Investigation on reconstruction methods applied to 3D terahertz computed tomography

The Use of Terahertz Computed Tomography and Time Domain Spectroscopy to Evaluate Symmetry in 3D Printed Parts

3D printing has become essential to many fields for its low-cost production and rapid prototyping abilities. As 3D printing becomes an alternative manufacturing tool, developing methods to non-destructively evaluate defects for quality control is essential. This study integrates the non-destructive terahertz (THz) analysis methods of terahertz time-domain spectroscopy (THz-TDS) and terahertz computed tomography (THz CT) to image and assess 3D printed resin structures for defects. The terahertz images were reconstructed using MATLAB, and the rotational symmetry of various structures before and after the introduction of defects was evaluated by calculating the mean squared deviation (MSD), which served as a symmetry parameter to indicate the presence of defects. Structures A and B had MSD values that were at least three standard deviations larger after introducing defects to their structures, showing a significant change in symmetry and indicating the existence of defects. Similarly, in structure C, blockages in parts made with different post-cures were identified based on the increase in MSD values for those slices. For structure D, the presence of a defect increased the MSD value by 14%. The results of this study verify that the MSD calculated for the rotational symmetry of the structures was greater when defects were present, accurately reflecting the anticipated breaks in symmetry. This paper demonstrates that terahertz imaging, combined with MSD analysis, is a viable procedure to identify and quantify defects in rotationally symmetric 3D printed structures.

Metal artifact suppression in terahertz computed tomography

Metal artifact suppression in images of terahertz computed tomography is a bottleneck problem that hinders the development of this technique, and few studies have been conducted so far. In this paper, we propose a metal artifact suppression method containing 8 steps based on the idea of sinogram restoration. The method has been applied to the slice images of several metal objects and the effects before and after metal artifact suppression have been compared to verify the effectiveness of the method. And it provides a reliable reference for the subsequent solution of this problem.

Terahertz deep learning fusion computed tomography

Terahertz (THz) tomographic imaging based on time-resolved THz signals has raised significant attention due to its non-invasive, non-destructive, non-ionizing, material-classification, and ultrafast-frame-rate nature for object exploration and inspection. However, the material and geometric information of the tested objects is inherently embedded in the highly distorted THz time-domain signals, leading to substantial computational complexity and the necessity for intricate multi-physics models to extract the desired information. To address this challenge, we present a THz multi-dimensional tomographic framework and multi-scale spatio-spectral fusion Unet (MS3-Unet), capable of fusing and collaborating the THz signals across diverse signal domains. MS3-Unet employs multi-scale branches to extract spatio-spectral features, which are subsequently processed through element-wise adaptive filters and fused to achieve high-quality THz image restoration. Evaluated by geometry-variant objects, MS3-Unet outperforms other peer methods in PSNR and SSIM. In addition to the superior performance, the proposed framework additionally provides high scalable, adjustable, and accessible interface to collaborate with different user-defined models or methods.

Breaking the limitations with sparse inputs by variational frameworks (BLIss) in terahertz super-resolution 3D reconstruction

Data acquisition, image processing, and image quality are the long-lasting issues for terahertz (THz) 3D reconstructed imaging. Existing methods are primarily designed for 2D scenarios, given the challenges associated with obtaining super-resolution (SR) data and the absence of an efficient SR 3D reconstruction framework in conventional computed tomography (CT). Here, we demonstrate BLIss, a new approach for THz SR 3D reconstruction with sparse 2D data input. BLIss seamlessly integrates conventional CT techniques and variational framework with the core of the adapted Euler-Elastica-based model. The quantitative 3D image evaluation metrics, including the standard deviation of Gaussian, mean curvatures, and the multi-scale structural similarity index measure (MS-SSIM), validate the superior smoothness and fidelity achieved with our variational framework approach compared with conventional THz CT modal. Beyond its contributions to advancing THz SR 3D reconstruction, BLIss demonstrates potential applicability in other imaging modalities, such as X-ray and MRI. This suggests extensive impacts on the broader field of imaging applications.

Large Scale Optical Projection Tomography without the Use of Refractive-Index-Matching Liquid

The practical, rapid, and accurate optical 3D reconstruction of transparent objects with contemporary non-contact optical techniques, has been an open challenge in the field of optical metrology. The combination of refraction, reflection, and transmission in transparent objects makes it very hard to use common off-the-shelf 3D reconstruction solutions to accurately reconstruct transparent objects in three dimensions without completely coating the object with an opaque material. We demonstrate in this work that a specific class of transparent objects can indeed be reconstructed without the use of opaque spray coatings, via Optical Projection Tomography (OPT). Particularly, the 3D reconstruction of large thin-walled hollow transparent objects can be achieved via OPT, without the use of refractive-index-matching liquid, accurately enough for use in both cultural heritage and beverage packaging industry applications. We compare 3D reconstructions of our proposed OPT method to those achieved by an industrial-grade 3D scanner and report average shape differences of ±0.34 mm for 'shelled' hollow objects and ±0.92 mm for 'non-shelled' hollow objects. A disadvantage of using OPT, which was noticed on the thicker 'non-shelled' hollow objects, as opposed to the 'shelled' hollow objects, was that it induced partial filling of hollow areas and the deformation of embossed features.

Making the Invisible Visible: Toward High-Quality Terahertz Tomographic Imaging via Physics-Guided Restoration

Terahertz (THz) tomographic imaging has recently attracted significant attention thanks to its non-invasive, non-destructive, non-ionizing, material-classification, and ultra-fast nature for object exploration and inspection. However, its strong water absorption nature and low noise tolerance lead to undesired blurs and distortions of reconstructed THz images. The diffraction-limited THz signals highly constrain the performances of existing restoration methods. To address the problem, we propose a novel multi-view Subspace-Attention-guided Restoration Network (SARNet) that fuses multi-view and multi-spectral features of THz images for effective image restoration and 3D tomographic reconstruction. To this end, SARNet uses multi-scale branches to extract intra-view spatio-spectral amplitude and phase features and fuse them via shared subspace projection and self-attention guidance. We then perform inter-view fusion to further improve the restoration of individual views by leveraging the redundancies between neighboring views. Here, we experimentally construct a THz time-domain spectroscopy (THz-TDS) system covering a broad frequency range from 0.1 to 4 THz for building up a temporal/spectral/spatial/material THz database of hidden 3D objects. Complementary to a quantitative evaluation, we demonstrate the effectiveness of our SARNet model on 3D THz tomographic reconstruction applications.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11263-023-01812-y.

Selection criteria of image reconstruction algorithms for terahertz short-range imaging applications

Terahertz (THz) imaging has been regarded as cutting-edge technology in a wide range of applications due to its ability to penetrate through opaque materials, non-invasive nature, and its increased bandwidth capacity. Recently, THz imaging has been extensively researched in security, driver assistance technology, non-destructive testing, and medical applications. The objective of this review is to summarize the selection criteria for current state-of-the-art THz image reconstruction algorithms developed for short-range imaging applications over the last two decades. Moreover, we summarize the selected algorithms' performance and their implementation process. This study provides an in-depth understanding of the fundamentals of image reconstruction algorithms related to THz short-range imaging and future aspects of algorithm processing and selection.

Selected Applications of Terahertz Pulses in Medicine and Industry

This article contains a brief summary of areas where terahertz technology is making an impact in research and industrial applications. We cover some of its uses in the pharmaceutical setting, where both imaging and spectroscopy play important roles. Medical applications are also being pursued in many research laboratories, primarily for imaging purposes and following on from the first results just over 20 years ago. The three-dimensional imaging capability of pulsed terahertz allows for the observation of tumours below the surface of tissue, such as basal cell carcinoma of skin. The recent use of the technology in studies of cultural heritage has shown to increase our understanding of the past. The power of terahertz is exemplified by the discussion on its importance in different industries, such as semiconductor circuit manufacturing and automotive assembly.

THz medical imaging: from in vitro to in vivo

Terahertz (THz) radiation has attracted considerable attention in medical imaging owing to its nonionizing and spectral fingerprinting characteristics. To date, most studies have focused on in vitro and ex vivo objects with water-removing pretreatment because the water in vivo excessively absorbs the THz waves, which causes deterioration of the image quality. In this review, we discuss how THz medical imaging can be used for a living body. The development of imaging contrast agents has been particularly useful to this end. In addition, we also introduce progress in novel THz imaging methods that could be more suitable for in vivo applications. Based on our discussions, we chart a developmental roadmap to take THz medical imaging from in vitro to in vivo.

Discrete Fourier Transform Radar in the Terahertz-Wave Range Based on a Resonant-Tunneling-Diode Oscillator

We used a resonant-tunneling-diode (RTD) oscillator as the source of a terahertz-wave radar based on the principle of the swept-source optical coherence tomography (SS-OCT). Unlike similar reports in the terahertz range, we apply the stepwise frequency modulation to a subcarrier obtained by amplitude modulation instead of tuning the terahertz carrier frequency. Additionally, we replace the usual optical interference with electrical mixing and, by using a quadrature mixer, we can discriminate between negative and positive optical path differences, which doubles the measurement range without increasing the measurement time. To measure the distance to multiple targets simultaneously, the terahertz wave is modulated in amplitude at a series of frequencies; the signal returning from the target is detected and homodyne mixed with the original modulation signal. A series of voltages is obtained; by Fourier transformation the distance to each target is retrieved. Experimental results on one and two targets are shown.

Error Assessment and Mitigation Methods in Transient Radar Method

Transient Radar Method (TRM) was recently proposed as a novel contact-free method for the characterization of multilayer dielectric structures including the geometric details. In this paper, we discuss and quantify the intrinsic and systematic errors of TRM. Also, solutions for mitigating these problems are elaborated extensively. The proposed solution for error correction will be applied to quantify experimentally the thickness of several single-layer dielectric structures with thicknesses varying from larger to smaller than the wavelength. We will show how the error correction method allows sub-wavelength thickness measurements around λ/5.

2D tomographic terahertz imaging using a single pixel detector

A 2D tomographic terahertz imaging set-up using a single pixel imaging approach is realized, where a liquid helium cooled bolometer is utilized as a bucket detector and a mercury-arc lamp serves as a broadband terahertz source. The different patterns of the terahertz radiation, which are necessary for the single pixel imaging approach, are realized by spatially addressed photodoping of a high resistivity float zone silicon window, employing a near-infrared laser diode, which is spatially modulated by a digital micromirror device. The two investigated sample objects have cylindrical and cuboid shapes and consist of polypropylene. Both sample shapes cause strong influences of refraction, reflection and diffraction, which distort the measured projections and thus have to be considered in the tomographic reconstruction. In order to consider these effects, a model is developed which combines refraction and diffraction effects by a hybrid approach using ray tracing and scalar diffraction theory yielding finally projections of the sample objects. These simulated projections are compared to the measured projections and show a good agreement between the experimental results and the developed model. In accordance with this result, an optimization problem is formulated, which offers an approach for tomographic reconstruction using the developed model.

Synchrotron-Based Three-Dimensional Fourier-Transform Infrared Spectro-Microtomography of Murchison Meteorite Grain

We demonstrate nondestructive, three-dimensional, microscopic, infrared (IR) spectral in-situ imaging of an extraterrestrial sample. Spatially resolved chemical composition and spatial correlations are investigated within a single 45 µm grain of the Murchison meteorite. Qualitative and quantitative investigation through this analytical technique can help elucidate the origin and evolution of meteoritic compounds as well as parent body processes without damaging or altering the investigated samples.

Position and orientation measurement adopting camera calibrated by projection geometry of Plücker matrices of three-dimensional lines

A position and orientation measurement method is investigated by adopting a camera calibrated by the projection geometry of the skew-symmetric Plücker matrices of 3D lines. The relationship between the Plücker matrices of the dual 3D lines and the 2D projective lines is provided in two vertical world coordinate planes. The transform matrix is generated from the projections of the 3D lines. The differences between the coordinates of the reprojective lines and the coordinates of extracted lines are employed to verify the calibration validity. Moreover, the differences between the standard movement distance of the target and the measurement distance are also presented to compare the calibration accuracy of the 3D line to 2D line method and the point-based method. Furthermore, we also explore the noise immunity of the two methods by adding Gaussian noises. Finally, an example to measure the position and orientation of a cart is performed as an application case of this method. The results are tabled for the reproduction by the readers. The results demonstrate that the line to line method contributes higher calibration accuracy and better noise immunity. The position and orientation measurement adopting the line to line method is valid for the future applications.

Two-dimensional tomographic terahertz imaging by homodyne self-mixing

We realize a compact two-dimensional tomographic terahertz imaging experiment involving only one photoconductive antenna (PCA) simultaneously serving as a transmitter and receiver of the terahertz radiation. A hollow-core Teflon cylinder filled with α-Lactose monohydrate powder is studied at two terahertz frequencies, far away and at a specific absorption line of the powder. This sample is placed between the antenna and a chopper wheel, which serves as back reflector of the terahertz radiation into the PCA. Amplitude and phase information of the continuous-wave (CW) terahertz radiation are extracted from the measured homodyne self-mixing (HSM) signal after interaction with the cylinder. The influence of refraction is studied by modeling the set-up utilizing ZEMAX and is discussed by means of the measured 1D projections. The tomographic reconstruction by using the Simultaneous Algebraic Reconstruction Technique (SART) allows to identify both object geometry and α-Lactose filling.

Low-frequency noise effect on terahertz tomography using thermal detectors

In this paper, the impact of low-frequency noise on terahertz-computed tomography (THz-CT) is analyzed for several measurement configurations and pyroelectric detectors. We acquire real noise data from a continuous millimeter-wave tomographic scanner in order to figure out its impact on reconstructed images. Second, noise characteristics are quantified according to two distinct acquisition methods by (i) extrapolating from experimental acquisitions a sinogram for different noise backgrounds and (ii) reconstructing the corresponding spatial distributions in a slice using a CT reconstruction algorithm. Then we describe the low-frequency noise fingerprint and its influence on reconstructed images. Thanks to the observations, we demonstrate that some experimental choices can dramatically affect the 3D rendering of reconstructions. Thus, we propose some experimental methodologies optimizing the resulting quality and accuracy of the 3D reconstructions, with respect to the low-frequency noise characteristics observed during acquisitions.

Ordered subsets convex algorithm for 3D terahertz transmission tomography

We investigate in this paper a new reconstruction method in order to perform 3D Terahertz (THz) tomography using a continuous wave acquisition setup in transmission mode. This method is based on the Maximum Likelihood for TRansmission tomography (ML-TR) first developed for X-ray imaging. We optimize the Ordered Subsets Convex (OSC) implementation of the ML-TR by including the Gaussian propagation model of THz waves and take into account the intensity distributions of both blank calibration scan and dark-field measured on THz detectors. THz ML-TR reconstruction quality and accuracy are discussed and compared to other tomographic reconstructions.

Multi-resolution imaging with an optimized number and distribution of sampling points

We propose an approach of interest in Imaging and Synthetic Aperture Radar (SAR) tomography, for the optimal determination of the scanning region dimension, of the number of sampling points therein, and their spatial distribution, in the case of single frequency monostatic multi-view and multi-static single-view target reflectivity reconstruction. The method recasts the reconstruction of the target reflectivity from the field data collected on the scanning region in terms of a finite dimensional algebraic linear inverse problem. The dimension of the scanning region, the number and the positions of the sampling points are optimally determined by optimizing the singular value behavior of the matrix defining the linear operator. Single resolution, multi-resolution and dynamic multi-resolution can be afforded by the method, allowing a flexibility not available in previous approaches. The performance has been evaluated via a numerical and experimental analysis.

Computed tomography using broadband Bessel THz beams and phase contrast

We present new results demonstrating the capability of performing computed tomography (CT) using broadband Bessel terahertz (THz) beams. Nondiffractive beams such as these exhibit propagation-invariant lines of focus with an extended depth-of-field compared to conventional Gaussian beams. Using this property, we demonstrate a considerable improvement in the 3D reconstruction image of a synthetic sample through the backprojection algorithm. Only when THz Bessel beams are used, a full reconstruction of the object structure is made. Moreover, we use phase-contrast mechanism which improves the spatial resolution and reconstructed images. Our results highlight the potential in using nondiffractive Bessel beams to significantly improve 3D-image reconstruction of THz CT.

THz phase-contrast computed tomography based on Mach-Zehnder interferometer using continuous wave source: proof of the concept

In this study, we propose a THz computed tomography (CT) method based on phase contrast, which retrieves the phase shift information at each data point through a phase modulation technique using a Mach-Zehnder interferometer with a continuous wave (CW) source. The THz CT is based on first-generation CT, which acquires a set of projections by translational and rotational scans using a thin beam. From the phase-shift projections, we reconstruct a spatial distribution of refractive indices in a cross section of interest. We constructed a preliminary system using a highly coherent CW THz source with a frequency of 0.54 THz to prove the concept and performed an imaging experiment using phantoms to investigate its imaging features such as artifact-immune imaging, quantitative measurement, and selective detection.

Pre- and post-processing for tomographic reconstruction of terahertz time-domain spectroscopy

Reflection-type terahertz tomography is obtained using time-domain spectroscopy. Due to different velocities of the terahertz ray in free space and inside a sample, the tomographic transverse plane is not obtained by a simple reconstruction using time index. A pre-processing method is proposed to compensate for the different velocities of the terahertz ray for tomographic reconstruction. Maximum intensity projection, averaging, and short-time Fourier transform are proposed as post-processing methods along the depth direction for the terahertz tomography. Log-scale display is also suggested for a better visualization. Some experimental results with the pre- and post-processing are demonstrated.

Fast three-dimensional terahertz computed tomography using real-time line projection of intense terahertz pulse

We demonstrated fast three-dimensional transmission terahertz computed tomography by using real-time line projection of intense terahertz beam generated by optical rectification in lithium niobate crystal. After emphasizing the advantage of intense terahertz pulse generation for two-dimensional spatio-temporal terahertz imaging, peak-to-peak amplitudes of pulsed terahertz electric field have been used to obtain a series of projection images at different rotation angles. Then a standard reconstruction algorithm has been employed to perform final three-dimensional reconstruction. Test samples including a medicine capsule have been investigated with a total acquisition time to only 6 minutes.

Three-dimensional terahertz computed tomography of human bones

Three-dimensional terahertz computed tomography has been used to investigate dried human bones such as a lumbar vertebra, a coxal bone, and a skull, with a direct comparison with standard radiography. In spite of lower spatial resolution compared with x-ray, terahertz imaging clearly discerns a compact bone from a spongy one, with strong terahertz absorption as shown by additional terahertz time-domain transmission spectroscopy.

Terahertz beam steering using interference of femtosecond optical pulses

A terahertz (THz) beam steering method is demonstrated by applying the characteristic of grating lobe (GL) radiation from a linear array antenna and the interference of femtosecond optical pulses. A photoconductive device is illuminated by two femtosecond laser beams combined at an angle of less than 0.5°. Considering the interference pattern as a THz point source array, THz GL radiation is generated through the superposition of radiation emitted from all point sources and steered by varying the interval of the interference pattern. The THz beam direction could be changed by 20° at 0.93THz by varying the relative incidence angle of the pump beams by 0.033°.

Propagation beam consideration for 3D THz computed tomography

In this paper, a model of the beam propagation is developed according to the physical properties of THz waves used in THz computed tomography (CT) scan imaging. This model is first included in an acquisition simulator to observe and estimate the impact of the Gaussian beam intensity profile on the projection sets. Second, the model is introduced in several inversion methods as a convolution filter to perform efficient tomographic reconstructions of simulated and real acquired objects. Results obtained with three reconstruction methods (BFP, SART and OSEM) are compared to the techniques proposed in this paper. We will demonstrate an increase of the overall quality and accuracy of the 3D reconstructions.

Terahertz tomographic imaging of XVIIIth Dynasty Egyptian sealed pottery

A monochromatic millimeter-wave imaging system coupled with an infrared temperature sensor has been used to investigate historic objects preserved at the Museum of Aquitaine (France). In particular, two-dimensional and three-dimensional analyses have been performed in order to reveal the internal structure of nearly 3500-year-old sealed Egyptian jars.

Real-time line projection for fast terahertz spectral computed tomography

We demonstrated fast terahertz spectral computed tomography by using real-time line projection of a terahertz beam. Two types of cross-sectional images of continuously rotating samples have been measured in only a few seconds. From temporal data, a peak-to-peak sinogram and cross sections have been reconstructed using a filtered backprojection algorithm. Using fast Fourier transform from temporal data, spectral cross sections of the sample have been obtained.