THz Imaging Technology Trends and Wide Variety of Applications: a Detailed Survey

Abstract

Terahertz (THz) imaging is a non-invasive and high spatial-resolution technique that uses non-ionizing electromagnetic signals in a frequency range of 0.1–10 THz. Hence, this article focuses on diverse THz imaging techniques, THz antennas and designing methods, image reconstruction algorithms, and its applications. The antennas include planar patch, photoconductive, dielectric-resonator, substrate-integrated waveguide, wire, and wave guide. In this study, it is noted that antennas with high efficient conducting materials having a compact size, high gain, and high directional properties are required for THz imaging. The image reconstruction algorithms cover back-projection algorithm, range migration algorithm, phase-shift migration algorithm, single-band compressed sensing reconstruction and compressed sensing hyper spectral image reconstruction. High-resolution image reconstruction algorithms and challenges are also reported. From this study, it is noted that a multi–input–multi–output-based phase shift migration algorithm is used for THz imaging due to its high-accuracy and low computation time. It is also noted that the image quality can be enhanced by introducing an inverse fresnel diffraction algorithm into THz images retrieved by compressed sensing. Applications of THz imaging focus on cell detection (tissue-detection, cancer-detection, and bacteria-detection), concealed objects detection, food safety and quality inspection, and monitoring the water level of plant leaves.

Introduction

Terahertz frequency band 0.1–10 THz is commonly considered an essential tool for addressing the requirements of technologies and applications that demand high-speed transmission and high-resolution imaging. These technologies are quickly developing and have an extensive range of potential applications including remote sensing, biological detection, ultra-fast short-range wireless communications, and basic material research. One of THz radiation’s most prominent benefits is its capacity to penetrate a variety of materials including those that are opaque to visible and near-infrared light or produce only low-contrast X-ray images, such as plastics, wood and paper, textiles, and semiconductors. As demonstrated in Fig. 1, the use of shorter wavelengths in the THz range results in noticeably higher imaging resolution, which is useful in many applications. Applications of THz technology include diagnostic imaging, sensing, communications, industrial quality assurance systems, security inspection, military and biomedical health, and technical diagnostic systems. As part of its black-body radiation, everything greater than around 10 K emits THz radiation [1]. For an accurate description of the cold (10–20 K) dust found in the Milky Way galaxy’s interstellar medium, observations at these frequencies are essential. However, in far-off starburst galaxies, this thermal emission is incredibly weak. Gyrotrons, backward wave oscillators (BWO), far-infrared lasers (also known as “fir lasers”), quantum cascade lasers, free electron lasers (Fel), synchrotron light sources, photo mixing sources, and single-cycle sources, including photoconductive, surface field, photo-Dember, and optical rectification emitters, are possible sources of THz radiation. In order to create waves in the THz band at 542 GHz, a novel source was created that employed a resonant tunneling diode (RTD) in which the voltage dropped as the current increased [1, 2].

Fig. 1

THz applications

THz imaging technology has a wide range of potential applications but has not yet been put into practical use due to the high equipment costs and/or the requirement for highly qualified operators. This is because, unlike the visible domain where all current smart phones have megapixel imaging arrays, it is challenging to construct a THz pixelated-detector array since there are not enough suitable materials available. Due to their narrowband or cryogenic temperature requirements, the majority of multipixel THz-detector arrays now in use are narrowband [3, 4]. However, micro bolometer arrays hold considerable potential because they are capable of wideband detection at room temperature [5]. Micro bolometer arrays have actually been used with digital holography to create amplitude and phase images at a single THz frequency [6, 7]. Contrarily, to achieve the sub-picosecond temporal resolution provided by THz-spectrometers, spectral pictures would need to be taken several times at different frequencies, which is necessary to see ultra-fast dynamics. Even though the aforementioned problems can be avoided by mapping out a THz image [8] using electro-optic THz detection and an optical CCD array, this method necessitates a Ti: Sapphire laser with a low repetition rate regeneration amplifier, which makes the system a whole expensive, bulky, and rigid.

Over the past two decades, THz science and technology have undergone significant development. New THz sources may allow for extremely quick THz imaging systems. Numerous THz imaging and spectroscopy systems are built on the foundation of photoconductive antennas, which also have exciting potential in a wide range of scientific domains. A commercial fiber-coupled photoconductive antenna is used as the THz source in this real-time THz imaging technique and an uncooled microbolometer camera is used as the detection device. However, compact and small THz antenna sources with on-chip manufacturing and excellent directivity are needed for imaging applications in order to produce a deep depth of field for greater picture resolution. High Q-factor graphene-loaded aperture antennas are also able to detect breast cancer cells. Better imaging can be achieved by combining an antenna with a radio in a technique that can be thought of as a sensor. THz digital holography (TDH) is positioned to replace conventional terahertz imaging methods in a useful, perhaps revolutionary way by integrating the advantages of widely available sources. A full-field phase imaging technique is reflective THz digital holography (TDH). It can acquire the surface profile and depth information of the sample and the amplitude and phase information from the numerical reconstruction of a recorded digital hologram. It has been employed for imaging of the sample concealed behind the material, which is transparent to THz wave, in contrast to the transmission TDH. Reflection TDH can record holograms using two parallel recording planes to produce high-resolution images. The iterative phase restoration algorithm eliminates the innate “twin image” problem [9]; however, it requires recording many holograms. Off-axis Fresnel reflection TDH imaging can capture a single-frame hologram that reveals the object’s complex amplitude. Fresnel or angular spectrum propagation in the reconstruction procedure calls for precise reconstruction distance and numerous Fourier transforms. A phase retrieval technique using THz radiation as an alternative to THz digital holography is named as THz ptychography. It is a non-holographic coherent lensless imaging technique. In the THz band, ptychography has recently been proved to be capable of reconstructing the intricate value distributions of both the illumination probe and the object at the same time [10]. It has developed into a desirable and essential imaging technique because it does not need a reference beam and can photograph lengthy samples. Ptychography is often realized using a localized probe to scan the object and several overlapped diffraction patterns, which results in a limited imaging throughput. One technique for obtaining a complex-valued reconstruction of a sample from the measurement of its diffraction pattern is iterative phase retrieval. A phase retrieval approach called the ptychographical iterative engine (or PIE) uses a sequence of diffraction patterns that are recorded as a known illumination function and is translated into a set of overlapping positions with respect to a target sample.

This work focuses on three diverse aspects involved in THz imaging trends. It involves THz antennas and reconstruction algorithms along with mathematical equations and application aspects. The different antennas that are used at THz frequencies include horn antennas, travelling wave corner cube antennas, log periodic antennas, graphene antennas, dielectric resonator antennas, photoconductive antennas, lens antennas, and on-chip antennas. Reconstruction algorithms are also thoroughly discussed along with their methodologies. Terahertz spectroscopy applications in cell detection, concealed object detection in terahertz ranges, food safety and quality inspection, and agricultural applications are discussed in-detail. This kind of extensive research survey study is not reported in the literature, which makes this article as unique for the community.

This paper is broadly divided into 5 major sections. The “THz Antennas” section discusses various THz antenna trends used for THz imaging applications. The “Algorithms for THz Image Reconstruction” section describes state-of-art in numerous algorithms adopted for THz image reconstruction. The “Application Specifics of THz Imaging” section presents different applications of THz imaging in wide variety areas and the “Conclusion” section highlights as a summary of our review.

THz Antennas

As mentioned earlier, compact and small THz antenna sources with on-chip manufacturing and excellent directivity are needed for imaging applications. So, this section explains how to tackle the obstacles and opportunities that come with developing a THz-enabled antenna. The THz system’s antenna is a crucial component that requires extreme precision. Compact, high-directional, and high-gain antennas are preferred for high-resolution, low-latency, and high-data-rate THz systems especially in applications with constrained space. When creating the antenna for THz, there are a number of challenges that must be overcome, which calls for the creation of original solutions. THz links will be crucial for high-data-rate communication over short distances. The authors of the paper [11] presented the following antennas for usage in short-range wireless communication systems. (1) In short-range wireless communication systems, a simple rectangular microstrip antenna operating at THz frequencies is used. This microstrip antenna is extremely small, making it ideal for satellite communication. (2) In the sub-THz range, a single-element antenna with a dipole and reflector is utilized. This antenna offers a gain of 5.14 dBi and 38.6% impedance bandwidth between 294 and 410 GHz. (3) Two systems are illustrated that use the same dipole structure but add more directors to boost gain while preserving roughly the same bandwidth. Gains of 8.01 dBi and 9.6 dBi are obtained. (4) To produce a maximum gain of 13.6 dBi with an efficiency of roughly 89% and a planar compact construction commensurate with state-of-the-art literature, an array of 1 × 4 elements is used. The electromagnetic wave propagation phenomenon in the atmosphere is the fundamental hurdle in creating THz-long-distance wireless communication networks. Satellite-to-satellite communications are unaffected by the environment. Three main design ideas may be derived for contemporary THz antennas based on the evolution of THz antennas as shown in Fig. 2.

Fig. 2

THz antenna design ideas [12]

Now, this section discusses THz antenna categories as follows. The antennas covered are dipole antenna, microstrip antenna, horn antenna, travelling wave corner cube antenna, log periodic antenna, planar graphene antenna, dielectric resonator antenna, photoconductive antenna, lens antenna, and on-chip antenna.

Microstrip Antennas

The microstrip antenna is an important part of THz-based wireless communication systems. Security to wireless communications with data rates greater than 10 GB/sec is possible [13, 14] with carrier frequencies above 300 GHz. This can be accomplished if oscillators and amplifier sources have fractional bandwidth of around 10%. If sufficiently powerful, compact, and wideband sources are available, this capacity may be realized using fairly straightforward, inexpensive amplitude modulation techniques. Modern advancements in wearable smart gadgets and ultra-high-speed THz communication systems need the development of low-cost, low-profile, highly efficient antenna designs with high directionality. A photonic crystal-based planar antenna for THz applications with photonic bandgap (PBG)-based crystal polyimide substrate is presented in [15]. At resonance frequency 0.63 GHz, this antenna performs optimally in terms of gain (9.45 dB), directivity (9.99 dBi), and exceptionally satisfactory VSWR (< 2). The effects of changing the sizes of the PBG unit cells are also examined in order to achieve a − 10 dB bandwidth of 28.97 GHz (0.616 to 0.64 THz) [15] (Fig. 3).

Fig. 3

a–d PBG-based THz antenna types A–D. e Inner view of Type D antenna [15]

In [16], a microstrip antenna based on a substrate with a synthesized photonic bandgap (PBG) is created. Authors used a finite integral technique for binary particle swarm optimization (BPSO) that improves the performance of the antenna in terms of side lobe reduction, return loss, and fractional bandwidth. The first design, a dual-band antenna, has a 5.39% lower return loss than the initial antenna built on the air-hole PBG substrate, and the second design has a 128% greater fractional bandwidth (bandwidth of 128 GHz). The gain of both antennas is about 9.17 dB. Initially, Eqs. (1) and (2) are used to compute the width (W_p) and length (L_p) of the rectangular patch, where ɛ_reff is the effective dielectric constant, f_r is the required resonance frequency, c is the speed of light, and h is the antenna substrate thickness [17]. The obtained values are then optimized by modelling metals as perfect electrical conductors.

$${W}_{p}= \frac{c}{2{f}_{r}}\sqrt{\frac{2}{{\varepsilon }_{reff}+1}}$$

(1)

$${L}_{p }= \frac{c}{2{f}_{r}\sqrt{{\varepsilon }_{reff}}} - 2\Delta l$$

(2)

where

$$\Delta l=0.412h\frac{({\varepsilon }_{reff}+0.3)(\frac{{W}_{p}}{h}+0.264)}{{(\varepsilon }_{reff}-0.258)(\frac{{W}_{p}}{h}+0.8)}$$

(3)

Figures 4 and 5 show the antennas 1, 2, and 3 and the corresponding optimized filling patterns of unit cells. As compared to the original antenna design, both of these optimization solutions show a reduction in side-lobes. The antennas have a resonance frequency of about 0.65 THz, which is needed for current wireless communication technologies as well as a range of other intriguing applications. According to return loss statistics, using the PBG structure is a smart strategy for lowering surface waves, leading to appreciable improvements.

Fig. 4

PBG structures: a antenna 1, b antenna 2, c antenna 3 [16]

Fig. 5

Optimized unit cell filling pattern: a antenna 1, b antenna 2 [16]

Horn Antennas

THz antennas are available in a variety of designs, including THz horn antennas, bow-tie dipole, graphene-based antennas, pyramidal cavity with a dipole, dielectric lens planar antennas, photo conductive antennas, and angle reflector array THz antennas for generating THz source radiation. Based on the material used in production, there are three different types of THz antennas: dielectric, metallic, and novel material antennas. In a high-speed THz communication system, the horn antennas shown in Fig. 6 can be utilized as stand-alone antennas or as a feed source for a lens antenna or a transmitting antenna. Horn antennas have been used extensively in high gain THz antennas due to their straight-forward construction, excellent performance, low cross-polarization, and wide frequency spectrum.

Fig. 6

a–d THz horn antennas [18,19,20,21]

A horn antenna is a form of metallic antenna that operates in the THz frequency spectrum. With a gain of 20 to 30 dBi and a low cross-polarization level of − 30 dB, corrugated and dual-mode antennas offer the advantage of symmetric radiation patterns with a coupling efficiency of 97–98%. Due to the THz wave’s incredibly high frequency and the horn antenna’s relatively small size, processing the horn’s tip end can be difficult, especially when creating antenna arrays [22]. The CSIRO ICT Center [23] has offered conventional antennas for THz communication systems such as horns (Fig. 7), transmitters, and lenses, as well as recommendations for THz antenna requirements.

Fig. 7

a Horn antenna at 0.84THz and b horn antenna at 1.7THz [23]

Travelling Wave Corner Cube and Log-Periodic Antennas

The travelling wave corner cube antenna [24, 25] is a different metallic antenna that consists of a travelling wave antenna hung within a longitudinal cavity etched on a silicon wafer and incorporated into a 1.2-micron dielectric layer, as illustrated in Fig. 8. Because of its simplistic design and low manufacturing costs, it can be used in frequency bands above 0.6 THz. The side lobe and cross-polarization levels of the antenna are higher, owing to its open structure. As a result, the coupling efficiency (about 50%) of the antenna is relatively low.

Fig. 8

Travelling wave corner cube antenna a configuration and b side view [24]

Log periodic sinusoidal antennas, logarithmic periodic antennas, dual U-shaped antennas, and butterfly antennas, as shown in Fig. 9, are examples of narrowband and wideband edge-emitting antennas. They can be utilized with low-impedance detectors for THz dielectric antennas. A dielectric substrate and an antenna radiator make up dielectric antennas. When constructed properly, dielectric antennas can achieve impedance matching with the detector which makes the antenna easy to manufacture, integrate, and use. More complicated bent-wire antenna shapes can also be designed using a genetic algorithm [26]. However, as the frequency reaches the THz range, a surface wave effect is formed because the dielectric antennas are connected to the dielectric substrate as shown in Fig. 10. This fatal fault causes significant energy loss and a drop in antenna radiation efficiency during operation. The higher-order modes inside the substrate increase in proportion to the thickness of the substrate. As the number of higher-order modes grows, so does the coupling efficiency between the antenna and the substrate medium. Energy is lost as a result of this condition. For decreasing the surface wave effect, three optimization schemes are used: The first is to load the lens onto the antennas, which increases gain by utilizing the antenna bunching feature. The second is to create electromagnetic waves in higher-order modes by reducing the thickness of the substrate. Third, spatial filtering features of an electromagnetic band gap (EBG) can be employed to suppress high-order modes by substituting an EBG for the substrate dielectric material.

Fig. 9

Planar THz antennas [12]

Fig. 10

Diagram illustrating the surface wave effect of an antenna [12]

Planar Graphene Antennas

Planar graphene antennas, shown in Fig. 11, are gaining popularity as a technique for boosting bandwidth and producing small antennas. Graphene has outstanding dynamic continuous control qualities by altering the bias voltage and the products of surface plasmons. Surface plasmons are present at the junction of substrates with positive and negative dielectric constants [27, 28]. The plasmon dispersion relation on the metal’s surface is described by the Drude model. However, the metal cannot naturally link to and transform energy from electromagnetic waves in free space. To stimulate the surface plasmon wave, further materials are required. When a metal conductor conducts electricity perpendicular to the surface, the surface plasmon wave attenuates rapidly which results in a skin effect [29, 30]. Obviously, the antennas’ performance falls dramatically in the high-frequency range due to their small size and skin effect, rendering them unsuitable for THz antennas. Graphene, on the other hand, can absorb and regulate light in a wide variety of wavelengths. THz frequencies are the most prevalent for graphene’s in-band transition. Graphene has better surface plasmon material properties thanks to collective plasma oscillation. The surface plasma of graphene not only increases binding and decreases loss, but it also allows for continuous electrical adjustment [31, 32]. Graphene also has a complicated conductivity in the THz frequency band. As a result, the THz plasma mode is linked to sluggish wave propagation. These properties demonstrate that graphene can be used in the THz frequency band to replace metal materials.

Fig. 11

a Nano-patch graphene antenna element. b Directional graphene antenna array [27]

For THz applications, authors in [33] implemented an annular dielectric resonator antenna (DRA). A graphene disc is put into a silicon-based DR to achieve frequency response tunability. Figure 12 depicts an antenna configuration with a silicon dioxide substrate (ϵ_s = 3.8) put on top of the conducting ground plane. Using the formulas in Eq. (4) [34], the dimensions were tweaked in an effort to get the intended result.

Fig. 12

a Geometry of silicon DR-based tunable DRA. b S₁₁ parameter, c gain, and d radiation efficiency [33]

$${f}_{lmn}= \frac{6.324c}{4{r}_{0}\pi \sqrt{{\varepsilon }_{r}+2}} \left[0.27+0.36 \left(\frac{{r}_{0}}{h}\right)+0.002 {\left(\frac{{r}_{0}}{h}\right)}^{2}\right]$$

(4)

In Eq. (4), the parameters l, m and n are the integers, refer to the field variation in terms of half-wavelength along the azimuth, radius, and height of the DR [35]. Two structures are implemented and evaluated to better understand antenna operation. One is without a graphene disc on top of the silicon DR, and another one is with a graphene disc on top of the silicon DR. Figure 12 shows the resonance of DRA, without a graphene disc at the top, is 4.088 THz. The graphene disc is then placed on top of the antenna, resulting in a new resonance frequency of 4.104 THz. The change in material profile and medium properties at the junction of the silicon DR and graphene barrier can be explained by the shift in resonant frequency that occurs after the graphene disc is installed. The change in resonant frequency also demonstrates that adding a graphene ring merely increases the value of the impedance’s inductive and capacitive components, which may be implemented as a parallel tank circuit using circuit theory [36]. Over the operational pass band, the antenna has a gain and radiation efficiency of above 3 dBi and 72%, respectively as shown in Fig. 12c, d.

Photoconductive Antennas, Horn Antennas, Lens Antennas, and On-Chip Antennas

THz photoconductive antennas, THz horn antennas, THz lens antennas, THz microstrip antennas, and THz on-chip antennas are among the typical five THz antennas. Photoconductive antennas (PCAs) are used to create and detect the THz wave. Photoconductive antenna development and invention have a considerable impact on the THz communication system and related fields. The photoconductive material was exposed to the laser pulse directly in the antenna gap. When a laser beam is shined on a photoconductive semiconductor (such as GaAs, InP, or other comparable materials), an electron–hole pair is produced. The electron–hole pair accelerates the motion to produce photocurrent under the influence of the bias electric field, modifying the conductance between the electrodes. The resulting photoconductive current generates the THz signal if the laser signal is sufficiently brief, roughly 100 fs. The laser used to excite the carriers in the semiconductor is in the infrared frequency range. The PCA is depicted schematically in Fig. 13.

Fig. 13

PCA Schematic [37]

Photoconductive antennas (PCA) exist in a variety of forms, although dipole antennas and big aperture antennas are the most popular. The bow-tie PCA is a dipole antenna deformation among them, while the logarithmic-helical antenna is commonly used for large aperture antenna integration. Bow-tie photoconductive antennas offer a number of benefits, including construction simplicity, compactness, miniaturization, and low cost. Photoconductive antennas can benefit from advancements in size, substrate material, and geometry. Log-helical antennas are commonly employed in photoconductive emitters because of their constant radiation impedance and low reactance. The current operational frequency band is mostly in the THz range, with little study in the higher frequency range. Future studies should concentrate on the THz frequency band, implying that log-helix antennas still have a lot of work ahead of them. Figure 14 compares the aperture efficiency, radiation efficiency, and directivity of several bow-tie PCAs. The bow-tie antenna surpasses other types of antennas in terms of radiation efficiency and aperture efficiency, whereas the grid antenna array has the best directivity, as shown in Fig. 14. These models offer good radiation efficiency, directivity, and aperture efficiency, and can be used as a reference for THz antenna designs.

Fig. 14

Comparison among different types of bow-tie PCAs [12]

The lens’s focusing and imaging characteristics help the THz antennas function better by lowering side-lobe, cross-polarization levels, obtaining high gain, and strong directivity. Lenses come in two varieties: accelerating lenses and delaying antennas. They are categorized based on how much the electromagnetic wave path’s electrical length is reduced or enhanced [38]. The former is normally a metal plate lens in the E-plane with a phase velocity larger than the speed of light; the latter is representative with a phase velocity less than the speed of light. The lens’ focusing properties may also be utilized to lower side lobes and cross-polarization levels, which is a great design feature for THz antennas. The same can be used to improve the performance of antennas with low directionality and gain (such as horn and waveguide). At the time, both silicone and metal lenses are frequently utilized (Fig. 15). In the construction of integrated antennas, silicon lenses are widely employed. Metal lenses can be produced by hand. More research on the use of lenses in conjunction with innovative technologies or other types of THz antennas is needed. Future THz lens antennas are expected to be able to be miniaturized to satisfy low-cost, high-gain needs.

Fig. 15

a–f THz lens antennas [39,40,41,42,43,44]

When antennas are interfaced with integrated circuits (ICs), it is said to be on-chip implementation. This kind of arrangement removes parasitic effects and uncertainty generated by interconnections [45, 50, 51]. This implementation design has flexibility [50] without the need for an additional matching network. So that it saves time, space, and money. But on-chip antennas have a few drawbacks like large losses, unreliable patterns, and low gain [46, 52, 53]. As shown in Fig. 16, an on-chip antenna with a chip-integrated dielectric resonator (CIDR) is presented in [54]. The hybrid DR cavity modes resulted in the increase of the bandwidth as well as the gain. A bandwidth of 28.6% from 284 to 377 GHz is attained for gains greater than 5 dBi. At 295 GHz, the manufactured sample has a peak gain of 8.6 dBi and a maximum radiation efficiency of 44%. The antenna is a potential choice for fully integrated THz transceiver systems due to its wide bandwidth, high gain, and low profile. To the authors’ best knowledge, this is the largest fully integrated on-chip antenna (OCA) operating at THz frequencies.

Fig. 16

a On-chip DRA. b On-chip antenna with silicon CIDR. c 3D view. d Directivity, gain and |S₁₁| [54]

Table 1 provides the performance comparison of different THz antennas. Microstrip antennas are best suitable for short-range wireless communication systems. In photonic crystal-based design, photonic bandgap (PBG) structures are integrated into microstrip patch antennas to achieve better radiation properties. They can achieve a gain of up to 9.17 dB and a radiation efficiency of 91.08%. Moreover, PBG-based substrates can be used to overcome the limitation of surface waves in planar microstrip antennas. Horn antennas are suitable for high-speed THz communication systems. Adding a dielectric lens to horn antennas improves overall antenna gain of 20 to 30 dBi. The remarkable features of graphene have been used to develop tiny and reconfigurable resonant, leaky-wave, and reflect array antennas with unsurpassed THz radiation efficiency and functionality. To accomplish frequency response tunability, a graphene disc is placed in a silicon-based dielectric resonator (DR) and achieves a radiation efficiency of 72–75%. For THz imaging applications, high-directional antennas with high gain and compact size are preferred.

Table 1 Performance comparison of different THz antennas

Algorithms for THz Image Reconstruction

THz imaging has been used in a variety of sectors, including biological imaging, non-destructive security evaluation, and industrial process control [55]. THz imaging on the other hand has faced numerous challenges such as limited resolution and definition. The time domain spectroscopic (TDS) technique is the most commonly used THz imaging method. With this technique, the determination of the field amplitude, phase, and polarization can be done simultaneously. THz near-field technology with sub-wavelength aperture size detecting probes improves the spatial resolution beyond the diffraction limit. However, sometimes it may not be practical during human screening scenarios. Charge-coupled devices (CCDs) [56] and bolo meters [57] in the THz frequency band can be adapted to suit specific imaging applications. Furthermore, the approach of three-dimensional electromagnetic imaging is also feasible because the frequency range employed in the tests is in the millimeter wave region of the electromagnetic spectrum, which lies in the low THz frequency range. Electromagnetic imaging will be the inverse of electromagnetic field scattering [58] if initial and boundary conditions are correct. It is guided by the scalar Helmholtz equation. An analytical solution is difficult to acquire due to the nonlinear nature of this equation. Fortunately, for the vast majority of practical issues, numerical answers are sufficient. With the help of Born approximation [59, 60], scalar Helmholtz equations become linear and can be solved in traditional ways. The objective was to convert complex data into two-dimensional (2D) or three-dimensional (3D) images. The direct method is to use linearized Helmholtz equations to generate an equation from samples from each channel. This is always an ill-posed problem, which is why regulation of the inverse problem is crucial for this form of processing. The image reconstruction techniques used in THz imaging are divided into two categories based on analytical reconstruction and iterative reconstruction. By using analytical reconstruction techniques, the issue of creating a picture and predicting the distribution can be solved mathematically directly. Iterative reconstruction approaches require a more difficult mathematical solution with multiple stages to produce images. Iterative reconstruction has drawn criticism for its computational overhead, which is claimed to be up to eight minutes for every iteration.

Back Projection Algorithm (BPA) and Range Migration Algorithm (RMA)

Synthetic aperture radar (SAR) imaging and focal plane imaging are the two most frequent working mechanisms for THz imaging. For digital focusing in SAR imaging, the two prominent algorithms used are back projection algorithm (BPA) and range migration algorithm (RMA). They implement calculations in the spatial domain and spatial frequency domain respectively. Because of the short wavelengths at THz frequencies, objects can be seen with extremely fine features. THz imaging, on the other hand, is not as advanced as microwave imaging. The near-field scenario can make a difference in determining whether we should merely duplicate earlier accomplishments at microwave frequencies. These two algorithms perform the same job, but in two different domains. In the study [61], BPA and RMA are compared in THz near-field imaging. Figure 17 depicts the facilities as well as the objects of interest. Metal foil is used to make the two letters A and H, which are separated by 6.5 cm. For data acquisition, frequency sweeping.

Fig. 17

THz near-field SAR imaging. a Experimental setup, b block diagram [61]

The raw results of experiments which are obtained are not visible due to diffraction. The letters’ edges are a little blurry. Furthermore, there is a low contrast ratio between the background and the target. Two imaging methods are used to recreate the items in order to see the letters clearly. Figure 18 shows restored photos that are much clearer than those of the raw results, thanks to the use of BPA and RMA. Although both methods are capable of recovering the letters, RMA outperforms BPA. BPA has a greater depth of focus in comparison. Threshold processing and averaging techniques are used with matching results to help visualize the result more clearly. As a result, the targets contour is better defined, and the noise in the target-free area is effectively suppressed.

Fig. 18

2-D images a and b by bp and c and d by RMA [61]

BPA and RMA can be used to create 3D images with a fine-range resolution. To see the data more clearly, point cloud processing is performed. To remove background noise from outside the target, threshold processing is performed. The bandwidth of the transceiver determines the range resolution of a SAR imaging system. Figure 19a shows a 3D image created using BPA, while Fig. 19b shows a 3D image created with RMA. BPA and RMA can be utilized to create fine-range resolution 3D pictures.

Fig. 19

3-D image of target, a BPA b RMA [61]

Phase Migration Algorithm (PMA)

The phase-shift migration algorithm (PMA) was created to address the shortcomings of the previous two algorithms. In comparison to RMA and BPA, PMA has a number of advantages. As per the experiments, positioning precision relative to RMA is quite exact and the ability to work without knowing the distance in advance is extremely useful. In the case of PMA, distance between the objective scene center and scanning array need not be known when the frequency sampling interval matches the scope requirement of the objective. In both mono-static and multi-static scenarios, the principle of the phase-shift migration algorithm (PMA) is deduced. In monostatic PMA, assume the antenna is located at (x, y, z_L), and the target’s dispersion point is located at (x, y, z). The imaging task goal is to reconstruct the reflection coefficient of (x, y, z), which is written as p (x, y, z). The antenna positions form a planar array in this case and it is always considered to be parallel to one of the coordinate planes, whose third coordinate component is z_L. Based on the assumptions made above, the system response (S) can be described using Eq. (5) as discussed in [62].

$$S\left({x}^{^{\prime}},{y}^{^{\prime}},k\right)= {\iiint }_{x,y,z}p\left(x,y,z\right){e}^{-j2k\sqrt{{(x-{x}^{^{\prime}})}^{2}+{(y-{y}^{^{\prime}})}^{2}+{(z-{z}_{L})}^{2}}}dx \;dy \;dz$$

(5)

where k indicates the wavenumber of the signal used and X, Y, and Z span the domain to be imaged, which is represented by the dashed rectangular box in Fig. 20.

Fig. 20

Monostatic case in phase-shift migration algorithm (PMA) [63]

The entire method may be realized in the mono-static situation by following stages. To begin, the signals must be converted to the frequency domain. The echoes are frequently complex base band signals. Hilbert transformation needs to be used if only real signals are available. Then 2D-FT in both cross-range directions will be performed on Eq. (6). The system response must be calculated from Eq. (7) if the excitation source is not a Dirac delta function. The pulse compression along the range direction is realized by Eq. (8). ∆k is an irrelevant factor in the process that can be ignored. Finally, 2D-FT and 2D-IFT will be realized by FFT.

$$S\left({k}_{{x}^{^{\prime}}},{k}_{{y}^{^{\prime}}},k\right)= {\int }_{z}P\left({k}_{{x}^{^{\prime}}},{k}_{{y}^{^{\prime}}},z\right){e}^{-j{k}_{z}(z-{z}_{L})}dz$$

(6)

where ${\mathrm{S}}\left({\mathrm{k}}_{{\mathrm{x}}^{^{\prime}}},{ \, {\mathrm{k}}}_{{\mathrm{y}}^{^{\prime}}}, \, {\mathrm{k}}\right)$ is 2D Fourier transformation (2D-FT) of ${\mathrm{S}}\left({\mathrm{x}}^{^{\prime}}\,{ \, {\mathrm{y}}}^{^{\prime}}, \, {\mathrm{k}}\right)$ relative to the position variables x, y and ${\text{P}}\left({\text{k}}_{{\text{x}}^{^{\prime}}}\text{,}{ \, {\text{k}}}_{{\text{y}}^{^{\prime}}}\text{,} \, {\text{z}}\right)$ is the 2D-FT of ${\text{p}}\left(\text{x,} \, \text{y,} \, {\text{z}}\right)$ relative to x and y. k_z is the wave number defined by ${\text{k}}_{\text{z}}= \text{ } \sqrt{{4}{\text{k}}^{2}-{\text{k}}_{{\text{x}}^{^{\prime}}}^{2}-{\text{k}}_{{\text{y}}^{^{\prime}}}^{2}}$.

$$S\left({k}_{{x}^{^{\prime}}},{k}_{{y}^{^{\prime}}},k\right)= \frac{E({k}_{{x}^{^{\prime}}},{k}_{{y}^{^{\prime}}},k)}{o(k)}$$

(7)

wherein ${\mathrm{E}}\left({\mathrm{k}}_{{\mathrm{x}}^{^{\prime}}},{ \, {\mathrm{k}}}_{{\mathrm{y}}^{^{\prime}}}, \, {\mathrm{k}}\right)$ refers to the received signal at the location $({x}^{^{\prime}},{y}^{^{\prime}})$ in wavenumber domain, and $\text{o(k)}$ refers to the transmitted signal in the wavenumber domain.

$$P\left({k}_{{x}^{^{\prime}}},{k}_{{y}^{^{\prime}}},z\right)= \sum\nolimits_{{k}_{i}}S\left({k}_{{x}^{^{\prime}}},{k}_{{y}^{^{\prime}}},{k}_{i}\right) {e}^{j\sqrt{4{k}_{i}^{2}-{k}_{{x}^{^{\prime}}}^{2}-{k}_{{y}^{^{\prime}}}^{2}(z-{z}_{L})}}\Delta k$$

(8)

where k_i is the sample in the wavenumber domain, ∆k is the sample interval of wavenumber k. In [63], authors used two types of targets to reconstruct the images with PMA as illustrated in Fig. 21. The first is seven extremely small metal points that are positioned in a precise way to test the performance of positioning and focusing. The second is a metal fan with eight blades that examines the algorithm capacity to present things with complex shapes. Figure 21 shows the 3D pictures reconstructed, PMA is significantly faster than BPA while maintaining BPA’s high precision, resulting in a compromise between BPA and RMA.

Fig. 21

PMA simulation result in monostatic case: a targets: seven metal points and metal fan, b slice figures, c 3-D reflectivity figures [63]

When MIMO technology is employed, the related scenario is referred to as the multistatic case. Figure 22 schematically depicts the array geometry, which is known as a plus array [64], as well as the experiment setup.

Fig. 22

Multistatic case in phase-shift migration algorithm (PMA) [63]

The responsiveness of the system in the multistatic case can be described by

$$S\left({x}_{t},{y}_{t},{x}_{r,}{y}_{r},k\right)={\iiint }_{x,y,z}P\left(x,y,z\right){e}^{-jk\sqrt{{(x-{x}_{t})}^{2}+{(y-{y}_{t})}^{2}+{(z-{z}_{t})}^{2}}}{e}^{-jk\sqrt{{(x-{x}_{r})}^{2}+{(y-{y}_{r})}^{2}+{(z-{z}_{r})}^{2}}}dxdydz$$

(9)

The objective to be imaged is the reflection coefficient function P(x, y, z), and the system response is a 5D matrix. In both monostatic and multistatic scenarios, the principle of phase-shift migration algorithm (PMA) is derived. In the multistatic scenario, the sample criteria and spatial resolution evaluation are obtained. The application and performance of PMA are confirmed by electromagnetic field simulation and experimental results (Fig. 23). In comparison to RMA and BPA, the advantages and disadvantages of PMA are stated as follows: (1) high positioning precision compared to RMA, as demonstrated in simulations and experiments, (2) the ability to operate without having a priori knowledge of the distance, (3) requires more calculation than RMA but can be done in parallel, (4) Must be used in a situation of equal-interval sampling.

Fig. 23

PMA simulation result in multistatic case a slice figure, b 3D reflectivity figure [63]

Compressed Sensing (CS)

There was a shortage of room temperature high power sources that are required for THz imaging along with recording focal plane arrays. Compressed imaging with a single pixel camera can be used to solve this problem [65]. The idea behind compressed imaging was to reconstruct a picture using low-dimensional detection and then solve the ill-posed inversion using computational procedures. Figure 24 shows the compressed sensing (CS) method for achieving THz single-pixel imaging technology for improving measurement efficiency [66]. It recovers a high-quality THz image with a lesser number of measurements than the total number of image pixels. Furthermore, the use of photo-induced semiconductor carriers is critical for improving the CS technique’s practicability [67]. It enables quick sampling of the THz wavefront and allows for the measurement mask to be changed voluntarily. Compressed sensing will be able to extract both the amplitude and phase information of a THz field at a time. The measuring masks are usually placed close to the sample to reduce the diffraction impact [67, 68]. CS recovers THz temporal images and the Fourier transformation, and IFD techniques are used to rebuild a sharp THz spectrum image.

Fig. 24

Image reconstruction scheme using compressed sensing (CS) technique [66]

Metals in the shapes of “T,” “H,” and “Z” are selected as the samples as shown in Fig. 25a. From Fig. 25b, due to diffraction, the image quality of the reconstructed image of three letters at the peak position is very poor. By utilizing Eq. (10), the reconstructed images are obtained, as shown in Fig. 26d.

$$U\left({x}_{1},{y}_{1}\right)=-\frac{{e}^{-jkd}}{j\lambda d}{\iint }_{\infty }U\left({x}_{0},{y}_{0}\right)exp\left\{-j\frac{k}{2d}\left[{({x}_{0}-{x}_{1})}^{2}+ {({y}_{0}-{y}_{1})}^{2}\right]\right\}{dx}_{0}{dy}_{0}$$

(10)

where $\text{U(}{\text{x}}_{0}\text{,}{\text{y}}_{0}\text{)}$ is the THz spectral image contaminated by the diffraction, $\left({\text{x}}_{0}\text{,}{\text{y}}_{0}\right)\text{and (}{\text{x}}_{1}\text{,}{\text{y}}_{1}\text{)}$ are the spatial coordinates on the sampling ad reconstruction planes. $k$ is the wave number of the THz field in a vacuum and λ is the wavelength. By using Fourier transformation, it is clear to see how the THz field’s diffraction phenomenon is greatly lessened and the quality of the image is significantly improved.

Fig. 25

a Pictures of the metals in the shape of T, H, and Z, b temporal image, c spectral images, d reconstructed THz image [66]

Fig. 26

Observation model for reconstructing HR image [69]

Reconstructing High-Resolution (HR) Image

CT (computed tomography) is a type of imaging that creates tomographic (cross-sectional) pictures by combining numerous transmission measurements from various angles. The most common methods for probing the sample are X-ray and ultrasound. Existing THz CT techniques frequently depends on continuous wave (CW) source and detector technologies because of their high output power. However, major drawback of CW systems is its low operating frequency, which results in low diffraction restricted resolution below several hundred GHz. Continuous wave (CW) and pulsed sources use methods that were established for X-ray CT to reconstruct cross-sectional images. These are primarily based on the Radon imaging model [70], which does not account for physical factors such as scattering, diffraction, and refraction in electromagnetic wave propagation. Image reconstruction has been reported to be improved using broadly valid imaging models such as Snell’s law of refraction or Helmholtz’s equation. However, this comes at the expense of requiring prior knowledge of the sample shape and/or a large increase in processing effort. Two types of algorithms include reconstructing an HR THz image from multiframe low resolution (LR) images and from an LR-degraded THz image. In [69], authors examined various strategies for reconstructing high-resolution (HR) THz pictures. Figure 26 depicts the observation model of HR reconstruction.

The continuous scene is considered to be band-limited and is appropriately sampled at or above the Nyquist rate in order to rebuild an HR image from numerous LR images. The outcome is an HR image, represented by the letter x, that is free of distortion and noise. An LR image, indicated as y_k, is created by warping, blurring, down sampling, and adding noise to an HR image. M, B, D, and n, respectively, are the matrix operators that represent each process. Equation (11) expresses the observation model [71] that describes the link between the HR picture x and the kth LR image:

$${y}_{k}=D{B}_{k}{M}_{k}x+{n}_{k}$$

(11)

This is a simple observation model that ignores the combined effect of many spoiling processes. The final goal is to figure out how to merge fresh information from distinct LR images to rebuild an HR image. As a result, HR reconstruction from multiple LR images is an inverse problem of the observation model, i.e., finding the best solution for x from y_k, 1 ≤ k ≤ p. Figure 27 depicts the basic workflow for implementing HR reconstruction. Registration, interpolation, and deblurring [71,72,73] are the three processes that make up the entire process. To get the optimum effect, these three stages are usually iterated.

Fig. 27

Basic reconstruction flow [69]

The projection onto convex sets (POCS) algorithm is a method for determining the best solution that meets the constraints which can be expressed as a series of convex sets. But it has a poor convergence speed and low algorithm efficiency [74]. The mean square error (MSE) reduces as the number of iterations increases, but the blurring effect worsens. The HR image is estimated using the iterative back projection (IBP) method by back projecting the error (difference) between the calculated LR pictures via image blur and the observed LR images. The ideal solution to the HR image matrix $\text{x[}{\text{n}}_{1}\text{,}{\text{n}}_{2}\text{]}$ is obtained by repeating this method iteratively to reduce the energy of error. When the largest difference of the elements between ${\text{x}}^{\text{n+1}}\text{[}{\text{n}}_{1}\text{,}{\text{n}}_{2}\text{]}$ and ${\text{x}}^{\text{n}}\text{[}{\text{n}}_{1}\text{,}{\text{n}}_{2}\text{]}$ is smaller than a particular threshold, the iteration process can be stopped. The IBP iteration process can be expressed as

$${\widehat{x}}^{n+1}\left[{n}_{1},{n}_{2}\right]={\widehat{x}}^{n}\left[{n}_{1},{n}_{2}\right]+\sum\nolimits_{{m}_{1},{m}_{2}\epsilon {y}_{k}^{{m}_{1},{n}_{1}}}({\widehat{y}}_{k}\left[{m}_{1},{m}_{2}\right]-{\widehat{y}}_{k}^{n}\left[{m}_{1},{m}_{2}\right]) X {h}^{BP}[{m}_{1},{m}_{2}:{n}_{1},{n}_{2}]$$

(12)

where ${\widehat{\mathrm{y}}}_{\mathrm{k}}^{\mathrm{n}}{=}{\mathrm{W}}_{\mathrm{k}}{\widehat{\mathrm{x}}}^{\mathrm{n}}$ are the calculated LR images from the approximation of xⁿ after n iterations, ${\upgamma }_{\mathrm{k}}^{{\mathrm{m}}_{1},{\mathrm{n}}_{1}}$ represents the set $\{{\text{m}}_{1}\text{,}{ \, {\text{m}}}_{2}\upepsilon {\mathrm{y}}_{\mathrm{k}}\left|{\text{m}}_{1}\text{,}{ \, {\text{m}}}_{2} \mathrm{is} \text{influenced by }{\text{n}}_{1}\text{,} \, {\text{n}}_{2}\text{ where }{\text{n}}_{1}\text{,}{ \, {\text{n}}}_{2}\upepsilon {\mathrm{x}}^{\mathrm{n}}\right.\}$ and ${\text{h}}^{\text{BP}}$ is the back projection kernel that controls the contributions of error $\text{(}{\widehat{\text{y}}}_{\text{k}}\left[{\text{m}}_{1}\text{,}{ \, {\text{m}}}_{2}\right]-{\widehat{\text{y}}}_{\text{k}}^{\text{n}}\left[{\text{m}}_{1}\text{,}{ \, {\text{m}}}_{2}\right]\text{ to }{\widehat{\text{x}}}^{\text{n}}\text{[}{\text{n}}_{1}\text{,}{ \, {\text{n}}}_{2}\text{]}$. The matrix ${\text{W}}_{\text{k}}$ represents the blurring and deterioration effects that relate to the calculated HR image $\widehat{\text{x}}$ and LR images ${\widehat{\text{y}}}_{\text{k}}$. With only the averaging effect taken into consideration, the matrix ${\text{W}}_{\text{k}}$ is chosen to be the PSF, which contains only the averaging operator. The choice of the back projection kernel (${\text{h}}^{\text{BP}}$) affects the characteristics of the optimal solution. When a priori knowledge of image noise is unknown, the Lucy–Richardson (L-R) HR Algorithm performs well, and in many cases, the gray-level distribution can be approximated by a Poisson field [75]. When THz waves scan imaging targets, the THz energy on each pixel can be seen as the transient time-scale interaction of several THz photons with the imaging dot, and each pixel is independent. As a result, a Poisson field might be used to approximate the gray-level distribution of the THz image. The L-R iteration can be expressed as follows:

$${\widehat{f}}_{k+1}\left(x,y\right)= {\widehat{f}}_{k}(x,y)\left[h\left(-x,-y\right)* \frac{g(x,y)}{h\left(x,y\right)*{\widehat{f}}_{k}(x,y)}\right]$$

(13)

where $\widehat{\text{f}}$ is the estimated value of the degraded image, g is the degraded image, and h is the PSF. The horizontal direction is represented by the coordinate x, and the positive direction is right, whereas the vertical direction is represented by the coordinate y, and the positive way is upward. While restoring the edges, L-R algorithm will produce low-frequency noise. To suppress this noise, the number of iterations needs to be increased. The pixel weight control can preserve the texture and edges while enhancing the imaging target-background contrast. The wavelet decomposition reconstruction approach is another high-resolution (HR) THz picture reconstruction methodology. The first step is to interpolate the LR THz image. Then, using 2D wavelet decomposition, the interpolated LR THz image is processed. Select the first layer wavelet coefficients for reconstruction (bi-orthogonal wavelet bases are used here) and finally, obtain the HR image. The abovementioned HR reconstruction technique is schematically depicted in Fig. 28. In the HR rebuilt image, there is a clear improvement in resolution. To improve contrast, the false-color image is created using the grayscale as illustrated.

Fig. 28

Schematic flow of wavelet decomposition reconstruction approach [69]

Angular Spectrum Method

In order to recreate an image from a hologram, digital holography (DH) uses the angular spectrum approach as its core component. With this method, the hologram can be accessed and altered digitally in its spatial frequency domain. Any wave field can be divided into individual plane waves flowing in various directions. The angular spectrum approach [80] takes advantage of this property. These plane waves combine to form an intricate wave field, like a hologram. The complex wave field at any other location in space can be recovered by digitally propagating the individual plane waves after breakdown into their component parts.

Given that the objects are often larger than the millimeter-scale wavelengths and the interferometer is meter-sized, the majority of TDH occurs just within the Fresnel diffraction region specified by Equation.

$${N}_{F} = \frac{{\left(2a\right)}^{2}}{\lambda d}$$

(14)

where N_F is the dimensionless Fresnel number of an optical component, a is the aperture (or object) radius, d is the path length and λ is the wavelength. An advantage of the Fresnel approximation is the fact that only one Fourier transform is required. But, because the Fresnel reconstruction method does not allow for digital filtering as part of the reconstruction process, it cannot take advantage of one of the major attributes of digital holography (DH). Furthermore, the second Fourier transform required for the angular spectrum method is easy to perform on a computer.

Ptychographic Iterative Engine (PIE)

The fundamental method of ptychography involves scanning an item across an illumination function at overlapping places and gathering a collection of diffraction patterns, often known as ptychograms [81]. It achieved its breakthrough by combining the ptychographic idea with iterative phase retrieval techniques used in coherent diffraction imaging (CDI) [82, 83], giving rise to what is known as ptychographic iterative engines (PIE). A schematic of ptychography in the transmission is shown in Fig. 29.

Fig. 29

Transmission ptychography [81]

PIE analyzes the diffraction patterns that were captured from an object that was irradiated by a largely localized, movable wave field. Traditional iterative techniques struggle to handle complex (phase and modulus) or soft (bandwidth-limited) illuminating functions. Extended ptychographic iterative engines (ePIE) [84] were developed by permitting simultaneous reconstruction of the probe beam which provides significant advancements in PIE’s convergence and robustness. Thereafter, by modifying the update functions and appropriating the momentum concept from the machine learning community. Recently, it has been demonstrated that optimizers that use automatic differentiation (AD) [85] can also be used to recover the object when solving the phase problem in ptychography instead of PIE-related techniques. Axial multi-image phase retrieval is a coherent diffractive imaging method that reconstructs the entire object wave field using a variety of diffraction patterns based on axial movement diversity.

Table 2 discusses different THz image reconstruction algorithms and applications. The back projection algorithm (BPA) and range migration algorithm (RMA) are two popular methods in SAR imaging. Early imaging algorithms relied heavily on monostatic SAR. Later, as bistatic SAR systems became available, numerous monostatic-based methods were adapted and made an extension to bistatic SAR imaging. For imaging applications with complex bistatic data, a traditional back-projection algorithm (BPA) based on phase-compensated and coherent summations in the time/space domain is a typical technology, although it has a high computational cost. A modified range Doppler technique for bistatic SAR focusing was described based on a Taylor series expansion. The aforementioned strategies cannot be immediately applied to the MIMO imaging process since the MIMO system differs from the SAR system in terms of data gathering. However, it is important to note that the development of the MIMO imaging technique has considerably benefited from bistatic SAR. MIMO-based developed algorithms are best suitable for THz imaging in a complex environment. On the other hand, THz ptychography is the trending lensless imaging technique based on ptychography iterative engine (PIE) algorithms.

Table 2 THz image reconstruction algorithms and applications

Application Specifics of THz Imaging

THz radiation has several notable characteristics like its low energy and non-ionizing nature for non-destructive testing. Hence, it is applicable in a variety of disciplines including medical diagnostics, drug detection, security screening, and material property analysis. Foreign body detection, chemical residue detection, and moisture content are all possible with THz time-domain spectroscopy (TDS). As a result, it can be used to monitor and control food processing [86,87,88,89,90]. Trees and plants can have their leaf water dynamics measured using a TDS device [91]. THz spectroscopy has also been used to analyze several pesticide compounds [92,93,94,95]. In recent years, reflection mode THz pulsed spectroscopy (TPS) has shown potential in detecting cancerous tissue [96, 97], as shown in Fig. 30. This technique demonstrates clear separation of malignant and healthy tissues in all recently removed tissues and cell types.

Fig. 30

Cancer detection in excised breast tumor using THz imaging system [96]

THz Spectroscopy Applications in Cell Detection

Early diagnosis of any disease requires accurate and quick detection. Flow cytometry, fluorescent molecular tomography, and multiphoton microscopy are examples of cell detection approaches that rely heavily on labeling technology. They have excellent precision, sensitivity, and selectivity. However, these technologies unavoidably involve chemical or biological tagging. THz spectroscopy with high resolution is evolving into a reagent-free, label-free, non-invasive, and optical approach for the detection and identification of living cells, thanks to new instruments.

Tissue THz Spectroscopy

Because of the increased interest in developing THz technology, THz spectroscopy may now be used to identify and distinguish healthy, dehydrated, burned, and sick tissues. THz spectroscopy allows time-resolved analysis of these dynamic processes. It is the process of determining phase and amplitude data, which are related to tissue absorption coefficient and index of refraction. Because of these characteristics, THz spectroscopy has the ability to detect tissue. Fresh tissue, like skin tissues (− 70% by volume), contains a large amount of water, which exhibits significant absorption at THz frequencies (u_a = 300 cm⁻¹, at 1.5 THz). Other tissue preparation methods which include paraffin, frozen and formalin-fixed tissues have been developed to remove the effects of significant optical absorption of water. Cancer patients’ paraffin-embedded tissues appeared to have greater refractive index and absorption coefficients than healthy tissues recently. Additionally, snap-frozen tissues were regularly evaluated to limit the influence of water, and several studies demonstrated that Alzheimer’s patients’ tissues absorbed less water than normal tissues. In the same manner, because water’s significant optical absorption causes just a few millimeters of penetration in biological tissues, THz in vivo spectroscopy applications are currently limited to the surface of biological tissues. Meanwhile, the ability to absorb a lot of water is useful since it allows for a delicate form of soft-tissue contrast. Different skin tissues have significantly variable refractive indexes and absorption coefficients.

THz Spectroscopy of Cancer Cells

THz spectroscopy can recognize cancer cells based on signal properties, real-time observation of minute structural changes, and study of intracellular water dynamics. The complete procedure is quick, real-time, non-invasive, and label-free. It could result in the creation of an innovative clinical analysis tool. Three THz images are generated for each fresh tissue sample: a fresh image, an FFPE image, and a pathology image, as illustrated in Fig. 31. In [98], authors summarize the procedure. In core THz system imaging, tissues are positioned on polystyrene slides for transmission or polystyrene panes for reflection [99, 100]. THz measurements are carried out by scanning the sample and calculating the signal emitted or reflected at each place in relation to a reference. To correct for any phase shifts, it’s critical to normalize the observed signal with a well-chosen reference [99]. Then the THz image can be created by measuring each location’s temporal domain peak or single frequency magnitude [101], deconvolution of reference signal [102], integration of frequency domain spectral power [98, 102,103,104], or using statistical signal processing for cancer classification [102, 103].

Fig. 31

Human breast cancer tissue captured in THz images [96]

According to recent research developments with respect to the advancement of near-field imaging technologies, THz imaging resolution is improving [105]. Figure 32 displays frequency domain photographs of an infiltrating ductal carcinoma at 1 THz, showing reduced transmission and increased reflection in malignant areas compared to surrounding normal fibrous and fatty tissue parts. Many additional researches have made similar findings. The observed disparity was explained by the increased THz vibration absorption, reflection, or refractive index that was caused by the presence of more water in malignant areas.

Fig. 32

Pictures of infiltrating ductal carcinoma. a and b The pathology for samples 1 and 2, respectively, c and d are the transmitted-magnitude pictures, e and f are the photos of the magnitude of reflection [99]

Imaging devices must be small and simple to use in order to be used in fast cancer screening during surgery. A notable example of such a system is the handheld THz pulsed imaging (TPI) system, which is represented schematically in Fig. 33 [106]. The quartz tip scans a 15 × 2 mm area in this TPI device and measurements are gathered in 26 pixels. The accuracy of this technique in identifying malignant regions was 75%. However, this ex-vivo examination has the problem that the material must be divided into pieces of uniform thickness (usually on the scale of micrometers) in order for THz waves to pass through. The human body is made up of several different components, including a significant amount of water, which prevents THz waves from penetrating it deeply. Because of this, most studies use ex-vivo tissue imaging, while very few do so with in-vivo tissue imaging. A 2.52 THz continuous wave was used to obtain images of brain gliomas with a resolution of 200 µm [107, 108]. Currently, in vivo THz imaging research is in its infancy. Two key difficulties remain in human body research. The first one is, compared to mouse tissue; human tissue includes substantially more types of components, complicating spectral analysis. The second is that variations in tissue composition between individuals will affect THz wave absorption and refraction differently. These two problems make it difficult to accurately identify malignant regions. THz pictures of cancer tissue are now mostly created using variations in the water content of normal and malignant tissue.

Fig. 33

Handheld TPI probe system [106]

THz radiation has an ability to penetrate only a few hundred micrometers in human skin [109]. Several organizations have suggested freezing ways to increase the depth of THz radiation penetration into wet tissues since the absorption coefficient of ice is lower than that of liquid water [110, 111]. THz radiation can therefore travel farther into the tissue when the water molecules are frozen. They were able to discriminate between benign and malignant tissue slices using the freezing method, which is challenging to do in fresh situations. The same team was able to identify lymphatic metastases that were difficult to see in the fresh form by freezing the lymph node. Brain tissue samples afflicted by Alzheimer’s disease are characterized using a freezing process. Up to a few millimeters below the surface, visual imaging and MR imaging function poorly [109] and are unable to identify the precise boundary below the skin’s surface. The general clinical picture, as depicted in Fig. 34, does not adequately detect the cancer spread beneath the skin surface. The THz images reveal the depth of the cancer invasion into the skin which was 250 µm in this case [112]. The medical professional can remove only the malignant location while minimizing the destruction of good tissue with such exact depth and border information. These advantages of THz imaging in epithelial tissues imply that it has a large potential for cancer diagnosis on the exterior of internal organs, which may be helpful in situations like oral and digestive tumors.

Fig. 34

a Cancer lesion on the arm of a patient. b THz image. c A THz picture of the tumor at a depth of 250-μm [112]

As shown in Fig. 35, the data gathered utilizing different imaging techniques were compared to the THz pictures of tumor-bearing brain tissues. Using animal brain tumor models, the authors of [113] proved that THz imaging can define the border of the malignant region. THz imaging, according to [107], should be highly useful in identifying brain cancers utilizing patient-derived cancer models with traits similar to the diffuse border of human brain tumors.

Fig. 35

THz images of tumor-bearing brain tissues [107]

Using blood constants, which offer qualitative and quantitative knowledge about significant constituents and waste products found in the human body, many diseases including cancer can be detected early. THz spectroscopy of blood cells on the other hand has not been substantially investigated. This is due to the fact that blood’s THz spectrum is highly impacted by water, a key ingredient of blood, and lacks any clinically important spectral features [114]. Between 50 and 650 cm⁻¹, there are no notable changes in the spectrum between blood serum and water. A new method is demonstrated for qualitative and quantitative blood cell measurement because the linearity of THz signals and erythrocyte concentrations is excellent.

THz Spectroscopy of Bacteria

Researchers have been examining the contributions of significant structural elements to the signature of the complete bacteria or spore as a result of the widespread use of THz technology for bacterial identification. Significant advances have been made in the areas of bacterial component characterization, spore identification, and cell detection [115]. THz waves can entirely penetrate through bacteria because of their small size and low absorption coefficient. Following that, microorganisms were examined qualitatively and quantitatively employing extensive research on bacteria, spores, and other bacterial components. Bacterial components namely DNA, dipicolinic acid (DPA), and metabolites are primarily responsible for the spectrum characteristics of bacteria or spores. The THz signature of bacterial cells and spores is produced by their DNA. THz spectroscopy can be used as a quick and label-free bacterial detection approach due to the diversity of biological contents [116]. Figure 36 depicts the basic analytical concepts of THz spectroscopy for bacterial detection.

Fig. 36

THz spectroscopy of bacteria. a Spectral signature. b Absorption coefficients of bacterial species. c Resonant frequency shifts [116]

THz metamaterials have recently risen to prominence as an effective method for detecting living and viable microbes [117,118,119]. Label-free detection has been developed by covering the substrate with an analyte-specific antibody [120,121,122,123,124,125,126,127,128]. The usage of antibody on the other hand is expensive and in general does not last making the sensors disposable. Therefore, a novel method for categorizing different types of microbes based on inherent characteristics, such as the dielectric constant, will be a game-changer in the development of an early detection tool. In [129], the authors studied the dielectric properties of molds, yeasts, and bacteria, adding to our basic understanding of microorganisms from a new perspective. This is predicated on the assumption that each group of microorganisms will have different dielectric characteristics due to their cellular shapes, as shown in Fig. 37. The composition of the cell wall is extremely important since many types of polysaccharides make up the rather thick walls of molds and yeasts in particular.

Fig. 37

a Mold, yeast, and bacterial cell wall compositions as well as their architectures. b Plots of dielectric constants that vary with frequency [129]

Concealed Object Detection in THz Ranges

THz imaging has four essential qualities that make it an effective tool in security screening applications, viz., 2D imaging, high-resolution 3D imaging, spectroscopy, and non-ionizing THz radiation. The measurement approach was created to test the possibility of detecting things wrapped in various types of fabrics. The measuring approach includes the hardware setup as well as the methodologies and algorithms employed during the measurements. A thermo-higro-barometer, four cameras, and two thermo elements make up the measurement setup [130, 131]. The four cameras used in the tests are commercially available namely a visible light (VIS) camera, a passive THz camera, and two infrared cameras.

Figure 38 depicts the measuring setup. The potential for finding concealed objects in the THz spectrum was tested using an imager operating at 250 GHz. To evaluate the viability of finding hidden objects in the infrared spectrum, two cameras were employed. A long-wavelength (LWIR) infrared camera is the first infrared camera utilized in the testing. A cooled InSbfocal plane array detector is used in the second infrared camera, which is a mid-wavelength (MWIR) infrared camera. Figure 39 depicts the collection of things. The experiment entailed gathering photographs of the person dressed in various outfits with various objects hidden beneath their clothing. The selection of objects to be disguised included both harmful and common objects, such as a wallet and a cell phone. The suggested algorithm was trained and tested using the data set of gathered photographs. The experiment has been broken down into 30-min sessions. The long-term measuring sessions were designed to gather images of several hidden objects with various contrasts and examine how decreasing contrast influenced detection and recognition. The preliminary research that established the session length showed that the hidden object used in this inquiry attained thermal equilibrium after 23–26 min. During measurement sessions, an individual clothed in various costumes with various objects concealed beneath clothing is captured in MWIR and THz images as shown in Fig. 40.

Fig. 38

Measurement setup. VIS camera: Visible light Camera; LWIR camera: Long-wavelength infrared camera; MWIR camera: Mid-wavelength infrared camera [132]

Fig. 39

Test objects [133]

Fig. 40

Images of a person hiding a bomb and a firearm while donning a thick cotton shirt. a MWIR pictures were captured at the beginning of the measurement b after 15 min and c after 30 min. d THz pictures are captured at the commencement of the measurement e after 15 min and f after 30 min [133]

Two approaches for detecting the various concealed items are discussed in [133]. Both approaches execute detection and classification in a single architecture using convolutional neural networks. You Only Look Once 3 (YOLO3) and R-FCN are the two deep learning-based techniques employed. Their architectures are depicted in Figs. 41 and 42.

Fig. 41

Architecture of YOLO3 in hidden object detection

Fig. 42

Architecture of R-FCN in hidden object detection

Food Safety and Quality Inspection

Food safety and food quality are one of the key public concerns. THz imaging techniques help to test the safety and quality of food. To make sure of it, foreign bodies must be detected in food products. In the food sector, X-ray imaging is commonly employed to detect thick foreign bodies based on their noticeable density disparities [134,135,136]. Using a THz-TDS system, the authors in [137] evaluated the absorption spectra of nutmeat slices, shell, inner separator, and insects. The findings revealed that insects have distinct spectral characteristics, implying that THz technology could be used to identify pest damage in pecans. The inside of peanut shells, as well as the amount of peanuts, was clearly identifiable using this reflection-mode CW-THz imaging system (Fig. 43). The findings suggest that THz imaging could be used to identify pest damage in pecans. THz imaging is more reliable than X-ray imaging for low-density foreign body identification because the dielectric contrast mechanisms are considerably more pronounced at THz frequencies [138,139,140].

Fig. 43

a Peanut affixed on an acrylic support, Reflection picture from THz: b one peanut in a shell c empty shell and d two peanuts in a shell [88]

Agricultural Applications

Initial applications of THz imaging included monitoring water content in plant leaves and detecting signs of plant dryness. THz has also been availed for pesticide and hazardous compound detection in crops, crop yield estimation, transgenics detection, seed quality management, and soil inspection. The authors in [152] looked at the THz properties of seven common plant leaves (Fig. 44). Transmission loss was calculated in strawberry, coffee, radish, lettuce, mint, cabbage, and rhubarb found a wide range of THz transmission loss between 0.3 and 0.4 THz. THz transmission loss varies depending on several aspects, including leaf texture, thickness, uniformity, and density. The THz transmission loss fluctuation was highest in cabbage leaves and lowest in coffee leaves. The texture and thickness of coffee leaves are consistent. The group also investigated the propagation of THz signals through thick layers of coffee leaves [141]. The thickness and permittivity measurements were used to make the calculations, which revealed a repetition pattern at around 130 GHz.

Fig. 44

a Continuous THz system, b THz transmission spectra of seven distinct plant leaves and c coffee leaf with several spots on the leaf [141]

For the estimation of water in rapeseed leaves, the spectral data was analyzed using the Savitzky-Golay method, followed by partial least squares (PLS), boosting-PLS, and kernel PLS (KPLS). KPLS model is providing accuracy compared to other methods. According to the authors in [153], to measure the amount of water in leaves in the field, THz spectroscopy must be combined with mathematical modelling methods. THz-TDS system has been used to explore a variety of food and agriculture items. This technique can offer information on both phase and amplitude. THz pictures of a leaf which is of 60 mm long at different frequency bands are shown in Fig. 45. In order to detect the veins in the leaf, water absorption maxima exceeding 0.5 THz are required. Above 1.0 THz, the thorns in the leaf can also be seen. The results of the experiments show that THz TDS can be utilized for agricultural item inspection or monitoring.

Fig. 45

Tree leaf THz pictures [153]

Using Swissto12 system, the authors in paper [154] conducted a preliminary investigation about the amount of water and any pesticides found in leaves. It also discovers the permittivity as well as the path-loss response of fresh and drought-stressed leaves. As illustrated in Fig. 46, the entire calibration process was designed to eliminate any measurement mistakes caused by the system or any other external source. The Swissto12 is compatible with frequencies between 0.75 and 1.2 THz and thicknesses between 40 and 4 mm. Furthermore, when running the experiments on various leaves, scattering parameters (S-parameters) were measured [155].

Fig. 46

Swissto12 THz system [154]

The experiment included six different fresh leaves: cauliflower, basil, iceberg, sage, cabbage, and lettuce, as shown in Fig. 47a. These leaves were all kept in the lab for 4 days with the same environmental factors. These leaves were not watered on the test days. The temperature maintained in the test environment was 23 °C ± 0.1 °C. The water content and any surface abnormalities on the leaves were assessed at three distinct points on the leaves. To examine the measurement findings of the leaves, Vernier callipers were used. The thickness of each leaf was measured independently under the same environmental circumstances. The thickness of the leaves at various positions was determined by repeating this process three times. During the process, it was discovered that the thickness rose steadily as the water content increased. According to the measurements, it was discovered that different leaves had varying levels of attenuation, which was obviously related to the amount of water in the leaves or the presence of pesticides. Cauliflower leaves are free of pesticides and have less water content than those of other plants, as seen in Fig. 47b. The leave reaction to path-loss is highly correlated with the amount of water in the leaves as well as their physical characteristics. As a result, it also emphasizes data on absorption loss, revealing the water content’s absorption and reflection by the leaves. Absorption loss might be brought on by surface flaws or a considerable absorption of water content at the time of measurement.

Fig. 47

a Samples of several fresh leaf types, b transmission response of various leaves [154]

Holography and Ptychography Applications

THz digital holography (TDH) deals with the acquisition and processing of holograms with digital holographic images. THz sources suitable are THz laser, backward wave oscillator (BWO), or frequency multiplier and amplifiers following a synthesized microwave signal source. Two complementary detector technologies used are the diode detector and sub harmonic mixer receiver. The illustrative applications include imaging the internal void structure of visibly opaque dielectrics and imaging a thick terahertz lens using the dual-wavelength reconstruction method. Using THz holographic imager [155], holograms of amplitude and phase objects in transmission are captured and reconstruction is performed using angular spectrum and Fresnel diffraction methods. The experimental setup used to obtain holograph is “prototypical THz holographic imager” as shown in Fig. 48.

Fig. 48

THz holographic imager [155]

The in-line CW TDH approach is used for the early detection and treatment of liver cancer in high-risk groups of patients. The THz phase image showed evidence of fibrosis in the liver cancer tissue, and at a resolution of 158 µm, the appearance of healthy liver tissue was more homogeneous than that of the cancerous tissue. Hepatocellular carcinoma (HCC) tissue is found using CW THz digital in-line holography imaging system working at 2.52 THz [156]. With the help of initial value optimization and constraint conditions, this method presented phase reconstruction methods for in-line digital holography, which increased calculation efficiency. The digital photo of the sample is shown in Fig. 49.

Fig. 49

a CW THz in-line holography of human liver cancer sample, b THz hologram, c reconstructed amplitude, and d phase images [156]

The forewing of cicadas (Cryptotympana atrata) was imaged using a CW THz ptychography imaging system made up of a FIRL 295 at 2.52 THz [157] and a pyrocam III detector, as illustrated in Fig. 50. During data collection, the sample was motorized by a 2-axis translation stage. The optical thickness of the membrane and veins can be obtained using CW THz ptychography using the complex-valued transmittance function that has been rebuilt. The THz scale venation has several features, making the reconstruction findings sensitive to probe translational errors. Phase retrieval algorithms find applications in terahertz coded aperture imaging and for non-destructive inspection applications [158].

Fig. 50

a CW THz ptychography b forewing of cicadas, PMs: parabolic mirrors, Sc: subcostal, Rs: radius (R₁, R₂, R₃, R₄, R₅), Ms: media (M₁, M₂) and “ + ” indicates the convex vein [157]

Table 3 provides THz frequencies and corresponding applications. THz technology has revealed major differences between infected and healthy tissues. THz radiation is generally non-ionizing and of low intensity, making it suitable for biological application to both living and removed tissue. Because of their shorter wavelength, THz frequencies outperform microwaves in terms of imaging resolution and outperform infrared methods in terms of fat tissue transmittance. Many tumors, including basal cell carcinoma, brain, colon, and breast cancer, have been treated by THz imaging. THz waves can be utilized for characterizing and identifying a variety of meals and packaging materials in addition to passing through them. THz imaging has been used successfully in the non-invasive detection of dangerous compounds, toxins, and pathogens in food, and it is a great replacement for X-rays in food inspection and quality control activities. Because clothing transmits a lot of THz energy in that range, most THz-based hidden object detection systems operate below 1 THz. THz-based concealed object detection is built on the capacity to pierce fabrics and other substances with low water content. THz has also been used for soil inspection, detecting pesticides and other dangerous substances in crops, monitoring seed quality, identifying transgenic organisms, and estimating crop production.

Table 3 THz frequencies and applications

Conclusion

The importance of THz technology and the numerous THz antennas used for THz imaging, also covering 6G frequencies, are discussed in this article. THz antennas were studied for their properties, features, and applications. A brief summary has been used to cover the THz communication. There has been discussion on the value of opening up the THz band as well as its possible uses in wireless communication in the future. The literature includes a thorough analysis of the various THz antenna types and some discussion on the choice of THz antenna material. Various THz image reconstruction techniques were also discussed. The quality of the image and, thus, the radiation dose are significantly impacted by image reconstruction. The goal of picture reconstruction is to obtain the least amount of noise possible for a given radiation dose without losing image correctness or spatial resolution. Because images of the same quality can be recreated at a lower dose, image reconstructions that increase image quality can result in a reduction in radiation exposure. The paper examined two basic categories of reconstruction methods: analytical reconstruction and iterative reconstruction (IR). Furthermore, various THz imaging applications were addressed and compared. THz technology has shown great promise in biomedical research, but a number of challenges need to be removed before it can be widely used in clinical settings. THz irradiation’s biological safety is still unknown due to a lack of scientific evidence. THz waves have very low photon energies and were first believed to be harmless for human cells, tissues, and even the body. Researchers are reconsidering the bio-safety of THz irradiation in biomedical applications after recent studies showed that it can alter the genome, proteome, and transcriptome of cells and tissues at certain intensities and periods. This review identified some open research issues in the work, which offer up new research vistas.