CN111158131B - LED matrix correction method based on Fourier laminated imaging - Google Patents
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Abstract
The invention relates to an LED matrix correction method based on Fourier laminated imaging. The method models an imaging system and an LED matrix, and determines the initial position vector of each LED; calculating a cost function according to the captured low-resolution image; correcting the position deviation of each LED by taking the global optimal solution of the cost function as a target; according to the Fourier laminated imaging method, a high-resolution image of the target sample is reconstructed after correcting the position deviation of the LED illumination matrix. The invention completes the position correction of the illumination light source according to the optical calculation imaging theory and the data collected by the optical imaging system. For an imaging system with multiple light sources, if the position arrangement of the illuminating elements is not reasonable, a plurality of adverse effects such as imaging quality reduction and the like can be caused to the imaging system.
Description
Technical Field
The invention relates to the field of optical imaging, in particular to an LED matrix correction method based on Fourier laminated imaging.
Background
The Fourier stacked imaging (FPM) technology is a new computational microscopic imaging method in the field of optical imaging in recent years, overcomes the limitation of space bandwidth product under the condition of low numerical aperture of the traditional imaging system, can complete imaging with high resolution and wide visual field, has the advantages of low cost, high resolution, wide visual field and the like, and has wide application prospect in various fields of medical imaging, biological science and the like.
The Fourier laminated imaging technology utilizes the idea of synthetic aperture in principle, a programmable LED illumination matrix (the parameters of each LED element are the same) is arranged below a sample in an imaging process without using a mode of illuminating the sample by using a separate light source, each LED is lightened in turn to scan the sample to obtain a plurality of low-resolution target intensity maps, intensity constraint is applied, acquired image data are processed in a Fourier domain, each acquired low-resolution map can reconstruct a partial area of a high-resolution image after being processed, and when the acquired images are sufficient, the high-resolution image of the sample can be effectively reconstructed by an iterative imaging method.
When the LED is used to scan a sample, each light beam striking the sample corresponds to a specific incident angle (illumination angle) compared with the incident light hole due to the different positions of each LED. In a stacked imaging system illuminated by an LED array, the spectral area of each low resolution image is determined primarily by the illumination angle, which means that the quality of the high resolution image recovered from these low resolution images depends largely on the positional accuracy of each LED light source on the LED array panel. Therefore, it is necessary to correct the position of each LED when performing stack imaging.
Disclosure of Invention
The invention provides an LED matrix correction method based on Fourier laminated imaging, aiming at the problem that the final imaging quality is reduced due to the light source position deviation in laminated imaging. Firstly, an imaging system is used for acquiring low-resolution images of a sequence, a cost function is introduced according to an imaging effect and data of actually captured images, the influence of LED position deviation on imaging quality can be effectively reflected, then the position deviation of each LED element is reduced by using an iterative imaging principle and a gradient reduction method, the optimal solution of the whole LED matrix position is finally evaluated, and the reconstruction of a high-resolution image is completed. The whole correction process mainly comprises the following parts:
the first aspect is that modeling is carried out on an imaging system and an LED matrix, and an initial position vector of each LED is determined; the second aspect is to calculate a cost function from the captured low resolution image; in the third aspect, the position deviation of each LED is corrected by taking the global optimal solution of the cost function as a target; in the fourth aspect, a high-resolution image of the target sample is reconstructed after correcting the position deviation of the LED illumination matrix according to a Fourier stack imaging method.
The main scheme and implementation steps of the invention are as follows:
step 1: the imaging system is built and comprises an LED illumination matrix, a low-power objective lens, a microscope, a sample target and a CCD camera. The microscope is a common microscope and is matched with a low-power objective lens, and a sample to be distinguished is placed on an objective table; placing an LED illumination matrix at a proper distance (h is 6-9 cm) below a sample, wherein each LED element can emit a plane wave; a CCD camera is positioned at the imaging position to capture the low resolution image.
Step 2: and establishing a coordinate system model for the system. Taking the optical axis direction of the system as the z axis, and the plane of the LED illumination matrix perpendicular to the optical axis direction as the XOY plane, wherein the central LED element is taken as the central origin (x) of the XOY plane0,y0) The coordinates of each LED element can be determined.
And step 3: the high resolution sample image O (x, y) and the aperture spectral function P (u, v) are initialized and the sample function is fourier transformed to generate a corresponding spectrum O (u, v) in the fourier domain. Wherein F (-) represents a Fourier transform; o (x, y) represents the image in a matrix form, representing a matrix of data of the image in the spatial domain. The aperture of the objective lens is a circular aperture, and the parameter data can also be expressed in a matrix form P (u, v) in the frequency domain.
And 4, step 4: sequentially illuminating each LED light source in sequence, for each LED emitted incident wave vector (u)i,vi) Correspondingly generated low-resolution images can be evaluated according to the optical imaging theory
To enterThe irradiation continues to propagate along the direction of the optical axis after the sample plane, and finally, an actual low-resolution intensity image l is generated on the imaging planei(x, y), captured by a CCD.
And 5: from the evaluation image
And the actual image liAnd (x, y) designing a cost function E, namely f (x, y), wherein the cost function represents the deviation between the image acquired by the optical system and the theoretical imaging, and the deviation can be reduced to improve the imaging quality of the system.
Step 6: seeking the position deviation (delta x) of each LED element by a method of calculating function partial derivativei，Δyi) And updating and correcting the position of the element, and calculating an updated cost function.
And 7: and (4) repeatedly executing the step M for 4-6 times according to the step 4-6, further reducing the position deviation of the LED, and determining the final LED coordinate.
And 8: and selecting the position of the LED, and reconstructing a high-resolution image by using a Fourier stack imaging (FPM) method.
The invention aims to finish the position correction of the illumination light source according to the optical calculation imaging theory and the data collected by the optical imaging system. For an imaging system with multiple light sources, if the position arrangement of the illuminating elements is not reasonable, a plurality of adverse effects such as imaging quality reduction and the like can be caused to the imaging system.
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FIG. 1 is a block diagram of a Fourier stacked imaging system;
fig. 2 is a flow chart of LED matrix rectification based on fourier stacked imaging.
Detailed Description
Step 1: building a required hardware imaging system, wherein a common microscope is required, a low-power objective lens (numerical aperture NA is 0.08) is matched, and a sample to be distinguished is placed on an objective table; placing an LED light source at a position 7cm away from the lower part of the sample, forming a square illumination matrix by adopting 15 LED elements, wherein the distance d between every two adjacent LED elements is 5mm, and each LED element can emit plane waves with the central wavelength lambda of 632 nm; a CCD camera is placed in the imaging position above the system to capture the low resolution image as shown in fig. 1.
Step 2: and establishing a coordinate system model for the system. Taking the optical axis direction of the system as the z axis, and the plane of the LED illumination matrix perpendicular to the optical axis direction as the XOY plane, wherein the central LED element is taken as the central origin (x) of the XOY plane0,y0). Then the coordinates (x) of each LED element can be determinedi,yi) I is 1,2, … 15 × 15. The incident plane wave for each LED is:
where λ is the central wavelength of the light wave, x0,y0Respectively the abscissa, the ordinate, x, of the central LED elementi,yiAre the abscissa and ordinate of the corresponding ith LED element, and h is the distance from the central LED element to the sample image.
And step 3: the final high resolution image sought after for initialization is o (x, y), which corresponds to a spectrum in the fourier domain of: o (u, v) ═ F [ O (x, y) ];
wherein F (-) represents a Fourier transform; o (x, y) represents the image in a matrix form, representing a matrix of data of the image in the spatial domain. The aperture of the objective lens is a circular aperture, and the parameter data can also be expressed in a matrix form P (u, v) in the frequency domain.
And 4, step 4: illuminating the sample with each LED illuminated in turn, for each LED incident wave vector (u)i,vi) The image prediction value is: Ψi(u,v)＝O(u-ui,v-vi) P (u, v); evaluating the image value as Ie(u,v)＝|Ψi(u,v)|2(ii) a Corresponding to the spatial domain image:
wherein F-1(. -) represents an inverse fourier transform; li(x, y) is the actual low resolution image acquired by the CCD, corresponding to FourierSpectral image: i isi(u,v)＝F[li(x,y)]。
And 5: from evaluation image Ie(u, v) and actual image Ii(u, v) designing a cost function E, wherein each LED error function is as follows: costi＝[Ie(u,v)-Ii(u,v)]2(ii) a Since the LEDs are a 15 x 15 matrix, the cost function can also be written as:
the positional deviation of the LED elements does not usually exceed the millimeter level, so the deviation cost of each evaluation image from the actual imageiVery small, close to:
wherein E and E0Are all 15 by 15 matrices.
Step 6: solving the position deviation delta x, delta y of the LED element by a function partial derivative solving method:
wherein:
are all 15 x 15 matrices, the unknowns Δ x, Δ y are solved according to the error function and the cost function. Updating the position of each LED element: x'i＝xi-αxi，y'i＝yi-βyi(ii) a Wherein α ═ β ═ 0.2, are all adjustable parameters. Calculating each error function cost after coordinate updatingiIf cost is presentiDecreasing, then the corresponding x is updatedi＝xi'，yi＝yi'; otherwise xi，yiThe previous value is kept unchanged. The final Δ x, Δ y can thus be determined.
And 7: and (4) repeatedly executing for 4-6 times according to the steps 4-6, and further correcting the position error of the LED element to reduce the error function E as much as possible.
And 8: adjusting the positions of the LED elements, and reconstructing a high-resolution image of the sample according to a Fourier stack imaging (FPM) method: the method comprises the following specific steps:
1) selecting a sub-region omega of the spectrum for the initialized high-resolution sample spectrum O (u, v)iThe sub-region position corresponds to an incident wave (u)i,vi)；
2) Updating sub-region Ω with intensity constraintsi：
3) repeating the steps 1) -2) until all the regions of the sample spectrum O (u, v) are updated;
4) and repeating the steps 1) -3) until the image meets the resolution requirement of the imaging system, and then carrying out Fourier inversion on the updated frequency domain image to obtain a high-resolution image o (x, y) of the sample in a space domain.
Claims (4)
1. A Fourier laminated imaging-based LED matrix correction method is characterized in that: the method specifically comprises the following steps:
step 1: the construction of an imaging system comprises an LED illumination matrix, a low-power objective lens, a microscope, a sample target and a CCD camera; the microscope is a common microscope and is matched with a low-power objective lens, and a sample to be distinguished is placed on an objective table; placing an LED illumination matrix at a proper distance h of 6-9 cm below the sample, wherein each LED element can emit a plane wave; placing a CCD camera at the imaging position for capturing a low-resolution image;
step 2: establishing a coordinate system model for the system; taking the optical axis direction of the system as the z axis, and the plane of the LED illumination matrix perpendicular to the optical axis direction as the XOY plane, wherein the central LED element is taken as the central origin (x) of the XOY plane0,y0) Enabling determination of each LED element coordinate;
and step 3: initializing a high-resolution sample image O (x, y) and an aperture spectrum function P (u, v), and performing Fourier transform on the sample function to generate a corresponding spectrum O (u, v) in a Fourier domain;
and 4, step 4: sequentially illuminating each LED light source in sequence, for each LED emitted incident wave vector (u)i,vi) Evaluating the correspondingly generated low-resolution image according to the optical imaging theory
And the incident wave continuously propagates along the direction of the optical axis after being irradiated on the sample plane, and finally, an actual low-resolution intensity image l is generated on the imaging planei(x, y), captured by a CCD; the method specifically comprises the following steps:
illuminating the sample with each LED illuminated in turn, for each LED incident wave vector (u)i,vi) The image prediction value is: Ψi(u,v)＝O(u-ui,v-vi) P (u, v); evaluating the image value as Ie(u,v)＝|Ψi(u,v)|2；
Corresponding to the spatial domain image:
wherein F-1(. -) represents an inverse fourier transform; li(x, y) is the actual low resolution image obtained by the CCD, corresponding to the Fourier spectrum image: i isi(u,v)＝F[li(x,y)]；
And 5: from the evaluation image
And the actual image li(x, y) designing a cost function E ═ f (x, y), wherein the cost function represents the deviation between the image acquired by the optical system and the theoretical imaging, and the quality of the system imaging can be improved by reducing the deviation; the method specifically comprises the following steps:
from evaluation image Ie(u, v) and actual image Ii(u, v) designing a cost function E, wherein each LED error function is as follows: costi＝[Ie(u,v)-Ii(u,v)]2(ii) a Since the LEDs are a 15 x 15 matrix, the cost function can also be written as:
the positional deviation of the LED elements does not usually exceed the millimeter level, so the deviation cost of each evaluation image from the actual imageiVery small, close to:
wherein E and E+Are all 15 by 15 matrices;
step 6: seeking the position deviation (delta x) of each LED element by a method of calculating function partial derivativei，Δyi) Updating and correcting the element position, and calculating an updated cost function; the method specifically comprises the following steps:
solving the position deviation delta x, delta y of the LED element by a function partial derivative solving method:
wherein:
all the matrixes are 15-by-15, and unknowns are solved according to an error function and a cost function; updating the position of each LED element:
x′i＝xi-αxi，y′i＝yi-βyi(ii) a Wherein α ═ β ═ 0.2, both adjustable parameters; calculating each error function cost after coordinate updatingiIf cost is presentiDecreasing, then the corresponding x is updatedi＝xi′，yi＝yi'; otherwise xi，yiKeeping the previous value unchanged;
and 7: repeatedly executing the step M for 4-6 times according to the step 4-6, further reducing the position deviation of the LED, and determining the final LED coordinate;
and 8: and selecting the position of the LED, and reconstructing a high-resolution image by using a Fourier laminated imaging method.
2. The method of claim 1 for fourier stack imaging based LED matrix correction, wherein: determining coordinates (x) of each LED element in said step 2i,yi) 1,2, … 15 × 15; the incident plane wave for each LED is:
where λ is the central wavelength of the light wave, x0,y0Respectively the abscissa, the ordinate, x, of the central LED elementi,yiAre the abscissa and ordinate of the corresponding ith LED element, and h is the distance from the central LED element to the sample image.
3. The method of claim 1 for fourier stack imaging based LED matrix correction, wherein: the step 3 corresponds to a fourier domain frequency spectrum O (u, v) ═ F [ O (x, y) ]; wherein F (-) represents a Fourier transform; o (x, y) represents the image in a matrix form, representing a data matrix of the image in the spatial domain; the aperture of the objective lens is a circular aperture, and the parameter data can also be expressed in a matrix form P (u, v) in the frequency domain.
4. The method of claim 1 for fourier stack imaging based LED matrix correction, wherein: the step 8 is to reconstruct a high-resolution image of the sample according to a Fourier stack imaging method: the method comprises the following specific steps:
1) selecting a sub-region omega of the spectrum for the initialized high-resolution sample spectrum O (u, v)iThe sub-region position corresponds to an incident wave (u)i,vi)；
2) Updating sub-region Ω with intensity constraintsi：
3) repeating the steps 1) -2) until all the regions of the sample spectrum O (u, v) are updated;
4) and repeating the steps 1) -3) until the image meets the resolution requirement of the imaging system, and then carrying out Fourier inversion on the updated frequency domain image to obtain a high-resolution image o (x, y) of the sample in a space domain.
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