic algorithm and a Hooke-Jeeves algorithm (pattern search method) are used. The specific process is as follows: initial gray scale order distribution m for a given initial multi-order diffractive lens 0 ，m 0 Is a random vector with length of 2560, each component takes on the value of 1-192, and the gray scale order distribution m is initialized 0 Is shown in figure 1. And then binarizing the population to be used as an initial population optimized by a binary genetic algorithm, and optimizing by adopting the binary genetic algorithm. And then, taking the result obtained by the binary genetic algorithm as an initial value, further optimizing by adopting a Hooke-Jeeves algorithm, and calculating a quasi-global optimal solution, namely a schematic diagram of the gray scale order distribution m ' after search processing, namely the gray scale order distribution m ' after search processing, as shown in figure 2, the gray scale order distribution from the 1341 st ring to the 1400 th ring in figure 3 is shown, the rectangular protrusions in figure 3 are called as a unit structure, and the lenses corresponding to the distribution realize the 400-1100nm waveband achromatization function, namely, the light of the 400-1100nm waveband is focused to the same position after passing through the lenses distributed as m '.
(22) Smoothing process
The gray scale order distribution m 'of the multi-order diffraction lens after search processing has a larger depth-to-width ratio (more than 2: 1), and in order to meet the processing requirement, the m' needs to be smoothed to remove the structure with the larger depth-to-width ratio in the distribution. The specific process can be represented by the following formula:
where m ' is the distribution of the gradation levels after the smoothing process, α (m ') and α (m ') are the aspect ratios of the unit structures in the distribution of m ' and m ', i.e., the height to width ratios of the unit structures, α 0 For reference, 2 is taken here, and β is a constant, generally between 5 and 10. When the input alpha (m') is larger than alpha 0 Then α (m ") of the output of the above equation will be significantly less than α (m'); and when the input alpha (m') is less than alpha 0 When the output of the above equation is α (m ″) almost equal to α (m'). Therefore, the structure with a large aspect ratio in the distribution m 'can be changed into the structure with a small aspect ratio through the formula, and the structure with the small aspect ratio is almost kept unchanged, so that the obtained gray scale order distribution is m'; the schematic diagram of the smoothed gray scale order distribution m "is shown in fig. 4, and there is no structure with an aspect ratio > 2:1 in the smoothed gray scale order distribution m", which greatly reduces the processing difficulty.
(23) Gradient descent processing
Because the step (22) can cause the reduction of the optimization objective function value, the gradient reduction is adopted for processing, so that the optimization objective function value is further improved, and the integral lower depth-to-width ratio is kept; in this embodiment, a steepest descent method is adopted, and this step can be expressed as:
wherein m' ″ is the gray scale order distribution after the gradient descent processing, that is, the gray scale order distribution of the achromatic multi-order diffraction lens, and a schematic diagram thereof is shown in fig. 5, and fig. 6 is the gray scale order distribution of the 1341 st ring to the 1400 th ring; f is the objective function, in this problem f = min λ I (m ", λ), γ is a constant, representing the step of descent, and since the optimization goal is to maximize, γ takes on a positive number.
The achromatic multi-order diffraction lens is prepared according to the method, the initial multi-order diffraction lens before optimization processing is shown in figure 7, and the multi-order diffraction lens after search processing is shown in figure 8; the smoothed multiple-order diffractive lens is shown in FIG. 9; fig. 10 shows an achromatic multi-order diffraction lens according to the present invention, which is a multi-order diffraction lens after gradient down processing. The diameter of the achromatic multi-order diffraction lens is 1.024cm, the achromatic multi-order diffraction lens totally comprises 2560 rings, the maximum height is 15 mu m, the maximum height order is 192 orders, the gray order distribution is shown in figure 5, the maximum value of the depth-to-width ratio of a unit structure is not more than 2, the focal length of the lens is 5cm, and the achromatic wavelength band is 400nm-1100nm.
The achromatic performance of the achromatic multi-order diffraction lens can be verified through focusing experiments and imaging experiments, and FIG. 11 shows the result of the focusing experiments, wherein lights of different wave bands are focused on the same position on an optical axis; FIGS. 12 (a) - (b) are experimental results of white light imaging on resolution plates and Siemens star, showing that the achromatic multi-order diffractive lens of the present invention does not have significant chromatic aberration.
Claims (6)
1. An achromatization method for a multiple order diffractive lens comprising the steps of:
(1) According to the ring number and the gray scale order of the initial multi-order diffraction lens, the constraint optimization problem of the light field intensity I (m, lambda) of the focus of the light passing through the multi-order diffraction lens is designed, so that the focused light field at each wavelength is consistent, wherein m is the gray scale order distribution of the multi-order diffraction lens, and lambda is the wavelength of the light;
(2) Calculating a quasi-global optimal solution m' of the constraint optimization problem by combining a global optimization algorithm and a search algorithm;
(3) Smoothing m ' obtained in the step (2), removing a unit structure with a large depth-width ratio in m ', and obtaining a gray level order distribution m ' after smoothing;
(4) Performing gradient descending treatment on the m 'obtained in the step (3) to obtain the gray scale order distribution m' of the achromatic multi-order diffraction lens;
the step (2) is as follows:
(21) Carrying out binarization processing on the gray level order distribution of the initial multi-order diffraction lens;
(22) Calculating a solution of the constraint optimization problem in the step (1) by using a binary genetic algorithm;
(23) And (3) taking the solution obtained in the step (2) as an initial value, and calculating a quasi-global optimal solution m' of the constraint optimization problem in the step (1) by using a pattern search method.
2. The achromatization method for multi-order diffraction lenses of claim 1 wherein the constrained optimization problem of step (1) is a maxmin optimization.
3. The method for achromatizing an optical diffraction lens of claim 1 wherein the constraint optimization problem of step (1) is formulated as:
s.t.1≤m i ≤M
i＝1,2…N
wherein m is i The number of gray scale orders of the ith ring height is N, the number of rings of the multi-order diffraction lens is N, and M is the maximum value of the gray scale orders.
4. An achromatization method for multi-order diffraction lenses as claimed in claim 1, characterized in that the calculation formula of the aspect ratio α (m ") of the gradation order distribution m" after the smoothing in step (3) is as follows:
wherein beta is a constant, beta is more than or equal to 5 and less than or equal to 10, and alpha 0 Is a reference value for the aspect ratio α (m ') of m'.
5. The achromatization method of multi-order diffraction lenses of claim 1, wherein step (4) uses the steepest descent method to perform gradient descent processing on m "obtained in step (3).
6. An achromatic multi-order diffractive lens produced by a method as claimed in any one of claims 1 to 5, consisting of annular structures of different heights, the maximum value of the aspect ratio of the unit structures of the gray-scale order distribution of each annular height being not more than 2.
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| CN202111043831.3A CN113866979B (en) | 2021-09-07 | 2021-09-07 | Achromatic method for multi-order diffraction lens and achromatic multi-order diffraction lens |
| PCT/CN2021/119737 WO2023035322A1 (en) | 2021-09-07 | 2021-09-23 | Achromatic method of multi-order diffractive lens and achromatic multi-order diffractive lens |
| KR1020227025896A KR102685840B1 (en) | 2021-09-07 | 2021-09-23 | Color canceling method of multi-order diffractive lens and color canceling multi-order diffractive lens |
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| JP3996685B2 (en) * | 1996-11-15 | 2007-10-24 | オリンパス株式会社 | Achromatic lens |
| US5912770A (en) * | 1996-11-15 | 1999-06-15 | Olympus Optical Co., Ltd. | Achromatic lens system |
| US6917472B1 (en) * | 2001-11-09 | 2005-07-12 | Xradia, Inc. | Achromatic fresnel optics for ultraviolet and x-ray radiation |
| JP2011215267A (en) * | 2010-03-31 | 2011-10-27 | Nagoya Univ | Achromatic lens, method for manufacturing the same, and optical device equipped with achromatic lens |
| CN109343217A (en) * | 2018-11-13 | 2019-02-15 | 南京大学 | A kind of achromatism light field camera system and colour killing difference method based on super structure lens array |
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