CN114371549A - Quantitative phase imaging method and system based on multi-focus multiplexing lens - Google Patents

Quantitative phase imaging method and system based on multi-focus multiplexing lens Download PDF

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CN114371549A
CN114371549A CN202111616433.6A CN202111616433A CN114371549A CN 114371549 A CN114371549 A CN 114371549A CN 202111616433 A CN202111616433 A CN 202111616433A CN 114371549 A CN114371549 A CN 114371549A
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朱金龙
赵杭
董正琼
李泽迪
于哲
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Huazhong University of Science and Technology
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Abstract

The invention discloses a quantitative phase imaging method and system based on a multi-focus multiplexing lens, and belongs to the technical field of optical imaging and microscopy. The method comprises the following steps: step 1, generating an incident laser beam, and irradiating the incident laser beam on a sample to be detected after the incident laser beam is collimated to form a collimated laser beam; step 2, performing optical microscopic amplification on the illuminated sample to be detected, and adjusting an imaging view field on an imaging surface; step 3, relaying the image with the adjusted imaging field of view through a 4F system, modulating the image through a liquid crystal spatial light modulator loaded with a multi-focus multiplexing lens phase model, and imaging the image on a CCD camera, wherein the liquid crystal spatial light modulator is arranged on a Fourier surface of the 4F system; and 4, recovering the phase of the sample to be detected from the image imaged on the CCD camera through a light intensity transmission equation. The method and the system can realize simultaneous imaging of a plurality of defocused intensity images of a single frame on one CCD camera, have higher flexibility and can meet the high-speed real-time phase imaging of dynamic samples such as biological cells and the like.

Description

Quantitative phase imaging method and system based on multi-focus multiplexing lens
Technical Field
The invention belongs to the technical field of optical imaging and microscopy, and particularly relates to a quantitative phase imaging method and system based on a multi-focus multiplexing lens.
Background
The quantitative phase recovery based on the light intensity transmission equation is a non-interference phase imaging method, so that a complex optical path structure and phase unwrapping calculation are not needed, and the method is widely applied to the fields of optical measurement, biomedical imaging and the like. Solving the light intensity transmission equation needs to obtain a plurality of defocusing intensity images to estimate the axial intensity difference, the traditional axial scanning is generally realized by adopting a moving CCD mode, but the mechanical movement not only introduces extra errors, but also reduces the acquisition speed of a phase imaging system.
Therefore, researchers have proposed using special optical devices such as an electrically controlled variable focus lens or a spatial light modulator to avoid mechanical movement during defocusing scanning, but multiple intensity maps still need to be zoomed and collected in sequence, and the phase imaging speed cannot be further increased. In the aspect of simultaneous acquisition of multiple defocused surfaces in quantitative phase imaging, researchers propose that 2 or 4 CCD cameras are additionally arranged on a light splitting optical path to perform simultaneous acquisition of a focal surface and a defocused surface, and a spatial light modulator is combined with a similar Michelson interference structure to achieve simultaneous imaging of two intensity images. The number of the defocused images acquired at one time in the former is greatly limited, the defocused images are dependent on hardware configuration, the defocused distance is not convenient to flexibly adjust, although the spatial light modulator can be controlled to adjust the defocused amount, the total number of the defocused images acquired at one time is only 2, and the accuracy of the axial difference of the intensity is easily reduced.
Disclosure of Invention
Aiming at the defects and the improvement requirements of the prior art, the invention provides a quantitative phase imaging method and a quantitative phase imaging system based on a multi-focus multiplexing lens, and aims to realize simultaneous imaging of a plurality of defocused intensity images of a single frame on one CCD camera.
To achieve the above object, according to a first aspect of the present invention, there is provided a method for quantitative phase imaging based on a multi-focus multiplexing lens, comprising the steps of:
step 1, generating an incident laser beam, forming a collimated laser beam after collimation, and irradiating the collimated laser beam on a sample to be detected;
step 2, performing optical microscopic amplification on the illuminated sample to be detected, and adjusting an imaging view field on an imaging surface of the microscopic amplification;
step 3, relaying the image with the adjusted imaging field of view through a 4F system, and modulating the image through a liquid crystal spatial light modulator loaded with a multi-focus multiplexing lens phase model to realize simultaneous imaging of a plurality of defocusing intensity images of a single frame on a CCD camera; the multi-focus multiplexing lens phase model is a fusion phase model formed by randomly sampling a plurality of Fresnel lens phase models and a plurality of corresponding blazed grating phase models; wherein the liquid crystal spatial light modulator is arranged on a Fourier plane of the 4F system;
and 4, respectively cutting a plurality of out-of-focus intensity images of a single frame imaged on the CCD camera into a single out-of-focus intensity image, and recovering the phase of the sample to be detected through a light intensity transmission equation.
Further, the multi-focus multiplexing lens comprises a plurality of Fresnel lenses with different focal lengths and a plurality of corresponding blazed gratings with different diffraction angles.
Further, the step of programming the liquid crystal spatial light modulator to realize the multi-focus multiplexing lens is as follows:
s1, determining the focal length f of the Fresnel lens when the sample to be measured is focusedrAnd an axial offset distance zrAnd the diffraction angles of the corresponding blazed gratings in the x direction and the y direction;
s2, based on the focal length f of the Fresnel lens during focusingrAxial offset distance zrDetermining the focal lengths of Fresnel lenses at K defocusing positions and the diffraction angles of corresponding K blazed gratings in the x direction and the y direction, wherein K is more than or equal to 1;
s3, determining phase models of K +1 Fresnel lenses and corresponding phase models of K +1 blazed gratings based on the focal lengths of the K +1 Fresnel lenses and the diffraction angles of the corresponding K +1 blazed gratings in the x direction and the y direction, and fusing the phase models to obtain corresponding K +1 fused phase models;
s4, randomly extracting in each fused phase model
Figure BDA0003436817780000031
And recombining the extracted values to form the phase model of the multi-focus multiplexing lens and loading the phase model on the liquid crystal spatial light modulator, wherein W x H is the resolution of the liquid crystal spatial light modulator.
Further, S1 includes the sub-steps of:
s1.1, randomly collecting an axial offset distance z through a CCD cameratLight intensity image P oftSetting the light intensity image PtThe corresponding Fresnel lens has a focal length ftAnd f istSatisfies the following conditions:
Figure BDA0003436817780000032
wherein f isFThe focal lengths of two lenses in a 4F system, and M is the magnification of the sample to be measured for optical microscopic amplification;
s1.2, under the condition of satisfying Nyquist sampling condition, the light intensity image PtThe focal length of the corresponding Fresnel lens satisfies the following conditions:
Figure BDA0003436817780000033
wherein, WXH is the resolution of the liquid crystal spatial light modulator, d is the pixel center distance, and lambda is the wavelength of the incident laser beam;
s1.3, based on the steps S1.1 and S1.2, obtaining the maximum axial scanning range, wherein different axial offset distances z are within the maximum axial scanning rangetObtaining a corresponding light intensity image P through a definition evaluation operatortEvaluation value F oftWhen F istAt minimum, on coke formationAxial offset distance zr。
Further, the focal length f of the i-th Fresnel lens in S2iComprises the following steps:
Figure BDA0003436817780000034
the number K of the Fresnel lenses at the defocusing positions is set to be 2n, the n +1 th Fresnel lens is used for focusing the sample to be measured, i is 1, a.
Further, the phase model of the Fresnel lens at the ith defocus position in S3
Figure BDA0003436817780000041
And corresponding blazed grating phase model
Figure BDA0003436817780000042
Respectively as follows:
Figure BDA0003436817780000043
Figure BDA0003436817780000044
wherein the content of the first and second substances,
Figure BDA0003436817780000045
θxi、θyithe diffraction angles of the corresponding blazed grating in the x direction and the y direction are respectively.
According to a second aspect of the present invention, there is provided an imaging system for implementing the method for quantitative phase imaging based on a multi-focus multiplexing lens according to any one of the first aspect, sequentially comprising, along an optical path transmission direction: the device comprises a laser, a collimating lens, a microscope objective, a first tube lens, an adjustable rectangular diaphragm, a first lens, a liquid crystal spatial light modulator, a second lens and a CCD camera; wherein, the sample to be measured is a transmission sample and is arranged in the working distance of the microscope objective; the microscope objective and the first lens barrel lens form a double telecentric imaging system, and the first lens and the second lens form an optical 4F system;
the laser is used for generating incident laser beams, and the incident laser beams are collimated by the collimating lens to form collimated laser beams which are irradiated on a sample to be measured; the illuminated sample to be measured is subjected to amplification imaging by the double telecentric imaging system, and an imaging field of view is adjusted by an adjustable rectangular diaphragm placed on an imaging surface of the sample to be measured; the light after the imaging field of view is adjusted to irradiate on the 4F system, the liquid crystal spatial light modulator is located on a Fourier face of the 4F system, the light passing through a first lens of the 4F system is modulated by the liquid crystal spatial light modulator loaded with a phase model of a multi-focus multiplexing lens, and then is imaged on a CCD camera through a second lens, so that a plurality of defocusing intensity images of a single frame are imaged on the CCD camera at the same time; and respectively cutting a plurality of out-of-focus intensity images of a single frame imaged on the CCD camera into a single out-of-focus intensity image, and recovering the phase of the sample to be detected through a light intensity transmission equation.
Further, the clipping range includes an imaging boundary of the adjustable rectangular diaphragm in the CCD camera after passing through the 4F system.
Further, the adjustable diaphragm is arranged between the collimating lens and the microscope objective and used for adjusting the diameter of the collimated light beam;
and/or further comprising a rotatable polarizer disposed between the collimating lens and the microscope objective for controlling the polarization direction of the formed collimated laser beam.
According to a third aspect of the present invention, there is provided an imaging system for implementing the method for multi-focus multiplexing lens-based quantitative phase imaging according to any one of the first aspect, sequentially comprising, along an optical path transmission direction: the device comprises a laser, a collimating lens, a second tube lens, a microscope objective, a beam splitter, a first tube lens, an adjustable rectangular diaphragm, a first lens, a liquid crystal spatial light modulator, a second lens and a CCD camera; wherein, the sample to be measured is a reflection sample and is arranged in the working distance of the microscope objective; the microscope objective and the first lens barrel lens form a double telecentric imaging system, and the first lens and the second lens form an optical 4F system;
the laser is used for generating incident laser beams, and the incident laser beams are collimated by the collimating lens to form collimated laser beams which are irradiated to the second lens cone lens to converge the collimated laser beams; the converged light beams are irradiated on the beam splitter; the light beam reflected by the beam splitter is reflected to the microscope objective to form a parallel light beam to irradiate a sample to be measured, the light irradiated to the sample to be measured is reflected to the microscope objective again and transmitted to the first tube lens for amplified imaging, and an imaging view field is adjusted through an adjustable rectangular diaphragm arranged on an imaging surface of the first tube lens; the light after the imaging field of view is adjusted to irradiate on the 4F system, the liquid crystal spatial light modulator is located on a Fourier face of the 4F system, the light passing through a first lens of the 4F system is modulated by the liquid crystal spatial light modulator loaded with a phase model of a multi-focus multiplexing lens, and then is imaged on a CCD camera through a second lens, so that a plurality of defocusing intensity images of a single frame are imaged on the CCD camera at the same time; and respectively cutting a plurality of out-of-focus intensity images of a single frame imaged on the CCD camera into a single out-of-focus intensity image, and recovering the phase of the sample to be detected through a light intensity transmission equation.
Generally, by the above technical solution conceived by the present invention, the following beneficial effects can be obtained:
(1) the invention places the digital multiplexing lens programmed and controlled by the liquid crystal spatial light modulator on the Fourier surface of the 4F optical system, the multi-focus multiplexing lens phase model is a fusion phase model formed by randomly sampling a plurality of Fresnel lens phase models with different focal lengths and axial defocusing step distances and a plurality of corresponding blazed grating phase models with different diffraction angles, and is combined with microscopic imaging to realize single-frame imaging of a plurality of defocusing intensity images on one CCD camera, and the image imaged on the CCD camera is restored to the phase of a sample to be measured through a light intensity transmission equation, compared with the axial scanning device used in the prior art, the three-dimensional phase microscopic imaging device can greatly reduce the acquisition time of a plurality of defocused intensity images, improve the response speed of a phase imaging system, and meet the requirement of real-time three-dimensional phase microscopic imaging of samples such as dynamic biological cells.
(2) The invention can realize single acquisition of a plurality of defocusing intensity images, the defocusing distance and the number of the defocusing intensity images can be modified by controlling the liquid crystal spatial light modulator, and the invention has higher flexibility and can meet the high-speed real-time phase imaging of dynamic samples such as biological cells and the like.
(3) The system of the invention forms a double telecentric imaging system by the microscope objective and the first lens cone group, thereby realizing that a plurality of defocusing intensity images with fixed magnification realize single-frame imaging on one CCD camera.
(4) According to the invention, the clearest imaging section of the light beam on the CCD camera is obtained by determining the maximum axial scanning range and the evaluation value of the basic light intensity image in the range, and no additional mechanical devices such as an electric control displacement table and the like are needed, so that the method is simpler and more convenient to operate; and the method for automatically searching the determined clearest imaging section through the computer is more accurate compared with mechanical devices such as an electric control displacement table and the like.
(5) Preferably, in the system of the present invention, the diameter of the collimated laser beam formed after collimation is adjusted by the adjustable diaphragm arranged between the collimator lens and the microscope objective lens, so that the illumination area of the collimated beam is matched with the surface area of the sample to be measured.
(6) Preferably, when the obtained single-frame multiple defocus intensity maps are clipped into a single defocus intensity map, the clipping range comprises the boundary of the image of the adjustable rectangular diaphragm, so that the Noemann boundary condition in solving the light intensity transmission equation can be met, the restored three-dimensional phase has no boundary artifact, and the finally obtained three-dimensional phase is more accurate.
In summary, the method and the system of the invention can realize simultaneous imaging of a plurality of defocusing intensity maps of a single frame on one CCD camera, and the defocusing distance and the number of the defocusing intensity maps can be modified by controlling the liquid crystal spatial light modulator, so that the method and the system have higher flexibility and can meet the high-speed real-time phase imaging of dynamic samples such as biological cells.
Drawings
Fig. 1 is a diagram of a multi-focus multiplexing lens-based quantitative phase imaging system (a sample to be measured is a transmission sample) of the present invention.
Fig. 2 is a schematic diagram of a single-frame image with multiple defocus sections according to an embodiment of the present invention.
FIG. 3 is a single cross-sectional intensity plot taken in an embodiment of the present invention.
Fig. 4 is a diagram of the multi-focus multiplexing lens-based quantitative phase imaging system (the sample to be measured is a reflection sample) of the present invention.
The same reference numbers will be used throughout the drawings to refer to the same or like elements or structures, wherein:
1-laser 1, 2-collimating lens, 3-adjustable diaphragm, 4-rotatable polarizer, 5-sample to be measured, 6-microobjective, 7-first tube lens, 8-adjustable rectangular diaphragm, 9-first lens, 10-liquid crystal spatial light modulator, 11-second lens, 12-CCD camera, 13-second tube lens and 14-beam splitter.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
In the present invention, the terms "first", "second", and the like in the description and the drawings are used for distinguishing similar objects, and are not necessarily used for describing a particular order or sequence.
The invention provides a quantitative phase imaging method based on a multi-focus multiplexing lens, which comprises the following steps:
step 1, generating an incident laser beam, forming a collimated laser beam after collimation, and irradiating the collimated laser beam on a sample to be detected;
step 2, performing optical microscopic amplification on the illuminated sample to be detected, and adjusting an imaging view field on an imaging surface of the microscopic amplification to enable a plurality of defocusing intensity images acquired by a CCD camera to be independent;
step 3, relaying the image after the imaging field is adjusted through a 4F system, and modulating the image through a liquid crystal spatial light modulator loaded with a multi-focus multiplexing lens phase model to realize simultaneous imaging of multiple sections on a CCD camera; the multi-focus multiplexing lens phase model is a fusion phase model formed by random sampling of phase models of a plurality of Fresnel lenses and corresponding phase models of a plurality of blazed gratings; the liquid crystal spatial light modulator is arranged on a Fourier surface of the 4F system;
the multi-focus multiplexing lens comprises a plurality of Fresnel lenses with different focal lengths and a plurality of corresponding blazed gratings with different diffraction angles.
Specifically, the steps of programming the liquid crystal spatial light modulator to realize the multi-focus multiplexing lens are as follows:
s1, determining the focal length f of the Fresnel lens when the sample to be detected is focused (namely when the best clear imaging is carried out)rAnd an axial offset distance zrAnd the diffraction angles of the corresponding blazed gratings in the x direction and the y direction;
s2 focal length f based on Fresnel lens in focusingrAxial offset distance zrDetermining the focal lengths of Fresnel lenses at K defocusing positions and the diffraction angles of corresponding K blazed gratings in the x direction and the y direction, wherein K is more than or equal to 1; wherein, the defocusing step distance delta z is larger than the depth of the sample to be measured so as to ensure defocusing.
S3, determining phase models of K +1 Fresnel lenses and corresponding phase models of K +1 blazed gratings based on the focal lengths of the K +1 Fresnel lenses and the diffraction angles of the corresponding K +1 blazed gratings in the x direction and the y direction, and fusing the phase models to obtain corresponding K +1 fused phase models;
s4, random extraction in each fused phase model
Figure BDA0003436817780000081
Values at different coordinate positions and extracted coordinates in different fused phase models are not repeated, the extracted values are recombined to form a phase model of the multi-focus multiplexing lens and the phase model is loaded on the liquid crystal spatial light modulator, wherein Wf isAnd H is the resolution of the liquid crystal spatial light modulator.
Specifically, S1 includes the sub-steps of:
s1.1, randomly collecting an axial offset distance z through a CCD cameratLight intensity image PtSetting the light intensity image PtThe corresponding Fresnel lens has a focal length ftAnd f istSatisfies the following conditions:
Figure BDA0003436817780000091
wherein f isFThe focal lengths of two lenses in a 4F system, and M is the magnification of the sample to be measured for optical microscopic amplification;
s1.2, under the condition of satisfying Nyquist sampling condition, the light intensity image PtThe focal length of the corresponding Fresnel lens satisfies the following conditions:
Figure BDA0003436817780000092
where, wxh is the resolution of the liquid crystal spatial light modulator, d is the pixel center-to-center distance, and λ is the wavelength of the incident laser beam.
S1.3, based on the steps S1.1 and S1.2, obtaining the maximum axial scanning range, and aiming at different axial offset distances z in the maximum axial scanning rangetObtaining a corresponding light intensity image P through a definition evaluation operatortEvaluation value F oftWhen F istAt the minimum, the axial offset z in the process of focusing is obtainedr(ii) a To shift the axial by a distance zrSubstituting into the formula in S1.1 to obtain the corresponding focal length frI.e. the focal length of the fresnel lens at the location where the beam is focused. Wherein when axially offset by a distance ztWhen 0, the corresponding focal length is infinity.
And 4, recovering the phase of the sample to be detected from the image imaged on the CCD camera through a light intensity transmission equation.
As shown in FIG. 1, the present invention provides a multi-focus multiplexing lens based on the above-mentionedThe system structure of the phase measuring imaging method sequentially comprises the following steps along the transmission direction of an optical path: the device comprises a laser 1, a collimating lens 2, an adjustable diaphragm 3, a rotatable polarizer 4, a microscope objective 6, a first tube lens 7, an adjustable rectangular diaphragm 8, a first lens 9, a liquid crystal spatial light modulator 10, a second lens 11 and a CCD camera 12. The laser 1, the collimating lens 2, the adjustable diaphragm 3, the rotatable polarizer 4, the microscope objective 6 and the first tube lens 7 form a microscope imaging system; the first lens 9 and the second lens 11 constitute an optical 4F system. Wherein, the sample 5 to be measured is a transmission sample, is arranged between the rotatable polarizer 4 and the microscope objective 6 and is positioned in the working range of the microscope objective; the microscope objective 6 and the first tube lens 7 form a double telecentric imaging system to ensure that the magnification of an image space is constant when the image space is out of focus. Input light from a laser is collimated into parallel light beams through a collimating lens, the diameter of the light beams is adjusted through an adjustable diaphragm, the polarization direction of the light beams is controlled by a rotatable polarizer and then the light beams directly irradiate a sample, the light penetrating through the sample is collected by a microscope objective and is magnified and imaged through a first tube lens, the magnified and imaged light is matched with an imaging field of a CCD camera through an adjustable rectangular diaphragm arranged on an imaging surface of a microscope imaging system, mutual interference among a plurality of defocusing intensity images is prevented, and each defocusing intensity image is independent; the light beam after being adjusted to pass through the imaging field of view irradiates a 4F system comprising a liquid crystal spatial light modulator, wherein the liquid crystal spatial light modulator is positioned on a Fourier surface of the 4F system, a focus of a lens on one side of the 4F system, which is close to an imaging surface (an adjustable rectangular diaphragm), is also positioned on an imaging surface of a microscopic imaging system, and finally output light of the 4F system is received by a CCD. Wherein the focal lengths of the first lens and the second lens are both fFThe distances between the first lens and the liquid crystal spatial light modulator and the imaging surface (namely the adjustable diaphragm) of the microscopic imaging system are both fFThe distances between the second lens and the liquid crystal spatial light modulator and the CCD camera are fFEmergent light of the microscopic imaging system is irradiated to the liquid crystal spatial light modulator through the first lens, and is imaged on the CCD camera 12 through the second lens 11 after being modulated. And recovering the phase of the sample to be detected from the acquired image through a light intensity transmission equation.
The liquid crystal spatial light modulator can realize the function of a digital multi-focus multiplexing lens in a programming way, and the digital multi-focus multiplexing lens comprises a plurality of Fresnel lenses with different focal lengths and a plurality of blazed gratings with different diffraction angles, so that a plurality of defocused intensity images are imaged on a CCD camera at the same time.
The adjustable diaphragm 3 is preferably used for adjusting the diameter of the parallel light beam collimated by the collimating lens 2, so that the illumination area of the collimated light beam is matched with the surface area of the sample 5 to be measured. The rotatable polarizer 4 is preferably used to control the polarization direction of the collimated parallel beam to become a single polarization direction.
Specifically, the multi-focal-plane intensity image acquisition and three-dimensional morphology recovery are realized by using the multi-focal-multiplexing-lens-based quantitative phase imaging system, and the method comprises the following steps:
step one, because of the uncertainty of the sample size, a liquid crystal spatial light modulator is used for realizing Fresnel lenses with different focal lengths before measurement, and clear imaging section searching is carried out, specifically as follows:
when the focal length is f is realized by the liquid crystal spatial light modulatortFor the Fresnel lens, it is necessary to generate a kinoform according to the phase model of the following formula and load the kinoform to the liquid crystal spatial light modulator,
Figure BDA0003436817780000111
wherein the content of the first and second substances,
Figure BDA0003436817780000112
w × H is the resolution of the liquid crystal spatial light modulator, d is the pixel center-to-center spacing, and λ is the light source wavelength (i.e., the wavelength of the incident laser beam).
Namely, the defocusing distance z can be collected by the CCDtImage P oftAnd obtaining the image P by a definition evaluation operatortEvaluation value F oftWherein:
Figure BDA0003436817780000113
wherein M is the magnification of the microscope objective.
And due to the discretization characteristic of the liquid crystal spatial light modulator, the generated Fresnel lens has the limitation of minimum focal length under the condition of satisfying the Nyquist sampling condition, namely:
Figure BDA0003436817780000114
according to the above two formulas, the maximum axial scanning range can be determined, and the suitable searching range can be determined in the range, and different focal lengths f can be obtained in the searching rangetLower sharpness evaluation value FtWhen the smallest F is foundtWhen the Fresnel lens is in use, the best clear imaging section can be found, and the focal length of the Fresnel lens at the moment is recorded as frDefocus distance of zr。
And step two, when carrying out axial differential estimation on the light intensity, at least two intensity maps are needed, namely one in-focus image and one out-of-focus image. In order to ensure the accuracy of the light intensity axial difference estimation, the embodiment determines the collection number 2n +1 of the defocus intensity maps by using a center difference method, that is, K is 2n, n is greater than or equal to 1, the defocus step distance of each intensity map in the object space is Δ z, where the ith intensity map is denoted as
Figure BDA0003436817780000115
And i is 1, 2n +1, j is i-n-1, n +1 intensity map
Figure BDA0003436817780000116
For a clear intensity map acquired during focusing (i.e. focal length f determined in step one)rDefocus distance of zrThe fresnel lens generated on the CCD camera), and the rest are defocused intensity maps.
Step three, establishing a phase model of the multi-focus multiplexing lens according to the acquisition number 2n +1 and the defocusing step distance delta z specified in the step two, wherein the phase model comprises the following specific steps:
firstly, calculating the required focal lengths of 2n +1 Fresnel lenses, wherein the focal length of the ith Fresnel lens is as follows:
Figure BDA0003436817780000121
wherein M is the magnification of the microscope objective, and n is more than or equal to 1.
Secondly, according to the deviation of the center of the ith intensity chart relative to the center of the CCD area array in the x and y directions and fFThe diffraction angle theta of the i-th blazed grating in the x and y directions can be estimated by using an arctangent functionxiAnd thetayi. Fig. 2 shows a schematic diagram of a single-frame image of 9 out-of-focus cross sections when n is 4, and the table below shows a corresponding combination manner of diffraction angles, where θ represents the diffraction angle value of a blazed grating at a specific position in both x and y directions.
Table 1 shows diffraction angles in x and y directions when n is 4
i 1 2 3 4 5 6 7 8 9
θxi -θ 0 θ -θ 0 θ -θ 0 θ
θyi θ θ θ 0 0 0 -θ -θ -θ
Meanwhile, in order to ensure higher diffraction efficiency, the number of the periodic unit steps of the blazed grating is set to be 8, that is:
Figure BDA0003436817780000122
the phase model of the ith blazed grating is:
Figure BDA0003436817780000123
then, the phase model of the fusion of the ith blazed grating and the ith fresnel lens is:
Figure BDA0003436817780000124
finally, at each phase coordinate (u, v), from the corresponding 2n +1 phase sets
Figure BDA0003436817780000125
Randomly selecting one, traversing all phase coordinates, and ensuring that the number of samples extracted from each phase model is
Figure BDA0003436817780000131
Phase model for forming multi-focus multiplexing lens
Figure BDA0003436817780000132
And generating a corresponding kinoform by using a computer according to the model.
And step three, writing the kinoform of the multi-focus multiplexing lens in the step two into the liquid crystal spatial light modulator, and realizing simultaneous imaging of the multi-defocusing cross sections in the CCD. The liquid crystal spatial light modulator realizes the function of a multi-focus multiplexing lens through programming, so that a plurality of defocused intensity images of a single frame are imaged on a CCD camera simultaneously.
And (3) intercepting the acquired single-frame image to obtain 2n +1 intensity maps (one of the intensity maps is the in-focus intensity map of the sample to be detected, and the 2n intensity maps is the out-of-focus intensity map), wherein the interception range needs to be ensured to include the boundary of the adjustable rectangular diaphragm during interception, as shown in fig. 3, so as to meet the boundary condition of Noemann during solving the light intensity transmission equation. And then carrying out strength axial differential estimation by using the central finite difference, namely:
Figure BDA0003436817780000133
wherein the weight aiCan be derived from Taylor expansion, which can be specifically derived from the following formula:
Figure BDA0003436817780000134
step four, axially differentiating the intensity calculated in the step three
Figure BDA0003436817780000135
And intensity map at focal plane
Figure BDA00034368177800001310
Substituting the intensity diagram (namely the intensity diagram when the sample to be measured is focused) into the following formula, solving a light intensity transmission equation by utilizing discrete cosine transform, and solving the phase:
Figure BDA0003436817780000136
wherein k is a wave number,
Figure BDA0003436817780000137
in order to operate on the gradient, the operator,
Figure BDA0003436817780000138
the inverse laplacian operator.
Step five, substituting the phase obtained in the step four into the following formula to convert the phase into the actual scale of the sample to be measured:
Figure BDA0003436817780000139
in the formula, Δ n is the difference between the refractive index of the sample to be measured and the refractive index of the environment medium.
Although the quantitative phase imaging system based on the multi-focus multiplexing lens provided by the invention takes a transmissive sample as an example, the illumination optical path can be slightly modified to be used for measurement of a reflective sample, and the basic optical imaging and phase recovery method is still applicable, so that the above formula also provides a method for converting the actual physical height of the reflective sample. As shown in fig. 4, the imaging system of the method for quantitatively phase imaging based on the multi-focus multiplexing lens for a reflection sample according to the present invention sequentially includes, along the optical path transmission direction: the device comprises a laser 1, a collimating lens 2, a second tube lens 13, a microscope objective 6, a beam splitter 14, a first tube lens 7, an adjustable rectangular diaphragm 8, a first lens 9, a liquid crystal spatial light modulator 10, a second lens 11 and a CCD camera 12; wherein, the sample to be measured is a reflection sample and is arranged in the working distance of the microscope objective 6; the microscope objective 6 and the first tube lens 7 form a double telecentric imaging system, and the first lens 9 and the second lens 11 form an optical 4F system;
the laser device 1 is used for generating incident laser beams, forming collimated laser beams after being collimated by the collimating lens 2, irradiating the collimated laser beams to the second tube lens 13 to converge the collimated laser beams, and irradiating the converged light beams to the beam splitter 14; the light beam passing through the beam splitter 14 is reflected to the microscope objective 6 to form a parallel light beam to irradiate a sample to be measured, the light irradiated to the sample to be measured is reflected to the microscope objective 6 again and transmitted to the first tube lens 7 for amplified imaging; the imaging field of view is adjusted by an adjustable rectangular diaphragm 8 placed on the imaging surface; the light after the imaging field of view is adjusted to irradiate on a 4F system, a liquid crystal spatial light modulator 10 is positioned on a Fourier face of the 4F system, and the light passing through a first lens 9 of the 4F system is modulated by the liquid crystal spatial light modulator 10 loaded with a phase model of a multi-focus multiplexing lens and then imaged on a CCD camera 12 through a second lens 11, so that a plurality of defocusing intensity images are imaged on the CCD camera at the same time; and respectively cutting a plurality of defocus intensity maps of a single frame imaged on the CCD camera 12 into a single defocus intensity map, and recovering the phase of the sample to be detected through a light intensity transmission equation.
Most preferably, an adjustable diaphragm 3 and a rotatable polarizer 4 are further provided between the collimator lens and the microscope objective lens, for adjusting the diameter of the collimated beam and controlling the polarization direction of the formed collimated laser beam, respectively.
It will be understood by those skilled in the art that the foregoing is merely a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included within the scope of the present invention.

Claims (10)

1. A quantitative phase imaging method based on a multi-focus multiplexing lens is characterized by comprising the following steps:
step 1, generating an incident laser beam, forming a collimated laser beam after collimation, and irradiating the collimated laser beam on a sample to be detected;
step 2, performing optical microscopic amplification on the illuminated sample to be detected, and adjusting an imaging view field on an imaging surface of the microscopic amplification;
step 3, relaying the image with the adjusted imaging field of view through a 4F system, and modulating the image through a liquid crystal spatial light modulator loaded with a multi-focus multiplexing lens phase model to realize simultaneous imaging of a plurality of defocusing intensity images of a single frame on a CCD camera; the multi-focus multiplexing lens phase model is a fusion phase model formed by randomly sampling a plurality of Fresnel lens phase models and a plurality of corresponding blazed grating phase models; wherein the liquid crystal spatial light modulator is arranged on a Fourier plane of the 4F system;
and 4, respectively cutting a plurality of out-of-focus intensity images of a single frame imaged on the CCD camera into a single out-of-focus intensity image, and recovering the phase of the sample to be detected through a light intensity transmission equation.
2. The imaging method according to claim 1, wherein the multi-focus multiplexing lens comprises a plurality of fresnel lenses having different focal lengths and a corresponding plurality of blazed gratings having different diffraction angles.
3. The imaging method according to claim 1, wherein the step of programming the multi-focus multiplexing lens by the liquid crystal spatial light modulator is as follows:
s1, determining the focal length f of the Fresnel lens when the sample to be measured is focusedrAnd an axial offset distance zrAnd the diffraction angles of the corresponding blazed gratings in the x direction and the y direction;
s2, based on the focal length f of the Fresnel lens during focusingrAxial offset distance zrDetermining the focal lengths of Fresnel lenses at K defocusing positions and the diffraction angles of corresponding K blazed gratings in the x direction and the y direction, wherein K is more than or equal to 1;
s3, determining phase models of K +1 Fresnel lenses and corresponding phase models of K +1 blazed gratings based on the focal lengths of the K +1 Fresnel lenses and the diffraction angles of the corresponding K +1 blazed gratings in the x direction and the y direction, and fusing the phase models to obtain corresponding K +1 fused phase models;
s4, randomly extracting in each fused phase model
Figure FDA0003436817770000021
And recombining the extracted values to form the phase model of the multi-focus multiplexing lens and loading the phase model on the liquid crystal spatial light modulator, wherein W x H is the resolution of the liquid crystal spatial light modulator.
4. The imaging method according to claim 3, characterized in that S1 includes the sub-steps of:
s1.1, randomly collecting an axial offset distance z through a CCD cameratLight intensity image P oftSetting the light intensity image PtThe corresponding Fresnel lens has a focal length ftAnd f istSatisfies the following conditions:
Figure FDA0003436817770000022
wherein f isFThe focal lengths of two lenses in a 4F system, and M is the magnification of the sample to be measured for optical microscopic amplification;
s1.2, under the condition of satisfying Nyquist sampling condition, the light intensity image PtThe focal length of the corresponding Fresnel lens satisfies the following conditions:
Figure FDA0003436817770000023
wherein, WXH is the resolution of the liquid crystal spatial light modulator, d is the pixel center distance, and lambda is the wavelength of the incident laser beam;
s1.3, based on the steps S1.1 and S1.2, obtaining the maximum axial scanning range, wherein different axial offset distances z are within the maximum axial scanning rangetObtaining a corresponding light intensity image P through a definition evaluation operatortEvaluation value F oftWhen F istAt the minimum, the axial offset z in the process of focusing is obtainedr。
5. The imaging method according to claim 4, wherein the focal length f of the i-th Fresnel lens in S2iComprises the following steps:
Figure FDA0003436817770000031
the number K of the Fresnel lenses at the defocusing positions is set to be 2n, the n +1 th Fresnel lens is used for focusing the sample to be measured, i is 1, a.
6. The imaging method according to claim 5, wherein the phase model of the Fresnel lens at the ith off-focus position in S3
Figure FDA0003436817770000032
And corresponding blazed grating phase model
Figure FDA0003436817770000033
Respectively as follows:
Figure FDA0003436817770000034
Figure FDA0003436817770000035
wherein the content of the first and second substances,
Figure FDA0003436817770000036
θxi、θyithe diffraction angles of the corresponding blazed grating in the x direction and the y direction are respectively.
7. An imaging system for implementing the multi-focus multiplexing lens-based quantitative phase imaging method according to any one of claims 1 to 6, sequentially comprising, along the optical path transmission direction: the device comprises a laser (1), a collimating lens (2), a microscope objective (6), a first tube lens (7), an adjustable rectangular diaphragm (8), a first lens (9), a liquid crystal spatial light modulator (10), a second lens (11) and a CCD camera (12); wherein, the sample to be measured is a transmission sample and is arranged in the working distance of the microscope objective (6); the microscope objective (6) and the first tube lens (7) form a double telecentric imaging system, and the first lens (9) and the second lens (11) form an optical 4F system;
the laser (1) is used for generating an incident laser beam, and the incident laser beam is collimated by the collimating lens (2) to form a collimated laser beam which is irradiated on a sample to be measured; the illuminated sample to be measured is amplified and imaged by the double telecentric imaging system, and the imaging field of view is adjusted by an adjustable rectangular diaphragm (8) arranged on the imaging surface of the sample to be measured; the light after the imaging field of view is adjusted is irradiated on the 4F system, the liquid crystal spatial light modulator (10) is located on a Fourier face of the 4F system, the light passing through a first lens (9) of the 4F system is modulated by the liquid crystal spatial light modulator (10) loaded with a phase model of a multi-focus multiplexing lens, and then is imaged on a CCD camera (12) through a second lens (11), so that a single-frame multi-defocusing intensity image is simultaneously imaged on the CCD camera (12); and respectively cutting a plurality of defocusing intensity images of a single frame imaged on a CCD camera (12) into a single defocusing intensity image, and recovering the phase of the sample to be detected through a light intensity transmission equation.
8. The imaging system of claim 7, wherein the cropping range comprises an imaging boundary of the adjustable rectangular aperture in the CCD camera after passing through the 4F system.
9. The imaging system according to claim 7, further comprising an adjustable diaphragm (3) arranged between the collimator lens (2) and the microscope objective (6) for adjusting the diameter of the collimated beam;
or/and further comprising a rotatable polarizer (4) arranged between the collimator lens (2) and the microscope objective (6) for controlling the polarization direction of the formed collimated laser beam.
10. An imaging system for implementing the multi-focus multiplexing lens-based quantitative phase imaging method according to any one of claims 1 to 6, sequentially comprising, along the optical path transmission direction: the device comprises a laser (1), a collimating lens (2), a second tube lens (13), a microscope objective (6), a beam splitter (14), a first tube lens (7), an adjustable rectangular diaphragm (8), a first lens (9), a liquid crystal spatial light modulator (10), a second lens (11) and a CCD camera (12); wherein, the sample to be measured is a reflection sample and is arranged in the working distance of the microscope objective (6); the microscope objective (6) and the first tube lens (7) form a double telecentric imaging system, and the first lens (9) and the second lens (11) form an optical 4F system;
the laser (1) is used for generating incident laser beams, and the incident laser beams are collimated by the collimating lens (2) to form collimated laser beams which are irradiated to the second lens barrel lens (13) to converge the collimated laser beams; the converged light beams are irradiated onto the beam splitter (14); the light beam reflected by the beam splitter (14) is reflected to the microscope objective (6) to form a parallel light beam to irradiate a sample to be measured, the light irradiated to the sample to be measured is reflected to the microscope objective (6) again and transmitted to the first tube lens (7) for amplified imaging, and an imaging field of view is adjusted through an adjustable rectangular diaphragm (8) arranged on an imaging surface of the first tube lens; the light after the imaging field of view is adjusted is irradiated on the 4F system, the liquid crystal spatial light modulator (10) is located on a Fourier face of the 4F system, the light passing through a first lens (9) of the 4F system is modulated by the liquid crystal spatial light modulator (10) loaded with a phase model of a multi-focus multiplexing lens, and then is imaged on a CCD camera (12) through a second lens (11), so that a single-frame multi-defocusing intensity image is simultaneously imaged on the CCD camera (12); and respectively cutting a plurality of defocusing intensity images of a single frame imaged on a CCD camera (12) into a single defocusing intensity image, and recovering the phase of the sample to be detected through a light intensity transmission equation.
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