Broadband PSF and original image reconstruction method based on weighted superposition and equivalent wavelength

Abstract

The application relates to the field of microscopic imaging technology, and particularly discloses a broadband PSF and original image construction method based on weighted superposition and equivalent wavelength, which comprises the following steps: in the super-resolution microscopic imaging process after analog fluorescence passes through a filter and a detector response, within the band-pass range of the filter, the fluorescence wavelength is discretized into a sequence containing a plurality of wavelengths; for each wavelength in the sequence, the relative emission intensity of the corresponding wavelength is corrected based on the filter transmittance and the detector quantum efficiency to obtain an effective relative emission intensity; the weight of each wavelength is calculated based on the effective relative emission intensity; the Gaussian point spread functions corresponding to all the wavelengths in the sequence are superposed according to the weights to obtain a final point spread function; or, the equivalent wavelength is calculated based on the weights of all the wavelengths in the sequence, and a single-wavelength Gaussian point spread function is constructed based on the equivalent wavelength as the final point spread function. The application can significantly improve the effective photon number and significantly improve the structural continuity and resolution of the super-resolution reconstructed image.

Description

Technical Field

[0001] This invention relates to the field of microscopic imaging technology, and more specifically to a broadband PSF based on weighted superposition and equivalent wavelength and a method for constructing original images. Background Technology

[0002] Dynamic observation of intracellular micro- and nanoscale structures is a core requirement of life science research. Optical microscopy, with its non-invasive and specific labeling advantages, has become the mainstream method for cell microscopic imaging. However, constrained by the far-field diffraction limit, traditional wide-field microscopes have a lateral resolution of only about 200 nm and an axial resolution of about 500 nm, unable to resolve fine structures at the subcellular level. Super-resolution microscopy can overcome the diffraction limit, improving resolution to the nanometer scale. Stochastic optical reconstruction microscopy (STORM), based on the principle of single-molecule localization, can achieve a lateral resolution of about 20 nm and an axial resolution of 50 nm, and is one of the most widely used super-resolution microscopy techniques currently.

[0003] STORM ensures non-overlapping diffraction spots for single-molecule imaging through sparse excitation, requiring the acquisition of tens of thousands of images to complete super-resolution reconstruction. This results in slow imaging speed and complex experimental procedures, making it difficult to apply to the observation of dynamic processes in live cells. To improve imaging efficiency, compressed sensing (CS) theory has been introduced into STORM, forming the CS-STORM technique. This method can achieve precise localization even in scenarios with overlapping diffraction spots of high-density fluorescent molecules, significantly reducing the number of original image frames required and substantially improving temporal resolution.

[0004] The positioning accuracy of CS-STORM is highly dependent on the accuracy of the point spread function (PSF) modeling. The PSF not only determines the shape of the single-molecule diffraction spot but also forms the basis for constructing the compressed sensing measurement matrix. Typically, narrowband filters are used to acquire narrowband signals near the fluorescence emission peak, constructing a Gaussian PSF using the fluorescence peak wavelength or the center wavelength of the narrowband. Fluorescent dyes often have very broad emission spectra. While this method provides sufficient accuracy in narrowband conditions, it results in many fluorescent photons not being effectively collected and utilized, limiting the imaging signal-to-noise ratio and positioning accuracy in low-light environments. Using broadband filters, although improving photon utilization, results in fluorescence signals covering a wider wavelength range. The standard deviation of the Gaussian PSF varies across different wavelengths, and directly using the peak wavelength to construct the PSF introduces systematic modeling errors, ultimately leading to a decrease in the quality of the super-resolution reconstructed image.

[0005] Therefore, how to solve the problems of low effective photon count in narrowband fluorescence detection and mismatch in point spread function (PSF) modeling under broadband detection in compressed sensing-based stochastic optical reconstruction microscopy (CS-STORM) is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] In view of the above problems, the present invention proposes a broadband PSF and original image construction method based on weighted superposition and equivalent wavelength, so as to overcome the above problems or at least partially solve the above problems.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] In a first aspect, the present invention provides a method for constructing a broadband PSF based on weighted superposition and equivalent wavelength, comprising the following steps: In the super-resolution microscopic imaging process simulating the response of fluorescence after passing through a filter and detector, the fluorescence wavelength is discretized into a sequence containing several wavelengths within the bandpass range of the filter. For each wavelength in the sequence, the relative emission intensity of the corresponding wavelength is corrected based on the filter transmittance and the detector quantum efficiency to obtain the effective relative emission intensity; The weight of each wavelength is calculated based on the effective relative emission intensity; The final point spread function is obtained by weighting and superimposing the Gaussian point spread functions corresponding to all wavelengths in the sequence; or, the equivalent wavelength is calculated based on the weights of all wavelengths in the sequence, and a single-wavelength Gaussian point spread function is constructed based on the equivalent wavelength as the final point spread function.

[0009] Furthermore, the formula for calculating the effective relative emission intensity at any wavelength is:

[0010] in, Represents the i-th wavelength The relative emission intensity, Represents the i-th wavelength The corresponding filter transmittance, Represents the i-th wavelength The corresponding quantum efficiency; Represents the i-th wavelength The effective relative emission intensity.

[0011] Furthermore, the weight of any wavelength is defined as the ratio of the effective relative emission intensity of that wavelength to the effective relative emission intensity of all wavelengths within the bandpass range, calculated using the following formula:

[0012] in, Represents the i-th wavelength The weight, Represents the i-th wavelength The effective relative emission intensity, This represents the total number of discretized wavelengths within the bandpass range.

[0013] Furthermore, by weighting and superimposing the Gaussian point spread functions corresponding to all wavelengths in the sequence, the final expression for the point spread function is obtained. for:

[0014] in, This represents the total number of discretized wavelengths within the bandpass range; Represents the i-th wavelength The weights; is the independent variable, representing the spatial coordinates on the image plane; , represents the scaling factor, and NA represents the numerical aperture of the microscope objective.

[0015] Furthermore, the equivalent wavelength is defined as the weighted harmonic average of all wavelengths within the bandpass range, and its calculation formula is as follows:

[0016] in, For equivalent wavelength, For the i-th wavelength The weight, This indicates the total number of wavelengths within the bandpass range.

[0017] Furthermore, a single-wavelength Gaussian point spread function is constructed based on the equivalent wavelength. The expression is:

[0018] in, Indicates the proportionality coefficient; is the independent variable, representing the spatial coordinates on the image plane.

[0019] Secondly, the present invention provides a method for reconstructing an original image based on weighted superposition and equivalent wavelength, comprising the following steps: Calculate the weight of each wavelength using the method described above; The weight of each wavelength is multiplied by the original super-resolution image to obtain the super-resolution image component for each wavelength. The original image component of each wavelength is obtained by convolving the super-resolution image component of each wavelength with the corresponding Gaussian point spread function; or the original image component of each wavelength is obtained by multiplying the super-resolution image component of each wavelength with a single-wavelength Gaussian point spread function constructed based on the equivalent wavelength. The original image components of all wavelengths within the sequence are added together to obtain the final synthesized original image.

[0020] Furthermore, the final synthesis formula for the original image is expressed as: =

[0021] in, This represents the original image used in the final synthesis. Represents the original image component at the i-th wavelength; or ; This represents the Gaussian point spread function for the i-th wavelength. Let i represent the super-resolution image component at the i-th wavelength. This represents the single-wavelength Gaussian point spread function constructed based on the equivalent wavelength. This represents the convolution operation; , Represents the original super-resolution image. This represents the weight of the i-th wavelength.

[0022] Thirdly, the present invention provides a broadband PSF construction system based on weighted superposition and equivalent wavelength, which employs the broadband PSF construction method based on weighted superposition and equivalent wavelength as described above, including: The discretization module is used to discretize the fluorescence wavelength into a sequence containing several wavelengths within the bandpass range of the filter during the imaging process of simulated fluorescence after passing through the filter and detector response. The correction module is used to correct the relative emission intensity of each wavelength in the sequence based on the filter transmittance and detector quantum efficiency to obtain the effective relative emission intensity. The weight calculation module is used to calculate the weight of each wavelength based on the effective relative emission intensity; The point spread function construction module is used to superimpose the Gaussian point spread functions corresponding to all wavelengths in the sequence according to their weights to obtain the final point spread function; or, it calculates the equivalent wavelength based on the weights of all wavelengths in the sequence, and constructs a single-wavelength Gaussian point spread function based on the equivalent wavelength as the final point spread function.

[0023] Fourthly, the present invention provides a system for constructing original images based on weighted superposition and equivalent wavelength, employing the broadband PSF construction method based on weighted superposition and equivalent wavelength as described above, including: The super-resolution image component calculation module is used to multiply the weight of each wavelength by the original super-resolution image to obtain the super-resolution image component for each wavelength. The original image component calculation module is used to convolve the super-resolution image component of each wavelength with the corresponding Gaussian point spread function to obtain the original image component of each wavelength; or to multiply the super-resolution image component of each wavelength with a single-wavelength Gaussian point spread function constructed based on the equivalent wavelength to obtain the original image component of each wavelength. The original image synthesis module is used to add the original image components of all wavelengths in the sequence to obtain the final original image.

[0024] As can be seen from the above technical solution, compared with the prior art, the present invention has the following beneficial effects: This invention first integrates fluorescence emission spectroscopy, filter transmittance, and detector quantum efficiency to construct weights for different wavelengths, representing the broadband Gaussian point spread function (PSF) as a weighted superposition of Gaussian PSFs at different wavelengths. Based on this, an analytical expression for the equivalent wavelength is derived through Taylor series expansion and order matching. Theoretically, it is proven that while the broadband PSF does not strictly satisfy a Gaussian distribution, its non-Gaussianity is negligible within the passband of 655–800 nm, allowing for a Gaussian approximation using the equivalent wavelength. Compared to the traditional peak wavelength method, this invention significantly increases the effective photon count within a 145 nm bandwidth, while also significantly improving the structural continuity and resolution of the super-resolution reconstructed image. Furthermore, this invention is directly compatible with the existing CS-STORM reconstruction framework, providing an effective PSF modeling scheme for high-speed super-resolution microscopy in low-light environments. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0026] Figure 1 This is a flowchart of a broadband PSF construction method based on weighted superposition and equivalent wavelength provided in an embodiment of the present invention; Figure 2 This is a schematic diagram showing the spectral characteristics of the fluorescent dye, filter, and detector provided in the embodiments of the present invention, as well as the corrected effective detection spectrum. Figure 3This is a schematic diagram of a two-dimensional point expansion function and its cross-section provided in an embodiment of the present invention; Figure 4 The narrowband and broadband simulated original image frames (containing Poisson and Gaussian (variance 0.01) noise) and super-resolution reconstructed images provided in the embodiments of the present invention have a scale bar of 1 μm. Figure 5 The images provided in this embodiment are narrowband and broadband original image frames and super-resolution reconstructed images, with a scale bar of 1 μm. Detailed Implementation

[0027] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0028] like Figure 1 As shown, this embodiment of the invention discloses a method for constructing a broadband PSF based on weighted superposition and equivalent wavelength, including the following steps: S1. In the imaging process of simulated fluorescence after passing through the filter and detector response, within the bandpass range of the filter, the fluorescence wavelength is discretized into a sequence containing several wavelengths. S2. For each wavelength in the sequence, the relative emission intensity of the corresponding wavelength is corrected based on the filter transmittance and detector quantum efficiency to obtain the effective relative emission intensity. S3. Calculate the weight of each wavelength based on the effective relative emission intensity; S4. Superimpose the Gaussian point spread functions corresponding to all wavelengths in the sequence according to their weights to obtain the final point spread function; or, calculate the equivalent wavelength based on the weights of all wavelengths in the sequence, construct a single-wavelength Gaussian point spread function based on the equivalent wavelength, and use it as the final point spread function.

[0029] The specific implementation methods of the above steps will be further explained below.

[0030] The emission spectrum (relative emission intensity) of S1, fluorescent dye Alexa647 is as follows: Figure 2 As shown in (a) above, the number of emitted fluorescent photons varies at different wavelengths. If a filter with a passband range of [b1, b2] is used, the wavelengths within the passband are discretized into a sequence {λi}, where i = 1, 2, ..., N, and λi = ... i ∈[b1,b2].

[0031] S2, the transmittance spectrum of the filter and the quantum efficiency spectrum of the detector are respectively as follows: Figure 2As shown in (b) and (c) of the figure, in a microscope imaging system, the effective number of photons received by the detector depends not only on the emission spectrum of the fluorescent dye but also on the modulation of the filter transmittance T(λ) and the detector quantum efficiency η(λ). Therefore, it is necessary to correct the relative emission intensity for each wavelength. For any wavelength, the formula for calculating the corrected effective relative emission intensity is: (1) in, Represents the i-th wavelength The relative emission intensity, Represents the i-th wavelength The corresponding filter transmittance, Represents the i-th wavelength The corresponding quantum efficiency; Represents the i-th wavelength The effective relative emission intensity.

[0032] S3, the weight c corresponding to each wavelength i Defined as the ratio of the relative emission intensity at that wavelength to the total relative emission intensity within the passband, as shown below: (2) Among them, all weights satisfy the normalization condition. .

[0033] Depend on Figure 2 As shown in (b), after 655 nm, the transmittance spectrum within the passband of the filter (LP02-647RU) is flat, with fluctuations of less than 5%. Figure 2 As can be seen in (c), the quantum efficiency spectrum of the detector exhibits a significant spectral dependence on wavelength at different wavelengths. Figure 2 (d) in the text is Figure 2 The local curves (a)-(c) in the passband 655nm~800nm ​​and the corrected effective relative emission intensity spectra are shown. I(λ) is collectively referred to as the original relative emission intensity of the fluorescent dye at different wavelengths, T(λ) is collectively referred to as the transmittance of the filter at different wavelengths, and η(λ) is collectively referred to as the quantum efficiency of the detector at different wavelengths. e (λ) is collectively referred to as the corrected effective relative emission intensity at different wavelengths. For any wavelength... Corrected effective relative emission intensity Substituting into equation (2), we can obtain the weights based on the imaging system response. At this point, for any wavelength... The weight is redefined as the ratio of the effective relative emission intensity of that wavelength to the effective relative emission intensity of all wavelengths within the bandpass range, calculated using the following formula: (3) in, Represents the i-th wavelength The weight, Represents the i-th wavelength The effective relative emission intensity, This represents the total number of discretized wavelengths within the bandpass range.

[0034] S4. In wide-field fluorescence microscopy systems, the imaging spot (PSF) of a point source can be described by the Airy disk, and in engineering, a Gaussian function is often used for high-precision approximation. For an objective with a numerical aperture of NA, the one-dimensional Gaussian PSF corresponding to a single wavelength of λ can be expressed as: (4) in, , where represents the scaling factor, and NA represents the numerical aperture of the microscope objective. The full width at half maximum (FWHM) of the PSF is expressed as: Standard deviation of PSF Gaussian function Equation (4) is the result of equivalent transformation of the standard deviation of the Gaussian function using λ and k. The standard deviation of the PSF is positively correlated with the fluorescence wavelength and negatively correlated with the numerical aperture of the objective lens.

[0035] Specifically, in this invention, the final point spread function is constructed in two ways. One way is to superimpose the Gaussian point spread functions corresponding to all wavelengths in the sequence according to their weights to obtain the final point spread function, the expression of which is... for: (5) in, This represents the total number of discretized wavelengths within the bandpass range; Represents the i-th wavelength The weights; is the independent variable, representing the spatial coordinates on the image plane.

[0036] Figure 3 Images (a) and (b) are the original images generated based on the peak wavelength (670 nm) and passband (655 nm ~ 800 nm), respectively. A single fluorescent molecule is located at the "+" position in the image. Because there is only one fluorescent molecule in the image, Figure 3 (a) and (b) in the figure can also be regarded as two-dimensional PSFs. Figure 3 (c) in the middle is based on Figure 3 A one-dimensional PSF is constructed using the grayscale values ​​and pixel positions of the pixels marked by red lines in (a) and (b). For ease of comparison of their shapes, it is assumed that both fluorescent molecules emit an effective number of 4636 photons. Figure 3As can be seen in (c), the peak value of the single-wavelength PSF is significantly higher than that of the broadband PSF.

[0037] In traditional STORM super-resolution microscopy, the single-wavelength photon emission frequency (PSF) corresponding to narrowband detection is essentially a special case of broadband PSF when the detection bandwidth approaches zero. If the effective photon number emitted by fluorescent molecules based on the passband (655nm~800nm, bandwidth 145nm) is 4636, then the effective photon number emitted by fluorescent molecules based on the passband (655nm-675nm, bandwidth 20nm) is only 1766. The latter is only 38% of the former. Figure 3 (d) in the text is Figure 3 (c) introduces a comparison of the PSF after bandwidth, filter, and detector corrections. Figure 3 As shown in (d), there are significant differences in morphology and amplitude between broadband and single-wavelength PSFs. The peak value of the latter is much lower than that of the former, and the effective photon count of the latter is much lower than that of the former. PSF is the core foundation for constructing the compressed sensing measurement matrix. The differences in bandwidth and PSF morphology and amplitude inevitably lead to systematic deviations in the measurement matrix, ultimately affecting the super-resolution reconstruction accuracy.

[0038] A broadband PSF can be considered as a single-wavelength PSF in narrowband conditions and as a weighted superposition of PSFs of different wavelengths in wideband conditions. In STORM, a single-wavelength PSF can be approximated as a Gaussian function, as shown in Equation (4). The Gaussian function can be expanded using a Taylor series. Therefore, in wideband conditions, a broadband PSF can be considered as a weighted superposition of PSFs of different wavelengths after Taylor series expansion.

[0039] The weighted superposition model of Equation (5) is used to construct the PSF, which requires calculation and summation for each wavelength, resulting in relatively high computational complexity. To simplify the calculation, another method for constructing the PSF is introduced. This method introduces the concept of equivalent wavelength and attempts to use a single-wavelength Gaussian PSF to approximate the broadband superposition PSF optimally. The analytical expression is derived through Taylor series expansion and order matching, and the rationality and error boundary of the approximation are analyzed. The specific derivation process is as follows: If there exists a wavelength λe such that a single-wavelength Gaussian PSF based on λe (as shown in Equation (4)) can be optimally approximated by a weighted superposition of broadband PSFs (as shown in Equation (5)) under a specific criterion, then λe is called the equivalent wavelength.

[0040] To quantitatively measure the degree of approximation, the two types of PSFs are expanded using Taylor series at the origin (x=0, i.e., the center of the PSF) (as shown in equations (6) and (7)). By matching the expansion coefficients of different orders, the equivalent wavelength under the corresponding criteria is obtained. Since the PSF has centrosymmetry, the expansion only contains even-order terms of x.

[0041] (6) (7) The coefficients of the lowest-order terms (n = 0, i.e., peak / constant terms) in equations (6) and (7) are matched, requiring them to be equal. The constant k cancels out, yielding equation (8). The equivalent wavelength λe is the wavelength of each wavelength in terms of c. i It is a weighted harmonic average of the weights.

[0042] (8) Next, the coefficients of the first-order (n = 1, i.e., curvature at the peak) term are matched, requiring them to be equal. Similarly, k cancels out, resulting in equation (9). More generally, matching the nth-order term gives a set of equivalent wavelengths, as shown in equation (10).

[0043] (9) (10) Equation (10) is for weight c i The (2n + 1)th power-law average (Hölder average). Unless all λ i Equal (i.e., zero bandwidth), otherwise λ en As n changes strictly, therefore λ e0 ≠ λ e1 ≠λ e2 This indicates that even if the PSFs based on different wavelengths are all Gaussian functions, the broadband PSF obtained by their weighted superposition cannot achieve a full-order match with any Gaussian function. The broadband PSF is inherently non-Gaussian.

[0044] Although the broadband PSF does not satisfy a strictly Gaussian distribution, the λ used i Since the wavelengths are all above 600 nm, the contribution of higher-order expansion terms decays rapidly, and the non-Gaussianity becomes negligible. Numerical calculations show that first-order and higher-order terms contribute less than 0.1% to the PSF shape. Therefore, a single-wavelength Gaussian PSF constructed using the zero-order equivalent wavelength can achieve sufficient approximation accuracy.

[0045] Substituting the zero-order equivalent wavelength into equation (4), we obtain the single-wavelength Gaussian point spread function. As the final point spread function, its specific expression is: (11) Next, the effectiveness of the single-wavelength Gaussian point spread function constructed based on the zero-order equivalent wavelength is verified. Table 1 shows the equivalent wavelengths of the fluorescent dye Alexa Fluor 647 in different passbands before and after the introduction of the filter and detector. With the effective number of photons.

[0046] Table 1. Equivalent wavelength and effective photon number before and after introducing filters and detectors

[0047] As shown in Table 1, the effective number of photons per molecule is approximately 4636 in the passband of 655–800 nm (bandwidth 145 nm). =690 nm; in the passband 655–675 nm (bandwidth 20 nm), the effective photon number drops to 1766. = 666 nm. Compared to a narrow bandwidth of 20 nm, the effective photon count of a wide bandwidth of 145 nm is increased by 1.625 times, which can significantly improve the quality of super-resolution reconstructed images. After introducing filters and detectors, the wide bandwidth in the passband of 655–800 nm... = 689 nm, only 1 nm shifted from before the introduction, with a wide bandwidth in the passband of 655–675 nm. = 666 nm, consistent with the original value, indicating that the equivalent wavelength within this passband is mainly determined by the emission spectrum of the fluorescent dye, and the influence of the imaging system response is negligible.

[0048] Figure 3 The dashed lines in (c) and (d) represent single-wavelength Gaussian PSFs generated based on the equivalent wavelength λe0, and it can be seen that they almost completely overlap with the broadband superimposed PSFs. The maximum relative deviation obtained by numerical calculation is only 0.04%, which further verifies the high accuracy of the zero-order equivalent wavelength approximation and fully meets the requirements of engineering applications.

[0049] Based on the same inventive concept, in other embodiments, the present invention also provides a broadband PSF construction system based on weighted superposition and equivalent wavelength, which employs the broadband PSF construction method based on weighted superposition and equivalent wavelength as described above, including: The discretization module is used to discretize the fluorescence wavelength into a sequence containing several wavelengths within the bandpass range of the filter during the imaging process of simulated fluorescence after passing through the filter and detector response. The correction module is used to correct the relative emission intensity of each wavelength in the sequence based on the filter transmittance and detector quantum efficiency to obtain the effective relative emission intensity. The weight calculation module is used to calculate the weight of each wavelength based on the effective relative emission intensity; The point spread function construction module is used to superimpose the Gaussian point spread functions corresponding to all wavelengths in the sequence according to their weights to obtain the final point spread function; or, it calculates the equivalent wavelength based on the weights of all wavelengths in the sequence, and constructs a single-wavelength Gaussian point spread function based on the equivalent wavelength as the final point spread function.

[0050] In one embodiment, based on the broadband PSF construction method based on weighted superposition and equivalent wavelength, the present invention proposes an original image reconstruction method based on weighted superposition and equivalent wavelength, comprising the following steps: 1) Multiply the weight of each wavelength by the original super-resolution image to obtain the super-resolution image component for each wavelength; (12) in, Let i represent the super-resolution image component at the i-th wavelength. Represents the original super-resolution image. This represents the weight of the i-th wavelength.

[0051] 2) Convolve the super-resolution image component of each wavelength with the corresponding Gaussian point spread function to obtain the original image component of each wavelength. The calculation formula is as follows: (13) in, This represents the Gaussian point spread function for the i-th wavelength. This represents the convolution operation.

[0052] Alternatively: Multiply the super-resolution image component for each wavelength by the single-wavelength Gaussian point spread function constructed based on the equivalent wavelength to obtain the original image component for each wavelength. The calculation formula is as follows: (14) in, This represents the single-wavelength Gaussian point spread function constructed based on the equivalent wavelength.

[0053] 3) Add the original image components of all wavelengths within the sequence to obtain the final synthesized original image. The calculation formula is as follows: = (15) in, This represents the original image used in the final synthesis. This represents the original image component at the i-th wavelength.

[0054] Based on the same inventive concept, the present invention also provides a system for constructing an original image based on weighted superposition and equivalent wavelength, comprising: The super-resolution image component calculation module is used to multiply the weight of each wavelength by the original super-resolution image to obtain the super-resolution image component for each wavelength. The original image component calculation module is used to convolve the super-resolution image component of each wavelength with the corresponding Gaussian point spread function to obtain the original image component of each wavelength; or to multiply the super-resolution image component of each wavelength with a single-wavelength Gaussian point spread function constructed based on the equivalent wavelength to obtain the original image component of each wavelength. The original image synthesis module is used to add the original image components of all wavelengths in the sequence to obtain the final original image.

[0055] Next, the performance of the method of the present invention will be experimentally verified on an optical experimental system.

[0056] The optical experimental system was constructed based on an inverted optical microscope (IX-71, Olympus) equipped with a 100x oil immersion objective (Uplan SAPo, numerical aperture 1.40, Olympus). A 641 nm laser (CUBE 640-100C; Coherent) was used to excite Alexa-647 fluorescence, and a bandpass fluorescence filter (FF01-676 / 37, Semrock) was used to filter the fluorescence signal. A relay system with 3.5x image magnification was added between the original imaging plane of the microscope and the detector; this system consisted of two lenses with focal lengths of 50 cm and 175 cm, respectively. Finally, an EMCCD camera (DU-897U-CV0, Andor) was used to acquire the fluorescence signal. The exposure time for each original image was set to 30 ms, and a total of 20 frames were acquired for image reconstruction. The grid size of the super-resolution image was 11.43 nm. The effective pixel size of the original image is 45.714 nm, which is consistent with the pixel size of the microscope system and is approximately equal to half the standard deviation of the system's point spread function (PSF).

[0057] Based on the aforementioned optical experimental system, narrowband and broadband raw images were acquired, and the narrowband peak wavelength method and broadband weighted superposition (i.e., equivalent wavelength method) were used respectively. Figure 3 As shown in (c) and (d), the reconstruction results of the weighted superposition method and the equivalent wavelength method are exactly the same. CS-STORM super-resolution reconstruction is performed, and the simulated and real experimental results of the original image and the super-resolution reconstructed image are as follows: Figure 4 and Figure 5 As shown. Figure 4 (a) and Figure 5 (a) is one of the 20 frames of narrowband raw images captured. Figure 4 (b) and Figure 5 (b) is one of the 20 frames of wideband raw images captured. Figure 4 and Figure 5 (c) and (d) are super-resolution images reconstructed using the interior point method based on narrowband peak wavelength and broadband equivalent wavelength, respectively.

[0058] Due to insufficient effective photon collection, Figure 4 The super-resolution reconstructed image in (c) is blurry and the microtubule structure is almost impossible to identify. Figure 5 The microtubule structure in the super-resolution reconstructed image in (c) shows a number of breaks; Figure 4 The weighted superposition and equivalent wavelength method in (d) fully utilizes broadband photons, while ensuring accurate PSF modeling. The microtube structure obtained by super-resolution reconstruction is continuous and delicate, with superior detail resolution. Experimental results demonstrate that the equivalent wavelength method can effectively solve the PSF modeling mismatch problem under broadband detection, improving the effective photon count while maintaining super-resolution reconstruction accuracy.

[0059] Simulation and experimental results show that, within a 145 nm bandwidth of 655–800 nm passband, the method of this invention can increase the effective photon count by 1.625 times. Simultaneously, the resolution and structural continuity of the super-resolution reconstructed image are significantly superior to the traditional peak wavelength method.

[0060] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0061] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A broadband PSF construction method based on weighted superposition and equivalent wavelength, characterized in that, Includes the following steps: In the super-resolution microscopy process simulating the response of fluorescence after passing through a filter and detector, the fluorescence wavelength is discretized into a sequence containing several wavelengths within the bandpass range of the filter. For each wavelength in the sequence, the relative emission intensity of the corresponding wavelength is corrected based on the filter transmittance and the detector quantum efficiency to obtain the effective relative emission intensity; The weight of each wavelength is calculated based on the effective relative emission intensity; The final point spread function is obtained by weighting and superimposing the Gaussian point spread functions corresponding to all wavelengths in the sequence; or, the equivalent wavelength is calculated based on the weights of all wavelengths in the sequence, and a single-wavelength Gaussian point spread function is constructed based on the equivalent wavelength as the final point spread function.

2. The broadband PSF construction method based on weighted superposition and equivalent wavelength as described in claim 1, characterized in that, The formula for calculating the effective relative emission intensity at any wavelength is: in, Represents the i-th wavelength The relative emission intensity, Represents the i-th wavelength The corresponding filter transmittance, Represents the i-th wavelength The corresponding quantum efficiency; Represents the i-th wavelength The effective relative emission intensity.

3. The broadband PSF construction method based on weighted superposition and equivalent wavelength as described in claim 1, characterized in that, The weight of any wavelength is defined as the ratio of the effective relative emission intensity of that wavelength to the effective relative emission intensity of all wavelengths within the passband, calculated using the following formula: in, Represents the i-th wavelength The weight, Represents the i-th wavelength The effective relative emission intensity, This represents the total number of discretized wavelengths within the bandpass range.

4. The broadband PSF construction method based on weighted superposition and equivalent wavelength as described in claim 1, characterized in that, The final expression for the point spread function is obtained by weighting and summing the Gaussian point spread functions corresponding to all wavelengths in the sequence. for: in, This represents the total number of discretized wavelengths within the bandpass range; Represents the i-th wavelength The weights; is the independent variable, representing the spatial coordinates on the image plane; , represents the scaling factor, and NA represents the numerical aperture of the microscope objective.

5. The broadband PSF construction method based on weighted superposition and equivalent wavelength as described in claim 1, characterized in that, The equivalent wavelength is defined as the weighted harmonic average of all wavelengths within the bandpass range, and its calculation formula is as follows: in, For equivalent wavelength, For the i-th wavelength The weight, This indicates the total number of wavelengths within the bandpass range.

6. The broadband PSF construction method based on weighted superposition and equivalent wavelength as described in claim 5, characterized in that, Single-wavelength Gaussian point spread function constructed based on equivalent wavelength The expression is: in, Indicates the proportionality coefficient; is the independent variable, representing the spatial coordinates on the image plane.

7. A method for reconstructing the original image based on weighted superposition and equivalent wavelength, characterized in that, Includes the following steps: The weight of each wavelength is calculated according to the method described in any one of claims 1-6; The weight of each wavelength is multiplied by the original super-resolution image to obtain the super-resolution image component for each wavelength. The original image component of each wavelength is obtained by convolving the super-resolution image component of each wavelength with the corresponding Gaussian point spread function; or the original image component of each wavelength is obtained by multiplying the super-resolution image component of each wavelength with a single-wavelength Gaussian point spread function constructed based on the equivalent wavelength. The original image components of all wavelengths within the sequence are added together to obtain the final synthesized original image.

8. The original image reconstruction method based on weighted superposition and equivalent wavelength as described in claim 7, characterized in that, The final synthesis formula for the original image is expressed as: = in, This represents the original image used in the final synthesis. Represents the original image component at the i-th wavelength; or ; This represents the Gaussian point spread function for the i-th wavelength. Let i represent the super-resolution image component at the i-th wavelength. This represents the single-wavelength Gaussian point spread function constructed based on the equivalent wavelength. This represents the convolution operation; , Represents the original super-resolution image. This represents the weight of the i-th wavelength.

9. A broadband PSF construction system based on weighted superposition and equivalent wavelength, characterized in that, It employs the broadband PSF construction method based on weighted superposition and equivalent wavelength as described in any one of claims 1-6, comprising: The discretization module is used to discretize the fluorescence wavelength into a sequence containing several wavelengths within the bandpass range of the filter during the imaging process of simulated fluorescence after passing through the filter and detector response. The correction module is used to correct the relative emission intensity of each wavelength in the sequence based on the filter transmittance and detector quantum efficiency to obtain the effective relative emission intensity. The weight calculation module is used to calculate the weight of each wavelength based on the effective relative emission intensity; The point spread function construction module is used to superimpose the Gaussian point spread functions corresponding to all wavelengths in the sequence according to their weights to obtain the final point spread function; or, it calculates the equivalent wavelength based on the weights of all wavelengths in the sequence, and constructs a single-wavelength Gaussian point spread function based on the equivalent wavelength as the final point spread function.

10. A system for constructing original images based on weighted superposition and equivalent wavelength, characterized in that, The broadband PSF construction method based on weighted superposition and equivalent wavelength as described in any one of claims 1-6 includes: The super-resolution image component calculation module is used to multiply the weight of each wavelength by the original super-resolution image to obtain the super-resolution image component for each wavelength. The original image component calculation module is used to convolve the super-resolution image component of each wavelength with the corresponding Gaussian point spread function to obtain the original image component of each wavelength; or to multiply the super-resolution image component of each wavelength with a single-wavelength Gaussian point spread function constructed based on the equivalent wavelength to obtain the original image component of each wavelength. The original image synthesis module is used to add the original image components of all wavelengths in the sequence to obtain the final original image.

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