CN112666061A - Quasi-spherical cell measuring method based on light intensity model of lens-free imaging system - Google Patents
Quasi-spherical cell measuring method based on light intensity model of lens-free imaging system Download PDFInfo
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Abstract
The invention discloses a quasi-spherical cell measuring method based on a light intensity model of a lens-free imaging system, which is characterized in that a straight-edge Fresnel diffraction model is simplified according to the characteristics of the lens-free imaging system; based on the straight-side Fresnel diffraction model, an arc-side diffraction model is established; on the basis, diffraction superposition is considered to obtain a lens-free imaging light intensity model, and further the relation between the light intensity and the radius of the quasi-spherical cell is obtained; and finally, measuring the size of the aligned spherical cells by using a quasi-spherical cell diffraction pattern light intensity model. The method is simple to operate, is very suitable for POTC, is accurate in measurement of the characteristic dimension of the torispherical cells, is high in real-time performance, and has very important significance in detecting the characteristic information of the cells by utilizing diffraction images.
Description
Technical Field
The invention belongs to the technical field of medical image analysis, and relates to a quasi-spherical cell measuring method based on a lens-free imaging system light intensity model.
Background
Quasi-spherical cell size measurement plays an important role in medical testing. Many biological cells have a spherical or quasi-spherical shape, such as Red Blood Cells (RBCs), White Blood Cells (WBCs), egg cells, cancer cells, and the like. Different biological cell types have characteristic dimensions, and thus cell size can be used to identify a biological cell type.
In recent years, due to the development Of high and new technologies, the progress Of medical science, and the efficient and fast-paced working method, Point-Of-Care Testing (POCT) with the advantages Of miniaturization Of experimental instruments, simplification Of operation, and instantaneity Of report results is becoming more popular. The traditional biological cell size measurement methods, such as microscopes and flow cytometers, are bulky and expensive, depend on professional operation, and cannot be well applied to POCT. The Lab-On-a-Chip (LOC) technology using a lensless imaging system provides a good solution for obtaining the quasi-spherical cell size.
However, the cellular image collected by the lens-free imaging system has the problems of diffraction effect and low resolution. A typical lensless imaging system consists of a light source and a CMOS image sensor. The biological cells are placed directly on the CMOS image sensor and form shadows on the CMOS image sensor. Since there is no lens between the cells and the CMOS image sensor, the images of the cells cannot be actually formed on the CMOS image sensor, and only diffraction fringes of the cells can be formed. Therefore, how to detect the characteristic information of the cells by using the diffraction image has important significance in the lens-free imaging system.
Disclosure of Invention
The invention aims to provide a quasi-spherical cell measuring method based on a lens-free imaging system light intensity model, which realizes the accurate measurement of the characteristic dimension of a quasi-spherical cell by utilizing a quasi-spherical cell diffraction pattern light intensity model.
The technical scheme adopted by the invention is that the quasi-spherical cell measuring method based on the light intensity model of the lens-free imaging system is implemented according to the following steps:
step 1, preparing a biological cell sample containing a quasi-sphere cell to be detected;
step 2, opening a monochromatic point light source of the lens-free imaging system, wherein the monochromatic point light source passes through a micropore arranged on the focal length of a convex lens and is refracted into a uniform parallel light source through the lens to irradiate on a biological cell sample;
step 3, placing the biological cell sample on a CMOS image sensor, forming a diffraction image of the biological cell on the CMOS image sensor, and uploading the diffraction image to a data processing device;
step 4, based on the imaging diffraction principle of the lens-free imaging system, the Fresnel diffraction is conformed, and a straight-edge Fresnel diffraction model of the lens-free imaging system is simplified;
step 5, calculating diffraction light intensity amplitude and diffraction period sequence of Fresnel diffraction;
step 6, establishing an arc edge diffraction model;
step 7, taking the superposition of diffraction into consideration to obtain a lens-free imaging light intensity model, and further obtaining the relation between the superposition light intensity distribution of the diffraction pattern of the quasi-spherical cells and the radius of the quasi-spherical cells;
and 8, processing the diffraction image of the biological cell by a lens-free imaging light intensity model at the data processing device end to obtain the characteristic dimension of the biological cell and finish the quasi-spherical cell measurement.
The present invention is also characterized in that,
the step 4 specifically comprises the following steps:
since the relationship between the diffraction edge position and the diffraction fringe intensity can be well described by the straight-edge fresnel diffraction, when the diffraction occurs on a semi-infinite plane bounded by a sharp straight edge, the light intensity I on the imaging plane, i.e. the straight-edge fresnel diffraction model, is expressed as:
in the formula (1), I0Is the average light intensity, C (w), S (w) are Fresnel integrals;
c (w), S (w) are represented by:
in the formula (3), r 'is the distance from the light source to the biological cell sample, s' is the distance from the biological cell sample to the CMOS image sensor, x is the distance from the diffraction ring to the real cell boundary in the diffraction image of the biological cell sample, and λ is the optical wavelength;
since the distance from the light source to the biological cell sample in a lens-less imaging system tends to be infinite, w is reduced to
And (3) substituting the simplified w into the formula (1) to obtain the simplified straight-edge Fresnel diffraction model.
Step 5 is specifically implemented according to the following steps:
step 5.1, obtaining the compound by the formula (1),
specific expressions of C '(w) and S' (w) are given by equations (2), (3):
the formula (4) and (5) are solved:
fresnel integrated cousinew upper k2，k4，...，k2nThe positions of the points (a) and (b) represent the positions of the fresnel diffraction bright and dark stripes, which alternate in sequence, and n is 1,2,3.
Step 5.2, obtaining the cosine function from the formula (1)
Obtaining the wave crest and the wave trough of the cosine function, wherein the position values of the wave crest and the wave trough are sequentially alternated to be k2，k4，...，k2nA position value of (a); by I/I01, obtain cosine function and straight line I/I0Intersection k of 11、k3、...、k2n-1A position value of (a); when the distance x from the diffraction ring to the real cell boundary in the diffraction image of the biological cell sample is a negative value, I/I0Monotonically decreasing toward zero;
since the collimated light source in the lens-less imaging system is illuminated on the biological cell sample, k is2，k4，...，k2nPosition value x (k) of2n) Expressed as:
in the formula (8), m2nIs k2nThe fresnel diffraction period sequence of (a);
k1，k3，...，k2n-1the position value of (d) is expressed as:
in the formula (9), m2n-1Is k2n-1The fresnel diffraction period sequence of (a);
k0the position value of (d) is expressed as:
in the formula (10), m0Is k0The sequence of fresnel diffraction periods of (a),
in summary,expressing the Fresnel diffraction period sequence as mi，i＝1,2,3......。
Step 6 is implemented according to the following steps:
step 6.1, the actual light intensity I is obtained by converting the formula (1) in consideration of the intensity distribution of amplitude attenuationarcComprises the following steps:
in formula (11), α is an attenuation coefficient;
the attenuation coefficient alpha not only changes the amplitude of the diffraction light intensity, but also changes the distribution curve of the diffraction light intensity. Thus at k2，k4，...，k2nThe intensity of light at can be expressed as
In formula (12), h is 2,4,6arcIs the radius of the arc edge of the diffraction ring,
k0the light intensity is expressed as
Step 6.2, according to the diffraction light intensity amplitude and the diffraction period sequence, expressing an arc edge diffraction model as,
in formula (13), r is 0,1,2,3r),x(kr+1)]。
The step 7 specifically comprises the following steps:
according to the fresnel diffraction theory, the line width of the cell diffraction pattern is larger than the cell diameter, therefore, the diffraction pattern is the result of multi-position diffraction superposition, the diffraction superposition can seriously affect the light intensity distribution of the diffraction pattern, and with the center of the quasi-spherical cell as the origin of coordinates, the superposed light intensity distribution of the diffraction pattern of the quasi-spherical cell, namely the lens-free imaging light intensity model, is expressed as:
in the formula (14), IcellIs the absolute light intensity distribution of the diffractogram of the quasi-spherical cell;
the relationship between the intensity distribution and the radius of the quasi-spherical cell can be obtained by the formula (14) by superimposing the diffraction pattern of the quasi-spherical cell.
The step 8 specifically comprises the following steps:
and acquiring the superposed light intensity distribution of the diffraction patterns of the quasi-spherical cells in the diffraction images of the biological cells at the data processing device end, and processing the superposed light intensity distribution by a lens-free imaging light intensity model to obtain the characteristic dimension of the biological cells in the biological cell sample so as to finish the measurement of the quasi-spherical cells.
The invention has the beneficial effects that:
the quasi-spherical cell measuring method based on the lens-free imaging system light intensity model uploads the diffraction image of the biological cell sample to the data processing device, and the straight-side Fresnel diffraction model is simplified on the data processing device according to the characteristics of the lens-free imaging system. Based on a straight-edge Fresnel diffraction model, an arc-edge diffraction model is established, on the basis, superposition of diffraction is considered, a lens-free imaging light intensity model is obtained, the relation between the light intensity and the radius of the quasi-spherical cell is obtained, and finally the characteristic dimension of the quasi-spherical cell is obtained through the lens-free imaging light intensity model; the method is simple to operate, is very suitable for POTC, is accurate in measurement of the characteristic dimension of the torispherical cells, is high in real-time performance, and has very important significance in detecting the characteristic information of the cells by utilizing diffraction images.
Drawings
FIG. 1 is a schematic structural diagram of a lensless imaging system in which the present invention is implemented;
FIG. 2 is a canonian plot of Fresnel integration in step 5 of the present invention.
In the figure, 15 is a monochromatic point light source, 16 is a convex lens, 17 is a CMOS image sensor, 18 is a micropore, 19 is a parallel light source, 20 is a biological cell sample, 21 is a data processing device.
Detailed Description
The present invention will be described in detail with reference to the following embodiments.
The invention discloses a quasi-spherical cell measuring method based on a light intensity model of a lens-free imaging system, which implements measurement through the lens-free imaging system, the lens-free imaging system is shown in figure 1 and comprises a monochromatic point light source 15, a convex lens 16 and a CMOS image sensor 17, light of the monochromatic point light source 15 penetrates through a micropore 18 and is refracted through the convex lens 16 to form a parallel light source 19, a biological cell sample 20 is placed on the CMOS image sensor 17, the CMOS image sensor 17 can collect biological cell diffraction images of the biological cell sample 20, and the CMOS image sensor 17 is connected with a data processing device 21.
The invention relates to a quasi-spherical cell measuring method based on a light intensity model of a lens-free imaging system, which is implemented according to the following steps:
step 1, a biological cell sample 20 containing the quasi-spherical cells to be detected is prepared.
And 2, opening a monochromatic point light source 15 of the lens-free imaging system, wherein the monochromatic point light source 15 passes through a micropore 18 arranged on the focal length of a convex lens 16, is refracted into a uniform parallel light source 19 through the lens, and irradiates on a biological cell sample 20.
And 3, placing the biological cell sample 20 on the CMOS image sensor 17, forming a diffraction image of the biological cell on the CMOS image sensor 17, and uploading the diffraction image to the data processing device 21.
Step 4, based on the imaging diffraction principle of the lens-free imaging system, the Fresnel diffraction is conformed, and a straight-edge Fresnel diffraction model of the lens-free imaging system is simplified;
the step 4 specifically comprises the following steps:
since the relationship between the diffraction edge position and the diffraction fringe intensity can be well described by the straight-edge fresnel diffraction, when the diffraction occurs on a semi-infinite plane bounded by a sharp straight edge, the light intensity I on the imaging plane, i.e. the straight-edge fresnel diffraction model, is expressed as:
in the formula (1), I0Is the average light intensity, C (w), S (w) are Fresnel integrals;
c (w), S (w) are represented by:
in the formula (3), r 'is the distance from the light source to the biological cell sample 20, s' is the distance from the biological cell sample 20 to the CMOS image sensor 17, x is the distance from the diffraction ring to the real cell boundary in the diffraction image of the biological cell sample 20, and λ is the optical wavelength;
since the distance from the light source to the biological cell sample 20 in the lens-less imaging system tends to be infinite, w is simplified to be infinite
And (3) substituting the simplified w into the formula (1) to obtain the simplified straight-edge Fresnel diffraction model.
Step 5, calculating diffraction light intensity amplitude and diffraction period sequence of Fresnel diffraction;
step 5 is specifically implemented according to the following steps:
step 5.1, obtaining the compound by the formula (1),
specific expressions of C '(w) and S' (w) are given by equations (2), (3):
the formula (4) and (5) are solved:
as shown in fig. 2, k on the conus spiral of fresnel integration2，k4，...，k2nThe positions of the points (a) and (b) represent the positions of the fresnel diffraction bright and dark stripes, which alternate in sequence, and n is 1,2,3.
Step 5.2, obtaining the cosine function from the formula (1)
Obtaining the wave crest and the wave trough of the cosine function, wherein the position values of the wave crest and the wave trough are sequentially alternated to be k2，k4，...，k2nA position value of (a); by I/I01, obtain cosine function and straight line I/I0Intersection k of 11、k3、...、k2n-1A position value of (a); when the distance x from the diffraction ring to the real cell boundary in the diffraction image of the biological cell sample 20 is negative, I/I0Monotonically decreasing toward zero;
since the collimated light source 19 in the lensless imaging system is illuminated on the biological cell sample 20, k is therefore2，k4，...，k2nPosition value x (k) of2n) Expressed as:
in the formula (8), m2nIs k2nThe fresnel diffraction period sequence of (a);
k1，k3，...，k2n-1the position value of (d) is expressed as:
in the formula (9), m2n-1Is k2n-1The fresnel diffraction period sequence of (a);
k0the position value of (d) is expressed as:
in the formula (10), m0Is k0The sequence of fresnel diffraction periods of (a),
in summary, the Fresnel diffraction period sequence is represented as mi，i＝1,2,3......。
Step 6, establishing an arc edge diffraction model;
step 6 is implemented according to the following steps:
step 6.1, the actual light intensity I is obtained by converting the formula (1) in consideration of the intensity distribution of amplitude attenuationarcComprises the following steps:
in formula (11), α is an attenuation coefficient;
the attenuation coefficient alpha not only changes the amplitude of the diffraction light intensity, but also changes the distribution curve of the diffraction light intensity. Thus at k2，k4，...，k2nThe intensity of light at can be expressed as
In formula (12), h is 2,4,6arcIs the radius of the arc edge of the diffraction ring,
k0the light intensity is expressed as
Step 6.2, according to the diffraction light intensity amplitude and the diffraction period sequence, expressing an arc edge diffraction model as,
in formula (13), r is 0,1,2,3r),x(kr+1)]。
And 7, taking the superposition of diffraction into consideration to obtain a lens-free imaging light intensity model, and further obtaining the relation between the superposition light intensity distribution of the diffraction pattern of the quasi-spherical cells and the radius of the quasi-spherical cells.
The step 7 specifically comprises the following steps:
according to the fresnel diffraction theory, the line width of the cell diffraction pattern is larger than the cell diameter, therefore, the diffraction pattern is the result of multi-position diffraction superposition, the diffraction superposition can seriously affect the light intensity distribution of the diffraction pattern, and with the center of the quasi-spherical cell as the origin of coordinates, the superposed light intensity distribution of the diffraction pattern of the quasi-spherical cell, namely the lens-free imaging light intensity model, is expressed as:
in the formula (14), IcellIs the absolute light intensity distribution of the diffractogram of the quasi-spherical cell;
the relationship between the intensity distribution and the radius of the quasi-spherical cell can be obtained by the formula (14) by superimposing the diffraction pattern of the quasi-spherical cell.
And 8, processing the diffraction image of the biological cell by a lens-free imaging light intensity model at the end of the data processing device 21 to obtain the characteristic dimension of the biological cell and finish the quasi-spherical cell measurement.
The step 8 specifically comprises the following steps:
and acquiring the superposed light intensity distribution of the diffraction patterns of the quasi-spherical cells in the diffraction images of the biological cells at the end of the data processing device 21, and processing the superposed light intensity distribution by a lens-free imaging light intensity model to obtain the characteristic dimension of the biological cells in the biological cell sample 20 so as to finish the measurement of the quasi-spherical cells.
According to the quasi-spherical cell measuring method based on the light intensity model of the lens-free imaging system, the straight-edge Fresnel diffraction model is simplified according to the characteristics of the lens-free imaging system; based on the straight-side Fresnel diffraction model, an arc-side diffraction model is established; on the basis, diffraction superposition is considered to obtain a lens-free imaging light intensity model, and further the relation between the light intensity and the radius of the quasi-spherical cell is obtained; and finally, measuring the size of the aligned spherical cells by using a quasi-spherical cell diffraction pattern light intensity model. The invention realizes the real-time accurate measurement of the characteristic dimension of the alignment spherical cell.
The theory of demonstrating that the diffraction of the lens-free imaging system conforms to the Fresnel diffraction is specifically as follows:
based on the fresnel-kirchhoff diffraction integral formula, considering that the source point of a monochromatic wave propagates through the opening in a planar opaque screen, the total perturbation U that propagates at the observation point (the optical perturbation is to be determined) is a function of the distance from the light source to the biological cell sample 20, the distance from the biological cell sample 20 to the CMOS image sensor 17, and the optical wavelength.
The lensless imaging system employs a collimated light source 19 to illuminate the biological cell sample 20 so that the distance from the monochromatic point light source 15 to the biological cell sample 20 can approach approximately infinity, and a cover slip is provided between the cells and the photosensitive surface of the entire CMOS image sensor 17 so that the distance from the biological cell sample 20 to the CMOS image sensor 17 is on the order of hundreds of microns to millimeters. The monochromatic point light source 15 in the lensless imaging system typically uses a visible light source, and thus the optical wavelength is on the order of hundreds of nanometers. Since the above parameters of the lens-free system are not negligible, it can be known that the lens-free imaging system does not conform to the approximate range of fraunhofer diffraction, and the imaging diffraction principle conforms to fresnel diffraction.
Claims (6)
1. A quasi-spherical cell measuring method based on a light intensity model of a lens-free imaging system is characterized by comprising the following steps:
step 1, preparing a biological cell sample containing a quasi-sphere cell to be detected;
step 2, opening a monochromatic point light source of the lens-free imaging system, wherein the monochromatic point light source passes through a micropore arranged on the focal length of a convex lens and is refracted into a uniform parallel light source through the lens to irradiate on a biological cell sample;
step 3, placing the biological cell sample on a CMOS image sensor, forming a diffraction image of the biological cell on the CMOS image sensor, and uploading the diffraction image to a data processing device;
step 4, based on the imaging diffraction principle of the lens-free imaging system, the Fresnel diffraction is conformed, and a straight-edge Fresnel diffraction model of the lens-free imaging system is simplified;
step 5, calculating diffraction light intensity amplitude and diffraction period sequence of Fresnel diffraction;
step 6, establishing an arc edge diffraction model;
step 7, taking the superposition of diffraction into consideration to obtain a lens-free imaging light intensity model, and further obtaining the relation between the superposition light intensity distribution of the diffraction pattern of the quasi-spherical cells and the radius of the quasi-spherical cells;
and 8, processing the diffraction image of the biological cell by a lens-free imaging light intensity model at the data processing device end to obtain the characteristic dimension of the biological cell and finish the quasi-spherical cell measurement.
2. The quasi-spherical cell measuring method based on the light intensity model of the lens-free imaging system according to claim 1, wherein the step 4 specifically comprises:
since the relationship between the diffraction edge position and the diffraction fringe intensity can be well described by the straight-edge fresnel diffraction, when the diffraction occurs on a semi-infinite plane bounded by a sharp straight edge, the light intensity I on the imaging plane, i.e. the straight-edge fresnel diffraction model, is expressed as:
in the formula (1), I0Is the average light intensity, C (w), S (w) are Fresnel integrals;
c (w), S (w) are represented by:
in the formula (3), r 'is the distance from the light source to the biological cell sample, s' is the distance from the biological cell sample to the CMOS image sensor, x is the distance from the diffraction ring to the real cell boundary in the diffraction image of the biological cell sample, and λ is the optical wavelength;
since the distance from the light source to the biological cell sample in a lens-less imaging system tends to be infinite, w is reduced to
And (3) substituting the simplified w into the formula (1) to obtain the simplified straight-edge Fresnel diffraction model.
3. The quasi-spherical cell measuring method based on the light intensity model of the lens-free imaging system as claimed in claim 2, wherein the step 5 is implemented by the following steps:
step 5.1, obtaining the compound by the formula (1),
specific expressions of C '(w) and S' (w) are given by equations (2), (3):
the formula (4) and (5) are solved:
fresnel integrated cousinew upper k2，k4，...，k2nThe positions of the points (a) and (b) represent the positions of the fresnel diffraction bright and dark stripes, which alternate in sequence, and n is 1,2,3.
Step 5.2, obtaining the cosine function from the formula (1)
Obtaining the wave crest and the wave trough of the cosine function, wherein the position values of the wave crest and the wave trough are sequentially alternated to be k2，k4，...，k2nA position value of (a); by I/I01, obtain cosine function and straight line I/I0Intersection k of 11、k3、...、k2n-1A position value of (a); when the distance x from the diffraction ring to the real cell boundary in the diffraction image of the biological cell sample is a negative value, I/I0Monotonically decreasing toward zero;
since the collimated light source in the lens-less imaging system is illuminated on the biological cell sample, k is2，k4，...，k2nPosition value x (k) of2n) Expressed as:
in the formula (8), m2nIs k2nThe fresnel diffraction period sequence of (a);
k1，k3，...，k2n-1the position value of (d) is expressed as:
in the formula (9), m2n-1Is k2n-1The fresnel diffraction period sequence of (a);
k0the position value of (d) is expressed as:
in the formula (10), m0Is k0The sequence of fresnel diffraction periods of (a),
in summary, the Fresnel diffraction period sequence is represented as mi，i＝1,2,3......。
4. The quasi-spherical cell measuring method based on the light intensity model of the lens-free imaging system as claimed in claim 3, wherein the step 6 is implemented according to the following steps:
step 6.1, the actual light intensity I is obtained by converting the formula (1) in consideration of the intensity distribution of amplitude attenuationarcComprises the following steps:
in formula (11), α is an attenuation coefficient;
the attenuation coefficient alpha not only changes the amplitude of the diffraction light intensity, but also changes the distribution curve of the diffraction light intensity. Thus at k2，k4，...，k2nThe intensity of light at can be expressed as
In formula (12), h is 2,4,6arcIs the radius of the arc edge of the diffraction ring,
k0the light intensity is expressed as
Step 6.2, according to the diffraction light intensity amplitude and the diffraction period sequence, expressing an arc edge diffraction model as,
in formula (13), r is 0,1,2,3r),x(kr+1)]。
5. The quasi-spherical cell measuring method based on the light intensity model of the lens-free imaging system according to claim 4, wherein the step 7 specifically comprises:
according to the fresnel diffraction theory, the line width of the cell diffraction pattern is larger than the cell diameter, therefore, the diffraction pattern is the result of multi-position diffraction superposition, the diffraction superposition can seriously affect the light intensity distribution of the diffraction pattern, and with the center of the quasi-spherical cell as the origin of coordinates, the superposed light intensity distribution of the diffraction pattern of the quasi-spherical cell, namely the lens-free imaging light intensity model, is expressed as:
in the formula (14), IcellIs the absolute light intensity distribution of the diffractogram of the quasi-spherical cell;
the relationship between the intensity distribution and the radius of the quasi-spherical cell can be obtained by the formula (14) by superimposing the diffraction pattern of the quasi-spherical cell.
6. The quasi-spherical cell measuring method based on the light intensity model of the lens-free imaging system according to claim 5, wherein the step 8 specifically comprises:
and acquiring the superposed light intensity distribution of the diffraction patterns of the quasi-spherical cells in the diffraction images of the biological cells at the data processing device end, and processing the superposed light intensity distribution by a lens-free imaging light intensity model to obtain the characteristic dimension of the biological cells in the biological cell sample so as to finish the measurement of the quasi-spherical cells.
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