Structured illumination obvious micro-imaging method based on high modulation degree coefficient mapping

Abstract

The invention discloses a structured illumination obvious micro-imaging method based on high modulation degree coefficient mapping, and the method comprises the steps: constructing a mathematical model of the Euclidean distance between the positive and negative first-order poles of an illumination structured light spectrum and the original point of the spectrum, and the light frequency of a stripe structure; the whole pixel position of a fringe frequency spectrum pole is estimated only through the structured light fringe frequency and the illumination direction angle, illumination parameter dimensionality reduction is achieved through a method based on principal component analysis, interference components irrelevant to illumination vectors in actual imaging are removed, a first principal component of a core in illumination parameters is obtained, and the first principal component of the core in the illumination parameters is obtained. Therefore, the transverse illumination wave vector with sub-pixel-level precision can be rapidly and accurately obtained without iteration, the problem of illumination parameter estimation errors caused by the fact that the fringe frequency is increased along with the increase of the super-resolution multiplying power of a DMD-SIM system in the prior art is solved, and the super-resolution multiplying power upper limit and the microscopic imaging capability of the system are improved.

Description

Technical Field

[0001] This invention belongs to the field of super-resolution fluorescence microscopy imaging technology, specifically a structured illumination microscopy imaging method based on high-modulation coefficient mapping, used for real-time super-resolution cell observation and optical section tomography. Background Technology

[0002] Among numerous super-resolution imaging techniques, structured light super-resolution microscopy (SIM) has become one of the most widely implemented fluorescence super-resolution modes in life sciences due to its unique advantages such as wide field of view, rapid imaging, and low phototoxicity and photobleaching. Because of its low phototoxicity, low photobleaching effect, and large field of view, SIM is well-suited for long-term super-resolution microscopy of living cells and has attracted widespread attention in the life sciences field. However, traditional SIM systems use laser-modulated optical paths, resulting in high cost, large size, and complex structures that hinder industrialization. Structured light super-resolution microscopy systems based on digital micromirror devices (DMDs) can modulate incoherent light, significantly reducing system size and the number of devices. The emergence of DMD-SIM has made the widespread adoption of SIM technology possible. However, compared to traditional laser-based SIM systems, DMD-SIM systems using incoherent light have a significant gap in optical modulation effects. In particular, the insufficient modulation capability of DMD devices and the resulting inadequate fringe modulation make accurate estimation of illumination parameters difficult, becoming the main reason hindering DMD-SIM from achieving higher super-resolution magnification and ultimate resolution. Summary of the Invention

[0003] The purpose of this invention is to propose a structured light illumination micro-imaging method based on high-modulation coefficient mapping, in order to solve the problem that the traditional DMD-SIM system is limited by insufficient downmodulation of high-frequency structured light projection in DMD, resulting in incorrect estimation of illumination parameters and thus insufficient super-resolution capability due to the inability to use high-frequency structured light stripe projection.

[0004] The technical solution to achieve the purpose of this invention is: a structured illumination micro-imaging method based on high-modulus coefficient mapping, the specific steps of which are as follows:

[0005] Step 1: Project a set of low-frequency structured light stripes with phase angles differing by 120° in three directions using DMD modulation, and acquire three low-frequency images;

[0006] Step 2: Perform Fourier transform on the acquired low-frequency stripe image to obtain the image spectrum, filter the image spectrum to obtain the positive and negative first-order spectrum position information in three directions, calculate the direction angle of the poles and the pole center distance of each Fourier spectrum image after filtering, determine the direction angle of the spectrum poles under the projection direction, find the relationship between the center distance of the integer pixel poles and the stripe frequency, and construct the HCM model.

[0007] Step 3: Imaging is performed by modulating a specific high-frequency fringe projection with DMD to obtain a wide-field illumination original image with superimposed high-frequency fringe projection;

[0008] Step 4: Using the HCM mathematical model, map the illumination parameters of the low-frequency fringe projection image to the illumination parameters of the high-frequency fringe projection image, and calculate the integer pixel positions of the positive and negative first-order poles of the image spectrum at a specific frequency and direction.

[0009] Step 5: Using the integer pixel positions of the positive and negative first-order poles of the image spectrum obtained in Step 4 as the reference region for sub-pixel estimation, the illumination parameter estimation method of principal component analysis is used to obtain the sub-pixel level illumination parameters and determine the super-resolution image spectrum;

[0010] Step 6: Based on the spectrum of the super-resolution image, perform super-resolution reconstruction through inverse Fourier transform.

[0011] Compared with existing technologies, the significant advantages of this invention are: It achieves near-physical-limit super-resolution imaging using an illumination parameter calibration method based on high-tone coefficient mapping without increasing the size and cost of the DMD-SIM system, thus greatly improving the system's super-resolution capability. This provides a rapid, high-quality, and low-light-damage observation method for studying the nanoscale subcellular structural features, motion states, interactions, and protein functions in biological microscopy. It is expected to promote the discovery of new biological phenomena and open up new possibilities for solving problems in cell biology, cancer research, developmental biology, and neuroscience, holding significant importance for related fields of life sciences.

[0012] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0013] Figure 1 Schematic diagram of the calibration model for HCM high-key regime mapping of integer pixel illumination parameters

[0014] Figure 2 The results of integer pixel parameter calibration of the HCM model in a real imaging experiment.

[0015] Figure 3 The flowchart of this invention

[0016] Figure 4 Flowchart for determining lighting parameters for HCM model

[0017] Figure 5 shows the super-resolution imaging results of nanoscale mitochondrial cell samples using the present invention. In Figure 5(a), the wide-field imaging results of the mitochondrial sample are compared with the super-resolution imaging results of HCMPCA-SIM. In Figure 5(b), the super-resolution capability of HCMPCA-SIM is compared with the change in fringe frequency gain.

[0018] Figure 6 To image Ascaris sections using this invention, an Olympus IX81 microscope with an NA1.42 40× oil immersion objective lens was used to image the cells. Detailed Implementation

[0019] A structured illumination micro-imaging method based on high-key regulation coefficient mapping is proposed. The method involves estimating illumination parameters using this high-key regulation coefficient mapping. Low-frequency integer-pixel fringe projection illumination parameters detectable by the system are mapped to high-frequency integer-pixel fringe projection illumination parameters undetectable by the system, namely the high-frequency fringe projection illumination direction angle and the integer-pixel illumination wave vector length, to obtain the ±1-order spectral pole positions at the integer-pixel scale. Using these ±1-order spectral pole positions as a reference, sub-pixel illumination parameter estimation is performed within a small frequency domain window adjacent to them. A dimensionality reduction tool based on principal component analysis is used to reduce the dimensionality of the phase quantities of the illumination parameters within the window, extracting the first principal component dominated by the illumination parameters, eliminating irrelevant noise and interference components, significantly reducing computational load, and achieving fast, non-iterative, and accurate illumination parameter estimation. These illumination parameters are then used as the parameters for subsequent deconvolution operations, employing a deconvolution method to achieve high-precision super-resolution image reconstruction. The flowchart of this invention is shown below. Figure 1 As shown, the specific steps are as follows:

[0020] Step 1: Modulate a set of low-frequency structured light stripes with phase angles 120° apart in three directions using DMD and acquire three low-frequency stripe projection images.

[0021] From the perspective of Fourier optics, the spectral information of the acquired low-frequency fringe image can be represented as:

[0022]

[0023] = •

[0024] The above formula describes the image spectral information acquisition process of structured light illumination super-resolution microscopy. The imaging spectrum superimposed with sinusoidal spatial structured light illumination has three components: wide-field imaging spectrum. The positive first-order spectrum obtained by frequency domain extension and negative first-order spectrum .

[0025] By inverse solution It can be observed that for two extended spectra, the coordinates of their spectral poles vary. That is, the length of the illumination wave vector is broadened to In other words, the spread spectrum involves frequency domain broadening, introducing high-frequency information beyond the original optical system's transfer function, thus improving its spatial domain imaging resolution. The amount of spectral broadening in the spread spectrum is related to the fringe frequency. This direct proportionality means that the structured light fringe frequency directly affects the super-resolution magnification. Reflected in the imaging spectrum, this means that the ±1-order spectral information is shifted in the frequency domain relative to the 0-order spectrum. Furthermore, the frequency shift of the spectral poles is directly related to the fringe frequency. They exhibit a linear mathematical relationship.

[0026] Step 2: Perform Fourier transform on the acquired low-frequency stripe image to obtain the image spectrum. Filter the image spectrum to obtain the positive and negative first-order spectrum position information in three directions. Calculate the direction angle of the poles and the center distance of the integer pixel poles in each filtered spectrum image to determine the direction angle of the spectrum poles under the projection direction. Find the relationship between the center distance of the integer pixel poles and the stripe frequency to construct the HCM model (High-key illumination parameter mapping mathematical model) to estimate the direction angle of the spectrum poles and the center distance of the integer pixel poles under high-frequency stripe projection.

[0027] Step 2.1: Perform a Fourier transform on the low-frequency stripe image to obtain a spectrum image. After blocking the maximum intensity value at the origin of the spectrum image with a notch filter, traverse the entire spectrum image to find the other two maximum values ​​at the integer pixel scale, and check whether the coordinates of the two maximum values ​​are symmetrical about the central origin. If the coordinates of the two maximum values ​​are symmetrical, they are the correct positive and negative first-order spectrum positions. If they are not symmetrical, continue to lower the stripe frequency and repeat the projection image modulation and acquisition process of Step 1 and Step 2.1.

[0028] Step 2.2: Calculate the pole orientation angle and pole center distance of the spectral poles based on the positive and negative first-order spectral pole position information of the low-frequency fringe image obtained in Step 2.1. The pole orientation angle and pole center distance are expressed as follows:

[0029] = =

[0030] In the formula, The coordinates of the pole location relative to the center of the spectrum.

[0031] Since the illumination modulation direction angle of SIM technology is strictly fixed, the direction angle of its spectral poles is also strictly fixed in different frequency illumination projection modes. Therefore, the direction angle of the poles of the low-frequency stripe projection image spectrum can be simply used as the direction angle of the poles of the high-frequency stripe projection image spectrum.

[0032]

[0033] In the formula, The pole orientation angles of the high-frequency fringe projection image spectrum are given. The center distance between the ±1st order poles of the high-frequency fringe projection image spectrum needs to be further estimated in step 2.3.

[0034] Step 2.3: ±1 order pole center distance and fringe frequency based on the spectrum By using prior knowledge that exhibits a linear mathematical relationship, the pole center distance of the low-frequency fringe projection image spectrum is linearly mapped to the pole center distance of the high-frequency fringe projection image spectrum, thus overcoming the obstacle that the incoherent DMD-SIM system cannot calculate the pole center distance of the high-frequency fringe projection image spectrum.

[0035] =

[0036] In the formula, and For high and low frequency structured light illumination frequencies, and These are the reconstructed illumination wave vector parameters corresponding to the high and low frequency structured light illumination frequencies, respectively.

[0037] Step 2.4: Since the spectral pole center distances obtained in steps 2.1 to 2.2 contain unavoidable subpixel level errors, in order to reduce the impact of the errors, repeat steps 2.1 to 2.2, change the frequency of the low-frequency fringe projection multiple times and re-acquire the original image of the corresponding fringe projection, and calculate the pole center distances corresponding to multiple different fringe frequencies through Fourier transform and frequency domain filtering.

[0038] Calculate the ratio of the pole center distance to the fringe frequency for each group. The system then performs linear regression fitting on multiple ratios to obtain the final error-corrected high-modulus linear mapping coefficients. First, let the regression expression for the center distance of the poles in the image spectrum be:

[0039] =

[0040] In the formula, The low-frequency fringe projection frequency, For the corresponding illumination wave vector length, To fit the high-pitched linear mapping coefficients of the system to be determined during regression, The random error term follows a normal distribution. , For the intercept, since wide-field unadjusted uniform illumination cannot achieve spectral transformation, let .

[0041] The high-frequency linear mapping coefficients after error elimination are solved by minimizing the residual sum of squares (RSS) evaluation method. :

[0042]

[0043] In the formula, Let be the order of the fringe transformation. When the sum of squared residuals reaches its minimum value, the high-tone regime mapping coefficient solution with the minimum error is obtained. :

[0044]

[0045] In the formula, and These represent the mean fringe frequency and the mean wave vector length in the calibration data pair, respectively; thus, the HCM mathematical model is constructed, which is based solely on the projection frequency of the currently modulated structured light fringe. mapping coefficient with high-profile system The length of the illumination wave vector is obtained. The HCM mathematical model is expressed as follows:

[0046] = =

[0047] In the formula, and For high and low frequency structured light illumination frequencies, and These are the reconstructed illumination wave vector parameters for the two, respectively.

[0048] Step 3: Imaging is performed by modulating a specific high-frequency fringe projection using DMD to obtain a wide-field original image with superimposed high-frequency fringe projection. The spectrum of the high-frequency fringe projection image is obtained by Fourier transforming the wide-field original image and filtering it in the frequency domain.

[0049] Step 4: Using the HCM mathematical model, the illumination parameters of the low-frequency fringe projection image are mapped to the illumination parameters of the high-frequency fringe projection image. The specific method for calculating the integer pixel positions (including pole center distance and pole orientation angle) of the positive and negative first-order poles of the image spectrum at a specific frequency and direction is as follows:

[0050] Since the optical path of the SIM system is stable, there is no need to calibrate the pole orientation angles. The pole orientation angles of the low-frequency fringe projection image spectrum from step 2.2 are used. This can be used as the orientation angle of the HCM model:

[0051]

[0052] In the formula, The pole orientation angle is the frequency spectrum of the high-frequency stripe projection image.

[0053] The high-frequency stripe projection frequency modulated in step 3 Substituting the HCM mathematical model obtained in step 2, we obtain the center distance of the spectral poles at the projection frequency, which is the length of the illumination wave vector.

[0054] =

[0055] Then, the pole center distance at that frequency was calculated. Rounding up yields the integer pixel pole center distance at that frequency. :

[0056]

[0057] In the formula, The center distance between integer pixel poles at this frequency. To round down the pole center distance, i.e., the wave vector length, the polar coordinate integer pixel positions of the ±1 order spectral poles are calculated through the above four steps. )and + ), where the polar coordinate radius parameter and angle parameter correspond to the integer pixel wave vector length and pole direction angle in the illumination parameters.

[0058] Step 5: Use the image spectrum obtained in Step 4 to locate the integer pixel positions of ±1 order poles. )and + Using the image as a reference region for subpixel estimation, principal component analysis is employed for data dimensionality reduction to remove irrelevant interference terms and accurately estimate subpixel-level illumination parameters. This step uses the integer pixel positions of ±1 order poles in the image spectrum. )and + A square signal window is established centered on the data to reduce the amount of computation and ensure the success rate of subsequent data dimensionality reduction. The reference area window size is generally 3-5 pixels.

[0059] Step 5.1: Using the integer pixel positions of the positive and negative first-order poles obtained in Step 4 )and + Using a point (e.g., 0.05 pixels) as the center of the window and a width of 3-5 pixels, a sub-pixel-level illumination parameter estimation range window is drawn. This signal window is sufficient to cover more than 95% of the illumination parameter information, while isolating most of the noise, thus greatly reducing the computational load.

[0060] Step 5.2: Using the signal window defined in Step 5.1 as the sub-pixel level illumination parameter estimation range, perform an inverse Fourier transform on the window signal to obtain the structured light illumination phase term. Under perfectly ideal conditions, the illumination parameter phase term introduced by sinusoidal fringe projection can be expressed as... This phase function is essentially a rank-one matrix, which can be represented as the product of two vectors:

[0061] =

[0062] in, = , = The subscripts of the two and Represents the coordinate values ​​along the horizontal and vertical directions. This represents the complex conjugate transpose. The phase term of the illumination parameter can be decomposed into along... and The direction-independent vector product provides the foundation for subsequent singular value decomposition (SVD) of the phase term of the illumination parameters and extraction of the first principal component (PCA).

[0063] The ideal lighting parameter phase term is a rank-one matrix, whose phase angle values ​​are... Ideally, the phasor matrix should be an ideal plane. However, due to the non-uniformity of illumination modulation, optical aberrations, and noise, the actual illumination phase matrix inevitably introduces complex noise interference terms, leading to high-dimensional distortion of the phase angle value plane. An ideal phasor matrix model should contain only one principal component, describing the phasor matrix as existing in a single-dimensional "eigenvalue subspace" in a least-squares sense. However, interference noise in actual imaging environments causes additional high-dimensional components in the phasor matrix. Therefore, we employ Principal Component Analysis (PCA) and Singular Value Decomposition (SVD) to obtain the eigenvalues ​​of the actual illumination phase matrix.

[0064]

[0065] In the formula, It is a +1 level spectrum. This represents the inverse Fourier transform. It is a positive semi-definite diagonal matrix, whose diagonal elements are the singular values ​​(eigenvalues) of the illumination phase matrix. , These are unitary matrices formed by the left and right singular vectors, respectively; superscript This represents the transpose of a matrix. This decomposes the complex two-dimensional vector estimation problem into an independent one-dimensional data fitting problem.

[0066] The left and right singular vectors corresponding to the first principal component obtained by SVD , Phase expansion and least squares fitting are performed along the x-axis and y-axis in one dimension, respectively. The slopes of the linear expressions along the x-axis and y-axis are obtained after fitting along the x-axis and y-axis directions, respectively. , ) and constant term ( , ), and then the slopes obtained by fitting will be ( , ) and constant term ( , The sum of the vectors yields the illumination parameters, i.e., the wave vectors, on the two-dimensional plane. and initial phase wave vector and initial phase This will serve as the calculation parameters for subsequent construction of super-resolution spectra, guiding high-precision spectrum reconstruction and being used to determine other lighting parameters.

[0067] The obtained wave vector and initial phase Substitute lighting modulation system The regression formula can accurately represent Move it to the correct position and perform complex linear regression calculations to obtain the modulation index of the illumination field. :

[0068]

[0069] In the formula, the superscript * denotes the conjugate of the original object. Therefore, by introducing PCA to extract the first principal component of the illumination phase matrix, noise and other interfering components can be effectively removed, thus enabling a simple and efficient method to accurately retrieve the sub-pixel-level initial phase. Sum of wave vectors .

[0070] Step 5.3: Calculate the initial phase using the method described in Step 5.2. Adjustment system Wave vector Afterwards, the complete super-resolution spectrum reconstruction parameters are obtained. By substituting the illumination parameters calculated in step 5.2 into the deconvolution formula, the super-resolution spectrum is reconstructed. Since each separated spectrum is attenuated to varying degrees by the system's OTF, and there are overlapping regions between different spectral components, the directly synthesized spectrum will exhibit an uneven distribution. To obtain high-quality super-resolution images, the most common approach is to deconvolve the super-resolution image spectrum acquired by the SIM system using Wiener deconvolution technology and then perform a weighted average to complete the reconstruction. The initial phase obtained in step 5.2 is then used... Adjustment system Wave vector Substituting into the following Wiener deconvolution formula, the super-resolution spectrum is calculated:

[0071]

[0072] In the formula This represents the calculated super-resolution spectrum. , This indicates the structured light illumination angle and spectral order, where , , The Wiener constant is determined based on experimental experience. Due to the Gibbs effect, to avoid oscillating patterns at the edges of the reconstructed image, the spectral edges are generally cropped.

[0073] Step 6: Based on the super-resolution image spectrum obtained in Step 5 Super-resolution reconstruction is achieved through inverse Fourier transform. To avoid edge oscillations caused by the Gibbs effect, an apodization function is typically used. The final spatial domain result of the super-resolution image is as follows:

[0074]

[0075] In the above formula This is the symbol for the inverse Fourier transform. It is the apodization function, which is generally determined empirically.

[0076] This invention provides a guarantee for high-precision sub-pixel level parameter estimation, enabling the super-resolution capability of the DMD-SIM system to approach the physical limit, and significantly improving the super-resolution capability of the system without increasing the system size and cost.

[0077] Example

[0078] To test the feasibility and real-time performance of this invention, super-resolution reconstruction of fixed cell mitochondrial samples was first performed using the method described in this invention. From Figure 3 As can be seen, in traditional wide-field mode, due to insufficient resolution and the influence of out-of-focus background, it is almost impossible to see the details of mitochondria. The HCMPCA-SIM system can greatly improve the details and effectively suppress the occurrence of artifacts. From Figure 4 As can be seen, compared with the imaging effect of traditional microscopes on Ascaris sections, the HCMPCA-SIM system has stronger detail resolution and defocus background separation ability for thick samples. This indicates that the HCMPCA-SIM system has great potential in the mainstream field of biological microscopy imaging, breaking the limitation of DMD-SIM in achieving high-magnification super-resolution.

Claims

1. A structured illumination micro-imaging method based on high-tone regime coefficient mapping, characterized in that, The specific steps are as follows: Step 1: Project a set of low-frequency structured light stripes with phase angles differing by 120° in three directions using DMD modulation, and acquire three low-frequency images; Step 2: Perform Fourier transform on the acquired low-frequency stripe image to obtain the image spectrum, filter the image spectrum to obtain the positive and negative first-order spectrum position information in three directions, calculate the direction angle of the poles and the pole center distance of each Fourier spectrum image after filtering, determine the direction angle of the spectrum poles under the projection direction, find the relationship between the center distance of the integer pixel poles and the stripe frequency, and construct the HCM model. Step 3: Imaging is performed by modulating a specific high-frequency fringe projection with DMD to obtain a wide-field illumination original image with superimposed high-frequency fringe projection; Step 4: Using the HCM mathematical model, map the illumination parameters of the low-frequency fringe projection image to the illumination parameters of the high-frequency fringe projection image, and calculate the integer pixel positions of the positive and negative first-order poles of the image spectrum at a specific frequency and direction. Step 5: Using the integer pixel positions of the positive and negative first-order poles of the image spectrum obtained in Step 4 as the reference region for sub-pixel estimation, the illumination parameter estimation method of principal component analysis is used to obtain the sub-pixel level illumination parameters and determine the super-resolution image spectrum; Step 6: Based on the spectrum of the super-resolution image, perform super-resolution reconstruction through inverse Fourier transform.

2. The structured illumination micro-imaging method based on high-key illumination parameter mapping according to claim 1, characterized in that, The specific spectral information of the acquired low-frequency stripe image is as follows: ； In the formula, For wide-field imaging spectrum, The positive first-order spectrum obtained by frequency domain extension The negative first-order spectrum obtained by frequency domain extension Stripe frequency.

3. The structured illumination micro-imaging method based on high-key illumination parameter mapping according to claim 1, characterized in that, The image spectrum is obtained by performing a Fourier transform on the acquired low-frequency fringe image. The image spectrum is then filtered to obtain the positive and negative first-order spectral position information in three directions. The orientation angle and pole center distance of each Fourier spectrum image after filtering are calculated to determine the spectral pole orientation angle under the projection direction. The relationship between the integer pixel pole center distance and the fringe frequency is also found. An HCM model is constructed to construct the specific method for estimating the orientation angle and integer pixel pole center distance of the spectral pole under high-frequency fringe projection. Step 2.1: Perform a Fourier transform on the low-frequency stripe image to obtain a spectrum image. After masking the maximum value at the origin of the spectrum image with a notch filter, traverse the rows and columns of the spectrum image to find the other two maximum values ​​at the integer pixel scale, and check whether the coordinates of the two maximum values ​​are symmetrical about the central origin. If they are symmetrical, the coordinates of the two maximum values ​​are the correct positive and negative first-order spectrum position information. If they are not symmetrical, lower the stripe frequency and return to step 1. Step 2.2: Calculate the pole orientation angle and pole center distance of each Fourier spectrum image after filtering based on the positive and negative first-order spectral position information of the low-frequency stripe image; Step 2.3: Linearly map the pole-center distance of the high-frequency fringe projection image spectrum using the pole-center distance of the low-frequency fringe projection image spectrum: ； In the formula, and For high and low frequency structured light illumination frequencies, and These are the reconstructed illumination wave vector parameters for the two, respectively; Step 2.4: Repeat steps 2.1 to 2.2, change the frequency of the low-frequency fringe projection multiple times and re-acquire the original image of the corresponding fringe projection. Calculate the pole center distances corresponding to multiple different fringe frequencies through Fourier transform and frequency domain filtering. Calculate the ratio of the pole center distance to the fringe frequency for each group. The system then performs linear regression fitting on multiple ratios to obtain the final error-corrected high-modulus linear mapping coefficients. ; A mathematical model of HCM is constructed based on the linear mapping coefficients of the high-profile system.

4. The structured illumination micro-imaging method based on high-key illumination parameter mapping according to claim 3, characterized in that, Calculate the ratio of the pole center distance to the fringe frequency for each group. The system then performs linear regression fitting on multiple ratios to obtain the final error-corrected high-modulus linear mapping coefficients. The specific method is as follows: Let the regression expression for the image spectrum pole center distance be: ； In the formula, The low-frequency fringe projection frequency, For the corresponding illumination wave vector length, To fit the high-pitched linear mapping coefficients of the system to be determined during regression, The random error term follows a normal distribution. The intercept; The high-frequency linear mapping coefficients after error elimination are obtained by minimizing the sum of squared residuals. : ； In the formula, Let be the order of the fringe transformation. When the sum of squared residuals reaches its minimum value, the solution of the high-tone regime mapping coefficients with the minimum error is obtained. : ； In the formula, and These represent the mean fringe frequency and the mean wave vector length in the calibration data pair, respectively.

5. The structured illumination micro-imaging method based on high-key illumination parameter mapping according to claim 3, characterized in that, The HCM mathematical model is expressed as follows: = = ； In the formula, and For high and low frequency structured light illumination frequencies, and These are the reconstructed illumination wave vector parameters for the two, respectively. and These represent the mean fringe frequency and the mean wave vector length in the calibration data pair, respectively.

6. The structured illumination micro-imaging method based on high-key illumination parameter mapping according to claim 1, characterized in that, The specific method for mapping the illumination parameters of low-frequency fringe projection images to those of high-frequency fringe projection images using the HCM mathematical model, thereby calculating the integer pixel positions of the positive and negative first-order poles of the image spectrum at a specific frequency and direction, is as follows: The pole orientation angles of the low-frequency fringe projection image spectrum from step 2.2 are used. As the orientation angle of the HCM model: ； In the formula, The pole orientation angle of the spectrum of the high-frequency stripe projection image; The high-frequency stripe projection frequency modulated in step 3 Substituting into the HCM mathematical model, we obtain the distance between the center points of the spectral poles at the projected frequency, which is the length of the illumination wave vector: = ； The obtained spectral pole center distance Rounding up yields the integer pixel pole center distance. : ； In the formula, The center distance of the integer pixel poles at this frequency. To round down the pole center distance, i.e., the wave vector length, the polar coordinate integer pixel positions of the ±1 order spectral poles were calculated. )and + ), where the polar coordinate radius parameter and angle parameter correspond to the integer pixel wave vector length and pole direction angle in the illumination parameters.

7. The structured illumination micro-imaging method based on high-key illumination parameter mapping according to claim 1, characterized in that, Using the integer pixel positions of the positive and negative first-order poles of the image spectrum obtained in step 4 as the reference region for sub-pixel estimation, the illumination parameter estimation method of principal component analysis is used to obtain sub-pixel level illumination parameters. The specific method for determining the super-resolution image spectrum is as follows: Step 5.1: Using the integer pixel positions of the positive and negative first-order poles obtained in Step 4 )and + Using the center of the window as the reference point and a width of 3-5 pixels as the window width, a sub-pixel level illumination parameter estimation range window is drawn. Step 5.2: Using the signal window defined in Step 5.1 as the sub-pixel level illumination parameter estimation range, perform an inverse Fourier transform on the window signal to obtain the structured light illumination phase term. The phase function is essentially a rank-one matrix, represented as the product of two vectors: ； in, , The subscripts of the two and Represents the coordinate values ​​along the horizontal and vertical directions. Representing the complex conjugate transpose, the phase term of the illumination parameter is decomposed into along... and Direction-independent vector product; Eigenvalues ​​of the actual illumination phase matrix are obtained through singular value decomposition: ； In the formula, It is a +1 level spectrum. This represents the inverse Fourier transform. It is a positive semi-definite diagonal matrix, whose diagonal elements are the singular values ​​of the illumination phase matrix. , These are unitary matrices formed by the left and right singular vectors, respectively; superscript Represents the transpose of a matrix; The left and right singular vectors corresponding to the first principal component obtained by SVD , Phase expansion and least squares fitting are performed along the x-axis and y-axis in one dimension, respectively. The slopes of the linear expressions along the x-axis and y-axis are obtained after fitting along the x-axis and y-axis directions, respectively. , ) and constant term ( , ), and then the slopes obtained by fitting will be ( , ) and constant term ( , The sum of the vectors yields the illumination parameters, i.e., the wave vectors, on the two-dimensional plane. and initial phase ; The obtained wave vector and initial phase Substitute lighting modulation system The regression formula will Move it to the correct position and perform complex linear regression calculations to obtain the modulation index of the illumination field. : ； In the formula, the superscript * indicates the conjugate of the original object; Step 5.3: The initial phase calculated in step 5.2 Adjustment system Wave vector Then, the complete super-resolution spectrum reconstruction parameters are obtained. By substituting the illumination parameters calculated in step 5.2 into the deconvolution formula, the super-resolution spectrum can be reconstructed.

8. The structured illumination micro-imaging method based on high-key illumination parameter mapping according to claim 7, characterized in that, Modulation of illumination light field Specifically: ； In the formula, the superscript * indicates the conjugate of the original object.

9. The structured illumination micro-imaging method based on high-key illumination parameter mapping according to claim 7, characterized in that, The super-resolution spectrum is specifically as follows: ； In the formula, This represents the calculated super-resolution spectrum. , This indicates the structured light illumination angle and spectral order, where , , The Wiener constant is determined based on experimental experience.

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