Transmission interferogram

The next class of VCD instruments to be developed was centered around a Fourier transform infrared (FT-IR) spectrometer. The idea was to design the sample compartment to be the same as in a dispersive VCD instrument, including a photoelastic modulator. To measure VCD, the detector signal is first sent to a lock-in amplifier to demodulate the high-frequency polarization modulation. The output of the lock-in is a VCD interferogram which is Fourier transformed in much the same way as the ordinary transmission interferogram. 

Transmission infrared spectra of species adsorbed on the catalyst were taken with a Digilab FTS-10M Fourier-transform infrared spectrometer, using a resolution of 4 cm-l. To improve the signal-to-noise ratio, between 10 and 100 interferograms were co-added. Spectra of the catalyst taken following reduction in H2 were subtracted from spectra taken in the presence of NO to eliminate the spectrum of the support. Because of the very short optical path through the gas in the reactor and the low NO partial pressures used in these studies, the spectrum of gas-phase NO was extremely weak and did not interfere with the observation of the spectrum of adsorbed species. 

FT Spectrometers FT spectrometers (Figure 3) differ from scanning spectrometers by the fact that the recorded signal is an interferogram [14] (see Chapter 6.2). They can be coupled to a microscope or macrochamber with an FPA detector. FT chemical imaging systems (CISs) are available for Raman, NIR, and IR spectroscopy. However, they can only be considered as research instruments. For example, most IR imaging systems are FT spectrometers coupled to microscopes. This type of spectrometer allows the acquisition of spectra in reflection, attenuated total reflection (ATR), or transmission mode. 

Figure 20-29 Fourier transform infrared spectrum of polystyrene film. The Fourier transform of the background interferogram gives a spectrum determined by the source intensity, beamsplitter efficiency, detector response, and absorption by traces of H20 and C02 in the atmosphere. The sample compartment is purged with dry N2 to reduce the levels of H20 and C02. The transform of the sample interferogram is a measure of all the instrumental factors, plus absorption by the sample. The transmission spectrum is obtained by dividing the sample transform by the background transform.

If the detector signal bypasses the lock-in and is Fourier transformed directly, the ordinary transmission is obtained. Since there are two interferograms generated simultaneously by the instrument, this general approach to measurements with a FT-IR spectrometer is called double modulation [5,6,11]. The concept of carrying... 

Fig. 26. Transmission and reflection study with a Fourier spectrometer, a) background spectrum and interferogram b) sample spectrum and interferogram c) ratio of both spectra (reflectivity of CdCr2Sc4 in this example). —These data were obtained with a Beckman-RIIC Fourier spectrometer FS 720 with a Fourier transform computer FTC 300 attached to it...

The grand maximum of the sample interferogram is sliifted to higher wave numbers than the background interferogram (Fig. 33). If the reflectivity R of the sample is small and if the absorption coefficient x is small compared to the refractive index n, the magnitude and the phase of the transmission coefficient may be approximated by... 

Fig. 33. Transmission (a) and reflection measurements (b) by means of asymmetric Fourier transform spectroscopy. The samples are polyethylene (PET) and mylar (transmission), and KBr (reflection). The difierent curves show background and sample interferograms as well as power transmittance (reflectance) and phase angle spectra. Data taken from Ref. 59)...

Eq. (4.19) simply shows the basic relationship and the influence of flnite interferogram, apodization, and digitizing is not considered in detail. We recall that 7o( ) is the background intensity already determined, and the essential results of the Fourier transform are T v) and from which both optical constants can be evaluated. In other words, the complex amplitude transmission coefficient... 

In the case of reflection measurements, the sample replaces one of the mirrors in the Michelson interferometer (see Fig. 32). The reference mirror is assumed to be 100% reflecting in the far-infrared, and in the sample interferogram the power reflectance R of the sample and the phase shift y> at the reflection (usually n for nonabsorbing media with w > 1) take over the role of T and q> in transmission measurements. The interferogram obtained in this case is also somewhat shifted and as3nmnetiic (see Fig. 33, KBr sample). By means of the cosine and sine Fourier transforms, R and y>, and finally n and x, are evaluated from the experimental data. 

It can be shown that the detector D, which measures the intensity of interference as a function of M3 mirrors position (so depending on the optical path difference 5 between the two routes) records an interferogram which depends on inverse Fourier transform of emission spectrum of the source LS and on inverse Fourier transform of transparency (transmission) spectrum of the sample S (sample). After Fourier transform of detector D signal and some additional mathematical operations on detector signal the transmission (or optional absorption spectrum) spectrum of the sample S in known form is obtained. 

The mathematical procedure, which is employed to convert the IR interferogram (intensity versus time, also called time domain) to an IR spectrum (intensity versus frequency, also called frequency domain), is called Fourier transformation. Sample and reference interferograms are separately transformed. Afterwards, the ratio of both is automatically calculated and displayed as instrument-independent IR transmission spectrum (Fig. 4.3). 

The essential steps for obtaining an FT-IR spectrum are to produce an interferogram with and without a sample in the beam and then transform these interferograms into spectra of the source with sample absorption and the source without sample absorption (see for instance MIR files GLYCIN, WATER, and VASELINE). The ratio of the former and the latter is the IR transmission spectrum of the sample. 

Fig. 2.6 Forman phase correction method. The real and imaginary part of the spectrum corresponding to the transmission of the atmosphere from 0 to 42 cm has been distorted (top-left) with a linear phase error (top-right). The measured interferogram is not symmetric anymore (centre-left). After extracting the convolution kernel (centre-right) and applying the correction method 5 times, the interferogram symmetry is improved (bottom-left). Fourier transforming the corrected interferogram, the spectrum is recovered (bottom-right) and is real...

The thermal system includes the Warm Optics Module and the Cold Optics Module, which given the optical set-up and the optical parameters of the different optical elements calculates the transmission of the sky map through the instmment. At this point the physical properties of the instrument are defined and the Double Fourier Modulation can be performed at the Double Fourier Module. Here is where the interferograms are computed analytically for different baseline positions. If pointing errors are selected, the Pointing Errors Module generates them and they are fed to the Double Fourier Moduie. 

In photoacoustic spectroscopy, signal amplitude increases only when absorption occurs. Thus, photoacoustic spectra will be absorption spectra as opposed to FTIR spectra which are transmission spectra. FTPAS interferograms should then show modulation at high values of retardation as well as near zero retardation. This comes about as a consequence of the properties of Fourier transforms which cause very broad general feature information to be collected at low retardation, with narrow and sharp features ("high frequency") to be collected at higher retardation. 

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