Optical diffraction tomography microscopy method based on opposite illumination

Abstract

The present invention discloses an optical diffraction tomography microscopy system and method based on counter-illumination. The method employs an LED array as a forward-angle scanning illumination source. By sequentially illuminating the LEDs, the sample is illuminated from different angles, collecting a series of sample intensity maps under forward-angle scanning illumination. A supercontinuum laser is then used as a backward-wavelength scanning illumination source. Light of varying wavelengths is filtered through an acousto-optic tunable co-filter to illuminate the sample, collecting a series of sample intensity maps under backward-wavelength scanning illumination. The present invention employs a non-interference Fourier stacking method to iteratively update the counter-illumination intensity image into a three-dimensional scattering potential spectrum. This method is unaffected by speckle and parasitic interference, directly restoring the sample's three-dimensional refractive index distribution.

Description

Technical Field

[0001] The present invention belongs to the field of optical microscopy measurement and three-dimensional refractive index imaging technology, and in particular to an optical diffraction tomography microscopy imaging method based on opposite illumination. Background Art

[0002] In the field of biomedical microscopy, most living cells and unstained biological specimens are colorless and transparent. This is because the refractive index and thickness of the microstructures within the cell vary. When light waves pass through, the wavelength and amplitude do not change, only the phase shifts. This phase shift is invisible to the human eye. This necessitates chemical or biological methods to stain cells to make them visible under a microscope. Because different substances within biological cells have different absorption rates for colored dyes, the internal structures of biological cells and their distinct biological characteristics can ultimately be seen under a microscope.

[0003] Optical diffraction tomography (ODT) is a microscopic imaging technique that exploits the refractive index, an intrinsic property of biological samples, to enable three-dimensional visualization or quantitative characterization of cellular features. Compared to incoherent fluorescence imaging techniques such as confocal microscopy and light-sheet microscopy, ODT effectively avoids the phototoxicity and photobleaching of fluorescent dyes in biological samples and enables non-invasive, label-free three-dimensional volumetric imaging. As a result, it has been widely used in biophysics, cell biology, hematology, and microbiology. However, a key challenge in conventional transmission optical diffraction tomography is the inability to measure certain spatial frequency components along the axial direction due to the limited projection angle imposed by the numerical aperture of a single objective lens. This limitation, often referred to as the missing cone problem, results in axial resolution that is several times worse than the lateral resolution and severely hinders the accuracy of reconstructing refractive index values.

[0004] In optical diffraction tomography, in order to record characteristic frequencies beyond the aperture limit of a single objective lens, there are usually three ways to solve the missing cone problem and improve axial resolution. (1) Fill the missing cone by rotating the sample (Lee M, Kim K, Oh J, et al. Isotropically resolved label-free tomographic imaging based ontomographic moulds for optical trapping [J]. Light: Science & Applications, 2021, 10 (1): 102.). This type of reconstruction has a complex experimental setup because it requires a customized sample stage and the sample to rotate around a fixed axis or in a microfluidic channel (Merola F, Memmolo P, Miccio L, et al. Tomographic flow cytometry by digital holography [J]. Light: Science & Applications, 2017, 6 (4): e16241-e16241.). Therefore, these methods are almost unsuitable for cells growing on a substrate and are not ideal for long-term observation of living cells. (2) Use regularization constraints (Lim JW, Lee KR, Jin KH, et al. Comparative study of iterative reconstruction algorithms for missing cone problems in optical diffraction tomography [J]. Optics express, 2015, 23 (13): 16933-16948.) or deep learning (Chung H, Huh J, Kim G, et al. Missing cone artifact removal in ODT using unsupervised deep learning in the projection domain [J]. IEEE Transactions on Computational Imaging, 2021, 7: 747-758.) to alleviate the missing cone problem. However, this type of method is based on the prior knowledge of the sample refractive index distribution and the inherent properties of the experimental instrument, ignoring the physical interaction between light and the sample being measured, and therefore lacks versatility in the case of real, complex cell samples.(3) Use transmission optical diffraction tomography combined with reflection optical coherence tomography (OCT) to solve the missing cone problem (Krauze W, Ossowski P, Nowakowski M, et al. Enhanced QPI functionality by combining OCT and ODT methods [C]. Quantitative Phase Imaging VII. SPIE, 2021, 11653: 19-24.). However, although reflection optical coherence tomography can indeed receive the backscattered field used to fill the axial spectrum, it is only applicable to strongly scattering samples that generate strong backscattered signals, which conflicts with the weak scattering conditions of the objects measured in our optical diffraction tomography. In addition, optical coherence tomography relies on interferometry, which will introduce additional interference noise and requires the construction of the reference optical path required for interference, which is difficult to couple into existing commercial microscopy technology. Summary of the Invention

[0005] The object of the present invention is to provide an optical diffraction tomography microscopy imaging system based on opposite illumination.

[0006] The technical solution for implementing the present invention is: an optical diffraction tomography microscopy system based on opposite illumination, the system is used to collect a series of original intensity images of a sample under test under forward angle scanning and reverse wavelength scanning illumination. The system includes a programmable LED array, a sample under test, a microscope objective, a beam splitter prism, an imaging tube lens, a camera, a lens, an acousto-optic tunable filter, and a supercontinuum laser. The center of the programmable LED array is coaxial with the microscope objective and is placed at a predetermined height above the sample under test so that the illumination numerical aperture of the LED array is equal to the numerical aperture of the microscope objective; the optical paths of the microscope objective, the beam splitter prism, and the imaging tube lens are coaxial; the optical paths of the lens, the acousto-optic tunable filter, and the supercontinuum laser are coaxial and perpendicular to the optical path of the microscope objective; the back focal plane of the microscope objective coincides with the front focal plane of the imaging tube lens, the front focal plane of the lens coincides with the back focal plane of the microscope objective after reflection by the beam splitter prism, and the camera is placed on the back focal plane of the imaging tube lens.

[0007] The present invention also proposes an optical diffraction tomography microscopy imaging method based on opposite illumination, the steps of which are as follows:

[0008] Step 1: Acquire raw intensity images under forward angle scanning and backward wavelength scanning illumination;

[0009] Step 2: Construct a three-dimensional all-zero matrix as the initialization spectrum of the measured sample;

[0010] Step 3: Determine the corresponding positions of the intensity images collected at different angles or wavelengths on the three-dimensional spectrum;

[0011] Step 4: Use a series of original intensity images measured under forward angle scanning illumination to update the corresponding areas of the 3D spectrum determined in step 3, until all acquired images are updated, to obtain the updated 3D spectrum of the measured sample;

[0012] Step 5: Continue to use a series of original intensity images obtained by measuring under reverse wavelength scanning illumination on the three-dimensional spectrum obtained in step 4 to update the corresponding area determined in step 3 until all acquired images are updated to obtain the updated three-dimensional spectrum of the measured sample;

[0013] Step 6: Use the non-negative constraint to calculate and fill the axial missing area in the three-dimensional spectrum updated in step 5;

[0014] Step 7: Perform a three-dimensional inverse Fourier transform on the spectrum obtained in step 6 to obtain the three-dimensional refractive index distribution of the sample, thereby achieving non-contact and sample-displacement isotropic high-resolution three-dimensional diffraction tomography.

[0015] Preferably, a through-illumination microscopic imaging system is used to collect a series of original intensity images of the sample under test under forward angle scanning and reverse wavelength scanning illumination. The through-illumination microscopic imaging system includes a programmable LED array, a sample under test, a microscope objective, a beam splitter prism, an imaging tube lens, a camera, a lens, an acousto-optic tunable filter and a supercontinuum laser. The center of the programmable LED array is coaxial with the microscope objective and is placed at a predetermined height above the sample under test so that the illumination numerical aperture of the LED array is equal to the numerical aperture of the microscope objective; the optical paths of the microscope objective, the beam splitter prism and the imaging tube lens are coaxial; the optical paths of the lens, the acousto-optic tunable filter and the supercontinuum laser are coaxial and perpendicular to the optical path of the microscope objective; the rear focal plane of the microscope objective coincides with the front focal plane of the imaging tube lens, the front focal plane of the lens coincides with the rear focal plane of the microscope objective after reflection by the beam splitter prism, and the camera is placed on the rear focal plane of the imaging tube lens.

[0016] Preferably, during forward angle scanning illumination imaging, the LEDs are lit one by one, and the quasi-monochromatic plane waves illuminate the sample from different angles according to the position of the LEDs, and converge onto the camera imaging plane after passing through the objective lens, the dichroic prism, and the imaging tube lens, thereby recording a series of original light intensity maps; during reverse wavelength scanning illumination, the supercontinuum laser is used as the illumination light source, and after filtering through the acousto-optic tunable co-filter, quasi-monochromatic plane waves of different wavelengths are generated in sequence, which pass through the lens, the dichroic prism, and the objective lens in sequence and are emitted as parallel light to illuminate the sample. The backscattered light of the sample passes through the objective lens, the dichroic prism, and the imaging tube lens and converges onto the camera imaging plane, thereby recording a series of original light intensity maps.

[0017] Preferably, the specific method for determining the corresponding positions of the intensity images collected at different angles or wavelengths on the three-dimensional spectrum in step 3 is:

[0018] Step 3.1 describes the scattering potential of a three-dimensional object at different wavelengths. The specific formula is defined as:

[0019]

[0020] Where f(x) represents the three-dimensional scattering potential of the sample, x≡(x,y,z)≡(x T ,z) represents the shorthand symbol of three-dimensional coordinates in space, x T =(x,y) represents the two-dimensional coordinates of the plane, k0 = 2π / λ represents the wave number in vacuum, λ represents the illumination wavelength, n m represents the refractive index of the background medium, and n(x) represents the refractive index distribution of the sample;

[0021] Step 3.2, based on the Rytov approximation, assuming that light is refracted only once in the object, the approximate first-order scattering field U is obtained s1 (x) is:

[0022]

[0023] Among them, U in (x) represents the plane wave irradiating the sample, U s (x) represents the scattered field generated by the object under illumination. The total field U(x) collected by the camera is the superposition of the incident field and the scattered field, that is, U(x) = U in (x)+U s (x); the total field is expressed as follows under the Rytov approximation: Where exp[] represents the exponential function operation with the natural constant e as the base, represents the complex phase function related to the scattered field; the first-order scattered field U s1 The linear relationship between (x) and the sample scattering potential f(x) is further expressed as:

[0024] U s1 (x)=[f(x)U in (x)]*G(x)

[0025] Where G(x) is the outgoing spherical wave in the surrounding medium, * represents the three-dimensional convolution;

[0026] In step 3.3, the linear relationship formula between the one-dimensional scattered field and the sample scattering potential in step 3.2 is transformed into a three-dimensional Fourier transform, and the corresponding positions of the intensity images collected at different angles or wavelengths on the three-dimensional spectrum are obtained according to the light transmission path:

[0027]

[0028] Where, k=(k T ,k z )=(k x ,k y ,k z ) represents the three-dimensional frequency space coordinate, k i =(k iT ,k iz )=(k ix ,k iy ,k iz ) is the three-dimensional vector of the incident plane wave, j is the imaginary unit, and are f(x) and U s1 (X T ; z≡z D )’s Fourier transform; In the ideal case, it is a three-dimensional coherent transfer function, whose spectral support domain is the restricted Ewald sphere limited by the imaging objective aperture, k m Indicates the wave number of the currently used illumination wavelength in the medium, The Fourier spectrum representing the scattering potential is the result of the translation of the incident plane wave.

[0029] Preferably, in step 4, a series of original intensity images measured under forward angle scanning illumination are used to sequentially update the spectrum regions at corresponding positions in the three-dimensional spectrum of the measured sample, and the updating method is:

[0030] Step 4.1: For the i-th illumination angle, determine and extract the corresponding area in the three-dimensional scattering potential spectrum from step 3.3, and project it along the axial frequency coordinate. The specific formula is defined as:

[0031]

[0032] Where i = 1, 2, 3, ... N, N is the total number of illumination angles used in forward angle scanning illumination, represents the two-dimensional sub-spectrum obtained after projection;

[0033] Step 4.2, for the two-dimensional sub-spectrum obtained in step 4.2 Perform inverse Fourier transform to the spatial domain and then perform normalization to obtain the normalized first-order scattered field

[0034]

[0035] Where, yes The inverse Fourier transform of is the incident plane wave corresponding to the i-th illumination angle;

[0036] Step 4.3, use the measured raw intensity image The normalized first-order scattered field obtained in step 4.2 is Implement the amplitude constraint and obtain the updated normalized first-order scattered field

[0037] Where ln() represents the logarithmic operation with the constant e as the base, and exp() represents the exponential function operation with the natural constant e as the base;

[0038] Step 4.4, update the normalized first-order scattered field Perform Fourier transform to obtain the updated two-dimensional spectrum Remap the formula in step 3.3 back to the corresponding position of the three-dimensional spectrum of the measured sample to complete the update of the spectrum corresponding to the original image;

[0039] In step 4.5, repeat steps 4.1-4.4 until all images acquired during the forward angle scan are updated.

[0040] Preferably, in step 5, a series of original intensity images measured under reverse wavelength scanning illumination are used to sequentially update the spectrum regions at corresponding positions in the three-dimensional spectrum of the measured sample, and the updating method is:

[0041] Step 5.1: For the first illumination wavelength, determine and extract the corresponding area in the three-dimensional scattering potential spectrum from step 3.3, and project it along the axial frequency coordinate. The specific formula is defined as:

[0042]

[0043] Where l = 1, 2, 3, ... M, M is the total number of wavelengths used in reverse wavelength scanning illumination, represents the two-dimensional sub-spectrum obtained after projection;

[0044] Step 5.2: Use the reference wavelength to analyze the two-dimensional sub-spectrum Perform normalization:

[0045]

[0046] In the formula represents the normalized spectrum, λ l Indicates the wavelength used by the currently updated spectrum, λ t Indicates the reference wavelength;

[0047] Step 5.3, normalized spectrum Perform inverse Fourier transform to obtain the normalized first-order scattered field Use the measured raw intensity image Apply amplitude constraints to the normalized first-order scattered field and obtain the updated normalized first-order scattered field

[0048]

[0049] Step 5.4, update the normalized first-order scattered field Perform Fourier transform to obtain the updated two-dimensional spectrum Remap the formula in step 3.3 back to the corresponding position of the three-dimensional spectrum of the measured sample to complete the update of the spectrum corresponding to the original image;

[0050] Step 5.5: Repeat steps 5.1-5.4 until all acquired images during the reverse wavelength scan are updated.

[0051] Compared with the prior art, the present invention has the following significant advantages:

[0052] (1) The present invention is based on the counter-illumination technology of forward angle scanning plus reverse wavelength scanning. It can improve the axial imaging resolution to the same as the lateral resolution without sample displacement, reach the incoherent diffraction limit, and realize isotropic high-resolution three-dimensional diffraction tomography. It is suitable for cells growing on a matrix and is easy to achieve long-term observation of living cells.

[0053] (2) The diffraction tomography technology based on non-interference measurement does not require the introduction of complex and unstable interference optical paths and devices, making the experimental device easy to combine with traditional microscopes, and avoiding the speckle noise and parasitic interference caused by the high spatial coherence laser light source required for interferometric measurement, thereby improving the imaging quality.

[0054] (3) The present invention only requires placing the sample at the focal plane position and collecting a series of original intensity images under the object illumination to reconstruct the three-dimensional structural information of the sample. This makes the technology easy to combine with ordinary microscopes, and does not require the microscope to have an axial scanning function. In addition, the system does not introduce mechanical displacement, thereby improving imaging stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 This is a schematic diagram of an isotropic high-resolution optical diffraction tomography microscopy system based on opposite illumination.

[0056] Figure 2 The present invention is a flow chart of an optical diffraction tomography microscopy system and method based on opposite illumination.

[0057] Figure 3 It is the position on the three-dimensional spectrum corresponding to the original intensity image collected under forward angle scanning illumination and backward wavelength scanning illumination.

[0058] Figure 4 This is a schematic diagram of the spectrum shape corresponding to the final reconstructed sample refractive index distribution.

[0059] Figure 5 This is a rendering of the three-dimensional refractive index distribution of a double-layer glass fiber reconstructed using this method. DETAILED DESCRIPTION

[0060] like Figure 1 As shown, an optical diffraction tomography microscopy system based on opposite illumination is used to collect a series of original intensity images of a sample under forward angle scanning and reverse wavelength scanning illumination. The system includes a programmable LED array 1, a sample under test 2, a microscope objective 3, a beam splitter prism 4, an imaging tube lens 5, a camera 6, a lens 7, an acousto-optic tunable filter 8, and a supercontinuum laser 9. The center of the programmable LED array 1 is coaxial with the microscope objective 3 and is placed above the sample under test. The height position is such that the illumination numerical aperture of the LED array 1 is equal to the numerical aperture of the microscope objective 3; the optical paths of the microscope objective 3, the beam splitter prism 4, and the imaging tube lens 5 are coaxial; the optical paths of the lens 7, the acousto-optic tunable filter 8, and the supercontinuum laser 9 are coaxial and perpendicular to the optical path of the microscope objective 3; the rear focal plane of the microscope objective 3 coincides with the front focal plane of the imaging tube lens 5, and the front focal plane of the lens 7 coincides with the rear focal plane of the microscope objective 3 after being reflected by the beam splitter prism 4, and the camera 6 is placed on the rear focal plane of the imaging tube lens.

[0061] During forward angle scanning illumination imaging, the LEDs are lit one by one, and the quasi-monochromatic plane waves illuminate the sample from different angles according to the position of the LEDs. After passing through the objective lens, the beam splitter prism, and the imaging tube lens, they converge on the camera imaging plane, thereby recording a series of original light intensity maps. During reverse wavelength scanning illumination, the supercontinuum laser is used as the illumination light source. After filtering through the acousto-optic tunable co-filter, quasi-monochromatic plane waves of different wavelengths are generated in sequence. After passing through the lens, the beam splitter prism, and the objective lens in sequence, they are emitted as parallel light to illuminate the sample. The backscattered light of the sample passes through the objective lens, the beam splitter prism, and the imaging tube lens and converges on the camera imaging plane, recording a series of original light intensity maps.

[0062] An optical diffraction tomography microscopy method based on opposite illumination includes the following seven steps:

[0063] Step 1: A series of raw intensity images are collected using an isotropic high-resolution optical diffraction tomography microscopy system based on counter-illumination.

[0064] like Figure 2As shown, the present invention is based on an isotropic high-resolution optical diffraction tomography microscopy system with opposite illumination. The opposite illumination microscopy system comprises: a programmable LED array 1, a sample 2, a microscope objective 3, a beam splitter prism 4, an imaging tube 5, a camera 6, a lens 7, an acousto-optic tunable filter 8, and a supercontinuum laser 9. The programmable LED array 1 (39×39 elements, 2mm pixel size, central wavelength 465nm, spectral bandwidth 20nm) is coaxial with the microscope objective 3 (LCPLN100XIR, 100x magnification, numerical aperture 0.85) and is placed 24mm above the sample. It provides variable-angle quasi-monochromatic plane wave illumination with a maximum illumination angle of 58.4°, corresponding to a maximum illumination numerical aperture of 0.85. The optical paths of the microscope objective 3, the beam splitter prism 4, and the imaging tube lens 5 are coaxial; the optical paths of the lens 7, the acousto-optic tunable filter 8 (YSLAOTFPro, bandwidth: 2-11 nm, RF1: 430-780 nm, RF2: 780-1450 nm), and the supercontinuum laser 9 (SC-Pro7, bandwidth 400-2400 nm) are coaxial and perpendicular to the optical path of the microscope objective 3; the rear focal plane of the microscope objective 3 coincides with the front focal plane of the imaging tube lens 5, and the front focal plane of the lens 7 coincides with the rear focal plane of the microscope objective 3 after reflection from the beam splitter prism 4. A camera 6 (AVT Goldeye G-130TEC1, 1280×1024, 5 μm pixel pitch) is placed on the rear focal plane of the imaging tube lens 5.

[0065] The specific implementation process is as follows: during forward angle scanning illumination imaging, the LED units in the programmable LED array 1 are lit one by one, and the quasi-monochromatic plane wave illuminates the sample 2 from different angles according to the position of the LED. After passing through the microscope objective 3, the dichroic prism 4, and the imaging tube lens 5, it converges on the imaging plane of the camera 6, thereby recording a series of original light intensity maps. During reverse wavelength scanning illumination imaging, the supercontinuum laser 9 is used as the illumination light source. After being filtered by the acousto-optic tunable co-filter 8, quasi-monochromatic plane waves of different wavelengths are generated in sequence. After passing through the lens 7, the dichroic prism 4, and the microscope objective 3 in sequence, they are emitted as parallel light to illuminate the sample 2. The backscattered light emitted by the sample 2 after illumination passes through the microscope objective 3, the dichroic prism 4, and the imaging tube lens 5 and converges on the imaging plane of the camera 6, thereby recording a series of light intensity maps.

[0066] Step 2: Construct a three-dimensional all-zero matrix as the initialization spectrum of the measured sample.

[0067] Construct an initial three-dimensional spectrum of the sample under test with a large field of view and high resolution. The specific implementation process is as follows:

[0068] A three-dimensional all-zero matrix is ​​constructed, and the spectrum support domain and spectrum sampling rate of the three-dimensional matrix meet the final imaging resolution and field of view size.

[0069] Step 3: Determine the corresponding positions of the intensity images collected at different angles or wavelengths on the three-dimensional spectrum. The specific implementation process is as follows:

[0070] Step 3.1, at the illumination wavelength λ, use the formula:

[0071]

[0072] represents the three-dimensional scattering potential f(x) of the sample being measured. Where x≡(x,y,z)≡(x T ,z) represents the shorthand symbol of three-dimensional coordinates in space, x T =(x,y) represents the plane coordinates, k0 = 2π / λ represents the wave number in vacuum, λ represents the illumination wavelength, n m represents the refractive index of the background medium, and n(x) represents the refractive index distribution of the sample;

[0073] Step 3.2, based on the Rytov approximation, assuming that light is refracted only once in the object, the approximate first-order scattering field U is obtained s1 (x), the formula is as follows:

[0074]

[0075] Among them, U in (x) represents the plane wave irradiating the sample, U s (x) represents the scattered field generated by the object under illumination. The total field U(x) collected by the camera is the superposition of the incident field and the scattered field, that is, U(x) = U in (x)+U s (x); the total field is expressed as follows under the Rytov approximation: Where exp[] represents the exponential function operation with the natural constant e as the base, represents the complex phase function related to the scattered field; the first-order scattered field U s1 The linear relationship between (x) and the sample scattering potential f(x) is further expressed as:

[0076] U s1 (x)=[f(x)U in (x)]*G(x)

[0077] Where G(x) is the outgoing spherical wave in the surrounding medium, * represents the three-dimensional convolution;

[0078] Step 3.3: Perform a three-dimensional Fourier transform on the linear relationship between the one-dimensional scattered field and the sample scattering potential in step 3.2, and according to the light transmission path (i.e., illumination angle / illumination numerical aperture), the following can be obtained: Figure 3 The corresponding positions of the intensity images collected at different angles or wavelengths on the three-dimensional spectrum are calculated as follows:

[0079]

[0080] Where, k=(k T ,k z )=(k x ,k y ,k z ) represents the three-dimensional frequency space coordinate, k i =(k iT ,k iz )=(k ix ,k iy ,k iz ) is the three-dimensional vector of the incident plane wave, j is the imaginary unit, and are f(x) and U s1 (X T ; z=z D )’s Fourier transform; k m Indicates the wave number of the currently used illumination wavelength in the medium, The Fourier spectrum of the scattering potential is the result of the translation of the incident plane wave; In the ideal case, it is a three-dimensional coherent transfer function, and its spectral support domain is as follows Figure 3 A confined Ewald sphere shown, restricted by the microscope objective aperture.

[0081] Step 4: Use a series of original intensity images measured under forward angle scanning illumination to sequentially update the spectrum area at the corresponding position in the three-dimensional spectrum of the measured sample. The specific implementation process is as follows:

[0082] Step 4.1: For the illumination angle i, determine and extract the corresponding area in the three-dimensional scattering potential spectrum from step 3.3, and project it along the axial frequency coordinate:

[0083]

[0084] Get a two-dimensional sub-spectrum Where i = 1, 2, 3, ... N, N is the total number of illumination angles used in forward angle scanning illumination;

[0085] Step 4.2, for the two-dimensional sub-spectrum obtained in step 4.2 Perform inverse Fourier transform to the spatial domain and then perform normalization to obtain the normalized first-order scattered field The formula is as follows:

[0086]

[0087] Where, yes The inverse Fourier transform of is the incident plane wave corresponding to the i-th illumination angle;

[0088] Step 4.3, use the measured raw intensity image The normalized first-order scattered field obtained in step 4.2 is Implement amplitude constraint, the formula is as follows:

[0089]

[0090] Get the updated normalized first-order scattered field Where ln() represents the logarithmic operation with the constant e as the base, and exp() represents the exponential function operation with the natural constant e as the base;

[0091] Step 4.4, update the normalized first-order scattered field Perform Fourier transform to obtain the updated two-dimensional spectrum Remap the formula in step 3.3 back to the corresponding position of the three-dimensional spectrum of the measured sample to complete the update of the spectrum corresponding to the original image;

[0092] In step 4.5, repeat steps 4.1-4.4 until all images acquired during the forward angle scan are updated.

[0093] Step 5: Use a series of original intensity images measured under reverse wavelength scanning illumination to sequentially update the spectrum area at the corresponding position in the three-dimensional spectrum of the measured sample. The specific implementation process is as follows:

[0094] Step 5.1: For the illumination wavelength l, determine and extract the corresponding area in the three-dimensional scattering potential spectrum from step 3.3, and project it along the axial frequency coordinate. The specific formula is defined as:

[0095]

[0096] Get a two-dimensional sub-spectrum Where l = 1, 2, 3, ... M, M is the total number of wavelengths used in reverse wavelength scanning illumination;

[0097] Step 5.2: Use the reference wavelength to analyze the two-dimensional sub-spectrum Perform normalization:

[0098]

[0099] In the formula represents the normalized spectrum, λ l Indicates the wavelength used by the currently updated spectrum, λ t Indicates the reference wavelength;

[0100] Step 5.3, normalized spectrum Perform inverse Fourier transform to obtain the normalized first-order scattered field Use the measured raw intensity image Apply amplitude constraints to the normalized first-order scattered field and obtain the updated normalized first-order scattered field

[0101]

[0102] Step 5.4, update the normalized first-order scattered field Perform Fourier transform to obtain the updated two-dimensional spectrum Remap the formula in step 3.3 back to the corresponding position of the three-dimensional spectrum of the measured sample to complete the update of the spectrum corresponding to the original image;

[0103] Step 5.5: Repeat steps 5.1-5.4 until all acquired images are updated during the reverse wavelength scan. Figure 4 The range covered by the updated spectrum in the three-dimensional spectrum space under the object lighting condition is shown.

[0104] Step 6: Use non-negativity constraints to calculate and fill in the missing information in the synthesized scattering potential spectrum.

[0105] The specific implementation process is as follows: Based on prior knowledge of the sample, it is assumed that (1) the refractive index of the sample in the spatial domain is always higher than that of the background medium; and (2) the frequency values ​​of the regions updated from the measured original image in the frequency domain are all valid. By applying constraints in both the spatial and frequency domains and repeating the iterations, the missing cone problem near the zero-frequency region in the scattering potential spectrum can be further alleviated, making the reconstruction result more realistic.

[0106] Step 7: Perform a three-dimensional inverse Fourier transform on the three-dimensional spectrum of the sample to be measured obtained by the final calculation, so as to obtain the three-dimensional refractive index distribution of the sample.

[0107] The specific implementation process is: perform inverse Fourier transform on the three-dimensional spectrum obtained in step 6 to obtain the three-dimensional scattering potential f(x). Since the relationship between the three-dimensional scattering potential f(x) of the measured sample and the three-dimensional refractive index n(x) of the measured sample is expressed as Therefore, the three-dimensional refractive index n(x) of the sample can be calculated. The calculation formula is:

[0108]

[0109] Figure 5 Rendering of the three-dimensional refractive index distribution of a double-layer glass fiber reconstructed using this method.

[0110] The present invention utilizes a counter-illuminated imaging device, capturing a series of intensity images through forward angle scanning illumination and reverse wavelength scanning illumination. The device then uses a non-interferometric Fourier stack reconstruction algorithm based on multi-angle and multi-wavelength illumination to couple these intensity images into a three-dimensional spectrum, thereby reconstructing the sample's three-dimensional refractive index distribution. This method improves the axial imaging resolution to the same level as the lateral resolution, reaching the incoherent diffraction limit, and the imaging results are unaffected by speckle and parasitic interference. This method eliminates the need for complex modifications to conventional commercial microscopes or the need for an axial scanning function. It avoids mechanical disturbances and disruptions to the sample's inherent state introduced by mechanical scanning and sample displacement. It is suitable for cells grown adherent to a substrate and facilitates long-term observation of living cells.

Claims

1. An optical diffraction tomography microscopy method based on opposite illumination, characterized in that: The imaging steps are as follows: Step 1: Use an optical diffraction tomography microscopy system based on opposite illumination to collect raw intensity images under forward angle scanning and backward wavelength scanning illumination; The system comprises a programmable LED array (1), a sample to be measured (2), a microscope objective lens (3), a beam splitter prism (4), an imaging tube lens (5), a camera (6), a lens (7), an acousto-optic tunable filter (8), and a supercontinuum laser (9). The center of the programmable LED array (1) is coaxial with the microscope objective lens (3) and is placed at a predetermined height above the sample to be measured so that the numerical aperture of the illumination of the LED array (1) is equal to the numerical aperture of the microscope objective lens (3). The optical paths of the microscope objective lens (3), the beam splitter prism (4), and the imaging tube lens (5) are coaxial; the optical paths of the lens (7), the acousto-optic tunable filter (8), and the supercontinuum laser (9) are coaxial and perpendicular to the optical path of the microscope objective lens (3); the rear focal plane of the microscope objective lens (3) coincides with the front focal plane of the imaging tube lens (5); the front focal plane of the lens (7) coincides with the rear focal plane of the microscope objective lens (3) after being reflected by the beam splitter prism (4); and the camera (6) is placed on the rear focal plane of the imaging tube lens; Step 2: Construct a three-dimensional all-zero matrix as the initialization spectrum of the measured sample; Step 3: Determine the corresponding positions of the intensity images collected at different angles or wavelengths on the three-dimensional spectrum. The specific method is: Step 3.1 describes the scattering potential of a three-dimensional object at different wavelengths. The specific formula is defined as: Where f(x) represents the three-dimensional scattering potential of the sample, x≡(x,y,z)≡(x T ,z) represents the shorthand symbol of three-dimensional coordinates in space, x T =(x,y) represents the two-dimensional coordinates of the plane, k0 = 2π / λ represents the wave number in vacuum, λ represents the illumination wavelength, n m represents the refractive index of the background medium, and n(x) represents the refractive index distribution of the sample; Step 3.2, based on the Rytov approximation, assuming that light is refracted only once in the object, the approximate first-order scattering field U is obtained s1 (x) is: Among them, U in (x) represents the plane wave irradiating the sample, U s (x) represents the scattered field generated by the object under illumination. The total field U(x) collected by the camera is the superposition of the incident field and the scattered field, that is, U(x) = U in (x)+U s (x); the total field is expressed as follows under the Rytov approximation: Where exp[] represents the exponential function operation with the natural constant e as the base, represents the complex phase function related to the scattered field; the first-order scattered field U s1 The linear relationship between (x) and the sample scattering potential f(x) is further expressed as: U s1 (x)=[f(x)U in (x)]*G(x) Where G(x) is the outgoing spherical wave in the surrounding medium, * represents the three-dimensional convolution; In step 3.3, the linear relationship formula between the one-dimensional scattered field and the sample scattering potential in step 3.2 is transformed into a three-dimensional Fourier transform, and the corresponding positions of the intensity images collected at different angles or wavelengths on the three-dimensional spectrum are obtained according to the light transmission path: Where, k=(k T ,k z )=(k x ,k y ,k z ) represents the three-dimensional frequency space coordinate, k i =(k iT ,k iz )=(k ix ,k iy ,k iz ) is the three-dimensional vector of the incident plane wave, j is the imaginary unit, and are f(x) and U s1 (X T ; z=z D )’s Fourier transform; In the ideal case, it is a three-dimensional coherent transfer function, whose spectral support domain is the restricted Ewald sphere limited by the imaging objective aperture, k m Indicates the wave number of the currently used illumination wavelength in the medium, The Fourier spectrum of the scattering potential is the result of the translation of the incident plane wave; Step 4: Use a series of original intensity images measured under forward angle scanning illumination to update the corresponding areas of the 3D spectrum determined in step 3, until all acquired images are updated, to obtain the updated 3D spectrum of the measured sample; Step 5: Continue to use a series of original intensity images obtained by measuring under reverse wavelength scanning illumination on the three-dimensional spectrum obtained in step 4 to update the corresponding area determined in step 3 until all acquired images are updated to obtain the updated three-dimensional spectrum of the measured sample; Step 6: Use the non-negative constraint to calculate and fill the axial missing area in the three-dimensional spectrum updated in step 5; Step 7: Perform a three-dimensional inverse Fourier transform on the spectrum obtained in step 6 to obtain the three-dimensional refractive index distribution of the sample, thereby achieving non-contact and sample-displacement isotropic high-resolution three-dimensional diffraction tomography.

2. The optical diffraction tomography microscopy imaging method based on opposite illumination according to claim 1, characterized in that: During forward angle scanning illumination imaging, the LEDs are lit one by one, and the quasi-monochromatic plane waves illuminate the sample from different angles according to the position of the LEDs. After passing through the objective lens, the beam splitter prism, and the imaging tube lens, they converge on the camera imaging plane, thereby recording a series of original light intensity maps. During reverse wavelength scanning illumination, the supercontinuum laser is used as the illumination light source. After filtering through the acousto-optic tunable filter, quasi-monochromatic plane waves of different wavelengths are generated in sequence. After passing through the lens, the beam splitter prism, and the objective lens in sequence, they are emitted as parallel light to illuminate the sample. The backscattered light of the sample passes through the objective lens, the beam splitter prism, and the imaging tube lens and converges on the camera imaging plane, recording a series of original light intensity maps.

3. The optical diffraction tomography microscopy imaging method based on opposite illumination according to claim 1, characterized in that: In step 4, a series of original intensity images measured under forward angle scanning illumination are used to sequentially update the spectrum regions at corresponding positions in the three-dimensional spectrum of the measured sample. The updating method is: Step 4.1: For the i-th illumination angle, determine and extract the corresponding area in the three-dimensional scattering potential spectrum from step 3.3, and project it along the axial frequency coordinate. The specific formula is defined as: Where i = 1, 2, 3, ... N, N is the total number of illumination angles used in forward angle scanning illumination, represents the two-dimensional sub-spectrum obtained after projection; Step 4.2, for the two-dimensional sub-spectrum obtained in step 4.1 Perform inverse Fourier transform to the spatial domain and then perform normalization to obtain the normalized first-order scattered field Where, yes The inverse Fourier transform of is the incident plane wave corresponding to the i-th illumination angle; Step 4.3, use the measured raw intensity image The normalized first-order scattered field obtained in step 4.2 is Implement the amplitude constraint and obtain the updated normalized first-order scattered field Where ln() represents the logarithmic operation with the constant e as the base, and exp() represents the exponential function operation with the natural constant e as the base; Step 4.4, update the normalized first-order scattered field Perform Fourier transform to obtain the updated two-dimensional spectrum Remap the formula in step 3.3 back to the corresponding position of the three-dimensional spectrum of the measured sample to complete the update of the spectrum corresponding to the original image; In step 4.5, repeat steps 4.1-4.4 until all images acquired during the forward angle scan are updated.

4. The optical diffraction tomography microscopy imaging method based on opposite illumination according to claim 1, characterized in that: In step 5, a series of original intensity images obtained by measuring under reverse wavelength scanning illumination are used to sequentially update the spectrum regions at corresponding positions in the three-dimensional spectrum of the measured sample. The updating method is: Step 5.1: For the first illumination wavelength, determine and extract the corresponding area in the three-dimensional scattering potential spectrum from step 3.3, and project it along the axial frequency coordinate. The specific formula is defined as: Where l = 1, 2, 3, ... M, M is the total number of wavelengths used in reverse wavelength scanning illumination, represents the two-dimensional sub-spectrum obtained after projection; Step 5.2: Use the reference wavelength to analyze the two-dimensional sub-spectrum Perform normalization: In the formula represents the normalized spectrum, λ l Indicates the wavelength used by the currently updated spectrum, λ t Indicates the reference wavelength; Step 5.3, normalized spectrum Perform inverse Fourier transform to obtain the normalized first-order scattered field Use the measured raw intensity image Apply amplitude constraints to the normalized first-order scattered field and obtain the updated normalized first-order scattered field Step 5.4, update the normalized first-order scattered field Perform Fourier transform to obtain the updated two-dimensional spectrum Remap the formula in step 3.3 back to the corresponding position of the three-dimensional spectrum of the measured sample to complete the update of the spectrum corresponding to the original image; In step 5.5, repeat steps 5.1-5.4 until all acquired images during the reverse wavelength scan are updated.

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