Characterization of coated optical fibers by Fourier-domain optical coherence tomography

The application of Fourier Transform properties in radio broadcasting is multifaceted, enabling significant advancements in the way signals are transmitted and received. Key areas where these properties are utilized include simultaneous multi-channel transmission, audio clip speed adjustments, live broadcast delays for different time zones, audio frequency adjustments, and signal demodulation.
In radio broadcasting, multiple audio signals often need to be transmitted simultaneously. The Fourier...

The Fourier Transform (FT) is an essential mathematical tool in signal processing, transforming a time-domain signal into its frequency-domain representation. This transformation elucidates the relationship between time and frequency domains through several properties, each revealing unique aspects of signal behavior.
The Frequency Shifting property of Fourier Transforms highlights that a shift in the frequency domain corresponds to a phase shift in the time domain. Mathematically, if x(t) has...

Tomography refers to imaging by sections. Computed tomography (CT) is a non-invasive imaging technique that uses computers to analyze several cross-sectional X-rays to reveal minute details about structures in the body.
The technique was invented in the 1970s and is based on the principle that as X-rays pass through the body, they are absorbed or reflected at different levels. In the technique, a patient lies on a motorized platform while a computerized axial tomography (CAT) scanner rotates...

Atomic force microscopy (AFM) is a type of scanning probe microscopy that can analyze topographic details of various specimens like ceramics, glass, polymers, and biological samples. AFM offers over 1000 times more resolution than the optical imaging system. Images generated from AFM are three-dimensional surface profiles, offering an advantage over the flat, two-dimensional images from other imaging techniques.
The AFM Probe
The probe is regarded as the heart of any AFM setup and comprises the...

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...

The Fourier series is instrumental in representing periodic functions, offering a powerful method to decompose such functions into a sum of sinusoids. This technique, however, necessitates modification when applied to nonperiodic functions. Consider a pulse-train waveform consisting of a series of rectangular pulses. When these pulses have a finite period, they can be accurately represented by a Fourier series. Yet, as the period approaches infinity, resulting in a single, isolated pulse, the...