Structured illumination microscopy with four-beam interference-based super-resolution

Abstract

The application discloses a kind of structure light illumination super-resolution microscopic imaging methods based on four-beam interference.The method uses four-beam coherent interference illumination design, and combines the composite frequency domain filtering strategy based on three-dimensional OTF physical constraint, under the premise that no need to carry out any hardware modification to the light path of traditional interference structure light microscope (SIM) system, first realize the lateral two times super-resolution improvement and excellent optical sectioning ability, effectively overcome the off-focus background interference problem faced in thick sample imaging in the prior art.In addition, the application introduces an illumination parameter estimation algorithm based on principal component analysis (PCA), while significantly reducing the computational complexity, further improves the accuracy and stability of parameter estimation.Experimental results show that the method can high-resolution, high-fidelity, high-robustness and high-efficiency imaging for thick living cell samples, break through the limitation that traditional two-dimensional super-resolution SIM is mainly suitable for thin living cell imaging, has wide application potential and practical value.

Description

Technical Field

[0001] This invention belongs to the field of super-resolution fluorescence microscopy imaging technology, specifically a structured light illumination super-resolution microscopy imaging method based on four-beam interference, which is used to achieve high-resolution and high-optical-section performance of live cells in thick samples and complex imaging scenarios. Background Technology

[0002] Structured illumination microscopy (SIM), a typical fluorescence super-resolution imaging method, introduces spatially modulated illumination fringes on the sample surface to shift high-frequency information beyond the system's cutoff frequency to the detectable frequency band. While compatible with conventional fluorescent probes, it can achieve dynamic observation of live cells at approximately twice the diffraction limit, making it an important tool for studying subcellular processes. Classical two-dimensional super-resolution SIM (2D SR-SIM) uses high-frequency grating stripe illumination, improving lateral resolution through spectral shifting. However, its optical transfer function (OTF) suffers from a missing cone effect in the axial direction, resulting in a lack of axial frequency support regions, significant defocus background interference, and insufficient fidelity of three-dimensional structural information, limiting its application in thick samples or strongly scattering biological tissues.

[0003] To overcome the aforementioned shortcomings, existing technologies propose three-dimensional SIM (3D-SIM), which generates a three-dimensional modulated illumination pattern through the interference of three coherent beams, expanding axial frequency support to simultaneously improve lateral and axial resolution. However, 3D-SIM requires the acquisition of multiple image stacks, placing extremely high demands on the stability and alignment accuracy of the interference optical path, leading to a significant increase in system complexity, light dose, and data processing overhead, making it difficult to simultaneously meet the requirements of high temporal resolution and low phototoxicity. To enhance optical slicing capabilities while retaining the lateral super-resolution advantages of SR-SIM, existing technologies propose weighted linear reconstruction structured illumination microscopy (WLR-SIM). This type of method, based on the frequency domain reconstruction of 2D SR-SIM, introduces weights based on modulation density or spatial frequency to weight and synthesize different order spectra to suppress defocus background and obtain a certain optical slicing capability. However, due to the weakening of high-frequency information weights, the lateral resolution improvement of WLR-SIM is usually significantly lower than the nearly two-fold diffraction-limited improvement achieved by standard SR-SIM, making it difficult to simultaneously achieve significant lateral super-resolution and strong optical slicing capabilities.

[0004] In addition, image stack-based deconvolution algorithms and statistical prior computational slicing methods (such as Dark-SIM) have also been attempted for application in SIM imaging. The former reduces blurring by modeling the defocus contribution, but requires multi-layer 3D data acquisition, and its computational complexity and phototoxicity burden are comparable to 3D-SIM; the latter relies on empirical priors such as dark channels for frequency domain separation. Although it does not require hardware modification, it is prone to accidentally suppressing weak signals in high-density labeled samples, resulting in edge blurring and loss of detail, and it cannot compensate for the loss of axial information caused by the OTF cone effect.

[0005] In summary, existing super-resolution imaging (SIM) technologies face the following bottlenecks in the application of thick samples and complex cellular environments: traditional 2D SR-SIM is limited by the cone-shaped defect and defocused background interference, resulting in insufficient accuracy in 3D structure reconstruction; while 3D-SIM and improved schemes can improve axial performance, their high system complexity and phototoxicity make them difficult to meet the needs of dynamic observation of live cells; integrated optical slicing functions or post-processing-based methods suffer from problems such as lateral resolution loss, weak signal suppression, or excessive computational overhead. Therefore, without requiring complex hardware modifications to existing SIM systems, how to simultaneously achieve nearly twice the lateral super-resolution improvement and efficient optical slicing capabilities, and obtain high-fidelity, robust real-time super-resolution images of live cells in thick samples, remains a pressing technical challenge in this field. Summary of the Invention

[0006] The purpose of this invention is to provide a structured light illumination super-resolution microscopy imaging method based on four-beam interference, which can simultaneously achieve a nearly two-fold increase in lateral super-resolution and a synergistic enhancement of efficient optical slicing capabilities in thick biological cell samples and complex imaging environments without requiring complex hardware modifications to existing SIM systems. This results in high-fidelity, high-robustness, and efficient real-time observation of living thick cells.

[0007] The technical solution to achieve the objective of this invention is: a structured light illumination super-resolution microscopic imaging method based on four-beam interference, the steps of which are as follows:

[0008] Step 1: Modulate composite structured light illumination of the sample using four-beam interference;

[0009] Step 2: Obtain nine frames of original lighting images;

[0010] Step 3: Introduce principal component analysis algorithm to accurately estimate lighting parameters;

[0011] Step 4: Use an asynchronous phase shift matrix to separate the 0th, ±1st, and ±2nd order spectra;

[0012] Step 5: Construct a filter based on 3D OTF physical constraints to filter the high and low frequency spectra;

[0013] Step 6: Fuse the filtered high and low frequency components to reconstruct the super-resolution image.

[0014] Compared with existing technologies, the significant advantages of this invention are as follows: The structured light illumination super-resolution microscopy imaging method based on four-beam interferometry proposed in this invention achieves super-resolution reconstruction in thick biological cell samples and complex imaging environments while simultaneously achieving nearly two times the lateral super-resolution and excellent optical slicing capabilities. This is achieved through the lateral and axial frequency support of the four-beam coherent interferometric extension system OTF, combined with a composite frequency domain filtering strategy based on three-dimensional OTF physical constraints. This significantly suppresses defocus background and reconstruction artifacts, and improves the fidelity and contrast of three-dimensional structural information. This method maintains the data acquisition efficiency and live cell compatibility of traditional 2D-SIM, and has the ability to achieve high-resolution, robust, and efficient real-time observation of thick living cells. It can provide a stable and reliable imaging method for studying life processes such as cytoskeleton reconstruction, organelle interactions, and signal transduction at the nanoscale, and is expected to be widely promoted in life sciences, medical research, and related biological imaging applications. The invention will be further described in detail below with reference to the accompanying drawings. Attached Figure Description

[0015] Figure 1 This is a flowchart of the present invention.

[0016] Figure 2 The results are obtained by super-resolution reconstruction of fixed BPAE cell samples (DAPI-labeled cell nuclei, AlexaFluor™ 568-labeled actin, and MitoTracker™ Green FM-labeled mitochondria) and fixed autofluorescent Ascaris samples using the present invention and conventional methods.

[0017] Figure 3 This invention provides real-time super-resolution reconstruction results of mitochondria in living human myofibroblasts under complex high-glucose conditions at different time points. Detailed Implementation

[0018] A structured light illumination super-resolution microscopy imaging method based on four-beam interferometry extends the optical transfer function frequency support of existing structured light microscopy imaging systems through four-beam interferometry, solving the problem of balancing resolution improvement and optical slicing capability in traditional SIM systems for thick biological samples and complex imaging environments. Furthermore, to improve the estimation accuracy of illumination parameters and address computational time consumption, a principal component analysis (PCA) algorithm is introduced. By employing a dual-window mask operator, PCA is performed on the filtered phasor matrix, significantly reducing computational load while filtering out substantial noise. To further improve imaging accuracy, a frequency-domain composite filtering strategy is introduced. A filtering algorithm based on three-dimensional OTF physical constraints filters high-frequency and low-frequency components separately, significantly improving the quality of the super-resolution image, suppressing defocused backgrounds and reconstruction artifacts, and enhancing image fidelity and contrast. The flowchart of this invention is shown below. Figure 1 As shown, the specific steps are as follows:

[0019] Step 1: Using a structured light-illuminated micro-imaging system, a composite fringe structured light source, formed by the superposition of horizontal and vertical interference fringes, is employed as the illumination source. A nine-step asynchronous phase-shift strategy is used to control the phase change of the illumination fringes, increasing the phase step size, improving modulation accuracy, and reducing the number of image acquisitions. A precision slit mask is used to perform spectral filtering of the illumination field in the Fourier plane, retaining only the ±1st order diffraction components in the orthogonal directions and shielding the 0th order diffraction light. Finally, a four-beam interference illumination field is formed on the sample plane, achieving composite structured light illumination modulation. The composite illumination field is formed by four coherent interference beams and can be expressed by the following formula:

[0020] (1)

[0021] in, The intensity distribution of the composite lighting light field. The spatial position vector of the image plane. and These represent the spatial wave vectors of the horizontal and vertical stripes, respectively. and These represent the original phases of the horizontal and vertical stripes, respectively; The subscripts 1, 2, 3, and 4 represent the additional initial phase introduced, and their subscripts 1, 2, 3, and 4 correspond to four different interference directions, respectively. This indicates the modulation scheme corresponding to the four interference directions mentioned above.

[0022] When using a nine-step asynchronous phase shift strategy to control the phase change of illumination stripes, the specific phase shift configuration is as follows:

[0023]

[0024] Frame1-9 represent the frame numbers for acquiring the original lighting images. and These represent the original phases of the horizontal and vertical stripes, respectively.

[0025] Step 2: The fluorescence signal emitted by the sample modulated by the composite structured light is detected and collected using an sCMOS camera. To ensure time synchronization between the SLM and image acquisition, the camera exposure is precisely controlled by the SLM controller. The nine acquired raw illumination images are represented in the frequency domain as follows:

[0026] (2)

[0027] in, The frequency domain representation of fluorescence intensity detected by the sCMOS camera, with its subscript... Represents the frame number of the illumination image, symbol Indicates Fourier transform, It is a spatial frequency vector; Let be the optical transfer function of the system; This represents the original spectrum of the sample. and These represent the high-frequency sample spectral components that have been shifted into the system bandwidth after first-level and second-level modulation, respectively. and These represent the spatial wave vectors of the horizontal and vertical stripes, respectively. and These represent the original phases of the horizontal and vertical stripes, respectively; The subscripts 1, 2, 3, and 4 represent the additional initial phase introduced, and their subscripts 1, 2, 3, and 4 correspond to four different interference directions, respectively. This indicates the modulation scheme corresponding to the four interference directions mentioned above.

[0028] Step 3: Introduce principal component analysis algorithm to accurately estimate lighting parameters, specifically:

[0029] Step 3.1: Frequency domain representation of the nine original illumination images obtained in Step 2 Linear calculations were performed to initially separate the spectra and extract the zero-order spectrum of the sample. and +1 level spectrum , can be represented as:

[0030] (3)

[0031] (4)

[0032] Furthermore, the +1 level spectrum Perform integer pixel offset compensation, specifically as follows:

[0033] (5)

[0034] in, To calibrate the obtained integer pixel wave vector, Let be the subpixel wave vector to be estimated.

[0035] Step 3.2: Based on the sample 0th-order spectrum obtained in Step 3.1 and +1 level spectrum Construct the heterospectral autocorrelation expression as follows:

[0036] (6)

[0037] in, This is the inverse Fourier transform operation. This represents the spatial domain image of the separated 0th-order spectrum. This represents the spatial domain image of the separated +1 order spectrum. It is the spatial position vector of the image plane.

[0038] Step 3.3: Extract the phase matrix using the heterospectral autocorrelation expression from Step 3.2, specifically as follows:

[0039] (7)

[0040] Where exp is an exponential function with base e. This is a function that returns the phase.

[0041] Step 3.4: To improve the computational efficiency and robustness of the algorithm when processing large-scale data, a dual-window mask operator is used. Pre-filtering is performed to extract the illumination vector factors. The dual-window mask operator is defined as follows:

[0042] (8)

[0043] in, Invalid point, , These represent the left or lower boundary of the signal window in the dual-window mask operator in the horizontal (x) and vertical (y) directions, respectively. , These represent the right or top boundary of the signal window in the dual-window mask operator in the horizontal (x) and vertical (y) directions, respectively. Let be the dimensions of the blank window in the horizontal and vertical directions of the dual-window mask operator. , These are the frequency coordinates along the horizontal (x) and vertical (y) directions, respectively.

[0044] Step 3.5: Perform singular value decomposition on the extracted lighting vector factors, specifically:

[0045] (9)

[0046] in, and These are the left and right singular matrices of the illumination vector factors, respectively. The feature matrix of the illumination vector factors, with superscript... This represents the matrix transpose operation.

[0047] Step 3.6: After completing the singular value decomposition of the illumination vector factors, perform the following steps on the left singular matrix: And right singular matrix The first row and first column elements are phase-expanded, and a linear fit is performed using the least squares method. The slope obtained from the linear fit is the subpixel wave vector. The components in the x and y directions are used to obtain the final subpixel wave vector. .

[0048] Step 3.7: Take the illumination vector factor in The phase at that point is used as the initial phase. The subpixel wave vector obtained through step 3.6 For +1 level spectrum Perform sub-pixel-level shifting, resulting in the +1 level spectrum. With the 0th order spectrum Deconvolution followed by complex linear regression yields the modulation index. Specifically:

[0049] (10)

[0050] in, This represents the spatial domain image of the separated 0th-order spectrum. This represents the spatial image of the separated +1 order spectrum, with superscript […]. This indicates the conjugate operation. It is the spatial position vector of the image plane.

[0051] Step 4: Substitute the lighting parameters accurately estimated in Step 3 into the asynchronous phase shift matrix to construct the corresponding matrix solution process, achieving decoupling and separation of the nine spectral components. Specifically:

[0052] (11)

[0053] Where the matrix It includes the initial phase Harmony system The complex exponential coefficient matrix, except for the first column, has odd-numbered columns whose elements are complex conjugates of the preceding even-numbered columns, specifically:

[0054] (12)

[0055] Based on the above solution process, the spectral components of each order can be decoupled and separated from the mixed spectrum, specifically as follows:

[0056] 0th order spectrum:

[0057] (13)

[0058] ±1st order spectrum:

[0059] , (14)

[0060] in, In the frequency domain The spectral components corresponding to the location In the frequency domain The spectral components corresponding to the location;

[0061] ±2nd order spectrum:

[0062] , (15)

[0063] in, In the frequency domain The spectral components corresponding to the location In the frequency domain The spectral components corresponding to the location The subscripts 1, 2, 3, and 4 represent the additional initial phase introduced, and their subscripts 1, 2, 3, and 4 correspond to four different interference directions, respectively. This indicates the modulation degree corresponding to the four interference directions.

[0064] Step 5: Construct a filter based on 3D OTF physical constraints to filter the high and low frequency spectra obtained in Step 4. Specifically:

[0065] Step 5.1: Based on the specific optical parameters of the microscopic imaging system (including objective lens numerical aperture, system magnification, camera pixel size, and imaging wavelength), the three-dimensional point spread function (PSF) of the system is calculated using a point spread function (PSF) simulation model. This PSF accurately characterizes the three-dimensional spatial response characteristics of the optical system to a point light source and is a fundamental indicator of the system's imaging quality. A three-dimensional Fourier transform is performed on the obtained three-dimensional PSF to obtain the system's three-dimensional optical transfer function (OTF). This OTF describes the system's transfer characteristics to different spatial frequency components in the frequency domain, providing a foundation for subsequent processing. Combining the spatial frequency distribution characteristics of four-beam interference composite structured light illumination, the above three-dimensional OTF is frequency-domain extended to ensure coverage of all spectral components generated by the four-beam interference. Based on this, a spectral translation operation is performed on the extended OTF according to the specific spatial frequency offset of the four illumination beams, resulting in four translated OTF components. According to the intensity distribution of the four illumination beams, these four translated OTF components are superimposed to construct a complete three-dimensional OTF physical model under four-beam interference composite structured light illumination conditions. This model accurately describes the frequency domain response characteristics of the system under structured light illumination, providing key physical constraints for subsequent image reconstruction and effectively improving the quality and reliability of super-resolution imaging.

[0066] Step 5.2: Based on the three-dimensional optical transfer function physical model constructed in Step 5.1, the three-dimensional OTF corresponding to the high-frequency spectrum and the low-frequency spectrum are respectively analyzed in the axial frequency direction. Integral projection is performed on the surface to obtain the corresponding effective two-dimensional optical transfer function. The high-frequency spectrum is composed of a combination of the zero-order spectrum and the second-order spectrum, and its corresponding three-dimensional OTF is denoted as... The low-frequency spectrum is composed of first-order spectra, and its corresponding three-dimensional OTF is denoted as . By measuring the above three-dimensional OTF along the axial frequency... By performing integral projection along the direction, we can obtain their respective projections in the transverse plane (i.e., ...). Effective two-dimensional OTFs on a plane. Among them, high-frequency effective two-dimensional OTFs can be represented as:

[0067] (16)

[0068] Low-frequency two-dimensional effective OTF can be represented as:

[0069] (17)

[0070] in, The frequency coordinates of the projection plane Represents frequency coordinates in three-dimensional space. A three-dimensional OTF representing the high-frequency spectrum. A three-dimensional OTF representing the low-frequency spectrum.

[0071] Step 5.3: Based on the high-frequency and low-frequency two-dimensional effective OTFs obtained in Step 5.2, corresponding high-frequency and low-frequency filters are constructed respectively, and the corresponding high-frequency and low-frequency spectra are filtered to suppress noise and enhance the spectral components of the target signal while satisfying the physical characteristics of the three-dimensional OTF of the imaging system. Specifically:

[0072] High-frequency filtering:

[0073] (18)

[0074] Low-frequency filtering:

[0075] (19)

[0076] in, and These represent the high-frequency spectrum and low-frequency spectrum after filtering, respectively. and These represent the high-frequency and low-frequency spectra before filtering, respectively, with superscripts indicating the frequency. This indicates the conjugate operation. is Wiener's empirical constant.

[0077] Step 6: Filter the high-frequency spectrum obtained in Step 5 after physical constraints based on the three-dimensional optical transfer function. Compared with the low-frequency filtered spectrum The superimposed spectra are then obtained by superimposing the spectra in the frequency domain. Subsequently, an inverse Fourier transform is performed on the superimposed spectra to obtain the reconstructed real-time super-resolution image. , can be represented as:

[0078] (20)

[0079] Example

[0080] To test the feasibility and real-time performance of this invention, super-resolution reconstruction was first performed on fixed BPAE cell samples and fixed autofluorescent Ascaris samples using the method (4I-SIM) described in this invention. Figure 2 As shown, Figure 2 a and c in the figure: Comparison between the super-resolution image obtained using this invention and the wide-field imaging result. The original image resolution is 1024×1024, acquired using a 100×1.45NA objective lens. Figure 2Figures b and d in the diagram show magnified views of the areas indicated by the blue box in figure a and the green box in figure c, respectively. The results are presented sequentially as follows: wide-field image (WF), conventional two-dimensional super-resolution SIM reconstruction result (SIM), reconstruction result using only the zeroth and first-order frequency components (Fr.), reconstruction result using only the zeroth and second-order frequency components (Sec.), reconstruction result without three-dimensional OTF constraint filtering (unfiltered), and the reconstruction result of this invention (4I). Each experiment was independently repeated 10 times, and the results were consistent.

[0081] like Figure 2 As shown in b and 2d, in thick sample regions with severe defocus backgrounds, both traditional 2D super-resolution SIM and second-level spectral reconstruction images exhibit significant defocus artifacts. While first-level spectral reconstruction effectively suppresses defocus backgrounds, it has significant limitations in improving lateral resolution. Reconstruction results without 3D OTF constraint filtering show some improvement in lateral resolution and optical slicing capability compared to traditional methods, but the improvement is still limited. In contrast, the method described in this invention achieves higher image contrast and lateral resolution without significant defocus artifacts. Therefore, compared to traditional 2D super-resolution SIM, this invention significantly enhances the imaging capability of thick biological samples through a composite structured light illumination mode generated by four-beam interference and a 3D OTF constraint filtering algorithm, providing a technical foundation for real-time super-resolution observation of live cells in complex biological environments. This embodiment demonstrates the high-resolution, high-fidelity, and robust super-resolution reconstruction performance of this invention and showcases its potential for long-term live cell imaging applications in complex biological environments.

[0082] One important application of this invention is the real-time monitoring of dynamic changes in subcellular structures under complex biological environments. To verify this, this invention was used to conduct real-time observations of mitochondria in living human myofibroblasts under high glucose conditions. Figure 3 As shown, mitochondria are tagged with PK Mito Red. Figure 3 In the figure, a and d represent the comparison between super-resolution images and wide-field imaging results obtained using the present invention at different time frames. Figure 3 b, c, e, and f in the figure correspond to magnified views of the blue and green boxed areas in figures a and d, respectively. The wide field image (WF), conventional two-dimensional super-resolution SIM reconstruction results (SIM), reconstruction results using only the zeroth and first order frequency components (Fr.), reconstruction results using only the zeroth and second order frequency components (Sec.), and reconstruction results of the present invention (4I) are given in sequence.

[0083] like Figure 3 As shown in a and 3d, the mitochondrial morphology of living human myofibroblasts at different times under the influence of a high glucose environment was clearly captured. Figure 3Figures bc and 3e-f further demonstrate the superior super-resolution reconstruction performance of the method described in this invention under complex biological environments such as high glucose, clearly revealing the structural details of mitochondria while effectively suppressing nonspecific fluorescence background and defocus signals. These experimental phenomena are of great significance for studying the behavior and interactions of mitochondria within cells under complex biological environments. This embodiment fully demonstrates the advantages of this invention in the dynamic observation of living cell structures under complex biological environments, providing key technical support for elucidating the correlation between organelle dysfunction and metabolic regulation.

Claims

1. A structured illumination microscopy imaging method based on four-beam interference, characterized in that, The specific process is as follows: Step 1: Modulate composite structured light illumination of the sample using four-beam interference; Step 2: Obtain nine frames of original lighting images; Step 3: Introduce principal component analysis algorithm to accurately estimate lighting parameters; Step 4: Use an asynchronous phase shift matrix to separate the 0th, ±1st, and ±2nd order spectra; Step 5: Construct a filter based on 3D OTF physical constraints to filter the high and low frequency spectra; Step 6: Fuse the filtered high and low frequency components to reconstruct the super-resolution image.

2. The structured light illumination super-resolution microscopy imaging method based on four-beam interference according to claim 1, characterized in that, In step 1, composite structured light illumination modulation of the sample is performed using four-beam interference, specifically as follows: The sample under test is used as the illumination modulation object. The composite fringe structured light formed by the superposition of horizontal and vertical interference fringes is used as the illumination source. The phase change of the illumination fringe is controlled by a nine-step asynchronous phase shift strategy. The illumination light field is spectrally filtered by inserting a mask in the Fourier plane, retaining only the ±1st order diffraction components in the orthogonal direction and shielding the 0th order diffraction light, thereby forming a four-beam interference composite illumination light field on the sample plane to achieve structured light illumination.

3. The structured light illumination super-resolution microscopy imaging method based on four-beam interference according to claim 2, characterized in that, The structural features of the composite illumination light field are as follows: ； in, The intensity distribution of the composite lighting light field. The spatial position vector of the image plane. and These represent the spatial wave vectors of the horizontal and vertical stripes, respectively. and These represent the original phases of the horizontal and vertical stripes, respectively; The subscripts 1, 2, 3, and 4 represent the additional initial phase introduced, and their subscripts 1, 2, 3, and 4 correspond to four different interference directions, respectively. This indicates the modulation degree corresponding to the four interference directions.

4. The structured light illumination super-resolution microscopy imaging method based on four-beam interference according to claim 2, characterized in that, When using a nine-step asynchronous phase shift strategy to control the phase change of illumination stripes, the specific phase shift configuration is as follows: ； Frame1-9 represent the frame numbers for acquiring the original lighting images. and These represent the original phases of the horizontal and vertical stripes, respectively.

5. The structured light illumination super-resolution microscopy imaging method based on four-beam interference according to claim 1, characterized in that, Step 2 involves obtaining nine frames of original lighting images, specifically: The fluorescence signal emitted by the sample modulated by the composite structured light was detected and collected by an sCMOS camera. The nine frames of original illumination images acquired are specifically in the frequency domain as follows: ； in, The frequency domain representation of fluorescence intensity detected by the sCMOS camera, with its subscript... Represents the frame number of the illumination image, symbol Indicates Fourier transform, It is a spatial frequency vector; Let be the optical transfer function of the system; This represents the original spectrum of the sample. and These represent the high-frequency sample spectral components that have been shifted into the system bandwidth after first-level and second-level modulation, respectively. and These represent the spatial wave vectors of the horizontal and vertical stripes, respectively. and These represent the original phases of the horizontal and vertical stripes, respectively; The subscripts 1, 2, 3, and 4 represent the additional initial phase introduced, and their subscripts 1, 2, 3, and 4 correspond to four different interference directions, respectively. This indicates the modulation scheme corresponding to the four interference directions mentioned above.

6. The structured light illumination super-resolution microscopy imaging method based on four-beam interference according to claim 1, characterized in that, The specific method for accurately estimating lighting parameters using principal component analysis algorithm in step 3 is as follows: Step 3.1: Frequency domain representation of the nine original illumination images obtained in Step 2 Linear calculations were performed to initially separate the spectra and extract the zero-order spectrum of the sample. and +1 level spectrum Specifically: ； ； in, and These represent the spatial wave vectors of the horizontal and vertical fringes, respectively. Let be the optical transfer function of the system; This represents the original spectrum of the sample. It is a spatial frequency vector. This represents the high-frequency sample spectral components that are shifted into the system bandwidth after primary modulation. +1 level spectrum The integer pixel offset is expressed as: ； in, To calibrate the obtained integer pixel wave vector, The subpixel wave vector to be estimated; Step 3.2: The zero-order spectrum of the sample obtained from Step 3.1 and +1 level spectrum The expression for heterospectral autocorrelation is obtained as follows: ； in, This is the inverse Fourier transform operation. This represents the spatial domain image of the separated 0th-order spectrum. This represents the spatial domain image of the separated +1 order spectrum. The spatial position vector of the image plane; Step 3.3: Extract the phase matrix using the heterospectral autocorrelation expression from Step 3.2, specifically as follows: ； Where exp is an exponential function with base e. A function that returns the phase; Step 3.4: Apply the dual-window mask operator to the +1 level spectrum after integer pixel offset. Pre-filtering is performed to extract the lighting vector factors, specifically: ； in, Invalid point, , These represent the left or lower boundary of the signal window in the dual-window mask operator along the horizontal x and vertical y directions, respectively. , These represent the right or top boundary of the signal window in the dual-window mask operator along the horizontal x and vertical y directions, respectively. Let be the dimensions of the blank window in the horizontal and vertical directions of the dual-window mask operator. , These are the frequency coordinates along the horizontal x and vertical y directions, respectively; Step 3.5: Perform singular value decomposition on the illumination vector factor, specifically as follows: ； in, The spatial position vector of the image plane. and These are the left and right singular matrices of the illumination vector factors, respectively. The feature matrix of the illumination vector factors, with superscript... This represents the matrix transpose operation; Step 3.6: Extract subpixel wave vectors Specifically: For the left singular matrix respectively And right singular matrix The first row and first column elements are phase-expanded, and a linear fit is performed using the least squares method. The slope obtained from the linear fit is the subpixel wave vector. Components in the x and y directions; Step 3.7: Calculate the initial phase Harmony system Specifically: Take the lighting vector factor after dimensionality reduction of the data in step 3.

5. The phase at that point is used as the initial phase. +1 order spectrum after subpixel offset With the 0th order spectrum Deconvolution followed by complex linear regression yields the modulation index. Specifically: ； in, This represents the spatial domain image of the separated 0th-order spectrum. This represents the spatial image of the separated +1 order spectrum, with superscript […]. This indicates the conjugate operation. It is the spatial position vector of the image plane.

7. The structured light illumination super-resolution microscopy imaging method based on four-beam interference according to claim 6, characterized in that, In step 4, the 0th, ±1st, and ±2nd order spectra are separated using an asynchronous phase shift matrix, specifically as follows: The lighting parameters, accurately estimated using principal component analysis, are substituted into the asynchronous phase shift matrix to construct the corresponding matrix solution process, thereby achieving the decoupling and separation of the nine spectral components. Specifically: ； Among them, matrix It includes the initial phase Harmony system The complex exponential coefficient matrix, except for the first column, has odd-numbered columns whose elements are complex conjugates of the preceding even-numbered columns, specifically: Based on the above solution process, the spectral components of each order are obtained by decoupling and separating them from the mixed spectrum, specifically: 0th order spectrum: ； ±1st order spectrum: ， ； in, In the frequency domain The spectral components corresponding to the location In the frequency domain The spectral components corresponding to the location; ±2nd order spectrum: ， ； in, In the frequency domain The spectral components corresponding to the location In the frequency domain The spectral components corresponding to the location The subscripts 1, 2, 3, and 4 represent the additional initial phase introduced, and their subscripts 1, 2, 3, and 4 correspond to four different interference directions, respectively. This indicates the modulation degree corresponding to the four interference directions.

8. The structured light illumination super-resolution microscopy imaging method based on four-beam interference according to claim 1, characterized in that, In step 5, a filter is constructed based on the three-dimensional OTF physical constraints to filter the high and low frequency spectra, specifically as follows: Step 5.1: Based on the optical parameters of the microscopic imaging system, the three-dimensional point spread function of the microscopic imaging system is obtained using the microscopic imaging point spread function simulation model. The three-dimensional point spread function is then subjected to a three-dimensional Fourier transform to obtain the three-dimensional optical transfer function of the microscopic imaging system. Combined with the spatial frequency distribution of the four-beam interference composite structured light illumination, the three-dimensional optical transfer function is frequency domain extended and the spectrum is shifted and weighted according to the spatial frequency shift of the four illumination beams, thereby constructing a three-dimensional OTF physical model under the four-beam interference composite structured light illumination condition. Step 5.2: Based on the three-dimensional OTF physical model constructed in Step 5.1, analyze the three-dimensional optical transfer function corresponding to the high-frequency and low-frequency spectra in the axial frequency direction. Integral projection is performed on the surface to obtain the high-frequency two-dimensional effective OTF and the low-frequency two-dimensional effective OTF; wherein, the high-frequency spectrum is a combination of the zero-order spectrum and the second-order spectrum, and the low-frequency spectrum is a combination of the first-order spectrum, specifically: High-frequency two-dimensional effective OTF: ； Low-frequency two-dimensional effective OTF: ； in, The frequency coordinates of the projection plane Represents frequency coordinates in three-dimensional space. A three-dimensional OTF representing the high-frequency spectrum. A three-dimensional OTF representing the low-frequency spectrum; Step 5.3: Based on the high-frequency two-dimensional effective OTF and low-frequency two-dimensional effective OTF obtained in Step 5.2, construct high-frequency Wiener filters and low-frequency Wiener filters based on three-dimensional OTF physical constraints, respectively, and perform filtering processing on the corresponding high-frequency spectrum and low-frequency spectrum to suppress noise and enhance the spectral components of the target signal while satisfying the three-dimensional OTF physical characteristics of the imaging system.

9. The structured light illumination super-resolution microscopy imaging method based on four-beam interference according to claim 8, characterized in that, The specific methods for filtering high-frequency and low-frequency spectra are as follows: Low-frequency Wiener filter: ； Low-frequency Wiener filtering: ； in, and These represent the high-frequency spectrum and low-frequency spectrum after Wiener filtering, respectively. and These represent the high-frequency and low-frequency spectra before filtering, respectively, with superscripts indicating the frequency. This indicates the conjugate operation. is Wiener's empirical constant.

10. The structured light illumination super-resolution microscopy imaging method based on four-beam interference according to claim 9, characterized in that, Step 6 involves fusing the filtered high and low frequency components to reconstruct the super-resolution image, specifically as follows: The high-frequency spectrum obtained in step 5 after physical constraint filtering using the three-dimensional optical transfer function is analyzed. and low frequency spectrum The superimposed images are then processed in the frequency domain, and an inverse Fourier transform is performed on the superimposed spectrum to obtain the reconstructed real-time super-resolution image. Specifically: 。

Images