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The Interferogram to Spectrum command converts an interferogram into a spectrum and performs the same operations which immediately run after AQP data acquisition:

Apodization

Phase computation

Zerofilling

Fourier Transformation of the interferogram

Phase correction

This allows to repeat spectra calculation after measurement, using different parameter settings for apodization, zerofilling and phase correction.

The original data files have to be interferograms. You specify these data files on the Select Files tab. The frequency range of these files has to be between the upper and lower folding limit parameters used during measurement.

In addition to the spectrum calculated, which is always a single-channel spectrum, you can also save the phase and power spectrum on the Store tab. The latter two spectra are calculated by the double-sided known part of the interferogram, using the phase resolution setting.

Use the Apodization tab to select the apodization function and zerofilling factor. Due to the finite mirror travel, the interferogram is only recorded up to a certain point (i.e. a finite resolution). This leads to artificial side lobes on spectral lines which natural width is smaller than or comparable with the measured resolution. These side lobes can be suppressed, however at the expense of line broadening, by multiplying the interferogram by means of an apodization function.

A detailed description of the apodization function would go beyond the scope of this manual. In case of standard measurements in liquid or solid phases the Blackman-Harris-3-term is recommended. To obtain the highest resolution, you either select no (Boxcar) or at best a weak apodization function (Norton-Beer, Weak).

Zerofilling means adding zeros to both ends of the interferogram before performing Fourier transformation. This increases the number of data points in the spectrum, which is equivalent to an interpolation. The number of data points can be increased by zerofilling using the factors selected (e.g. 2, 4, 8,..., 512).

In case of a zerofilling factor of 1 zeros are added up to the next power of 2. If the number of data points has already been a power of 2, no zeros will be added.

Single-sided interferograms require a minimum zerofilling factor of 2. In case of double-sided interferograms, the zerofilling factor can be halved in comparison to single-sided interferograms. By increasing the number of data points in the spectrum the depiction improves by sharper lines (a mere cosmetic effect). However, an n-fold zerofilling requires an n-fold computing time and n-fold storage space (depending on the computing method).

Select the Limit Data tab to define the resolution.

If you activate the Limit resolution to check box, you can vary the resolution by entering a value which is greater than or at least equal to the value used during measurement. In this case only a fraction of the measured interferogram is used for computation.

In the Phase resolution group field you specify how precise the phase has to be determined. Generally, you should enter the same value as being used for the measurement. The value is limited by the length of the double-sided part of interferogram.

In case of interferograms recorded in forward/backward mode you can specify which direction(s) of mirror travel have to be evaluated during transformation. If both mirror travels should be evaluated, the forward and backward scans will be transformed separately, phase corrected and averaged.

If data have been recorded in multiplex mode, the interferogram contains alternating data from two analog-to-digital converters (ADCs). The Even and Odd option allow the data from both ADCs to be evaluated separately. There is no such option in case of backward scans. Therefore, record multiplex measurements only by using the Forward mode.

If you activate the Even option button, the intensity values I0, I2 ... of the first ADC will be transformed. If you activate the Odd option button, the intensity values I1, I3 ... of the second ADC will be transformed.

The phase correction can be compared with an interferogram symmetrizing, which is always necessary due to the asymmetry of any measured interferogram. Click on the Phase Correction tab.

Several phase correction modes are available:

Mertz: this is the standard procedure for phase correction.

Mertz Signed: modified Mertz function which is used if the single- channel spectrum is expected to contain negative contributions.

Power Spectrum: this can be used instead of Mertz or Foreman, but only for double-sided interferograms, if the spectrum includes wide ranges of low light intensity (total absorption, Raman, emission). Disadvantage: up to ÷2 more noise compared with Mertz or Forman.

Mertz/Stored Phase: like Mertz, whereas the phase is not re-calculated but based on previously existing data which have been calculated by using the regular Mertz method. This method can be useful, if the single-channel spectrum includes less-defined ranges (i.e. an undefined phase), which frequently occurs in case of emission measurements. Furthermore, it can also be useful if the spectra are expected to contain negative contributions. In this case, the phase stored should derive from a spectrum with absolute positive values.

No/Save Complex Data: the data will not be phase-corrected but Fourier-transformed in complex form and stored as real and imaginary parts.

Forman: a method mathematically equivalent to Mertz, offers a slightly higher precision which requires, however, higher a computational period.

In a single-channel spectrum there should be no signal below the absorption edge of the detector. The non-linear detector response causes the signal to be non-zero below this edge. The non-linearity of the detector can be calculated from the ratio of the intensity of these artifacts and the total energy flow in the detector. As soon as the non-linearity is known a corrected spectrum can be calculated showing less artifacts. As a rule, the interferograms stored will not be modified. The non-linearity correction only effects the spectra.

To ensure a successful non-linearity correction the following conditions have to be fulfilled:

The spectrum must be recorded from 0cm-1 up to the maximum wavenumber at which the detector can send a signal.

Electronic filters must not be used. Spectra have to undergo a broad-band recording to avoid aliasing.

The Phase resolution FT parameter should be set to result in at least 500 phase interferogram points. Too low a phase resolution results in an inaccurate non-linearity correction.

After phase correction the non-linearity correction coefficients are calculated, using all the data points of the single-channel spectrum.

The modulation efficiency causes an additional multiplicative correction of the entire spectrum. It can be set either to the correct value (typically between 0.7 and 1.0), or to 1.0 if the correct value is unknown. If you use a preamplifier which reverses the signal polarity, the value of the detection limit has to be multiplied by -1.

Use the Peak Search tab to select the position of the zero path difference (ZPD):

Absolute largest value searches the peak with the highest absolute intensity.

Maximum searches the highest peak with the largest positive value.

Minimum searches the lowest peak, if known that the peak has a negative intensity.

Mid between Min./Max. calculates a value between the minimum and maximum limit.

No peak search uses the position saved in the interferogram. If this value is known, it can be entered manually.

Mid between largest two searches the peak between the two largest values.

Take from stored phase uses the value calculated for the phase stored.

The position of the peak can be influenced by considering additional data points apart from the range evaluated by one of the algorithms mentioned before. Each position will be tested for its symmetry or asymmetry. The position with the highest symmetry will be defined as ZPD. Check the respective option button in the Symmetry of the Interferogram group field.