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The method of Fourier-transform spectroscopy can also be used for absorption spectroscopy. The primary example is " FTIR Spectroscopy ", a common technique in chemistry. In general, the goal of absorption spectroscopy is to measure how well a sample absorbs or transmits light at each different wavelength.
The result of Fourier transformation is a spectrum of the signal at a series of discrete wavelengths. The range of wavelengths that can be used in the calculation is limited by the separation of the data points in the interferogram. The shortest wavelength that can be recognized is twice the separation between these data points.
The Fourier series is an example of a trigonometric series. [2] By expressing a function as a sum of sines and cosines, many problems involving the function become easier to analyze because trigonometric functions are well understood. For example, Fourier series were first used by Joseph Fourier to find solutions to the heat equation. This ...
The measured spectra are used to determine the chemical composition and physical properties of astronomical objects (such as their temperature, density of elements in a star, velocity, black holes and more). [12] An important use for spectroscopy is in biochemistry. Molecular samples may be analyzed for species identification and energy content ...
A number of authors, notably Jean le Rond d'Alembert, and Carl Friedrich Gauss used trigonometric series to study the heat equation, [20] but the breakthrough development was the 1807 paper Mémoire sur la propagation de la chaleur dans les corps solides by Joseph Fourier, whose crucial insight was to model all functions by trigonometric series ...
An Elementary Treatise on Fourier's Series: And Spherical, Cylindrical, and Ellipsoidal Harmonics, with Applications to Problems in Mathematical Physics (2 ed.). Ginn. p. 30. Carslaw, Horatio Scott (1921). "Chapter 7: Fourier's Series". Introduction to the Theory of Fourier's Series and Integrals, Volume 1 (2 ed.). Macmillan and Company. p. 196.
Fourier transform, the type of linear canonical transform that is the generalization of the Fourier series; Fourier operator, the kernel of the Fredholm integral of the first kind that defines the continuous Fourier transform; Fourier inversion theorem, any one of several theorems by which Fourier inversion recovers a function from its Fourier ...
The spectra are plotted in units of log inverse reflectance (log 1/R) versus wavenumber. Alternative plots of Kubelka-Munk units can be used, which relate reflectance to concentration using a scaling factor. A reflectance standard is needed in order to quantify the reflectance of the sample because it cannot be determined directly. [2] [3]