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There are many effective medium models that accurately describe the dielectric properties of mixtures. However, these models assume that the components are non-interacting. This assumption is not valid for solutions of polar liquids, resulting in significant deviations between the measured and theoretically predicted values of the complex index of refraction of the mixtures. We present three effective medium theories by expanding the well-known Debye relaxation model for solutions of polar liquids in the terahertz (THz) regime. The new effective medium models proposed in this paper predict the individual relaxation Debye parameters based on the cooperative motion dynamics and self-associative properties of each mixture, and therefore explain the deviation of the dielectric functions of the solutions from the traditional effective medium models. These models are verified through reflection measurements of four alcohol-water solutions acquired through THz time-domain spectroscopy (THz-TDS). Compared to the current mixed medium models, the new effective Debye theorem predicts the dielectric properties of polar solutions more accurately and has the potential to explain inter-species mixing schemes and interactions.

We demonstrate spectroscopic THz reflection imaging through turbid media. We show that the detection of resonant features in the extinction spectrum can be made possible using multiresolution analysis based on wavelet transforms. We determine that the spatial resolution of this imaging technique is only diffraction limited.

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

Dielectric heterogeneity in addition to wavelength-scale air voids and granular particles lead to significant electromagnetic scattering in the transmission-mode THz-TDS. These scattering processes result in the distorted or obscured resonant signatures, a frequency-dependent extinction loss, and the appearance of anomalous spectral artifacts, imposing severe challenges on the real-world automatic material characterization schemes. In this work, we use a combination of the wavelet multiresolution analysis, the principal component analysis, and the bimodality coefficient to simultaneously identify all the resonant frequencies of a heterogeneous sample embedded beneath a highly scattering turbid medium.

To solve the phase ambiguity problem in the THz reflection spectroscopy, current material parameter extraction methods require the sample to make an ideal contact with an optically transparent window. We treat these samples as a multilayer system and present a new algorithm that estimates the thickness of the potential air gap and calculates the complex refractive index of the samples.

The rough surface scattering in the reflection-mode THz-TDS can result in inaccurate phase spectra, reduced signal to noise ratios, distorted or obscured resonant fingerprints, and the appearance of anomalous spectral artifacts. In this work, we demonstrate the implementation of a wavelet shrinkage technique for the retrieval of obscured resonant frequencies from the derivative of THz reflectivity of solid dielectric materials. We examine the robustness of this technique over controlled levels of rough surface scattering created using sandpapers of different grits on sample disks made from 4-aminobenzoic acid (PABA).

We have developed a terahertz time-domain polarimetry (THz-TDP) system by applying frequency modulation to electro-optic sampling detection in a nonlinear crystal. We characterized the precision of this system in determining the polarization angles to be 1.3° for fixed time delay, and 0.5° for complete time-domain waveform. Furthermore, we calculated the Jones matrix of the optical components used for beam propagation to calibrate the induced systematic error. The advantages of employing this calibration approach are demonstrated on a sapphire crystal investigated at different sample test positions in transmission configuration, and using high resistivity Si, AlN and quartz in reflection geometry. The new THz-TDP technique has the advantage of not using any external polarizers, and therefore is not constrained by their optical performance limitations, such as restricted bandwidths and frequency-dependent extinction ratio. Finally, the THz-TDP technique can be easily implemented on existing time-domain spectroscopy (TDS) systems.

Terahertz imaging often involves seeing through inhomogeneous and highly scattering media. We propose a wavelet multiresolution analysis approach to mitigate the scattering effects and produce highly-resolved reflection spectral images for chemical mapping through turbid media.

We present two improved mixed media models for solutions of polar liquids in the THz regime. Simple effective media models do not consider intermolecular interactions or hydrogen bond network distributions in polar liquid solutions, and therefore yield inaccurate estimates of the effective dielectric functions. We present two new models: a volumetric modification to the Bruggeman equation and an effective time constant calculation in Debye-like relaxations. Furthermore, we will discuss the limitations of each model in predicting the dielectric functions.

We report on the development and performance characterization of a telecentric terahertz spectroscopic scanner using an f-θ objective lens and a single gimballed scanning mirror for image formation. We derived a beam steering transform to compensate for the intercoupling of the gimballed mirror axes and the distortions caused by an imperfect scanning lens. We characterize the optical performance of the system in both the time and spatial domains, demonstrating a constant diffraction-limited imaging resolution over the entire field of view. Finally, given the large depth of focus of the objective lens, we demonstrate the broadband imaging capability at different depths using a Boehler star target. This imaging setup has the potential to be miniaturized into portable form factors for field-deployable scenarios.

Terahertz (THz) imaging is a widely used technique in the study and detection of many chemicals and biomolecules in polycrystalline form because the spectral absorption signatures of these target materials often lie in the THz frequencies. When the size of dielectric grain boundaries are comparable to the THz wavelengths, spectral features can be obscured due to electromagnetic scattering. In this study, we first investigate this granular scattering effect in identification of chemicals with THz spectral absorption features. We then will propose a signal processing technique in the so-called "quefrency" domain to improve the ability to resolve these spectral features in the diffuse scattered THz images. We created a pellet with α-lactose monohydrate and riboflavin, two biologically significant materials with well-known vibrational spectral resonances, and buried the pellet in a highly scattering medium. THz transmission measurements were taken at all angles covering the half focal plane. We show that, while spectral features of lactose and riboflavin cannot be distinguished in the scattered image, application of cepstrum filtering can mitigate these scattering effects. By employing our quefrency-domain signal processing technique, we were able to unambiguously detect the dielectric resonance of lactose in the diffused scattering geometries. Finally we will discuss the limitation of the new proposed technique in spectral identification of chemicals.

We have designed and fabricated a terahertz full-polarimetry instrument, based on control of terahertz polarization in a gas-plasma source, and fast measurement of polarization direction and chirality of the terahertz field in the time-domain without using any external polarizers. We will present details on this new experimental technique including synchronization and calibration of the measurement apparatus against wire-grid polarizers, and derivation of the Jones matrix representation of the propagation optics. The new terahertz time-domain polarimetry (THz-TDP) system extends the polarimetry frequency range to the full bandwidth of gas-plasma sources, and offers accuracy of approximately 1 degrees.

Previously, it has been shown that scattering of terahertz waves by surface roughness of a target can alter the terahertz absorption spectrum and thus obscure the detection of some chemicals in both transmission and reflection geometries. In this paper it is demonstrated that by employing Maximal Overlap Discrete Wavelet Transform (MODWT) coefficients, wavelet-based methods can be used to retrieve spectroscopic information from a broadband terahertz signal reflected from a rough surface target. It is concluded that while the commonly used direct frequency domain deconvolution method fails to accurately characterize and detect the resonance in the dielectric constant of rough surface lactose pellets, wavelet techniques were able to successfully identify such features.

The existence of unique absorption spectrum patterns for many chemicals at terahertz frequencies has opened an exciting avenue in non-contact safe detection of such materials by terahertz spectroscopy. However, scattering of THz waves, which have wavelengths on the order of material grain sizes, by surface roughness challenges the sensitivity of this detection scheme in practice. In this work, we present terahertz time domain spectroscopy results for materials with rough surfaces. Both reflection from and transmission through lactose, which has sharp absorption peaks in the terahertz regime, are studied and the effect of increasing scattering through controlled surface roughness is investigated. Such electromagnetic scattering can alter the terahertz absorption spectrum and thus obscure the detection of chemicals. Furthermore we examine electro-optic detection of terahertz signals reflected from randomly rough targets with a theoretical electromagnetic system perspective and provide a method to retrieve coherent reflection responses from rough surface targets.