Extending Murty interferometry to the Terahertz part of the spectrum

We discuss some novel technologies that enable the implementation of shearing interferometry at the terahertz part of the spectrum. Possible applications include the direct measurement of lens parameters, the measurement of refractive index of materials that are transparent to terahertz frequencies, determination of homogeneity of samples, measurement of optical distortions and the non-contact evaluation of thermal expansion coefficient of materials buried inside media that are opaque to optical or infrared frequencies but transparent to THz frequencies. The introduction of a shear to a Gaussian free-space propagating terahertz beam in a controlled manner also makes possible a range of new encoding and optical signal processing modalities.

Quantifying user perception of foodstuffs using THz spectrometry

We discuss the potential of using THz spectrometry for the direct observation of phase transitions in foodstuffs, with the aim of quantifying consumer perception. Experimental results from phase transitions using a continuous wave dispersive Fourier transform spectrometer and a cyclotron enhanced liquid helium cooled bolometric detector are reported.

Terahertz pulse investigation of paleolithic wall etchings

Results are presented of an examination of flow rock-covered Paleoloithic cave art using time-domain terahertz reflectometry.

Complex extreme learning machine applications in terahertz pulsed signals feature sets

This paper presents a novel approach to the automatic classification of very large data sets composed of terahertz pulse transient signals, highlighting their potential use in biochemical, biomedical, pharmaceutical and security applications. Two different types of THz spectra are considered in the classification process. Firstly a binary classification study of poly-A and poly-C ribonucleic acid samples is performed. This is then contrasted with a difficult multi-class classification problem of spectra from six different powder samples that although have fairly indistinguishable features in the optical spectrum, they also possess a few discernable spectral features in the terahertz part of the spectrum. Classification is performed using a complex-valued extreme learning machine algorithm that takes into account features in both the amplitude as well as the phase of the recorded spectra. Classification speed and accuracy are contrasted with that achieved using a support vector machine classifier. The study systematically compares the classifier performance achieved after adopting different Gaussian kernels when separating amplitude and phase signatures. The two signatures are presented as feature vectors for both training and testing purposes. The study confirms the utility of complex-valued extreme learning machine algorithms for classification of the very large data sets generated with current terahertz imaging spectrometers. The classifier can take into consideration heterogeneous layers within an object as would be required within a tomographic setting and is sufficiently robust to detect patterns hidden inside noisy terahertz data sets. The proposed study opens up the opportunity for the establishment of complex-valued extreme learning machine algorithms as new chemometric tools that will assist the wider proliferation of terahertz sensing technology for chemical sensing, quality control, security screening and clinic diagnosis. Furthermore, the proposed algorithm should also be very useful in other applications requiring the classification of very large datasets.

Application of complex extreme learning machine to multiclass classification problems with high dimensionality: a THz spectra classification problem

We extend extreme learning machine (ELM) classifiers to complex Reproducing Kernel Hilbert Spaces (RKHS) where the input/output variables as well as the optimization variables are complex-valued. A new family of classifiers, called complex-valued ELM (CELM) suitable for complex-valued multiple-input–multiple-output processing is introduced. In the proposed method, the associated Lagrangian is computed using induced RKHS kernels, adopting a Wirtinger calculus approach formulated as a constrained optimization problem similarly to the conventional ELM classifier formulation. When training the CELM, the Karush–Khun–Tuker (KKT) theorem is used to solve the dual optimization problem that consists of satisfying simultaneously smallest training error as well as smallest norm of output weights criteria. The proposed formulation also addresses aspects of quaternary classification within a Clifford algebra context. For 2D complex-valued inputs, user-defined complex-coupled hyper-planes divide the classifier input space into four partitions. For 3D complex-valued inputs, the formulation generates three pairs of complex-coupled hyper-planes through orthogonal projections. The six hyper-planes then divide the 3D space into eight partitions. It is shown that the CELM problem formulation is equivalent to solving six real-valued ELM tasks, which are induced by projecting the chosen complex kernel across the different user-defined coordinate planes. A classification example of powdered samples on the basis of their terahertz spectral signatures is used to demonstrate the advantages of the CELM classifiers compared to their SVM counterparts. The proposed classifiers retain the advantages of their ELM counterparts, in that they can perform multiclass classification with lower computational complexity than SVM classifiers. Furthermore, because of their ability to perform classification tasks fast, the proposed formulations are of interest to real-time applications.

Image retrieval techniques for THz applications in cultural heritage

Techniques to retrieve reliable images from complicated objects are described, overcoming problems introduced by uneven surfaces, giving enhanced depth resolution and improving image contrast. The techniques are illustrated with application to THz imaging of concealed wall paintings.

Sample-induced beam distortions in terahertz time domain spectroscopy and imaging systems

It is demonstrated that distortion of the terahertz beam profile and generation of a cross-polarised component occur when the beam in terahertz time domain spectroscopy and imaging systems interacts with the sample under test. These distortions modify the detected signal, leading to spectral and image artefacts. The degree of distortion depends on the optical design of the system as well as the properties of the sample.

Pulse shaping using state space algorithms

We discuss the use of pulse shaping for optimal excitation of samples in time-domain THz spectroscopy. Pulse shaping can be performed in a 4f optical system to specifications from state space models of the system's dynamics. Subspace algorithms may be used for the identification of the state space models.

Quantification of boundary definition using pulsed terahertz radiation for wedged geometries

The interaction of a terahertz beam with a sample containing a material boundary across the profile of the terahertz beam produces characteristic spectroscopic detail. A full vectorial model is presented to quantify boundary definition for a series of wedged geometries. As a result of this work, using simple geometric forms, we wish to be able to extend these ideas to characterize boundaries in more irregular samples, impacting most application areas of pulsed terahertz radiation.

Classification of lactose and mandelic acid THz spectra using subspace and wavelet-packet algorithms

This work compares classification results of lactose, mandelic acid and dl-mandelic acid, obtained on the basis of their respective THz transients. The performance of three different pre-processing algorithms applied to the time-domain signatures obtained using a THz-transient spectrometer are contrasted by evaluating the classifier performance. A range of amplitudes of zero-mean white Gaussian noise are used to artificially degrade the signal-to-noise ratio of the time-domain signatures to generate the data sets that are presented to the classifier for both learning and validation purposes. This gradual degradation of interferograms by increasing the noise level is equivalent to performing measurements assuming a reduced integration time. Three signal processing algorithms were adopted for the evaluation of the complex insertion loss function of the samples under study; a) standard evaluation by ratioing the sample with the background spectra, b) a subspace identification algorithm and c) a novel wavelet-packet identification procedure. Within class and between class dispersion metrics are adopted for the three data sets. A discrimination metric evaluates how well the three classes can be distinguished within the frequency range 0. 1 - 1.0 THz using the above algorithms.