Three-dimensional spectrum allocation interpolation and weighted stacking method for optical diffraction tomography reconstruction
Through the three-dimensional spectrum allocation interpolation and weighted superposition method, the problems of missing frequency domain information and axial artifacts in optical diffraction tomography are solved, and efficient and high-quality three-dimensional refractive index reconstruction is achieved, which improves imaging accuracy and contrast and is suitable for biomedical and industrial detection.
Patent Information
- Application Number
- CN202511220329.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-08-29
- Publication Date
- 2025-10-14
AI Technical Summary
Existing optical diffraction tomography reconstruction suffers from frequency domain information loss and axial artifact problems, resulting in low refractive index reconstruction accuracy. In addition, existing algorithms are highly complex and computationally intensive, making it difficult to achieve efficient and high-quality three-dimensional imaging under limited viewing angles and hardware conditions.
The three-dimensional spectrum allocation interpolation and weighted superposition method is adopted. Through multi-angle hologram acquisition and complex amplitude reconstruction, combined with Fourier transform and phase unwrapping, it is converted into three-dimensional frequency domain information. The spectrum intensity difference at different angles is used for weighted synthesis, filling non-integer spectrum points and assigning different weights to improve spectrum coverage and accuracy.
It significantly improves the peak signal-to-noise ratio and total signal-to-noise ratio of refractive index reconstruction, reduces artifacts, improves the contrast and resolution of refractive index distribution, and achieves efficient calculation. It is suitable for biological tomography reconstruction and high-precision imaging of complex structure samples.
Smart Images
Figure CN120779692A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of optical imaging and computational optics, and in particular relates to a three-dimensional spectrum allocation interpolation and weighted superposition method for optical diffraction tomography reconstruction. Background Art
[0002] Optical Diffraction Tomography (ODT) is an extremely influential label-free and non-invasive technology. With its ability to perform three-dimensional reconstruction of refractive index distribution, it excels in quantitative characterization in life sciences and industrial testing. It is particularly suitable for minimally invasive three-dimensional imaging of unstained living cell specimens.
[0003] To minimize the risk of biological sample damage, ODT systems for biomedical applications often employ illumination scanning to avoid physical manipulation of the sample. While this method can obtain projections of fixed samples at different angles, the limited-angle illumination results in a significant loss of frequency-domain information in the scattering potential during 3D inversion. This results in a calculated refractive index that is lower than the true refractive index, produces axial artifacts, and reduces axial resolution, severely impacting subsequent biological material analysis and interpretation.
[0004] To obtain the missing frequency domain information, more projection illumination angle data and more complex iterative optimization algorithms are often required. Although this can obtain a three-dimensional refractive index distribution with near-isotropic resolution, it also cannot ignore the multi-angle registration problem of the hologram, the number of images collected, and the time cost. Furthermore, this method places high demands on computer performance, limiting its application. Therefore, it is of great significance to develop an optimization algorithm for filling in frequency domain information in optical diffraction tomography, reducing the impact of non-zero interpolation on inversion reconstruction, and thus improving the quality of ODT reconstruction.
[0005] In optical diffraction tomography (ODT) reconstruction, in order to achieve high-quality three-dimensional refractive index imaging, it is necessary to obtain three-dimensional frequency domain information that is as complete and accurate as possible. The more valid non-zero spectral values in the object transfer function (OTF), the closer the reconstructed refractive index is to the true value. To this end, an intuitive approach is to reduce the illumination angle between two adjacent images of oblique illumination and increase the acquisition angle of view, but this not only brings a large amount of redundant data and has limited improvement in reconstruction accuracy, but also significantly increases the amount of calculation and places higher requirements on the accuracy of the lighting device. Another hardware solution is to rotate the sample and the incident light beam simultaneously to obtain frequency domain information multiple times, but the system structure is complex and the cost is high.
[0006] At the algorithmic level, frequency domain holes can be filled by improving reconstruction algorithms: the filtered backpropagation (FBP) method can effectively alleviate the spectrum loss caused by direct interpolation; non-negativity constraints and regularization techniques can be used as spatial domain post-processing to compensate for missing frequencies. However, these methods often rely on empirical parameter tuning, which not only increases computational overhead but also requires multiple verifications to achieve optimal results due to sample differences. In summary, how to achieve higher frequency domain filling efficiency with less data under limited viewing angles and hardware conditions remains a key issue that needs to be addressed in the field of ODT 3D imaging.
[0007] The current optical diffraction tomography reconstruction algorithm has two major bottlenecks in three-dimensional spectrum processing: first, most of the Kz components calculated from the two-dimensional spectrum coordinates do not fall on integer grid points. Although this can be alleviated through sub-pixel matching, it will significantly increase the computational complexity; second, a constant weight is used for the spectrum of each incident angle, resulting in the reconstruction being overly biased towards low-frequency components and ignoring high-frequency details, reducing the contrast and resolution of the refractive index distribution.
[0008] In summary, there is still a lack of a three-dimensional spectrum allocation and weighted superposition method that can be used quickly and efficiently for optical diffraction tomography to achieve high-quality tomographic reconstruction.
[0009] To this end, the present invention proposes a three-dimensional spectrum allocation interpolation and weighted superposition method for optical diffraction tomography reconstruction. Summary of the Invention
[0010] The purpose of the present invention is to provide a three-dimensional spectrum allocation interpolation and weighted superposition method for optical diffraction tomography reconstruction, which is suitable for improving the quality of optical diffraction tomography reconstruction.
[0011] The technical solutions adopted by the present invention are as follows:
[0012] A three-dimensional spectrum allocation interpolation and weighted superposition method for optical diffraction tomography reconstruction includes the following steps:
[0013] Step 1: Multi-angle hologram acquisition and complex amplitude reconstruction;
[0014] Specifically in step 1: in the constructed digital holographic tomography system:
[0015] First, the sample to be tested is illuminated with a low-coherence light source. The angle between the incident light beam and the sample is precisely adjusted by driving the galvanometer voltage, and the corresponding multi-angle hologram sequence is continuously captured by a CMOS camera.
[0016] Subsequently, based on the Fourier domain complex amplitude recovery method of off-axis digital holography, a two-dimensional Fourier transform is performed on each hologram, and the positive first-order diffraction spectrum is intercepted and bandpass filtered; then, after phase unwrapping and aberration correction processing, the complex amplitude distribution at each viewing angle is reconstructed; this step can obtain high-fidelity amplitude and phase information, providing a reliable data basis for subsequent frequency domain interpolation, weighted superposition and three-dimensional refractive index reconstruction.
[0017] Step 2: 3D spectrum space parameter setting;
[0018] Specifically in step 2:
[0019] Calculate the spatial wave vector of the incident wavelength based on the incident wavelength λ and the background refractive index n Then, according to the system magnification M, the two-dimensional spatial image size l of the acquired image side CMOS x 、l y And the size l of the three-dimensional voxel field propagating along the optical axis z , determine the object space sampling step size, and obtain the three-dimensional minimum size d of the object space corresponding to the calculation and reconstruction process x d y and d z ; and the minimum three-dimensional frequency division value dk that needs to be corresponding in the three-dimensional frequency domain space x 、dk y and dk z ; and calculate the maximum cutoff frequency k based on the numerical aperture of the lighting element and the numerical aperture of the imaging lens max .
[0020] Step 3: Convert the two-dimensional spectrum information into three-dimensional frequency domain information;
[0021] Specifically in step 3:
[0022] The amplitude and phase information of step 1 are obtained by Fourier transform, and the two-dimensional offset value of the positive first-order spectrum point of each angle relative to the normal incidence is obtained. At this time, according to the Fourier shift theorem, the two-dimensional offset value can be used as the tilt angle value of each angle relative to the normal incidence; the unpacked complex amplitude distribution is log-processed, converted into a complex phase distribution, and converted into a two-dimensional frequency domain space by two-dimensional Fourier transform; the spectrum point distribution center corresponding to the complex phase distribution data of the normal incident illumination is moved to the center of the calculated two-dimensional frequency domain space, and according to the spectrum point offset kx and ky values of other illumination angles for the normal incidence, the complex phase distribution data corresponding to other angles are moved to the corresponding two-dimensional frequency domain space positions.
[0023] Step 4: single-angle three-dimensional spectrum allocation processing;
[0024] Specifically in step 4:
[0025] Since the spectral information obtained in step 3 is two-dimensional spectral information, the two-dimensional spatial frequency from the single hologram data is mapped to the spherical cap region of the spherical surface in the three-dimensional Fourier space; from the formula k x 2 +k y 2 +k z 2 = k0 2 , the transverse k x and k y coordinates of the two-dimensional frequency domain are used to calculate the axial coordinate k z The non-equidistant scatter values are calculated, and the other angle spectral values of step 3 are moved to the corresponding three-dimensional frequency domain space positions; analysis is performed according to the actual coordinate point positions (k x , k y , k z ) of each spectral point distributed in the three-dimensional frequency domain space; for the part of the spectral points whose k z is an integer multiple of dk z , the original position is kept unchanged; for the part of the spectral points whose k z is not an integer multiple of dk z , the complex phase value on the spectral point is filled in the two integer multiple spectral points adjacent to it in the k z direction by copying, and the complex phase values on the adjacent two spectral points are normalized and weighted averaged according to the distance between the actual position of the point and the two k z adjacent voxel points. The operation of step 4 is repeated for all spectral points within the numerical aperture NA range under single-angle acquisition, and the total frequency energy value is kept unchanged.
[0026] Step 5: synthesis of multi-angle spectral data;
[0027] The specific steps in step 5 are:
[0028] After the three-dimensional spectral data of each angle is processed according to step 4, when there is an overlapping region in the three-dimensional spectral data of multiple angles, it is weighted and synthesized according to the weight factor, and the number of repeated filling times Π i is recorded; then, according to the difference in spectral energy intensity under each angle, ω i is the weight factor, whose value is determined by the spherical cap power spectral density of each illumination direction, and the three-dimensional spectral data of each angle is weighted and normalized using the function c, wherein the c function is a normalization factor, which depends on the filling times Π i and the weight factor ω i of the three-dimensional spectral data of each angle; therefore, for the three-dimensional spectral data of each angle, the coefficient of each spectral point data is i represents the angle number.
[0029] Step 6: reconstruct the three-dimensional refractive index distribution of the object.
[0030] The specific steps in step 6 are as follows:
[0031] The three-dimensional spectral data of the object synthesized by step 5 is subjected to inverse three-dimensional Fourier transform, and is converted into the refractive index distribution of the object in three-dimensional space by combining the scattering potential formula.
[0032] The technical effects obtained by the present application are as follows:
[0033] In the present application, first, the complex amplitude distribution obtained under each viewing angle is converted into a three-dimensional frequency domain point set. For the spectral points falling on the non-integer coordinates on the k z axis, the proportion is calculated according to the distance from the adjacent integer points, and the point energy is distributed to the two sides of the integer frequency, so as to obtain more effective non-negative spectral information. Secondly, by using the difference of spectral intensity under different incident angles, different weights are given to the frequency domain data of each viewing angle, and the contribution of oblique illumination is highlighted, so as to improve the refractive index contrast and edge extraction ability after reconstruction. This method significantly enhances the coverage and accuracy of the three-dimensional spectral filling of the scattering potential, reduces the interpolation error in the discrete Fourier space, effectively alleviates the problems of low refractive index and axial artifacts caused by limited angle illumination. Under the premise of keeping the hardware configuration and acquisition time of the imaging system unchanged, the algorithm can realize efficient calculation only relying on general CPU. When applied to biological tomographic reconstruction, the present method can obtain a three-dimensional refractive index distribution with higher precision and better contrast, which provides a solid foundation for subsequent cell segmentation, organelle recognition, cell classification and component change analysis.
[0034] The present application provides a three-dimensional spectral allocation interpolation and weighted superposition method for optical diffraction tomographic reconstruction. Compared with traditional direct interpolation and nearest neighbor interpolation algorithms, the present method can significantly improve the refractive index reconstruction imaging quality: the peak signal-to-noise ratio (PSNR) is increased by about 1.42 dB, and the total signal-to-noise ratio (SNR) is increased by about 1.6 dB. In addition, the sample refractive index reconstructed by the present method is more accurate, and the axial artifacts are effectively suppressed, and the excellent applicability of the present method has been verified in the reconstruction of complex structure samples. Under the premise of keeping the imaging system parameters and acquisition time unchanged, the present application can efficiently complete the entire calculation process only relying on general CPU. Through the algorithm optimization of the direct inversion process, the reconstruction result can be greatly accelerated after the preliminary inversion; then combined with an advanced iterative algorithm for further fine adjustment, the reconstruction accuracy is significantly improved. The present method has high universality, and is not only suitable for the present optical diffraction tomographic reconstruction, but also can be extended to all three-dimensional tomographic reconstruction scenes based on frequency domain information processing (such as CT reconstruction), thereby laying a solid foundation for realizing high-precision three-dimensional imaging. BRIEF DESCRIPTION OF DRAWINGS
[0035] Figure 1 is the reconstruction flow chart of three-dimensional spectrum assignment interpolation and weighted superposition for optical diffraction tomography in the present application;
[0036] Figure 2 is the method schematic diagram of each component module for three-dimensional spectrum assignment interpolation and weighted superposition for optical diffraction tomography in the present application. (a) represents the method schematic diagram of the double nearest neighbor assignment module (DNI) for single-angle three-dimensional spectrum assignment processing, and (b) is the method schematic diagram of the power spectrum weighted module (PSW) for multi-angle spectrum data synthesis.
[0037] Figure 3 is the numerical reconstruction result of simulating five spatial distribution beads in the present application. (a)-(f) respectively represent the reconstruction results of the true value (GT), the nearest neighbor interpolation method (NNI), the power spectrum weighted assignment (PSW), the double nearest neighbor assignment method (DNI), and the power spectrum weighted + double nearest neighbor assignment method (PSWDNI).
[0038] Figure 4 is the refractive index distribution of the dashed section line in the present application. Figure 3 (a) is the dashed line 1, and (b) is the dashed line 2.
[0039] Figure 5 is the refractive index reconstruction result of Hela cells in the present application. (a)-(d) respectively represent the reconstruction results of NNI, PSW, DNI, and PSWDNI.
[0040] Figure 6 is the refractive index distribution of the dashed section line in the present application. Figure 5 (a) is the dashed line 1, and (b) is the dashed line 2. DETAILED DESCRIPTION
[0041] In order to make the objects and advantages of the present application clearer, the present application will be specifically described below in combination with embodiments. It should be understood that the following text is only used to describe one or several specific embodiments of the present application, and does not strictly limit the specific protection scope of the present application.
[0042] As shown in Figure 1 - Figure 6 A three-dimensional spectrum assignment interpolation and weighted superposition method for optical diffraction tomography reconstruction includes the following steps:
[0043] Step 1: Multi-angle hologram acquisition and complex amplitude reconstruction;
[0044] In the step 1, specifically, in the digital holographic tomography system built:
[0045] First, a low-coherence light source is used to illuminate the sample to be tested. The angle of the incident light beam illuminating the sample is precisely adjusted by driving the galvanometer voltage, and the corresponding multi-angle hologram sequence is continuously captured by a CMOS camera.
[0046] Subsequently, based on the Fourier domain complex amplitude recovery method of off-axis digital holography, a two-dimensional Fourier transform is performed on each hologram, and the positive first-order diffraction spectrum is intercepted and bandpass filtered; then, after phase unwrapping and aberration correction processing, the complex amplitude distribution at each viewing angle is reconstructed; this step can obtain high-fidelity amplitude and phase information, providing a reliable data basis for subsequent frequency domain interpolation, weighted superposition and three-dimensional refractive index reconstruction.
[0047] Step 2: 3D spectrum space parameter setting;
[0048] Specifically in step 2:
[0049] Calculate the spatial wave vector of the incident wavelength based on the incident wavelength λ and the background refractive index n Then, according to the system magnification M, the two-dimensional spatial image size l of the acquired image side CMOS x 、l y And the size l of the three-dimensional voxel field propagating along the optical axis z , determine the object space sampling step size, and obtain the three-dimensional minimum size d of the object space corresponding to the calculation and reconstruction process x d y and d z ; and the minimum three-dimensional frequency division value dk that needs to be corresponding in the three-dimensional frequency domain space x 、dk y and dk z ; and calculate the maximum cutoff frequency k based on the numerical aperture of the lighting element and the numerical aperture of the imaging lens max .
[0050] Step 3: Convert the two-dimensional spectrum information into three-dimensional frequency domain information;
[0051] Specifically in step 3:
[0052] The amplitude and phase information of step 1 are obtained by Fourier transform, and the two-dimensional offset value of the positive first-order spectrum point of each angle relative to the normal incidence is obtained. At this time, according to the Fourier shift theorem, the two-dimensional offset value can be used as the tilt angle value of each angle relative to the normal incidence; the unpacked complex amplitude distribution is log-processed, converted into a complex phase distribution, and converted into a two-dimensional frequency domain space by two-dimensional Fourier transform; the center of the spectrum point corresponding to the complex phase distribution data of the normal incident illumination is moved to the center of the calculated two-dimensional frequency domain space, and according to the kx and ky values of the spectrum point offsets of other illumination angles for the normal incidence, the complex phase distribution data corresponding to other angles are moved to the corresponding two-dimensional frequency domain space positions.
[0053] Step 4: single-angle three-dimensional spectrum allocation processing;
[0054] Specifically in step 4:
[0055] Since the spectrum information obtained in step 3 is two-dimensional spectrum information, the two-dimensional spatial frequency from the single hologram data is mapped to the spherical cap area on the surface of the sphere in the three-dimensional Fourier space; according to the formula k x 2 +k y 2 +k z 2 =k0 2 , according to the lateral k in the two-dimensional frequency domain x and k y Coordinate calculation axial coordinate k z The non-equidistant discrete values are calculated, and the other angle spectrum values of step 3 are moved to the corresponding three-dimensional frequency domain space positions; according to the actual coordinate point position (k x ,k y ,k z ) for analysis; for k z Equal to an integer multiple of dk z Some spectrum points of k remain at the origin; z Not equal to an integer multiple of dk z The complex phase value of the spectrum point is filled in along k by copying the complex phase value of the spectrum point z Two integer multiple spectrum points sampled adjacently in the direction, and according to the actual position of the point and the two k z The distance between adjacent voxels is used as a weight factor, and the normalized weighted average of the complex phase values at two adjacent spectrum points is performed. In this way, step 4 is repeated for all spectrum points within the numerical aperture range under single-angle acquisition, keeping the total frequency domain energy value unchanged.
[0056] Step 5: Synthesis of multi-angle spectrum data;
[0057] Specifically in step 5:
[0058] After processing the three-dimensional spectrum data of each angle according to step 4, when there is an overlapping area in the three-dimensional spectrum data of multiple angles, it will be weighted and synthesized according to the weight factor, and the number of repeated fillings π will be recorded at the same time. i ; Then, according to the difference in spectrum energy intensity at each angle, ω iis the weight factor, whose value is determined by the spherical cap power spectrum density of each illumination direction. The three-dimensional spectrum data of each angle is weighted separately and normalized using the function c, where the c function is a normalization factor that depends on the number of filling times π of the three-dimensional spectrum data of each angle. i and weight factor ω i ; Therefore, for the three-dimensional spectrum data at each angle, the coefficient of each spectrum point data is i represents the angle number.
[0059] Step 6: Reconstruct the three-dimensional refractive index distribution of the object.
[0060] Specifically in step 6:
[0061] The three-dimensional spectrum data of the object synthesized in step 5 is used to perform a three-dimensional inverse Fourier transform, and is converted into the refractive index distribution of the object in three-dimensional space in combination with the scattering potential formula.
[0062] In the present invention; Figure 3 Simulated numerical reconstruction results of five spatially distributed spheres. (a)-(f) show the ground truth (GT), reconstruction using NNI, PSW, DNI, and PSWDNI, respectively. The proposed PSWDNI method achieves the highest peak signal-to-noise ratio, improving by 1.42 dB compared to the traditional NNI reconstruction algorithm.
[0063] like Figure 1 - Figure 6 As shown, the present invention first converts the complex amplitude distribution obtained at each viewing angle into a three-dimensional frequency domain point set. z For the spectrum points with non-integer coordinates on the axis, the weight is calculated according to the inverse of the distance between them and the adjacent integer points, and the energy of the point is distributed to the integer frequencies on both sides to obtain more non-negative spectrum information. Secondly, the difference in spectrum intensity under different incident angles is used to assign different weights to the frequency domain data of each viewing angle, highlighting the contribution of oblique illumination, thereby improving the refractive index contrast and edge extraction capabilities after reconstruction. This method significantly enhances the coverage and accuracy of the three-dimensional spectrum filling of the scattering potential, reduces the discrete Fourier space interpolation error, and effectively alleviates the problems of low refractive index and axial artifacts caused by limited-angle illumination. Under the premise of keeping the hardware configuration and acquisition time of the imaging system unchanged, the algorithm can achieve efficient calculation by relying only on a general-purpose CPU. When applied to biological tomography reconstruction, this method can obtain three-dimensional refractive index distribution with higher accuracy and better contrast, providing a solid foundation for subsequent cell segmentation, organelle identification, cell classification and component change analysis.
[0064] This paper proposes a three-dimensional spectrum allocation interpolation and weighted superposition method for optical diffraction tomography reconstruction. Compared with traditional direct interpolation and nearest neighbor interpolation algorithms, this method can significantly improve the quality of refractive index reconstruction imaging: the peak signal-to-noise ratio (PSNR) is increased by approximately 1.42dB, and the total signal-to-noise ratio (SNR) is improved by approximately 1.6dB. In addition, this method reconstructs the sample refractive index with higher accuracy and effectively suppresses axial artifacts. Its excellent applicability has been verified in the reconstruction of samples with complex structures.
[0065] While maintaining constant imaging system parameters and acquisition time, this method efficiently completes the entire computational process using only a general-purpose CPU. By optimizing the algorithm for the direct inversion process, reconstruction results can be significantly accelerated after the initial inversion. This method is then combined with advanced iterative algorithms for further fine-tuning, significantly improving reconstruction accuracy. This highly versatile method is applicable not only to this optical diffraction tomography reconstruction but also to all frequency-domain information processing-based 3D tomographic reconstruction scenarios, such as CT reconstruction, laying a solid foundation for achieving high-precision 3D imaging.
[0066] The foregoing is merely a preferred embodiment of the present invention. It should be noted that those skilled in the art may make various improvements and modifications without departing from the principles of the present invention, and such improvements and modifications are also within the scope of protection of the present invention. Structures, devices, and operating methods not specifically described or explained herein shall, unless otherwise specified or limited, be implemented in accordance with conventional means in the art.
Claims
1. A three-dimensional spectrum allocation interpolation and weighted superposition method for optical diffraction tomography reconstruction, characterized by: The following steps are involved: Step 1: Multi-angle hologram acquisition and complex amplitude reconstruction; Step 2: 3D spectrum space parameter setting; Step 3: Convert the two-dimensional spectrum information into three-dimensional frequency domain information; Step 4: single-angle three-dimensional spectrum allocation processing; Step 5: Synthesis of multi-angle spectrum data; Step 6: Reconstruct the three-dimensional refractive index distribution of the object.
2. The three-dimensional spectrum allocation interpolation and weighted superposition method for optical diffraction tomography reconstruction according to claim 1, characterized in that: Specifically in step 1: in the constructed digital holographic tomography system: First, a low-coherence light source is used to illuminate the sample to be tested. The angle of the incident light beam illuminating the sample is precisely adjusted by driving the galvanometer voltage, and the corresponding multi-angle hologram sequence is continuously captured by a CMOS camera. Subsequently, based on the Fourier domain complex amplitude recovery method of off-axis digital holography, a two-dimensional Fourier transform is performed on each hologram, and the positive first-order diffraction spectrum is intercepted and bandpass filtered; then, after phase unwrapping and aberration correction processing, the complex amplitude distribution at each viewing angle is reconstructed.
3. The three-dimensional spectrum allocation interpolation and weighted superposition method for optical diffraction tomography reconstruction according to claim 2, characterized in that: Specifically in step 2: Calculate the spatial wave vector of the incident wavelength based on the incident wavelength λ and the background refractive index n Then, according to the system magnification M, the two-dimensional spatial image size l of the acquired image side CMOS x 、l y And the size l of the three-dimensional voxel field propagating along the optical axis z , determine the object space sampling step size, and obtain the three-dimensional minimum size d of the object space corresponding to the reconstruction process x d y and d z ; And the three-dimensional frequency minimum division value dk that needs to be corresponding in the three-dimensional frequency domain space x 、dk y and dk z ; and calculate the maximum cutoff frequency k based on the numerical aperture of the lighting element and the numerical aperture of the imaging lens max .
4. The three-dimensional spectrum allocation interpolation and weighted superposition method for optical diffraction tomography reconstruction according to claim 3, characterized in that: Specifically in step 3: The amplitude and phase information of step 1 are obtained by Fourier transform, and the two-dimensional offset value of the positive first-order spectrum point of each angle relative to the normal incidence is obtained. At this time, according to the Fourier shift theorem, the two-dimensional offset value can be used as the tilt angle value of each angle relative to the normal incidence; the unpacked complex amplitude distribution is log-processed and converted into a complex phase distribution, and a two-dimensional Fourier transform is performed to convert it into a two-dimensional frequency domain space; the center of the spectrum point corresponding to the complex phase distribution data of the normal incident illumination is moved to the center of the calculated two-dimensional frequency domain space, and the spectrum point offset k for the normal incidence at other illumination angles is calculated. x and k y The complex phase distribution data corresponding to other angles are moved to the corresponding two-dimensional frequency domain space position.
5. The three-dimensional spectrum allocation interpolation and weighted superposition method for optical diffraction tomography reconstruction according to claim 4, characterized in that: Specifically in step 4: Since the spectrum information obtained in step 3 is two-dimensional spectrum information, the two-dimensional spatial frequency from the single hologram data is mapped to the spherical cap area on the surface of the sphere in the three-dimensional Fourier space; according to the formula k x 2 +k y 2 +k z 2 =k0 2 , according to the lateral k in the two-dimensional frequency domain x and k y Coordinate calculation axial coordinate k z The non-equidistant discrete values are calculated, and the other angle spectrum values of step 3 are moved to the corresponding three-dimensional frequency domain space positions; according to the actual coordinate point position (k x ,k y ,k z ) for analysis; for k z Equal to an integer multiple of dk z Some spectrum points of k remain at the origin; z Not equal to an integer multiple of dk z The complex phase value of the spectrum point is filled in along k by copying the complex phase value of the spectrum point z Two integer multiple spectrum points sampled adjacently in the direction, and according to the actual position of the point and the two k z The distance between adjacent voxels is used as a weight factor, and the normalized weighted average of the complex phase values at two adjacent spectrum points is performed. In this way, step 4 is repeated for all spectrum points within the numerical aperture range under single-angle acquisition, keeping the total frequency domain energy value unchanged.
6. The three-dimensional spectrum allocation interpolation and weighted superposition method for optical diffraction tomography reconstruction according to claim 5, characterized in that: Specifically in step 5: After processing the three-dimensional spectrum data of each angle according to step 4, when there is an overlapping area in the three-dimensional spectrum data of multiple angles, it will be weighted and synthesized according to the weight factor, and the number of repeated fillings π will be recorded at the same time. i ; Then, according to the difference in spectrum energy intensity at each angle, ω i is the weight factor, whose value is determined by the spherical cap power spectrum density of each illumination direction. The three-dimensional spectrum data of each angle is weighted separately and normalized using the function c, where the c function is a normalization factor that depends on the number of filling times π of the three-dimensional spectrum data of each angle. i and weight factor ω i ; Therefore, for the three-dimensional spectrum data at each angle, the coefficient of each spectrum point data is i represents the angle number.
7. The three-dimensional spectrum allocation interpolation and weighted superposition method for optical diffraction tomography reconstruction according to claim 6, characterized in that: Specifically in step 6: The three-dimensional spectrum data of the object synthesized in step 5 is used to perform a three-dimensional inverse Fourier transform, and is converted into the refractive index distribution of the object in three-dimensional space in combination with the scattering potential formula.