Analogous to transmission imaging, a full time-dependent waveform is acquired for each pixel in reflection. So the data-set obtained in a reflection measurement is also a hyper-spectral cube, containing information about the composition of the sample under study. However, in many cases the useful information that can be extracted from these images is related not to spectroscopic composition but to the geometrical structure of heterogeneous samples, and particularly of layered media. When a sample has a complicated structure that incorporates interfaces within it, as long as all the materials involved are reasonably transparent, the contrast of their refractive indices will imply the existence of Fresnel reflections at each interface. Since the terahertz electromagnetic transients are rather short in time, owing to their small temporal coherence, their propagation through a sample with interfaces will lead to a series of reflected “copies” of the pulse separated in time. The time separation between them encodes the spatial separation between subsequent interfaces, therefore allowing the reconstruction of the internal structure of the sample in a similar fashion to B-scan ultrasonograms.
3.1 Tomographic image reconstruction
The possibility of non-contact reconstruction of the internal geometry of complex layered material structures has attracted attention in many areas. In the earliest examples, the flatness of interfaces and prior knowledge about material composition led to relatively straightforward problem in image reconstruction [50]. Of course, when the sample under study has a complicated non-planar surface, a simple normal-incidence reflection configuration is no longer effective, and a more complicated approach is need [8]. One interesting recent approach to overcome this challenge has been described by Stübling et al. By placing a THz-TDS system at the end of a robotic arm, and extracting sample shape information from visible images or using structured light illumination, one can form THz reflection images of samples with arbitrary, even quite complex, shapes [51, 52]. This approach has been recently used in combination with photogrammetry to assess the age and composition of ancient pottery shreds, as shown in Fig. 2 [53]. Other groups have implemented more advanced signal processing approaches to tomographic image reconstruction, as discussed in Ref. [54].
3.2 Medical imaging
Using terahertz as a probe in the medical area is an attractive option. For instance, terahertz radiation is non-ionizing, and therefore very safe to use as long as the average power is low enough to avoid producing significant heating of the tissues. Furthermore, it allows the water content of tissues to be determined in a contactless fashion. A topic that was highlighted in the original article was the assessment of tissue burns by reflection geometry. A few preliminary measurements consisting of one-dimensional scans across a burnt section of chicken breast tissue were presented at that time. Since then, a wealth of progress has been made on that front, particularly over the last decade. Terahertz imaging has proven its potential for the discrimination of the depth of the burns, which is hard to assess clinically. Such studies have been done both ex vivo [55] and in vivo [56] on various animal models such as Sprague–Dawley rats [57] and Landrace Yorkshire cross pigs [59] whose skin have similarities with humans. Furthermore, differences in the post-burn water accumulation dynamics caused by edema have been well studied with terahertz methods [59, 60]. In such studies, an initial depletion of the hydration at the burn site, in the minutes following the injury, produces a decrease of the terahertz reflection at the cutaneous surface. However, the subsequent inflammatory response generates an accumulation of water over the following few hours, which increases the reflection. This effect is more pronounced in third degree “full thickness” burns than in first- or second-degree “partial thickness” burns as shown in Fig. 3.
A wealth of other applications of terahertz imaging in the medical field have been proposed over the last two decades. Of course skin is a type of tissue that is a natural candidate for terahertz inspection, since it is easily accessible. The first in vivo measurements of skin [61] were reported in the early 2000s; however, the degree of sophistication required for actual medical applications has maintained interest in the topic up to the present day [62]. As one important example, diabetic foot syndrome, a consequence of diabetes, is a condition for which there is currently no objective diagnostic test, particularly in early stages. Many diabetic patients experience a combination of symptoms, that include the loss of sensation (neuropathy) related to a neurological deterioration in their lower limbs, poor irrigation (vasculopathy) and dehydration of the skin of their feet. In many cases this condition evolves into ulcers in the feet, and can result in partial or total amputations of the limbs. Indeed, this is the most common cause of amputations after traumatic accidents. Since skin dehydration accompanies this condition, terahertz imaging has been proposed as a potential tool for its objective and early diagnosis [63, 64], showing potential to become a valuable tool on this front. The most recent imaging study of diabetic foot [65] included a cohort of 178 human subjects (see Fig. 4), being to the best of our knowledge, the largest human population to ever be imaged with terahertz radiation for medical purposes. This work provides evidence that supports neurological deterioration as the underlying cause for dehydration, which is an open debate among clinicians.
Another tissue that is easily accessible without the need of endoscopes or surgery is the cornea. The possibility of non-contact monitoring of the corneal hydration has also attracted attention recently [66, 67]. The water content of the cornea is an important indicator of the ocular health [68], and could be used for the diagnosis and progression assessment of various ophthalmological conditions such as post-transplant corneal rejection, Fuchs dystrophy, keratoconus, trauma, infection, and other vision-impairing diseases [69].
Finally, we would be remiss if we did not mention that many efforts have been made to use terahertz imaging in oncology [70, 71]. Studies have focused on detection of breast [72], skin [73, 74], and colon [75,76,77] cancer, among other types [78,79,80] of cancer. In many of these studies, it has been demonstrated that terahertz imaging can indeed distinguish cancerous tissue from the surrounding healthy tissue. However, the exact mechanisms that lead to contrast in terahertz images is still a topic of debate [81], and this uncertainty has hindered widespread adoption of the technique in clinical settings.