Terahertz time-gated spectral imaging for content extraction through layered structures

Temperature-tunable terahertz metamaterial device based on VO2 phase transition principle

Terahertz devices play an irreplaceable role in the development of terahertz technology. However, at present, it is difficult for most natural materials to respond in the terahertz band, making the devices made of them perform poorly. In order to realize the diversity and tunability of device functions, we designed a terahertz metamaterial device composed of the thermally-induced phase change material VO2. The device structure is composed of a Au bottom layer, a SiO2 dielectric layer and a VO2 top layer. Through software simulation, we found that when T = 313 K, the device has complete reflection ability in the whole terahertz band. When T = 342 K, the average absorptivity is above 95% in the ultra-wide band range of 4.71-9.41 THz, and the absorptivity reaches an amazing 0.99999 at 6.31 THz. Thus, the maximum thermal modulation range of the device is 0.001-0.99999. The Bruggeman effective medium theory clarifies the phase transition characteristics of vanadium dioxide. The Drude model establishes the functional relationship between the conductivity of vanadium dioxide and temperature. The basic principle of high absorption was described using the impedance matching theory. We also drew the electric field intensity diagram during the temperature rise of the device to further confirm the reason for the change in the device performance. In addition, the influence of the absence of different structural layers on the absorptivity was simulated, which reflected the role of each layer structure more intuitively. We also explored the influence of the geometric size of the device on the absorptivity, which provided a certain reference value for practical application. In short, we have designed a tunable terahertz device with simple structure, high absorptivity, and wide absorption bandwidth, which can be used in the fields of energy collection, electromagnetic stealth, and modulation.

An intelligent sensing platform for detecting and identifying biochemical substances based on terahertz spectra

This paper presents the development of an intelligent sensing platform dedicated to accurately identifying terahertz (THz) spectra obtained from various biochemical substances. The platform currently has two distinct identification modes, which focus on identifying five amino acids, namely phenylalanine, methionine, lysine, leucine, and threonine, and five carbohydrates, namely aspartame, fructose, glucose, lactose monohydrate, and sucrose based on their THz spectra. The first mode, called One-dimensional THz Spectrum Identification (OTSI), combines THz time-domain spectroscopy (THz-TDS) with the proposed mini convolutional neural network (MCNN) model. THz-TDS detects biochemical substances, while the MCNN model identifies the THz spectra. The MCNN model has a simple structure and only needs to deal with the THz absorption coefficients of biochemical substances, which are less computationally intensive and easily converged. The model can achieve 99.07 % accuracy in identifying one-dimensional THz spectra of the ten biochemical substances. The second mode, THz Spectrum Image-based Identification (TSII), applies the YOLO-v5 target detection model to THz spectral image recognition. The YOLO-v5 model uses THz absorption peaks as identification features and can identify biochemical substances based on only one or several THz absorption peaks. The overall identifying accuracy of the YOLO-v5 model for ten biochemical substances is 96.20 %. We also compared the MCNN and YOLO-v5 models with other deep learning and machine learning models, which demonstrate that they have better performance. This feature broadens the platform's utility in biomolecular analysis and paves the way for further research and development in detecting and analyzing diverse biological compounds.

Identification of heavy metal pollutants in wheat by THz spectroscopy and deep support vector machine

This paper proposes to detect heavy metal pollutants in wheat using terahertz spectroscopy and deep support vector machine (DSVM). Five heavy metal pollutants, arsenic, lead, mercury, chromium, and cadmium, were considered for detection in wheat samples. THz spectral data were pre-processed by wavelet denoising. DSVM was introduced to further enhance the accuracy of the SVM classification model. According to the relationship between the accuracy and the training time with the number of hidden layers ranging from 1 to 4, the model performs the best when the hidden layer network has three layers. Besides, using the back-propagation algorithm to optimize the entire DSVM network. Compared with Deep neural network (DNN) and SVM models, the comprehensive evaluation index of the proposed model optimized by DSVM has the highest accuracy of 91.3 %. It realized the exploration enhanced the classification accuracy of the heavy metal pollutants in wheat.

Overlapping speckle correlation algorithm for high-resolution imaging and tracking of objects in unknown scattering media

Optical imaging in scattering media is important to many fields but remains challenging. Recent methods have focused on imaging through thin scattering layers or thicker scattering media with prior knowledge of the sample, but this still limits practical applications. Here, we report an imaging method named 'speckle kinetography' that enables high-resolution imaging in unknown scattering media with thicknesses up to about 6 transport mean free paths. Speckle kinetography non-invasively records a series of incoherent speckle images accompanied by object motion and the inherently retained object information is extracted through an overlapping speckle correlation algorithm to construct the object's autocorrelation for imaging. Under single-colour light-emitting diode, white light, and fluorescence illumination, we experimentally demonstrate 1 μm resolution imaging and tracking of objects moving in scattering samples, while reducing the requirements for prior knowledge. We anticipate this method will enable imaging in currently inaccessible scenarios.

Hidden-information extraction from layered structures through terahertz imaging down to ultralow SNR

Noninvasive inspection of layered structures has remained a long-standing challenge for time-resolved imaging techniques, where both resolution and contrast are compromised by prominent signal attenuation, interlayer reflections, and dispersion. Our method based on terahertz (THz) time-domain spectroscopy overcomes these limitations by offering fine resolution and a broadband spectrum to efficiently extract hidden structural and content information from layered structures. We exploit local symmetrical characteristics of reflected THz pulses to determine the location of each layer, and apply a statistical process in the spatiotemporal domain to enhance the image contrast. Its superior performance is evidenced by the extraction of alphabetic characters in 26-layer subwavelength papers as well as layer reconstruction and debonding inspection in the conservation of Terra-Cotta Warriors. Our method enables accurate structure reconstruction and high-contrast imaging of layered structures at ultralow signal-to-noise ratio, which holds great potential for internal inspection of cultural artifacts, electronic components, coatings, and composites with dozens of submillimeter layers.

Scan-free time-of-flight-based three-dimensional imaging through a scattering layer

Reconstructing an object's three-dimensional shape behind a scattering layer with a single exposure is of great significance in real-life applications. However, due to the little information captured by a single exposure while strongly perturbed by the scattering layer and encoded by free-space propagation, existing methods cannot achieve scan-free three-dimensional reconstruction through the scattering layer in macroscopic scenarios using a short acquisition time of seconds. In this paper, we proposed a scan-free time-of-flight-based three-dimensional reconstruction method based on explicitly modeling and inverting the time-of-flight-based scattering light propagation in a non-confocal imaging system. The non-confocal time-of-flight-based scattering imaging model is developed to map the three-dimensional object shape information to the time-resolved measurements, by encoding the three-dimensional object shape into the free-space propagation result and then convolving with the scattering blur kernel derived from the diffusion equation. To solve the inverse problem, a three-dimensional shape reconstruction algorithm consisting of the deconvolution and diffractive wave propagation is developed to invert the effects caused by the scattering diffusion and the free-space propagation, which reshapes the temporal and spatial distribution of scattered signal photons and recovers the object shape information. Experiments on a real scattering imaging system are conducted to demonstrate the effectiveness of the proposed method. The single exposure used in the experiment only takes 3.5 s, which is more than 200 times faster than confocal scanning methods. Experimental results show that the proposed method outperforms existing methods in terms of three-dimensional reconstruction accuracy and imaging limit subjectively and objectively. Even though the signal photons captured by a single exposure are too highly scattered and attenuated to present any valid information in time gating, the proposed method can reconstruct three-dimensional objects located behind the scattering layer of 9.6 transport mean free paths (TMFPs), corresponding to the round-trip scattering length of 19.2 TMFPs.

Frequency-domain terahertz spectroscopy using long-carrier-lifetime photoconductive antennas

We present a telecommunication-compatible frequency-domain terahertz spectroscopy system realized by novel photoconductive antennas without using short-carrier-lifetime photoconductors. Built on a high-mobility InGaAs photoactive layer, these photoconductive antennas are designed with plasmonics-enhanced contact electrodes to achieve highly confined optical generation near the metal/semiconductor surface, which offers ultrafast photocarrier transport and, hence, efficient continuous-wave terahertz operation including both generation and detection. Consequently, using two plasmonic photoconductive antennas as a terahertz source and a terahertz detector, we successfully demonstrate frequency-domain spectroscopy with a dynamic range more than 95 dB and an operation bandwidth of 2.5 THz. Moreover, this novel approach to terahertz antenna design opens up a wide range of new possibilities for many different semiconductors and optical excitation wavelengths to be utilized, therefore bypassing short-carrier-lifetime photoconductors with limited availability.

Stratigraphy of Fresco Paintings: A New Approach with Photoacoustic and SORS Imaging

Photoacoustic (PA) imaging is a novel, powerful diagnostic technique utilized in different research fields. In particular, during recent years it has found several applications in Cultural Heritage (CH) diagnostics. PA imaging can be realized in transmittance or epi-illumination (reflectance) modes, obtaining variable levels of contrast and spatial resolution. In this work, we confirmed the applicability of the PA technique as a powerful tool for the imaging of one of the most challenging artwork objects, namely fresco wall paints, to obtain precise stratigraphic profiles in different layered fresco samples. In this regard, we studied some multi-layered fragments of the vault of San Giuseppe Church in Cagliari (1870 AD) and some mock-ups realized specifically to test the potentiality of this technique. Due to complex structures of the frescoes, we used the Spatially Off-set Raman Spectroscopy (SORS) technique to provide complementary information. The experimental results were in agreement for both techniques, even for the three-layered complex structure, and were confirmed with Scanning Electron Microscopy (SEM) analysis of cross-sections. The combined use of these two techniques proved useful to investigate detailed hidden information on the fresco samples.

[Research Progress in the Application of Terahertz Spectroscopy and Imaging Technology in Stomatology]

Terahertz waves, the electromagnetic waves in the range of 0.1 to 10 THz, has the advantages of being damage-free, causing no ionizing radiation injury, and being capable of recognizing the fingerprint spectrum of molecular characteristics, thus holding encouraging prospects for wide applications in the field of biomedicine. Terahertz spectrum can be used to identify and characterize biological structures of different levels, from biomolecules such as proteins to cells and tissues, through the spectral signals and/or restored images of the samples. Herein, we summarized the current stomatogical application of and research progress in terahertz spectroscopy and imaging in dentistry, reported the latest research findings, strengths and limitations from three perspectives, tooth anatomical structure, the extent of caries progression, and oral soft tissue, and suggested possible directions for future exploration.

Deep learning for terahertz image denoising in nondestructive historical document analysis

Historical documents contain essential information about the past, including places, people, or events. Many of these valuable cultural artifacts cannot be further examined due to aging or external influences, as they are too fragile to be opened or turned over, so their rich contents remain hidden. Terahertz (THz) imaging is a nondestructive 3D imaging technique that can be used to reveal the hidden contents without damaging the documents. As noise or imaging artifacts are predominantly present in reconstructed images processed by standard THz reconstruction algorithms, this work intends to improve THz image quality with deep learning. To overcome the data scarcity problem in training a supervised deep learning model, an unsupervised deep learning network (CycleGAN) is first applied to generate paired noisy THz images from clean images (clean images are generated by a handwriting generator). With such synthetic noisy-to-clean paired images, a supervised deep learning model using Pix2pixGAN is trained, which is effective to enhance real noisy THz images. After Pix2pixGAN denoising, 99% characters written on one-side of the Xuan paper can be clearly recognized, while 61% characters written on one-side of the standard paper are sufficiently recognized. The average perceptual indices of Pix2pixGAN processed images are 16.83, which is very close to the average perceptual index 16.19 of clean handwriting images. Our work has important value for THz-imaging-based nondestructive historical document analysis.

Terahertz imaging for non-destructive porosity measurements of carbonate rocks

Within the petrochemical industry, accurate measurement of microporosity and its distribution within core samples, particularly those from carbonate reservoirs, has garnered intense interest because studies have suggested that following primary and secondary depletion, a majority of the residual and bypassed oil may reside in these porosities. Ideally, the microporosity and its distribution would be determined accurately, quickly, and efficiently. Imaging techniques are commonly used to characterize the porosity and pores but accurate microporosity characterization can be challenging due to resolution and scale limitations. To this end, this study describes the development and verification of a novel method to characterize microporosity in carbonate rocks using terahertz time-domain spectroscopy and exploiting the high signal absorption due to water at these high frequencies. This new method is able to measure microporosity and the results agree well with other bulk measurements and produce microporosity maps which is not possible with many bulk characterization or imaging methods. These microporosity maps show the spatial variation of micropores within a sample and offers insights into the heterogeneity of reservoir materials.

Dual-color terahertz spatial light modulator for single-pixel imaging

Spatial light modulators (SLM), capable of dynamically and spatially manipulating electromagnetic waves, have reshaped modern life in projection display and remote sensing. The progress of SLM will expedite next-generation communication and biomedical imaging in the terahertz (THz) range. However, most current THz SLMs are adapted from optical alternatives that still need improvement in terms of uniformity, speed, and bandwidth. Here, we designed, fabricated, and characterized an 8 × 8 THz SLM based on tunable liquid crystal metamaterial absorbers for THz single-pixel compressive imaging. We demonstrated dual-color compressive sensing (CS) imaging for dispersive objects utilizing the large frequency shift controlled by an external electric field. We developed auto-calibrated compressive sensing (ACS) algorithm to mitigate the impact of the spatially nonuniform THz incident beam and pixel modulation, which significantly improves the fidelity of reconstructed images. Furthermore, the complementary modulation at two absorption frequencies enables Hadamard masks with negative element values to be realized by frequency-switching, thereby halving the imaging time. The demonstrated imaging system paves a new route for THz single-pixel multispectral imaging with high reliability and low cost.

A boundary migration model for imaging within volumetric scattering media

Effectively imaging within volumetric scattering media is of great importance and challenging especially in macroscopic applications. Recent works have demonstrated the ability to image through scattering media or within the weak volumetric scattering media using spatial distribution or temporal characteristics of the scattered field. Here, we focus on imaging Lambertian objects embedded in highly scattering media, where signal photons are dramatically attenuated during propagation and highly coupled with background photons. We address these challenges by providing a time-to-space boundary migration model (BMM) of the scattered field to convert the scattered measurements in spectral form to the scene information in the temporal domain using all of the optical signals. The experiments are conducted under two typical scattering scenarios: 2D and 3D Lambertian objects embedded in the polyethylene foam and the fog, which demonstrate the effectiveness of the proposed algorithm. It outperforms related works including time gating in terms of reconstruction precision and scattering strength. Even though the proportion of signal photons is only 0.75%, Lambertian objects located at more than 25 transport mean free paths (TMFPs), corresponding to the round-trip scattering length of more than 50 TMFPs, can be reconstructed. Also, the proposed method provides low reconstruction complexity and millisecond-scale runtime, which significantly benefits its application.

Imaging in scattering media is challenging due to signal attenuation and strong coupling of scattered and signal photons. The authors present a boundary migration model of the scattered field, converting scattered measurements in spectral form to scene information in temporal domain, and image Lambertian objects in highly scattering media.

Translation-Invariant Zero-Phase Wavelet Methods for Feature Extraction in Terahertz Time-Domain Spectroscopy

Wavelet transform is an important tool in the computational signal processing of terahertz time-domain spectroscopy (THz-TDS) measurements. Despite its prevalence, the effects of using different forms of wavelet transforms in THz-TDS studies have not been investigated. In this paper, we explore the implications of using the maximal overlap discrete wavelet transform (MODWT) versus the well-known discrete wavelet transform (DWT). We demonstrate that the spectroscopic features extracted using DWT can vary over different overlapping frequency ranges. On the contrary, MODWT is translation-invariant and results in identical features, regardless of the spectral range used for its implementation.We also demonstrate that the details coefficients obtained by the multiresolution analysis (MRA) using MODWT are associated with zero-phase filters. In contrast, DWT details coefficients suffer from misalignments originated from the down- and upsampling operations in DWT pyramid algorithm. Such misalignments have adverse effects when it is critical to retain the exact location of the absorption lines. We study the differences of DWT and MODWT both analytically and experimentally, using reflection THz-TDS measurements of α-lactose monohydrate. This manuscript can guide the researchers to select the right wavelet analysis tool for their specific application of the THz spectroscopy.

Ultralow-frequency ultranarrow-bandwidth coherent terahertz imaging for nondestructive testing of mortar material

Nondestructive testing of concrete materials is essential in civil engineering to maintain social infrastructure such as buildings or bridges. In this study, we constructed an ultralow-frequency, ultranarrow-bandwidth, coherent terahertz (THz) imaging system based on THz time-domain spectroscopy (THz-TDS). Based on its ultralow-frequency-localized THz wave and coherent detection, the present system achieved a wide dynamic range of THz power over 100 dB at 0.046 THz, which is appropriate to measure the mortar material. The achieved dynamic range of the THz power was 59 dB larger than that of a commercialized THz-TDS system and 49 dB larger than that of an ultralow-frequency noncoherent THz imaging system equipped with a high-power electric THz source. Ultimately, the proposed system could visualize the inner structure of a mortar sample with a thickness of 10 mm, and the present system can investigate a mortar sample with a thickness of over 130 mm. The proposed method is an attractive tool for non-destructive testing of thick concrete structures characterized by non-invasiveness and non-contact remoteness.

Computational adaptive optics for high-resolution non-line-of-sight imaging

Non-line-of-sight (NLOS) imaging has aroused great interest during the past few years, by providing a unique solution for the observation of hidden objects behind obstructions or scattering media. As such, NLOS imaging may facilitate broad applications in autonomous driving, remote sensing, and medical diagnosis. However, existing NLOS frameworks suffer from severe degradation of resolution and signal-to-noise ratio (SNR) due to aberrations induced by scattering media and system misalignment, restricting its practical applications. This paper proposes a computational adaptive optics (CAO) method for NLOS imaging to correct optical aberrations in post-processing without the requirement of any hardware modifications. We demonstrate the effectiveness of CAO with a confocal NLOS imaging system in Terahertz (THz) band by imaging different samples behind occlusions for both low- and high-order aberrations. With appropriate metrics used for iterative CAO in post-processing, both the resolution and SNR can be increased by several times without reducing the data acquisition speed.

Revealing Underdrawings in Wall Paintings of Complex Stratigraphy with a Novel Reflectance Photoacoustic Imaging Prototype

Revealing precious hidden features by a completely non-invasive approach is one of the crucial issues in the Heritage Science field. In this regard, concealed fresco paintings still represent an analytical challenge. This paper addresses the specific issue in wall painting diagnostics by the photoacoustic (PA) imaging technique, already proven to be efficient in revealing underdrawings and internal stratigraphy in movable paintings on paper and canvas. A newly set-up reflection PA prototype was applied here for the first time to probe the charcoal, graphite and sinopia hidden sketch drawings in concealed (gypsum, limewash, overpainted) wall paintings. The results presented here push forward the frontiers of the PA imaging technique and point to its potential effectiveness of revealing hidden underdrawings in historical wall paintings with complex stratigraphy.

Diffuse terahertz spectroscopy in turbid media using a wavelet-based bimodality spectral analysis

Current terahertz (THz) spectroscopy techniques only use the coherent light beam for spectral imaging. In the presence of electromagnetic scattering, however, the scattering-mitigated incoherent beams allow for flexible emitter-detector geometries, which enable applications such as seeing through turbid media. Despite this potential, THz spectroscopy using diffuse waves has not been demonstrated. The main obstacles are the very poor signal to noise ratios of the diffused fields and the resonance-like spectral artifacts due to multiple Mie scattering events that obscure the material absorption signatures. In this work, we demonstrate diffuse THz spectroscopy of a heterogeneous sample through turbid media using a novel technique based on the wavelet multiresolution analysis and the bimodality coefficient spectrum, which we define here for the first time using the skewness and kurtosis of the spectral images. The proposed method yields broadband and simultaneous material characterization at detection angles as high as 90° with respect to the incident beam. We determined the accuracy of the wavelet-based diffuse spectroscopy at oblique detection angles, by evaluating the area under the receiver operating characteristic curves, to be higher than 95%. This technique is agnostic to any a priori information on the spectral signatures of the sample materials or the characteristics of the scattering medium, and can be expanded for other broadband spectroscopic modalities.

Terahertz photoconductive antenna based on antireflection dielectric metasurfaces with embedded plasmonic nanodisks

By taking advantage of dielectric metasurfaces and plasmonic nanostructures, a terahertz photoconductive antenna (THz-PCA) is proposed and investigated in detail. The designed dielectric metasurfaces can reduce the optical reflection down to 1.4% and accelerate the switching process (electric conductive to resistive) that broadens the THz spectrum emitted from THz-PCA. Simultaneously, the embedded plasmonic nanostructures can realize 11.2 times enhancement in local electric field without affecting the switching process and the damage threshold of the THz-PCA. Simulated results indicate that the proposed THz-PCA is 70.56 times stronger in THz radiation power than that of the traditional THz-PCA. The significant enhancement ensures the proposed THz-PCA has great prospects in promoting THz technology based on the THz-PCA.

Revealing Hidden Features in Multilayered Artworks by Means of an Epi-Illumination Photoacoustic Imaging System

Photoacoustic imaging is a novel, rapidly expanding technique, which has recently found several applications in artwork diagnostics, including the uncovering of hidden layers in paintings and multilayered documents, as well as the thickness measurement of optically turbid paint layers with high accuracy. However, thus far, all the presented photoacoustic-based imaging technologies dedicated to such measurements have been strictly limited to thin objects due to the detection of signals in transmission geometry. Unavoidably, this issue restricts seriously the applicability of the imaging method, hindering investigations over a wide range of cultural heritage objects with diverse geometrical and structural features. Here, we present an epi-illumination photoacoustic apparatus for diagnosis in heritage science, which integrates laser excitation and respective signal detection on one side, aiming to provide universal information in objects of arbitrary thickness and shape. To evaluate the capabilities of the developed system, we imaged thickly painted mock-ups, in an attempt to reveal hidden graphite layers covered by various optically turbid paints, and compared the measurements with standard near-infrared (NIR) imaging. The obtained results prove that photoacoustic signals reveal underlying sketches with up to 8 times improved contrast, thus paving the way for more relevant applications in the field.

Terahertz time-domain derivative spectrometer using a large-aperture piezoelectric micromachined device

The engineering of optomechanical systems has exploded over the past decades, with many geometries and applications arising from the coupling of light with mechanical motion. The modulation of electromagnetic radiation in the terahertz (THz) frequency range through optomechanical systems is no exception to this research effort. However, some fundamental modulation capabilities for THz communications and/or high-speed data processing applications are yet to be established. Here, we demonstrate a THz time-domain derivative spectrometer based on a piezoelectric micromachined (PM) device. Insertion of the PM device into the THz beam path provides reference modulation for the lock-in detection unit, which in turn provides access to the nth-order derivative information of the incoming THz signal. Strikingly, the integration of the recorded derived signal leads to a recovered reference signal with an equivalent or even better signal-to-noise ratio, opening the door to a new type of highly sensitive THz measurements in the time domain.

Spatial Domain Terahertz Image Reconstruction Based on Dual Sparsity Constraints

Terahertz time domain spectroscopy imaging systems suffer from the problems of long image acquisition time and massive data processing. Reducing the sampling rate will lead to the degradation of the imaging reconstruction quality. To solve this issue, a novel terahertz imaging model, named the dual sparsity constraints terahertz image reconstruction model (DSC-THz), is proposed in this paper. DSC-THz fuses the sparsity constraints of the terahertz image in wavelet and gradient domains into the terahertz image reconstruction model. Differing from the conventional wavelet transform, we introduce a non-linear exponentiation transform into the shift invariant wavelet coefficients, which can amplify the significant coefficients and suppress the small ones. Simultaneously, the sparsity of the terahertz image in gradient domain is used to enhance the sparsity of the image, which has the advantage of edge preserving property. The split Bregman iteration scheme is utilized to tackle the optimization problem. By using the idea of separation of variables, the optimization problem is decomposed into subproblems to solve. Compared with the conventional single sparsity constraint terahertz image reconstruction model, the experiments verified that the proposed approach can achieve higher terahertz image reconstruction quality at low sampling rates.

Optimal allocation of quantized human eye depth perception for multi-focal 3D display design

Creating immersive 3D stereoscopic, autostereoscopic, and lightfield experiences are becoming the center point of optical design of future head mounted displays and lightfield displays. However, despite the advancement in 3D and light field displays, there is no consensus on what are the necessary quantized depth levels for such emerging displays at stereoscopic or monocular modalities. Here we start from psychophysical theories and work toward defining and prioritizing quantized levels of depth that would saturate the human depth perception. We propose a general optimization framework, which locates the depth levels in a globally optimal way for band limited displays. While the original problem is computationally intractable, we manage to find a tractable reformulation as maximally covering a region of interest with a selection of hypographs corresponding to the monocular depth of field profiles. The results indicate that on average 1731 stereoscopic and 7 monocular depth levels (distributed optimally from 25 cm to infinity) would saturate the visual depth perception. Such that adding further depth levels adds negligible improvement. Also the first 3 depth levels should be allocated at (148), then (83, 170), then (53, 90, 170) distances respectively from the face plane to minimize the monocular error in the entire population. The study further discusses the 3D spatial profile of the quantized stereoscopic and monocular depth levels. The study provides fundamental guidelines for designing optimal near eye displays, light-field monitors, and 3D screens.

Complex-Valued Pix2pix—Deep Neural Network for Nonlinear Electromagnetic Inverse Scattering

Nonlinear electromagnetic inverse scattering is an imaging technique with quantitative reconstruction and high resolution. Compared with conventional tomography, it takes into account the more realistic interaction between the internal structure of the scene and the electromagnetic waves. However, there are still open issues and challenges due to its inherent strong non-linearity, ill-posedness and computational cost. To overcome these shortcomings, we apply an image translation network, named as Complex-Valued Pix2pix, on the inverse scattering problem of electromagnetic field. Complex-Valued Pix2pix includes two parts of Generator and Discriminator. The Generator employs a multi-layer complex valued convolutional neural network, while the Discriminator computes the maximum likelihoods between the original value and the reconstructed value from the aspects of the two parts of the complex: real part and imaginary part, respectively. The results show that the Complex-Valued Pix2pix can learn the mapping from the initial contrast to the real contrast in microwave imaging models. Moreover, due to the introduction of discriminator, Complex-Valued Pix2pix can capture more features of nonlinearity than traditional Convolutional Neural Network (CNN) by confrontation training. Therefore, without considering the time cost of training, Complex-Valued Pix2pix may be a more effective way to solve inverse scattering problems than other deep learning methods. The main improvement of this work lies in the realization of a Generative Adversarial Network (GAN) in the electromagnetic inverse scattering problem, adding a discriminator to the traditional Convolutional Neural Network (CNN) method to optimize network training. It has the prospect of outperforming conventional methods in terms of both the image quality and computational efficiency.

Terahertz detection by upconversion to the near-infrared using picosecond pulses

The detection of terahertz photons by using silicon-based devices enabled by visible photons is one of the fundamental ideas of quantum optics. Here, we present a classical detection principle using optical upconversion of terahertz photons to the near-infrared spectral range in the picosecond pulse regime, which finally enables the detection with a conventional sCMOS camera. By superimposing terahertz and optical pump pulses in a periodically poled lithium-niobate crystal, terahertz photons at 0.87 THz are converted to optical photons with wavelengths close to the central pump wavelength of 776 nm. A tunable delay between the pulses helps overlap the pulses and enables time-of-flight measurements. Using a sCMOS camera, we achieve a dynamic range of 47.8 dB with a signal to noise ratio of 23.5 dB at a measurement time of one second, in our current setup.

Three-dimensional imaging through scattering media based on confocal diffuse tomography

Optical imaging techniques, such as light detection and ranging (LiDAR), are essential tools in remote sensing, robotic vision, and autonomous driving. However, the presence of scattering places fundamental limits on our ability to image through fog, rain, dust, or the atmosphere. Conventional approaches for imaging through scattering media operate at microscopic scales or require a priori knowledge of the target location for 3D imaging. We introduce a technique that co-designs single-photon avalanche diodes, ultra-fast pulsed lasers, and a new inverse method to capture 3D shape through scattering media. We demonstrate acquisition of shape and position for objects hidden behind a thick diffuser (≈6 transport mean free paths) at macroscopic scales. Our technique, confocal diffuse tomography, may be of considerable value to the aforementioned applications.

Confocal terahertz SAR imaging of hidden objects through rough-surface scattering

Terahertz (THz) radar imaging has gained great interests in various applications due to its capability of deep penetration in some specific contents such as plastic and non-conductive materials without water. However, the image quality would be highly degraded by the scattering of the rough surfaces, which remains a challenge in the area. Here, we propose a confocal terahertz synthetic aperture radar (SAR) to alleviate the scattering issues with both improved signal-to-noise ratio (SNR) and resolution. Inspired by the confocal non-line-of-sight imaging in visible wavelength, a convex lens is added into the conventional SAR system to localize the effect of scattering within each spatial sampling point by the confocal configuration. Then, the random phase aberration caused by scattering could be corrected through a simple shift in temporal domain. The performance of the proposed method under different roughness occlusions is evaluated through experiments. All the results demonstrate great enhancements in both resolution and SNR over the conventional methods.

Multi-layered full-field phase imaging using continuous-wave terahertz ptychography

Due to the unique properties of terahertz (THz) waves, THz phase imaging has been widely investigated to retrieve the absorption and phase modulation of dielectric two-dimensional thin samples, as well as multiple stacked samples. In this Letter, we apply the three-dimensional ptychographic iterative engine algorithm for continuous-wave THz full-field multi-layered phase imaging. The complex-valued transmission function of two-layered polypropylene thin plates and the corresponding probe function are reconstructed, respectively, which are immune to crosstalk of different layers. The phenomenon of the field-of-view enlargement at the second object layer is observed. This lensless compact imaging method can be potentially used for THz three-dimensional imaging.

Plasmonics-enhanced photoconductive terahertz detector pumped by Ytterbium-doped fiber laser

We present a photoconductive terahertz detector operating at the 1 µm wavelength range at which high-power and compact Ytterbium-doped femtosecond fiber lasers are available. The detector utilizes an array of plasmonic nanoantennas to provide sub-picosecond transit time for the majority of photo-generated carriers to enable high-sensitivity terahertz detection without using a short-carrier-lifetime substrate. By using a high-mobility semiconductor substrate and preventing photocarrier recombination, the presented detector offers significantly higher sensitivity levels compared with previously demonstrated broadband photoconductive terahertz detectors operating at the 1 µm wavelength range. We demonstrate pulsed terahertz detection over a 4 THz bandwidth with a record-high signal-to-noise ratio of 95 dB at an average terahertz radiation power of 6.8 µW, when using an optical pump power of 30 mW.

THz coherent lensless imaging

Imaging with THz radiation has proved an important tool for both fundamental science and industrial use. Here we review a class of THz imaging implementations, named coherent lensless imaging, that reconstruct the coherent response of arbitrary samples with a minimized experimental setup based only on a coherent source and a camera. After discussing the appropriate sources and detectors to perform them, we detail the fundamental principles and implementations of THz digital holography and phase retrieval. These techniques owe a lot to imaging with different wavelengths, yet innovative concepts are also being developed in the THz range and are ready to be applied in other spectral ranges. This makes our review useful for both the THz and imaging communities, and we hope it will foster their interaction.

Terahertz continuous wave system using phase shift interferometry for measuring the thickness of sub-100-μm-thick samples without frequency sweep

A terahertz continuous wave system is demonstrated for thickness measurement using Gouy phase shift interferometry without frequency sweep. One arm of the interferometer utilizes a collimated wave as a reference, and the other arm applies a focused beam for sample investigation. When the optical path difference (OPD) of the arms is zero, a destructive interference pattern is produced. Interference signal intensity changes induced by the OPD changes can be easily predicted by calculations. By minimizing the difference between the measured and the calculated signal against the OPD, the thicknesses of sub-100-μm-thick samples are determined at 625 GHz.

Machine-learning reprogrammable metasurface imager

Conventional microwave imagers usually require either time-consuming data acquisition, or complicated reconstruction algorithms for data post-processing, making them largely ineffective for complex in-situ sensing and monitoring. Here, we experimentally report a real-time digital-metasurface imager that can be trained in-situ to generate the radiation patterns required by machine-learning optimized measurement modes. This imager is electronically reprogrammed in real time to access the optimized solution for an entire data set, realizing storage and transfer of full-resolution raw data in dynamically varying scenes. High-accuracy image coding and recognition are demonstrated in situ for various image sets, including hand-written digits and through-wall body gestures, using a single physical hardware imager, reprogrammed in real time. Our electronically controlled metasurface imager opens new venues for intelligent surveillance, fast data acquisition and processing, imaging at various frequencies, and beyond.

Conventional imagers require time-consuming data acquisition, or complicated reconstruction algorithms for data post-processing. Here, the authors demonstrate a real-time digital-metasurface imager that can be trained in-situ to show high accuracy image coding and recognition for various image sets.

Application of a robotic THz imaging system for sub-surface analysis of ancient human remains

We used a robotic-based THz imaging system to investigate the sub-surface structure of an artificially mummified ancient Egyptian human left hand. The results obtained are compared to the results of a conventional CT and a micro-CT scan. Using such a robotic THz system promises new insights into the sub-surface structure of human remains. The depth resolution of the THz images exceeds the resolution of a conventional CT scan and is comparable with a micro-CT scan. The advantage of THz measurements over micro-CT scans is the fact that even comparatively large samples, like complete bodies, can be scanned. These would not fit into a conventional micro-CT scanner.

Virtual cleaning and unwrapping of non-invasively digitized soiled bamboo scrolls

In ancient China, symbols and drawings captured on bamboo and wooden slips were used as main communication media. Those documents are very precious for cultural heritage and research, but due to aging processes, the discovered pieces are sometimes in a poor condition and contaminated by soil. Manual cleaning of excavated slips is a demanding and time-consuming task in which writings can be accidentally deleted. To counter this, we propose a novel approach based on conventional 3-D X-ray computed tomography to digitize such historical documents without before manual cleaning. By applying a virtual cleaning and unwrapping algorithm, the entire scroll surface is remapped into 2-D such that the hidden content becomes readable. We show that the technique also works for heavily soiled scrolls, enabling an investigation of the content by the naked eye without the need for manual labor. This digitization also allows for recovery of potentially erased writings and reconstruction of the original spatial information.

Nanostructure-Enhanced Photoconductive Terahertz Emission and Detection

Photoconductive antennas are commonly used for terahertz wave generation and detection. However, their relatively low radiation power and detection sensitivity often place limitations on the signal-to-noise ratio and operation bandwidth of terahertz imaging and spectroscopy systems. Several different techniques are attempted to address these limitations. The most promising ones take advantage of the unique tools provided by nanotechnology. In this review, the recent nanotechnology-enabled advances in photoconductive antennas, which use nanostructures, such as optical nanoantennas, plasmonic structures, and optical nanocavities, to increase the interaction of the optical pump beam with the photoconductive semiconductor, are discussed. All of these techniques are experimentally demonstrated to be efficient tools for enhancing the performance of photoconductive antennas for terahertz wave generation and detection.

Browsing through sealed historical manuscripts by using 3-D computed tomography with low-brilliance X-ray sources

Severely damaged historical documents are extremely fragile. In many cases, their secrets remain concealed beneath their cover. Recently, non-invasive digitization approaches based on 3-D scanning have demonstrated the ability to recover single pages or letters without the need to open the manuscripts. This can even be achieved using conventional micro-CTs without the need for synchrotron hardware. However, not all manuscripts may be suited for such techniques due to their material and X-ray properties. In order to recommend which manuscripts and which inks are best suited for such a process, we investigate six inks that were commonly used in ancient times: malachite, three types of iron gall, Tyrian purple, and buckthorn. Image contrast is explored over the complete pipeline, from the X-ray CT scan and page extraction to the virtual flattening of the page image. We demonstrate, that all inks containing metallic particles are visible in the output, a decrease of the X-ray energy enhances the readability, and that the visibility highly depends on the X-ray attenuation of the ink’s metallic ingredients and their concentration. Based on these observations, we give recommendations on how to select the appropriate imaging parameters.

Virtual Recovery of Content from X-Ray Micro-Tomography Scans of Damaged Historic Scrolls

There is a large body of historical documents that are too fragile to be opened or unrolled, making their contents inaccessible. Recent improvements in X-ray scanning technology and computer vision techniques make it possible to perform a "virtual" unrolling of such documents. We describe a novel technique to process a stack of 3D X-ray images to identify the surface of parchment scrolls, unroll them, and create a visualization of their written contents. Unlike existing techniques, we can handle even challenging cases with minimal manual interaction. Our novel approach was deployed on two 15th and 16th century damaged historic scrolls from the manors of Bressingham and Diss Heywood. The former has become fused, probably due to exposure to moisture, and cannot be fully unrolled. The latter was severely burnt several hundred years ago, becoming thoroughly charred, heat-shrunken, and distorted, with all the sheets now brittle and fused together. Our virtual unrolling revealed text that has been hidden for centuries.

Extracting the Principal Shape Components via Convex Programming

We present a general method for extracting a region from an image (or 3D object) that can be expressed, or approximated, by taking unions and set differences from a collection of template shapes in a dictionary. We build on recent work that shows how this geometric problem can be recast in the language of linear algebra, with set operations on shapes translated into linear combinations of vectors, and solved using convex programming. This paper presents a set of sufficient conditions for which this convex program returns the "correct" shape. These conditions are robust in that they can account for the shapes that have indistinct boundaries, or model mismatch between the shapes in the dictionary and the target region in the image. We also present two different methods for solving the convex extraction program. The first method simply recasts the problem as a linear program, while the second uses the alternating direction method of multipliers with a series of easily computed proximal operators. We present a number of numerical experiments that use the framework to perform image segmentation, optical character recognition, and find multi-resolution geometrical descriptions of 3D objects.

Twenty years of terahertz imaging [Invited]

The birth of terahertz imaging approximately coincides with the birth of the journal Optics Express. The 20^th anniversary of the journal is therefore an opportune moment to consider the state of progress in the field of terahertz imaging. This article discusses some of the compelling reasons that one may wish to form images in the THz range, in order to provide a perspective of how far the field has come since the early demonstrations of the mid-1990's. It then focuses on a few of the more prominent frontiers of current research, highlighting their impacts on both fundamental science and applications.

New Possibilities of Substance Identification Based on THz Time Domain Spectroscopy Using a Cascade Mechanism of High Energy Level Excitation

Using an experiment with thin paper layers and computer simulation, we demonstrate the principal limitations of standard Time Domain Spectroscopy (TDS) based on using a broadband THz pulse for the detection and identification of a substance placed inside a disordered structure. We demonstrate the spectrum broadening of both transmitted and reflected pulses due to the cascade mechanism of the high energy level excitation considering, for example, a three-energy level medium. The pulse spectrum in the range of high frequencies remains undisturbed in the presence of a disordered structure. To avoid false absorption frequencies detection, we apply the spectral dynamics analysis method (SDA-method) together with certain integral correlation criteria (ICC).

Global mapping of stratigraphy of an old-master painting using sparsity-based terahertz reflectometry

The process by which art paintings are produced typically involves the successive applications of preparatory and paint layers to a canvas or other support; however, there is an absence of nondestructive modalities to provide a global mapping of the stratigraphy, information that is crucial for evaluation of its authenticity and attribution, for insights into historical or artist-specific techniques, as well as for conservation. We demonstrate sparsity-based terahertz reflectometry can be applied to extract a detailed 3D mapping of the layer structure of the 17th century easel painting Madonna in Preghiera by the workshop of Giovanni Battista Salvi da Sassoferrato, in which the structure of the canvas support, the ground, imprimatura, underpainting, pictorial, and varnish layers are identified quantitatively. In addition, a hitherto unidentified restoration of the varnish has been found. Our approach unlocks the full promise of terahertz reflectometry to provide a global and detailed account of an easel painting’s stratigraphy by exploiting the sparse deconvolution, without which terahertz reflectometry in the past has only provided a meager tool for the characterization of paintings with paint-layer thicknesses smaller than 50 μm. The proposed modality can also be employed across a broad range of applications in nondestructive testing and biomedical imaging.

Terahertz scattering and water absorption for porosimetry

We use terahertz transmission through limestone sedimentary rock samples to assess the macro and micro porosity. We exploit the notable water absorption in the terahertz spectrum to interact with the pores that are two orders of magnitude smaller (<1μm) than the terahertz wavelength. Terahertz water sensitivity provides us with the dehydration profile of the rock samples. The results show that there is a linear correlation between such a profile and the ratio of micro to macro porosity of the rock. Furthermore, this study estimates the absolute value of total porosity based on optical diffusion theory. We compare our results with that of mercury injection capillary pressure as a benchmark to confirm our analytic framework. The porosimetry method presented here sets a foundation for a new generation of less invasive porosimetry methods with higher penetration depth based on lower frequency (f<10THz) scattering and absorption. The technique has applications in geological studies and in other industries without the need for hazardous mercury or ionizing radiation.

Object classification through scattering media with deep learning on time resolved measurement

We demonstrate an imaging technique that allows identification and classification of objects hidden behind scattering media and is invariant to changes in calibration parameters within a training range. Traditional techniques to image through scattering solve an inverse problem and are limited by the need to tune a forward model with multiple calibration parameters (like camera field of view, illumination position etc.). Instead of tuning a forward model and directly inverting the optical scattering, we use a data driven approach and leverage convolutional neural networks (CNN) to learn a model that is invariant to calibration parameters variations within the training range and nearly invariant beyond that. This effectively allows robust imaging through scattering conditions that is not sensitive to calibration. The CNN is trained with a large synthetic dataset generated with a Monte Carlo (MC) model that contains random realizations of major calibration parameters. The method is evaluated with a time-resolved camera and multiple experimental results are provided including pose estimation of a mannequin hidden behind a paper sheet with 23 correct classifications out of 30 tests in three poses (76.6% accuracy on real-world measurements). This approach paves the way towards real-time practical non line of sight (NLOS) imaging applications.

Photoacoustic imaging reveals hidden underdrawings in paintings

A novel, non-invasive, imaging methodology, based on the photoacoustic effect, is introduced in the context of artwork diagnostics with emphasis on the uncovering of hidden features such as underdrawings or original sketch lines in paintings. Photoacoustic microscopy, a rapidly growing imaging method widely employed in biomedical research, exploits the ultrasonic acoustic waves, generated by light from a pulsed or intensity modulated source interacting with a medium, to map the spatial distribution of absorbing components. Having over three orders of magnitude higher transmission through strongly scattering media, compared to light in the visible and near infrared, the photoacoustic signal offers substantially improved detection sensitivity and achieves excellent optical absorption contrast at high spatial resolution. Photoacoustic images, collected from miniature oil paintings on canvas, illuminated with a nanosecond pulsed Nd:YAG laser at 1064 nm on their reverse side, reveal clearly the presence of pencil sketch lines coated over by several paint layers, exceeding 0.5 mm in thickness. By adjusting the detection bandwidth of the optically induced ultrasonic waves, photoacoustic imaging can be used for looking into a broad variety of artefacts having diverse optical properties and geometrical profiles, such as manuscripts, glass objects, plastic modern art or even stone sculpture.

Nonlinear optical detection of terahertz-wave radiation from resonant tunneling diodes

The sensitive detection of terahertz (THz)-wave radiation from compact sources at room temperature is crucial for real-world THz-wave applications. Here, we demonstrate the nonlinear optical detection of THz-wave radiation from continuous-wave (CW) resonant tunneling diodes (RTDs) at 0.58, 0.78, and 1.14 THz. The up-conversion process in a MgO:LiNbO₃ crystal under the noncollinear phase-matching condition offers efficient wavelength conversion from a THz wave to a near-infrared (NIR) wave that is detected using a commercial NIR photodetector. The minimum detection limit of CW THz-wave power is as low as 5 nW at 1.14 THz, corresponding to 2-aJ energy and 2.7 × 10³ photons within the time window of a 0.31-ns pump pulse. Our results show that the input frequency and power of RTD devices can be calibrated by measuring the output wavelength and energy of up-converted waves, respectively. This optical detection technique for compact electronic THz-wave sources will open up a new opportunity for the realization of real-world THz-wave applications.