1. Introduction

Since Hu and Nuss’ first pioneering experiments in 1995 [1], Terahertz (THz) imaging has evolved into one of the most practical applications of THz time-domain spectroscopy (THz-TDS). The reason for this continuing success is due to its broadband, sub-picosecond temporal resolution and phase sensitive coherent detection combined with the innate properties of a variety of dielectric materials, which are transparent in the THz regime. These properties, as well as the fact that many materials have characteristic absorption bands at THz frequencies, make THz-TDS a very promising technique for imaging. To date, THz-TDS has been proven to be very successful for object and spectral imaging in a number of different areas, such as drug identification [2], concealed object recognition [3], chemical composition analysis of explosives [4], quality control and monitoring for industrial processes, as well as biological applications in medicine [5]. These successes have led to commercialization based upon emerging state of the art technologies [6].

Most of today’s terahertz imaging systems employ sub-picosecond pulsed [7] radiation sources and construct images based on the coherent detection of the transmission and/or reflection spectrum of the object to be imaged. This technique has been shown to provide the capability of two-dimensional real-time imaging [8], as well as the ability to reconstruct three-dimensional tomographic images [9] over a broad range of THz frequencies. A comprehensive review on the field of THz imaging can be found in [9,10]. An equally important implementation of THz-TDS to imaging is the detection of objects buried within a host material. In such an imaging modality, the average collected THz power, the degree of polarization contrast, or the arrival time of the THz pulse transients are collected and analyzed to reconstruct an image of the hidden object. Owing to the opacity of metals in the THz regime, this method has been used extensively to image metallic objects hidden deep within dielectric packages. However, because of this fact, it is impossible to probe dielectric matter or voids buried within a metallic host. This is the case only when the thickness of the metallic layer is greater than the THz radiation skin depth (i.e. ~100 nm) since the metallic layer possesses very high reflectivity (i.e. is perfectly conducting) and no radiation can interact with the dielectric object.

In the current study, we report on a potential application of pulsed terahertz imaging in which dielectric objects embedded inside a random collection of metallic particles are successfully realized. This imaging technique is mediated via the coupling of the THz electric field to THz particle plasmons which spatially map out the embedded dielectric objects. Unlike conventional THz point-to-point imaging, the particle plasmons couple with each other in a random fashion via 3D near-field channels; thus, images of the dielectric objects are constructed from multiple particle plasmon sources re-radiating the THz electric field in the vicinity of the objects. Furthermore, we show that by utilizing a super-resolution image reconstruction algorithm in conjunction with various object shape training sets, an enhanced resolution image beyond the sampling space is realizable. To our knowledge, this is the first time that imaging inside a metallic media has been demonstrated.

Here, we outline the principles of this imaging process. In this configuration, a small dielectric object is immersed in a random collection of sub-wavelength metallic particles. A THz pulse incident on the sample excites localized, non-resonant surface plasmons on the metallic particles which coherently couple and propagate throughout the sample via near-field particle-particle oscillations [11–13]. Notably, even though the host material is made up of metallic particles having large negative real permittivity, the media collectively transports the THz electromagnetic energy via near-field particle plasmon coupling. This makes the media partially transparent to the THz radiation implying that it possesses an effective positive real permittivity. Basically, the random collection of metallic particles appears dielectric rather than metallic to the THz radiation. In this regard, imaging a dielectric object buried inside the metallic particle collection is akin to the THz transmission imaging experiments used to detect power attenuation signatures from a dielectric embedded inside a dissimilar dielectric host. Embedding dielectric objects having sufficient thickness (i.e. much larger than the THz radiation wavelength) between adjacent metallic particle collections impedes the near-field particle-particle coupling. Under this circumstance, the particle plasmons in the vicinity of the front surface of the dielectric object reradiate the THz electric field. After the THz radiation propagates through the dielectric object, this far-field radiation is again captured by the metallic particles on the opposite side from where it continues to propagate via near-field particle plasmon oscillations. Essentially, the THz electric field is transformed into propagating particle plasmons at the entrance of the metallic particle collection, re-radiated through the dielectric object, and then collected by the randomly placed metallic particles at the other face of the object and propagated outside the collection of particles from where it is detected. This fact manifests itself as an innate difference in the THz pulse arrival time, phase, and attenuation of the electric field when the pulse is incident on a location containing only metallic particles versus a location containing metallic particles with embedded dielectric. Using these ideas as a basis, THz pulses are transmitted through a sample, detected, and analyzed over a two-dimensional grid, and an image of the embedded dielectric object is successfully constructed.

2. Experimental methods

In this experiment, dielectric objects have been placed inside a metallic media composed of close-packed, poly-disperse Cu microparticles having a mean dimension of ~70 µm and a packing fraction of 0.6. The dielectric objects were cut from Teflon sheets into triangular and polygon geometries having different sizes and thicknesses. In preparing the samples, a 3 mm thick and 1.5 cm wide plastic container transparent to THz radiation was filled with the Cu particles. The Teflon triangular- and polygon-shaped objects were then fully embedded in the middle of the Cu particle collection. The target was raster scanned by an x-y translation stage with a resolution of 0.6 mm/pixel over a 9.6 × 7.8 mm² area, corresponding to 16 × 13 = 208 pixels for the triangular-shaped object and a 6 × 7.2 mm² area, corresponding to 10 × 12 = 120 pixels for the polygon-shaped object.

In order to image the sample, THz-TDS was employed to perform the two-dimensional scans. Here, single-cycle, linearly polarized, 1 ps wide THz pulses having a central frequency of 0.6 THz and a bandwidth of 0.5 THz were employed [14]. These THz pulses were focused onto the target sample via a 5 cm focal length, off axis gold-coated parabolic mirror and the transmitted radiation was collected using an identical parabolic mirror from where it was passed to the detection setup. In the detection system, the transmitted THz and optical probe pulses are focused collinearly onto a 500 µm thick <111> ZnSe electro-optic crystal. From here, complete information regarding the time-domain of the THz electric field is obtained with a temporal resolution of 0.08 ps and a signal-to-noise ratio of 10000. Using this setup, THz-TDS of the sample was obtained for each point over the two-dimensional grid, and images of the shapes of the Teflon objects were successfully constructed. It should be noted that no signal averaging schemes have been performed in this experiment. The data acquired at each point are the result of a single transmitted THz temporal pulse.

3. Experimental results and analysis

Figure 1 illustrates the THz electric field time domain signal, E_THz(t), transmitted through a single location on the sample containing only Cu particles. In comparison to the free-space propagating E_THz(t) signal, the amplitude of the transmitted electric field is attenuated by ~98% due to the high reflectivity of the host Cu particles. Also shown is the THz electric field time domain signal transmitted through a single location on the sample where the Teflon object is embedded.

 

Fig. 1 Transmitted THz electric field through the metallic ensemble. (blue) free space time domain signal, (light blue) time domain signal through the Cu and (purple) time domain signal through Cu and Teflon.

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In order to obtain an unambiguous representative image of the embedded Teflon test object, a time-domain electric field scan was performed on samples containing a 0.8 mm thick triangular-shaped and 1.1 mm thick polygon-shaped Teflon objects shown in Fig. 2 (a,b) . An illustrative diagram depicting the transmission of the THz electric field through these samples is given in Fig. 2 (c). Since small changes in the transmitted THz signal are of interest, contrasts in the arrival times and slight differences in the electric field amplitudes can be better registered by evaluating the instantaneous power, ${\left|E_{THz}\left(t\right)\right|}^2$, and the spectral power,${\left|E_{THz}\left(\omega \right)\right|}^2$, respectively. ${\left|E_{THz}\left(t\right)\right|}^2$ and ${\left|E_{THz}\left(\omega \right)\right|}^2$ are acquired at every pixel in the grid by utilizing Hilbert and Fourier transforms on the time domain signals, respectively. The Hilbert transform, H, produces the original signal plus the transformed (imaginary) part of the signal ($\colorbox[rgb]{}{$H$}\left(E_{THz}\left(t\right)\right)=E_{THz}\left(t\right)+iE{*}_{THz}\left(t\right)$, where $E_{THz}\left(t\right)$ is the original and $E^{*}{}_{THz}\left(t\right)$ contains the complex conjugate of the signal). To obtain the integrated instantaneous power, we calculate $\left|E_{THz}\left(t\right)E^{\ast }{}_{THz}\left(t\right)\right|$ and integrate it over the pulse duration. Henceforth, “instantaneous power integrated over the pulse duration” refers to “instantaneous power” for brevity.

 

Fig. 2 (a,b) Pictures of the Teflon objects used in the experiment. (c) An illustration depicting the THz electric field (E_THz) transmitted through the samples.

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Figure 3 illustrates a 2D image of the total transmitted instantaneous power ${{\displaystyle \colorbox[rgb]{}{$\int $}}}^{\text{}}{E}_{THz}\left(t\right)E_{THz}^{*}\left(t\right)dt$ integrated over the duration of the pulse for both the triangular- and polygon-shaped objects. The raw images appear very noisy and smeared out beyond the actual size of the physical objects. This is due to the nature of the multiple, indirect random paths taken by the THz radiation as it is channeled via particle plasmons through the sample as well as the non-directional collection of the THz electric field by the receiving particle plasmons in the vicinity of the embedded dielectric object. The low contrast of the images is due to the fact that the Teflon samples are thin (~1 mm), resulting in only a small observable difference in absorption between the embedded Teflon object and the Cu background; however, thicker Teflon objects can produce much higher image contrast. Nevertheless, there are subtle enough differences in the detected instantaneous powers to discern the region where the Teflon objects are located.

 

Fig. 3 Acquired raw transmitted instantaneous power images of the embedded integrated over the duration of the pulse (a) 0.8 mm thick triangular-shaped object at a resolution of (16 × 13) pixels and (b) 1.1 mm thick polygon-shaped object at a resolution of (10 × 12) pixels. The dashed lines indicate the location of the embedded object.

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While such low contrast might not be obvious, the signature of the objects on the THz pulse power can be enhanced if sophisticated digital image processing techniques are applied to the acquired low resolution images. In particular, the spatial resolution of the objects can be improved by enhancing the original images using the super-resolution through neighbor embedding technique [15]. This super-resolution algorithm is used to produce high resolution enlargements from low resolution images, which helps overcome the limitations of the low pixel image acquisition system. However, prior to its application some preprocessing steps are adopted to suppress noise and increase the image contrast.

Since the raw data contains background noise from the random nature of the excitation and propagation of THz particle plasmons, a 3 × 3 median filter [16] is employed. This filter replaces the value of a given pixel by the median of the intensity levels in a neighborhood centered on that pixel. Furthermore, to eliminate image blurring a threshold is set to select noisy pixels to which filtering is selectively applied. Finally, to bring out the object of interest from the background and make it more distinguished, the method of contrast stretching [16] is applied to the filtered images.

The neighbor embedding based super-resolution technique is then applied to the preprocessed low resolution images to enhance the spatial resolution of the embedded objects. This algorithm requires learning from an object training set [15] generated using a set of 7 high resolution images. First, a 3 × 3 averaging filter is applied to the high resolution images to model the blurring effect introduced during image acquisition. Next, the blurred images are down-sampled by a factor of three in both the horizontal and vertical directions. Each high resolution image is then divided into patches having dimensions of 9 × 9 pixels, and for each patch in the high resolution image the corresponding 3 × 3 pixel patch is generated for the low resolution image. This step provides a set of 16157 pairs of low resolution and high resolution patches used to reconstruct the acquired images.

Given a low resolution test image, $X_t$, the reconstruction process includes both neighbor searching and target generation. Similar to generating the training set, the low resolution images are divided into 3 × 3 patches, $x_t$, but with an overlap of one row or one column between adjacent patches. Next, for each $x_t$ in $X_t$, the 3 × 3 training set patches are searched for two nearest neighbor patches, $x_s^1$ and $x_s^2$, having the smallest Euclidean distance with respect to $x_t$. A weighted combination is then calculated such that $x_t=a_1{x}_s^1+a_2{x}_s^2$ has the smallest mean-square error when compared to the original $x_t$. Now, let $y_s^1$ and $y_s^2$ be the corresponding high resolution patches of $x_s^1$ and $x_s^2$, respectively, in the training set. A weighted target high resolution patch $y_t=a_1{y}_s^1+a_2{y}_s^2$ can then be generated. By repeating this process for all the patches in $X_t$, a high quality image, $Y_0$, can be constructed. To enforce local compatibility between adjacent overlapping patches in $Y_0$, pixel values in the overlapped regions must be averaged. Finally, to enforce global reconstruction constraints,$Y_0$ is projected onto the solution space of $DHY=X_t$, where D is the down-sampling operator and H is a 3 × 3 averaging filter. This can be efficiently computed using the iterative back-projection method [17], which gives the final estimate of the high resolution target image, $Y_t$.

The above mentioned super-resolution image processing was applied to the two acquired raw THz images depicted in Fig. 3. Figure 4 illustrates the resultant 9-fold increase in the spatial resolution of the images. It is evident that there is significant image enhancement in the post processed images compared to the originally acquired ones. However, it can be

 

Fig. 4 The super-resolved images of those presented in Fig. 3. The high-resolution images are based on total transmitted instantaneous power with a 9-fold increase in spatial resolution for the original (a) (16 × 13) pixel triangular-shaped and (b) (10 × 12) pixel polygon-shaped Teflon objects. The dashed lines indicate the location of the embedded object.

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observed that even though the resolution and contrast of the images has been enhanced, the exact shapes of the embedded objects are indistinguishable from such instantaneous power maps. As mentioned earlier, this is attributed to the fact that the Teflon samples are thin, resulting in only a small observable difference in absorption between the embedded dielectric object and the metallic particle environment. This makes it very challenging to detect the hidden objects by only observing the transmitted THz power.

To further study the THz plasmonic imaging technique, other property maps of the transmitted THz pulse, such as arrival time and phase magnitude were studied. Using the time domain electric field of the transmitted THz pulse, the temporal position of the peak pulse intensity was acquired from the centroid of ${\left|E_{THz}\left(t\right)\right|}^2$ for each detected pixel. The peak intensity corresponds to the time at which the maximum number of photons is detected. Considering that the pulse arrival time varies as the THz pulse travels from the metallic region through the dielectric region of thickness L, the time difference can be represented by$\Delta t=\left(L/c\right)\left(n_d-n_m\right)$, where n_d and n_m are the refractive index of the dielectric and the effective refractive index of the metallic mediums, respectively. Consequently, Δt is dependent on the location of the dielectric object within the sample; therefore, the location and shape of the embedded object can be mapped by acquiring such time differences as shown in Fig. 5 .

 

Fig. 5 Acquired raw 2D maps of the THz pulse arrival time of (a) 0.8 mm thick triangular-shaped object at a resolution of (16 × 13) pixels and (b) 1.1 mm thick polygon-shaped object at a resolution of (10 × 12) pixels. The dashed lines indicate the location of the embedded object.

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Using this image representation, it is evident from the figure that both the embedded triangular- and polygon-shaped Teflon objects are clearly distinguishable from the background metallic media. Unlike the transmitted pulse instantaneous power, which is based on the average power loss due to near field interactions between the particles along the propagation path, the time arrival representation shows higher contrast. However, the exact boundaries of the objects are not well defined. The low resolution on the edges is attributed to the spatial spread of the particle plasmons coupling radiation as discussed earlier.

Since the THz radiation transport through the random metallic media was previously reported to be a coherent phenomenon [12], it is only natural to investigate the phase magnitude of the transmitted THz pulse for potential phase contrast imaging. In this study, the phase magnitude at a frequency of 0.15 THz (corresponding to the maximum pulse power when the signal travelled only through metallic particles) was selected at each pixel. Shown in Fig. 6 are the phase magnitude images for both the triangular- and polygon-shaped Teflon objects. It is evident from the figure that the raw phase contrast images are less distinctive compared to the arrival time images; nevertheless, they show features of the embedded objects. The phase magnitude of the transmitted pulse depends on the refractive index of the media in which the pulse has traveled. The reason behind this high contrast is the near field particle-particle plasmon which propagates the THz electric field inside the metallic particle sample. In areas of the sample with pure metallic particles, these near field particle-particle plasmons travel through the sample continuously, whereas in areas where the dielectric object is present, these near fields have to be reradiated and coupled back to particle-particle plasmons in the vicinity of the dielectric object. Clearly, there is a difference in the phase accumulated in the two regions as a result of refractive index difference (high contrast) at different locations within the sample.

 

Fig. 6 Acquired raw 2D maps of the phase magnitude taken at 0.15 THz for the (a) 0.8 mm thick triangular-shaped object at a resolution of (16 × 13) pixels and (b) 1.1 mm thick polygon-shaped object at a resolution of (10 × 12) pixels.

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To enhance the resolution of the arrival time and phase contrast images, the aforementioned super-resolution algorithm was applied to the raw data. Figure 7 illustrates the post processed high resolution images resulting from this technique. In all cases, the visual quality is improved as the resolution level increases, and from the enhanced images more details of the embedded dielectric objects are visually recognizable. More specifically,

 

Fig. 7 The super-resolved images with a 9-fold increase in resolution for the acquired (a,c) pulse arrival time images and for (b,d) phase magnitude images. The dashed lines indicate the location of the embedded object.

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sharper edges make the objects of interest more distinguishable from the background metallic media. According to the information known about the shape of the objects, pulse arrival time gives the most informative depiction of the objects. Phase magnitude basically conveys similar information, but the edges are not as clear as that of the pulse arrival time images. This demonstrates that super resolution can be effectively implemented to produce more detailed information from low quality images acquired via THz plasmonic imaging of dielectric objects embedded in metallic media.

4. Conclusion

In this work dielectric objects embedded in metallic media were imaged via THz-TDS. The mechanism for our technique involved coupling the THz electric field to particle plasmons and propagating it through the metallic medium. To enhance the low quality images acquired, a super-resolution image processing algorithm was applied. Unlike conventional THz imaging methods using the transmitted pulse power, it is shown that pulse arrival time and phase magnitude information provide more detailed images of the embedded object. This technique may prove useful for the detection of foreign objects buried in metallic powders.