Method for manufacturing a flat objective and flat objective

Abstract

This invention provides a method for fabricating a flat plate objective and the flat plate objective itself. The fabrication method includes: acquiring the property information of a Fresnel zone plate; calculating the diffraction field of each zone within a target region based on the zone radius; searching for an optimized phase using an optimization algorithm, and obtaining the phase factor of each zone based on the optimized phase; multiplying the phase factor by the complex amplitude of the light field of each zone within the target region, and then coherently superimposing them to obtain the total complex amplitude of the diffraction field at the target region; obtaining the total diffraction field intensity through the total complex amplitude of the diffraction field, calculating the root mean square error (RMSE) of the total diffraction field intensity and the target intensity, and obtaining the RMSE; determining the total diffraction field as the target total diffraction field when the RMSE characterization of the total diffraction field meets preset conditions; superimposing the optimized phase that achieves the target total diffraction field with the phase of the Fresnel zone plate to obtain the phase of the flat plate objective, and fabricating the target flat plate objective based on the phase of the flat plate objective.

Description

Technical Field

[0001] This invention relates to the field of far-field label-free super-resolution microscopy based on micro-nano structures, specifically to a method for fabricating a flat objective and the flat objective itself. Background Technology

[0002] In recent years, planar diffractive lenses (PDLs), such as superoscillating lenses (SOL) and supercritical lenses (SCL), have attracted widespread interest due to their excellent focusing performance and their ability to be miniaturized and customized.

[0003] Unlike traditional objectives that use refraction to achieve diffraction-limited focusing, planar diffractive lenses utilize micro / nano structures (zones, circular apertures, etc.) to precisely manipulate the coherent constructive and destructive phases of the diffracted light field to achieve breakthrough diffraction-limited focusing. However, their focal length is not improved compared to traditional confocal scanning microscopes, and planar diffractive lenses have low focusing efficiency and poor wide-field imaging capabilities, making them unsuitable for simultaneous use as collecting lenses in reflective confocal scanning microscopes. The fundamental reason is the flaw in their design methodology. Currently, designing planar diffractive lenses with sub-diffraction-limited focusing capabilities mainly involves optimizing the position of transparent zones with a fixed width. Since the position of the transparent zones changes in each iteration, the total diffraction field of the optimized device needs to be recalculated for comparison with the objective function. Therefore, simultaneously optimizing a planar diffractive lens with thousands of zones using this method is extremely time-consuming and yields minimal results. While maintaining a high numerical aperture, planar diffractive lenses designed using this method cannot have long focal lengths. Furthermore, amplitude modulation results in low focusing efficiency for planar diffractive lenses. The failure to consider the wide-field imaging capabilities of planar diffractive lenses during optimization leads to severe aberrations. Summary of the Invention

[0004] To address the above problems, the present invention provides a method for preparing a flat plate objective lens and the flat plate objective lens itself.

[0005] The first aspect of the present invention provides a method for preparing a flat objective lens, comprising:

[0006] Obtain the attribute information of the Fresnel zone plate, including the ring radius;

[0007] Based on the above-mentioned ring radius, calculate and save the diffraction field of each ring in the target region, wherein the above-mentioned diffraction field is represented by the complex amplitude of the optical field;

[0008] An optimization algorithm is used to search for an optimal phase to determine the phase factor for each of the above rings;

[0009] Multiply the above phase factor by the complex amplitude of the optical field in the target region for each of the above rings, and then coherently superimpose them to obtain the total diffraction optical field in the target region.

[0010] The total diffracted light field intensity is obtained by taking the square of the modulus of the complex amplitude of the total diffracted light field, and the root mean square error is calculated by using the total diffracted light field intensity and the target intensity.

[0011] If the above root mean square error characterizes the above total diffraction field and satisfies the preset conditions, the above total diffraction field is determined as the target total diffraction field.

[0012] The optimized phase corresponding to the total diffraction field of the target and the phase of the Fresnel zone plate are added together to obtain the phase of the flat plate objective. The target flat plate objective is then fabricated based on the phase of the flat plate objective.

[0013] According to an embodiment of the present invention, the target area includes:

[0014] The first target area includes the area defined by the set focal plane and the area with a focal length greater than or equal to 1 mm;

[0015] The second target region includes the optical axis region before and after the target focal point, where the target focal point is the intersection of the focal plane and the optical axis.

[0016] According to an embodiment of the present invention, an optimization algorithm is used to search for an optimized phase to determine the phase factor of each of the above-mentioned ring bands;

[0017] The aforementioned phase factor is determined using formula (I):

[0018]

[0019] In Formula (1), For the phase of the aforementioned Fresnel zone plate, The optimized phase is described above. According to an embodiment of the present invention, the target intensity includes a first target intensity and a second target intensity; the first target intensity satisfies the super-diffraction-limited focused light field distribution; the second target intensity satisfies the light field distribution along the optical axis near the focal point.

[0020] According to an embodiment of the present invention, the method for preparing a flat objective lens further includes:

[0021] If the root mean square error (RMSE) characterizing the total diffracted field does not meet the preset condition, but the number of times the RMSE is obtained is less than the preset search termination number, the following processing operation is iteratively performed until the RMSE meets the preset condition, or the number of times the RMSE is obtained is equal to the preset search termination number. The processing operation includes:

[0022] Search for new optimized phases and determine new phase factors;

[0023] Multiplying the new phase factor by the complex amplitude of the optical field at the target region for each of the aforementioned rings, and then coherently superimposing them, yields the new total complex amplitude of the diffracted optical field; and

[0024] The new root mean square error is calculated using the new total diffraction field intensity and the target intensity, until the new root mean square error satisfies the preset condition, or the number of times the new root mean square error is obtained is equal to the preset number of search terminations.

[0025] According to an embodiment of the present invention, the optimized phase corresponding to the total diffraction field of the target and the phase of the Fresnel zone plate are added to obtain the phase of the flat plate objective. The target flat plate objective is then fabricated based on the phase of the flat plate objective, comprising:

[0026] Based on the phase of the aforementioned flat plate objective, the sample flat plate objective is etched on a dielectric substrate to obtain the aforementioned target flat plate objective.

[0027] According to an embodiment of the present invention, the property information of the Fresnel zone plate further includes at least one of the following:

[0028] Focal length, numerical aperture, operating wavelength, working medium, maximum number of annular bands, and phase distribution information.

[0029] The second aspect of this disclosure provides a flat plate objective lens, prepared according to the preparation method described in any one of the preceding claims, wherein the flat plate objective lens has a thickness of less than or equal to 1 mm, a focal length of greater than or equal to 1 mm, a numerical aperture of greater than or equal to 0.9, a focal spot smaller than the diffraction limit of 0.5λ / NA, a focusing efficiency of greater than 10%, and an imaging numerical aperture of greater than 0.8.

[0030] According to an embodiment of the present invention, the diffraction field of each annulus within the target region is first calculated; the phase is optimized using an optimization algorithm to obtain a phase factor; the phase factor is multiplied by the diffraction field of each annulus within the target region, and then coherently superimposed to obtain the complex amplitude of the total diffraction field corresponding to the target region. This overcomes the technical problem that the annulus position changes with each iteration of calculation, requiring the total diffraction field to be recalculated; and the total diffraction field is calculated using simple addition and multiplication, which is simple, computationally efficient, and can quickly fabricate large-size flat objective lenses with thousands of annulus to achieve ultra-thin thickness (≤1mm), super-diffraction-limited focusing (<0.5λ / NA), high focusing efficiency (>10%), long focal length (≥1mm), high numerical aperture (≥0.9), and an imaging numerical aperture greater than 0.8, further achieving excellent wide-field imaging capabilities. Attached Figure Description

[0031] The foregoing contents, as well as other objects, features, and advantages of this disclosure, will become clearer from the following description of embodiments with reference to the accompanying drawings, in which:

[0032] Figure 1 This is a flowchart illustrating the fabrication process of a flat objective lens according to an embodiment of the present invention;

[0033] Figure 2 The phase distribution of the Fresnel zone plate according to an embodiment of the present invention Schematic diagram;

[0034] Figure 3 This is a flowchart of the particle swarm optimization algorithm for searching and optimizing phases according to an embodiment of the present invention;

[0035] Figure 4 The optimized phase, the Fresnel zone plate phase, and the planar objective phase obtained by adding the Fresnel zone plate phase and the optimized phase according to embodiments of the present invention are:

[0036] Figure 5 This is a photograph of a flat objective lens according to an embodiment of the present invention;

[0037] Figure 6 This is a schematic diagram of the focusing and imaging functions of a flat objective lens according to an embodiment of the present invention. Detailed Implementation

[0038] The embodiments of the present disclosure will now be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of the disclosure. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the embodiments of the present disclosure for ease of explanation. However, it will be apparent that one or more embodiments may be practiced without these specific details. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concepts of the present disclosure.

[0039] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit this disclosure. The terms “comprising,” “including,” etc., as used herein indicate the presence of the stated features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.

[0040] All terms used herein (including technical and scientific terms) have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein are to be interpreted in a manner consistent with the context of this specification, and not in an idealized or overly rigid way.

[0041] When using expressions such as "at least one of A, B, and C", they should generally be interpreted in accordance with the meaning that is commonly understood by a person skilled in the art (e.g., "a system having at least one of A, B, and C" should include, but is not limited to, a system having A alone, a system having B alone, a system having C alone, a system having A and B, a system having A and C, a system having B and C, and / or a system having A, B, and C, etc.).

[0042] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0043] Figure 1 This is a flowchart illustrating the fabrication process of a flat objective lens according to an embodiment of the present invention.

[0044] like Figure 1 As shown, the preparation method of a flat objective lens may include operations S110 to S170.

[0045] In operation S110, the attribute information of the Fresnel zone plate is obtained, including the ring radius.

[0046] According to an embodiment of the present invention, the attribute information further includes at least one of the following:

[0047] Focal length, numerical aperture, operating wavelength, working medium, maximum number of annular bands, and phase distribution information.

[0048] According to an embodiment of the present invention, the maximum radius threshold of the Fresnel zone plate is determined based on the focal length and numerical aperture of the Fresnel zone plate.

[0049] According to an embodiment of the present invention, the maximum radius threshold of the Fresnel zone plate is calculated by formula (1):

[0050]

[0051] In formula (1), n index θ represents the refractive index of the working medium, θ represents the convergence angle of the beam generated by the outermost ring, R represents the ring radius, f represents the focal length, and NA' represents the numerical aperture.

[0052] According to an embodiment of the present invention, preferably, the preset numerical aperture NA of the Fresnel zone plate is 0.9, the focal length is 1mm, and the calculated maximum radius threshold of the Fresnel zone plate is 2mm.

[0053] According to an embodiment of the present invention, the working medium includes air, oil immersion, and water immersion; when the working medium is air, oil immersion, and water immersion, the corresponding refractive indices are 1, 1.5, and 1.3, respectively.

[0054] According to an embodiment of the present invention, preferably, when the Fresnel zone plate operates in an air medium, the numerical aperture is the sine of the convergence angle.

[0055] According to an embodiment of the present invention, the maximum number of annular zones is calculated based on the maximum radius threshold of the Fresnel zone plate.

[0056] According to an embodiment of the present invention, the radius corresponding to each ring is calculated based on the operating wavelength, focal length, and maximum number of rings of the Fresnel zone plate.

[0057] According to embodiments of the present invention, Fresnel zone plates include one of phase-type Fresnel zone plates and amplitude-type Fresnel zone plates; phase-type Fresnel zone plates include binary phase-type Fresnel zone plates and multi-phase phase-type Fresnel zone plates, etc.

[0058] According to an embodiment of the present invention, the maximum number of rings in the phase-type Fresnel zone plate and the radius corresponding to each ring are calculated by formula (2):

[0059]

[0060] In formula (2), N represents the number of rings, λ represents the working wavelength (λ = 405 nm); M represents the number of elements of the phase-type Fresnel zone plate, M = 2 represents two elements, M = 4 represents four elements, and so on.

[0061] Figure 2 The phase distribution of the Fresnel zone plate according to an embodiment of the present invention Schematic diagram.

[0062] like Figure 2 As shown, with a Fresnel zone plate diameter of 4 mm, a focal length of 1 mm, and a working wavelength of 405 nm, each ring has a different phase, specifically an alternating distribution of 0 phase and π phase.

[0063] In operation S120, the diffraction field of each ring zone in the target region is calculated and saved according to the ring zone radius. The diffraction field is represented by the complex amplitude of the light field.

[0064] According to an embodiment of the present invention, the target area includes:

[0065] The first target region includes the region jointly defined by the set focal plane and the focal length greater than or equal to 1 mm (preferably, f = 1 mm here); specifically, the first target region includes the region in space represented by formula (3):

[0066] f z =1mm and r=(0:0.01:1)*λ; (3)

[0067] In formula (3), r represents the matrix within the first target region, and f z This indicates that the distance from the focal plane to the Fresnel zone plate is 1 mm;

[0068] The second target region includes the optical axis regions before and after the target focal point, where the target focal point is the intersection of the focal plane and the optical axis; specifically, the second target region includes the region in space represented by formula (4):

[0069] z = (950:0.1:1050)μm and f r =0; (4)

[0070] In formula (4), z represents the matrix within the second target region, and f r This indicates the intersection of the focal plane and the optical axis.

[0071] According to an embodiment of the present invention, preferably, the diffraction field of each ring of the Fresnel zone plate is calculated by formula (5):

[0072]

[0073] In formula (5), x0 and y0 represent the spatial coordinates of the input surface, U(x0,y0) represents the given electric field of the input surface, g(x-x0,y-y0,z,λ) represents the propagation factor, z represents the distance between the input surface and the target surface, and λ represents the wavelength of light.

[0074] According to an embodiment of the present invention, the diffraction field of each ring of the Fresnel zone plate can also be calculated by other diffraction integrals.

[0075] According to an embodiment of the present invention, since the position of the ring zone of the Fresnel zone plate is fixed, only the phase is reversed; and without considering the phase of the ring zone, the diffraction field of each ring zone on the design plane is calculated in advance and saved; this method can avoid the technical problem that the position of the ring zone changes in each iteration calculation, so that the total diffraction field needs to be recalculated by diffraction integral in the optimization iteration, thereby making the calculation efficiency higher.

[0076] In operation S130, an optimization algorithm is used to search for and optimize the phase in order to determine the phase factor of each ring band.

[0077] The phase factor is determined by formula (6):

[0078]

[0079] In formula (6), For the phase of the Fresnel zone plate, To optimize the phase.

[0080] In operation S140, the phase factor is multiplied by the complex amplitude of the optical field in the target region for each ring zone, and then coherently superimposed to obtain the total complex amplitude of the diffracted optical field in the target region.

[0081] According to an embodiment of the present invention, given the complex amplitude of the optical field of each ring zone within the target region, the total diffraction field is calculated by simple addition and multiplication. The method is simple and computationally efficient. Therefore, this method can be used to quickly fabricate large-size planar micro / nano structures with thousands of ring zones to achieve their high numerical aperture and long focal length.

[0082] When operating S150, the total diffraction field intensity is obtained by taking the square of the modulus of the complex amplitude of the total diffraction field, and the root mean square error is calculated using the total diffraction field intensity and the target intensity.

[0083] According to an embodiment of the present invention, the target intensity includes a first target intensity and a second target intensity. The first target intensity satisfies the super-diffraction-limited focused light field distribution; the second target intensity satisfies the light field distribution along the optical axis near the focal point.

[0084] The intensity of the first target is calculated using formula (7):

[0085] goalx = abs(J0(krNA)) 2 (7)

[0086] In formula (7), J0 represents the first-order Bessel function, r = (0:0.01:1)*λ, k represents the wave vector, and NA represents the preset numerical aperture.

[0087] The intensity of the second target is calculated using formula (8):

[0088]

[0089] In formula (8), z = (950:0.1:1050)um, f = 1000um. (sinθ=NA=0.9), f represents the focal length, and DOF represents the depth of focus.

[0090] The root mean square error of the first target intensity is calculated using formula (9):

[0091]

[0092] The root mean square error of the second target intensity is calculated using formula (10):

[0093]

[0094] In formulas (9) and (10), Ir and Iz represent the total diffraction field intensity of the ring zone in their respective target regions, length(r) represents the number of elements contained in the matrix in the first target region, and length(z) represents the number of elements contained in the matrix in the second target region.

[0095] The root mean square error of the complex amplitude of the total diffracted light field is calculated using formula (11):

[0096] Root mean square error = C * RMSE1 + RMSE2; (11)

[0097] In formula (11), C represents a constant with a value of 1*e -10 .

[0098] According to an embodiment of the present invention, the preset value is 1*e -10 In other words, the smaller the root mean square error, the closer it is to the target.

[0099] In operation S160, if the root mean square error characterization of the total diffraction field meets the preset conditions, the total diffraction field is determined as the target total diffraction field.

[0100] In operation S170, the optimized phase corresponding to the total diffraction field of the target is added to the phase of the Fresnel zone plate to obtain the phase of the flat plate objective. The target flat plate objective is then fabricated based on the phase of the flat plate objective.

[0101] According to an embodiment of the present invention, the method for preparing a flat objective lens further includes:

[0102] If the root mean square error (RMSE) characterization of the total diffracted field does not meet the preset condition, but the number of times the RMSE is obtained is less than the preset search termination number, the following processing operations are iteratively performed until the RMSE meets the preset condition, or the number of times the RMSE is obtained is equal to the preset search termination number. The processing operations include:

[0103] Search for a new optimized phase and determine a new phase factor.

[0104] Multiplying the new phase factor by the complex amplitude of the optical field at the target region for each ring zone, and then coherently superimposing them, yields the new total complex amplitude of the diffracted optical field; and

[0105] The root mean square error is obtained by comparing the new total diffraction field intensity with the target intensity until the new root mean square error meets the preset conditions, or the number of times the new root mean square error is obtained is equal to the preset number of search terminations.

[0106] According to embodiments of the present invention, the optimization algorithm includes one of the following: particle swarm optimization algorithm, genetic algorithm, ant colony optimization algorithm, simulated annealing algorithm, and tabu search algorithm. Preferably, the present invention uses particle swarm optimization algorithm.

[0107] Figure 3 This is a flowchart of the particle swarm optimization algorithm for searching and optimizing phases according to an embodiment of the present invention.

[0108] like Figure 3 As shown, the particle swarm optimization algorithm in this embodiment may include operations S310 to S340 in searching for the ring boundary value.

[0109] In operation S310, the particle swarm optimization algorithm is used to search for and optimize the phase in order to determine the phase factor of each ring.

[0110] In operation S320, the total diffracted light field is determined based on the phase factor in order to determine the root mean square error of the total diffracted light field.

[0111] When operating S330, it is determined whether the root mean square error meets the preset conditions, that is, whether the root mean square error is less than the preset value.

[0112] If the judgment result of operation S330 is yes, the iterative search process is terminated.

[0113] If the result of operation S330 is negative, operation S340 can be executed to determine whether the iterative search conditions have reached the preset search termination conditions.

[0114] If the judgment result of operation S340 is yes, the iterative search process is terminated.

[0115] If the result of operation S340 is negative, continue to iteratively execute operations S310 to S340 until the matching result meets the preset conditions, or the number of matching results obtained is equal to the preset number of search terminations.

[0116] According to embodiments of the present invention, the Fresnel zone plate made of SiO2 transparent glass material has high focusing efficiency and good wide-field imaging function similar to a lens.

[0117] According to an embodiment of the present invention, the diffraction-limited focal spot is determined by a spatial frequency of... The coherent superposition of diffracted light within a certain range does not offer a resolution advantage compared to traditional objectives. However, according to the super-oscillation theory, sub-diffraction-limited focusing can be achieved by reversing the phase of some rings in a Fresnel zone plate, thereby altering the weight of diffracted light with different spatial frequencies. Furthermore, when the proportion of phase-reversed rings in the Fresnel zone plate is small, the original high focusing efficiency and good wide-field imaging capability of the Fresnel zone plate will not change significantly.

[0118] Figure 4 The optimized phase, the Fresnel zone plate phase, and the planar objective phase obtained by adding the Fresnel zone plate phase and the optimized phase according to embodiments of the present invention are described.

[0119] like Figure 4 As shown, Figure 4 Figure (a) shows the optimized phase obtained by the optimization algorithm. Figure 4 Figure (b) shows the phase profile of the Fresnel zone plate near ring 283. Figure 4 Figure (c) shows the phase profile of the optimized phase near ring 283. Figure 4 Figure (d) in the diagram is a cross-sectional view of the target flat objective lens phase near the 283rd ring. R i This represents the ring radius corresponding to the i-th ring. Specifically, R283, R850, R1046, R1256, and R6391 represent the ring radii of the 283rd, 850th, 1046th, 1256th, and 6391st rings, respectively.

[0120] According to an embodiment of the present invention, fabricating a target flat objective lens based on the target phase parameters of the total target diffraction field includes:

[0121] The sample flat objective lens is etched according to the target phase parameters to obtain the target flat objective lens.

[0122] According to an embodiment of the present invention, the flat objective lens is obtained by etching a certain depth directly on SiO2 transparent glass according to the target phase parameters.

[0123] According to an embodiment of the present invention, the etching depth is calculated using formula (11):

[0124]

[0125] In formula (11), the refractive index of air is 1, n' represents the refractive index of the processed material, and the phase difference is... Wave Loss ΔL represents the optical path difference between the etched area and the unetched area.

[0126] According to an embodiment of the present invention, preferably, when the processing material is SiO2 transparent glass, its corresponding refractive index is about 1.5, and the phase difference to be prepared is v, so the obtained etching depth is about one wavelength, i.e., 405nm.

[0127] Figure 5 This is a photograph of a flat objective lens according to an embodiment of the present invention.

[0128] According to an embodiment of the present invention, when planar light is incident on a planar objective lens, the wavefront phases are equal. After passing through the planar objective lens, the wavefront phase difference between the etched region and the unetched region is π.

[0129] According to embodiments of the present invention, the flat objective lens prepared by this method can achieve ultra-thin optical elements, sub-diffraction-limited focusing, high focusing efficiency, high numerical aperture, long focal length (millimeter level), and wide-field imaging capability.

[0130] According to embodiments of the present invention, this preparation method is also applicable to the preparation of planar micro / nano structures of amplitude-type Fresnel zone plates.

[0131] According to an embodiment of the present invention, preferably, compared to amplitude-type Fresnel zone plates, binary phase-type Fresnel zone plates have a diffraction efficiency of up to 40.5% due to the dominant coherent and constructive phase.

[0132] According to embodiments of the present invention, this preparation method can utilize micro-nano fabrication technology to mass-produce flat objective lenses, resulting in lower production costs compared to traditional objective lenses with the same high numerical aperture.

[0133] Figure 6 This is a schematic diagram of the focusing and imaging functions of a flat objective lens according to an embodiment of the present invention.

[0134] like Figure 6 As shown, Figure 6 Figure (a) shows the three-dimensional diffraction field distribution information of the focal spot; Figure 6 Figure (b) in the figure shows the one-dimensional distribution information of the focal spot size in the simulation and experiment; Figure (c) in the figure shows the lateral size of the diffracted light field along the optical axis. Figure 6 Figure (d) in the diagram is a basic principle diagram of the edge cutting method; Figure 6 Figure (e) shows the experimentally measured edge spread function (ESF), the fitted edge spread function (ESF.fitting), and its line spread function (LSF); Figure 6 Figure (f) in the figure shows the measured modulation transfer function (MTF); in the figure, the Rayleigh criterion is expressed as... The superoscillation criterion is expressed as follows: Where λ represents the working wavelength, NA' represents the numerical aperture; the Rayleigh criterion and the superoscillation criterion are used to determine the resolving power of a flat lens and measure its ability to separate two adjacent object points; x, y, and z all represent Cartesian coordinates, and r represents the distance between the corresponding coordinate point and the optical axis.

[0135] like Figure 6 As shown, Figure 6 Figures (a) to (c) in the figure represent the focusing characteristics of the flat plate objective lens; Figure 6 Figures (d) to (f) in the figure represent the imaging characteristics of the flat lens.

[0136] like Figure 6 As shown in Figure (a), with a working wavelength of 405 nm and a focal length of 1 mm, the morphology of the focal spot near the focal field of the flat objective lens is measured to be distributed along the Z-axis; Figure 6 As shown in Figure (b), the lateral dimension of the focal spot along the focal plane, characterized by full width at half maximum (FWHM), is actually 200 nm, exceeding the diffraction limit; as Figure 6 As shown in Figure (c), the 5µm sub-diffraction-limited optical needle is beneficial for 3D object scanning imaging. Furthermore, this flat objective lens also possesses excellent wide-field imaging capabilities, as demonstrated by the modulation transfer function of the flat objective lens measured using the edge-cutting method. Figure 6 As shown in Figure (d), the sharp edge is placed at the object plane of the flat lens, which is located 1.2f in front of the lens. An image of the sharp edge is then obtained on the image plane, which is located 6f behind the lens, where f represents the focal length. Figure 6 As shown in Figure (e), the edge spread function (ESF) is first measured using the edge-to-edge method, and then the line spread function (LSF) is obtained; the modulation transfer function (MTF) is obtained by performing a Fourier transform on the LSF. Figure 6 As shown in Figure (f), the cutoff frequency of the MTF is 4 lp / um, which means the resolution is 1 / 4um (250nm), the corresponding imaging numerical aperture is 0.83, and the experimentally measured focusing efficiency is as high as 12.3%.

[0137] According to an embodiment of the present invention, the flat objective lens can achieve sub-diffraction-limited focusing while ensuring high focusing efficiency and good wide-field imaging capability.

[0138] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for preparing a flat objective lens, comprising: Obtain the attribute information of the Fresnel zone plate, wherein the attribute information of the Fresnel zone plate further includes at least one of the following: focal length, numerical aperture, operating wavelength, operating medium, maximum number of annular zones, and phase distribution information. ; The positions of the Fresnel zone plates are fixed, and only the phase is reversed. Based on the zone radius, the diffraction field of each zone within the target region is calculated and stored. The diffraction field is represented by the complex amplitude of the optical field. The target region includes a first target region and a second target region. The first target region includes the area jointly determined by a set focal plane and a focal length greater than or equal to 1 mm. The second target region includes the optical axis region before and after the target focal point. The target focal point is the intersection of the focal plane and the optical axis. An optimization algorithm is used to search for an optimized phase to determine the phase factor for each ring band; Multiply the phase factor by the complex amplitude of the optical field of each ring in the target region, and then coherently superimpose them to obtain the total complex amplitude of the diffracted optical field in the target region; The total diffraction field intensity is obtained by taking the square of the modulus of the complex amplitude of the total diffraction field, and the root mean square error is calculated using the total diffraction field intensity and the target intensity. The target intensity includes a first target intensity and a second target intensity. The first target intensity satisfies the super-diffraction-limited focused light field distribution. The second target intensity satisfies the light field distribution along the optical axis near the focal point. When the root mean square error characterizes the total diffraction field and the condition is satisfied, the total diffraction field is determined as the target total diffraction field. The optimized phase corresponding to the total diffraction field of the target is added to the phase of the Fresnel zone plate to obtain the phase of the flat plate objective. The target flat plate objective is then fabricated based on the phase of the flat plate objective. The radius of each ring of the Fresnel zone plate is calculated using the following formula: ； N represents the number of rings. Indicates the operating wavelength. M represents the element number of a phase-type Fresnel zone plate.

2. The method according to claim 1, wherein, An optimization algorithm is used to search for an optimized phase to determine the phase factor for each ring band; The phase factor is determined by formula (I): ;(one) In formula (1), The phase of the Fresnel zone plate. The optimized phase.

3. The method according to claim 1, further comprising: If the root mean square error (RMSE) characterizes the total diffracted field but does not meet the preset condition, but the number of times the RMSE is obtained is less than the preset search termination number, the following processing operation is iteratively performed until the RMSE meets the preset condition, or the number of times the RMSE is obtained is equal to the preset search termination number. The processing operation includes: Search for a new optimized phase and determine a new phase factor; Multiplying the new phase factor by the complex amplitude of the optical field at the target region for each ring zone, and then coherently superimposing them, yields a new total complex amplitude of the diffracted optical field; and A new root mean square error is calculated using the new total diffraction field intensity and the target intensity, until the new root mean square error satisfies the preset condition, or the number of times the new root mean square error is obtained is equal to the preset search termination number.

4. The method according to claim 1, wherein, The optimized phase corresponding to the total diffraction field of the target is added to the phase of the Fresnel zone plate to obtain the phase of the flat plate objective. The target flat plate objective is then fabricated based on the phase of the flat plate objective, including: The target flat objective lens is obtained by etching the sample flat objective lens using the flat objective lens.

5. A flat objective lens, prepared according to any one of claims 1 to 4, wherein the flat objective lens has a thickness of less than or equal to 1 mm, a focal length of greater than or equal to 1 mm, a numerical aperture of greater than or equal to 0.9, and a focal spot smaller than the diffraction limit. The focusing efficiency is greater than 10%, and the imaging numerical aperture is greater than 0.8.

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