Attenuated total reflectance (ATR) infrared spectroscopy is a powerful analytical technique used to study the composition of materials. It is widely employed in chemistry, materials science, forensic science, and other fields where sample characterization is required. ATR has several advantages over traditional transmission IR spectroscopy, including the requirement of little to no sample preparation and the ability to analyze a wide range of samples.
The ATR process begins by directing a beam...

Atomic absorption spectroscopy (AAS) is a technique used to analyze elements by measuring electromagnetic radiation (EMR) absorbed by atoms, which causes them to transition to a higher-energy orbit. The most crucial step in AAS is atomization, where the analyte is converted into gas-phase atoms, typically through a flame or furnace. Some of these atoms become thermally excited in the flame, while most remain in the ground state.
When irradiated by EMR of a particular wavelength, these...

Atomic absorption spectroscopy (AAS) relies on the Beer-Lambert law, which requires that the radiation source emits a narrow range of wavelengths to match the absorption characteristics of the analyte atom. The primary criteria for choosing an appropriate radiation source in AAS is to provide a precise and intense emission at specific wavelengths that will allow accurate detection of the analyte.
Two common narrow-range 'line' sources used in AAS are hollow-cathode lamps (HCLs) and...

Atomic fluorescence spectroscopy (AFS) is an analytical technique that involves the electronic transitions of atoms in a flame, furnace, or plasma being excited by electromagnetic (EM) radiation. When these atoms absorb energy, they become excited and subsequently release energy as they return to their original state. This emitted light, or "fluorescence," is observed at a right angle to the incident beam. Both absorption and emission processes transpire at distinct wavelengths, which are...

The Fourier series is a powerful mathematical tool for representing periodic signals as an infinite sum of complex exponentials. In practice, this infinite series is truncated to a finite number of terms, yielding a partial sum. This truncation makes the approximation of the signal feasible but introduces certain challenges, particularly near discontinuities, known as the Gibbs phenomenon.
The Gibbs phenomenon refers to the persistent oscillations and overshoots that occur near discontinuities...

The Fast Fourier Transform (FFT) is a computational algorithm designed to compute the Discrete Fourier Transform (DFT) efficiently. By breaking down the calculations into smaller, manageable sections, the FFT significantly reduces the computational complexity involved. Direct computation of an N-point DFT requires N2 complex multiplications, whereas the FFT algorithm needs only (N/2)log⁡2N multiplications, offering a much faster performance.
The computational efficiency of the FFT becomes...