Figure 2.1 Schematic diagram of Michelson interferometer used in FTIR spectrometer [24]. For a monochromatic source, the interferogram can be denoted by a cosine wave [25]. Intensity of interferogram is a function of retardation and is defined as shown in Equation δ 2.1 below. (2.1) I0 [1+cos(2 π δ υ)] is the intensity of interferogram at zero retardation and is the wavenumber (cm-1) I0 υ and equal to 1/λ, where is the wavelength of the light. λ In most of the FTIR spectrometers, a sample is placed before the detector and a broadband source is used to collect the raw spectrum of the sample. For a polychromatic or a broadband continuous light source, equation 2.1 can be extended to I ( dυ (2.2) = cos (2 υ) π δ υ) The location where and all the light frequencies interfere constructively is known as the point of Zero Path Difference (ZPD). As a result, interferogram has maximum intensity at the point of ZPD and is also termed as centerburst. From Equation 2.2, it is apparent that the sample spectrum is the Fourier transform of B(υ) the intensity of interferogram. (υ) dδ (2.3) B = cos (2 δ) π δ υ) As is symmetric at Zero Path Difference, Equation 2.3 can be rewritten as shown below. δ) (υ) dδ (2.4) = B δ) cos (2 π δ υ) In Equation 2.4, integration is performed with respect to and the maximum of value of it is δ chosen by the moving range of movable mirror used in the FTIR spectrometer.
Figure 2.1 Schematic diagram of Michelson interferometer used in FTIR spectrometer [24]. For a monochromatic source, the interferogram can be denoted by a cosine wave [25]. Intensity of interferogram is a function of retardation δ and is defined as shown in Equation 2.1 below. I0 [1+cos(2 π δ υ)] (2.1) I0 is the intensity of interferogram at zero retardation and υ is the wavenumber (cm-1) and equal to 1/λ, where λ is the wavelength of the light. In most of the FTIR spectrometers, a sample is placed before the detector and a broadband source is used to collect the raw spectrum of the sample. For a polychromatic or a broadband continuous light source, equation 2.1 can be extended to I ( = υ) cos (2 π δ υ) dυ (2.2) The location where and all the light frequencies interfere constructively is known as the point of Zero Path Difference (ZPD). As a result, interferogram has maximum intensity at the point of ZPD and is also termed as centerburst. From Equation 2.2, it is apparent that the sample spectrum B(υ) is the Fourier transform of the intensity of interferogram. B (υ) = δ) cos (2 π δ υ) dδ (2.3) As δ) is symmetric at Zero Path Difference, Equation 2.3 can be rewritten as shown below. B (υ) = δ) cos (2 π δ υ) dδ (2.4) In Equation 2.4, integration is performed with respect to δ and the maximum of value of it is chosen by the moving range of movable mirror used in the FTIR spectrometer.
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