Complex Insertion Loss Research Articles

Classification of THz pulse signals using two-dimensional cross-correlation feature extraction and non-linear classifiers

This work provides a performance comparison of four different machine learning classifiers: multinomial logistic regression with ridge estimators (MLR) classifier, k-nearest neighbours (KNN), support vector machine (SVM) and naïve Bayes (NB) as applied to terahertz (THz) transient time domain sequences associated with pixelated images of different powder samples. The six substances considered, although have similar optical properties, their complex insertion loss at the THz part of the spectrum is significantly different because of differences in both their frequency dependent THz extinction coefficient as well as differences in their refractive index and scattering properties. As scattering can be unquantifiable in many spectroscopic experiments, classification solely on differences in complex insertion loss can be inconclusive. The problem is addressed using two-dimensional (2-D) cross-correlations between background and sample interferograms, these ensure good noise suppression of the datasets and provide a range of statistical features that are subsequently used as inputs to the above classifiers. A cross-validation procedure is adopted to assess the performance of the classifiers. Firstly the measurements related to samples that had thicknesses of 2mm were classified, then samples at thicknesses of 4mm, and after that 3mm were classified and the success rate and consistency of each classifier was recorded. In addition, mixtures having thicknesses of 2 and 4mm as well as mixtures of 2, 3 and 4mm were presented simultaneously to all classifiers. This approach provided further cross-validation of the classification consistency of each algorithm. The results confirm the superiority in classification accuracy and robustness of the MLR (least accuracy 88.24%) and KNN (least accuracy 90.19%) algorithms which consistently outperformed the SVM (least accuracy 74.51%) and NB (least accuracy 56.86%) classifiers for the same number of feature vectors across all studies. The work establishes a general methodology for assessing the performance of other hyperspectral dataset classifiers on the basis of 2-D cross-correlations in far-infrared spectroscopy or other parts of the electromagnetic spectrum. It also advances the wider proliferation of automated THz imaging systems across new application areas e.g., biomedical imaging, industrial processing and quality control where interpretation of hyperspectral images is still under development.

Optimal discrimination and classification of THz spectra in the wavelet domain

In rapid scan Fourier transform spectrometry, we show that the noise in the wavelet coefficients resulting from the filter bank decomposition of the complex insertion loss function is linearly related to the noise power in the sample interferogram by a noise amplification factor. By maximizing an objective function composed of the power of the wavelet coefficients divided by the noise amplification factor, optimal feature extraction in the wavelet domain is performed. The performance of a classifier based on the output of a filter bank is shown to be considerably better than that of an Euclidean distance classifier in the original spectral domain. An optimization procedure results in a further improvement of the wavelet classifier. The procedure is suitable for enhancing the contrast or classifying spectra acquired by either continuous wave or THz transient spectrometers as well as for increasing the dynamic range of THz imaging systems.

The effect of detector port radiation on the determination of insertion loss by Fourier transform spectrometry

It is demonstrated that the identification of the measured power insertion loss of a specimen with the power transmission or reflection of that specimen in conventional Fourier transform spectrometry using internal modulation is susceptible to systematic error. The error arises from the presence of radiation from the detector port of the interferometer in its interferometrically modulated output, and is particularly significant at millimetre and long submillimetre wavelengths and when the specimen temperature differs from that of the interferometer. It is shown that such an error is not present in the determination of complex insertion loss by dispersive Fourier transform spectrometry owing to the greater symmetry of the experimental configuration with respect to the various radiation fluxes passing through the interferometer. The effect is demonstrated by the results of transmission measurements on specimens of the polymers polystyrene and TPX.

Submillimetre wave measurements of optical constants of water at various temperatures

A polarization interferometer employing free standing wire grid polarizer and beamsplitter and reflection dispersive Fourier transform spectrometry are used to determine the optical constants of water in the region 5–220cm −1. The liquid cell uses a single crystal semiconductor or quartz window. The complex evaluation method first determines the optical constants of the window material and then takes into account all the interface contributions in terms of ‘complex insertion loss’ formalism and thus determines the precise values of optical constants of liquids. Power absorption coefficient and refractive index data of hyperpure silicon, and power absorption coefficient, refractive index and real and imaginary parts of complex relative permittivity data of liquid water at 4. 30 and 57°C are presented and discussed.

Interface effects in fourier transform spectrometry

Attention is drawn both to the details of the contributions to the msasured transmission of a plane-parallel solid or liquid specimen arising from reflection effects at the boundaries of the medium and to the errors resulting from neglect of these contributions. Typical values for commonly encountered infrared materials are given and curves are presented which enable incorrect literature values of the power absorption coefficient to be corrected. The large magnitude of the effects is emphasised. A similar account is given for dispersive Fourier transform spectrometry with particular emphasis on the phase corrections. Bell's account for a solid specimen is extended to the case of a liquid. The use of complex insertion loss aids both discussions.