WO2023169062A1 - 一种生成准无衍射光片的光瞳掩模及其优化设计方法 - Google Patents

一种生成准无衍射光片的光瞳掩模及其优化设计方法 Download PDF

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WO2023169062A1
WO2023169062A1 PCT/CN2022/142906 CN2022142906W WO2023169062A1 WO 2023169062 A1 WO2023169062 A1 WO 2023169062A1 CN 2022142906 W CN2022142906 W CN 2022142906W WO 2023169062 A1 WO2023169062 A1 WO 2023169062A1
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particle
light sheet
design method
optimal solution
diffraction
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唐城
李剑平
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Shenzhen Institute of Advanced Technology of CAS
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Shenzhen Institute of Advanced Technology of CAS
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    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B21/00—Microscopes
    • G02B21/06—Means for illuminating specimens
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00

Definitions

  • the present application relates to the field of biological microscopic imaging, and in particular to a pupil mask that generates a quasi-diffraction-free light sheet and its optimal design method.
  • Light sheet fluorescence microscopy technology adopts an orthogonal light path design, using a thin light sheet to excite the sample from the side, and using a microscope objective and a digital camera to capture a two-dimensional fluorescence image of the sample in the direction perpendicular to the light sheet.
  • a microscope objective and a digital camera to capture a two-dimensional fluorescence image of the sample in the direction perpendicular to the light sheet.
  • a light sheet generation method that solves the mutual constraints between the observation field of view and axial resolution is to use beams with non-diffraction characteristics, such as Bessel beams and Airy beams, which can greatly increase the available field of view.
  • These diffraction-free beams require dynamic scanning to form a light sheet, but the scanning process may miss fast-moving objects, such as samples in high-throughput imaging flow cytometry, and produce a transient peak intensity that may Can produce harmful effects such as increased phototoxicity and photobleaching effects.
  • Lattice light sheets or Bessel beam arrays reduce scan range, peak intensity, and photobleaching by distributing light in a plane.
  • a light sheet that continuously unfolds in a plane is a two-dimensional static light sheet that does not require scanning and can be produced using simple, cheap cylindrical lenses. Inserting a mask in front of a cylindrical lens produces a quasi-diffraction-free static light sheet.
  • a strictly diffraction-free static light sheet is a cosine beam with side lobes as strong as the main lobe.
  • the side lobes of a cosine beam or a cosine Gaussian beam can either be used as structured light or suppressed using the harmonics of the cosine beam.
  • What static light sheets and scanning light needles have in common is the conflict between thickness, non-diffraction range and side lobe intensity.
  • the diffraction-free light sheet has the advantage of a large field of view, but is often accompanied by significant side lobes and sacrifices thickness. How to optimize the light sheet as a whole and achieve a balance between thickness, non-diffraction range and side lobe intensity has important research significance.
  • the purpose of the present invention is to provide a pupil mask that generates a quasi-diffraction-free light sheet and an optimal design method thereof, aiming to solve the problem that existing light sheets cannot achieve the same goal in terms of thickness, non-diffraction range and side-lobe intensity. It is a matter of achieving a balance between the three.
  • one aspect of the present invention provides an optimized design method for a pupil mask that generates a quasi-diffraction-free light sheet, including the following steps:
  • the structural parameters to be solved are obtained from the global optimal solution.
  • ⁇ r (z) is defined as the maximum width at r times of the peak value
  • min ( ⁇ r ) is the minimum value of ⁇ r (z) obtained near the focus of the cylindrical lens
  • NDR (r) is the non-diffraction range, defined as The thickness of the light sheet diverges to less than its minimum thickness times the distance
  • ⁇ is the wavelength.
  • the pupil mask includes alternating strip intervals of amplitude modulation or phase modulation.
  • the structure of the pupil mask has upper and lower symmetry, and the total number of intervals is an odd number.
  • the structural parameter to be solved is the width of each interval in the pupil mask.
  • step S3 includes:
  • step S301 includes:
  • Randomize the speed and position of each particle use the position of the particle to represent the numerical solution of the width of each interval, use the speed of the particle to represent the changing trend of the numerical solution of the width of each interval, and the particle position and speed are also M-dimensional vectors;
  • the historical optimal solution of each individual particle in the initial generation particle swarm and the global optimal solution of the particle group are obtained.
  • step S302 includes:
  • i is the index of the particle
  • d is the index of the interval of each particle
  • m i,d is the current position of each particle
  • M i,d is the existing optimal solution of each particle
  • G i,d is the group
  • the existing optimal solution of , w is the inertia weight, ⁇ p is the individual coefficient, and ⁇ g is the group coefficient;
  • r p and r g are random numbers between 0 and 1;
  • the historical optimal solution of each particle and the global optimal solution of the particle swarm are updated according to the evaluation function of each particle in the new particle swarm.
  • Another aspect of the present invention also provides a pupil mask, which is obtained according to the above-mentioned optimization design method.
  • Another aspect of the present invention also provides a quasi-diffraction-free static light sheet, including the above-mentioned pupil mask and cylindrical lens.
  • the present invention provides a pupil mask that generates quasi-diffraction light sheets and its optimal design method.
  • the structural design process of the pupil mask is converted into the optimal solution of the solution function.
  • the optimal solution directly carries out the pupil mask structure design of the quasi-diffraction-free light sheet, thus optimizing the light-sheet thickness, non-diffraction range and side lobes of the light-sheet microscopy as a whole.
  • the non-diffraction range of the light sheet is expanded by 50% relative to the Gaussian beam, while the side lobes are suppressed below the 20% level.
  • This method can be applied to the design of amplitude masks or phase masks. What is particularly worth mentioning is that the overall efficiency of the optimized phase mask reaches more than 50%.
  • the novel light sheet generated by the pupil mask provided by the present invention can image biological samples with an enlarged field of view without affecting the axial resolution.
  • Figure 1(a) is a schematic diagram of the pupil mask structure in the embodiment of the present invention
  • Figure 1(b) is a schematic diagram of the implementation principle of the quasi-diffraction static light sheet in the embodiment of the present invention
  • Figure 3 is a flow chart of a mask optimization design method in an embodiment of the present invention.
  • Figure 4 is a convergence curve diagram in the embodiment of the present invention.
  • Figure 5 is a schematic diagram of the simulation results corresponding to the amplitude mask obtained through optimized design in the embodiment of the present invention.
  • Figure 6 is a schematic diagram of experimental results corresponding to the amplitude mask obtained through optimized design in the embodiment of the present invention.
  • Figure 7 is a schematic diagram of the simulation results corresponding to the phase mask obtained through optimized design in the embodiment of the present invention.
  • FIG. 8 is a schematic diagram of experimental results corresponding to the phase mask obtained through optimized design in the embodiment of the present invention.
  • the invention provides a pupil mask and its numerical optimization method, which optimizes the light sheet thickness, non-diffraction range and side lobes of light sheet microscopy as a whole. Using this method, the non-diffraction range of the light sheet is expanded by 50% relative to the Gaussian beam, while the side lobes are suppressed below the 20% level.
  • This method can be applied to the design of amplitude masks or phase masks. In particular, the overall efficiency of the optimized phase mask reaches over 50%.
  • the novel light sheet generated by the pupil mask provided by the present invention can image biological samples with an enlarged field of view without affecting the axial resolution.
  • Embodiments of the present invention provide an optimized design method for pupil masks that generate quasi-diffraction-free light sheets, including the following steps:
  • the present invention adopts the device shown in Figure 1(a) and Figure 1(b).
  • the Gaussian beam passes through the pupil mask matched with the aperture (shown in black part in the figure) and the cylindrical lens, it can generate light near the focus of the lens. Quasi-diffraction-free static light sheet.
  • the pupil mask can be either amplitude modulated or phase modulated, or both amplitude and phase can be modulated. Due to the invariance of this device in the y-axis direction, it can be simplified to a one-dimensional scale for analysis.
  • the pupil mask consists of alternating strip intervals of amplitude modulation or phase modulation.
  • the total number of intervals is an odd number.
  • the interval is symmetrical with respect to the optical axis, so the present invention only considers the interval in the positive direction of the x-axis, and divides the middle interval into two.
  • the thickness of the light sheet ⁇ r (z) is a function of the transmission distance z and can be measured as the ratio of the maximum intensity at z to the full width at r.
  • ⁇ 0.5 (z) is commonly known as the full width at half maximum (FWHM).
  • FWHM full width at half maximum
  • the full width at half maximum of the main lobe is a partial view of the light sheet because it ignores the side lobes. Taking the side lobes into account, ⁇ r (z) is defined as the maximum width at r times the peak value.
  • ⁇ r (z) takes the minimum value min( ⁇ r ) near the focus of the cylindrical lens.
  • NDR non-diffraction range
  • the present invention defines the non-diffraction range (NDR), a function of the scale factor r and the pupil mask, where the thickness of the light sheet diverges to less than its minimum thickness. times the distance:
  • NDR(r) is also equal to the range in which the side lobe remains below r times of the main lobe. Then, compare NDR(r) to the Rayleigh distance of a Gaussian beam with the same minimum width:
  • the factor 2ln(1/r) comes from the conversion of ⁇ r to Gaussian beam waist diameter (1/e 2 ). In the case of Gaussian light sheets, this evaluation factor is exactly equal to 1. Therefore, 1/metric(r) describes how much the diffraction-free range is expanded compared to a Gaussian beam, and the problem then becomes minimizing the evaluation factor while the scale factor r sets the admissible level of side lobes.
  • the light field distribution is calculated based on the mask structure.
  • the incident light on the pupil mask is a collimated Gaussian beam whose field is multiplied by the pupil mask.
  • the field passes through a cylindrical lens, which is modeled as an infinitely thin lens with cylindrical phase modulation.
  • the present invention models the field, mask and cylindrical lens on a one-dimensional scale since they are invariant along y. From the field transmitted through the cylindrical lens, we calculate the light field propagated around the focus using the Rayleigh-Sommerfeld method. By scanning the propagation distance near the focal length, the two-dimensional light field distribution around the focus can be obtained, and the evaluation factor is calculated based on the light field distribution.
  • the embodiment of the present invention adopts a numerical optimization method.
  • the particle swarm optimization algorithm (PSO) is used to search for the global minimum.
  • the specific process is shown in Figure 3.
  • the particle swarm optimization algorithm is an evolutionary computing technique that mimics the foraging behavior of a swarm of bees, whose initial positions are completely random.
  • step S301 specifically includes:
  • Randomize the speed and position of each particle use the position of the particle to represent the numerical solution of the width of each interval, use the speed of the particle to represent the changing trend of the numerical solution of the width of each interval, and the particle position and speed are also M-dimensional vectors;
  • the historical optimal solution of each individual particle in the initial generation particle swarm and the global optimal solution of the particle group are obtained.
  • An M-dimensional vector ⁇ m1, m2, m3, m4 ⁇ composed of each interval width m1, m2, m3, m4 is regarded as a particle, and the numerical solution of each basic structural parameter is represented by the position of the particle, and the speed of the particle is represented.
  • the changing trend of the numerical solution of each basic structural parameter, and the particle position and velocity are both M-dimensional vectors.
  • the randomly generated particle position initial values m i,d and velocity initial values v i,d are shown in Table 1 and Table 2 respectively (units are microns, where i is the label of the particle and d is the number of each particle. interval number):
  • i is the index of the particle
  • d is the index of the interval of each particle
  • m i,d is the current position of each particle
  • M i,d is the existing optimal solution of each particle
  • G i,d is the group
  • the existing optimal solution of , w is the inertia weight, ⁇ p is the individual coefficient, and ⁇ g is the group coefficient;
  • r p and r g are random numbers between 0 and 1;
  • the historical optimal solution of each particle and the global optimal solution of the particle swarm are updated according to the evaluation function of each particle in the new particle swarm.
  • Figure 4 shows the convergence curve of this embodiment. It can be seen that convergence is achieved when the number of iterations is about 1000.
  • the structural parameters to be solved are obtained from the global optimal solution.
  • the optimal solution is [122.30190817, 143.22780712, 83.0393262, 126.4309585].
  • the optimal binary amplitude mask obtained in this embodiment contains a total of 7 intervals except the outer aperture, and the central interval is opaque. This is equivalent to two pairs of symmetrical slits on a piece of opaque material, with the width of the outer slit being 0.88 times the width of the inner slit.
  • the optimal evaluation factor obtained is 0.65, which shows that the non-diffraction range is increased by 50%, while the side lobes remain below 20% of their local maximum.
  • Figure 5 shows the simulation results.
  • the amplitude mask is made on a soda lime glass substrate, which is coated with a layer of chromium, and a layer of photoresist is coated on the chromium.
  • the mask pattern is projected onto the photoresist by laser direct writing with an accuracy of 0.5 ⁇ m, and exposed The photoresist is dissolved, exposing the chromium underneath. The chromium is then etched away, revealing the clear glass underneath. After removing the remaining photoresist, the amplitude mask is ready.
  • Characterization of the light sheet was performed using a diode laser that can output 445 nm light through a fiber optic cable.
  • the laser was collimated with a fiber collimator.
  • the collimated laser was Gaussian with a beam waist radius of 0.66 mm.
  • the present invention chooses not to use a telescope made of planar convex lenses to expand the collimated laser beam to avoid introducing aberrations to the Gaussian beam, while also simplifying the setup.
  • the selected cylindrical lens is made of N-SF11 with a refractive index of 1.82, so the spherical aberration is small.
  • a cylindrical lens with an appropriate focal length will further improve the evaluation factor, but cylindrical lenses have a limited focal length.
  • the mask of the present invention is inserted before the cylindrical lens. Because the beam is collimated before the cylindrical lens, the spacing between the mask and the cylindrical lens is not critical. Because the thickness of the light sheet is comparable to the pixel pitch of a digital camera, this invention uses a Nikon 20X objective lens and a tubular lens to amplify the intensity distribution of the light sheet on the x-y plane to form an image on a FLIR Blackfly CMOS digital camera. The objective lens can be translated along the optical z-axis to focus on cross-sections of the light sheet at different z-axes. Figure 6 shows the experimentally observed intensity distribution using an amplitude mask.
  • the present invention provides a pupil mask and its numerical optimization method, which optimizes the light sheet thickness, non-diffraction range and side lobes of light sheet microscopy as a whole.
  • the non-diffraction range of the light sheet is expanded by 50% relative to the Gaussian beam, while the side lobes are suppressed below the 20% level.
  • This method can be applied to the design of amplitude masks or phase masks. In particular, the overall efficiency of the optimized phase mask reaches over 50%.
  • the novel light sheet generated by the pupil mask provided by the present invention can image biological samples with an enlarged field of view without affecting the axial resolution.

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Abstract

一种生成薄而宽光片的光瞳掩模及其优化设计方法。薄而宽的光片对于具有大视场和近衍射极限分辨率的光片显微镜至关重要。无衍射光片的跨度范围很宽，但通常带有强旁瓣或增加的厚度。通过数值优化方法来设计光瞳掩模以生成薄而宽的光片，平衡了光片厚度、无衍射范围和旁瓣之间的矛盾。理论和实验表明，优化的掩模将静态光片的无衍射范围扩大了50%，同时使其旁瓣低于 20%，生成的静态光片可以在不牺牲轴向分辨率的情况下，对样品进行更大视野成像。

Description

一种生成准无衍射光片的光瞳掩模及其优化设计方法 技术领域
本申请涉及生物显微成像领域，特别涉及一种生成准无衍射光片的光瞳掩模及其优化设计方法。
背景技术
光片荧光显微技术采用正交光路设计，用一层薄光片从侧面激发样品，并在垂直于光片的方向上利用显微物镜和数字相机拍摄样品的二维荧光图像，通过轴向扫描光片或移动样品逐面成像，即可获取不同深度处的层析图像并实现样品的三维信息重构。激发光束越薄，轴向分辨率越高，却越容易发生衍射，限制了可用的视场。解决观测视场与轴向分辨率相互制约的一种光片生成方式是采用具有无衍射特性的光束，如贝塞尔光束和艾里光束，能够大大增加可用的视场。这些具有无衍射特性的光束需要动态扫描才能形成一个光片，但扫描过程可能会错过快速移动的物体，如高通量成像流式细胞术中的样本，并产生一个瞬时峰值强度，由此可能会产生有害影响，如增大光毒性和光漂白效应。晶格光片或贝塞尔光束阵列通过在平面钟分布光来减小扫描范围、峰值强度和光漂白。
在平面中连续展开的光片是二维静态光片，不需要扫描，可以使用简单、廉价的柱面透镜制作。在柱面透镜前插入掩模可产生准无衍射静态光片。严格无衍射的静态光片是余弦光束，其旁瓣与主瓣一样强。余弦光束或余弦高斯光束的旁瓣既可以用作结构光，也可以使用余弦光束的谐波来抑制。静态光片和扫描光针的共同点是厚度、无衍射范围和旁瓣强度之间的矛盾。虽然可以使用分析模型单独处理这些属性，但平衡这些矛盾的解析模型尚无报道。
由此可见，无衍射光片具有大视野的优点，但往往伴随着显著的 旁瓣并牺牲了厚度。如何从整体上对光片进行优化，在厚度、无衍射范围和旁瓣强度这三者之间达到平衡具有重要的研究意义。
发明内容
针对相关技术的缺陷，本发明的目的在于提供一种生成准无衍射光片的光瞳掩模及其优化设计方法，旨在解决现有光片无法在厚度、无衍射范围和旁瓣强度这三者之间达到平衡的问题。
为实现上述目的，本发明的一个方面提供了一种生成准无衍射光片的光瞳掩模的优化设计方法，包括以下步骤：
S1.根据生成准无衍射光片的光学系统的参数要求，确定光瞳掩模的结构和待求解的结构参数；
S2.建立综合考虑光片厚度、无衍射范围和旁瓣强度的评价函数；
S3.利用粒子群算法搜索所述评价函数的全局最小值，得到对应的全局最优解；
由所述全局最优解获取所述待求解的结构参数。
进一步地，所述评价函数为
Figure PCTCN2022142906-appb-000001
Figure PCTCN2022142906-appb-000002
其中ω r(z)的定义为峰值r倍处的最大宽度，min(ω r)为ω r(z)在柱透镜的焦点附近取得的最小值，NDR(r)是无衍射范围，定义为光片厚度发散到小于它的最小厚度的
Figure PCTCN2022142906-appb-000003
倍的距离，λ是波长。
进一步地，所述光瞳掩模包括幅度调制或相位调制的交替的条状区间。
进一步地，所述光瞳掩模的结构具有上下对称性，且所述区间的总个数为奇数。
进一步地，所述待求解的结构参数为所述光瞳掩模中各个区间的宽度。
进一步地，所述步骤S3包括：
S301.将待求解的结构参数构成的向量视作一个粒子，随机化每个粒子的速度与位置，并获取初代粒子群中每个粒子个体的历史最优解和粒子群体的全局最优解；
S302.进行迭代，在每次迭代时将每个粒子的速度与位置进行更新；
S303.重复上述步骤，直到解不再更新为止。
进一步地，所述步骤S301包括：
设置学习因子、惯性因子和种群规模，并将各区间宽度组成的M维向量视作一个粒子；
随机化每个粒子的速度与位置；以粒子的位置代表各区间宽度的数值解，以粒子的速度代表各区间宽度的数值解的变化趋势，且粒子位置和速度也均为M维向量；
基于所述评价函数获取初代粒子群中每个粒子个体的历史最优解和粒子群体的全局最优解。
进一步地，所述步骤S302包括：
依据以下公式更新每个粒子的速度：
v i,d←w v i,d+φp r p(M i,d-m i,d)+φg r g(G i,d-m i,d)
其中i是粒子的指标，d是每个粒子的区间的指标，m i,d是每个粒子的当前位置，M i,d是每个粒子的现有最优解，G i,d是群体的现有最优解，w是惯性权重，φp是个体系数，φg是群体系数；
其中r p,r g为0～1之间的随机数；
用粒子的速度更新粒子的位置:m i,d←m i,d+v i,d；
根据新粒子群中每个粒子的评价函数更新每个粒子的历史最优解和粒子种群的全局最优解。
本发明的另一方面还提供了一种光瞳掩模，所述光瞳掩模按照上述的优化设计方法获得。
本发明的又一方面还提供了一种准无衍射静态光片，包括上述的光瞳掩模和柱透镜。
综上，本发明提供了一种生成准无衍射光片的光瞳掩模及其优化设计方法，基于粒子群算法将光瞳掩模的结构设计过程转化为求解函数的最优解，通过获取的最优解直接进行准无衍射光片的光瞳掩模结构设计，从而整体上优化了光片厚度、非衍射范围和旁瓣的光片显微。使用这种方法，光片的非衍射范围相对于高斯光束被扩大了50％，而旁瓣被抑制在20％的水平以下。该方法可应用于振幅掩模或相位掩模的设计。尤其值得一提的是优化后的相位掩模的总效率达到了50％以上。本发明所提供的由光瞳掩模产生的新型光片，可在不影响轴向分辨率的情况下，对具有扩大视场的生物样本进行成像。
附图说明
为了更清楚地说明本申请实施例中的技术方案，下面将对实施例描述中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本申请的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他的附图。
图1(a)是本发明实施例中的光瞳掩模结构示意图，图1(b)本发明实施例中准无衍射静态光片实现原理示意图；
图2中的(a)是本发明实施例振幅掩模示意图，图2中的(b)是本发明实施例相位掩模示意图；
图3是本发明实施例中掩模优化设计方法的流程图；
图4是本发明实施例中收敛曲线图；
图5是本发明实施例中经优化设计得到的振幅掩模对应的仿真结果示意图；
图6是本发明实施例中经优化设计得到的振幅掩模对应的实验结果示意图；
图7是本发明实施例中经优化设计得到的相位掩模对应的仿真结果示意图；
图8是本发明实施例中经优化设计得到的相位掩模对应的实验结果示意图。
具体实施方式
为了使本发明的目的、技术方案及优点更加清楚明白，以下结合附图及实施例，对本发明进行进一步详细说明。应当理解，此处所描述的具体实施例仅仅用以解释本发明，并不用于限定本发明。此外，下面所描述的本发明各个实施方式中所涉及到的技术特征只要彼此之间未构成冲突就可以相互组合。
本发明提供了一种光瞳掩模及其数值优化方法，从整体上优化了光片厚度、非衍射范围和旁瓣的光片显微。使用这种方法，光片的非衍射范围相对于高斯光束被扩大了50％，而旁瓣被抑制在20％的水平以下。该方法可应用于振幅掩模或相位掩模的设计。特别地，优化后的相位掩模的总效率达到了50％以上。本发明所提供的由光瞳掩模产生的新型光片，可在不影响轴向分辨率的情况下，对具有扩大视场的生物样本进行成像。
本发明实施例提供了一种生成准无衍射光片的光瞳掩模的优化设计方法，包括以下步骤：
S1.根据生成准无衍射光片的光学系统参数要求，确定光瞳掩模的结构和待求解的结构参数。
本发明采用如图1(a)和图1(b)所示装置，将高斯光束通过与孔径(图中黑色部分所示)配合的光瞳掩模以及柱透镜后，可在透镜焦点附近生成准无衍射静态光片。其中光瞳掩模既可以是幅值调制，也可以是相位调制，还可以幅值和相位均进行调制。由于这套装置在y轴方向上的不变性，可简化到一维尺度上进行分析。
如图2(a)和图2(b)所示，光瞳掩模由幅度调制或相位调制的交替的条状区间组成。为了使光瞳掩模关于光轴对称，区间总个数为奇数。区间相对于光轴是对称的，因而本发明只考虑x轴正方向的区间，并把正中间的区间一分为二。X轴正区间的宽度(m＝{m 1,m 2,m 3…})定义了掩模的结构。因此所述待求解的结构参数为所述光瞳掩模中各个区间的宽度。
S2.建立综合考虑厚度、无衍射范围和旁瓣强度的评价函数。
为了将厚度、无衍射范围和旁瓣强度全部考虑进来，本发明引入一个重要的参量——评价因子。光片的厚度ω r(z)是传输距离z的函数，可以用z处的最大强度的比例r处的全宽来度量。当r取0.5时，ω 0.5(z)就是通常所说的半峰全宽(FWHM)。主瓣的半峰全宽是光片的部分视角因为它忽略了旁瓣，将旁瓣考虑进来的话，ω r(z)的定义为峰值r倍处的最大宽度。因此，若旁瓣增长超过峰值的r倍，ω r(z)会迅速增长为关于光轴对称的两旁瓣之间的间距，且旁瓣间距通常是主瓣宽度的两倍以上。ω r(z)在柱透镜的焦点附近取得最小值min(ω r)。参照高斯光束瑞利距离的定义，本发明定义了比例因子r 和光瞳掩模的函数——无衍射范围(NDR)，光片厚度发散到小于它的最小厚度的
Figure PCTCN2022142906-appb-000004
倍的距离：
Figure PCTCN2022142906-appb-000005
经数值计算证实，NDR(r)也等于旁瓣维持在主瓣r倍以下的范围。然后，将NDR(r)与有着相同最小宽度的高斯光束瑞利距离相比：
Figure PCTCN2022142906-appb-000006
其中，因子2ln(1/r)来源于ω r到高斯束腰直径(1/e 2)的转化。在高斯光片的情形下，该评价因子正好等于1。因此，1/metric(r)描述了相较于高斯光束无衍射范围扩大了多少，于是问题转化为在比例因子r设定旁瓣的可容许水平的情况下最小化评价因子。
评价光片质量的度量有很多，主要包括三个方面：光片厚度、光片的无衍射范围以及光片的旁瓣强度。而这三个参数是相互制衡的。只考虑其中部分参数的做法相对比较片面。本发明所提出的评价因子将这三个参数浓缩到了一个函数中。而且，本领域的技术人员容易理解，以上公式(2)仅为一种优选的函数形式而已，并不用以限制本发明，凡在本发明的精神和原则之内对公式(2)所作的任何修改、等同替换和改进等，均应包含在本发明的保护范围之内。
根据掩模结构计算光场分布，光瞳掩模上的入射光是准直的高斯光束，其场乘以光瞳掩模。场通过一个柱面透镜，它被建模作为具有圆柱相位调制的无限薄透镜。本发明在一维尺度上对场、掩模和柱透镜进行建模，因为它们沿y不变。从透过柱面透镜的场，我们使用瑞利-索末菲法计算得到光场传播到焦点周围的光场。在焦距附近扫描 传播距离，可以获得焦点周围的二维光场分布，根据光场分布计算评价因子。
S3.利用粒子群算法搜索所述评价函数的全局最小值，得到对应的全局最优解。
由于评价因子的最小化是非凸函数，有很多局部最小值，本发明实施例采用数值优化方法，具体地，采用粒子群优化算法(PSO)搜索全局最小值。具体流程如图3所示。粒子群优化算法是一种进化计算技术，模仿一群蜜蜂的觅食行为，它们的初始位置是完全随机的。本发明利用该算法来寻找最好的光瞳掩模带宽(预设比例因子r为一个定值，一般r＝0.2是显微中可以接受的旁瓣强度，此方法可以根据具体需要调整r值)，把光瞳掩模的带宽作为优化的粒子，在一定范围内不断改变粒子的速度和位置，将评价因子作为设定的目标函数——评价函数来计算适应值，对每组优化粒子进行评估，最终找到全局最优解。而且，每一轮优化设定一个区间总个数，但进入到下一轮优化过程时改变区间总数，如此可以找到最优的区间数。
S301.将待求解的结构参数构成的向量视作一个粒子，随机化每个粒子的速度与位置，并获取初代粒子群中每个粒子个体的历史最优解和粒子群体的全局最优解。
以上步骤S301具体包括：
设置学习因子、惯性因子和种群规模，并将各区间宽度组成的M维向量视作一个粒子；
随机化每个粒子的速度与位置；以粒子的位置代表各区间宽度的数值解，以粒子的速度代表各区间宽度的数值解的变化趋势，且粒子位置和速度也均为M维向量；
基于所述评价函数获取初代粒子群中每个粒子个体的历史最优解和粒子群体的全局最优解。
通常使用16到32个粒子/蜜蜂寻找使评价因子最小化的掩模几何形状。粒子数越多，计算量越大，越利于寻找全局最优值。本发明实施例中用了32个粒子，即群体规模N＝32，区间总数为7且具有上下对称性，因此只需确定其中任意一半，即4个区间的宽度{m1,m2,m3,m4}即可定义掩模的结构，可见输入参数的维度为M＝4。根据设计经验选定个体系数φp＝0.3，群体系数φg＝0.9，惯性因子ω＝0.5，以上参数都在0～1区间内；较小的个体系数φp和较大的群体系数φg，虽然会减缓收敛的速度，但有利于寻找到全局最优值。将由各区间宽度m1、m2、m3、m4构成的一个M维向量{m1,m2,m3,m4}视作一个粒子，并以粒子的位置代表各基本结构参数的数值解，以粒子的速度代表各基本结构参数的数值解的变化趋势，且粒子位置和速度均为M维向量。
本实施例中，随机生成的粒子位置初始值m i,d和速度初始值v i,d分别如表1和表2所示(单位微米,其中i是粒子的标号，d是每个粒子的区间的编号)：
表1
  区间1 区间2 区间3 区间4
粒子1 154.4450278 195.2849364 118.8671168 6.4029191
粒子2 61.03378599 169.6719456 96.60432127 147.6899471
粒子3 69.66310204 185.3078319 1.72953754 218.2995285
粒子4 35.32114085 86.94172841 167.5924389 185.1446918
粒子5 140.6185595 137.6435941 106.4437768 90.29406962
粒子6 56.14195814 186.9943604 113.0809786 118.7827028
粒子7 142.1115303 94.73156449 102.8573093 135.299596
粒子8 203.2043936 17.88413397 104.3906694 149.520803
粒子9 174.576296 28.91753434 31.98072122 239.5254484
粒子10 326.2905376 26.50204981 45.63595142 76.57146118
粒子11 98.24203469 52.2961644 169.1209589 155.340842
粒子12 66.06761895 14.72011434 204.5014434 189.7108233
粒子13 161.7475021 79.8244873 23.39990286 210.0281078
粒子14 150.027733 14.00827584 172.0110187 138.9529724
粒子15 86.27621227 244.5055973 0.3726812 143.8455093
粒子16 108.1914918 168.103768 74.38393157 124.3208086
粒子17 140.8143257 58.48722226 169.2129452 106.4855069
粒子18 19.66088848 82.33989174 275.1378561 97.8613637
粒子19 15.12836567 259.5112808 92.87202574 107.4883278
粒子20 38.53093747 35.50046339 186.3793322 214.5892669
粒子21 1.72142909 134.2535276 269.2563513 69.76869204
粒子22 158.8032981 160.1976165 9.42616919 146.5729163
粒子23 4.34394396 218.8602733 15.02160815 206.7741746
粒子24 206.9181519 96.91904138 165.0180548 6.14475185
粒子25 162.5104817 106.8252141 134.8773172 70.78698704
粒子26 146.5234335 36.63802865 210.1969165 81.64162142
粒子27 9.54238477 206.4282294 79.42220213 179.6071837
粒子28 119.7894068 12.43278597 160.4016932 182.376114
粒子29 204.2884256 22.95397008 201.1990434 46.55856092
粒子30 193.6580553 94.46593 148.0431835 38.83283119
粒子31 26.27950006 56.61196696 196.0630481 196.0454849
粒子32 153.5034725 77.90663385 111.5501213 132.0397724
表2
  区间1 区间2 区间3 区间4
粒子1 57.32 -192.45 -72.63 207.76
粒子2 125.65 -143.86 31.63 -13.43
粒子3 22.87 -24.47 153.92 -152.31
粒子4 52.46 58.84 -49.15 -62.14
粒子5 -4.45 0.80 76.33 -72.68
粒子6 -53.32 -27.22 110.25 -29.71
粒子7 -65.84 57.21 -30.34 38.97
粒子8 -22.40 54.45 12.93 -44.98
粒子9 -24.63 78.80 140.56 -194.74
粒子10 -312.00 100.14 194.89 16.97
粒子11 -28.72 22.98 -60.72 66.46
粒子12 100.53 55.93 -87.80 -68.66
粒子13 31.28 35.28 103.05 -169.60
粒子14 -132.94 112.41 22.99 -2.46
粒子15 86.23 -160.75 71.96 2.57
粒子16 38.81 -46.79 59.92 -51.93
粒子17 -70.82 151.63 -158.64 77.82
粒子18 249.06 64.30 -218.28 -95.09
粒子19 139.36 -221.62 2.49 79.77
粒子20 50.94 128.52 -45.31 -134.15
粒子21 36.47 24.94 -139.13 77.72
粒子22 -67.44 -32.55 77.94 22.05
粒子23 180.94 -212.68 16.54 15.20
粒子24 -33.16 -31.12 -62.67 126.95
粒子25 -42.64 59.33 -81.50 64.81
粒子26 -47.53 123.04 -53.66 -21.84
粒子27 187.01 -64.22 -33.35 -89.44
粒子28 20.89 97.18 -32.36 -85.71
粒子29 -165.80 243.96 -83.42 5.26
粒子30 -20.32 129.69 -85.90 -23.47
粒子31 127.24 48.13 -96.22 -79.14
粒子32 -15.07 53.22 47.69 -85.84
S302.进行迭代，在每次迭代时将每个粒子的速度与位置进行更新。
依据以下公式更新每个粒子的速度：
v i,d←w v i,d+φp r p(M i,d-m i,d)+φg r g(G i,d-m i,d)
其中i是粒子的指标，d是每个粒子的区间的指标，m i,d是每个粒子的当前位置，M i,d是每个粒子的现有最优解，G i,d是群体的现有最优解，w是惯性权重，φp是个体系数，φg是群体系数；
其中r p,r g为0～1之间的随机数；
用粒子的速度更新粒子的位置:m i,d←m i,d+v i,d
根据新粒子群中每个粒子的评价函数更新每个粒子的历史最优解和粒子种群的全局最优解。
S303.重复上述步骤，直到解不再更新为止。
图4示出了本实施例的收敛曲线，可见在迭代次数为1000左右时达到收敛。由所述全局最优解获取所述待求解的结构参数。本实施例中，最优解为[122.30190817,143.22780712,83.0393262,126.4309585]。
本实施例得到的最佳二元振幅掩模除了外孔径一共包含7条区间，中心区间不透光。这相当于一片不透光材料上的两对对称狭缝，外缝宽度是内缝宽度的0.88倍。当比例因子r为0.2时，得到的最优评价因子为0.65，这表明非衍射范围增大了50％，而旁瓣维持在其局部最大值的20％以下。图5为仿真结果。
振幅掩模是在一块钠石灰玻璃基板上制作的，上面涂有一层铬，在铬上涂有一层光刻胶，掩模图案以0.5μm的精度通过激光直写投影到光刻胶上，暴露的光刻胶被溶解，露出下面的铬，然后铬被蚀刻掉，露出下面的透明玻璃，在清除残留的光刻胶后，振幅掩模准备就绪。
光片的表征使用二极管激光器进行，该激光器可以通过光纤电缆输出445nm的光，激光用光纤准直器进行准直，准直激光是高斯型的，束腰半径为0.66mm。本发明选择不使用由平面凸透镜制成的望远镜来扩展准直激光束，以避免对高斯光束引入像差，同时也简化了设置。相反，本发明使用一个具有短焦距的柱透镜(f＝12.5mm，Edmund#68-043)来形成一个5μm厚的光片。所选的柱透镜由N-SF11制成，折射率为1.82，因此球面像差较小。使用具有适当焦距的柱透镜将进一步提高评价因子，但柱透镜的焦距有限。本发明的掩模插入在柱透镜之前。因为光束在柱透镜之前是准直的，所以掩模和柱透镜之间的间距不是关键的。因为光片的厚度与数码相机的像素间距相当，本发明使用尼康20X物镜和管状镜头放大x-y平面上的光片强度分布，在FLIR Blackfly CMOS数字相机上形成一个图像。物镜可以沿光学z轴平移，聚焦于光片不同z轴处的横截面。图6显示了使用振幅掩模的实验观察到的强度分布。其厚度和非衍射范围与仿真结果吻合较好。旁瓣从20％略有增加到25％，这主要是由于仿真焦距与实验焦距存在5％的误差。此外，相位掩模的仿真结果和实验结果在图7和图8示出。
综上，本发明提供了一种光瞳掩模及其数值优化方法，从整体上优化了光片厚度、非衍射范围和旁瓣的光片显微。使用这种方法，光片的非衍射范围相对于高斯光束被扩大了50％，而旁瓣被抑制在20％的水平以下。该方法可应用于振幅掩模或相位掩模的设计。特别地，优化后的相位掩模的总效率达到了50％以上。本发明所提供的由光瞳掩模产生的新型光片，可在不影响轴向分辨率的情况下，对具有扩大视场的生物样本进行成像。
本领域的技术人员容易理解，以上所述仅为本发明的较佳实施例而已，并不用以限制本发明，凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等，均应包含在本发明的保护范围之内。

Claims (10)

  1. 一种生成准无衍射光片的光瞳掩模的优化设计方法，其特征在于，包括以下步骤：
    S1.根据生成准无衍射光片的光学系统参数要求，确定光瞳掩模的结构和待求解的结构参数；
    S2.建立综合考虑光片厚度、无衍射范围和旁瓣强度的评价函数；
    S3.利用粒子群算法搜索所述评价函数的全局最小值，得到对应的全局最优解；
    由所述全局最优解获取所述待求解的结构参数。
  2. 如权利要求1所述的优化设计方法，其特征在于，所述评价函数为
    Figure PCTCN2022142906-appb-100001
    Figure PCTCN2022142906-appb-100002
    其中ω r(z)的定义为峰值r倍处的最大宽度，min(ω r)为ω r(z)在柱透镜的焦点附近取得的最小值，NDR(r)是无衍射范围，定义为光片厚度发散到小于它的最小厚度的
    Figure PCTCN2022142906-appb-100003
    倍的距离，λ是波长。
  3. 如权利要求1所述的优化设计方法，其特征在于，所述光瞳掩模包括幅度调制或相位调制的交替的条状区间。
  4. 如权利要求3所述的优化设计方法，其特征在于，所述光瞳掩模的结构具有上下对称性，且所述区间的总个数为奇数。
  5. 如权利要求3所述的优化设计方法，其特征在于，所述待求解的结构参数为所述光瞳掩模中各个区间的宽度。
  6. 如权利要求1所述的优化设计方法，其特征在于，所述步骤S3包括：
    S301.将待求解的结构参数构成的向量视作一个粒子，随机化每个粒子的速度与位置，并获取初代粒子群中每个粒子个体的历史最优解和粒子群体的全局最优解；
    S302.进行迭代，在每次迭代时将每个粒子的速度与位置进行更新；
    S303.重复上述步骤，直到解不再更新为止。
  7. 如权利要求1所述的优化设计方法，其特征在于，所述步骤S301包括：
    设置学习因子、惯性因子和种群规模，并将各区间宽度组成的M维向量视作一个粒子；
    随机化每个粒子的速度与位置；以粒子的位置代表各区间宽度的数值解，以粒子的速度代表各区间宽度的数值解的变化趋势，且粒子位置和速度也均为M维向量；
    基于所述评价函数获取初代粒子群中每个粒子个体的历史最优解和粒子群体的全局最优解。
  8. 如权利要求1所述的优化设计方法，其特征在于，所述步骤S302包括：
    依据以下公式更新每个粒子的速度：
    v i,d←w v i,d+φp r p(M i,d-m i,d)+φg r g(G i,d-m i,d)
    其中i是粒子的指标，d是每个粒子的区间的指标，m i,d是每个粒子的当前位置，M i,d是每个粒子的现有最优解，G i,d是群体的现有最优解，w是惯性权重，φp是个体系数，φg是群体系数；
    其中r p,r g为0～1之间的随机数；
    用粒子的速度更新粒子的位置:m i,d←m i,d+v i,d；
    根据新粒子群中每个粒子的评价函数更新每个粒子的历史最优解和粒子种群的全局最优解。
  9. 一种光瞳掩模，其特征在于，所述光瞳掩模按照权利要求1-8任一项所述的优化设计方法获得。
  10. 一种准无衍射静态光片生成装置，其特征在于，包括如权利要求9所述的光瞳掩模和柱面透镜，所述光瞳掩模插入在所述柱面透镜之前。
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