Single-sided interferograms

The position of ZPD (Zero Path Difference) is critical to the Fourier Transform calculation, since the algorithm assumes that the central burst in the interferogram is in fact the ZPD. However, due to the refractive index properties of the beamsplitter material, the ZPD is not at the same position for every wavelength measured. There are several ways to overcome these phase differences. The most common method is to use a correction factor, which is known as phase correction. This correction factor is calculated for every wavelength, based on a double sided interferogram, since this tends to minimize the effects of phase difference. In practice, most infrared spectrometers collect single sided interferograms, since this halves the mirror movement, and consequently the number of datapoints to be Fourier transformed. 

Figure 1.11 Synchronisation between the collection of FTIR spectra and the potential applied to the working electrode during potential modulation techniques. It is assumed that single-sided interferograms are collected during the forward sweep of the moving mirror (ZPD = zero path difference for the two paths of the interferometer).

Fig. 40. Phase errors a) linear phase error b) nonlinear phase error. — Interferograms /(s) and spectra I v) obtained from a single-sided interferogram (—) and from a double sided one (----- cos transform,------- sine transform). —The dotted line (.. . ) indicates the undis-...

As limited by the maximum number of data points (single scan, sample and background, widest spectral range, single-sided interferogram). Analogue computer. 

For single-sided interferograms a minimum factor of 2 is required. For doublesided interferograms, the zerofilling factor can be halved in comparison to single-sided collections. 

Fig. 39 a-d. Intensity errors a) Spectrumwrong by a constant factor b) Spectrum I (v) and in-terferogram J s) when /( >) is determined incorrectly c) Interferogram I(s) with linear drift of the mean value /(oo) and the spectra obtained from the single-sided (-—) and the double-sided... 

In other words, the correction of a phase error 95 requires a short double-sided interferogram around s = 0 regardless whether the whole interferogram is recorded single-sided or double-sided. The mostly used correction method was first proposed by M. Forman 68.70>, After determining tp v), the next step of this method is to calculate what can be called the Fourier transform of... 

The interferogram is measured on both sides. Data are acquired during the forward movement of the mirror. This mode yields an improvement in the signal-to-noise ratio as compared to the Single Sided mode. The resolution in time however amounts to half the value achieved in Single Sided mode. 

If there are N points in the interferogram, let us consider how many operations are required during the computation of a single-sided cosine transform. For each spectral point Vj, we perform N multiplications for Sa k)coslnvjkh. To add the values, we must do TV — 1 additions, so that a total of 2N operations is needed for each wavenumber Vj. To examine the complete spectrum, we must compute the spectrum at TV wavenumber values at least Thus, a total of approximately operations are needed for the conventional Fourier transform, not counting the time required to compute the cosine value. 

For D d, the envelope function is determined by the diffraction at the single slits. The width of the interferogram B is defined by the distance of the two first order minima on each side of the maximum as... 

As shown in Fig. 3.9, Aop increases as the baseUne increases. On the other side, as the forward modelling combines two single interferograms separated by a distance d, the optical path difference between the rays on each antenna can be extracted from the relative shift r between interferograms as... 

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