In the sciences and engineering, the process of decomposing a function into oscillatory components is often called Fourier analysis, while the operation of rebuilding the function from these pieces is known as Fourier synthesis. The subject of Fourier analysis encompasses a vast spectrum of mathematics. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer. In mathematics, Fourier analysis ( / ˈ f ʊr i eɪ, - i ər/) is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis reveals the oscillatory components of signals and functions. The spectrum of the sample is actually encoded into this interferogram.īased on the previous discussion, it is predictable that, without further translation, the raw data collected on a Fourier transform spectrometer will be quite difficult to read.Fourier transform of bass guitar time signal of open string A note (55 Hz). The raw data is actually the intensity of the interfering wave versus the optical path difference (also called Interferogram). So instead of obtaining a scan spectrum directly, raw data recorded by the detector in a Fourier transform spectrometer is less intuitive to reveal the property of the sample. If the beam is modified for each new data point by scanning the moving mirror along the axis of the moving arm, a series of intensity versus each optical path length difference are collected. Then by changing the position of the moving mirror, a different optical path difference is modified and the detector can measure another intensity of the total beam as the second data point. Rather than allowing only one wavelength to pass through the sample at a time, an interferometer can let through a beam with the whole wavelength range at once, and measure the intensity of the total beam at that optical path difference. To collect the full spectrum over a wide wavelength range, monochromator needs to vary the wavelength setting every time. Then measuring the intensity of a monochromic light with that particular wavelength becomes practical. It can block off all other wavelengths except for a certain wavelength of interest. With a Fourier transform spectrometer equipped with an interferometer, we can easily vary the parameter in time domain or spatial domain by changing the position of the movable mirror.īut how data are collected by a Fourier transform spectrometer? A quick comparison between a conventional spectrometer and a Fourier transform Spectrometer may help to find the answer. If they differ by a whole number and a half of wavelengths, destructive interference will cancel the intensity of the signal. If these two paths differ by a whole number of wavelengths, the resulting constructive interference will give a strong signal at the detector. Manipulating the difference between these two paths of light is the core of Michelson interferometer. After being reflected back, the two beams meet at the half-silvered mirror and recombine to produce an interference pattern, which is later detected by the detector. Scheme for Michelson interferometer (a) Stationary version (b) Movable version Īs shown in Figure 1.b, when a parallel beam of coherent light hits a half-silvered mirror, it is divided into two beams of equal intensities by partial reflection and transmission. Different from the classical Michelson interferometer with two fixed mirrors ( Figure 1.a), the interferometer used in Fourier transform spectrometer has a moving mirror at one arm ( Figure 1.b).įigure 1. In the experimental set-up, a Michelson interferometer is commonly used to solve this problem. How to introduce a time-domain or space-domain variable in the spectrometer is the primary question that needed to be addressed when we consider constructing a Fourier transform spectrometer. Interferometer-What it is used for and how it works? In this way, we can measure the properties of the electromagnetic wave in both conventional frequency domain and somehow more robust time domain. Regarding this case, we can use the term to transform between two variables in this pair, namely time and frequency.
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