Large depth-of-field reconstruction method based on Fourier lamination imaging

Abstract

The invention discloses a large depth-of-field reconstruction method based on Fourier lamination imaging. According to the method, the characteristics of redundant information can be fully utilized by utilizing the Fourier laminated imaging technology, a layered reconstruction model is established, after a high-resolution object of each layer is accurately reconstructed, information of the object of each layer is synthesized, and finally a reconstruction result with a large view field, high resolution and a large depth of field is obtained. Compared with the traditional Fourier lamination imaging technology, the reconstruction method disclosed by the invention has the advantages that the field depth range of system imaging is obviously expanded, and the reconstruction method is very suitable for pathological imaging of thick samples.

Description

Technical Field

[0001] The present invention belongs to optical microscopic imaging, and in particular to a large depth of field reconstruction method based on Fourier stack imaging. Background Art

[0002] In the field of traditional microscopic imaging, there has always been an irreconcilable contradiction, namely the contradiction between imaging field of view and imaging resolution. Images with a larger field of view can be obtained through a low-power microscope, but the resolution is low; high-resolution images can be obtained through a high-power microscope, but the field of view is small. Fourier stack imaging technology is a computational microscopic imaging technology developed in recent years. This method integrates the concepts of phase recovery and synthetic aperture, and performs alternating iterations based on the light intensity information recorded in the spatial domain and a certain fixed mapping relationship in the frequency domain, and finally achieves imaging results with a large field of view and high resolution at the same time. In the traditional Fourier stack imaging system, the sample is illuminated by plane waves from different angles and imaged through a low numerical aperture objective. Two-dimensional thin objects are illuminated by plane waves from different angles, and the frequency spectrum of the object on the back focal plane of the objective is translated to corresponding different positions. Therefore, some frequency components that originally exceeded the numerical aperture of the objective are translated into the numerical aperture of the objective, so that they can be transferred to the imaging surface for imaging. On the other hand, incident light at different angles can be equivalent to overlapping pupil functions (subapertures) at different positions on the spectrum. Each time the spectrum passes through the subapertures at different positions, it forms a stack in the frequency domain. Then, a series of low-resolution images taken by the camera are iterated in the frequency domain to update the spectrum information in the corresponding subapertures in turn. The overlapping of subapertures expands the bandwidth of the frequency domain and restores high-frequency information that exceeds the spatial resolution limit of the objective lens, and finally reconstructs the large-field-of-view high-resolution light intensity and phase image of the object at the same time. In this way, a low numerical aperture and low magnification objective lens is used to obtain a large-field-of-view and high-resolution imaging result.

[0003] However, the traditional Fourier stack imaging model has a strong assumption: the object being measured is a two-dimensional, thin, flat object. However, in actual situations, the sample to be observed is often a three-dimensional object with thickness. When reconstructing such an object, artifacts and other errors are very likely to occur. In response to the above problems, Tian Lei et al. combined the classic multi-slice model in the field of CT and MRI with the FPM imaging method to construct a three-dimensional FPM reconstruction algorithm framework and achieved super-resolution reconstruction of three-dimensional samples (Tian L, Waller L. 3D intensity and phase imaging from light field measurements in an LED array microscope [J]. optica, 2015, 2 (2): 104-111.). The MultiSlice model models the three-dimensional sample as a series of two-dimensional sample slices with specific spacing in the spatial domain, and connects each sample slice through the free propagation of light waves during the forward modeling and reverse recovery process. This algorithm can achieve high-resolution reconstruction results for each layer of two overlapping resolution plates. Zuo Chao et al. proposed a Fourier stack diffraction tomography technique, which extends the traditional FPM model to three dimensions and performs phase recovery and phase reconstruction in the three-dimensional Fourier domain (Zuo C, Sun J, Li J, et al. Wide-field high-resolution 3D microscopy with Fourierptychographic diffraction tomography [J]. Optics and Lasers in Engineering, 2020, 128: 106003.). They derived the spectral support domain of the system through the numerical aperture of the illumination and the numerical aperture of the objective lens of the microscope system, and obtained the specific structure of the support domain, realizing the imaging method of Fourier stacking of three-dimensional objects. These methods often require a large amount of data acquisition and tomographic calculations to obtain high-precision three-dimensional reconstruction results. However, these technologies are difficult to apply to the pathological diagnosis industry because: on the one hand, when making a diagnosis, doctors often do not need to obtain high-resolution three-dimensional information, but only need to obtain two-dimensional image information with a large depth of field; on the other hand, the above algorithms take a lot of time to calculate, which limits the development of these technologies in practical applications. Summary of the invention

[0004] The purpose of the present invention is to propose a large depth of field reconstruction method based on Fourier stack imaging to solve the problem of artifacts and other errors generated when Fourier stack imaging reconstructs thicker objects, and to achieve high-speed, high-resolution, large field of view, and large depth of field pathological imaging.

[0005] The technical solution to achieve the purpose of the present invention is: a large depth of field reconstruction method based on Fourier stack imaging, the steps are as follows:

[0006] Step 1: Original intensity image acquisition: Use a ring-shaped LED board as the illumination source of the microscope, light up the three RGB lamp beads of each LED in turn, and the light emitted by the lamp beads after irradiating the sample is regarded as plane monochromatic light. By synchronously triggering the camera and scanning the lamp bead array, the corresponding low-resolution bright field image of each lamp bead is acquired;

[0007] Step 2: determine the low-frequency cutoff frequency according to the numerical aperture of the microscope objective and the wavelength of the incident light, and calculate the spatial frequency of the incident light corresponding to each LED lamp bead according to the coordinate position of the LED lamp bead in space;

[0008] Step 3: add and average all the captured low-resolution bright field images, then perform linear interpolation and amplification to obtain the initial solution of the high-resolution image, and divide the initial solution into several layers of complex amplitude objects;

[0009] Step 4, setting the defocus values ​​corresponding to the complex amplitude objects at different layers. For each layer of complex amplitude objects, first convert the complex amplitudes of each layer referred to by it to the frequency domain through Fourier transform, and then multiply the low-pass filter function corresponding to the tilted light angle and the transfer function corresponding to the defocus amount in the frequency domain to obtain each updated sub-aperture spectrum of each layer, and then convert each updated sub-aperture spectrum of each layer back to the spatial domain through inverse Fourier transform to obtain the complex amplitude objects corresponding to each sub-aperture at different defocus positions of each layer;

[0010] Step 5, according to the distribution of the light intensity of each layer of complex amplitude objects corresponding to the same sub-aperture, the update coefficient of each sub-aperture in each layer is set;

[0011] Step 6: Iterative reconstruction. Use Fourier stack imaging technology to transfer the complex amplitude object corresponding to each sub-aperture to the frequency domain at each layer, and perform synthetic aperture calculations one by one in the frequency domain according to the update coefficients calculated in step 5. When the cost function of each layer is less than the set threshold, stop the iteration and obtain the high-resolution result of each layer. Otherwise, return to step 4.

[0012] Step seven: synthesize the high-resolution results obtained by converging different layers to obtain the final large depth of field image.

[0013] Preferably, the specific formula for determining the low-frequency cutoff frequency according to the numerical aperture of the microscope objective and the wavelength of the incident light is:

[0014]

[0015] In the formula, is the low frequency cut-off frequency, λ iis the wavelength of the incident light, NA obj is the numerical aperture of the microscope objective.

[0016] Preferably, the specific method for calculating the spatial frequency of the incident light corresponding to each LED lamp bead according to the coordinate position of the LED lamp bead in space is:

[0017] Calculate the spatial frequency of the incident light corresponding to each LED lamp bead according to its coordinate position in space Where n represents the number of the lamp beads. The image captured when is a bright field image; when The image captured For dark field images, When the illumination is considered to be matched illumination, the illumination aperture NA ill =NA obj , is the low frequency cutoff frequency.

[0018] Preferably, the high-resolution image initial solution gus Specifically:

[0019]

[0020] Where P{} is the bilinear interpolation upsampling, is the low-resolution bright field image captured, and m is the total number of images captured.

[0021] Preferably, in step 3, the initial solution I gus Divided into several layers of complex amplitude objects Each layer is the initial solution of the corresponding layer, and the calculation formula is as follows;

[0022]

[0023] In the formula, j is the number of layers.

[0024] Preferably, the complex amplitude object corresponding to each sub-aperture at different defocus positions in step 4 Specifically:

[0025]

[0026] Where n represents the number of the lamp beads, j is the number of layers, F represents the Fourier transform operation, and F -1 Represents the inverse Fourier transform operation, S n It represents the shift operation of the spectrum. The shift amount is determined by the angle of the inclined light corresponding to each lamp bead. CTF is the low-pass filter function, f x ,f y is the spatial frequency, k i is the wave number, is the low frequency cut-off frequency, λ i is the wavelength of the incident light.

[0027] Preferably, the update coefficient is set according to the light intensity distribution of the complex amplitude object corresponding to each sub-aperture of each layer.

[0028]

[0029] In the formula, n represents the number of lamp beads, j is the number of layers, and m is the total number of images taken. is a complex amplitude object with different sub-apertures at different defocus positions, {} * represents the conjugate operation, and |*| represents the absolute value operation.

[0030] Preferably, the specific method of iterative reconstruction in step six is:

[0031] Fourier stack imaging technology is used to update the complex amplitude object corresponding to each sub-aperture of each layer At the same time, multiply the exponent by the update coefficient in step 5

[0032]

[0033] in, is the updated complex amplitude object corresponding to each sub-aperture of each layer, n represents the number of the lamp bead, is the update coefficient, P{} is the bilinear interpolation upsampling, This is a low-resolution bright field image captured. is the complex amplitude object before updating, m is the total number of images taken, and j is the number of layers;

[0034] The updated complex amplitude object of each sub-aperture of each layer Fourier transform to the frequency domain and update the complex amplitude object using the updated subaperture spectrum The part corresponding to the subaperture;

[0035]

[0036] in, represents the updated complex amplitude object, F represents the Fourier transform operation, F -1 Represents the inverse Fourier transform operation, S n It represents the shift operation of the spectrum. The shift amount is determined by the angle of the inclined light corresponding to each lamp bead. CTF is the low-pass filter function, f x ,f y is the spatial frequency, k i is the wave number, is the low frequency cut-off frequency, λi is the wavelength of the incident light. α is the update step size.

[0037] Finally, calculate the cost function COST;

[0038]

[0039] {} * represents the conjugate operation, |*| represents the absolute value operation, and COST is the cost function.

[0040] When the cost function of each layer is less than the set threshold, stop the iteration and obtain the high-resolution result of each layer. Otherwise, keep the complex amplitude object in step 6. Replace it with the complex amplitude object in step 5 Repeat step 5 to perform a new round of complex amplitude analysis for each layer and each sub-aperture. calculation and iteration.

[0041] Preferably, in step 7, the high-resolution results obtained by converging different layers are synthesized to obtain the final large depth of field image I result Specifically:

[0042]

[0043] in, is the complex amplitude result of each layer after update, {} * Represents the conjugate operation.

[0044] Compared with the prior art, the present invention has the following significant advantages: (1) Compared with the traditional Fourier stack imaging technology, the present invention has a larger depth of field imaging range, which solves the problem of artifacts and other errors generated when reconstructing thick objects in the traditional algorithm. (2) Compared with other imaging algorithms for obtaining three-dimensional information of objects, the present invention has a smaller amount of collected data and a faster reconstruction speed, and can achieve high-speed high-throughput reconstruction; at the same time, the object information within a certain depth range is synthesized into a two-dimensional image, which is convenient for observation and judgment during pathological diagnosis.

[0045] The present invention is further described in detail below in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is a schematic diagram of the actual device of a ring lighting single LED illuminating an object.

[0047] Figure 2 It is a flowchart of the iterative reconstruction method of the present invention.

[0048] Figure 3 This is the reconstruction result of a thick HPV cell sample with a large depth of field according to the present invention. Figure 3(a) is the reconstruction result obtained using traditional Fourier stack imaging. Figure 3 (b) is the reconstruction result obtained by the large depth of field reconstruction method proposed in the present invention. DETAILED DESCRIPTION

[0049] like Figure 1 , 2 As shown, a large depth of field reconstruction method based on Fourier stack imaging, the specific steps are:

[0050] Step 1: Original intensity image acquisition: Use a ring LED board as the illumination source for the microscope, and light up the three RGB lamp beads of each LED element in turn. The light emitted by the lamp beads after irradiating the sample can be regarded as a wavelength of λ i (i=1,2,3) plane monochromatic light. The center of the annular light panel is on the optical axis of the microscope objective system. The incident light irradiates the sample and passes through the microscope objective system. By synchronously triggering the camera and scanning the lamp array, the corresponding low-resolution bright field image of each lamp bead is collected as follows: Where n is the lamp bead number of the lamp board.

[0051] The present invention is based on the setting of a ring-shaped lighting light source LED light board 4. Compared with the traditional bright field microscope, the traditional light source needs to be replaced by a ring-shaped LED array. The LED array is placed under the object 3, and other parts of the microscope such as the microscope objective lens and the camera acquisition module are consistent with the traditional bright field microscope. Among them, f is the focal length of the objective lens 2, which is generally about 10 mm, and the center of the ring-shaped lighting light source is on the optical axis of the system. The LED light board illuminates the object, and the object information is finally imaged on the camera 1 through the objective lens. The LED array includes a number of LED lamp beads, and each lamp bead is composed of three colors of red, green and blue. Its typical wavelengths are: red light 620nm, green light 550nm, blue light 460nm. The distance between each LED lamp bead and the center point is 2cm, 4cm, 6cm... The LED array can be purchased directly from the market. Table 1 shows a parameter diagram of a ring-shaped LED light board that can be purchased on the market. The light board contains a total of 5 circles of concentric ring lamp bead arrays. The number of lamps from the inside to the outside is 8, 16, 24, 32, and 48, and the brightness of each lamp bead is above 1000cd / m2.

[0052] Table 1:

[0053]

[0054] Each lamp bead in the LED array can be lit individually. Its control method includes but is not limited to single chip microcomputer, ARM and other technologies.

[0055] Step 2: Determine the low-frequency cutoff frequency based on the numerical aperture of the microscope objective and the wavelength of the incident light, and calculate the spatial frequency of the incident light corresponding to each LED lamp bead based on the coordinate position of the LED lamp bead in space. The specific process is as follows:

[0056] According to the numerical aperture NA of the microscope objective obj and the wavelength λ of the incident light i Determine the low frequency cutoff The calculation formula is:

[0057]

[0058] Calculate the spatial frequency of the incident light corresponding to each LED lamp bead according to its coordinate position in space Where n represents the number of the lamp beads. The image captured is a bright field image; when The image captured For dark field images, When , the illumination is considered to be matching illumination, and the illumination aperture NA ill =NA obj The algorithm requires that the lighting is exactly matching lighting. Since the distance from each lamp bead on the ring light board to the center point is equal and the center point is on the optical axis, when the spatial position of one lamp bead meets the matching lighting condition, all lamp beads meet the matching lighting condition.

[0059] Step 3: Image initialization: All low-resolution bright field images captured Add and average, then perform linear interpolation to obtain the initial solution of the high-resolution image. gus ,The initial solution calculation formula is as follows:

[0060]

[0061] Where P{} is the bilinear interpolation upsampling. gus Divided into several layers of complex amplitude j is the number of layers. Each layer is considered to be the initial solution of the corresponding layer, and the calculation formula is as follows;

[0062]

[0063] Step 4: Layer setting: The defocus value corresponding to the objects in different layers is set to z j For each layer of objects First, it is converted to the frequency domain through Fourier transform, and then multiplied by the low-pass filter function corresponding to the tilted light angle and the defocus amount z in the frequency domain jThe corresponding transfer function is then converted back to the spatial domain through inverse Fourier transform to obtain the complex amplitude objects with different sub-apertures at different defocus positions.

[0064]

[0065]

[0066] Where n represents the number of the lamp beads, j is the number of layers, F represents the Fourier transform operation, and F -1 Represents the inverse Fourier transform operation, S n It represents the shift operation of the spectrum. The shift amount is determined by the angle of the inclined light corresponding to each lamp bead. CTF is the low-pass filter function, f x ,f y is the spatial frequency, k i is the wave number, is the low frequency cut-off frequency, λ i is the wavelength of the incident light.

[0067] Step 5: Calculate the update coefficient based on the light intensity distribution of the complex amplitude object corresponding to each sub-aperture in each layer.

[0068]

[0069] In the formula, n represents the number of lamp beads, j is the number of layers, and m is the total number of images taken. is a complex amplitude object with different sub-apertures at different defocus positions, {} * represents the conjugate operation, and |*| represents the absolute value operation.

[0070] Step 6, iterative reconstruction, using Fourier stack imaging technology to transfer the complex amplitude object corresponding to each sub-aperture in each layer to the frequency domain, and perform synthetic aperture calculations one by one in the frequency domain according to the update coefficients calculated in step 5. When the cost function of each layer is less than the set threshold, stop the iteration and obtain the high-resolution result of each layer. Specifically: Use Fourier stack imaging technology to update the complex amplitude object corresponding to each sub-aperture in each layer At the same time, multiply the exponent by the update coefficient in step 5

[0071]

[0072] in, is the updated complex amplitude object corresponding to each sub-aperture of each layer, n represents the number of the lamp bead, is the update coefficient, P{} is the bilinear interpolation upsampling, This is a low-resolution bright field image captured. is the complex amplitude object before updating, m is the total number of images taken, and j is the number of layers;

[0073] The updated complex amplitude object of each sub-aperture of each layer Fourier transform to the frequency domain and update the complex amplitude object using the updated subaperture spectrum The part corresponding to the subaperture;

[0074]

[0075] Where F represents the Fourier transform operation, F -1 Represents the inverse Fourier transform operation, S n It represents the shift operation of the spectrum. The shift amount is determined by the angle of the inclined light corresponding to each lamp bead. CTF is the low-pass filter function, f x ,f y is the spatial frequency, k i is the wave number, is the low frequency cut-off frequency, λ i is the wavelength of the incident light. α is the update step size.

[0076] Finally, calculate the cost function COST;

[0077]

[0078] {} * represents the conjugate operation, |*| represents the absolute value operation, and COST is the cost function.

[0079] When the cost function of each layer is less than the set threshold, stop the iteration and obtain the high-resolution result of each layer. Otherwise, keep the complex amplitude object in step 6. Replace it with the complex amplitude object in step 5 Repeat step 5 to perform a new round of complex amplitude analysis for each layer and each sub-aperture. calculation and iteration.

[0080] Step 7: synthesize the high-resolution results obtained by converging different layers to obtain the final large depth of field image I result Specifically:

[0081]

[0082] in, is the complex amplitude result of each layer after update, {} * Represents the conjugate operation.

[0083] Figure 3 The reconstruction result of a thick HPV cell sample is shown. The system uses a 10x objective lens (NA = 0.4) for imaging. Figure 3(a) is the reconstruction result using traditional Fourier stack imaging. Since the depth of field of the ten-fold microscope is shallow, when imaging thick samples such as HPV cells, the focus is on the inside of the cell nucleus, and the cytoplasm below the cell nucleus cannot be seen clearly due to defocus. Figure 3 (b) is the large depth of field reconstruction result obtained using this algorithm. It can be seen that while the cell nucleus is clearly focused, the cytoplasm morphology of the lower layer can also be clearly seen, which is convenient for doctors to diagnose the cell status.

Claims

1. A large depth of field reconstruction method based on Fourier stack imaging, characterized in that: Here are the steps: Step 1: Original intensity image acquisition: Use a ring-shaped LED board as the illumination source of the microscope, light up the three RGB lamp beads of each LED in turn, and the light emitted by the lamp beads after irradiating the sample is regarded as plane monochromatic light. By synchronously triggering the camera and scanning the lamp bead array, the corresponding low-resolution bright field image of each lamp bead is acquired; Step 2: determine the low-frequency cutoff frequency according to the numerical aperture of the microscope objective and the wavelength of the incident light, and calculate the spatial frequency of the incident light corresponding to each LED lamp bead according to the coordinate position of the LED lamp bead in space; Step 3: add and average all the captured low-resolution bright field images, then perform linear interpolation and amplification to obtain the initial solution of the high-resolution image, and divide the initial solution into several layers of complex amplitude objects; Step 4, setting the defocus values ​​corresponding to the complex amplitude objects at different layers. For each layer of complex amplitude objects, first convert the complex amplitudes of each layer referred to by it to the frequency domain through Fourier transform, and then multiply the low-pass filter function corresponding to the tilted light angle and the transfer function corresponding to the defocus amount in the frequency domain to obtain each updated sub-aperture spectrum of each layer, and then convert each updated sub-aperture spectrum of each layer back to the spatial domain through inverse Fourier transform to obtain the complex amplitude objects corresponding to each sub-aperture at different defocus positions of each layer; Step 5, according to the distribution of the light intensity of each layer of complex amplitude objects corresponding to the same sub-aperture, the update coefficient of each sub-aperture in each layer is set; Step 6: Iterative reconstruction. Use Fourier stack imaging technology to transfer the complex amplitude object corresponding to each sub-aperture to the frequency domain at each layer, and perform synthetic aperture calculations one by one in the frequency domain according to the update coefficients calculated in step 5. When the cost function of each layer is less than the set threshold, stop the iteration and obtain the high-resolution result of each layer. Otherwise, return to step 4. Step seven: synthesize the high-resolution results obtained by converging different layers to obtain the final large depth of field image.

2. The large depth of field reconstruction method based on Fourier stack imaging according to claim 1, characterized in that: The specific formula for determining the low-frequency cutoff frequency based on the numerical aperture of the microscope objective and the wavelength of the incident light is: In the formula, is the low frequency cut-off frequency, λ i is the wavelength of the incident light, NA obj is the numerical aperture of the microscope objective.

3. The large depth of field reconstruction method based on Fourier stack imaging according to claim 1, characterized in that: The specific method to calculate the spatial frequency of the incident light corresponding to each LED lamp bead according to the coordinate position of the LED lamp bead in space is: Calculate the spatial frequency of the incident light corresponding to each LED lamp bead according to its coordinate position in space Where n represents the number of the lamp beads. The image captured is a bright field image; when The image captured For dark field images, When the illumination is considered to be matched illumination, the illumination aperture NA ill =NA obj , is the low frequency cutoff frequency.

4. The large depth of field reconstruction method based on Fourier stack imaging according to claim 1, characterized in that: High-resolution image initial solution I gus Specifically: Where P{} is the bilinear interpolation upsampling, is the low-resolution bright field image captured, and m is the total number of images captured.

5. The large depth of field reconstruction method based on Fourier stack imaging according to claim 1, characterized in that: In step 3, the initial solution I gus Divided into several layers of complex amplitude objects Each layer is the initial solution of the corresponding layer, and the calculation formula is as follows; In the formula, j is the number of layers.

6. The large depth of field reconstruction method based on Fourier stack imaging according to claim 1, characterized in that: The complex amplitude object corresponding to each sub-aperture at different defocus positions in step 4 Specifically: Where n represents the number of the lamp beads, j is the number of layers, F represents the Fourier transform operation, and F -1 Represents the inverse Fourier transform operation, S n It represents the shift operation of the spectrum. The shift amount is determined by the angle of the inclined light corresponding to each lamp bead. CTF is the low-pass filter function, f x ,f y is the spatial frequency, k i is the wave number, is the low frequency cut-off frequency, λ i is the wavelength of the incident light.

7. The large depth of field reconstruction method based on Fourier stack imaging according to claim 1, characterized in that: Set the update coefficient according to the light intensity distribution of the complex amplitude object corresponding to each sub-aperture of each layer. In the formula, n represents the number of lamp beads, j is the number of layers, and m is the total number of images taken. is a complex amplitude object with different sub-apertures at different defocus positions, {} * represents the conjugate operation, and |*| represents the absolute value operation.

8. The large depth of field reconstruction method based on Fourier stack imaging according to claim 1, characterized in that: The specific method of iterative reconstruction in step six is: Fourier stack imaging technology is used to update the complex amplitude object corresponding to each sub-aperture of each layer At the same time, multiply the exponent by the update coefficient in step 5 in, is the updated complex amplitude object corresponding to each sub-aperture of each layer, n represents the number of the lamp bead, is the update coefficient, P{} is the bilinear interpolation upsampling, This is a low-resolution bright field image captured. is the complex amplitude object before updating, m is the total number of captured images, and j is the number of layers; The updated complex amplitude object of each sub-aperture of each layer Fourier transform to the frequency domain and update the complex amplitude object using the updated subaperture spectrum The part corresponding to the subaperture; in, represents the updated complex amplitude object, F represents the Fourier transform operation, F -1 Represents the inverse Fourier transform operation, S n It represents the shift operation of the spectrum. The shift amount is determined by the angle of the inclined light corresponding to each lamp bead. CTF is the low-pass filter function, f x ,f y is the spatial frequency, k i is the wave number, is the low frequency cut-off frequency, λ i is the wavelength of the incident light; α is the update step size; Calculate the cost function COST; when the cost function of each layer is less than the set threshold, stop the iteration and obtain the high-resolution result of each layer, otherwise keep the complex amplitude object in step 6 Replace it with the complex amplitude object in step 5 Repeat step 5 to perform a new round of complex amplitude analysis for each layer and each sub-aperture. calculation and iteration.

9. The large depth of field reconstruction method based on Fourier stack imaging according to claim 8, characterized in that: The cost function COST is specifically: {} * represents the conjugate operation, |*| represents the absolute value operation, and COST is the cost function.

10. The large depth of field reconstruction method based on Fourier stack imaging according to claim 8, characterized in that: In step 7, the high-resolution results obtained by converging different layers are synthesized to obtain the final large depth of field image I result Specifically: in, is the complex amplitude result of each layer after update, {} * Represents the conjugate operation.

Images