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CN109186452B - A high-precision positioning method for the axial position of non-spherical particles - Google Patents

A high-precision positioning method for the axial position of non-spherical particles Download PDF

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CN109186452B
CN109186452B CN201811017262.3A CN201811017262A CN109186452B CN 109186452 B CN109186452 B CN 109186452B CN 201811017262 A CN201811017262 A CN 201811017262A CN 109186452 B CN109186452 B CN 109186452B
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CN109186452A (en
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龚湘君
黄桂
张广照
田文章
戚萌
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South China University of Technology SCUT
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Abstract

The invention discloses a high-precision positioning method for the axial position of non-spherical particles, which comprises the following steps: recording a real-time hologram by using a coaxial digital holographic microscope, reconstructing a scattered light field of non-spherical particles by numerical values, pre-positioning an axial position by using local maximum light intensity, and fitting the axial light intensity distribution by using Gaussian distribution to obtain an accurate axial position of each particle; the invention can axially track a plurality of non-spherical particles such as bacteria, cells, viruses and the like in real time, has positioning accuracy superior to 100nm, and is suitable for monitoring the dynamic behaviors of a plurality of particles simultaneously.

Description

High-precision positioning method for axial position of non-spherical particles
Technical Field
The invention relates to the research field of particle axial position measurement, in particular to a high-precision positioning method for the axial position of non-spherical particles.
Background
The measurement of the real-time three-dimensional position, especially the axial position, of the microparticles is a prerequisite for observing and studying the dynamic behavior of the microparticles, and can be used for studying, for example, the interaction of nanoparticles, the adhesion process of microorganisms, various responses of cells and viruses to the surrounding environment, and the like.
The digital holographic microscope records an interference pattern-hologram formed by the coherence of object light and reference light, and then reconstructs the light field information of a measured object in the hologram through numerical value, thereby acquiring the real-time three-dimensional coordinates of the object. It does not need fluorescent mark, and is a nondestructive imaging method. The spatial variation range of the particle motion is generally tens to hundreds of microns, and the imaging depth of the digital holographic microscope can reach tens to hundreds of microns, so that the digital holographic microscope is very suitable for dynamically tracking the particle motion. However, the size of individual particles is on the order of microns, and to accurately record their real-time three-dimensional position, the positioning accuracy needs to reach sub-micron or even higher levels. The positioning accuracy, in particular the axial positioning accuracy, of digital holographic microscopes depends on the positioning method used, more precisely on the accuracy with which the algorithm finds the focal plane. Generally speaking, the axial positioning accuracy of digital holographic microscopes is far less than the lateral positioning accuracy, limited by the imaging principles and instrument hardware. At present, the positioning method of the digital holographic microscope at the axial position mainly comprises a cross-correlation method, a Mie scattering matching method, a Rayleigh-Sommerfeld algorithm and the like. The cross-correlation method comprises the steps of firstly establishing a database of holograms at different positions of a sample to be detected, then carrying out cross-correlation function calculation on the hologram recorded in an experiment and a picture in the database, and selecting an image with the maximum correlation coefficient to determine the real-time position of the sample. The axial positioning accuracy of the cross-correlation method depends on the spatial resolution of the images in the database, is time-consuming and is not suitable for positioning multiple particles simultaneously. The axial positioning accuracy of the mie scatterometry method can be below 10nm, but it can only be used to measure regularly shaped particles and is equally unsuitable for tracking multiple particles simultaneously. The Rayleigh-Sommerfeld algorithm is suitable for simultaneously measuring a plurality of particles with any shapes, but the axial positioning precision can only reach a submicron level, and the precision is not as high as that of the former two methods. The reported method for improving the axial positioning accuracy of the Rayleigh-Sommerfeld algorithm is to first obtain the light intensity distribution near the calculated axial position and then fit the light intensity distribution by polynomial distribution to obtain the optimized position. The method is already used for improving the axial positioning precision of the spherical colloidal particles, but the axial positioning precision of the non-spherical particles cannot be optimized. Non-spherical particles such as microorganisms, cells, etc. will take on different orientations and configurations in the medium, requiring extremely high demands on the axial positioning algorithm compared to spherical particles.
Disclosure of Invention
The invention mainly aims to overcome the defects of the prior art and provide a high-precision positioning method for the axial position of non-spherical particles, which comprises the steps of recording a real-time hologram by using a coaxial digital holographic microscope, numerically reconstructing a scattered light field of the non-spherical particles by using a Rayleigh-Sommerfeld algorithm, pre-positioning the axial position by using local maximum light intensity, fitting the axial light intensity distribution by using Gaussian distribution to obtain the accurate axial position of each particle, wherein the positioning precision can be better than 100 nm.
The purpose of the invention is realized by the following technical scheme:
a high-precision positioning method for the axial position of non-spherical particles comprises the following steps:
s1, recording a holographic image sequence on the sample to obtain an original holographic image, and recording a background image in a blank area of the sample, or carrying out light intensity averaging on the original holographic image to obtain a background image, wherein the sample is a particle;
s2, carrying out background subtraction on the original holographic image through the background image, and eliminating background noise to obtain a background-subtracted holographic image;
s3, carrying out numerical reconstruction on the background-subtracted holographic image to obtain information of three-dimensional reconstruction intensity distribution of the particles;
s4, obtaining initial three-dimensional positions of a plurality of particles by filtering the three-dimensional reconstruction intensity distribution information of the particles through a threshold value and searching a local maximum value of light intensity;
s5, selecting specific rectangular areas on the corresponding sections with different heights by taking the coordinate as the center according to the initial transverse coordinate of the particles, overlapping the light intensity of all pixel points in the rectangular areas to obtain the total light intensity of the particles with different heights, and further obtaining the distribution curve of the total light intensity in the axial direction;
and S6, fitting a distribution curve of the total intensity of the light intensity in the axial direction by adopting Gaussian distribution to obtain a central peak coordinate, namely the axial coordinate of the particle.
Further, the microparticles are non-spherical microparticles;
further, in step S1, the average light intensity specifically includes: and averaging the light intensity of the holographic image sequence to obtain a background image, wherein the calculation is as follows:
Figure GDA0002369296530000021
in the formula Ib(x, y) is the gray scale value of the pixel at the (x, y) position in the background image, N is the total frame number of the holographic image, t is the time, It(x, y) is the gray value of the pixel at the (x, y) position in the original holographic image at the time t;
further, after the background is deducted, the light intensity value of each pixel point in the holographic image is as follows:
Is(x,y)＝It(x,y)-Ib(x,y)。
further, in step S3, the specific process is as follows: carrying out numerical reconstruction on the background-subtracted holographic image to obtain the information of the three-dimensional reconstruction intensity distribution of the particles, and calculating as follows:
Figure GDA0002369296530000031
U(r,z)＝FT-1(FT(Is(r,0)·H(q,-z)))，
wherein h (r, -z) is a propagation operator, r is an initial transverse coordinate of the particle, and z is an initial axial coordinate of the particle; i is an imaginary unit; k is the wave number; r is the light propagation distance; i issIs the light intensity of the sample; FT-1Is inverse Fourier transform; FT is Fourier transform; h (q, -z) is the Fourier transform of H (r, -z);
the value of the reconstruction axial interval is larger than the axial imaging range of the instrument, and the stepping is that the size of the pixel is divided by the magnification of the objective lens. (ii) a
Further, in step S4, the specific process is as follows: setting a light intensity threshold, filtering noise in a reconstructed light field, and then searching a local light intensity maximum point by point in a cube with side length close to an integral value of the particle size;
further, the light intensity threshold is less than 10%;
further, in step S5, the rectangular area is: taking the transverse coordinate of the particle as a center, and taking an integral value of the pixel size by the side length;
further, in the step S6, the fitting specifically includes performing, by using a fitting formula:
Iint＝aexp(-(z-zc)2/b)，
wherein, IintIs the sum of the light intensity in the rectangular area; a is peak height, b is peak width, zcAs the central peak coordinates.
Compared with the prior art, the invention has the following advantages and beneficial effects:
the invention adopts a coaxial digital holographic microscope to record a real-time hologram, reconstructs a scattered light field of non-spherical particles through Rayleigh-Sommerfeld algorithm numerical value, positions the axial position in advance by utilizing the maximum local light intensity, and fits the axial light intensity distribution by utilizing Gaussian distribution to obtain the accurate axial position of each particle, can track a plurality of non-spherical particles in real time in the axial direction, has positioning precision superior to 100nm, and is suitable for monitoring the dynamic behavior of a plurality of particles simultaneously.
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FIG. 1 is a flow chart of a method for high-precision positioning of the axial position of non-spherical particles according to the present invention;
FIG. 2 is a diagram illustrating the axial light intensity distribution of the scattered light field of the particle and the result of Gaussian fitting according to an embodiment of the present invention;
FIG. 3 is a graph showing the measurement results of the positioning accuracy of the axial position of the fine particles in the embodiment of the present invention;
FIG. 4 is a graph showing the distribution of the intensity of light in the direction perpendicular to the bottom surface of the particles and the corresponding Gaussian fit results in an embodiment of the present invention;
FIG. 5 is a graph showing the distribution of the axial light intensity parallel to the bottom surface particles and the corresponding Gaussian fitting results in an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited thereto.
Examples
A high-precision positioning method for the axial position of non-spherical particles is disclosed, as shown in figure 1, and comprises the following steps:
the first step is as follows: recording a holographic image sequence on a sample to obtain an original holographic image, wherein the sample is a particle; recording a background image in a blank area of a sample, or carrying out light intensity averaging on an original holographic image to obtain the background image, wherein the specific process comprises the following steps: and averaging the light intensity of the holographic image sequence to obtain a background image, wherein the calculation is as follows:
Figure GDA0002369296530000041
in the formula Ib(x, y) is the gray scale value of the pixel at the (x, y) position in the background image, N is the total frame number of the holographic image, t is the time, It(x, y) is the gray value of the pixel at the (x, y) position in the original holographic image at the time t;
recording a holographic image, specifically: dispersing non-spherical particles in a sample cell, and recording a holographic image sequence by using a coaxial digital holographic microscopic imaging system; the coaxial digital holographic microscopic imaging system comprises an LED light source, a high-power microscope objective and an sCMOS camera; the sample cell comprises a cover glass and a polydimethylsiloxane gasket; the non-spherical particles used in this example were E.coli; in order to realize the control and measurement of the movement of the escherichia coli, the escherichia coli is fixed on a cover glass through electrostatic force, and a sample cell is fixed on an electric displacement table; recording and storing a hologram and a background image of escherichia coli at an off-focus distance (d) of 10-40 μm by controlling an electric displacement table, wherein the background image is obtained at a sample blank consistent with the off-focus distance of the hologram, the step of the displacement table is 1 μm, and 100 frames of holograms are recorded at each height; to eliminate the influence of twinning phases, the holograms collected in the experiment were all below 10 μm in the focal plane, i.e. d0＝10μm，0≤d-d0≤30μm；
The second step is that: background subtraction is carried out on the original holographic images at different positions through the background image, background noise is eliminated, and the light intensity value I of each pixel point in the hologram after the background subtraction is carried outs(x,y)：
Is(x,y)＝It(x,y)-Ib(x,y)；
The third step: carrying out numerical reconstruction on the background-subtracted holographic image by using a Rayleigh-Sommerfeld algorithm to obtain the intensity distribution of the escherichia coli in a three-dimensional space, namely obtaining the information of the three-dimensional reconstruction intensity distribution of the escherichia coli, wherein the calculation formula is as follows:
Figure GDA0002369296530000051
U(r,z)＝FT-1(FT(Is(r,0)·H(q,-z)))，
wherein h (r, -z) is a propagation operator, r is an initial transverse coordinate of the particle, and z is an initial axial coordinate of the particle; i is an imaginary unit; k is the wave number; r is the light propagation distance; i issIs the light intensity of the sample; FT-1Is inverse Fourier transform; FT is Fourier transform; h (q, -z) is the Fourier transform of H (r, -z);
the reconstruction axial interval is (-60-0 μm), is larger than the maximum defocusing distance (40 μm below the focal plane) of the holographic image in the experiment, and is stepped to the pixel size of 0.1625 μm.
The fourth step: filtering the information of the three-dimensional reconstruction intensity distribution of the escherichia coli obtained by reconstructing the light field through a threshold value and searching a local maximum value of light intensity to obtain an initial three-dimensional position of the escherichia coli; firstly setting a light intensity threshold value which is 7 percent, filtering noise in a reconstructed light field, and then searching and recording the three-dimensional position of the local light intensity maximum value point by point in a cube with the side length close to the integral value of the particle size, namely the cube with the side length of 13 mu m;
the fifth step: according to the information of the three-dimensional reconstructed intensity distribution of the escherichia coli and the initial three-dimensional position of the escherichia coli, selecting rectangular areas with the side length of 1.625 mu m on the sections corresponding to different heights by taking the position as the center, and superposing the light intensities of all pixel points in the rectangular areas to obtain the total light intensity I of the particles at different heightsintTo obtain the total intensity of light intensity IintA profile in the axial direction, as shown in fig. 2;
and a sixth step: using Gaussian distribution to total intensity of light IintFitting the distribution curve in the axial direction to obtain a central peak position, namely the axial position of the escherichia coli;
the fitting process is carried out by a fitting formula:
Iint＝aexp(-(z-zc)2/b)，
wherein, IintIs the sum of the light intensity in the rectangular area; a is peak height, b is peak width, zcAs the coordinates of the central peak;
the axial positioning accuracy at each height is equal to the root-mean-square value of the error between the measured value (z) and the theoretical value (d), as shown in fig. 3, the weighted average (98nm) of the axial positioning accuracy at each height is the axial positioning accuracy of the algorithm to escherichia coli.
To further test the practicability of the algorithm, the algorithm was applied to the positioning of the axial positions of escherichia coli in different orientations in the solution, and fig. 4 and 5 are schematic diagrams of the axial light intensity distribution of escherichia coli perpendicular and parallel to the bottom surface and the corresponding gaussian fitting results, respectively.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.

Claims (9)

1.一种非球形微粒轴向位置的高精度定位方法，其特征在于，包括以下步骤：1. a kind of high-precision positioning method of non-spherical particle axial position, is characterized in that, comprises the following steps: S1、对样品记录全息图像序列，得到原始全息图像，在样品空白区记录背景图，或对原始全息图像进行光强平均，得到背景图，所述样品为微粒；S1. Record a holographic image sequence on the sample to obtain an original holographic image, record a background image in the blank area of the sample, or perform light intensity averaging on the original holographic image to obtain a background image, and the sample is a particle; S2、通过背景图，对原始全息图像进行背景扣除，消除背景噪声，得到扣除背景的全息图像；S2, performing background subtraction on the original holographic image through the background image, eliminating background noise, and obtaining a background-deducting holographic image; S3、对扣除背景的全息图像进行数值重建，得到微粒三维重构强度分布的信息；S3, performing numerical reconstruction on the background-deducted holographic image to obtain information on the three-dimensional reconstructed intensity distribution of the particles; S4、对微粒三维重构强度分布的信息，通过阈值过滤和寻找光强局部最大值，获取多个微粒初始的三维位置；S4. For the information of the three-dimensional reconstructed intensity distribution of the particles, the initial three-dimensional positions of the multiple particles are obtained by threshold filtering and searching for the local maximum value of the light intensity; S5、根据微粒的初始横向坐标，选取以该坐标为中心在不同高度对应剖面上特定的矩形区域，叠加矩形区域内所有像素点的光强，得到不同高度上微粒的光强总强度，进而获得光强总强度在轴向上的分布曲线；S5. According to the initial lateral coordinate of the particle, select a specific rectangular area on the corresponding section at different heights with the coordinate as the center, and superimpose the light intensities of all pixels in the rectangular area to obtain the total light intensity of the particles at different heights, and then obtain The distribution curve of the total intensity of light intensity in the axial direction; S6、采用高斯分布对光强总强度在轴向上的分布曲线进行拟合，得到中心峰坐标，即为微粒轴向坐标。S6, using Gaussian distribution to fit the distribution curve of the total light intensity in the axial direction, and obtain the center peak coordinate, which is the particle axial coordinate. 2.根据权利要求1所述的一种非球形微粒轴向位置的高精度定位方法，其特征在于，所述微粒为非球形微粒。2 . The high-precision positioning method for the axial position of non-spherical particles according to claim 1 , wherein the particles are non-spherical particles. 3 . 3.根据权利要求1所述的一种非球形微粒轴向位置的高精度定位方法，其特征在于，步骤S1中，所述平均光强，具体过程为：对全息图像序列进行光强平均，得到背景图，计算如下：3. The high-precision positioning method for the axial position of non-spherical particles according to claim 1, characterized in that, in step S1, the average light intensity, the specific process is: performing light intensity averaging on the holographic image sequence, To get the background image, the calculation is as follows:
Figure FDA0002369296520000011
Figure FDA0002369296520000011
 式中，Ib(x,y)为背景图中(x,y)位置处像素的灰度值，N为全息图像的总帧数，t为时间，It(x,y)为t时刻原始全息图像中(x,y)位置处像素的灰度值。In the formula, I b (x, y) is the gray value of the pixel at the position (x, y) in the background image, N is the total number of frames of the holographic image, t is the time, and I t (x, y) is the time t. The gray value of the pixel at the (x,y) position in the original holographic image. 4.根据权利要求1所述的一种非球形微粒轴向位置的高精度定位方法，其特征在于，所述步骤S2，具体过程为：扣除背景后的全息图像中各像素点的光强值：4. the high-precision positioning method of a kind of non-spherical particle axial position according to claim 1, is characterized in that, described step S2, the concrete process is: the light intensity value of each pixel in the holographic image after deducting the background : Is(x,y)＝It(x,y)-Ib(x,y)。Is (x, y)=I t ( x , y)-I b (x, y). 5.根据权利要求1所述的一种非球形微粒轴向位置的高精度定位方法，其特征在于，所述步骤S3，具体过程为：对扣除背景的全息图像进行数值重建，得到微粒三维重构强度分布的信息，计算如下：5. a kind of high-precision positioning method of the axial position of non-spherical particles according to claim 1, is characterized in that, described step S3, the concrete process is: carry out numerical reconstruction to the holographic image of deducted background, obtain the three-dimensional weight of particle. The information on the distribution of structural strength is calculated as follows:
Figure FDA0002369296520000021
Figure FDA0002369296520000021
 U(r,z)＝FT-1(FT(Is(r,0)·H(q,-z)))，U(r,z)=FT -1 ( FT (Is(r,0)·H(q,-z))), 其中，h(r,-z)为传播算子，r为微粒的初始横向坐标，z为微粒的初始轴向坐标；i为虚数单位；k为波数；R为光传播距离；Is为样品的光强；FT-1为傅里叶逆变换；FT为傅里叶变换；H(q,-z)为h(r,-z)的傅里叶变换；Among them, h(r,-z) is the propagation operator, r is the initial lateral coordinate of the particle, z is the initial axial coordinate of the particle; i is the imaginary unit; k is the wave number; R is the light propagation distance; Is is the sample The light intensity of ; FT -1 is the inverse Fourier transform; FT is the Fourier transform; H(q,-z) is the Fourier transform of h(r,-z); 重建轴向区间的取值大于仪器在轴向的成像范围，步进为像素的大小除以物镜放大倍数。The value of the reconstructed axial interval is greater than the imaging range of the instrument in the axial direction, and the step is the size of the pixel divided by the magnification of the objective lens. 6.根据权利要求1所述的一种非球形微粒轴向位置的高精度定位方法，其特征在于，所述步骤S4，具体过程为：设置一个光强阈值，过滤冲重构光场内的噪声，然后在边长接近微粒尺寸的整数值的立方体内逐点寻找局部光强最大值。6. The high-precision positioning method for the axial position of non-spherical particles according to claim 1, characterized in that, in the step S4, the specific process is: setting a light intensity threshold, filtering the light in the reconstructed light field. noise, and then search for local light intensity maxima point by point within a cube with side lengths approaching integer values of particle size. 7.根据权利要求6所述的一种非球形微粒轴向位置的高精度定位方法，其特征在于，所述光强阈值小于10％。7 . The high-precision positioning method for the axial position of non-spherical particles according to claim 6 , wherein the light intensity threshold is less than 10%. 8 . 8.根据权利要求1所述的一种非球形微粒轴向位置的高精度定位方法，其特征在于，步骤S5中，所述矩形区域为：以微粒的横向坐标为中心，边长取像素尺寸的整数值。8. The high-precision positioning method for the axial position of non-spherical particles according to claim 1, wherein, in step S5, the rectangular area is: taking the lateral coordinate of the particle as the center, and the side length is the pixel size the integer value of . 9.根据权利要求1所述的一种非球形微粒轴向位置的高精度定位方法，其特征在于，所述步骤S6，拟合具体过程为，通过拟合公式进行：9. The high-precision positioning method for the axial position of non-spherical particles according to claim 1, characterized in that, in step S6, the fitting process is as follows: Iint＝aexp(-(z-zc)2/b)，I int = aexp(-(zz c ) 2 /b), 其中，Iint为矩形区域内光强总和；a为峰高，b为峰宽，zc为中心峰坐标。Among them, I int is the sum of the light intensity in the rectangular area; a is the peak height, b is the peak width, and z c is the center peak coordinate.
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