WO2020087966A1 - 基于led阵列编码照明的三维衍射层析显微成像方法 - Google Patents

基于led阵列编码照明的三维衍射层析显微成像方法 Download PDF

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WO2020087966A1
WO2020087966A1 PCT/CN2019/094886 CN2019094886W WO2020087966A1 WO 2020087966 A1 WO2020087966 A1 WO 2020087966A1 CN 2019094886 W CN2019094886 W CN 2019094886W WO 2020087966 A1 WO2020087966 A1 WO 2020087966A1
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dimensional
illumination
transfer function
refractive index
light source
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左超
陈钱
孙佳嵩
张玉珍
顾国华
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南京理工大学
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    • G01N15/1468—Optical investigation techniques, e.g. flow cytometry with spatial resolution of the texture or inner structure of the particle
    • G—PHYSICS
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    • G01N15/14—Optical investigation techniques, e.g. flow cytometry
    • G01N15/1434—Optical arrangements
    • G01N2015/144—Imaging characterised by its optical setup
    • G01N2015/1445—Three-dimensional imaging, imaging in different image planes, e.g. under different angles or at different depths, e.g. by a relative motion of sample and detector, for instance by tomography
    • G—PHYSICS
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    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N15/00—Investigating characteristics of particles; Investigating permeability, pore-volume or surface-area of porous materials
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    • G01N15/14—Optical investigation techniques, e.g. flow cytometry
    • G01N15/1434—Optical arrangements
    • G01N2015/1447—Spatial selection
    • G01N2015/145—Spatial selection by pattern of light, e.g. fringe pattern
    • G—PHYSICS
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    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N15/00—Investigating characteristics of particles; Investigating permeability, pore-volume or surface-area of porous materials
    • G01N15/10—Investigating individual particles
    • G01N15/14—Optical investigation techniques, e.g. flow cytometry
    • G01N2015/1493—Particle size
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N15/00—Investigating characteristics of particles; Investigating permeability, pore-volume or surface-area of porous materials
    • G01N15/10—Investigating individual particles
    • G01N15/14—Optical investigation techniques, e.g. flow cytometry
    • G01N2015/1497—Particle shape

Definitions

  • the invention belongs to optical microscopic measurement and three-dimensional refractive index imaging technology, in particular to a three-dimensional diffraction tomography microscopic imaging method based on LED array coding illumination.
  • imaging analysis and testing equipment is an important tool for observing the structure and life status of cells and biological tissues.
  • microscopic imaging instruments are becoming more and more important as the most commonly used imaging tools in biomedical research, while traditional optical The microscope can only obtain the two-dimensional distribution map of the sample to be tested, and cannot give the three-dimensional spatial information of the measured object, which is difficult to meet the requirements of the growing biomedical research.
  • Optical micro-tomography is a technical method that can measure the internal three-dimensional structure of the sample.
  • the refractive index of cells or biological tissues is used as the inherent contrast source of the sample to be tested, and contains important information parameters, such as the shape, size, and volume of cells or biological tissues. Morphological detection and medical diagnosis are essential. Therefore, in biological research, the study of the three-dimensional refractive index of the sample to be tested is of great significance for improving the accuracy of medical morphology detection and medical diagnosis.
  • phase microscopy techniques such as proportional microscopy, differential interference contrast microscopy, and quantitative phase microscopy have been developed. These microscopic techniques transform different refractive index distributions in the cells into different contrasts of the collected images, but under normal circumstances, the refractive index in the cells is very weak, which requires the modulation of the incident light wave to improve the resolution of the image .
  • the Zernik phase microscope uses a phase plate with zero frequency attenuation and a phase shift of 90 degrees for spatial filtering to convert the phase structure of the object into a light intensity distribution on the plane (F.Zernike, "Phase contrast, a new method for the microscopic observation of transparent objects, "Physica 9 (7) , 686-698 (1942);. using a differential interference microscope Wollaston prism so that two beams of light to produce an optical path difference, so that the interior of the test sample different refractive indices into the image Light and dark changes (G. Nomarski and A. Weill, "Application à la dillographie des profit interférentielles àdes on des polarologies," Rev.
  • the quantitative phase microscope developed in recent years The reference light is adjusted to make the sample beam and the reference light phase shift, and the refractive index difference is measured after interference.
  • the phase delay is proportional to the product of the refractive index and the path length, so only The average refractive index parameter of the cell is provided, but the detailed three-dimensional structure inside the cell cannot be obtained.
  • the object of the present invention is to provide a three-dimensional diffraction tomography micro-imaging method based on LED array coding illumination, which realizes high-resolution and high signal-to-noise ratio three-dimensional diffraction tomography micro-imaging of samples such as cells and tiny biological tissues.
  • the technical solution to achieve the object of the present invention is: a three-dimensional diffraction tomography micro-imaging method based on LED array coding illumination, the steps are as follows:
  • Step 1 Collect the original intensity image.
  • the object to be measured is in focus and the shape of the illumination light source is changed to a circle with coherence coefficients S1, S2, and S3 by changing the LED array coding, move the stage or use Controlled zoom lens to collect three sets of intensity image stacks at different defocus positions with
  • Step 2 Change the LED array code to make the illumination pattern into a ring shape with a coherence coefficient of S4, and then collect the intensity image stack of the object under test at different defocus positions by moving the stage or using an electronically controlled zoom lens
  • Step 3 Derivation of the three-dimensional phase transfer function of the microscopic imaging system of arbitrary shape illumination.
  • the three-dimensional transfer function model of the oblique coherent point light source is extended to the partial coherent illumination and ring illumination three-dimensional transfer function models.
  • Step 4 Three-dimensional diffraction tomography quantitative refractive index deconvolution reconstruction, three-dimensional Fourier transform is performed on the four sets of intensity image stacks collected to obtain three-dimensional spectrum under four lighting conditions, and the obtained four sets of three-dimensional spectrum are phased Add and divide in the frequency domain by the sum of the absolute values of the four three-dimensional phase transfer functions to obtain the three-dimensional scattering potential function;
  • Step 5 The quantitative three-dimensional refractive index distribution of the measured object, the inverse Fourier transform is performed on the three-dimensional scattering potential function, and the scattered potential function is converted into the refractive index distribution to obtain the quantitative three-dimensional refractive index distribution of the measured object.
  • the present invention has significant advantages: (1) LED coded illumination is used in three-dimensional diffraction tomography. By changing the LED array code, three circular and one circular illumination patterns with different coherence coefficients are obtained.
  • the camera collects four sets of image stacks at different defocus positions, and performs a three-dimensional Fourier transform on the four sets of intensity image stacks to obtain three-dimensional spectrum under four different lighting conditions.
  • the three-dimensional spectrum under four different lighting conditions is added, and then divided in the frequency domain by the sum of the absolute value of the three-dimensional phase transfer function to obtain the three-dimensional scattering potential function of the sample to be measured.
  • inverse Fourier transform is performed on the three-dimensional scattering potential function to convert the scattering potential function into the refractive index distribution of the sample to be measured.
  • the three-dimensional transfer function model of the oblique coherent point light source is extended to the three-dimensional transfer function model under partial coherent illumination and ring illumination, and the three-dimensional phase transfer function of the microscopic system under circular and ring illumination under different coherence coefficients is obtained.
  • Three-dimensional diffraction tomography uses the multi-frequency combination of a circular illumination pupil and multiple traditional circular illumination pupils, which not only expands the resolution of the system field imaging by 2 times, but also makes the acquired image stronger With a high contrast and a high signal-to-noise ratio, the theory can achieve a lateral resolution of 200nm and an axial resolution of 645nm. The noise of the image is reduced, and the image resolution reaches the incoherent diffraction limit.
  • FIG. 1 is a schematic diagram of a three-dimensional diffraction tomography imaging system of the present invention.
  • FIG. 2 is a schematic diagram of four sets of image stacks collected by the present invention under four different LED array illumination light sources.
  • FIG. 3 is a two-dimensional schematic diagram of the corresponding three-dimensional transfer function under four different LED array illumination light sources of the present invention.
  • FIG. 4 is a flowchart of a method for three-dimensional diffraction tomography quantitative refractive index deconvolution reconstruction of the present invention.
  • FIG. 5 is a graph of the three-dimensional imaging results of the present invention on micro-polystyrene beads, unstained S. vulgaris and Hella cells.
  • the three-dimensional diffraction tomography micro-imaging method of the present invention based on LED array coding illumination has the following process:
  • Step 1 Build a three-dimensional diffraction tomography imaging system: Combined with Figure 1, the microscope imaging system includes an LED array coded illumination light source, a microscopic objective lens, a tube lens, a plane mirror, a motorized zoom lens control module, a
  • the camera is composed of a computer, and the computer is connected to the electric zoom lens control module and the camera through signal lines, respectively.
  • the illumination light source adopts LED array coding lighting, and different patterns of illumination can be realized by changing the LED array coding.
  • Image acquisition is performed by CMOS camera, and the acquired image is transferred to computer for calculation and processing.
  • the axial scanning step of the electric zoom lens control module is 0.1 ⁇ m through the driving of an electric zoom lens control module to realize the axial scanning of the sample to be measured to acquire the image stack.
  • Four sets of pictures under different LED array coded illumination were measured. Each set of pictures included 100 images with a resolution of 400 ⁇ 400 and three circular illuminations.
  • the spatial sampling rates of x, y, and z are 0.065 ⁇ m, 0.065 ⁇ m, and 0.1 ⁇ m, respectively.
  • the stack time for acquiring images is 15 ms
  • the data processing time is 10 ms
  • the camera exposure time is 30 ms.
  • the computer is also equipped with MATLAB.
  • the process of processing the image is realized by using MATLAB to write the code, and the three-dimensional diffraction tomography micro-imaging based on the LED array coding illumination is realized through the three-dimensional diffraction tomography micro-imaging system.
  • Step 2 Acquire the original intensity image: when the sample of the thick object to be measured is in focus and the shape of the illumination light source is changed to a circle with coherent coefficients S1, S2, and S3 by changing the LED array code, move the stage or use Controlled zoom lens to collect three sets of intensity image stacks at different defocus positions with Then change the LED array code to make the illumination pattern into a ring shape with a coherent coefficient S4, and collect the intensity image stack of the object to be measured at different defocus positions by moving the stage or using an electronically controlled zoom lens
  • four different image stacks based on LED array coded illumination can be obtained by a CMOS camera, that is, the LED array coded illumination introduces the ring lighting scheme into the traditional circular bright field microscopy, and the image is taken under the ring-shaped illumination pattern
  • Figure 2 is an axial image stack diagram under four groups of different LED array coded illumination.
  • the circular illumination pattern is changed from small to large.
  • the fourth group changes the illumination pattern to a circular illumination pattern.
  • the electronically controlled zoom lens collects the object to be measured at different defocussing Position image stack under intensity.
  • the first line is the LED array coding illumination pattern
  • the second line is the image intensity map acquired at the axial Z1 position
  • the second line is the image stack image acquired at the axial Z2 position
  • the lens collects the intensity image stack of the object to be measured at different axial defocus positions. Under each LED array coding illumination pattern, 100 intensity maps with a resolution of 400 ⁇ 400 were collected respectively.
  • Step 3 Derivation of the three-dimensional phase transfer function of the microscopic imaging system with pupil illumination of arbitrary shape: the three-dimensional transfer function model of the oblique coherent point light source is extended to the partial coherent illumination and ring illumination three-dimensional transfer function models The three-dimensional phase transfer function of the microscopic system under circular and ring illumination under the coefficient.
  • the absorptivity n a (r) and refractive index n p (r) of a three-dimensional object correspond to the imaginary and real parts of the complex refractive index n (r), respectively.
  • the complex refractive index n (r) of the object and the surrounding medium The relationship of the refractive index n 0 (r) can be expressed as a three-dimensional scattering potential Wherein r is a three-dimensional space variable, k 0 is the wave number corresponding to the wavelength in vacuum, n m is the refractive index of the medium in which the object.
  • the intensity image I (r) measured for a three-dimensional object can represent:
  • B is the captured transmitted light component
  • a (r) and P (r) are the imaginary and real parts of the three-dimensional scattering potential of the object
  • H A (r) and H P (r) are the imaging, respectively.
  • Three-dimensional Fourier transform of the above formula can obtain the three-dimensional Fourier spectrum of the captured intensity map
  • T P ( ⁇ ) are the three-dimensional transfer function of the spectrum and phase of the phase part of the scattering potential
  • T A ( ⁇ ) are the frequency component of the absorption part of the scattering potential and the three-dimensional transfer function of absorption.
  • the three-dimensional transfer function corresponding to the phase component is:
  • ⁇ (u, v, w)
  • I the light source distribution function
  • I the absolute value of which can be expressed as
  • ⁇ P is the normalized cut-off frequency of the pupil of the microscope objective.
  • the three-dimensional phase transfer function corresponding to the light source can be obtained as:
  • the above three-dimensional transfer function can be divided into with That is, two spherical shells moved by the illumination light source in three-dimensional space with It is the definition function of Ewald spherical shell.
  • the light source is a ring light source, it can be defined as:
  • FIG. 3 is a two-dimensional schematic diagram on the u-w plane of a three-dimensional phase transfer function under different LED array coded illumination. From left to right, the circular lighting pattern under the LED array coded lighting conditions changes from small to large, and the last group is circular lighting. As can be seen from the first three sets of results, as the coherence coefficient increases under circular illumination, the high-frequency image information in its three-dimensional phase transfer function is compensated. However, due to the increase in the numerical aperture, the high-frequency information part is compensated and the low-frequency information part is weakened. Therefore, the result (d) uses ring lighting to achieve high-frequency signal compensation, and the effect of low-frequency signal enhancement is fully explained.
  • the three-dimensional phase transfer function can be accurately derived based on ring lighting, which proves the feasibility and accuracy of this ring lighting method.
  • Step 4 Three-dimensional diffraction tomography quantitative refractive index deconvolution reconstruction: the four sets of intensity image stacks collected are subjected to three-dimensional Fourier transform to obtain three-dimensional spectrum under four lighting conditions. The four sets of three-dimensional spectrums are added and divided by the sum of the absolute values of the four three-dimensional phase transfer functions in the frequency domain to obtain a three-dimensional scattering potential function.
  • T P ( ⁇ )
  • T P1 ( ⁇ ), T P2 ( ⁇ ), T P3 ( ⁇ ) and T P4 ( ⁇ ) respectively correspond to the three-dimensional phase transfer functions under four different illumination coherence coefficients.
  • the sum of the four intensity Fourier spectra is divided by the sum of the corresponding four three-dimensional phase transfer functions to obtain the Fourier spectrum of the three-dimensional scattering potential function of the measured object.
  • Step five quantitative three-dimensional refractive index distribution of the measured object. Inverse Fourier transform is performed on the three-dimensional scattering potential function of the measured object, and the scattered potential function is converted into the refractive index distribution, and then the quantitative three-dimensional refractive index distribution of the measured object can be obtained.
  • the scattering potential function is converted into the refractive index distribution by using the scattering potential calculation formula
  • the quantitative three-dimensional refractive index distribution of the measured object can be obtained.
  • FIG. 4 is a block diagram representation of a three-dimensional diffraction tomography quantitative refractive index deconvolution reconstruction method.
  • the numerator in the dotted frame represents the sum of the image stacks collected under the illumination of four sets of different LED arrays for Fourier transform, and the denominator represents the sum of the absolute values of the corresponding three-dimensional phase transfer functions, dividing the two.
  • the Fourier spectrum of the three-dimensional scattering potential function is obtained.
  • the three-dimensional inverse Fourier transform of the three-dimensional scattering potential function can obtain the quantitative three-dimensional refractive index distribution of the measured object.
  • FIG. 5 is a three-dimensional imaging result of three-dimensional diffraction tomography micro-imaging method based on LED array coding illumination on micro-polystyrene beads, unstained S. vulgaris and Hella cells.
  • Figure (a) is a quantitative three-dimensional refractive index distribution diagram of micropolystyrene beads with a diameter of 6 ⁇ m.
  • Figures (a1) and (a2) are three-dimensional slices on the XY plane and YZ plane of micropolystyrene beads, respectively.
  • Figure (a3) is a schematic diagram of the final reconstructed three-dimensional Fourier spectrum
  • Figure (a4) is a cross-sectional view of the axial and lateral three-dimensional refractive index of the micropolystyrene beads.
  • Figure (b) is a schematic diagram of the distribution of three-dimensional diffraction chromatography of unstained S. vulgaris on the XY plane, the XZ plane and the ZY plane.
  • S. spp. Is a green algae composed of 8, 16 or 32 cells In plants, internal cells form ellipsoids with obvious front and back polarities, which also makes S. euglena an ideal three-dimensional diffraction deconvolution object.
  • Figure (c) is a schematic diagram of the distribution of three-dimensional diffraction chromatography of HeLa cells on the XY plane, the XZ plane and the ZY plane. As shown in Figure 5, we can clearly see the micro-polystyrene beads. The distribution of individual cells and the various morphologies of the cells within the chlorella cells further confirmed the feasibility and accuracy of this three-dimensional diffraction deconvolution based on multi-frequency synthesis.

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Abstract

一种基于LED阵列编码照明的三维衍射层析显微成像方法，首先采集原始强度图像，通过移动载物台或利用电控变焦透镜采集在不同离焦位置下的三组强度图像堆栈，然后通过采集待测物体在不同离焦位置下的强度图像堆栈，对任意形状照明的显微成像系统的三维相位传递函数进行推导，得到在不同相干系数下的圆形和环状照明下显微系统的三维相位传递函数，并对三维衍射层析定量折射率反卷积重构，对三维散射势函数进行逆傅里叶变换，将散射势函数转换为折射率分布，即可得到被测物体的定量三维折射率分布。实现了对细胞、微小生物组织等样品高分辨率高信噪比三维衍射层析显微成像。

Description

基于LED阵列编码照明的三维衍射层析显微成像方法 技术领域
本发明属于光学显微测量、三维折射率成像技术，特别是一种基于LED阵列编码照明的三维衍射层析显微成像方法。
背景技术
随着生物医学的发展，成像分析测试设备是观测细胞与生物组织结构形态和生命状态的重要工具，其中显微成像仪器作为生物医学研究中最常用的成像工具越来越重要，而传统的光学显微镜只能获取待测样品二维分布图，并不能给出被测物体的三维空间信息，难以满足日益发展的生物医学研究的要求。光学显微层析成像技术就是一种能实现样品内部三维结构测量的技术手段。在光学显微成像技术中，细胞或生物组织的折射率作为待测样品固有的对比源，包含了重要的信息参数，如细胞或生物组织的形状，大小，以及体积，这些特征对于生物疾病的形态检测和医疗诊断至关重要。因此，在生物学研究中，对待测样品三维折射率的研究对于提高医学形态检测与医疗诊断的准确率有着非常重要的意义。
在生物细胞里，不同的折射率分布将引起不同的入射光波相位延迟，根据此原理，相位显微技术如相称显微镜，微分干涉差显微镜和定量相位显微镜等得到发展。这些显微技术将细胞内不同折射率分布转化为采集到的图像不同对比度，但是在通常情况下，细胞内的折射率是非常微弱的，这就需要对入射光波进行调制来提高图像的分辨率。Zernik相位显微镜使用一个零频衰减同时相移90度的相位板进行空间滤波，将物体相位结构转换成平面上的光强分布(F.Zernike,“Phase contrast,a new method for the microscopic observation of transparent objects,”Physica 9(7),686–698(1942) .；微分干涉差显微镜利用渥拉斯顿棱镜使两束光产生光程差，从而将待测样品内部折射率的不同转化为图像的明暗变化(G.Nomarski and A.Weill,“Application à la métallographie des méthodes interférentiellesàdeux ondes polarisées,”Rev.Metall 2,121–128(1955))。但是在实际生活中，样品是三维的，而相位显微镜和微分干涉差显微镜，这些技术提供的不是定量的相位变化，而且为了得到高分辨率系统一般采用大的数值孔径，更加导致得到的待测样品的三维折射率不够准确；传统的光学显微镜,比如用荧光染料的荧光显微镜,被广大生物医学研究者广泛应用。然而，用染料标记的显微镜 有很多问题，比如染料会改变细胞性质、由于漂白而难以长期测量以及染色过程耗费时间等。为了无需标记即可观察完整细胞的形态和光学性质，近年来发展的定量相位显微镜通过对参考光进行调试，使样品光束与参考光产生相移，干涉后测量折射率差异。虽然可以获取成活细胞的三维形态和光学性质，但是相位延迟正比于折射率与路径长度的乘积，因此只可以提供细胞的平均的折射率参数，而得不到细胞内部详细三维结构。
过去的几年中，在定量相位显微技术的基础上，许多可以测量生物细胞三维折射率分布的多种新型显微技术也得到了发展，如数字全息显微镜、光学扫描显微镜、断层显微显微镜等。数字全息显微层析术，将数字全息显微术和衍射层析术相结合,先全息记录下待测物体在各个观测角下的数字全息图，数值再现出全角度下的复振幅数据，然后运用一定的重建算法重构出物体内部结构的三维折射率分布。它具有成像速度快、宽光束照射且所需光功率低、无需荧光标记可实现无扰分析以及具有高空间分辨率的优点。数字全息显微衍射层析术获取不同角度物光场分布的方法主要有两种，一种是改变照明光倾斜方向而样品保持固定；另一种是转动样品而照明光方向保持不变。前者装置能保持样品固定不动,适用于生物细胞等活体样品,但是记录视角受显微物镜数值孔径限制,从而产生“锥形频谱缺失”问题。光学扫描显微镜，通过对待测样品的轴向扫描来实现三维折射率的定量成像，轴向扫描当照明光源的相干系数较小的时候，所拍摄的强度图对比度较高，所以信噪比较高，但是最终的三维频谱的轴向分辨率较低。当照明光源的相干系数较大时，最终重构的分辨率较高，但图像的衬度非常低，导致所拍摄的强度图的信噪比较差。因此，发展新的光学显微层析成像技术，对细胞、微小生物组织等样品实现无扰、高分辨、定量的显微分析是目前生物医学研究迫切需求的技术。
发明内容
本发明的目的在于提供一种基于LED阵列编码照明的三维衍射层析显微成像方法，实现了对细胞、微小生物组织等样品高分辨率高信噪比三维衍射层析显微成像。
实现本发明目的的技术解决方案为：一种基于LED阵列编码照明的三维衍射层析显微成像方法，步骤如下：
步骤一：采集原始强度图像，在被测厚物体为聚焦状态，且通过改变LED阵列编码使照明光源形状为相干系数S1、S2和S3的圆形的情况下，通过移动载物台或利用电控变焦透镜采集在不同离焦位置下的三组强度图像堆栈
Figure PCTCN2019094886-appb-000001
和
Figure PCTCN2019094886-appb-000002
步骤二：通过改变LED阵列编码使照明图案为相干系数S4的圆环形状，再通过移动载物台或利用电控变焦透镜采集待测物体在不同离焦位置下的强度图像堆栈
Figure PCTCN2019094886-appb-000003
步骤三：对任意形状照明的显微成像系统的三维相位传递函数进行推导，由倾斜相干点光源的三维传递函数模型推广至部分相干照明和环状照明三维传递函数模型，得到在不同相干系数下的圆形和环状照明下显微系统的三维相位传递函数；
步骤四：三维衍射层析定量折射率反卷积重构，对所采集的四组强度图像堆栈进行三维傅里叶变换得到四种照明情况下的三维频谱，将得到的四组三维频谱进行相加再在频域中除以四种三维相位传递函数绝对值之和，得到三维散射势函数；
步骤五：被测物体的定量三维折射率分布，对三维散射势函数进行逆傅里叶变换，将散射势函数转换为折射率分布，即可得到被测物体的定量三维折射率分布。
本发明与现有技术相比，其显著优点：(1)将LED编码照明运用于三维衍射层析成像中，通过改变LED阵列编码得到三个不同相干系数的圆形和一个环形照明图案，通过相机采集不同离焦位置下的四组图像堆栈，对四组强度图像堆栈进行三维傅里叶变换得到四种不同照明情况下的三维频谱。将四种不同照明情况下的三维频谱进行相加，然后在频域中除以三维相位传递函数绝对值之和得到待测样品的三维散射势函数。最后对三维散射势函数进行逆傅里叶变换，将散射势函数转换为待测样品的折射率分布。(2)重新推导了三维相位传递函数，使其可以得到在任意照明形状下的光瞳传递函数。由倾斜相干点光源的三维传递函数模型推广至部分相干照明和环状照明下的三维传递函数模型，得到在不同相干系数下的圆形和环状照明下显微系统的三维相位传递函数。(3)三维衍射层析成像利用环形照明光瞳和多个传统的圆型照明光瞳的多频率结合，不仅将系统场 成像分辨率拓展2倍分辨率，而且使所采集的图像具有较强的对比度和较高的信噪比，理论可以实现横向分辨率达200nm，轴向分辨率达645nm。降低了图像的噪声，图像分辨率达到非相干衍射极限。
下面结合附图对本发明作进一步详细描述。
附图说明
图1是本发明三维衍射层析显微成像系统示意图。
图2是本发明在四种不同LED阵列照明光源下采集的四组图像堆栈示意图。
图3是本发明四种不同LED阵列照明光源下对应的三维传递函数的二维示意图。
图4是本发明三维衍射层析定量折射率反卷积重构方法的流程图。
图5是本发明对微聚苯乙烯珠、未染色实球藻和海拉细胞的三维成像结果图。
具体实施方式
本发明基于LED阵列编码照明的三维衍射层析显微成像方法，其过程如下：
步骤一，搭建三维衍射层析显微成像系统：结合图1，该显微成像系统包括一个LED阵列编码照明光源、一个显微物镜、一个筒镜、一个平面镜、电动变焦透镜控制模块、一台相机以及一台计算机组成，其中计算机与电动变焦透镜控制模块和相机之间分别通过信号线相连。照明光源采用LED阵列编码照明，可通过改变LED阵列编码实现不同图案的照明。图像采集通过CMOS相机进行采集，采集到图像传递到计算机进行计算处理。通过一个电动变焦透镜控制模块的驱动实现待测样品轴向扫描采集图像堆，电动变焦透镜控制模块的轴向扫描步长为0.1μm。测量在不同LED阵列编码照明下的四组图，每组图包括100张图像，每张图像的分辨率为400×400，三个圆形照明。x、y、z的空间采样率分别为0.065μm，0.065μm和0.1μm。基于不同相干系数下的圆形和环状照明条件，采集图像堆栈时间为15ms，数据处理时间为10ms，相机曝光时间为30ms。计算机中还装有MATLAB，采集完图像后，处理图像的过程都是利用MATLAB编写代码所实现，通过三维衍射层析显微成像系统实现基于LED阵列编码照明的三维衍射层析显微成像。
步骤二，采集原始强度图像：在被测厚物体样本为聚焦状态，通过改变LED 阵列编码使照明光源形状为相干系数S1、S2和S3的圆形的情况下，通过移动载物台或利用电控变焦透镜采集在不同离焦位置下的三组强度图像堆栈
Figure PCTCN2019094886-appb-000004
和
Figure PCTCN2019094886-appb-000005
然后通过改变LED阵列编码使照明图案为相干系数S4圆环形状，通过移动载物台或利用电控变焦透镜采集待测物体在不同离焦位置下的强度图像堆栈
Figure PCTCN2019094886-appb-000006
这样可以通过CMOS相机得到基于LED阵列编码照明下的四组不同图像堆栈，即通过LED阵列编码照明将环形照明方案引入传统的圆形明场显微中，并拍摄了在圆环形状照明图案下沿轴向的一系列光强图像堆栈
Figure PCTCN2019094886-appb-000007
图2分别为四组不同LED阵列编码照明下的轴向图像堆栈图。通过改变LED阵列编码使的圆形照明图案由小变大，第四组将照明图案改成圆环照明图案，然后在每种照明条件下，通过电控变焦透镜采集待测物体在不同离焦位置下的强度图像堆栈。第一行为LED阵列编码照明图案，第二行为在轴向Z1位置下采集到的图像强度图，第二行为在轴向Z2位置下采集到的图像堆栈图，以此类推，通过改变电控变焦透镜采集待测物体在轴向不同离焦位置下的强度图像堆栈。每种LED阵列编码照明图案照明图案下，分别采集分辨率400×400的100张强度图。
步骤三，对任意形状光瞳照明的显微成像系统的三维相位传递函数进行推导：由倾斜相干点光源的三维传递函数模型推广至部分相干照明和环状照明三维传递函数模型，得到在不同相干系数下的圆形和环状照明下显微系统的三维相位传递函数。三维物体的吸收率n a(r)和折射率n p(r)分别对应着复折射率n(r)的虚部和实部，将物体的复折射率n(r)与所包围的介质的折射率n 0(r)的关系可表示为三维散射势
Figure PCTCN2019094886-appb-000008
其中r为三维空间变量，k 0为真空中对应波长的波数，n m为物体所处介质的折射率。
在传统的透射明场显微成像系统中，对三维物体所测量到的强度图像I(r)可表示：
Figure PCTCN2019094886-appb-000009
其中B为所拍的到的透射光线分量，而A(r)和P(r)分别为物体三维散射势中的 虚部和实部，H A(r)和H P(r)分别为成像系统对物体吸收部分和相位部分的点扩散函数。
对上式作三维傅里叶变换可得到所拍摄强度图的三维傅里叶频谱；
Figure PCTCN2019094886-appb-000010
其中Bδ(ρ)为对应的强度图像的零频分量，
Figure PCTCN2019094886-appb-000011
和T P(ρ)分别为散射势相位部分的频谱和相位的三维传递函数，而
Figure PCTCN2019094886-appb-000012
和T A(ρ)分别为散射势吸收部分的频率成分和吸收的三维传递函数。而相位分量所对应的三维传递函数为：
Figure PCTCN2019094886-appb-000013
其中ρ＝(u,v,w)，λ为所对应的照明光源波长，
Figure PCTCN2019094886-appb-000014
为光源分布函数，
Figure PCTCN2019094886-appb-000015
和
Figure PCTCN2019094886-appb-000016
为一对由显微物镜所定义的共轭光瞳函数，其绝对值可表示为
Figure PCTCN2019094886-appb-000017
其中ρ P为显微物镜光瞳的归一化截止频率。
对于一个在光源面上的任一点的相干点光源来说，即
Figure PCTCN2019094886-appb-000018
将该光源函数代入上式中，即可得到该光源对应的三维相位传递函数为：
Figure PCTCN2019094886-appb-000019
以上三维传递函数的可以分为
Figure PCTCN2019094886-appb-000020
和
Figure PCTCN2019094886-appb-000021
即在三维空间中两个被照明光源所移动的球壳
Figure PCTCN2019094886-appb-000022
和
Figure PCTCN2019094886-appb-000023
即为埃瓦尔德球壳的定义函数。
当光源为传统的圆形图案时即：
Figure PCTCN2019094886-appb-000024
将光源的表达式S(u)代入三维相位传递函数，可得到在不同相干系数ρ S下的部分相干照明圆形光源对应的三维相位传递函数。
当光源为环状光源时可被定义为：
Figure PCTCN2019094886-appb-000025
代入三维相位传递函数得到在环状照明下的传递函数的形式。通过由倾斜相干点光源的三维传递函数模型推广至圆形部分相干照明和环状照明模型，得到在不同相干系数下的圆形和环状照明下显微系统的三维相位传递函数。
结合图3为基于不同LED阵列编码照明下的三维相位传递函数在u-w平面上的二维示意图。从左到右LED阵列编码照明条件下的圆形照明图案由小变大，最后一组为环状照明。从前三组结果图中看出，随着圆形照明条件下相干系数的增大，其三维相位传递函数中的图像高频信息得到弥补。但由于数值孔径的增大，高频信息部分得到了弥补的同时其低频信息部分得到了削弱，因此结果图(d)利用环状照明实现了高频信号弥补，低频信号加强的效果，充分说明了基于环状照明可以准确推导出三维相位传递函数，证明了这种环状照明方法具有可行性与准确性。
步骤四，三维衍射层析定量折射率反卷积重构：将所采集的四组强度图像堆栈进行三维傅里叶变换得到四种照明情况下的三维频谱。将得到的四组三维频谱进行相加再在频域中除以四个三维相位传递函数绝对值之和，得到三维散射势函数。
在相干系数分别为S1、S2和S3的圆形光源下的所拍摄到的强度堆栈I s1(r)、I s2(r)和I s3(r)进行傅里叶变换，得到其分别的强度图傅里叶频谱为
Figure PCTCN2019094886-appb-000026
Figure PCTCN2019094886-appb-000027
和
Figure PCTCN2019094886-appb-000028
再将环状光源下相干系数分别为S4拍摄的强度堆栈I s4(r)变换至其傅里叶频谱得到
Figure PCTCN2019094886-appb-000029
将所得到的四个强度堆栈傅里叶频谱相加之和除以四个三维相位传递函数T P1、T P2、T P3和T P4绝对值相加之和。四个强度堆栈傅里 叶频谱相加之和为：
Figure PCTCN2019094886-appb-000030
其中
Figure PCTCN2019094886-appb-000031
和
Figure PCTCN2019094886-appb-000032
分别为相干系数为S1、S2、S3和S4照明光源下拍摄到的强度堆栈进行傅里叶变换得到的强度图傅里叶频谱。
四个三维传递函数绝对值的相加之和为：
T P(ζ)＝|T P1(ζ)|+|T P2(ζ)|+|T P3(ζ)|+|T P4(ζ)|
其中T P1(ζ)、T P2(ζ)、T P3(ζ)和T P4(ζ)分别对应四个不同照明相干系数下的三维相位传递函数。四个强度傅里叶频谱相加之和除以所对应的四个三维相位传递函数之和，得到被测物体三维散射势函数的傅里叶频谱。
步骤五，被测物体的定量三维折射率分布。对被测物体三维散射势函数进行逆傅里叶变换，将散射势函数转换为折射率分布，即可得到被测物体的定量三维折射率分布。
Figure PCTCN2019094886-appb-000033
在利用散射势计算公式将P(r)将散射势函数转换为折射率分布，即可得到被测物体的定量三维折射率分布。
结合图4为对三维衍射层析定量折射率反卷积重构方法的框图表示。虚线框里分子表示为四组不同LED阵列编码照明下采集的图像堆栈相加之和进行傅里叶变换，分母表示为对应的三维相位传递函数绝对值相加之和，将两者相除，得到三维散射势函数的傅里叶频谱。对三维散射势函数进行三维逆傅里叶变换，可得到被测物体的定量三维折射率分布。
图5为基于LED阵列编码照明的三维衍射层析显微成像方法分别对微聚苯乙烯珠，未染色实球藻和海拉细胞三维成像结果。图(a)是直径为6μm微聚苯乙烯珠的定量三维折射率分布图，其中图(a1)和图(a2)分别是对微聚苯乙烯珠的X-Y平面上和Y-Z平面上的三维切片示意图；图(a3)是最终重构的三维傅里叶频谱示意图；图(a4)是微聚苯乙烯珠的轴向与横向三维折射率的剖面图。图(b)分别为是未染色实球藻的三维衍射层析在X-Y平面上，X-Z平面上以及Z-Y平面上 的分布示意图，实球藻是一种由8，16或32细胞组成的绿色藻类植物，内部细胞形成具有明显前后极性的椭球体，这也使得实球藻成为理想的三维衍射反卷积对象。图(c)分别是是海拉细胞的三维衍射层析在X-Y平面上，X-Z平面上以及Z-Y平面上的分布示意图，正如图5所展示，我们可以清楚的看到微聚苯乙烯珠，实球藻细胞内部各个独立的细胞是如何分布的以及细胞的各个角度形态，更进一步证实了这种基于多频率合成的三维衍射反卷积的可行性与精确性。

Claims (6)

  1. 一种基于LED阵列编码照明的三维衍射层析显微成像方法，其特征在于步骤如下：
    步骤一：采集原始强度图像，在被测厚物体为聚焦状态，且通过改变LED阵列编码使照明光源形状为相干系数S1、S2和S3的圆形的情况下，通过移动载物台或利用电控变焦透镜采集在不同离焦位置下的三组强度图像堆栈
    Figure PCTCN2019094886-appb-100001
    和
    Figure PCTCN2019094886-appb-100002
    步骤二：通过改变LED阵列编码使照明图案为相干系数S4的圆环形状，再通过移动载物台或利用电控变焦透镜采集待测物体在不同离焦位置下的强度图像堆栈
    Figure PCTCN2019094886-appb-100003
    步骤三：对任意形状照明的显微成像系统的三维相位传递函数进行推导，由倾斜相干点光源的三维传递函数模型推广至部分相干照明和环状照明三维传递函数模型，得到在不同相干系数下的圆形和环状照明下显微系统的三维相位传递函数；
    步骤四：三维衍射层析定量折射率反卷积重构，对所采集的四组强度图像堆栈进行三维傅里叶变换得到四种照明情况下的三维频谱，将得到的四组三维频谱进行相加再在频域中除以四种三维相位传递函数绝对值之和，得到三维散射势函数；
    步骤五：被测物体的定量三维折射率分布，对三维散射势函数进行逆傅里叶变换，将散射势函数转换为折射率分布，即可得到被测物体的定量三维折射率分布。
  2. 根据权利要求1所述的方法，其特征在于在步骤二中：通过LED阵列编码照明将环形照明方案引入传统的圆形明场显微中，并拍摄了在圆环形状照明图案下沿轴向的一系列光强图像堆栈
    Figure PCTCN2019094886-appb-100004
  3. 根据权利要求2所述的方法，其特征在于通过改变LED阵列编码使的圆形照明图案由小变大，第四组将照明图案改成圆环照明图案，然后在每种照明条件下，通过电控变焦透镜采集待测物体在不同离焦位置下的强度图像堆栈。第一行为LED阵列编码照明图案，第二行为在轴向Z1位置下采集到的图像强度图，第二行为在轴向Z2位置下采集到的图像堆栈图，依次类推，通过改变电控变焦透镜采集待测物体在轴向不同离焦位置下的强度图像堆栈。
  4. 根据权利要求1所述的方法，其特征在于步骤三的具体实现方式为：三维物体的吸收率n a(r)和折射率n p(r)分别对应着复折射率n(r)的虚部和实部，将物体的复折射率n(r)与所包围的介质的折射率n 0(r)的关系表示为三维散射势
    Figure PCTCN2019094886-appb-100005
    其中r为三维空间变量，k 0为真空中对应波长的波数，n m为物体所处介质的折射率，而在传统的透射明场显微成像系统中，对三维物体所测量到的强度图像I(r)可表示：
    Figure PCTCN2019094886-appb-100006
    其中B为所拍的到的透射光线分量，而A(r)和P(r)分别为物体三维散射势中的虚部和实部，H A(r)和H P(r)分别为成像系统对物体吸收部分和相位部分的点扩散函数；
    对上式作三维傅里叶变换得到所拍摄强度图的三维傅里叶频谱；
    Figure PCTCN2019094886-appb-100007
    其中Bδ(ρ)为对应的强度图像的零频分量，
    Figure PCTCN2019094886-appb-100008
    和T P(ρ)分别为散射势相位部分的频谱和相位的三维传递函数，而
    Figure PCTCN2019094886-appb-100009
    和T A(ρ)分别为散射势吸收部分的频率成分和吸收的三维传递函数，而相位分量所对应的三维传递函数为：
    Figure PCTCN2019094886-appb-100010
    其中ρ＝(u,v,w)，λ为所对应的照明光源波长，
    Figure PCTCN2019094886-appb-100011
    为光源分布函数，
    Figure PCTCN2019094886-appb-100012
    和
    Figure PCTCN2019094886-appb-100013
    为一对由显微物镜所定义的共轭光瞳函数，其绝对值可表达为
    Figure PCTCN2019094886-appb-100014
    其中ρ P为显微物镜光瞳的归一化截止频率；
    对于一个在光源面上的任一点的相干点光源来说，即
    Figure PCTCN2019094886-appb-100015
    将该光源函数代入上式中，即可得到该光源对应的三维相位传递函数为：
    Figure PCTCN2019094886-appb-100016
    以上三维传递函数分为
    Figure PCTCN2019094886-appb-100017
    和
    Figure PCTCN2019094886-appb-100018
    即在三维空间中两个被照明光源所移动球壳
    Figure PCTCN2019094886-appb-100019
    和
    Figure PCTCN2019094886-appb-100020
    即为埃瓦尔德球壳的定义函数；
    当光源为传统的圆形图案时即：
    Figure PCTCN2019094886-appb-100021
    将光源的表达式S(u)代入三维相位传递函数，得到在不同相干系数ρ S下的部分相干照明圆形光源对应的三维相位传递函数；
    当光源为环状光源时被定义为：
    Figure PCTCN2019094886-appb-100022
    代入三维相位传递函数得到在环状照明下的传递函数的形式，通过由倾斜相干点光源的三维传递函数模型推广至圆形部分相干照明和环状照明模型，得到在不同相干系数下的圆形和环状照明下显微系统的三维相位传递函数。
  5. 根据权利要求1所述的方法，其特征在于步骤四实现方式为：在相干系数S1、S2和S3的圆形光源下的所拍摄到的强度堆栈I s1(r)、I s2(r)和I s3(r)进行傅里叶变换，得到其分别对应的强度图傅里叶频谱
    Figure PCTCN2019094886-appb-100023
    和
    Figure PCTCN2019094886-appb-100024
    再将环状光源下拍摄的强度堆栈I s4(r)变换至其傅里叶频谱得到
    Figure PCTCN2019094886-appb-100025
    将所得到的四个强度堆栈傅里叶频谱相加之和除以所对应的四个三维相位传递函数T P1、T P2、T P3和T P4绝对值相加之和，四个强度堆栈傅里叶频谱相加之和为：
    Figure PCTCN2019094886-appb-100026
    其中
    Figure PCTCN2019094886-appb-100027
    和
    Figure PCTCN2019094886-appb-100028
    分别为相干系数为S1、S2、S3和S4照明光源下拍摄到的强度堆栈进行傅里叶变换得到的强度图傅里叶频谱；
    四个三维传递函数绝对值的相加之和为：
    T P(ζ)＝|T P1(ζ)|+|T P2(ζ)|+|T P3(ζ)|+|T P4(ζ)|
    其中T P1(ζ)、T P2(ζ)、T P3(ζ)和T P4(ζ)分别对应四个不同照明相干系数下的三维相位传递函数，四个强度堆栈傅里叶频谱相加之和除以所对应的四个三维相位传递函数T P1、T P2、T P3和T P4绝对值相加之和，得到三维散射势函数的傅里叶频谱。
  6. 根据权利要求1所述的方法，其特征在于步骤五实现的方式为：对三维散射势函数进行三维逆傅里叶变换：
    Figure PCTCN2019094886-appb-100029
    在利用散射势计算公式将P(r)将散射势函数转换为折射率分布，即可得到被测物体的定量三维折射率分布。
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