Super-resolution structured light half-spectrum real part fast reconstruction method

Abstract

The application discloses a kind of super-resolution structured light half-spectrum real part fast reconstruction methods, belong to the technical field of microscopic optical imaging. Including S1, take three different phase wide-field structure modulation original graphs of a sample or two different phase virtual structure modulation original graphs, construct a spatial domain linear equation group, solve the spatial domain distribution of +1 order spectrum or-1 order spectrum, and carry out phase shift calculation in spatial domain, obtain the spatial domain distribution of high-order spectrum after frequency shift;S2, the real part processing of high-order spectrum spatial domain distribution after frequency shift in S1 is carried out, and is used for super-resolution reconstruction, and the super-resolution reconstruction image is obtained. This method directly solves the spatial domain distribution of +1 order spectrum or-1 order spectrum by spatial domain linear equation group, and carries out phase shift in spatial domain, avoids repeatedly fourier transform. The real part fast reconstruction method based on half-spectrum spatial domain distribution is proposed, the number of spectrum required for reconstruction is reduced, and the effect of fast reconstruction can be achieved.

Description

Technical Field

[0001] This invention belongs to the field of microscopic optical imaging, and more specifically, relates to a method for rapid reconstruction of the real part of the half-spectrum of super-resolution structured light. Background Technology

[0002] In fluorescence imaging, structured light illumination super-resolution imaging technology uses cosine fringes to illuminate the sample, causing a frequency shift in the sample spectrum. This shifts the super-resolution spectrum to the detection bandwidth of the objective lens, i.e., the optical transfer function (OTF), and then reconstructs the super-resolution image from the super-resolution spectrum.

[0003] The expression for the illumination field of the cosine fringes is:

[0004]

[0005] Where I(r) represents the illumination field of the cosine fringes, r represents the spatial coordinates, m represents the modulation contrast, and k0 represents the spatial frequency of the illumination fringes. Represents phase.

[0006] In the spatial domain, the imaging process of a microscope can be mathematically represented as the convolution of the sample after it has been modulated by structured illumination with the point spread function (PSF):

[0007]

[0008] Where D(r) represents the imaging result, S(r) represents the fluorescence intensity distribution of the sample, PSF(r) represents the point spread function, and B(r) represents the unmodulated background scattering signal in thick sample imaging. This represents the convolution operation.

[0009] Substituting the illumination field (1) into the imaging result (2) and taking the Fourier transform, the spectrum of the imaging result is obtained as follows:

[0010]

[0011] Where k represents the frequency coordinate, "~" represents the Fourier transform of the corresponding variable, and OTF(k) is the Fourier transform of PSF(r). It can be seen that after being modulated by cosine fringe structured light illumination, the sample's spectrum generates three components. The first component... The original spectrum of the sample is called the fundamental frequency component. The other two components... These represent the distances k0 that the sample's spectrum has shifted to the left (negative) and right (positive) respectively, and are called higher-order spectral components.

[0012] All three spectral components are low-pass filtered by the OTF. The cutoff frequency of the OTF for fluorescence imaging is:

[0013]

[0014] NA represents the numerical aperture of the objective lens. In conventional imaging, the spectrum of the original sample image is low-pass filtered by the OTF and then... The spectrum within the range. In super-resolution structured light imaging, the frequency-shifted spectral components. This will move the spectrum that was originally outside the cutoff frequency into the OTF bandwidth, thus increasing the total range of transmitted spectrum. Thus, super-resolution information was obtained.

[0015] Since the three order spectral components contained in equation (3) overlap, a super-resolution reconstruction algorithm is needed to separate the three order spectral components and move the higher-order spectral components back to their original correct positions in order to obtain the super-resolution result. The commonly used reconstruction algorithm is the frequency domain linear reconstruction algorithm. Its main process is as follows: S1, the sample is modulated three times using three different phase illumination structures to obtain three original modulation images. After the three original modulation images are transformed to the frequency domain, they can form a linear equation system; S2, the three spectral components are separated by solving the linear equation system. S3, use a Wiener filter to enhance the high-frequency signal; S4, move the three spectra to their correct positions before the frequency shift; S5, add and fuse the three spectral components to obtain the extended super-resolution spectrum; S6, perform an inverse Fourier transform to obtain the spatial domain super-resolution result.

[0016] In S4, the distance moved is the spatial frequency of the illumination fringe. This distance is often not an integer number of pixels, making direct movement in the frequency domain impossible. According to the Fourier shift theorem, frequency domain shifts can be converted into spatial domain phase shifts, and spatial domain phase shifts are not limited by pixels. Therefore, higher-order sub-spectrums are generally used... After transforming to the spatial domain, multiply by the corresponding phase, and then transform back to the frequency domain to achieve frequency domain shift.

[0017] It can be observed that the existing linear structured light super-resolution reconstruction algorithm requires repeated Fourier transforms and the calculation of three-order spectral components, resulting in a large computational load and a relatively long reconstruction time. Summary of the Invention

[0018] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a fast reconstruction method for the real part of the half-spectrum of super-resolution structured light, which aims to solve the technical problems of complex and slow speed of existing linear structured light super-resolution reconstruction process.

[0019] To achieve the above objectives, according to one aspect of the present invention, a method for fast reconstruction of the real part of the half-spectrum of super-resolution structured light is provided, comprising the following steps:

[0020] S1. Take three original wide-field structure modulation images with different phases or two original virtual structure modulation images with different phases from a sample, construct a system of linear equations in the spatial domain, solve for the spatial domain distribution of the +1 level spectrum or the -1 level spectrum, and perform phase shift calculation in the spatial domain to obtain the spatial domain distribution of the higher-order spectrum after frequency shift.

[0021] S2, after frequency shifting in S1, performs real part processing on the higher-order sub-spectral spatial domain distribution, and performs super-resolution reconstruction to obtain the super-resolution reconstructed image.

[0022] The above technical solution constructs a system of linear equations in the spatial domain, directly solving for the spatial domain distribution of the +1 or -1 order spectrum. Then, phase shifting is performed directly in the spatial domain, equivalent to frequency shifting in the frequency domain, avoiding repeated Fourier transforms and facilitating rapid reconstruction. The entire method only requires solving for one higher-order spectral component in the +1 or -1 order spectrum. Simultaneously, the spatial domain distribution of the frequency-shifted higher-order spectral component is processed by taking the real part for super-resolution reconstruction, reducing the number of spectra required for reconstruction and further accelerating the reconstruction speed.

[0023] Preferably, in S2, the real part extraction process specifically involves directly extracting the real part of the spatial domain distribution of the higher-order sub-spectrum after frequency shift.

[0024] Preferably, in S2, the real part extraction process specifically involves: transforming the frequency-shifted higher-order spectrum spatial domain distribution to the frequency domain, then using a mask to extract the standard half-spectrum, and then transforming it back to the spatial domain to extract the real part.

[0025] Preferably, in S2, the real part extraction process specifically involves: transforming the frequency-shifted higher-order spectrum spatial domain distribution to the frequency domain, then using a mask to extract the standard half-spectrum and performing Wiener filtering, and then transforming it back to the spatial domain to extract the real part.

[0026] Preferably, in S2, the super-resolution reconstruction specifically involves multiplying the obtained real part by 2.

[0027] Preferably, when three wide-field structure modulation original images are taken in S1, the constructed spatial domain linear equation system is as follows:

[0028]

[0029] Where D1(r), D2(r), and D3() represent the three original modulation images mentioned in S1, r represents the spatial coordinates, and m represents the modulation contrast. Let D1(r), D2(r), and D3() represent the phases on the left side of the equation, respectively, and let i represent the imaginary unit. This represents the spatial domain distribution of the 0th-order spectrum. This represents the spatial domain distribution of the +1 level spectrum. F represents the spatial domain distribution of the -1 level spectrum. -1 This represents the inverse Fourier transform. represents the distance k0 shifted by the sample spectrum in the negative and positive directions, respectively, i.e., the higher-order spectral components. OTF represents the optical transfer function, k represents the frequency coordinate, k0 represents the spatial frequency of the illumination fringe, and ~ represents the Fourier transform of the corresponding variable.

[0030] Preferably, when three wide-field structure modulation original images are taken in S1, their average image is subtracted from the three modulation original images, and then the spatial domain linear equation system is constructed. The spatial domain linear equation system is as follows:

[0031]

[0032] Where D1′(r), D2′(r), and D3′(r) represent the results obtained by subtracting their average from the three original modulation images mentioned in S1, respectively, r represents the spatial coordinates, and m represents the modulation contrast. These represent the phases of D1′(r), D2′(r), and D3′(r), respectively, where i represents the imaginary unit. This represents the spatial domain distribution of the +1 level spectrum. F represents the spatial domain distribution of the -1 level spectrum. -1 This represents the inverse Fourier transform. represents the distance k0 shifted by the sample spectrum in the negative and positive directions, respectively, i.e., the higher-order spectral components. OTF represents the optical transfer function, k represents the frequency coordinate, k0 represents the spatial frequency of the illumination fringe, and ~ represents the Fourier transform of the corresponding variable.

[0033] Preferably, when the original image of virtual structure modulation is taken in S1, the constructed system of linear equations in the spatial domain is:

[0034]

[0035] and These represent the two original virtual structure modulation images described in S1, where x represents the scan position. and These represent the phases of the original image modulated by the two virtual structures, This represents the spatial domain distribution of the +1 level spectrum. F represents the spatial domain distribution of the -1 level spectrum. -1denoted as inverse Fourier transform, OTF as optical transfer function, k as frequency coordinate, k0 as spatial frequency of illumination fringe, and ~ as Fourier transform of the corresponding variable.

[0036] Preferably, the acquisition of the original virtual structure modulation image specifically involves:

[0037] Obtain the original strip images L1(x)~L n (x), n≥2 and are integers;

[0038] Then, two digital gratings with different phases were used to refine the original strip images L1(x) to L... n (x) is modulated to obtain two virtual structure modulation original images with different phases. and Attached Figure Description

[0039] Figure 1 This is a schematic diagram of the half-spectrum distribution in this method;

[0040] Figure 2 (a) is a sample image;

[0041] Figure 2 (b) shows the simulation results for the wide field.

[0042] Figure 2 Image (c) shows the reconstruction result of the high-fidelity reconstruction mode of this application;

[0043] Figure 2 Image d shows the reconstruction result of the high-contrast reconstruction mode in this application;

[0044] Figure 2 Image (e) shows the reconstruction result of the high-speed reconstruction mode in this application;

[0045] Figure 2 In the diagram, (f) is the spectrum corresponding to (b);

[0046] Figure 2 In the middle, (g) is the spectrum corresponding to (c);

[0047] Figure 2 In the middle, (h) is the spectrum corresponding to (d);

[0048] Figure 2 In the diagram, (i) represents the spectrum corresponding to (e). Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0050] This invention proposes a fast method for reconstructing the real part of the half-spectrum of super-resolution structured light, comprising the following steps:

[0051] S1. Take three original wide-field structure modulation images with different phases or two original virtual structure modulation images with different phases from a sample, construct a system of linear equations in the spatial domain, solve for the spatial domain distribution of the +1 level spectrum or the -1 level spectrum, and perform phase shift calculation in the spatial domain to obtain the spatial domain distribution of the higher-order spectrum after frequency shift.

[0052] S2, after frequency shifting in S1, performs real part processing on the higher-order sub-spectral spatial domain distribution, and performs super-resolution reconstruction to obtain the super-resolution reconstructed image.

[0053] Existing techniques involve transforming a spatial domain image to the frequency domain, constructing a system of linear equations in the frequency domain, solving for the three frequency components, then transforming back to the spatial domain for phase shifting, and finally transforming back to the frequency domain. This shifts the higher-order spectral components back to their positions before modulation by cosine fringe structured light illumination. This repetitive Fourier transform is one reason for its time-consuming nature. Since the frequency domain equations are linear, performing an inverse Fourier transform on both sides of the equations still results in the equations remaining true, with the coefficient matrix unchanged, but the variables becoming the spatial domain distribution of the spectral components. Therefore, this application uses the original modulation image and the spatial domain distribution of the spectral components as variables, establishes a system of linear equations in the spatial domain with the same coefficient matrix, directly solves for the spatial domain distribution of the +1 or -1 order spectrum, and then directly performs a phase shift in the spatial domain, equivalent to a frequency shift in the frequency domain. This avoids repetitive Fourier transforms and achieves rapid reconstruction.

[0054] Furthermore, existing technologies fuse three spectral components, two of which are higher-order spectral components. However, since the captured image is represented by real numbers, and the spectrum of real numbers exhibits conjugate symmetry, only half of the spectrum is effective. Using two higher-order spectra for reconstruction during the fusion process is wasteful, as the frequency shifting, filtering, and fusion calculations for these two higher-order spectra prolong the reconstruction time. Because the distribution of the half-spectrums on both sides of the coordinate axis after transformation to the spatial domain also exhibits conjugate symmetry (i.e., the real parts are the same, while the imaginary parts have opposite signs), existing technologies using the complete spectrum to reconstruct super-resolution results in twice the real part, with the imaginary parts canceling each other out due to the opposite signs. Compared to existing technologies, this application solves only one of the higher-order spectral components (i.e., only the spatial domain distribution of the +1 or -1 order spectrum) and then performs real part processing on its spatial domain distribution for reconstruction. It proposes a fast reconstruction method based on the real part of the half-spectral spatial domain distribution, which reduces the number of spectra required for reconstruction. On the one hand, it directly constructs a system of linear equations in the spatial domain and performs phase shifting in the spatial domain, which is equivalent to frequency shifting in the frequency domain, avoiding repeated Fourier transforms. On the other hand, it utilizes conjugate symmetry to solve only one of the higher-order spectral components and perform real part processing to perform image reconstruction, thus improving the reconstruction speed in two ways.

[0055] In some embodiments, when three wide-field structure modulation original images are taken in S1, the constructed spatial domain linear equation system is:

[0056]

[0057] Where D1(r), D2(r), and D3(r) represent the three original modulation images mentioned in S1, r represents the spatial coordinates, and m represents the modulation contrast. Let D1(r), D2(r), and D3(r) represent the phases on the left side of the equation, respectively, and let i represent the imaginary unit. This represents the spatial domain distribution of the 0th-order spectrum. This represents the spatial domain distribution of the +1 level spectrum. F represents the spatial domain distribution of the -1 level spectrum. -1 This represents the inverse Fourier transform. represents the distance k0 shifted by the sample spectrum in the negative and positive directions, respectively, i.e., the higher-order spectral components. OTF represents the optical transfer function, k represents the frequency coordinate, k0 represents the spatial frequency of the illumination fringe, and ~ represents the Fourier transform of the corresponding variable.

[0058] In other embodiments, when three wide-field structure modulation original images are taken in S1, their average image is subtracted from the three modulation original images, and then the spatial domain linear equation system is constructed. The spatial domain linear equation system is as follows:

[0059]

[0060] Where D1′(r), D2′(r), and D3′(r) represent the results obtained by subtracting their average from the three original modulation images mentioned in S1, respectively, r represents the spatial coordinates, and m represents the modulation contrast. These represent the phases of D1′(r), D2′(r), and D3′(r), respectively, where i represents the imaginary unit. This represents the spatial domain distribution of the +1 level spectrum. F represents the spatial domain distribution of the -1 level spectrum. -1 This represents the inverse Fourier transform. represents the distance k0 shifted by the sample spectrum in the negative and positive directions, respectively, i.e., the higher-order spectral components. OTF represents the optical transfer function, k represents the frequency coordinate, k0 represents the spatial frequency of the illumination fringe, and ~ represents the Fourier transform of the corresponding variable.

[0061] D1(r), D2(r), and D3(r) represent three original modulation images. Subtracting their average image from the three original modulation images will remove the common zero-frequency component, thus achieving the effect of removing the background signal.

[0062] In some other embodiments, the original virtual structure modulation map is taken in S1, and the constructed spatial domain linear equation system is:

[0063]

[0064] and These represent the two original virtual structure modulation images described in S1, where x represents the scan position. and These represent the phases of the original image modulated by the two virtual structures, This represents the spatial domain distribution of the +1 level spectrum. F represents the spatial domain distribution of the -1 level spectrum. -1 denoted as inverse Fourier transform, OTF as optical transfer function, k as frequency coordinate, k0 as spatial frequency of illumination fringe, and ~ as Fourier transform of the corresponding variable.

[0065] Specifically, the acquisition of the original virtual structure modulation image involves:

[0066] Obtain the original strip images L1(x)~L n (x), n≥2 and are integers;

[0067] Then, two digital gratings with different phases were used to refine the original strip images L1(x) to L... n (x) is modulated to obtain two virtual structure modulation original images with different phases. and

[0068] Specifically, the original strip image is obtained by off-axis array detection of a multi-row detector in an existing line scan imaging system, where n represents the nth row of the off-axis array detection, x = 1:N-1, and N represents the total number of pixels in the sample.

[0069] The two digital gratings with different phases are respectively Positive and These represent the phases of the two digital gratings.

[0070]

[0071] After digital grating modulation, the original virtual structure modulation image obtained is as follows:

[0072]

[0073] n = 1: uT, where v represents the number of digital modulation periods contained in the virtual slit, and T represents the period of the digital grating. Ensure that the virtual slits are symmetrically distributed around the lighting points.

[0074] Existing technologies use three images to solve for three spectral components for super-resolution reconstruction, while this method only requires solving for one spectral component, i.e., the spatial domain distribution of the +1 level spectrum and the -1 level spectrum only needs to be solved for one of them, which can further improve the reconstruction speed.

[0075] When imaging fluorescence samples of a certain thickness, the three modulated original images captured by the camera contain a large amount of background signal. Existing techniques primarily use Wiener filtering during reconstruction to suppress low-frequency background signals, but this also suppresses low-frequency signals at the focal plane, resulting in signal loss. Our proposed method, however, uses only higher-order subspectral frequencies for super-resolution reconstruction, removing zero-frequency components and eliminating unmodulated background signals. This improves both reconstruction speed and image quality.

[0076] There are several methods for solving higher-order spectra in a system of linear equations in the spatial domain, such as multiplying by the inverse of the matrix, removing common zero-frequency components by difference, and then finding higher-order spectra. The spatial domain distribution expressions obtained by different methods may differ, but this does not affect the super-resolution reconstruction in S2.

[0077] When S1 contains three original wide-field structure modulation images:

[0078] by For example, one solution is obtained by left-multiplying the inverse of the coefficient matrix:

[0079]

[0080] The spatial domain distribution of the +1 order spectrum obtained by solving Spatial domain distribution of the -1 level spectrum Phase shift calculation for the +1 level spectrum involves multiplying its spatial domain distribution by... Phase shift calculations for the -1 level spectrum involve multiplying its spatial domain distribution by a factor.

[0081] The higher-order sub-spectral spatial domain distribution obtained after frequency shifting corresponds to the +1 level spectrum.

[0082] The spatial domain distribution of the higher-order sub-spectral frequency domain obtained after frequency shifting corresponds to the -1 level spectrum.

[0083] When S1 is taken as the original virtual structure modulation diagram, the solution can be obtained by left-multiplying the inverse of the coefficient matrix:

[0084] Solving for the spatial domain distribution of the +1 order spectrum: Spatial domain distribution of the -1 level spectrum: The +1 level spectrum is frequency shifted, which is based on the above spatial domain distribution multiplied by... The frequency shift of the -1 level spectrum is achieved by multiplying the spatial domain distribution described above by [missing information]. The obtained higher-order sub-spectral spatial domain distribution after frequency shift is as follows:

[0085]

[0086] In summary, different images available in S1 can be used to solve the problem in different ways, resulting in some differences in the expression of the final spatial domain distribution. Regardless of the specific expression, it does not affect subsequent operations such as frequency shifting and taking the real part. Therefore, this application only lists some solutions for reference and does not represent all solutions.

[0087] Further, in S2, the super-resolution reconstruction specifically involves multiplying the obtained real part by 2. Since this application directly takes the real part of the spatial domain distribution of a half-spectrum, the reconstruction process simply multiplies this real part by 2 to obtain the super-resolution reconstructed image. Figure 1As shown, the frequency-shifted higher-order spectral components used in S2 for reconstruction are the "half-spectrum" described in this application, which includes a standard half-spectrum and a small amount of opposing spectrum on the other side of the coordinate axis, and is modulated by the frequency-shifted OTF. The standard half-spectrum refers to the spectrum on the side containing super-resolution information at the spectral boundary and half of the spectrum on the boundary line. The boundary line is the perpendicular line from the origin to the line connecting the origin and the modulation frequency point on the spectrum. The real part of the frequency-shifted higher-order spectral spatial domain distribution can be processed in three different ways:

[0088] In some embodiments, a high-speed reconstruction mode is employed, ignoring the opposing spectrum and the modulation of the frequency-shifted OTF, and directly extracting the real part from the spatial domain of the higher-order sub-spectrum after the frequency shift, which allows for faster reconstruction. That is: or D HS Re represents the result of high-speed reconstruction, and Re represents the real part.

[0089] In other embodiments, a high-contrast reconstruction mode is employed. The spatial domain distribution of the frequency-shifted higher-order sub-spectrum is transformed to the frequency domain. A standard half-spectrum is extracted using a mask, and then inversely transformed back to the spatial domain to extract the real part. The mask extracts a standard half-spectrum located on one side of the coordinate axis, containing the super-resolution spectrum. This removes opposing spectra, and the frequency-shifted OTF has a low-frequency suppression effect, resulting in reconstruction with lower noise and higher contrast. or D HC Re represents the high-contrast reconstruction result, and Re represents the real part.

[0090] In some other embodiments, a high-fidelity reconstruction mode is employed. The spatial domain distribution of the frequency-shifted higher-order spectrum is transformed to the frequency domain. A standard half-spectrum is truncated using a mask and subjected to Wiener filtering, then transformed back to the spatial domain to obtain the real part. This method can remove the modulation of the frequency-shifted OTF after removing the opposing spectrum, obtaining the true half-spectrum, and the reconstruction result has high fidelity. That is: or D HF Re represents the high-contrast reconstruction result, and Re represents the real part.

[0091] More specifically, regarding the processing of wide-field structure modulation two-dimensional images (i.e., the original wide-field structure modulation image taken in S1), k0 is denoted as... The masks used for high-contrast reconstruction and high-fidelity reconstruction can be:

[0092] When rebuilding at +1 level:

[0093] When rebuilding at level -1:

[0094] More specifically, for processing line-scan virtual structure modulation 2D images (i.e., the original virtual structure modulation image taken in S1), the masks used for high-contrast reconstruction and high-fidelity reconstruction can be:

[0095] When rebuilding at +1 level:

[0096] When rebuilding at level -1:

[0097] Where, k x k y These represent the horizontal and vertical coordinates in the two-dimensional frequency domain, respectively.

[0098] This method employs three different modes during reconstruction: a high-speed reconstruction mode, where the entire process is performed in the spatial domain, resulting in rapid reconstruction; a high-contrast mode, utilizing the natural modulation of the frequency-shifted OTF to obtain a high-contrast super-resolution image; and a high-fidelity mode, using Wiener filtering to remove the influence of the system's OTF, yielding a super-resolution image with high fidelity. This fast reconstruction method of the real part of the half-spectrum of super-resolution structured light improves the efficiency of structured light super-resolution image reconstruction, saving time and computational resources, and greatly contributing to further expanding the application areas of super-resolution structured light imaging.

[0099] like Figure 2 As shown, a sample image is acquired, rotated 90 degrees, and placed at a depth of 0.5 micrometers as the background to construct a 3D sample. Figure 2 In (a), a wide-field simulation is performed using the convolutional three-dimensional point spread function method. The wide-field simulation results obtained are as follows: Figure 2 In section (b), the high-fidelity reconstruction mode of this method is used for reconstruction, and the obtained reconstruction result is as follows: Figure 2 In (c), the high-contrast reconstruction mode of this method is used for reconstruction, and the obtained reconstruction result is as follows: Figure 2 In section (d), using the high-speed reconstruction mode described in this paper, the reconstruction result obtained is: Figure 2 In Figures (a) to (e), the scale bar is 2 μm, and the sub-figures are magnified views of the white-framed areas with a scale bar of 0.5 μm. It can be observed that the resulting images obtained using any reconstruction mode of this method have higher resolution than those obtained using existing wide-field illumination methods. The high-fidelity mode recovers almost the same resolution and contrast as the sample, with no nonlinear distortion; the high-contrast mode has even higher contrast than the original sample, making dense signals easier to distinguish; the high-speed mode retains more low-frequency background compared to the other two modes, but still exhibits significant super-resolution performance. Figure 2In the diagram, (f) is the spectrum corresponding to (b), (g) is the spectrum corresponding to (c), (h) is the spectrum corresponding to (d), and (i) is the spectrum corresponding to (e). The scale bar in each of the diagrams (f) to (i) is 7 μm. -1 It can be observed that all three reconstruction modes can achieve spectral broadening and super-resolution reconstruction.

[0100] In general, the present invention can achieve the following beneficial effects:

[0101] (1) By using fast spectrum separation in the spatial domain, repeated Fourier transforms are avoided;

[0102] (2) Using only the real part of the half-spectral spatial domain distribution to quickly reconstruct the super-resolution results reduces the number of spectra required for reconstruction;

[0103] (3) It has three reconstruction modes: high speed, high contrast and high fidelity, which can respectively achieve the effects of high-speed reconstruction, obtaining high-contrast super-resolution images and obtaining super-resolution images with high fidelity.

[0104] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for fast reconstruction of the real part of the half-spectrum of super-resolution structured light, characterized in that, Includes the following steps: S1. Take three original wide-field structure modulation images with different phases or two original virtual structure modulation images with different phases from a sample, construct a system of linear equations in the spatial domain, solve for the spatial domain distribution of the +1 level spectrum or the -1 level spectrum, and perform phase shift calculation in the spatial domain to obtain the spatial domain distribution of the higher-order spectrum after frequency shift. S2, the real part of the higher-order sub-spectral spatial domain distribution after frequency shift in S1 is taken, and the obtained real part is multiplied by 2 to perform super-resolution reconstruction, thus obtaining the super-resolution reconstructed image. Specifically, in S2, the real part extraction process involves transforming the frequency-shifted higher-order spectrum spatial domain distribution to the frequency domain, then using a mask to extract the standard half-spectrum and performing Wiener filtering, and then transforming it back to the spatial domain to extract the real part.

2. The method according to claim 1, characterized in that, In S2, another specific way of taking the real part is to directly take the real part of the spatial domain distribution of the higher-order sub-spectrum after frequency shift.

3. The method according to claim 1, characterized in that, In S2, another specific method for the real part extraction process is to transform the frequency-shifted higher-order spectrum spatial domain distribution to the frequency domain, then use a mask to extract the standard half-spectrum, and then transform it back to the spatial domain to extract the real part.

4. The method according to claim 1, characterized in that, When S1 contains three original wide-field structure modulation images, the constructed spatial domain linear equation system is as follows: ； in, These represent the three original modulation images described in S1. Represents spatial coordinates, Indicates modulation contrast. They represent phase, Represents the imaginary unit. This represents the spatial domain distribution of the 0th-order spectrum. This represents the spatial domain distribution of the +1 level spectrum. This represents the spatial domain distribution of the -1 level spectrum. This represents the inverse Fourier transform. , These represent the sample spectrum shifted in the negative and positive directions, respectively. The distance, i.e., the higher-order spectral components, is represented by OTF, which stands for Optical Transfer Function. Represents frequency coordinates. denoted by , where is the spatial frequency of the illumination stripes, and ~ represents the Fourier transform of the corresponding variable.

5. The method according to claim 1, characterized in that, When S1 takes three original modulation images of a wide field structure, the average image of the three original modulation images is subtracted from them, and then the spatial domain linear equation system is constructed. The spatial domain linear equation system is as follows: ； in, These represent the results obtained by subtracting the average image from the three original modulation images described in S1. Represents spatial coordinates, Indicates modulation contrast. They represent phase, Represents the imaginary unit. This represents the spatial domain distribution of the +1 level spectrum. This represents the spatial domain distribution of the -1 level spectrum. This represents the inverse Fourier transform. , These represent the sample spectrum shifted in the negative and positive directions, respectively. The distance, i.e., the higher-order spectral components, is represented by OTF, which stands for Optical Transfer Function. Represents frequency coordinates. denoted by , where is the spatial frequency of the illumination stripes, and ~ represents the Fourier transform of the corresponding variable.

6. The method according to claim 1, characterized in that, When the original image of virtual structure modulation is taken in S1, the constructed system of linear equations in the spatial domain is as follows: ； and These represent the two original virtual structure modulation images described in S1. Indicates the scan position. and These represent the phases of the original modulated image of the two virtual structures, This represents the spatial domain distribution of the +1 level spectrum. This represents the spatial domain distribution of the -1 level spectrum. OTF stands for inverse Fourier transform, and OTF stands for optical transfer function. Represents frequency coordinates. The symbol represents the spatial frequency of the illumination fringes, and the symbol ~ represents the Fourier transform of the corresponding variable. It represents the imaginary unit.

7. The method according to claim 6, characterized in that, The acquisition of the original virtual structure modulation image is specifically as follows: Obtain the raw strip image ~ n≥2 and is an integer; Then, two digital rasterizers with different phases were used to refine the original strip image. ~ Modulation was performed to obtain two original virtual structure modulation images with different phases. and .

Images