Terahertz time-domain spectroscopyIn physics, terahertz time-domain spectroscopy (THz-TDS) is a spectroscopic technique in which the properties of matter are probed with short pulses of terahertz radiation. The generation and detection scheme is sensitive to the sample's effect on both the amplitude and the phase of the terahertz radiation. Typically, an ultrashort pulsed laser is used in the terahertz pulse generation process. In the use of low-temperature grown GaAs as an antenna, the ultrashort pulse creates charge carriers that are accelerated to create the terahertz pulse.
Reduced chi-squared statisticIn statistics, the reduced chi-square statistic is used extensively in goodness of fit testing. It is also known as mean squared weighted deviation (MSWD) in isotopic dating and variance of unit weight in the context of weighted least squares. Its square root is called regression standard error, standard error of the regression, or standard error of the equation (see ) It is defined as chi-square per degree of freedom: where the chi-squared is a weighted sum of squared deviations: with inputs: variance , observations O, and calculated data C.
Optical coherence tomographyOptical coherence tomography (OCT) is an imaging technique that uses low-coherence light to capture micrometer-resolution, two- and three-dimensional images from within optical scattering media (e.g., biological tissue). It is used for medical imaging and industrial nondestructive testing (NDT). Optical coherence tomography is based on low-coherence interferometry, typically employing near-infrared light. The use of relatively long wavelength light allows it to penetrate into the scattering medium.
Least squaresThe method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value provided by a model) made in the results of each individual equation. The most important application is in data fitting.
Residual sum of squaresIn statistics, the residual sum of squares (RSS), also known as the sum of squared residuals (SSR) or the sum of squared estimate of errors (SSE), is the sum of the squares of residuals (deviations predicted from actual empirical values of data). It is a measure of the discrepancy between the data and an estimation model, such as a linear regression. A small RSS indicates a tight fit of the model to the data. It is used as an optimality criterion in parameter selection and model selection.
Infrared spectroscopyInfrared spectroscopy (IR spectroscopy or vibrational spectroscopy) is the measurement of the interaction of infrared radiation with matter by absorption, emission, or reflection. It is used to study and identify chemical substances or functional groups in solid, liquid, or gaseous forms. It can be used to characterize new materials or identify and verify known and unknown samples. The method or technique of infrared spectroscopy is conducted with an instrument called an infrared spectrometer (or spectrophotometer) which produces an infrared spectrum.
Emission spectrumThe emission spectrum of a chemical element or chemical compound is the spectrum of frequencies of electromagnetic radiation emitted due to an electron making a transition from a high energy state to a lower energy state. The photon energy of the emitted photon is equal to the energy difference between the two states. There are many possible electron transitions for each atom, and each transition has a specific energy difference. This collection of different transitions, leading to different radiated wavelengths, make up an emission spectrum.
Sphere packingIn geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, and the space is usually three-dimensional Euclidean space. However, sphere packing problems can be generalised to consider unequal spheres, spaces of other dimensions (where the problem becomes circle packing in two dimensions, or hypersphere packing in higher dimensions) or to non-Euclidean spaces such as hyperbolic space.
Biological organisationBiological organisation is the organisation of complex biological structures and systems that define life using a reductionistic approach. The traditional hierarchy, as detailed below, extends from atoms to biospheres. The higher levels of this scheme are often referred to as an ecological organisation concept, or as the field, hierarchical ecology. Each level in the hierarchy represents an increase in organisational complexity, with each "object" being primarily composed of the previous level's basic unit.
Complex geometryIn mathematics, complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers. In particular, complex geometry is concerned with the study of spaces such as complex manifolds and complex algebraic varieties, functions of several complex variables, and holomorphic constructions such as holomorphic vector bundles and coherent sheaves. Application of transcendental methods to algebraic geometry falls in this category, together with more geometric aspects of complex analysis.
