A structured light super-resolution imaging method and device with high imaging rate

Abstract

The application belongs to the technical field of super-resolution imaging, and discloses a high-imaging-rate structured light super-resolution imaging method and device. The application carries out microscopic imaging on a sample to be observed, and reflects a light beam carrying sample information to be observed to a beam splitting unit; the beam splitting unit splits the incident light beam into m sub-beams, a spatial light modulator modulates the m sub-beams in m regions to obtain m structured lights carrying sample information to be observed; the m structured lights converge and image on an ultrafast camera after an imaging lens to obtain m images; and an image reconstruction unit takes the m images as a super-resolution image reconstruction source to reconstruct the images to obtain a super-resolution image. The application solves the problem of low imaging rate of the existing structured light illumination microscopic technology, and can improve the imaging rate while maintaining the super-resolution capability of the image.

Description

Technical Field

[0001] This invention belongs to the field of super-resolution imaging technology, and more specifically, relates to a structured light super-resolution imaging method and apparatus with high imaging rate. Background Technology

[0002] Super-resolution optical microscopy plays a crucial role in various fields, especially in life science research. However, the resolution of optical microscopes is limited by the diffraction limit. Super-resolution techniques aimed at overcoming the diffraction limit can be broadly categorized into four types: (1) stimulated emission depletion microscopy; (2) structured illumination microscopy; (3) single-molecule localization imaging techniques, such as photoactivated localization microscopy and stochastic optical reconstruction microscopy; and (4) super-resolution optical fluctuation imaging.

[0003] While optical super-resolution microscopy strives to improve spatial resolution, it should also leverage its unique advantages to enhance temporal resolution. However, current super-resolution techniques achieve ultra-high spatial resolution at the expense of temporal resolution. Therefore, capturing images of living cellular biological processes while maintaining high resolution is challenging. Among known super-resolution techniques, structured illumination microscopy achieves super-resolution by shifting high-frequency spectra, taking a frequency domain extension approach.

[0004] Compared to other super-resolution techniques, structured light microscopy has a significant advantage in temporal resolution. Traditional structured light microscopy can achieve an imaging rate of around 1000 fps, primarily limited by the refresh rate of the spatial light modulator. However, as scientific research progresses, more microscopic and ultrafast processes need to be captured, making the imaging rate of traditional structured light microscopy insufficient for most research environments. Summary of the Invention

[0005] This invention provides a structured light super-resolution imaging method and apparatus with a high imaging rate, thereby solving the problem of low imaging rate in existing structured light micro-imaging technologies.

[0006] This invention provides a high-imaging-rate structured light super-resolution imaging device, comprising: a laser, a first beam splitter, a microscope objective, a first reflecting mirror, a beam-splitting unit, a spatial light modulator, an imaging lens, an ultrafast camera, and an image reconstruction unit. The laser generates continuous laser light, which is transmitted through the first beam splitter, passes through the microscope objective, and is incident on the surface of a sample to be observed. The microscope objective is used to perform microscopic imaging of the sample. The beam carrying information about the sample is reflected by the first reflecting mirror, passes again through the microscope objective, and is reflected by the first beam splitter to the beam-splitting unit. The beam-splitting unit splits the incident beam into m sub-beams with the same intensity and no optical path difference. The spatial light modulator modulates the m sub-beams in m regions, loading different structured light patterns into different regions to obtain m beams of structured light carrying information about the sample. The m beams of structured light are converged and imaged on the ultrafast camera after passing through the imaging lens, resulting in m images. The image reconstruction unit uses the m images as the source for super-resolution image reconstruction to obtain a super-resolution image.

[0007] Preferably, the high-imaging-rate structured light super-resolution imaging device further includes: a shaping unit; the shaping unit is located between the laser and the first beam splitter, and the shaping unit is used to expand the continuous laser beam.

[0008] Preferably, the shaping unit includes a first convex lens and a second convex lens arranged sequentially along the optical path, wherein the focal length of the first convex lens is smaller than the focal length of the second convex lens.

[0009] Preferably, the high-imaging-rate structured light super-resolution imaging device further includes: a telescope lens; the telescope lens is located between the first beam splitter and the microscope objective, and the telescope lens is used to correct the phase difference caused by the microscope objective.

[0010] Preferably, the beam splitting unit is an i+1 level mesh structure, including an i-level structural component and two periscope arrays located at the exit end as the i+1 level structure; each structural component includes a beam splitter and two sets of reflectors located on both sides of the beam splitter; each periscope array includes m / 2 periscopes with different spacing arranged side by side;

[0011] The beam splitter in the first to i-1th stage structural components is used to split the incident light into two groups of light with the same intensity, and the two sets of reflectors are used to reflect the two groups of light obtained by beam splitting to the beam splitter in the next stage structural component.

[0012] The beam splitter in the i-th stage structural component is used to split the incident light into two groups of light with the same intensity, and the two sets of reflectors are used to ensure that the two groups of light obtained by splitting have no optical path difference and are in the same direction and are respectively emitted to the two periscope arrays.

[0013] The periscope array is used to eliminate the optical path difference between multiple sub-beams in each group of light.

[0014] Preferably, the spatial light modulator employs a digital micromirror device.

[0015] Preferably, the structured light pattern is a stripe pattern, and different stripe patterns loaded in different regions have different stripe orientation angles and / or different phases.

[0016] Preferably, the outgoing beam after passing through the beam splitting unit is aligned with the modulation region of the spatial light modulator, and the positional distribution of the structured light pattern loaded on the spatial light modulator corresponds to the incident position of the beam.

[0017] This invention provides a high-imaging-rate structured light super-resolution imaging method, implemented using the aforementioned high-imaging-rate structured light super-resolution imaging device. The method includes the following steps:

[0018] Step 1: A continuous laser is generated by a laser. The continuous laser is transmitted through a first beam splitter, passes through a microscope objective, and is incident on the surface of the sample to be observed. The microscope objective is used to perform microscopic imaging of the sample to be observed.

[0019] Step 2: The beam carrying the information of the sample to be observed is reflected by the first reflecting mirror, and after passing through the microscope objective again, it is reflected by the first beam splitter to the beam splitting unit; the beam splitting unit splits the incident beam into m sub-beams with the same light intensity and no optical path difference.

[0020] Step 3: The spatial light modulator modulates m sub-beams in m regions, with different structured light patterns loaded in different regions, to obtain m beams of structured light carrying information about the sample to be observed.

[0021] Step 4: m beams of structured light are converged and imaged on an ultrafast camera after passing through an imaging lens, resulting in m images;

[0022] Step 5: The image reconstruction unit uses m images as the source for super-resolution image reconstruction and performs image reconstruction to obtain a super-resolution image.

[0023] Preferably, step 5 includes the following sub-steps:

[0024] The spatial frequency and initial phase of the structured light illumination are determined using the super-resolution image reconstruction source.

[0025] The power spectrum of the super-resolution image reconstruction source is estimated to obtain each spectral component of the super-resolution image reconstruction source; after setting the quality adjustment factor, Wiener filtering is performed on the super-resolution image reconstruction source, and the shift and phase of the two offset spectral components are calibrated.

[0026] All spectral components are combined, and the super-resolution image is obtained by inverse Fourier transform.

[0027] One or more technical solutions provided in this invention have at least the following technical effects or advantages:

[0028] In this invention, continuous laser light generated by a laser is transmitted through a first beam splitter, passes through a microscope objective, and is incident on the surface of the sample to be observed. The microscope objective is used to perform microscopic imaging of the sample. The beam carrying information about the sample is reflected by a first reflecting mirror, passes through the microscope objective again, and is reflected by the first beam splitter to a beam splitting unit. The beam splitting unit splits the incident beam into m sub-beams with the same intensity and no optical path difference. Then, a spatial light modulator modulates the m sub-beams in m regions, loading different structured light patterns into different regions to obtain m beams of structured light carrying information about the sample. Subsequently, m images obtained by an imaging lens and an ultrafast camera are used as the source for super-resolution image reconstruction. The image reconstruction unit performs image reconstruction to obtain a super-resolution image. In other words, this invention uses a beam splitting unit to split continuous laser light and incident it onto a spatial light modulator with regionally loaded structured light patterns. This allows the spatial light modulator to load different modulation patterns only in different regions, rather than continuously refreshing and loading these different modulation patterns, effectively solving the problem that the imaging rate of existing structured light microscopy is limited by the refresh rate of the spatial light modulator. The solution provided by this invention achieves image super-resolution capabilities comparable to existing structured illumination micro-technology, while increasing the imaging rate to that of ultrafast cameras. Currently, industrially available ultrafast cameras can achieve imaging rates of around 100,000 fps, and theoretically, the solution provided by this invention can also reach an imaging rate of around 100,000 fps. This high-resolution imaging technology offers new methods and approaches for studying microscopic dynamic phenomena in life sciences, physics, chemistry, and industrial sciences. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of a high-imaging-rate structured light super-resolution imaging device provided in an embodiment of the present invention;

[0030] Figure 2 This is a schematic diagram of the beam-splitting unit in a high-imaging-rate structured light super-resolution imaging device provided in an embodiment of the present invention;

[0031] Figure 3 This is a schematic diagram of the periscope array in a high-imaging-rate structured light super-resolution imaging device provided in an embodiment of the present invention;

[0032] Figure 4 This is a schematic diagram of a pattern loaded on a spatial light modulator in a high-imaging-rate structured light super-resolution imaging device provided in an embodiment of the present invention. Detailed Implementation

[0033] To better understand the above technical solutions, the following will provide a detailed explanation of the technical solutions in conjunction with the accompanying drawings and specific implementation methods.

[0034] Example 1:

[0035] Example 1 provides a high-imaging-rate structured light super-resolution imaging method, comprising the following steps:

[0036] Step 1: A continuous laser is generated by a laser, and the continuous laser beam is expanded by a shaping unit. The expanded laser beam is transmitted through a first beam splitter, and then passes through a microscope lens and a microscope objective in sequence before being incident on the surface of the sample to be observed. The microscope objective can perform microscopic imaging on the sample to be observed, and the microscope lens can correct the phase difference introduced by the microscope objective.

[0037] Specifically, Example 1 utilizes a high-imaging-rate structured light super-resolution imaging device, see [link to example]. Figure 1 The system includes a laser 101, a shaping unit, a first beam splitter 104, a tube lens 105, a microscope objective 106, a first reflecting mirror 108, a beam splitting unit 109, a spatial light modulator 110, an imaging lens 111, an ultrafast camera 112, and an image reconstruction unit. The sample to be observed 107 is located between the microscope objective 106 and the first reflecting mirror 108.

[0038] The shaping unit includes a first convex lens 102 and a second convex lens 103 arranged sequentially along the optical path, wherein the focal length of the first convex lens 102 is smaller than the focal length of the second convex lens 103.

[0039] Step 2: The beam carrying the information of the sample to be observed is reflected by the first reflecting mirror, and then reflected again by the first beam splitter after passing through the microscope objective and the microscope tube lens. The beam splitter splits the incident beam into m identical sub-beams (that is, the outgoing light of the beam splitter is m continuous beams carrying the same information of the sample to be observed, having the same light intensity and no optical path difference).

[0040] Specifically, the beam-splitting unit is an i+1 level mesh structure, including an i-level structural component and two periscope arrays located at the exit end as the i+1 level structure; each structural component includes a beam splitter and two sets of reflectors located on both sides of the beam splitter; each periscope array includes m / 2 periscopes arranged side by side with different spacing. The beam splitter in the first to i-1 level structural components is used to split the incident light into two sets of light with the same intensity, and the two sets of reflectors are used to reflect the two sets of light obtained by beam splitting to the beam splitter in the next level structural component respectively; the beam splitter in the i-level structural component is used to split the incident light into two sets of light with the same intensity, and the two sets of reflectors are used to ensure that the two sets of light obtained by beam splitting have no optical path difference and are in the same direction, and are emitted to the two periscope arrays respectively; the periscope array is used to eliminate the optical path difference of multiple sub-beams in each set of light.

[0041] Step 3: The spatial light modulator modulates m sub-beams in m regions, with different structured light patterns loaded in different regions, to obtain m beams of structured light carrying information about the sample to be observed.

[0042] That is, m beams of continuous light are incident on the spatial light modulator. The spatial light modulator modulates the incident light by loading different structured light patterns in m regions corresponding to the incident position of the incident light, so as to obtain m beams of structured light carrying the information of the sample to be observed.

[0043] The structured light pattern is a stripe pattern, and different stripe patterns loaded in different regions have different stripe orientation angles and / or different phases.

[0044] The outgoing beam after passing through the beam splitting unit is aligned with the modulation region of the spatial light modulator, and the positional distribution of the structured light pattern loaded on the spatial light modulator corresponds to the incident position of the beam.

[0045] The spatial light modulator can be a digital micromirror device.

[0046] Step 4: m beams of structured light are converged and imaged on an ultrafast camera after passing through an imaging lens, resulting in m images.

[0047] Step 5: The image reconstruction unit uses m images as the source for super-resolution image reconstruction and performs image reconstruction to obtain a super-resolution image.

[0048] Step 5 includes the following sub-steps:

[0049] The spatial frequency and initial phase of the structured light illumination are determined using the super-resolution image reconstruction source.

[0050] The power spectrum of the super-resolution image reconstruction source is estimated to obtain each spectral component of the super-resolution image reconstruction source; after setting the quality adjustment factor, Wiener filtering is performed on the super-resolution image reconstruction source, and the shift and phase of the two offset spectral components are calibrated.

[0051] All spectral components are combined, and the super-resolution image is obtained by inverse Fourier transform.

[0052] The following examples illustrate this with specific parameters.

[0053] Step 1: A continuous laser is generated by a laser, and the continuous laser is expanded by a shaping unit. The expanded laser is transmitted through the first beam splitter, and then passes through the lens of the microscope tube and the microscope objective in sequence before being incident on the surface of the sample to be observed.

[0054] Step 2: The beam carrying the information of the sample to be observed is reflected by the first reflecting mirror, and then reflected again by the first beam splitter after passing through the microscope objective and the microscope tube lens. The beam splitter splits the incident beam into 16 identical sub-beams.

[0055] See Figure 2 The beam splitting unit is a 5-level mesh structure consisting of four beam splitters, nine reflectors and two periscope arrays, including 4 levels of structural components and two periscope arrays located at the exit end as the 5th level structure; each level of structural component includes a beam splitter and two sets of reflectors located on both sides of the beam splitter.

[0056] The beam splitters in the first to third stage structural components are used to split the incident light into two sets of light with the same intensity. The two sets of mirrors are used to reflect the two sets of light obtained by beam splitting to the beam splitters in the next stage structural component. Specifically, the first stage structural component includes a second beam splitter 201, a second mirror 205, and a third mirror 206; the second stage structural component includes a third beam splitter 202, a fourth mirror 207, and a fifth mirror 208; and the third stage structural component includes a fourth beam splitter 203, a sixth mirror 209, and a seventh mirror 210.

[0057] The beam splitter (i.e., the fifth beam splitter 204) in the fourth-level structural component is used to split the incident light into two sets of light with the same intensity. The two sets of reflectors (the first set of reflectors includes the ninth reflector 212 and the tenth reflector 213, and the second set of reflectors includes the eighth reflector 211) are used to ensure that the two sets of light obtained by beam splitting have no optical path difference and are emitted in the same direction to the two periscope arrays (i.e., the first periscope array 214 and the second periscope array 215).

[0058] Each of the periscope arrays consists of eight periscopes arranged side by side at different spacings, such as... Figure 3As shown, this is to eliminate the optical path difference between the eight sub-beams of each group of light.

[0059] Alternatively, the fourth-level structural components, together with the two periscope arrays, can be considered as the fourth-level structure, and the beam splitter unit can be considered as a fourth-level mesh structure. The three mirrors and two periscope arrays in the fourth-level structure are used to ensure that the optical path difference of the emitted pulse is consistent and to ensure that the emitted pulse is aligned with the modulation region of the spatial light modulator.

[0060] Step 3: The spatial light modulator modulates 16 sub-beams in 16 regions, with different structured light patterns loaded in different regions, to obtain 16 beams of structured light carrying information about the sample to be observed.

[0061] Specifically, after the continuous laser beam is emitted from the spatial light modulator, it generates two-dimensional striped structured light, see [reference needed]. Figure 4 The 16 structured light beams have fringe orientation angles spaced 45 degrees apart, phase differences of π / 2, and spatial frequencies of 150 lp / μm. A fringe pattern is loaded into each specific region using the spatial light modulator. By observing the fringe orientation and phase of the emitted structured light, the fringe pattern loaded by the spatial light modulator is set and adjusted to ensure that the required structured light is met.

[0062] Step 4: The 16 beams of structured light are converged and imaged on the ultrafast camera after passing through the imaging lens, resulting in 16 images.

[0063] Specifically, the 16 images are 16 images with different orientations and phases, each carrying sample information and modulated with structured light.

[0064] Step 5: The image reconstruction unit uses 16 images as the super-resolution image reconstruction source to perform image reconstruction and obtain a super-resolution image.

[0065] Among them, the image reconstruction algorithm can utilize the traditional structured illumination microscopy (SIM) image reconstruction algorithm, using 16 images captured with different structured light orientations and phases as the image reconstruction source to perform image super-resolution reconstruction.

[0066] Example 2:

[0067] Example 2 provides a high-imaging-rate structured light super-resolution imaging device, comprising: a laser, a shaping unit, a first beam splitter, a tube lens, a microscope objective, a first reflecting mirror, a beam splitter unit, a spatial light modulator, an imaging lens, an ultrafast camera, and an image reconstruction unit.

[0068] The laser is used to generate continuous laser light. The shaping unit is used to expand the continuous laser beam. The expanded continuous laser beam is transmitted through the first beam splitter, and after passing through the microscope lens and the microscope objective, it is incident on the surface of the sample to be observed. The microscope objective is used to perform microscopic imaging of the sample to be observed, and the microscope lens is used to correct the phase difference introduced by the microscope objective. The beam carrying the information of the sample to be observed is reflected by the first mirror, and after passing through the microscope objective and the microscope lens again, it is reflected by the first beam splitter to the beam splitting unit. The beam splitting unit splits the incident beam into m sub-beams with the same light intensity and carrying the same information of the sample to be observed. The spatial light modulator modulates the m sub-beams in m regions, and different structured light patterns are loaded in different regions to obtain m beams of structured light carrying the information of the sample to be observed. The m beams of structured light are converged and imaged on the ultrafast camera after passing through the imaging lens to obtain m images. The image reconstruction unit uses the m images as the source of super-resolution image reconstruction to perform image reconstruction to obtain a super-resolution image.

[0069] The high imaging rate structured light super-resolution imaging device provided in Example 2 corresponds to the high imaging rate structured light super-resolution imaging method provided in Example 1. Each device in Example 2 can realize the corresponding function of the method in Example 1, so it will not be described again.

[0070] In summary, when performing high-resolution structured light super-light imaging of the sample using the scheme provided by this invention, the sample is first imaged using a microscope objective. Then, the continuous light carrying the sample information is split into several parts by a beam-splitting unit. The required structured light pattern is then loaded into different regions by a spatial light modulator. After the continuous light carrying the sample information is incident, it is modulated, simultaneously generating multiple beams of structured light carrying sample information with different orientations and phases. Finally, these beams are converged by an imaging lens and captured by an ultrafast camera. The multiple images captured by the ultrafast camera can be used to reconstruct the super-resolution image of the sample using image reconstruction algorithms from traditional structured light microscopy. This invention solves the problem that the imaging rate of structured light microscopy is limited by the refresh rate of the spatial light modulator. This invention not only has the advantages of structured light super-resolution imaging but also has a high imaging rate, theoretically reaching the acquisition rate of an ultrafast camera.

[0071] Finally, it should be noted that the above specific embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to examples, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A high-imaging-rate structured light super-resolution imaging device, characterized in that, include: The system comprises a laser, a first beam splitter, a microscope objective, a first reflecting mirror, a beam-splitting unit, a spatial light modulator, an imaging lens, an ultrafast camera, and an image reconstruction unit. The laser generates continuous laser light, which is transmitted through the first beam splitter, passes through the microscope objective, and then incident on the surface of the sample to be observed. The microscope objective is used to perform microscopic imaging of the sample. The beam carrying information about the sample is reflected by the first reflecting mirror, passes again through the microscope objective, and is reflected by the first beam splitter to the beam-splitting unit. The beam-splitting unit splits the incident beam into m sub-beams with the same intensity and no optical path difference. The spatial light modulator modulates m sub-beams in m regions, with different structured light patterns loaded in different regions, to obtain m beams of structured light carrying information about the sample to be observed; the m beams of structured light converge on the ultrafast camera after passing through the imaging lens to obtain m images; the image reconstruction unit uses the m images as the source of super-resolution image reconstruction to perform image reconstruction and obtain a super-resolution image.

2. The high-imaging-rate structured light super-resolution imaging device according to claim 1, characterized in that, Also includes: Shaping unit; The shaping unit is located between the laser and the first beam splitter, and the shaping unit is used to expand the continuous laser beam.

3. The high-imaging-rate structured light super-resolution imaging device according to claim 2, characterized in that, The shaping unit includes a first convex lens and a second convex lens arranged sequentially along the optical path, wherein the focal length of the first convex lens is smaller than the focal length of the second convex lens.

4. The high-imaging-rate structured light super-resolution imaging device according to claim 1, characterized in that, Also includes: Tube lens; The tube lens is located between the first beam splitter and the microscope objective, and is used to correct the phase difference caused by the microscope objective.

5. The high-imaging-rate structured light super-resolution imaging device according to claim 1, characterized in that, The beam splitting unit is an i+1 level mesh structure, including an i-level structural component and two periscope arrays located at the exit end as the i+1 level structure; each structural component includes a beam splitter and two sets of reflectors located on both sides of the beam splitter; each periscope array includes m / 2 periscopes with different spacing arranged side by side. The beam splitter in the first to i-1th stage structural components is used to split the incident light into two groups of light with the same intensity, and the two sets of reflectors are used to reflect the two groups of light obtained by beam splitting to the beam splitter in the next stage structural component. The beam splitter in the i-th stage structural component is used to split the incident light into two groups of light with the same intensity, and the two sets of reflectors are used to ensure that the two groups of light obtained by splitting have no optical path difference and are in the same direction and are respectively emitted to the two periscope arrays. The periscope array is used to eliminate the optical path difference between multiple sub-beams in each group of light.

6. The high-imaging-rate structured light super-resolution imaging device according to claim 1, characterized in that, The spatial light modulator employs a digital micromirror device.

7. The high-imaging-rate structured light super-resolution imaging device according to claim 1, characterized in that, The structured light pattern is a stripe pattern, and different stripe patterns loaded in different regions have different stripe orientation angles and / or different phases.

8. The high-imaging-rate structured light super-resolution imaging device according to claim 1, characterized in that, The outgoing beam after passing through the beam splitting unit is aligned with the modulation region of the spatial light modulator, and the positional distribution of the structured light pattern loaded on the spatial light modulator corresponds to the incident position of the beam.

9. A high-imaging-rate structured light super-resolution imaging method, characterized in that, The method employs a high-imaging-rate structured light super-resolution imaging device as described in any one of claims 1-8, and includes the following steps: Step 1: A continuous laser is generated by a laser. The continuous laser is transmitted through a first beam splitter, passes through a microscope objective, and is incident on the surface of the sample to be observed. The microscope objective is used to perform microscopic imaging of the sample to be observed. Step 2: The beam carrying the information of the sample to be observed is reflected by the first reflecting mirror, and after passing through the microscope objective again, it is reflected by the first beam splitter to the beam splitting unit; the beam splitting unit splits the incident beam into m sub-beams with the same light intensity and no optical path difference. Step 3: The spatial light modulator modulates m sub-beams in m regions, with different structured light patterns loaded in different regions, to obtain m beams of structured light carrying information about the sample to be observed. Step 4: m beams of structured light are converged and imaged on an ultrafast camera after passing through an imaging lens, resulting in m images; Step 5: The image reconstruction unit uses m images as the source for super-resolution image reconstruction and performs image reconstruction to obtain a super-resolution image.

10. The high-imaging-rate structured light super-resolution imaging method according to claim 9, characterized in that, Step 5 includes the following sub-steps: The spatial frequency and initial phase of the structured light illumination are determined using the super-resolution image reconstruction source. The power spectrum of the super-resolution image reconstruction source is estimated to obtain each spectral component of the super-resolution image reconstruction source; After setting the quality adjustment factor, Wiener filtering is applied to the super-resolution image reconstruction source, and the spectral components of the two offsets are calibrated for shift and phase. All spectral components are combined, and the super-resolution image is obtained by inverse Fourier transform.

Images