CN113866979B - Achromatic method for multi-order diffraction lens and achromatic multi-order diffraction lens - Google Patents

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

Achromatic method of multi-order diffractive lens and achromatic multi-order diffractive lens

technical field

The invention relates to an achromatic method for a multi-order diffractive lens and an achromatic multi-order diffractive lens.

Background technique

In the field of optical imaging, obtaining wide-spectrum achromatic imaging is one of the important goals of optical imaging. In traditional imaging systems, compound lenses composed of a variety of different materials are usually used to eliminate the refractive chromatic aberration caused by material dispersion, so as to achieve clear imaging in the entire spectrum, or to combine multiple refractive lenses into a lens group to achieve accurate imaging. Suppression of chromatic aberration.

Achromatic compound lenses composed of a variety of different materials are currently roughly divided into three categories: achromat lenses, apochromat lenses, and superachromat lenses; among them, achromat lenses use at least two materials to eliminate two wavelengths ( Red light and blue light) chromatic aberration; apochromatic lenses use at least three materials to eliminate chromatic aberration at three wavelengths; superachromatic lenses use at least four materials to eliminate chromatic aberration at four wavelengths. Since the achromatic performance of this type of lens needs to be improved by increasing the types of materials, compared with ordinary lenses, it is larger in size, requires high processing precision, and is expensive to manufacture.

Refractive lenses with different materials and different curvatures have different dispersion laws, and achromatic aberration can also be achieved by combining multiple refractive lenses into a lens group. This solution doubles the volume and cost of the entire system. At the same time, the alignment between lenses is also a process that requires very high precision, which increases the difficulty of manufacturing and greatly limits the promotion and application of achromatic imaging devices.

Contents of the invention

Purpose of the invention: The purpose of the present invention is to provide an achromatic method for a multi-order diffractive lens, which can clearly image images in a wide spectral range, and an achromatic multi-order diffractive lens.

Technical solution: The achromatic method of the multi-order diffractive lens according to the present invention is characterized in that it comprises the following steps:

(1) According to the number of rings and gray scales of the initial multi-order diffractive lens, design the constrained optimization problem of the light field intensity I(m, λ) at the focal point after the light passes through the multi-order diffractive lens, so that the focusing at each wavelength The light field is consistent, where m is the gray scale distribution of the multi-order diffractive lens, and λ is the wavelength of light;

(2) calculate the quasi-global optimal solution m' of the constrained optimization problem in combination with the global optimization algorithm and the search algorithm;

(3) smoothing the m ' obtained in step (2), removing the unit structure with a large aspect ratio in m ', and obtaining the smoothed gray scale distribution m ";

(4) Gradient descent processing is performed on the m″ obtained in step (3), to obtain the gray scale distribution m″′ of the achromatic multi-order diffractive lens.

Further, the formula of the constrained optimization problem is:

st1≤m _i ≤M

i=1,2...N

Where m _i is the gray level of the i-th ring height, N is the ring number of the multi-order diffractive lens, and M is the maximum value of the gray level.

The achromatic multi-order diffractive lens of the present invention is composed of ring structures with different heights, and the maximum aspect ratio of the unit structure of the gray scale distribution of each ring height does not exceed 2:1.

Described step (2) is:

(21) Binarize the gray scale distribution of the initial multi-order diffractive lens;

(22) utilize binary genetic algorithm to calculate the solution of constraint optimization problem in described step (1);

(23) Using the solution obtained in step (2) as an initial value, using the pattern search method to calculate the quasi-global optimal solution m' of the constrained optimization problem in step (1).

The step (4) uses the steepest descent method to perform gradient descent processing on the m" obtained in the step (3).

Beneficial effects: Compared with the prior art, the present invention has the following advantages: (1) the focus intensity is used as the achromatic optimization target, and the calculation complexity is low and the time consumption is short; (2) by combining the global optimization algorithm and the local optimization algorithm, the relative Compared with only using the global optimization algorithm, the optimization speed is faster, the lens performance is improved, and high-quality achromatic imaging in a wide spectral range is realized; (3) the large-size wide-spectrum achromatic planar lens design is realized, and the traditional achromatic The system is compressed into a flat lens, which greatly reduces the volume and cost of the achromatic imaging system; (4) smoothing the structure height distribution greatly reduces the difficulty of processing, making the processing of multi-order diffractive lenses with large thickness become feasible;

Description of drawings

Fig. 1 is a schematic diagram of the initialization gray scale distribution ^m0 of the present invention;

Fig. 2 is a schematic diagram of the gray scale number distribution m' of the multi-order diffractive lens after the search process of the present invention;

Fig. 3 is a schematic diagram of the gray scale distribution of the heights from the 1341st ring to the 1400th ring in Fig. 2;

4 is a schematic diagram of the gray scale distribution m" of the smoothed multi-order diffractive lens;

Figure 5 is a schematic diagram of the gray scale distribution m"' of the achromatic multi-order diffractive lens;

Fig. 6 is a schematic diagram of the gray scale distribution of the heights from the 1341st ring to the 1400th ring in Fig. 5;

Figure 7 is a schematic diagram of the initial multi-order diffractive lens of the present invention;

FIG. 8 is a schematic diagram of a multi-order diffractive lens after search processing in the present invention;

Fig. 9 is a schematic diagram of the smoothed multi-order diffractive lens of the present invention;

Fig. 10 is a schematic diagram of the achromatic multi-order diffractive lens of the present invention;

Fig. 11 is a diagram of focusing experiment results of the achromatic multi-order diffractive lens of the present invention;

Fig. 12 is a white light imaging experiment result diagram of the achromatic multi-order diffractive lens of the present invention;

Figure (a) is the result of white light imaging on the resolution plate by the achromatic multi-order diffractive lens;

Figure (b) is the imaging result of Siemens star white light by achromatic multi-order diffraction lens.

detailed description

The achromatic method of the multi-order diffractive lens of the present invention comprises the following steps:

(1) Design the achromatic optimization objective of the multi-order diffractive lens

The multi-order diffractive lens is composed of a series of annular structures with different heights, and the phase of the lens can be expressed as:

where φ(r) represents the phase at the radial coordinate r, λ is the wavelength, n(λ) is the refractive index at the corresponding wavelength, and h(r) is the height of the structure at r.

In this embodiment, the width of each ring is a fixed value, which can be represented by Δr, and the number of rings forming the lens is N. Since the actual processing requires the use of gray-scale laser lithography, the height h is also a discrete distribution, and the height of each step is Δh, m is the gray-scale distribution of the multi-order diffractive lens, m={m _i }, i=1 _. The height h( _iΔr ) of can be expressed as mi Δh. After introducing the number of rings and gray levels, the optimization objective is expressed as follows:

Among them, I(m, λ) is the intensity of the light field converged at the focal point after the light of wavelength λ passes through the lens with the gray order distribution of m. The maxmin optimization method is used to ensure the consistency of the focused light field at each wavelength. sex. Using the focus intensity I as the objective function, the computational complexity means that the number of multiplications that need to be calculated is O(N), and if other objective functions are used, for example, the overall light field intensity of the focal plane is used as the objective function, the computational complexity is O (N ² ), so the focal intensity I takes less time as an objective function. The initial multi-order diffractive lens in this embodiment contains a total of 2560 rings, and the maximum number of gray scales is 192. Therefore, to realize the achromatic design of the above-mentioned multi-order diffractive lens, it is equivalent to solving the following constrained optimization problem:

(2) Solve the constrained optimization problem of multi-order diffractive lens

To solve the above constrained optimization problem, the optimization design scheme is divided into three parts: search, smoothing and gradient descent.

(21) Search processing

Combining the global optimization algorithm and the search algorithm to achieve a quasi-global optimal solution in a short period of time, if only the global optimization algorithm is used, the search speed will be one to two orders of magnitude slower, and the search speed will increase with the increase of the structure size And increase. In this embodiment, binary genetic algorithm and Hooke-Jeeves algorithm (pattern search method) are used. The specific process is as follows: Given the initial gray-scale distribution m ⁰ of the initial multi-order diffractive lens, m ⁰ is a random vector with a length of 2560, each component takes a value from 1 to 192, and initializes the gray-scale distribution m ⁰ The schematic diagram is shown in Figure 1. Then it is binarized as the initial population optimized by binary genetic algorithm, and optimized by binary genetic algorithm. Afterwards, the result obtained by binary genetic algorithm optimization is used as the initial value, and the Hooke-Jeeves algorithm is used for further optimization to calculate the quasi-global optimal solution, which is the gray-scale distribution m′ after search processing. The schematic diagram of the distribution m' is shown in Figure 2, and the gray scale distribution of the 1341st ring to the 1400th ring in Figure 3, the rectangular protrusions in Figure 3 are called the unit structure, and the lens corresponding to this distribution realizes the 400-1100nm band elimination Chromatic aberration function, that is, the light in the 400-1100nm band will be focused to the same position after passing through the lens with distribution m'.

(22) Smoothing

After search processing, the gray order distribution m' of the multi-order diffractive lens has a large aspect ratio (>2:1). In order to meet the processing requirements, m' needs to be smoothed to remove the large aspect ratio in the distribution. Structure. The specific process can be expressed by the following formula:

Among them, m″ is the smoothed gray scale distribution, and α(m′) and α(m″) are the aspect ratio of the unit structure in the m′ and m″ distributions respectively, that is, the ratio of the height to the width of the unit structure , α ₀ is a reference value, 2 is taken here, β is a constant, generally 5 to 10. When the input α(m′) is greater than α ₀ , the output α(m″) of the above formula will be significantly smaller than α(m ’); and when the input α(m′) is less than α ₀ , the output α(m″) of the above formula is almost equal to α(m′). Therefore, the distribution m′ with a large aspect ratio The structure becomes a structure with a small aspect ratio, while the structure with a small aspect ratio remains almost unchanged, so the obtained gray scale distribution is m″; the schematic diagram of the smoothed gray scale distribution m″ is as follows As shown in FIG. 4 , there is no structure with an aspect ratio > 2:1 in the smoothed gray scale distribution m″, which greatly reduces the processing difficulty.

(23) Gradient descent processing

Since step (22) will cause the optimization objective function value to decline, it is processed by gradient descent, thereby further improving the optimization objective function value while maintaining a lower overall aspect ratio; the steepest descent method is adopted in this embodiment, and this step can be Expressed as:

Among them, m″' is the gray scale distribution after gradient descent processing, that is, the gray scale distribution of the achromatic multi-order diffractive lens. The gray order distribution of the ring; f is the objective function, in this problem f=min _λ I(m″, λ), γ is a constant, representing the step size of the descent, since the optimization goal is to seek the maximum value, so γ is taken as A positive number.

The achromatic multi-order diffractive lens is prepared according to the above method. The initial multi-order diffractive lens before optimization is shown in Figure 7, and the multi-order diffractive lens after search processing is shown in Figure 8; the smoothed multi-order diffractive lens is shown as As shown in FIG. 9 ; the multi-order diffractive lens after gradient descent processing, that is, the achromatic multi-order diffractive lens of the present invention is shown in FIG. 10 . The achromatic multi-order diffractive lens of the present invention has a diameter of 1.024 cm, contains 2560 rings in total, has a maximum height of 15 μm, and has a maximum height order of 192. Its gray scale distribution is shown in Figure 5, where the unit structure aspect ratio The maximum value does not exceed 2:1, the focal length of the lens is 5cm, and the achromatic wave band is 400nm-1100nm.

Through focusing experiments and imaging experiments, the achromatic performance of the achromatic multi-order diffractive lens can be verified. Figure 11 shows the results of the focusing experiment, and the lights of different wavelength bands are all focused on the same position on the optical axis; The experimental results of resolution plate and Siemens star white light imaging show that there is no obvious chromatic aberration in the achromatic multi-order diffractive lens of the present invention.

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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