A coaxial digital holography-based continuous terahertz wave diffraction tomography method
By employing a continuous terahertz wave diffraction tomography method based on coaxial digital holography, utilizing a CO2-pumped terahertz laser and digital holography, combined with neural network phase restoration algorithms and diffraction tomography algorithms, the problem of observing the internal structure of samples in terahertz imaging was solved, achieving high-quality three-dimensional imaging.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- BEIJING UNIV OF TECH
- Filing Date
- 2023-07-12
- Publication Date
- 2026-08-04
AI Technical Summary
Existing terahertz two-dimensional imaging methods are insufficient to meet the observation requirements of the internal structure of samples. Furthermore, terahertz time-of-flight and computed tomography reconstructions are blurry when diffraction and scattering effects are present, making it impossible to effectively obtain the three-dimensional absorption coefficient and refractive index distribution of the sample.
A continuous terahertz wave diffraction tomography method based on coaxial digital holography was adopted. Using a CO2-pumped terahertz laser, a gold-plated off-axis parabolic mirror, an electric rotary stage, and a pyroelectric detector, the three-dimensional refractive index distribution of the sample was reconstructed by recording and normalizing coaxial digital holograms, combined with a physically enhanced neural network phase restoration algorithm and a diffraction tomography algorithm.
It enables label-free and non-destructive acquisition of the three-dimensional absorption coefficient and refractive index distribution of samples, with high imaging quality, simple and stable optical path structure, and is suitable for non-destructive testing and three-dimensional imaging.
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Figure CN117054366B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a method for continuous terahertz wave diffraction tomography, and particularly to a method for continuous terahertz wave diffraction tomography based on coaxial digital holography. Background Technology
[0002] Terahertz imaging is an important research direction in terahertz application technology. Commonly used two-dimensional terahertz imaging methods can only obtain the integral value of the sample's absorption coefficient or optical path length, which is insufficient for observing the internal structure of the sample. Three-dimensional imaging technology is one of the effective means to obtain information about the internal structure of a sample, and since its inception, it has been validated in microwave, terahertz wave, infrared, and visible light fields. In recent years, terahertz tomographic three-dimensional imaging methods have received widespread attention, such as terahertz time-of-flight tomography, terahertz computed tomography, and terahertz diffraction tomography. Terahertz time-of-flight tomography and terahertz computed tomography require that the diffraction and scattering effects of the sample be negligible; otherwise, their reconstruction results will become severely blurred and distorted. Terahertz diffraction tomography, on the other hand, is a tomographic imaging method that can take diffraction and scattering effects into account. It can simultaneously obtain the three-dimensional absorption coefficient and refractive index distribution of a sample in a label-free, non-destructive, and non-contact manner. Summary of the Invention
[0003] A continuous terahertz wave diffraction tomography method based on coaxial digital holography, the optical path device of the imaging system includes a CO2-pumped terahertz laser 1, a first gold-plated off-axis parabolic mirror 2 (focal length 25.4 mm), a second gold-plated off-axis parabolic mirror 3 (focal length 76.2 mm), an electric rotating stage 4, a sample under test 5, and a pyroelectric detector 6. A CO2-pumped terahertz laser 1 outputs a continuous terahertz wave with a center frequency of 2.52 THz, a wavelength of 118.83 μm, and a maximum output power of approximately 500 mW. A first gold-plated off-axis parabolic mirror 2 (focal length 25.4 mm) and a second gold-plated off-axis parabolic mirror 3 (focal length 76.2 mm) form a beam expander unit, which can increase the diameter of the terahertz wave output from the CO2-pumped terahertz laser 1 by a factor of 3. The expanded terahertz wave propagates onto the sample under test 5, which is placed on an electric rotary stage 4. By controlling the electric rotary stage 4, the transmitted light field of the sample under test at different rotation angles propagates to a pyroelectric detector 6. The pyroelectric detector 6 records a coaxial digital hologram H of the sample at different rotation angles. j (x,y;θ).
[0004] 1. A continuous terahertz wave diffraction tomography system based on coaxial digital holography, characterized in that it comprises a CO2-pumped terahertz laser, a first gold-plated off-axis parabolic mirror, a second gold-plated off-axis parabolic mirror, an electric rotary stage, a sample under test, and a pyroelectric detector; the CO2-pumped terahertz laser is used to output continuous terahertz waves; the first and second gold-plated off-axis parabolic mirrors form a beam expanding unit to enlarge the diameter of the terahertz wave spot output by the CO2-pumped terahertz laser, with parallel propagation directions; the expanded terahertz wave propagates onto the sample under test, the sample under test is placed on the electric rotary stage, and by controlling the electric rotary stage, the transmitted light waves of the sample under test at different rotation angles propagate to the pyroelectric detector, through which a coaxial digital hologram of the sample can be recorded.
[0005] A continuous terahertz wave diffraction tomography method based on coaxial digital holography includes the recording of coaxial digital holograms and the normalization process of coaxial digital holograms. During hologram recording, M frames of holograms with and without samples need to be acquired separately and then averaged.
[0006]
[0007]
[0008] H norm (x, y; θ) = H (x, y; θ) / H0 (x, y; θ)
[0009] Where (x, y) are the spatial coordinates of the recording plane, and θ is the rotation angle of the sample. and It is the sample hologram after superposition and averaging, and the background light. and These are the m-th frame sample hologram and the background light, respectively, where M is the number of holograms recorded. It is a normalized hologram of the sample.
[0010] A continuous terahertz wave diffraction tomography method based on coaxial digital holography includes a reconstruction algorithm for coaxial digital holography. When the normalized hologram is reconstructed using the angular spectrum propagation method, twin images will exist in the reconstructed image, resulting in poor image quality. By using a neural network phase restoration algorithm based on physical enhancement, a reconstructed image without twin image interference and with high quality can be obtained.
[0011] In the physically enhanced neural network phase restoration algorithm, the normalized coaxial digital hologram is... As input to the neural network, the output of the neural network is assumed to be the complex amplitude distribution of the sample without twin images.
[0012]
[0013] Where (x0, y0) are the spatial coordinates of the object plane. It is the complex amplitude distribution of the object plane, f represents the defined neural network, w is the weight parameter of the neural network, and z is the spatial coordinate along the optical axis.
[0014] The complex amplitude distribution of the sample on the object plane can be obtained using a neural network model. Then, the complex amplitude distribution on the recording plane is obtained by using the angular spectrum propagation method, which can be expressed as:
[0015]
[0016] in
[0017]
[0018] F -1 F represents the Fourier transform and the inverse Fourier transform, U z＝d The complex amplitude distribution on the (x,y;θ) recording plane. G z＝d (f x ,f y ) represents the transfer function, (f x ,f y ) represents the spatial spectral coordinates on the recording surface, λ is the wavelength, k0 = 2π / λ is the wavenumber, and d is the distance from the sample to the recording surface;
[0019] Using the complex amplitude distribution on the recording plane, the intensity distribution of the estimated hologram on the recording plane can be expressed as:
[0020]
[0021] in, It is the intensity distribution of the hologram on the recording surface;
[0022] Using the normalized holographic intensity distribution measured on the recording surface and the estimated holographic intensity distribution calculated, the loss function of the physically augmented neural network method can be expressed as follows:
[0023]
[0024] Where L(x,y;θ) is the loss function, and argmin||·|| represents the minimization operation;
[0025] Once the weight parameters w of the physically enhanced neural network method are optimized, the amplitude and phase of the sample without twins can be expressed as:
[0026]
[0027] and
[0028]
[0029] in, and These are the amplitude and phase distributions of the object plane, respectively. abs{·} is the amplitude operation, and angle{·} is the phase operation.
[0030] The process of reconstructing the three-dimensional refractive index distribution of a sample consists of three steps:
[0031] (1) By preprocessing the coaxial digital hologram and using a physically enhanced neural network phase restoration algorithm, the complex amplitude distribution of the projected light field of the sample under different rotation angles is obtained.
[0032] (2) The complex amplitude distribution of the projected light field of the sample under different rotation angles is approximated by weak scattering to obtain the scattered field distribution of the sample:
[0033]
[0034] Among them, O s (x0, y0; θ) is the scattering field distribution of the sample, O Rytov It is the Rytov approximation result of the sample reconstruction image, O in (x0, y0) is the complex amplitude distribution of the incident plane wave;
[0035] (3) After the complex amplitude distribution of the projected light field of the sample at all rotation angles has been processed by the Rytov approximation, the three-dimensional refractive index can be reconstructed using the diffraction tomography algorithm; the filtered backpropagation algorithm used is a spatial domain reconstruction algorithm of diffraction tomography, and its calculation process is as follows:
[0036]
[0037] in,
[0038] x θ =x0 cosθ + z0 sinθ
[0039] y θ =y0
[0040] z θ = -x0 sinθ + z0 cosθ
[0041] f(x0,y0,z) is the reconstructed sample scattering potential distribution. It is O s The two-dimensional spectral distribution of (x0, y0; θ), (x θ ,y θ ,zθ () represents the spatial coordinates of the object plane when the rotation angle is θ. These are the spatial spectral coordinates of the object plane;
[0042] The refractive index distribution of a sample can be calculated using the relationship between the scattering potential distribution f(x0,y0,z) and the refractive index distribution n(x0,y0,z).
[0043]
[0044] Where n0 represents the refractive index of the medium surrounding the sample, the three-dimensional complex refractive index distribution n(x0,y0,z) of the sample can be obtained using the above formula.
[0045] The continuous terahertz wave diffraction tomography method based on coaxial digital holography has the advantages of simple optical path structure and good stability, which can provide more possibilities for the application of terahertz wave diffraction tomography in non-destructive testing and three-dimensional imaging. Attached Figure Description
[0046] Figure 1 This is a system optical path for a continuous terahertz wave diffraction tomography method based on coaxial digital holography. The system optical path includes a CO2-pumped terahertz laser 1, a first gold-plated off-axis parabolic mirror 2 (focal length 25.4 mm), a second gold-plated off-axis parabolic mirror 3 (focal length 76.2 mm), an electric rotary stage 4, the sample under test 5, and a pyroelectric detector 6.
[0047] Figure 2 This is a flowchart of a physical augmentation-based neural network phase restoration algorithm. Detailed Implementation
[0048] The typical embodiments and features of the present invention will now be described in detail with reference to the accompanying drawings.
[0049] Composition structure of the present invention
[0050] This invention discloses a continuous terahertz wave diffraction tomography method based on coaxial digital holography, the optical path of which is as follows: Figure 1As shown, the experiment includes a CO2-pumped terahertz laser 1, a first gold-plated off-axis parabolic mirror 2 (focal length 25.4 mm), a second gold-plated off-axis parabolic mirror 3 (focal length 76.2 mm), an electric rotary stage 4, a sample under test 5, and a pyroelectric detector 6. The CO2-pumped terahertz laser 1 has a wavelength of 118.83 μm (frequency 2.52 THz) and can generate a continuous terahertz wave with a maximum output power of 500 mW. The pyroelectric detector 6 has 320 × 320 pixels, a pixel size of 75 μm × 75 μm, a pixel pitch of 80 μm × 80 μm, an effective area of 25.6 mm × 25.6 mm, and a frame rate of 50 Hz.
[0051] The test sample was a polystyrene foam isophase object. During operation, the sample was placed on an electric rotary stage 4, which had an accuracy of ±0.04°. In the experimental data acquisition, the electric rotary stage 4 was rotated 360° at 2° intervals. The pyroelectric detector 6 recorded a total of 180 holograms of the sample and 1 background light image.
[0052] This invention discloses a continuous terahertz wave diffraction tomography method based on coaxial digital holography, the process of reconstructing the three-dimensional refractive index distribution of a sample consists of three steps:
[0053] (1) By preprocessing the coaxial digital hologram and using a physical enhancement-based neural network phase restoration algorithm, the complex amplitude distribution of the projected light field of the sample under different rotation angles is obtained.
[0054] (2) The complex amplitude distribution of the projected light field of the sample under different rotation angles is approximated by weak scattering to obtain the scattered field distribution of the sample. s (x0, y0; θ):
[0055]
[0056] O Rytov It is the Rytov approximation of the sample reconstruction image, O in (x0, y0) is the complex amplitude distribution of the incident plane wave.
[0057] (3) Once the complex amplitude distribution of the projected light field of the sample at all rotation angles has been approximated by Rytov, the three-dimensional refractive index can be reconstructed using a diffraction tomography algorithm. The filtered backpropagation algorithm used is a spatial domain reconstruction algorithm for diffraction tomography, and its calculation process is shown below:
[0058]
[0059] in,
[0060] x θ=x0cosθ+z0sinθ
[0061] y θ =y0
[0062] z θ = -x0sinθ + z0cosθ
[0063] The refractive index distribution of a sample can be calculated using the relationship between the scattering potential distribution f(x0,y0,z) and the refractive index distribution n(x0,y0,z).
[0064]
[0065] Where n0 represents the refractive index of the surrounding medium, the three-dimensional complex refractive index distribution n(x0,y0,z) of the sample can be obtained.
[0066] Experimental results of typical embodiments of the present invention show that by rotating the sample and recording coaxial digital holograms of the sample at different rotation angles, the complex amplitude distribution of the projected light field of the sample at different rotation angles can be reproduced using hologram preprocessing methods and physically enhanced neural network methods. After performing Rytov approximation on the complex amplitude distribution of the projected light field of the sample, the scattering potential distribution of the sample is reconstructed using a filtered backpropagation algorithm. Finally, the refractive index distribution of the sample is calculated using the relationship between the scattering potential and the refractive index.
[0067] Although the invention has been described in detail with reference to specific embodiments, the embodiments described herein are not intended to be exhaustive or limited to the specific forms disclosed. Rather, the embodiments chosen to illustrate the problem are selected to enable those skilled in the art to practice the invention. Variations and modifications exist without departing from the spirit and scope of the invention as described and defined by the following claims.
Claims
1. A continuous terahertz wave diffraction tomography system based on coaxial digital holography, characterized in that: The system includes a CO2-pumped terahertz laser, a first gold-plated off-axis polished mirror, a second gold-plated off-axis polished mirror, an electric rotary stage, a sample under test, and a pyroelectric detector. The CO2-pumped terahertz laser outputs continuous terahertz waves. The first and second gold-plated off-axis polished mirrors form a beam expander unit, which enlarges the diameter of the terahertz wave beam output from the CO2-pumped terahertz laser, with parallel propagation directions. The expanded terahertz wave propagates onto the sample under test, which is placed on the electric rotary stage. By controlling the electric rotary stage, the transmitted light waves from the sample at different rotation angles propagate to the pyroelectric detector, which records a coaxial digital hologram of the sample. The implementation method of this system includes: recording coaxial digital holograms and normalizing coaxial digital holograms. During hologram recording, it is necessary to collect data separately. The holograms with and without samples are superimposed and averaged. in, These are the spatial coordinates of the recording plane. It is the rotation angle of the sample. and It is the sample hologram after superposition and averaging, and the background light. and These are the records of the first Frame sample hologram and background light, It is the number of holograms recorded. This is a normalized hologram of the sample; The reconstruction algorithm of the coaxial digital hologram of the system includes: when the normalized hologram is reproduced using the angular spectrum propagation method, there will be interference from twin images in the reproduced image, resulting in poor quality of the reproduced image. By using a neural network phase restoration algorithm based on physical enhancement, a reproduced image without twin image interference and with high quality can be obtained. In the physically enhanced neural network phase restoration algorithm, the normalized coaxial digital hologram is... As input to the neural network, the output of the neural network is assumed to be the complex amplitude distribution of the sample without twin images. in, These are the spatial coordinates of the object plane. It is the complex amplitude distribution of the object plane. This represents the defined neural network. These are the weight parameters of the neural network. These are spatial coordinates along the optical axis; The complex amplitude distribution of the sample on the object plane can be obtained using a neural network model. Then, the complex amplitude distribution on the recording plane is obtained by using the angular spectrum propagation method, which can be expressed as: in and This represents the Fourier transform and the inverse Fourier transform. It is the complex amplitude distribution on the recording surface. , Represents the transfer function. These are the spatial spectral coordinates on the recording plane. For wavelength, It is the wavenumber, and d is the distance from the sample to the recording surface; Using the complex amplitude distribution on the recording plane, the intensity distribution of the estimated hologram on the recording plane can be expressed as: in, It is the intensity distribution of the hologram on the recording surface; Using the normalized holographic intensity distribution measured on the recording surface and the estimated holographic intensity distribution calculated, the loss function of the physically augmented neural network method can be expressed as follows: in, It is a loss function. This indicates a minimization operation; When the weight parameters of the physical augmentation neural network method After optimization, the amplitude and phase of the sample without twin images are expressed as follows: and in, and These are the amplitude and phase distributions of the object plane, respectively. It is an amplitude measurement operation. It is a phase take operation.
2. The continuous terahertz wave diffraction tomography system based on coaxial digital holography according to claim 1, characterized in that: The process of reconstructing the three-dimensional refractive index distribution of a sample consists of three steps: (1) By preprocessing the coaxial digital hologram and using a physically enhanced neural network phase restoration algorithm, the complex amplitude distribution of the projected light field of the sample under different rotation angles is obtained; (2) The complex amplitude distribution of the projected light field of the sample under different rotation angles is approximated by weak scattering to obtain the scattered field distribution of the sample: in, It is the scattering field distribution of the sample. It is the Rytov approximation result of the sample reconstruction image. It is the complex amplitude distribution of the incident plane wave; (3) After the complex amplitude distribution of the projected light field of the sample at all rotation angles has been processed by the Rytov approximation, the three-dimensional refractive index can be reconstructed using the diffraction tomography algorithm; the filtered backpropagation algorithm used is a spatial domain reconstruction algorithm of diffraction tomography, and its calculation process is as follows: in, It is the reconstructed sample scattering potential distribution. yes Two-dimensional spectral distribution, The rotation angle is Spatial coordinates of the object plane, These are the spatial spectral coordinates of the object plane; Using the scattering potential distribution of the sample With refractive index distribution The relationship between these factors allows us to calculate the refractive index distribution of the sample: in, The above formula represents the refractive index of the medium surrounding the sample, and the three-dimensional complex refractive index distribution of the sample can be obtained using this formula. .