High-speed high-resolution three-dimensional diffraction tomography imaging method

Abstract

The application discloses a high-speed high-resolution three-dimensional diffraction tomography method. The application sets an aperture plane control device at the rear end of the microscope light hole, controls two intensity images with different defocusing distances to be separated horizontally on the target surface of the camera and collected synchronously, and adopts spatial filtering to obtain the intensity images corresponding to the two focal planes respectively. The application adopts a ring LED as an illumination light source, lights the LED in sequence to irradiate the sample from different angles, and combines the rear end aperture plane control device, so that the intensity stacks corresponding to the two focal planes can be obtained without introducing mechanical displacement. The application establishes a double-focal-plane light intensity transmission diffraction tomography theoretical model, determines the optimal defocusing distance based on the model, and obtains the three-dimensional refractive index result of the sample through single deconvolution, so that the problem that the time resolution and the spatial resolution cannot be compatible in the non-interference light intensity diffraction tomography is effectively solved.

Description

Technical Field

[0001] This invention pertains to three-dimensional refractive index imaging technology, specifically a high-speed, high-resolution three-dimensional diffraction tomography method. Background Technology

[0002] Optical diffraction tomography (ODT) is an emerging three-dimensional microscopy technique that utilizes the inherent refractive index of transparent biological samples as a natural contrast mechanism to achieve label-free imaging. It provides the ability to visualize and quantitatively characterize the internal structure of such samples in three dimensions. Unlike traditional fluorescence imaging methods, ODT does not require exogenous fluorescent dyes, avoiding potential problems such as phototoxicity and photobleaching. Therefore, this non-invasive and label-free method has been widely applied in various fields such as biophysics, cell biology, hematology, microbiology, and neuroscience, providing researchers with a powerful tool for biomedical research and clinical applications.

[0003] Over the past few decades, researchers have developed various optical diffraction tomography (ODT) techniques by combining the principles of holography and computed tomography. These coherent ODT techniques, whether based on object rotation or illumination scanning, rely on a coherent synthetic aperture to capture the necessary information. Non-interference ODT based on asymmetric illumination only requires utilizing the relative angular variation between the sample and the illumination beam to capture two-dimensional intensity images under different conditions. These images are then used to reconstruct the three-dimensional refractive index of the sample. Low-frequency phase components can only be fully transferred to the intensity image when the illumination angle is matched to the numerical aperture of the objective lens. However, high numerical aperture microscope systems often struggle to strictly meet the matched illumination conditions in experiments, thus frequently encountering the problem of low-frequency loss when improving the spatial resolution of ODT. Defocus modulation can transfer phase components in the low-frequency region to the intensity image, but axial defocus requires mechanical movement of the imaging system, preventing high-speed ODT and limiting its applicability in dynamic imaging of biological samples such as live cells. To date, obtaining high spatiotemporal resolution dynamic three-dimensional refractive index reconstruction in label-free non-interference optical diffraction tomography remains a major challenge. Summary of the Invention

[0004] The purpose of this invention is to provide a high-speed, high-resolution three-dimensional diffraction tomography method.

[0005] The technical solution to achieve the objective of this invention is as follows: a high-speed, high-resolution three-dimensional diffraction tomography method, comprising the following steps:

[0006] Step 1: Determine the three-dimensional transfer function model and the optimal defocus distance between the two focal planes, and construct a high-speed, high-resolution three-dimensional diffraction tomography system;

[0007] Step 2: Use a high-speed, high-resolution three-dimensional diffraction tomography system to acquire intensity stacks corresponding to two focal planes in parallel;

[0008] Step 3: Substitute the three-dimensional transfer function and the intensity stacks corresponding to the two focal planes into the reconstruction algorithm of the refractive index value inside the sample to obtain the three-dimensional refractive index distribution of the sample, thereby achieving non-contact and sample displacement-free high-resolution three-dimensional diffraction tomography.

[0009] Preferably, the three-dimensional transfer function model includes a phase transfer function model and an absorption transfer function model, specifically as follows:

[0010]

[0011] In the formula, k0=2π / λ represents the wave number, λ represents the illumination wavelength in free space, and u=(k x ,k y (k, z), where z is the spatial domain coordinate, (k x ,k y ) represents the frequency domain coordinates, u in =(k xi ,k yi ) represents the frequency of the incident field, η(x) represents the axial wave vector, and (k xi ,k yi ,k zi () represents the spatial frequency of the incident field. Δd refers to the axial defocus distance, k is the wave number in the surrounding medium, and P(u+u) in ) and P(uu in Let z be the Fourier transform of the point spread function modulated by the incident field, where z = mΔz, m is the number of slices, and Δz is the axial slice thickness.

[0012] Preferably, the specific method for determining the optimal defocus distance between the two focal planes is as follows:

[0013] The concepts of focal plane and defocal plane are used to distinguish the two planes obtained by parallel detection. The transfer function corresponding to dual-focal-plane parallel detection can be expressed as a five-dimensional transfer function:

[0014]

[0015] Where l is the lth... th Intensity images obtained at various illumination angles, l th Indicates the order of the lights, where d is the defocus distance;

[0016] Based on the oscillation distribution of the response curve of the three-dimensional phase transfer function, two sets of asymmetrical defocus distances are selected.

[0017] Preferably, the high-speed, high-resolution three-dimensional diffraction tomography system includes a programmable LED array, a sample under test, a microscope objective, a reflector 1, an imaging tube, an aperture, a lens 1, a reflector 2, a beam splitter, a spatial light modulator, a lens 2, and a camera. The programmable LED is coaxial with the microscope objective and is placed at a predetermined height above the sample under test. The imaging tube, aperture, lens 1, and beam splitter are coaxial. The center of the spatial light modulator is located on the optical axis of lens 1 and is tilted at a certain angle to the horizontal direction of the optical axis. The beam splitter, lens 2, and camera are coaxial. The center of the reflector 2 is located on the optical axis of lens 2 and is tilted at a certain angle to the horizontal direction of the optical axis. Lens 1 and lens 2 form a 4f system. The camera and aperture form a conjugate plane.

[0018] Preferably, the spatial light modulator is tilted at an angle of 2° to the horizontal direction of the optical axis.

[0019] Preferably, the reflector 2 is tilted at an angle of 2° to the horizontal direction of the optical axis.

[0020] Preferably, the specific method for parallel acquisition of intensity stacks corresponding to two focal planes using a high-speed, high-resolution three-dimensional diffraction tomography system is as follows:

[0021] During illumination imaging, LEDs are lit one by one. Quasi-monochromatic plane waves illuminate the sample from different angles according to the position of the LEDs. After passing through the microscope objective, mirror 1, imaging tube, aperture, and lens 1, the beams converge onto the beam splitter plane and are split into two beams. One beam is reflected back to the beam splitter by the spatial light modulator, then reflected again and converged onto the camera plane by the lens. The other beam is reflected by mirror 2 and converged onto the camera plane by lens 2. The two beams are laterally separated on the camera target plane, thereby recording a series of original light intensity maps of the two focal planes on the camera plane.

[0022] Preferably, the programmable LED array is synchronized with the camera by providing two coaxial cables for triggering and monitoring the exposure status, so as to obtain a dual-plane intensity set through parallel detection under camera exposure at a set frequency.

[0023] Preferably, the algorithm for reconstructing the refractive index values ​​inside the sample is as follows:

[0024]

[0025]

[0026] in, Represented as a two-dimensional inverse Fourier transform, where l is the l-th... th Intensity images obtained at illumination angles, where α and β are regularization parameters, H a and H p These are the absorption transfer function and the phase transfer function, respectively. The Fourier spectrum of the intensity image acquired in step 2 is given, where Δd refers to the axial defocus distance.

[0027] Preferably, according to and n Im =Δε Im / 2n Re The relationship between n and n is used to obtain the three-dimensional refractive index distribution of the sample, where n Re n is the real part of the sample's refractive index. Im Let n be the imaginary part of the sample's refractive index, n0 be the refractive index of the surrounding medium, and Δε be the refractive index of the medium. Re Let Δε be the real part of the dielectric constant of the sample. Im This represents the imaginary part of the dielectric constant of the sample.

[0028] Compared with the prior art, the present invention has the following significant advantages:

[0029] (1) Based on the parallel detection imaging technology of two focal planes, the present invention enables two intensity images with different defocus distances to be separated laterally on the target surface of the camera and acquired synchronously by adjusting the back aperture surface, so as to reconstruct the three-dimensional structural information of the sample. This makes the technology easy to combine with ordinary microscopes, and defocus modulation can be achieved without the introduction of axial mechanical displacement, thereby improving the image acquisition speed and imaging stability.

[0030] (2) This invention introduces a novel dual-focal plane three-dimensional transfer function model and determines the optimal defocus distance based on the dual-focal plane three-dimensional transfer function. While ensuring resolution, it achieves better low-frequency reconstruction effect and significantly improves imaging quality.

[0031] (3) This invention establishes a dual-focal-plane light intensity transmission diffraction tomography reconstruction algorithm, which directly solves the linear problem by single deconvolution to obtain the three-dimensional refractive index result of the sample. Compared with the traditional iterative method, it significantly improves the calculation speed and effectively solves the problem that time resolution and spatial resolution cannot be achieved simultaneously in non-interference optical diffraction tomography. Attached Figure Description

[0032] Figure 1 This is a flowchart of a high-speed, high-resolution three-dimensional diffraction tomography micro-imaging method.

[0033] Figure 2 It is a five-dimensional phase transfer function model.

[0034] Figure 3 It is a normalized spatial frequency coordinate graph of the three-dimensional phase transfer function.

[0035] Figure 4 This is a schematic diagram of a high-speed, high-resolution three-dimensional diffraction tomography system.

[0036] Figure 5These are rendering comparison images of the three-dimensional refractive index distribution of Hepg2 cells reconstructed using the method of this invention and the traditional optical intensity diffraction tomography method, respectively.

[0037] Figure 6 This is a rendering of the COS-7 cell apoptosis process reconstructed using the method of this invention with high spatiotemporal resolution. Detailed Implementation

[0038] like Figure 1 As shown, a high-speed, high-resolution three-dimensional diffraction tomography system and method includes the following three steps:

[0039] Step 1: Determine the three-dimensional transfer function model and the optimal defocus distance between the two focal planes, and construct a high-speed, high-resolution three-dimensional diffraction tomography system. The process is as follows:

[0040] Step 1.1: Determine the three-dimensional transfer function according to the Fourier diffraction theorem, and obtain the phase transfer function and absorption transfer function:

[0041]

[0042] Where k0=2π / λ represents the wave number, λ represents the illumination wavelength in free space, and u=(k x ,k y (z) represents frequency and spatial domain coordinates, (k x ,k y ) represents the frequency domain coordinates, u in =(k xi ,k yi () represents the frequency of the incident field. Represents the axial wave vector, (k xi ,k yi ,k zi () represents the spatial frequency of the incident field. Δd refers to the axial defocus distance.

[0043] Step 1.2: Use the concepts of focal plane and defocal plane to distinguish the two planes obtained by parallel detection. The transfer function corresponding to dual-focal-plane parallel detection can be expressed as a five-dimensional transfer function (its model is as follows). Figure 2 As shown):

[0044]

[0045] Where l is l th Intensity image obtained at the illumination angle.

[0046] Step 1.3, as follows Figure 3As shown, with increasing defocus distance, the low-frequency response improves, but the oscillation of the high-frequency response curve becomes faster, causing the curve to cross zero multiple times. When the defocus distance is small, the high-frequency response curve can be approximated as a linear function related to the frequency coordinate, effectively avoiding the function oscillation crossing zero points, but this reduces the low-frequency response of the transfer function. Therefore, based on the oscillation distribution of the response curve of the three-dimensional phase transfer function, two sets of asymmetrical defocus distances are selected to synthesize and optimize the phase transfer function, achieving better low-frequency and high-frequency reconstruction results simultaneously.

[0047] Step 1.4, construct a high-speed, high-resolution three-dimensional diffraction tomography system: such as Figure 4 As shown, the high-speed, high-resolution three-dimensional diffraction tomography system includes a programmable LED array (1), a sample under test (2), a microscope objective (3), a reflector 1 (4), an imaging tube (5), an aperture (6), a lens 1 (7), a reflector 2 (8), a beam splitter (9), a spatial light modulator (10), a lens 2 (11), and a camera (12). In the above system, the programmable LED is coaxial with the microscope objective and is placed at a predetermined height above the sample under test; the imaging tube, aperture, lens 1, and beam splitter are coaxial, and the center of the spatial light modulator is located on the optical axis of lens 1 and tilted at an angle of about 2° to the horizontal direction of the optical axis; the beam splitter, lens 2, and camera are coaxial, and the center of the reflector is located on the optical axis of lens 2 and tilted at an angle of about 2° to the horizontal direction of the optical axis; lens 1 and lens 2 form a 4f system; the camera and aperture form a conjugate plane.

[0048] Step 2: Use a high-speed, high-resolution three-dimensional diffraction tomography system to acquire intensity stacks corresponding to two focal planes in parallel.

[0049] During illumination imaging, LEDs are lit one by one. Quasi-monochromatic plane waves illuminate the sample from different angles according to the position of the LEDs. After passing through the microscope objective, mirror 1, imaging tube, aperture, and lens 1, the beams converge onto the beam splitter plane and are split into two beams. One beam is reflected back to the beam splitter by the spatial light modulator, then reflected again and converged onto the camera plane by the lens. The other beam is reflected by mirror 2 and converged onto the camera plane by lens 2. The two beams are laterally separated on the camera target plane, thereby recording a series of original light intensity maps of the two focal planes on the camera plane.

[0050] The specific implementation process is as follows: The illumination beam passes through the sample from different directions, and after passing through the objective lens, mirror 1, and imaging tube, a magnified image of the specimen is generated at the output port (image plane). At the rear end of the microscope's image plane, two lenses L1 and L2 (focal lengths f = f1 = f2 = 150 mm) form a 4f system. The imaging beam is split into a reflected beam and a transmitted beam by a beam splitter (BS). Then, these two beams are reflected onto their respective Fourier planes by a spatial light modulator (SLM) and a mirror (M). Figure 4As shown, to laterally separate and simultaneously acquire two intensity images at different defocus distances on the camera's target surface, the angles of the normals of the mirrors M and SLM relative to the horizontal direction of the optical axis are very small, α≈2°; therefore, the two reflected beams are laterally offset. After passing through lens L2, the angular offset is converted into a lateral separation of 2fsinα between the images. Simultaneously, to ensure that the two images do not overlap and to maximize the filling of the camera sensor area, an aperture stop is inserted at the image plane of the imaging tube for image plane filtering. A quadratic phase diagram corresponding to the free-space propagation transfer function is displayed on the spatial light modulator, further realizing the axial focusing displacement of the transmitted beam. The LED ring is synchronized with the camera via two coaxial cables providing triggering and monitoring of the exposure state, enabling the acquisition of a dual-plane intensity set through parallel detection at a speed of 15 frames per second under a 120Hz camera exposure.

[0051] Step 3: Calculate the three-dimensional refractive index according to the reconstruction algorithm. The algorithm for reconstructing the refractive index value inside the sample is as follows:

[0052]

[0053] in Represented as a two-dimensional inverse Fourier transform, where l is l th Intensity images obtained at the illumination angle, where α and β are regularization parameters, H a and H p These are discrete absorption and phase transfer function, respectively. The Fourier spectrum of the intensity image after background removal;

[0054] Substituting the three-dimensional transfer function and the intensity stacks corresponding to the two focal planes into the reconstruction algorithm, according to... and n Im =Δε Im / 2n Re The relationship between the two was used to obtain the three-dimensional refractive index distribution of the sample.

[0055] Furthermore, the algorithm for reconstructing the refractive index values ​​within the sample is derived based on the minimum total energy constraint and the Tikhonov regularization method. The specific process is as follows:

[0056] Step 3.1: Remove the background from each intensity image, then minimize the difference between the actual measured value and the predicted value using the minimum total energy constraint. The formula is derived using the minimum total energy constraint with Tikhonov regularization:

[0057]

[0058] in This represents the L2 norm of a vector, where α and β are regularization parameters. H is the Fourier transform of the intensity data obtained by normalization. p and H a These are the phase and absorption transfer function, respectively.

[0059] Step 3.2, will and Decompose into real and imaginary parts:

[0060]

[0061] Step 3.3, let the first derivative... If the result is zero, then:

[0062]

[0063] Step 3.4, rearrange the equations to obtain:

[0064]

[0065] Step 3.5: Perform an inverse Fourier transform to obtain a closed-form solution for the refractive index values ​​inside the sample.

[0066]

[0067]

[0068] in Represented as a two-dimensional inverse Fourier transform, where l is l th Intensity image obtained at the illumination angle, H a and H p These are discrete absorption and phase five-dimensional transfer functions, respectively. The Fourier spectrum of the intensity image after background removal.

[0069] Step 3.6, according to and n Im =Δε Im / 2n Re The relationship between the two was used to reconstruct the three-dimensional refractive index distribution of the sample.

[0070] Figure 5 These are rendering comparison images of the three-dimensional refractive index distribution of Hepg2 cells reconstructed using the method of this invention and the traditional optical intensity diffraction tomography method, respectively. The method of this invention has a significantly better low-frequency information reconstruction effect, and can obtain clear cell nuclear structure and cell outline, while the traditional method has a poor reconstruction effect.

[0071] Figure 6 The rendering of the COS-7 cell apoptosis process reconstructed using the method of this invention was achieved at a speed of 15 frames per second, producing a high-resolution result that clearly shows the organelle movement and apoptosis process, thus verifying the high speed and high resolution of this method.

[0072] This invention solves the challenging problem of axial mechanical displacement required under high numerical aperture and mismatched illumination conditions by combining intensity diffraction tomography under varying illumination with "light transmission" measurement based on dual-plane parallel detection. The method allows for the lateral separation and simultaneous acquisition of two intensity images at different defocus distances on the camera's target surface through back-end aperture plane adjustment, offering advantages such as flexible defocus distance adjustment and full compatibility with standard bright-field microscopy. This method eliminates the need for matched illumination conditions and axial mechanical displacement, enabling the reconstruction of three-dimensional scattering potentials under arbitrary illumination conditions in high numerical aperture imaging systems, thus achieving higher resolution three-dimensional diffraction tomography. High-resolution, non-interfering three-dimensional refractive index reconstruction at 300 nm was achieved using a high numerical aperture objective (40 x 0.95 NA). This method is a promising non-invasive tool for revealing the morphology and dynamics of biological processes at the cellular and subcellular levels.

Claims

1. A high-speed, high-resolution three-dimensional diffraction tomography method, characterized in that, The steps are as follows: Step 1: Determine the three-dimensional transfer function model and the optimal defocus distance between the two focal planes to construct a high-speed, high-resolution three-dimensional diffraction tomography system. The three-dimensional transfer function model includes a phase transfer function model and an absorption transfer function model, which are specifically as follows: In the formula, k0=2π / λ represents the wave number, λ represents the illumination wavelength in free space, and u=(k x ,k y (k, z), where z is the spatial domain coordinate, (k x ,k y ) represents the frequency domain coordinates, u in =(k xi ,k yi η(x) represents the frequency of the incident field, and η(x) represents the axial wave vector. Δd refers to the axial defocus distance, k is the wave number in the surrounding medium, and P(u+u) in ) and P(uu in ) is the Fourier transform of the point spread function modulated by the incident field, z = mΔz, where m is the number of slices and Δz is the axial slice thickness; Step 2: Use a high-speed, high-resolution three-dimensional diffraction tomography system to acquire intensity stacks corresponding to two focal planes in parallel; Step 3: Substitute the three-dimensional transfer function and the intensity stacks corresponding to the two focal planes into the algorithm for reconstructing the refractive index values ​​inside the sample to obtain the three-dimensional refractive index distribution of the sample, achieving non-contact and sample-displacement-free high-resolution three-dimensional diffraction tomography. The specific algorithm for reconstructing the refractive index values ​​inside the sample is as follows: n Im =No Im / 2n Re in, Represented as a two-dimensional inverse Fourier transform, where l is the l-th... th Intensity images obtained at illumination angles, where α and β are regularization parameters, H a and H p These are the absorption transfer function and the phase transfer function, respectively. The Fourier spectrum of the intensity image acquired in step 2, where Δd refers to the axial defocus distance, and Δε... Re Let Δε be the real part of the dielectric constant of the sample. Im n is the imaginary part of the dielectric constant of the sample. Re n is the real part of the sample's refractive index. Im n is the imaginary part of the sample's refractive index, and n0 is the refractive index of the surrounding medium.

2. The high-speed, high-resolution three-dimensional diffraction tomography method according to claim 1, characterized in that, The specific method for determining the optimal defocus distance between two focal planes is as follows: The concepts of focal plane and defocal plane are used to distinguish the two planes obtained by parallel detection. The transfer function corresponding to dual-focal-plane parallel detection can be expressed as a five-dimensional transfer function: Where l is the lth... th Intensity images obtained at various illumination angles, l th Indicates the order of the lights, where d is the defocus distance; Based on the oscillation distribution of the response curve of the three-dimensional phase transfer function, two sets of asymmetrical defocus distances are selected.

3. The high-speed, high-resolution three-dimensional diffraction tomography method according to claim 1, characterized in that, The high-speed, high-resolution three-dimensional diffraction tomography system includes a programmable LED array (1), a sample under test (2), a microscope objective (3), a reflector 1 (4), an imaging tube (5), an aperture (6), a lens 1 (7), a reflector 2 (8), a beam splitter (9), a spatial light modulator (10), a lens 2 (11), and a camera (12). The programmable LED array (1) is coaxial with the microscope objective (3) and is placed at a predetermined height above the sample under test. The imaging tube (5), aperture (6), lens 1 (7), and beam splitter (9) are coaxial. The center of the spatial light modulator (10) is located on the optical axis of lens 1 (7) and is tilted at a certain angle to the horizontal direction of the optical axis. The beam splitter (9), lens 2 (11), and camera (12) are coaxial. The center of the reflector 2 (8) is located on the optical axis of lens 2 (11) and is tilted at a certain angle to the horizontal direction of the optical axis. Lens 1 (7) and lens 2 (11) form a 4f system. The camera and aperture form a conjugate plane.

4. The high-speed, high-resolution three-dimensional diffraction tomography method according to claim 3, characterized in that, The spatial light modulator (10) is tilted at an angle of 2° to the horizontal direction of the optical axis.

5. The high-speed, high-resolution three-dimensional diffraction tomography method according to claim 4, characterized in that, The reflector 2(8) is tilted at an angle of 2° to the horizontal direction of the optical axis.

6. The high-speed, high-resolution three-dimensional diffraction tomography method according to claim 3, characterized in that, The specific method for parallel acquisition of intensity stacks corresponding to two focal planes using a high-speed, high-resolution three-dimensional diffraction tomography system is as follows: During illumination imaging, LEDs are lit one by one. Quasi-monochromatic plane waves illuminate the sample from different angles according to the position of the LEDs. After passing through the microscope objective, mirror 1, imaging tube, aperture, and lens 1, the beams converge onto the beam splitter plane and are split into two beams. One beam is reflected back to the beam splitter by the spatial light modulator, then reflected again and converged onto the camera plane by the lens. The other beam is reflected by mirror 2 and converged onto the camera plane by lens 2. The two beams are laterally separated on the camera target plane, thereby recording a series of original light intensity maps of the two focal planes on the camera plane.

7. The high-speed, high-resolution three-dimensional diffraction tomography method according to claim 1, characterized in that, By synchronizing the programmable LED array (1) with the camera (12) through two coaxial cables that provide triggering and monitoring of the exposure status, a dual-plane intensity set can be obtained through parallel detection under exposure of the camera (12) at a set frequency.

Images