CN116183568B - High-fidelity reconstruction method and device for three-dimensional structured light illumination super-resolution microscopic imaging - Google Patents
High-fidelity reconstruction method and device for three-dimensional structured light illumination super-resolution microscopic imaging Download PDFInfo
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Abstract
A method for high fidelity reconstruction of three-dimensional structured light illumination super-resolution microscopy imaging, comprising: dividing a beam of parallel light into three beams of parallel light beams with equal intensity and consistent polarization directions, carrying out interference on a sample to form a three-dimensional non-uniform illumination light field, and carrying out frequency shift on a frequency spectrum of the sample after the sample is modulated by the non-uniform illumination light field; receiving fluorescent signals sent by a sample through an objective lens, converging the fluorescent signals to an imaging image surface through a field lens, and receiving the fluorescent signals through a detector to obtain a low-resolution image mixed with high-low frequency information of the sample; the space displacement and the direction of the illumination light field are changed for a plurality of times, and fluorescent signals modulated by the light field are shot again to obtain a series of low-resolution images mixed with high-low frequency information of the sample, and the low-resolution images are used as original images. And performing subsequent image processing on the original image, firstly performing parameter estimation on the initial phase and the spatial frequency of the illumination light field, then separating each frequency band of the sample, and finally combining each frequency spectrum to reconstruct a high-fidelity super-resolution image of the sample.
Description
Technical Field
The invention relates to the field of optical super-resolution microscopic imaging, in particular to a high-fidelity reconstruction method and device for three-dimensional structured light illumination super-resolution microscopic imaging.
Background
The microscope has the advantages of small photodamage, strong specificity, high speed, large visual field, capability of three-dimensional imaging and the like, and is the only technology which can perform three-dimensional rapid imaging on living cells in the prior microscope technology. However, due to the existence of the optical diffraction limit, the transverse resolution of the conventional optical microscopic imaging is generally limited to the half-wavelength level, the axial resolution is lower, and the transverse resolution can only reach about one third of the transverse resolution, so that the requirement of living organelle observation under the sub-hundred nanometer scale in the cell can not be met. During the past two thirty years, various super-resolution imaging techniques, including stimulated radiation loss microscopy (STED), random light reconstruction microscopy (PALM/STORM), and structured light illumination super-resolution microscopy (SIM), have been proposed in succession, which have greatly contributed to the development of life sciences.
Among the many super-resolution microscopy imaging methods, SIM has many natural advantages for live cell imaging: for example, light is lost by high power (about GW/cm compared to STED 2 ) Realizing super resolution, the SIM has lower requirement on the excitation light intensity (at 10W/cm 2 Magnitude) and thus has the intrinsic advantage of low photobleaching and photodamage; it is also unnecessary to acquire thousands of original images to reconstruct a super-resolution image like single-molecule localization microscopy (SMLM), and the SIM only needs 9 frames (2D-SIM) or 15 frames (3D-SIM monolayer) for reconstructing a super-resolution image, so that the method has the intrinsic advantage of rapid imaging, and is particularly suitable for living biological cell imaging.
But since the acquisition of SIM super-resolution images also relies on a subsequent complex image reconstruction process. In the imaging process, the SIM modulates the sample by illuminating the sample with the structured light, and modulates the high-frequency information of the sample which cannot be detected originally into a low pass band by the moire fringe effect, so that the resolution is improved. However, since the detected image is an aliasing of each frequency band, the modulation degree a of the illumination light field is required for accurately separating each frequency band component m Spatial frequency k xy ToPhase and phaseAnd (5) performing accurate estimation. Modulation degree a m The value of (2) affects the ratio of the high frequency components throughout the reconstructed spectrum, ultimately affecting only the contrast of the image and therefore relatively little; the spatial frequency p can be obtained by a frequency spectrum component comparison method and the like, and the estimated precision can meet the requirement; while in solving the individual band components the exact phase is required to be known +.>If the value is not completely achieved when the spectrums are separated, each frequency band contains frequency spectrum components of other frequency bands, and the frequency spectrum residual errors are wrong when the frequency shift is carried out to the position of the frequency shift residual errors, so that artifacts are caused. The traditional method has estimation errors in the phase estimation through the spectrum peak position calculation or through an autocorrelation mode, and particularly when the image contains noise, the phase estimation is wrong, so that the quality of the final image reconstruction is affected.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a high-fidelity reconstruction method and device for three-dimensional structured light illumination super-resolution microscopic imaging.
Aiming at the problems, the invention provides a new phase estimation method in the image reconstruction process, and compared with the traditional phase estimation method, the method can accurately estimate the corresponding initial phase of the illumination light field when five steps of phase shifting are carried out by constructing an intermediate function; in addition, the method can also eliminate the influence caused by inaccurate phase estimation due to the influence of noise in the phase calculation process. By using the accurate phase calculation method provided by the invention, each frequency band component can be accurately separated, the influence of reconstruction artifacts caused by inaccurate phase estimation is eliminated, and finally, the high-fidelity reconstruction of the sample is obtained.
The invention discloses a high-fidelity reconstruction method for three-dimensional structured light illumination super-resolution microscopic imaging, which comprises the following steps of:
(1) Dividing a beam of parallel light into three parallel light beams with equal intensity and consistent polarization direction, converging the three parallel light beams to an entrance pupil surface of an objective lens, changing the three parallel light beams into three parallel light beams after passing through the objective lens, interfering the three parallel light beams on a sample to form an illumination light field illumination fluorescent sample with a periodic structure in the transverse direction and the axial direction, and generating frequency shift on a frequency spectrum after the fluorescent sample receives the modulation of the non-uniform illumination light field; after receiving fluorescent signals sent by a fluorescent sample by an objective lens, converging the fluorescent signals to an imaging image surface through a field lens, and receiving the fluorescent signals by a detector to obtain a low-resolution image mixed with high-low frequency information of the fluorescent sample;
(2) Repeatedly changing the space displacement and the direction of the illumination light field, and shooting fluorescent signals modulated by the stripe intensity again until a layer of corresponding image of the sample is shot; then changing the axial position of the sample, repeatedly shooting sample fluorescent signals under different illumination light field space positions and direction illumination, and obtaining a series of three-dimensional low-resolution images mixed with high-low frequency information of the fluorescent sample as original images;
(3) Performing subsequent image processing on the original image obtained in the step (2), and firstly performing parameter estimation including spatial frequency p of an illumination light field and phaseSecondly, separating each frequency band of the fluorescent sample; and finally, combining each frequency spectrum to reconstruct a high-fidelity super-resolution image of the sample.
Further, the objective lens adopted in the step (1) is an oil immersed objective lens with a numerical aperture NA of more than 1.33.
In the step (1), one of the three beams of light is converged at the center of the entrance pupil of the objective lens, then is perpendicularly incident on the sample after passing through the objective lens, the other two beams of parallel beams are converged at the edge of the entrance pupil of the objective lens, the straight line connected with the two focusing points passes through the center of the entrance pupil, the distance between the two focusing points is close to the diameter of the entrance pupil so as to fully utilize the numerical aperture of the objective lens as much as possible, the two beams of focused light passing through the objective lens are incident on the fluorescent sample at an angle exceeding the critical angle after exiting, and the three beams of light finally interfere on the sample to form a non-uniform illumination light field illumination sample.
Further, the step (2) of generating the original image includes the steps of:
(2.1) the illumination light field in each direction changes the optical path length of the central light path and simultaneously changes the optical path length of one light path in the edge light beam, so that the optical path length of the latter is twice as long as that of the former, the illumination light field moves transversely by one fifth of the period each time, and the axial light field is fixed relative to the objective lens, thereby realizing five-step phase shifting of illumination, as shown in fig. 2;
(2.2) sequentially changing the positions of two focusing light spots of two beams of edge light converged at the entrance pupil of the objective lens, so as to interfere to form illumination light fields corresponding to the transverse direction until the illumination light fields in 3 directions are uniformly generated in one pi azimuth angle, and providing resolution improvement of the two directions;
(2.3) each time when the space displacement or direction of the illumination light field and the axial position of the sample are changed, the fluorescent sample is modulated and then sends out a mixing signal to be received by the detector, so as to form a low resolution image, and 15 x n (n is the number of sample layers) original images are formed as original images for reconstruction of subsequent images;
further, in the step (3), the subsequent image processing process includes the following steps:
(3.1) first performing parameter estimation, including the spatial frequency k of the illumination light field xy And phase ofAs a precondition for recovering a Gao Zhiliang super-resolution image in a subsequent reconstruction process, the method specifically comprises the following sub-steps:
a. establishing an imaging model of an illumination light field in a certain direction during five-step phase shift illumination:
D(r)＝[S(r)·I(r)]*H(r)+D b (r), (1) wherein D (r) is an original image taken by the 3D-SIM, H (r) is a three-dimensional PSF of the system, S (r) is a distribution function of the sample,to illuminate the light field, k xy Is the transverse modulation frequency of the illumination field, r is the spatial coordinates,>is the phase of the illumination field, D b And (r) is background noise, and when the illumination light field axial direction is fixed relative to the objective lens, the following form can be rewritten by the formula (1):
b. transforming the above to Fourier space, and obtaining Fourier spectrum corresponding to the photographed original image at the nth phase shift:
in the method, in the process of the invention,is the OTF for each transverse component m and k is the coordinates in fourier space. As can be seen from the above equation, the spectrum of the obtained original image is aliasing of each frequency band;
c. the spectrum of the original image obtained by five steps of phase shifting is expressed in a matrix form:
wherein the vector isAnd->Respectively defined as->Andand vector->Element->Is thatAnd element M in matrix M nm Is->
d. The spectrum of the original image expressed by the formula (3) is subjected to autocorrelation, so that the transverse modulation frequency k of the illumination light field can be obtained xy ：
Indicating correlation, superscript indicates complex conjugate,/->Will be at k' =mk xy Obtaining the maximum intensity value, finding the corresponding coordinate to obtain mk xy Is a numerical value of (2);
e. an auxiliary function is constructed for recovering the phase of the illumination field, when the phase of each shift of the five steps is considered to be 2 pi/5, the following function is constructed:
the initial phase can thus be precisely determined according to the following formula:
wherein isAs is clear from equations (6) and (7), the background noise present in the original image is eliminated in the phase solving process.
f. Performing step a-e operation on the original image obtained under illumination of all the light spots to obtain modulation frequency k of all the illumination light fields xy And initial phase
(3.2) after the parameter estimation is completed, the image reconstruction is carried out, and the method specifically comprises the following steps:
a. according to the formula (4) and the obtained initial phase parameters of the illumination light field, each frequency band in the original image frequency spectrum is carried outIs expressed as:
wherein M is -1 An inverse matrix of M;
b. the process of frequency band separation in the step a is used for original images shot under the illumination of other two illumination light fields to obtain frequency bands separated in the corresponding directions
c. Finally, each obtained frequency band is subjected to frequency band splicing by utilizing deconvolution, and the frequency band splicing can be expressed as follows:
wherein,frequency spectrum omega corresponding to reconstructed super-resolution image 2 A (k) is the apodization function, the estimated value of the distribution function of the last object +.>By->And performing inverse Fourier transform.
The invention also comprises a high-fidelity reconstruction device for three-dimensional structured light illumination super-resolution microscopic imaging, which comprises a laser 1, a polarization-maintaining single-mode fiber 2, a collimator 3, a first reflecting mirror 4, a first half-wave plate 5, a first polarization beam splitter 6, a second half-wave plate 7, a second polarization beam splitter 8, a second reflecting mirror 9, a third half-wave plate 14, a first scanning galvanometer 15, a first scanning lens 16, a third reflecting mirror 12, a first piezoelectric ceramic 13, a second scanning galvanometer 10, a first scanning lens 11, a first beam combining lens 17, a first polarization rotator 18, a first lens 19, a fourth reflecting mirror 20, a second piezoelectric ceramic 21, a second lens 22, a second polarization rotator 23, a third lens 24, a second beam combining lens 25, a first field lens 26, dichroic mirrors 27, 28, a fluorescent sample 29, a second field lens 30, an EMCCD 31 and a computer 32.
The laser 1 emits linearly polarized light, and the linearly polarized light is collimated by the collimator 3 after being transmitted by the polarization maintaining fiber 2; the reflected light enters a first polarization beam splitter 6 of a first half wave plate 5 after being reflected by a first reflector 4, and the first half wave plate 5 is adjusted to lead the light intensity ratio of the reflected light to the transmitted light to be 1:2, the reflected light constitutes a central light beam for the illumination light field formed by the interference; the transmitted light passes through a first polarization beam splitter 8 of a second half wave plate 7, and the second half wave plate 7 is rotated to make the light intensity ratio of the reflected light to the transmitted light be 1:1, a step of; said transmitted and reflected light constituting an edge beam for the illumination field formed by the interference; the transmitted light is reflected by the second reflecting mirror 9 and enters the third half wave plate 14 and the first scanning galvanometer 15, and the third half wave plate 14 is rotated to change the polarization direction of the beam into vertical polarization; the light beam scanned by the first scanning galvanometer 15 is emitted and enters the first scanning lens 16 to be converged; the light beam reflected by the second polarization beam splitter is reflected by a third reflector 12 on which a first piezoelectric ceramic 13 is arranged and enters a second scanning galvanometer 10 for scanning; the scanning light beams are converged by the second scanning lens 11; the second polarization beam splitter 8 reflects and transmits the light beam to be combined through the first beam combiner 17; changing the polarization directions of the light beams at different scanning positions through a first polarization rotator; the combined beam is collimated by a first lens; the light beam reflected by the first polarization beam splitter 6 is reflected by a third reflector 21 on which a first piezoelectric ceramic 20 is arranged, then converged by a second lens 22, and collimated into parallel light by the third lens after changing the polarization direction by a second polarization rotator 23; the first polarization beam splitter 6 transmits and reflects, and the three light beams transmitted and reflected by the second polarization beam splitter are combined by the second beam combiner; the combined light is converged to an entrance pupil surface of the objective lens through a field lens, wherein two marginal light beam convergence points are positioned at the edge of the entrance pupil of the objective lens, the connecting line of the two marginal light beam convergence points passes through the center of the objective lens, and the central light beam is converged to the center position of the entrance pupil; the edge light beam and the central light beam are collimated by the objective lens and then are incident on the sample to interfere to form an illumination light field, wherein the central light beam is vertically incident on the sample, and the edge light beam is incident at an angle larger than the critical angle of total reflection so as to form an interference field illumination sample with minimum period; by controlling the piezoelectric ceramic 21 and the piezoelectric ceramic 13, the positions of the fourth reflecting mirror 20 and the second reflecting mirror are changed, the optical path of the central beam relative to the first edge beam and the optical path of the second edge beam relative to the first edge beam are changed, and the changed optical path is twice as long as the first edge beam, so that the phase shift of interference fringes is realized; the positions of the three beams of focusing light on the back focal plane of the objective lens are changed by controlling the scanning angles of the first scanning galvanometer 15 and the second scanning galvanometer 10, so that the directions of interference fringes are changed;
the fluorescent sample 29 emits fluorescence after being illuminated by an illumination light field, and the fluorescence is received by the objective lens 28, reflected by the dichroic mirror 27 and imaged by the second field lens 30 on the camera EMCCD 31; the computer 32 controls the movement of the first piezoelectric ceramic 15 and the second piezoelectric ceramic 21, the scanning of the first scanning galvanometer 15 and the second scanning galvanometer 10, and the acquisition of the original image by the EMCCD 31;
image processing is performed to recover super-resolution images of a sample.
By analyzing the technical scheme of the invention, the following steps can be obtained:
(1) As can be seen from formulas (6) and (7), the illumination light field has no approximation in the estimation process, and is an accurate numerical solution;
(2) As can be seen from equations (6) and (7), the background noise is cancelled out by the constructed function during the phase estimation process, thus eliminating the influence of noise on the phase estimation;
(3) Accurate phase solution can obtain accurate frequency band separation, and artifacts caused by reconstruction due to the fact that the frequency band is moved to the wrong position are avoided.
Compared with the prior art, the invention has the following beneficial technical effects:
compared with the traditional phase estimation method, the method can accurately estimate the corresponding initial phase when the illumination light field is subjected to five-step phase shifting; the invention can also eliminate the influence caused by inaccurate phase estimation due to the influence of noise in the phase calculation process; by utilizing the accurate phase calculation method provided by the invention, each frequency band component can be accurately separated, the influence of reconstruction artifacts caused by inaccurate phase estimation is eliminated, and the high-fidelity reconstruction of the sample is obtained; the invention is applicable to an interference type illumination light field formed by three light beams generated by a spatial light modulator or three light beams generated by polarization beam splitter splitting, and is also applicable to an illumination light field formed by digital micromirror through projection.
Drawings
FIG. 1 is a schematic diagram of a super-resolution microscopic imaging device according to an embodiment of the present invention;
FIG. 2 (a) is a schematic diagram of the positions of three beams of light at the entrance pupil plane of the objective lens, and three black dots represent the positions where the three beams of light converge; fig. 2 (b) shows angles at which three beams of light interfere after passing through the objective lens;
FIG. 3 is an axial distribution of corresponding illumination light field during five-step phase shifting according to the present invention, each time a fifth-cycle shift is generated in the transverse direction, and the axial direction is stationary relative to the objective lens;
fig. 4 is a flow chart of the method of the present invention.
Detailed Description
The invention is described in further detail below with reference to the drawings and the specific examples.
Example 1
The method for high-fidelity reconstruction of three-dimensional structured light illumination super-resolution microscopic imaging provided by the embodiment comprises the following steps:
(1) Dividing a beam of parallel light into three parallel light beams with equal intensity and consistent polarization direction, converging the three parallel light beams to an entrance pupil surface of an objective lens, changing the three parallel light beams into three parallel light beams after passing through the objective lens, interfering the three parallel light beams on a sample to form an illumination light field illumination fluorescent sample with a periodic structure in the transverse direction and the axial direction, and generating frequency shift on a frequency spectrum after the fluorescent sample receives the modulation of the non-uniform illumination light field; after receiving fluorescent signals emitted by a fluorescent sample, the objective lens converges to an imaging image surface through a field lens, and a detector is used for receiving the fluorescent signals to obtain a low-resolution image mixed with high-low frequency information of the fluorescent sample.
The method comprises the steps that an objective lens is used, the numerical aperture NA of the objective lens is larger than 1.33, one of three light beams is converged at the center of an entrance pupil of the objective lens and then vertically enters a sample after passing through the objective lens, the other two parallel light beams are converged at the edge of the entrance pupil of the objective lens, the straight line connected with two focusing points passes through the center of the entrance pupil, the distance between the two focusing points is close to the diameter of the entrance pupil so as to fully utilize the numerical aperture of the objective lens as far as possible, the two light beams passing through the objective lens are emitted and then enter a fluorescent sample at an angle exceeding a critical angle, and the three light beams finally interfere on the sample to form a non-uniform illumination light field illumination sample.
(2) Repeatedly changing the space displacement and the direction of the illumination light field, and shooting fluorescent signals modulated by the stripe intensity again until a layer of corresponding image of the sample is shot; then changing the axial position of the sample, repeatedly shooting sample fluorescent signals under different illumination light field space positions and direction illumination, and obtaining a series of three-dimensional low-resolution images mixed with high-low frequency information of the fluorescent sample as original images;
the steps for generating the original image are as follows:
(2.1) the illumination light field in each direction changes the optical path length of the central light path and simultaneously changes the optical path length of one light path in the edge light beam, so that the optical path length of the latter is twice as long as that of the former, the illumination light field moves transversely by one fifth of the period each time, and the axial light field is fixed relative to the objective lens, thereby realizing five-step phase shifting of illumination, as shown in fig. 2;
(2.2) sequentially changing the positions of two focusing light spots of two beams of edge light converged at the entrance pupil of the objective lens, so as to interfere to form illumination light fields corresponding to the transverse direction until the illumination light fields in 3 directions are uniformly generated in one pi azimuth angle, and providing resolution improvement of the two directions;
and (2.3) each time when the spatial displacement or direction of the illumination light field is changed, the fluorescent sample is modulated and then sends out a mixing signal to be received by the detector, so that a low-resolution image is formed, and 15 times n (n is the number of sample layers) original images are formed as the original images for reconstruction of subsequent images.
(3) Performing subsequent image processing on the original image obtained in the step (2), and firstly performing parameter estimation including spatial frequency p of an illumination light field and phaseSecondly, separating each frequency band of the fluorescent sample; and finally, combining each frequency spectrum to reconstruct a high-fidelity super-resolution image of the sample.
The image processing procedure is as shown in fig. 4, and includes the following steps:
(3.1) first performing parameter estimation, including the spatial frequency k of the illumination light field xy And phase ofAs a precondition for recovering a Gao Zhiliang super-resolution image in a subsequent reconstruction process, the method specifically comprises the following sub-steps:
a. establishing an imaging model of an illumination light field in a certain direction during five-step phase shift illumination:
D(r)＝[S(r)·I(r)]*H(r)+D b (r)， (1)
wherein D (r) is an original image shot by the 3D-SIM, H (r) is a three-dimensional PSF of the system, S (r) is a distribution function of the sample,to illuminate the light field, k xy Is the transverse modulation frequency of the illumination field, r is the spatial coordinates,>is the phase of the illumination field, D b And (r) is background noise, and when the illumination light field axial direction is fixed relative to the objective lens, the following form can be rewritten by the formula (1):
b. transforming the above to Fourier space, and obtaining Fourier spectrum corresponding to the photographed original image at the nth phase shift:
in the method, in the process of the invention,is the OTF for each transverse component m and k is the coordinates in fourier space. As can be seen from the above equation, the spectrum of the obtained original image is aliasing of each frequency band;
c. the spectrum of the original image obtained by five steps of phase shifting is expressed in a matrix form:
wherein,(Vector)and->Respectively defined as->Andand vector->Element->Is thatAnd element M in matrix M nm Is->
d. The spectrum of the original image expressed by the formula (3) is subjected to autocorrelation, so that the transverse modulation frequency k of the illumination light field can be obtained xy ：
Indicating correlation, superscript indicates complex conjugate,/->Will be at k' =mk xy Obtaining the maximum intensity value, finding the corresponding coordinate to obtain mk xy Is a numerical value of (2);
e. an auxiliary function is constructed for recovering the phase of the illumination field, when the phase of each shift of the five steps is considered to be 2 pi/5, the following function is constructed:
the initial phase can thus be precisely determined according to the following formula:
wherein isAs is clear from equations (6) and (7), the background noise present in the original image is eliminated in the phase solving process.
f. Performing step a-e operation on the original image obtained under illumination of all the light spots to obtain modulation frequency k of all the illumination light fields xy And initial phase
(3.2) after the illumination light field parameter estimation is completed, carrying out image reconstruction, and specifically comprising the following substeps:
a. according to the formula (4) and the obtained initial phase parameters of the illumination light field, each frequency band in the original image frequency spectrum is carried outIs expressed as:
wherein M is -1 An inverse matrix of M;
b. the process of frequency band separation in the step (3.1) and the step (3.2) is used for shooting under the illumination of other two illumination light fieldsOriginal image, obtaining frequency bands separated in corresponding directions
c. Finally, each obtained frequency band is subjected to frequency band splicing by utilizing deconvolution, and the frequency band splicing can be expressed as follows:
wherein,frequency spectrum omega corresponding to reconstructed super-resolution image 2 A (k) is the apodization function, the estimated value of the distribution function of the last object +.>By->And performing inverse Fourier transform.
Example 2
A three-dimensional structured light illuminated super-resolution microscopy imaged high-fidelity reconstruction device is shown in fig. 1, but is not limited to the device shown in fig. 1.
The device of this embodiment includes a laser 1, a polarization-maintaining single-mode fiber 2, a collimator 3, a first reflecting mirror 4, a first half-wave plate 5, a first polarization beam splitter 6, a second half-wave plate 7, a second polarization beam splitter 8, a second reflecting mirror 9, a third half-wave plate 14, a first scanning galvanometer 15, a first scanning lens 16, a third reflecting mirror 12, a first piezoelectric ceramic 13, a second scanning galvanometer 10, a first scanning lens 11, a first beam combiner 17, a first polarization rotator 18, a first lens 19, a fourth reflecting mirror 20, a second piezoelectric ceramic 21, a second lens 22, a second polarization rotator 23, a third lens 24, a second beam combiner 25, a first field lens 26, a dichroic mirror 27, an objective lens 28, a fluorescent sample 29, a second field lens 30, an emccd 31, and a computer 32.
The three-dimensional structured light illumination super-resolution microscopic imaging process realized by adopting the device shown in fig. 1 is as follows:
(1) The laser 1 emits linearly polarized light, and the linearly polarized light is collimated by the collimator 3 after being transmitted by the polarization maintaining fiber 2; the reflected light enters a first polarization beam splitter 6 of a first half wave plate 5 after being reflected by a first reflector 4, and the first half wave plate 5 is adjusted to lead the light intensity ratio of the reflected light to the transmitted light to be 1:2, the reflected light constitutes a central light beam for the illumination light field formed by the interference; the transmitted light passes through a first polarization beam splitter 8 of a second half wave plate 7, and the second half wave plate 7 is rotated to make the light intensity ratio of the reflected light to the transmitted light be 1:1, a step of; said transmitted and reflected light constituting an edge beam for the illumination field formed by the interference; the transmitted light is reflected by the second reflecting mirror 9 and enters the third half wave plate 14 and the first scanning galvanometer 15, and the third half wave plate 14 is rotated to change the polarization direction of the beam into vertical polarization; the light beam scanned by the first scanning galvanometer 15 is emitted and enters the first scanning lens 16 to be converged; the light beam reflected by the second polarization beam splitter is reflected by a third reflector 12 on which a first piezoelectric ceramic 13 is arranged and enters a second scanning galvanometer 10 for scanning; the scanning light beams are converged by the second scanning lens 11; the second polarization beam splitter 8 reflects and transmits the light beam to be combined through the first beam combiner 17; changing the polarization directions of the light beams at different scanning positions through a first polarization rotator; the combined beam is collimated by a first lens; the light beam reflected by the first polarization beam splitter 6 is reflected by a third reflector 21 on which a first piezoelectric ceramic 20 is arranged, then converged by a second lens 22, and collimated into parallel light by the third lens after changing the polarization direction by a second polarization rotator 23; the first polarization beam splitter 6 transmits and reflects, and the three light beams transmitted and reflected by the second polarization beam splitter are combined by the second beam combiner; the combined light is converged to an entrance pupil plane of the objective lens through a field lens, wherein two edge light beam convergence points are positioned at the edge of the entrance pupil of the objective lens, a connecting line of the two edge light beam convergence points passes through the center of the objective lens, and a central light beam is converged to the center position of the entrance pupil, as shown in fig. 2 (a); the edge light beam and the central light beam are collimated by the objective lens and then are incident on the sample to interfere to form an illumination light field, wherein the central light beam is vertically incident on the sample, and the edge light beam is incident at a critical angle greater than total reflection, as shown in fig. 2 (b), so as to form an interference field with minimum period to illuminate the sample; by controlling the piezoelectric ceramic 21 and the piezoelectric ceramic 13, the positions of the fourth reflecting mirror 20 and the second reflecting mirror are changed, so that the optical path length of the central beam relative to the first edge beam and the optical path length of the second edge beam relative to the first edge beam are changed, and the changed optical path length is twice as that of the first edge beam, so that the phase shift of interference fringes is realized, as shown in fig. 3; by controlling the scanning angles of the first scanning galvanometer 15 and the second scanning galvanometer 10, the positions of the three beams of focused light on the back focal plane of the objective lens are changed, thereby changing the directions of interference fringes, as shown in fig. 2 (a);
(2) The fluorescent sample 29 emits fluorescence after being illuminated by an illumination light field, and the fluorescence is received by the objective lens 28, reflected by the dichroic mirror 27 and imaged by the second field lens 30 on the camera EMCCD 31; the computer 32 controls the movement of the first piezoelectric ceramic 15 and the second piezoelectric ceramic 21, the scanning of the first scanning galvanometer 15 and the second scanning galvanometer 10, and the acquisition of the original image by the EMCCD 31;
(3) Image processing is performed to recover a three-dimensional super-resolution image of a sample in the steps shown in fig. 4:
1) Parameter estimation
a. Establishing an imaging model of an illumination light field in a certain direction during five-step phase shift illumination:
D(r)＝[S(r)·I(r)]*H(r)+D b (r), (1) wherein D (r) is an original image taken by the 3D-SIM, H (r) is a three-dimensional PSF of the system, S (r) is a distribution function of the sample,to illuminate the light field, k xy Is the transverse modulation frequency of the illumination field, r is the spatial coordinates,>is the phase of the illumination field, D b (r) is background noise, equation (1) can be applied when the illumination field is axially fixed relative to the objective lensTo be rewritten into the following form:
b. transforming the above to Fourier space, and obtaining Fourier spectrum corresponding to the photographed original image at the nth phase shift:
in the method, in the process of the invention,is the OTF for each transverse component m and k is the coordinates in fourier space. As can be seen from the above equation, the spectrum of the obtained original image is aliasing of each frequency band;
c. the spectrum of the original image obtained by five steps of phase shifting is expressed in a matrix form:
wherein the vector isAnd->Respectively defined as->Andand vector->Element->Is thatAnd element M in matrix M nm Is->
d. The spectrum of the original image expressed by the formula (3) is subjected to autocorrelation, so that the transverse modulation frequency k of the illumination light field can be obtained xy ：
Indicating correlation, superscript indicates complex conjugate,/->Will be at k' =mk xy Obtaining the maximum intensity value, finding the corresponding coordinate to obtain mk xy Is a numerical value of (2);
e. an auxiliary function is constructed for recovering the phase of the illumination field, when the phase of each shift of the five steps is considered to be 2 pi/5, the following function is constructed:
the initial phase can thus be precisely determined according to the following formula:
wherein isReal numbers, as can be seen from equations (6) and (7), appear in the original imageBackground noise is eliminated during this phase solving process.
f. Performing step a-e operation on the original image obtained under illumination of all the light spots to obtain modulation frequency k of all the illumination light fields xy And initial phase
2) Image reconstruction
a. According to the formula (4) and the obtained initial phase parameters of the illumination light field, each frequency band in the original image frequency spectrum is carried outIs expressed as:
wherein M is -1 An inverse matrix of M;
b. the process of frequency band separation in the step 1) and the step 2) a is used for the original image shot under the illumination of the illumination light fields of other two directions to obtain frequency bands separated in the corresponding directions
c. Finally, each obtained frequency band is subjected to frequency band splicing by utilizing wiener deconvolution, and the frequency band splicing can be expressed as follows:
wherein,frequency spectrum omega corresponding to reconstructed super-resolution image 2 A (k) is the apodization function, the estimated value of the distribution function of the last object +.>By->And performing inverse Fourier transform.
The foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (7)
1. The high-fidelity reconstruction method for three-dimensional structured light illumination super-resolution microscopic imaging is characterized by comprising the following steps of:
(1) Dividing a beam of parallel light into three parallel light beams with equal intensity and consistent polarization direction, converging the three parallel light beams to an entrance pupil surface of an objective lens, changing the three parallel light beams into three parallel light beams after passing through the objective lens, and interfering the three parallel light beams on a sample to form an illumination light field illumination fluorescent sample with a periodic structure in the transverse direction and the axial direction, wherein the frequency spectrum of the fluorescent sample is shifted after the fluorescent sample is modulated by a non-uniform illumination light field; after receiving fluorescent signals sent by a fluorescent sample by an objective lens, converging the fluorescent signals to an imaging image surface through a field lens, and receiving the fluorescent signals by a detector to obtain a low-resolution image mixed with high-low frequency information of the fluorescent sample;
(2) Repeatedly changing the space displacement and the direction of the illumination light field, and shooting fluorescent signals modulated by the stripe intensity again until a layer of corresponding image of the sample is shot; then changing the axial position of the sample, repeatedly shooting sample fluorescent signals under different illumination light field space positions and direction illumination, and obtaining a series of three-dimensional low-resolution images mixed with high-low frequency information of the fluorescent sample as original images; the steps for generating the original image are as follows:
(2.1) changing the optical path of the central optical path of the illumination light field in each direction, and simultaneously changing the optical path of one path of light in the edge light beam, so that the optical path of the latter is twice as long as that of the former, the illumination light field transversely moves by one fifth of the period each time, and the axial light field is fixed relative to the objective lens, thereby realizing five-step phase shifting of illumination;
(2.2) sequentially changing the positions of two focusing light spots of two beams of edge light converged at the entrance pupil of the objective lens, so as to interfere to form illumination light fields corresponding to the transverse direction until the illumination light fields in 3 directions are uniformly generated in one pi azimuth angle, and providing resolution improvement of the two directions;
(2.3) each time when the space displacement or direction of the illumination light field is changed, the fluorescent sample is modulated and then sends out a mixing signal to be received by the detector, so as to form a low-resolution image;
(2.4) after shooting one layer of the sample, moving the sample to the next layer, repeating the steps (2.1) - (2.3), and shooting low-resolution images corresponding to samples of different layers;
(3) Performing subsequent image processing on the original image obtained in the step (2), and firstly performing parameter estimation including spatial frequency p of an illumination light field and phaseSecondly, separating each frequency band of the fluorescent sample; finally, each frequency spectrum is combined and reconstructed to obtain a high-fidelity super-resolution image of the sample; the subsequent image processing process includes:
(3.1) first performing parameter estimation, including the spatial frequency k of the illumination light field xy And phase ofAs a precondition for recovering a Gao Zhiliang super-resolution image in a subsequent reconstruction process, the method specifically includes:
a. establishing an imaging model of an illumination light field in a certain direction during five-step phase shift illumination:
D(r)＝[S(r)·I(r)]*H(r)+D b (r)， (1)
wherein D (r) is an original image shot by the 3D-SIM, H (r) is a three-dimensional PSF of the system, S (r) is a distribution function of the sample,m=2 is the illumination light field, k xy Is the transverse modulation frequency of the illumination field, r is the spatial coordinates,>is the phase of the illumination field, D b And (r) is background noise, and when the illumination light field axial direction is fixed relative to the objective lens, the following form can be rewritten by the formula (1):
b. transforming the above to Fourier space, and obtaining Fourier spectrum corresponding to the photographed original image at the nth phase shift:
in the method, in the process of the invention,is the OTF corresponding to each transverse component m, k is the coordinates in fourier space; as can be seen from the above equation, the spectrum of the obtained original image is aliasing of each frequency band;
c. the spectrum of the original image obtained by five steps of phase shifting is expressed in a matrix form:
wherein the vector isAnd->Respectively defined as->Andand vector->Element->Is thatAnd element M in matrix M nm Is->
d. The spectrum of the original image expressed by the formula (3) is subjected to autocorrelation, so that the transverse modulation frequency k of the illumination light field can be obtained xy ：
Indicating correlation, superscript indicates complex conjugate,/->Will be at k' =mk xy Obtaining the maximum intensity value, finding the corresponding coordinate to obtain mk xy Is a numerical value of (2);
e. an auxiliary function is constructed for recovering the phase of the illumination field, when the phase of each shift of the five steps is considered to be 2 pi/5, the following function is constructed:
the initial phase can thus be precisely determined according to the following formula:
wherein isReal numbers, as can be seen from equations (6) and (7), background noise appearing in the original image is eliminated in the phase solving process;
f. performing step a-e operation on the original image obtained under illumination of all the light spots to obtain modulation frequency k of all the illumination light fields xy And initial phase
(3.2) performing subsequent image reconstruction using the parameters estimated in step (3.1).
2. The method for high-fidelity reconstruction of three-dimensional structured light illumination super-resolution microscopic imaging according to claim 1, wherein the objective lens adopted in the step (1) is an oil-immersed objective lens with a numerical aperture NA larger than 1.33.
3. The method for high-fidelity reconstruction of three-dimensional structured light illumination super-resolution microscopic imaging according to claim 1, wherein in the step (1), one of three beams of light is converged at the center of an entrance pupil of an objective lens, and then vertically enters a sample after passing through the objective lens, the other two beams of parallel beams are converged at the edge of the entrance pupil of the objective lens, a straight line connecting the two focusing points passes through the center of the entrance pupil, the distance between the two focusing points is close to the diameter of the entrance pupil to fully utilize the numerical aperture of the objective lens as much as possible, the two beams of focused light passing through the objective lens enter a fluorescent sample at an angle exceeding a critical angle after exiting, and the three beams of light finally interfere on the sample to form a non-uniform illumination light field illumination sample.
4. The method of claim 1, wherein in the step (2.4), 15 x n is formed in a conformal manner, the original image is used as the original image for the subsequent image reconstruction, and n is the number of sample layers.
5. The method of high fidelity reconstruction of three-dimensional structured light illumination super-resolution microscopic imaging according to claim 1, wherein the image reconstruction of step (3.2) specifically comprises:
a. according to the formula (4) and the obtained initial phase parameters of the illumination light field, each frequency band in the original image frequency spectrum is carried outIs expressed as:
wherein M is -1 An inverse matrix of M;
b. the process of frequency band separation in the step a is used for original images shot under the illumination of other two illumination light fields to obtain frequency bands separated in the corresponding directions
c. Finally, each obtained frequency band is subjected to frequency band splicing by utilizing wiener deconvolution, and the frequency band splicing can be expressed as follows:
wherein,frequency spectrum omega corresponding to reconstructed super-resolution image 2 For the wiener parameters A (k) is the apodization function, finally the estimated value of the distribution function of the object +.>By->Make Fu LiAnd (5) carrying out leaf inverse transformation.
6. Apparatus for carrying out the method of high fidelity reconstruction of a three-dimensional structured light illuminated super-resolution microimage as in one of claims 1-5, characterized in that: the polarization-maintaining single-mode fiber (2), a collimator (3), a first reflecting mirror (4), a first half-wave plate (5), a first polarization beam splitter (6), a second half-wave plate (7), a second polarization beam splitter (8), a second reflecting mirror (9), a third half-wave plate (14), a first scanning galvanometer (15), a first scanning lens (16), a third reflecting mirror (12), a first piezoelectric ceramic (13), a second scanning galvanometer (10), a first scanning lens (11), a first beam combining mirror (17), a first polarization rotator (18), a first lens (19), a fourth reflecting mirror (20), a second piezoelectric ceramic (21), a second lens (22), a second polarization rotator (23), a third lens (24), a second beam combining mirror (25), a first field lens (26), a dichroic mirror (27), an objective lens (28), a fluorescent sample (29), a second field lens (30), an EMCCD (31) and a computer (32).
7. The apparatus of claim 6, wherein:
the laser (1) emits linearly polarized light, and the linearly polarized light is collimated by the collimator (3) after being transmitted by the polarization maintaining fiber (2); the light enters a first polarization beam splitter (6) of a first half wave plate (5) after being reflected by a first reflector (4), and the first half wave plate (5) is regulated to enable the light intensity ratio of reflected light to transmitted light to be 1:2, the reflected light constitutes a central light beam for the illumination light field formed by the interference; the transmitted light passes through a second half wave plate (7) and a first polarization beam splitter (8), and the second half wave plate (7) is rotated to enable the light intensity ratio of the reflected light to the transmitted light to be 1:1, a step of; said transmitted and reflected light constituting an edge beam for the illumination field formed by the interference; the transmitted light is reflected by the second reflecting mirror (9) and enters the third half wave plate (14) and the first scanning vibrating mirror (15), and the third half wave plate (14) is rotated to enable the polarization direction of the beam to be changed into vertical polarization; the light beam scanned by the first scanning galvanometer (15) is emitted to enter the first scanning lens (16) to be converged; the light beam reflected by the second polarization spectroscope is reflected by a third reflecting mirror (12) on which a first piezoelectric ceramic (13) is arranged and enters a second scanning galvanometer (10) for scanning; the scanning light beams are converged through a second scanning lens (11); the second polarization spectroscope (8) reflects and transmits the light beams to be combined through the first beam combiner (17); changing the polarization directions of the light beams at different scanning positions through a first polarization rotator; the combined beam is collimated by a first lens; the light beams reflected by the first polarization spectroscope (6) are reflected by a third reflector (21) provided with a first piezoelectric ceramic (20) and then converged by a second lens 22), and the polarization direction of the light beams is changed by a second polarization rotator (23) and then collimated into parallel light by the third lens; the first polarization beam splitter (6) transmits and reflects, and three light beams transmitted and reflected by the second polarization beam splitter are combined by the second beam combiner; the combined light is converged to an entrance pupil surface of the objective lens through a field lens, wherein two marginal light beam convergence points are positioned at the edge of the entrance pupil of the objective lens, the connecting line of the two marginal light beam convergence points passes through the center of the objective lens, and the central light beam is converged to the center position of the entrance pupil; the edge light beam and the central light beam are collimated by the objective lens and then are incident on the sample to interfere to form an illumination light field, wherein the central light beam is vertically incident on the sample, and the edge light beam is incident at an angle larger than the critical angle of total reflection so as to form an interference field illumination sample with minimum period; the positions of the fourth reflecting mirror (20) and the second reflecting mirror are changed by controlling the piezoelectric ceramic (21) and the piezoelectric ceramic (13), so that the optical path of the central beam relative to the first edge beam and the optical path of the second edge beam relative to the first edge beam are changed, and the changed optical path is twice as long as the first edge beam, so that the phase shift of interference fringes is realized; the position of the three beams of focusing light on the back focal plane of the objective lens is changed by controlling the scanning angles of the first scanning galvanometer (15) and the second scanning galvanometer (10), so that the direction of interference fringes is changed;
the fluorescent sample (29) emits fluorescence after being illuminated by an illumination light field, the fluorescence is received by the objective lens (28), reflected by the dichroic mirror (27) and imaged on the camera EMCCD (31) by the second field lens (30); the computer (32) controls the movement of the first piezoelectric ceramic (15) and the second piezoelectric ceramic (21), the scanning of the first scanning galvanometer (15) and the second scanning galvanometer (10) and the acquisition of an original image by the EMCCD (31);
image processing is performed to recover super-resolution images of a sample.
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