Double-sided phase correction

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. 

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... 

When is transposed from one side to the other of Eq. 4.33, only the real terms are retained from the trigonometric expansion because the tme and amplitude spectra are real functions. Equation 4.34 represents a phase correction algorithm for double-sided interferograms. 

Phase correction may not always be possible. As stated above, the phase-angle spectrum is defined only where a signal exceeds the noise, which may not be the case for discrete emission spectra. In this instance, a double-sided interferogram must be collected and the magnitude spectrum computed. Discrete emission spectra are not commonly encountered in infrared spectrometry but occur in the ultraviolet-visible region for atomic emission spectrometry. 

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