Achromatic method for focal depth extension

Abstract

The invention relates to an achromatism method for focal depth extension, and belongs to the technical field of achromatism. Comprising the following steps: acquiring the wavelength of incident light, and determining the minimum wavelength and the maximum wavelength of the incident light; performing upward translation on the phase distribution curve of any wavelength between the minimum wavelength and the maximum wavelength according to a preset phase value; calculating a difference value between any wavelength and the maximum wavelength phase after translation; calculating the phase of the maximum wavelength to obtain a basic phase; compensating the phase difference between the maximum wavelength and other wavelengths according to the preset phase value, the difference value and the basic phase; according to the phase difference, phase distribution curves of different wavelengths are overlapped, and achromatism is completed. Meanwhile, the focal length in the basic phase is designed to achieve focal depth extension. The requirement for complex computing resources is greatly reduced, meanwhile, the regularity of the lens structure is guaranteed, and the machining process is more efficient and easy to implement. In addition, the achromatic metamaterial lens prepared by the method is small in size and low in cost.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of achromatic, in particular to a focal depth extended achromatic method. BACKGROUND

[0002] Chromatic aberration is a phenomenon in which the focal point position changes when different wavelengths of light are incident on a lens. This phenomenon has a significant impact on image quality when the light source is broad-spectrum. Traditionally, achromatic lenses reduce chromatic aberration by combining two lenses with different optical properties, but this approach often results in large lens volumes, complex manufacturing, high costs, and difficulty in integration with other devices.

[0003] With the advent of superlenses, achromatic technology has seen new developments. Superlenses use specific designs of metamaterials to achieve light focusing and chromatic aberration reduction by selecting appropriate periodic unit structures and optimizing unit structure arrangements. Achromatic theory in this field is constantly evolving, mainly including discrete multi-wavelength design and dispersion engineering. Discrete multi-wavelength design targets a few specific wavelengths for achromatic design, while dispersion engineering targets continuous achromatic design in a wide spectral range. Currently, reverse design method has become a potential design method for achromatic superlenses due to its high precision control and greater freedom in module light field. Although reverse design provides more design flexibility, it relies on a large amount of computing resources and high-precision manufacturing technology. SUMMARY

[0004] To this end, the technical problem to be solved by the present application is to overcome the problems of large volume, high cost, complex manufacturing process, and difficulty in processing and manufacturing in the prior art.

[0005] In order to solve the above technical problems, the present application provides a focal depth extended achromatic method, comprising:

[0006] S1, obtaining the wavelength of incident light, determining the minimum wavelength and the maximum wavelength of the wavelength;

[0007] S2, according to the preset phase value, the phase distribution curve of any wavelength between the minimum wavelength and the maximum wavelength is translated upwards;

[0008] S3, calculating the difference between the translated any wavelength and the maximum wavelength phase;

[0009] S4, calculating the phase of the maximum wavelength to obtain the basic phase; according to the focal length in the basic phase, the focal depth is extended; according to the preset phase value, the difference value and the basic phase, the phase difference between the maximum wavelength and other wavelengths is compensated; according to the phase difference, the phase distribution curves of different wavelengths are overlapped, and the achromatic is completed.

[0010] In one embodiment of the present invention, the step S2 further includes shifting the phase distribution curve of the minimum wavelength upward according to a preset offset.

[0011] In one embodiment of the present invention, the preset offset is determined by a maximum phase offset between a minimum wavelength and a maximum wavelength of the incident light.

[0012] In one embodiment of the present invention, the calculation formula of the preset phase value is:

[0013]

[0014] in, is the preset phase value, λ is any wavelength between the minimum wavelength and the maximum wavelength; a and b are constants; λ min is the minimum wavelength, λ max is the maximum wavelength; Γ is the maximum phase shift between the minimum wavelength and the maximum wavelength.

[0015] In one embodiment of the present invention, the phase difference between the maximum wavelength and other wavelengths is compensated, and the phase distribution mathematical expression of the other wavelengths is:

[0016]

[0017] in, is the phase distribution, is the basic phase, is the difference between the phase of different wavelengths and the phase of the maximum wavelength, r is the distance from any point on the metalens to the center of the metalens, λ is any wavelength between the minimum wavelength and the maximum wavelength, and λ max is the maximum wavelength, π is the circumference of a circle, is the preset phase value, and f is the focal length.

[0018] In one embodiment of the present invention, the phase difference between any wavelength after translation and the maximum wavelength is calculated in S3, and the calculation formula of the difference is:

[0019]

[0020] in, is the difference between the phase of different wavelengths and the phase of the maximum wavelength, r is the distance from any point on the metalens to the center of the metalens, λ is any wavelength between the minimum wavelength and the maximum wavelength, and λ max is the maximum wavelength, π is the circumference, and f is the focal length.

[0021] In one embodiment of the present invention, the phase of the maximum wavelength is calculated in S4 to obtain a basic phase, and the calculation formula of the basic phase is:

[0022]

[0023] in, is the basic phase, r is the distance from any point on the metalens to the center of the metalens, λ max is the maximum wavelength, π is the circumference of the circle, F is the focal length of the lens as it changes with r, f is the focal length, R is the maximum radius of the metalens, and Δf(·) is the extended focal depth.

[0024] In a second aspect, in order to solve the above technical problems, the present invention provides an achromatic meta-lens, which is prepared by the above-mentioned achromatic method with extended focal depth.

[0025] In one embodiment of the present invention, the metalens includes a unit structure, and a compensation phase linearly related to the wave number of the incident light is obtained by adjusting the length and width of the unit structure; and a geometric phase of 2θ is superimposed on the compensation phase by rotating the unit structure.

[0026] In one embodiment of the present invention, the nano-column material of the unit structure is hydrogenated amorphous silicon.

[0027] The above technical solution of the present invention has the following beneficial effects compared with the prior art:

[0028] (1) The achromatic aberration method for extending the depth of focus described in the present invention achieves fine control of the lens phase characteristics by accurately shifting the phase distribution curve corresponding to any wavelength between the minimum wavelength and the maximum wavelength upward. At the same time, the difference between the phase distribution after translation and the phase of the maximum wavelength, as well as the basic phase, are calculated, providing a scientific basis for subsequent phase compensation. This calculation process is efficient and reduces dependence on computing resources compared to inverse design, making the design process more economical and easy to implement. In addition, the present invention not only improves the achromatic aberration performance, but also achieves extended depth of focus.

[0029] (2) The present invention first achieves zero dispersion at the edge, thereby simplifying the calculation of the compensation phase. At the same time, the compensation phase ensures that light of different wavelengths converges at the same focal point, achieving achromatic focusing, thereby enhancing the applicability of the lens in various optical applications.

[0030] (3) The present invention improves the focusing capability of the lens over a wide bandwidth, enhancing its applicability. By precisely controlling the phase, the overall performance of the lens is significantly improved, particularly by providing clear imaging at different wavelengths on the same image plane. Furthermore, the achromatic metalens provided by the present invention is compact, low-cost, and simple to manufacture. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] For the purpose of making the content of the present application more easily understood, the present application is further described in detail below according to specific embodiments of the present application and in conjunction with the accompanying drawings, in which

[0032] Figure 1 A flow chart of the achromatic method for extending the depth of focus in the preferred embodiment of the present application;

[0033] Figure 2 A schematic diagram of the focusing position of a simple meta-lens, an achromatic meta-lens and an achromatic meta-lens with extended depth of focus;

[0034] Figure 3 A schematic diagram of the unit structure of the achromatic meta-lens with extended depth of focus in the preferred embodiment of the present application;

[0035] Figure 4 A simulated result diagram of the simple meta-lens, the achromatic meta-lens and the achromatic meta-lens with extended depth of focus in the preferred embodiment of the present application in the wavelength range of 550nm to 750nm. DETAILED DESCRIPTION

[0036] The present application is further described below in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present application and implement it.

[0037] Embodiment One

[0038] Referring to Figure 1 The present application provides an achromatic method for extending the depth of focus, including but not limited to the following steps:

[0039] S1, obtaining the wavelength of the incident light, determining the minimum wavelength and the maximum wavelength of the wavelength;

[0040] S2, according to the preset phase value, shifting the phase distribution curve of any wavelength between the minimum wavelength and the maximum wavelength upward;

[0041] S3, calculating the difference between the shifted any wavelength and the maximum wavelength phase;

[0042] S4, calculating the phase of the maximum wavelength to obtain the basic phase; realizing the extension of the depth of focus according to the focal length in the basic phase; compensating for the phase difference between the maximum wavelength and other wavelengths according to the preset phase value, the difference and the basic phase; making the phase distribution curves of different wavelengths overlap according to the phase difference, and completing the achromatization.

[0043] The embodiment of the present application provides a chromatic aberration correction method for extended depth of focus. The phase distribution curve of any wavelength between the minimum wavelength and the maximum wavelength is shifted upwards to realize accurate control of the phase. At the same time, the difference between the phase of any wavelength after shifting and the phase of the maximum wavelength is calculated, and the phase of the maximum wavelength, that is, the basic phase, is calculated to provide a basis for phase compensation. The above calculation process is efficient and reduces the dependence on computing resources compared to reverse design, making the design process more economical and easy to implement. The method provided by the embodiment of the present application not only realizes broadband focusing and improves the applicability of the lens, but also enhances the performance of the lens through accurate phase control. The improvement of chromatic aberration correction capability enables the lens to maintain clear imaging at different wavelengths, which is particularly important for high-precision imaging applications. At the same time, this design also improves the clarity of the image, enhances the flexibility and adjustability of the lens, and provides the possibility for designers to adjust the optical performance according to specific application requirements. In addition, the potential cost-effectiveness is also a big advantage of this design method, because it reduces the manufacturing cost by reducing the demand for complex optical elements while maintaining or improving the performance of the lens.

[0044] Specifically, in step S1, the method for obtaining the wavelength of incident light and determining the minimum and maximum wavelengths thereof includes using a spectrometer for spectral analysis to disperse the light beam and measure the intensity of each wavelength, using an interferometer such as a Michelson interferometer to accurately measure the wavelength through an interference pattern, applying the grating diffraction principle combined with the grating equation to calculate the wavelength, and using low-cost and easy-to-operate methods such as photoelastic modulation technology to achieve rapid measurement. In addition, dispersion-type measurement, adjustable filter-type measurement, optical fiber sensors or optical resonant cavities and other technologies can also be used. In actual application, the most suitable measurement method can be selected according to specific requirements and conditions.

[0045] Specifically, when the incident light is a wide spectrum, the focal point position of the single-focus metasurface lens will change with the wavelength, which can be referred to as Figure 2 In addition to the central point of the metasurface lens, the phase distribution curve at other positions also has a phase difference, and this phase difference increases significantly with the increase of the lens radius. Therefore, the phase difference at the edge of the lens reaches a maximum value, which is defined as the maximum phase shift, denoted by the symbol Γ. To realize the zero dispersion characteristic at the edge of the metasurface lens, the embodiment adopts the strategy of shifting the phase distribution curve corresponding to the minimum wavelength by the maximum phase shift Γ. Specifically, in step S2, the phase distribution curve of the minimum wavelength is shifted upwards by a preset offset, and the preset offset is the maximum phase shift Γ between the minimum wavelength and the maximum wavelength. This design cleverly realizes the zero dispersion at the edge, thereby simplifying the calculation of the subsequent compensation phase. At the same time, the compensation phase ensures that light of different wavelengths can converge at the same focal point, realizing chromatic aberration correction imaging, thereby enhancing the applicability of the lens in various optical applications.

[0046] Further, in step S2, for any wavelength λ between the minimum wavelength and the maximum wavelength, the amount of upward translation of its phase distribution curve, i.e., the calculation formula of the preset phase value is: min < λ < λ max , the calculation formula of the preset phase value is:

[0047]

[0048] wherein, is the preset phase value, a and b are constants, λ min is the minimum wavelength, λ max is the maximum wavelength. This translation strategy will not have a negative impact on the focusing performance of the metasurface lens, but cleverly locates the zero dispersion point at the edge of the lens. Such a design not only maintains the focusing efficiency of the lens, but also effectively controls the dispersion in the edge region, thereby optimizing the optical performance of the lens.

[0049] In the embodiment of the present application, the unit structure of the metasurface lens is cleverly designed to achieve the functions of achromatization and extended depth of focus. This design optimizes the focusing performance by precisely controlling the phase distribution of the metasurface lens. For the phase distribution, its mathematical expression is:

[0050]

[0051] wherein, is the phase distribution, r is the distance from any point on the metasurface lens to the center of the metasurface lens, is the working wavelength, v is the circular constant, and f is the focal length of the metasurface lens. In a conventional single-focus lens, the focal length f is usually set as a constant.

[0052] Further, when the focal length of the lens changes with the distance r, the focal length expression at this time is: F = f + f ′ (r), such a lens is called a lens with extended depth of focus (EDOF). In this expression, f represents the minimum focal length; f ′ (r) represents the extended depth of focus, usually represented as R represents the maximum radius of the metasurface lens. The advantage of this design is that it can achieve more uniform energy distribution, thereby improving the imaging quality. The lens with extended depth of focus can be regarded as composed of multiple single-focus lens rings corresponding to different focal lengths, and each ring is responsible for providing optimal focusing within a certain radius range. The design of this multi-focus structure makes the lens maintain good imaging performance at different distances, significantly expanding the depth of focus range of the lens.

[0053] This embodiment achieves the optical goal of achromatism by adjusting the phase distribution curves of different wavelengths to achieve perfect overlap. To this end, it is necessary to compensate for the phase difference between the maximum wavelength and other wavelengths. Therefore, the mathematical expression of the phase distribution of other wavelengths is:

[0054]

[0055] in, is the phase distribution; The phase representing the maximum wavelength is called the fundamental phase; The phase that needs to be compensated is called the compensation phase; is the difference between the phase at different wavelengths and the phase at the maximum wavelength. Thus, the phase of the achromatic focusing metalens is divided into two parts: the basic phase and the compensation phase. Next, this embodiment utilizes the propagation phase and the geometric phase to achieve the compensation phase and basic phase distributions, respectively.

[0056] Specifically, the propagation phase control method, based on effective medium theory and waveguide theory, provides a precise means of phase adjustment. This method achieves precise control of the accumulated phase of light waves propagating in the waveguide by finely adjusting the geometric parameters of the unit structure, such as the aspect ratio and height of the cross section. Specifically, after the light wave propagates a certain distance in the waveguide, it will accumulate a certain phase. The calculation formula is:

[0057]

[0058] Among them, n eff is the effective refractive index of the unit structure, and h is the height of the unit structure. By adjusting the parameters of different unit structures, such as the length and width of the unit structure cross section, n eff The value changes to achieve phase regulation.

[0059] Specifically, the geometric phase is controlled by rotating the anisotropic unit structure, which affects the polarization state and phase of the light wave. For this anisotropic structure, its transmission characteristics can be described by the Jones matrix T:

[0060]

[0061] Among them, t l and t s Represent the complex transmission coefficient along the fast axis and slow axis of the structure respectively. When the incident light is right-handed circularly polarized (RCP), it is expressed as:

[0062]

[0063] And the fast axis of the unit structure forms an angle θ with the X axis of the coordinate system, the electric field vector of the outgoing light can be expressed as:

[0064]

[0065] Where i represents the vertical component of the vector in the complex plane; E(θ) represents the rotation matrix, defined as:

[0066]

[0067] From the above expression of the electric field vector of the outgoing light, it can be seen that the first term on the right side of the expression (the term on the left side of the plus sign) has the same polarization state as the incident light, and the second term (the term on the right side of the plus sign) exhibits a cross-polarization state opposite to the incident light, with an additional phase of 2θ. This additional phase is only related to the rotation angle of the anisotropic unit structure, which is called the geometric phase.

[0068] Further, in combination with the propagation phase control method, in the process of compensating for the phase difference between the maximum wavelength and other wavelengths, the focal length f of the superlens is set as a constant. Therefore, when calculating the compensation phase, the mathematical expression of the required basic phase is:

[0069]

[0070] Further, in step S3, the difference between the phase of the translated arbitrary wavelength and the maximum wavelength is calculated, and the calculation formula is:

[0071]

[0072] Where, is the difference between the phases of different wavelengths and the maximum wavelength.

[0073] Further, when designing the phase corresponding to the maximum wavelength by the geometric phase control method (i.e., calculating the basic phase without calculating the compensation phase), the focal length of the superlens is designed as a function of r, and therefore the calculation formula of the basic phase is:

[0074]

[0075] Where F represents the lens focal length as a function of r; Δf(·) is the extended focal depth. Δf(·) can be set as needed to achieve different focal depth design schemes.

[0076] In the above design, when calculating the required compensation phase, the focal length f is fixed to a constant value to ensure that light of different wavelengths can converge on the same focal plane to achieve broadband focusing. This method simplifies the design process and provides an effective focusing solution for the application of broadband light sources. Furthermore, through the design of the geometric phase, the phase corresponding to the maximum wavelength is associated with the position r in the lens, making the focal length a function of position. This design allows for more precise phase control of light of different wavelengths, thereby compensating for the propagation differences of light of different wavelengths in the lens, effectively reducing chromatic aberration and improving imaging quality. In addition, by taking advantage of the geometric phase, by adjusting the rotation angle of the unit structure, an additional phase that is independent of the wavelength but related to the rotation angle of the structure is introduced, which helps to achieve a more efficient achromatic effect. This design method can flexibly change the focal length and phase distribution by adjusting the geometric parameters of the unit structure, thereby improving the flexibility and adjustability of the lens.

[0077] Example 2

[0078] This embodiment provides an achromatic meta-lens, which is prepared by the achromatic method for extending the depth of focus provided in the first embodiment.

[0079] Specifically, compared with traditional lenses, meta-lens has the advantages of being thin, lightweight, easy to integrate and multifunctional. It includes a unit structure, and by regulating the phase of these unit structures, a dispersion-free focusing effect can be achieved. In this embodiment, a compensation phase that is linearly related to the wave number (i.e., the inverse of the wavelength) is obtained by adjusting the length and width of the unit structure (adjusting the propagation phase described in Example 1), and at the same time, the unit structure is rotated to superimpose a geometric phase of 2θ on the compensation phase. The meta-lens designed in this way is small in size, low in cost and simple in manufacturing process.

[0080] In order to verify the effectiveness of the achromatic meta-lens prepared by the depth of focus extended achromatic method described in Example 1, this embodiment designs an achromatic meta-lens with an extended depth of focus and a diameter of 40 μm. In terms of the material selection of the lens unit structure, since hydrogenated amorphous silicon (aSiH) is compatible with mature CMOS processes, it brings convenience to the manufacture of visible light super-lenses. At the same time, the combination of SiO2 and a-Si-H performs well in anti-reflection performance, especially on a GaSb substrate, which can significantly reduce the reflectivity, thereby improving the optical efficiency of the lens. Therefore, in this embodiment, the preferred substrate material is SiO2, and the material of the nano-columns is a-Si-H. Such a material combination not only optimizes the performance of the lens, but also provides flexibility and cost-effectiveness for the manufacturing process.

[0081] Figure 3 A schematic diagram of the unit structure of the achromatic metalens is shown. The description of each sub-figure in the figure is as follows:

[0082] Figure 3 Subfigure (a) is a three-dimensional schematic diagram of the unit structure, showing an array of a-Si-H nanopillars arranged on a SiO2 substrate. To the right of subfigure (a) is a top-down view of the unit structure and a dielectric equivalent model. H represents the height of the nanopillars, L represents the length, and W represents the width. The unit structure has a uniform periodicity, expressed as P×P. In this embodiment, the unit structure's period P is set to 260nm, the height H is fixed at 950nm, and the width W and length L are limited to a range of 50-230nm.

[0083] Figure 3 Subfigure (b) shows the phase-frequency curve of the unit structure and the conversion efficiency (raised line) of right-handed circularly polarized light (RCP) to left-handed circularly polarized light (LCP). The unit structure's geometric parameters are set to: H = 950 nm, L = 140 nm, and W = 70 nm. The graph shows that the phase response to frequency is nearly linear.

[0084] Figure 3 Sub-figure (c) depicts the phase-frequency curves for different nanopillar rotation angles, with the same unit cell size as in sub-figure (b). It can be seen that the phase change is twice the rotation angle.

[0085] Figure 3 Sub-figure (d) shows the magnetic field distribution in the XZ plane at three specific wavelengths of 550nm, 650nm and 750nm when the geometric parameters of the unit structure are H = 950nm, L = 140nm and W = 70nm. The dotted line in the figure clearly outlines the outline of the unit structure. During the simulation, periodic boundary conditions are applied in the X and Y directions to simulate an infinite two-dimensional structure, which helps to reduce the influence of boundary effects on the simulation results. In the Z direction, a perfect matching layer boundary condition is applied, which is an absorbing boundary condition that can effectively absorb the incident wave and prevent interference from the reflected wave, thereby ensuring the accuracy of the simulation. In addition, it should be noted that the magnetic field in the XZ plane in the figure is mainly confined to the inside of the nanopillar, so the electromagnetic coupling effect between adjacent unit structures can be ignored.

[0086] In order to further demonstrate the superior performance of the achromatic meta-lens with extended depth of focus provided by this embodiment, a series of simulation tests were conducted. These tests covered three different types of meta-lenses: a simple meta-lens, an achromatic meta-lens, and an achromatic meta-lens with extended depth of focus. The simulated wavelength range was from 550nm to 750nm (specifically using five different incident wavelengths, namely 550nm, 600nm, 650nm, 700nm, and 750nm) to fully evaluate their performance in the visible spectrum. The simulation results can be referred to Figure 4As shown, each subgraph is explained as follows:

[0087] Figure 4 Subgraph (a) shows the electric field intensity distribution of the simple superlens, achromatic superlens and achromatic superlens with extended depth of focus in the X-Z plane at five different incident wavelengths.

[0088] Figure 4 Subgraph (b) shows the electric field intensity of the simple superlens along the Z axis (X=0 and Y=0) at five different incident wavelengths.

[0089] Figure 4 Subgraph (c) shows the electric field intensity of the achromatic superlens along the Z axis (X=0 and Y=0) at five different incident wavelengths.

[0090] Figure 4 Subgraph (d) shows the electric field intensity of the achromatic superlens with extended depth of focus along the Z axis (X=0 and Y=0) at five different incident wavelengths.

[0091] At the five selected wavelengths, it can be seen that the focal point position of the simple superlens has moved significantly. In contrast, the achromatic superlens and the achromatic superlens with extended depth of focus exhibit excellent performance, with their focal point positions changing very little, almost maintaining a straight line, which reflects their stability in focusing under wavelength changes. From Figure 4 The movement of the peak of the electric field intensity along the Z axis can also be observed from subgraph (c) and subgraph (d) of the achromatic superlens and the achromatic superlens with extended depth of focus, which again confirms the superiority of the achromatic superlens and the achromatic superlens with extended depth of focus in maintaining the stability of the focal point. In addition, after adding the design of extended depth of focus, the length of the focal point along the Z axis increases significantly. In order to quantify these observations, Table 1 lists the focal point positions corresponding to each wavelength under the three different lens designs in subgraph (a). Figure 4 Subgraph (a) in Table 1 fully demonstrates the performance advantages of the achromatic superlens with extended depth of focus provided by the embodiment in practical applications.

[0092] Table 1. Focal point positions of superlenses in three cases

[0093]

[0094] Obviously, the above embodiments are only examples for the sake of clarity, and are not limiting of the embodiments. Based on the above description, those skilled in the art can make other different forms of changes or variations. Here, it is not necessary and impossible to exhaust all the embodiments. The obvious changes or variations derived therefrom are still within the protection scope of the present application.

Claims

1. A method for achromatization with extended depth of focus, characterized in that: include: S1. Obtaining the wavelength of incident light, and determining the minimum wavelength and the maximum wavelength of the wavelength; S2. Shifting upward the phase distribution curve of any wavelength between the minimum wavelength and the maximum wavelength according to a preset phase value; S3, calculating the phase difference between any wavelength after translation and the maximum wavelength; S4. Calculate the phase of the maximum wavelength to obtain a basic phase; Achieve focal depth extension according to the focal length in the basic phase; compensate for the phase difference between the maximum wavelength and other wavelengths according to the preset phase value, the difference value and the basic phase; According to the phase difference, the phase distribution curves of different wavelengths are overlapped to achieve achromatism.

2. The achromatic method for extending the depth of focus according to claim 1, wherein: The S2 further includes shifting the phase distribution curve of the minimum wavelength upward according to a preset offset.

3. The achromatic method for extending the depth of focus according to claim 2, wherein: The preset offset is determined by a maximum phase offset between a minimum wavelength and a maximum wavelength of the incident light.

4. The achromatic method for extending the depth of focus according to claim 1, wherein: The calculation formula of the preset phase value is: in, is the preset phase value, λ is any wavelength between the minimum wavelength and the maximum wavelength; a and b are constants; λ min is the minimum wavelength, λ max is the maximum wavelength; Γ is the maximum phase shift between the minimum wavelength and the maximum wavelength.

5. The achromatic method for extending the depth of focus according to claim 1, wherein: To compensate for the phase difference between the maximum wavelength and other wavelengths, the phase distribution mathematical expression of the other wavelengths is: in, is the phase distribution, is the basic phase, is the difference between the phase of different wavelengths and the phase of the maximum wavelength, r is the distance from any point on the metalens to the center of the metalens, λ is any wavelength between the minimum wavelength and the maximum wavelength, and λ max is the maximum wavelength, π is the circumference of a circle, is the preset phase value, and f is the focal length.

6. The achromatic method for extending the depth of focus according to claim 1, wherein: In S3, the phase difference between any wavelength after translation and the maximum wavelength is calculated, and the calculation formula of the difference is: in, is the difference between the phase of different wavelengths and the phase of the maximum wavelength, r is the distance from any point on the metalens to the center of the metalens, λ is any wavelength between the minimum wavelength and the maximum wavelength, and λ max is the maximum wavelength, π is the circumference, and f is the focal length.

7. The achromatic method for extending the depth of focus according to claim 1, wherein: In S4, the phase of the maximum wavelength is calculated to obtain a basic phase. The calculation formula of the basic phase is: in, is the basic phase, r is the distance from any point on the metalens to the center of the metalens, λ max is the maximum wavelength, π is the circumference of the circle, F is the focal length of the lens as it changes with r, f is the focal length, R is the maximum radius of the metalens, and Δf(·) is the extended focal depth.

8. An achromatic metalens, characterized in that: The lens is prepared by the achromatic method for extending the focal depth according to any one of claims 1 to 7.

9. The achromatic metalens according to claim 8, wherein: The meta-lens includes a unit structure, and a compensation phase that is linearly related to the wave number of incident light is obtained by adjusting the length and width of the unit structure; and a geometric phase of 2θ is superimposed on the compensation phase by rotating the unit structure.

10. The achromatic metalens according to claim 9, wherein: The nano-column material of the unit structure is hydrogenated amorphous silicon.

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