Fourier transform spectral interferometry

Double Fourier Spatio-Spectral Interferometry is the application of a Fourier-transform spectrometer (FTS) to aperture synthesis interferometry. This technique was proposed for the near IR regime by Itoh and Ohtsuka (1986) with a single-pupil interferometry approach, and by Mariotti and Ridgway (1988) with multi-pupil interferometry for high spatial resolution. 

The fundamental quantity for interferometry is the source s visibility function. The spatial coherence properties of the source is connected with the two-dimensional Fourier transform of the spatial intensity distribution on the ce-setial sphere by virtue of the van Cittert - Zemike theorem. The measured fringe contrast is given by the source s visibility at a spatial frequency B/X, measured in units line pairs per radian. The temporal coherence properties is determined by the spectral distribution of the detected radiation. The measured fringe contrast therefore also depends on the spectral properties of the source and the instrument. 

E.N. Lewis, RJ. Treado, R.C. Reeder, G.M. Story, A.E. Dowrey, C. Marcott and I.W. Levin, Fourier transform step-scan imaging interferometry high-definition chemical imaging in the infrared spectral region. Anal. Ghent., 67, 3377-3381 (1995). 

Lewis, E.N. Treado, P.J. Reeder, R.C. Story, G.M. Dowrey, A.E. Marcott, C. 8c Levin, I.W., Fourier Transform Step-Scan Imaging Interferometry High-Definition Chemical Imaging in the Infrared Spectral Region Anal. Chem. 1995, 67, 3377-3381. 

In spectral interferometry, the interference in the spectral domain is exploited. The spectral modulation period is essentially determined by a time delay. This is at the heart of Fourier transform infrared spectrometers (FTIRs). 

We shall conclude this chapter with a few speculative remarks on possible future developments of nonlinear IR spectroscopy on peptides and proteins. Up to now, we have demonstrated a detailed relationship between the known structure of a few model peptides and the excitonic system of coupled amide I vibrations and have proven the correctness of the excitonic coupling model (at least in principle). We have demonstrated two realizations of 2D-IR spectroscopy a frequency domain (incoherent) technique (Section IV.C) and a form of semi-impulsive method (Section IV.E), which from the experimental viewpoint is extremely simple. Other 2D methods, proposed recently by Mukamel and coworkers (47), would not pose any additional experimental difficulty. In the case of NMR, time domain Fourier transform (FT) methods have proven to be more sensitive by far as a result of the multiplex advantage, which compensates for the small population differences of spin transitions at room temperature. It was recently demonstrated that FT methods are just as advantageous in the infrared regime, although one has to measure electric fields rather than intensities, which cannot be done directly by an electric field detector but requires heterodyned echoes or spectral interferometry (146). Future work will have to explore which experimental technique is most powerful and reliable. 

In spectral interferometry, two IR pulses separated by time r are sent to a monochromator and the total spectrum is measured. By dehnihon the two helds are the Fourier transforms ... 

Often in an experiment it is possible to eliminate the contributions from the two power spectra leaving only the interference term. It is only this interference term that is dependent on phase and phase fluctuations. Note that for two identical pulses the signal is simply proportional to 2 cos [cox /2], which is a series of peaks in the frequency domain separated by 2/cx cm. Thus a x = 1 ps delay yields a peak separation of 67 cm In general the peak separations in the frequency domain are not independent of frequency and instead depend on the spectral phase difference at each frequency. Therefore spectral interferometry presents a method by which to determine the phase differences of two pulses. When the pulses are the same, we can use spectral interferometry to determine their time separations. The inverse Fourier transforms of the first two contributions to the spectrogram in Eq. (18) peak at f = 0 whereas the cross term peaks at t = x. Therefore Fourier transformation of S (a) can permit a separation of the cross term from the power spectra of the signal and reference fields [72]. 

The previous discussions of the signal are nicely illustrated by an extremely simple model analysis using real fields and signals for two Lorenzian resonances at frequencies a and b. The sample is irradiated with two very short pulses whose spectra are flat. The real generated field from the sample is the real part of Eq. (21) or Eq. (33) with T set equal to zero for convenience since is in any case a multiplicative factor. In time-domain interferometry, this is measured directly along the indicated time axes as described above. In spectral interferometry the real generated field along with a real local oscillator field, delayed by time d, is dispersed (i.e., Fourier-transformed) by a monochromator, then squared by the detection to yield a spectrum on the array detector at each value of t ... 

Normal spontaneous Raman scattering suffers from lack of frequency precision and thus good spectral subtractions are not possible. Another limitation to this technique is that high resolution experiments are often difficult to perform [39]. These shortcomings have been circumvented by the development of Fourier transform (FT) Raman spectroscopy [40]. FT Raman spectroscopy employs a long wavelength laser to achieve viable interferometry,... 

To achieve the angular resolution and sensitivity required for FIRI, one can use the so-called Spectral-Spatial Interferometry, Double Fourier Modulation, multi-Fourier Transform Spectroscopy or Double Interferometry (Mariotti and Ridgway 1988 Ohta et al. 2006, 2007), as a result of a combination of two well-known techniques Stellar Interferometry and Fourier Transform Spectroscopy. 

The goal of Double Fourier Modulation is to measure the spectral and spatial characteristics of an object simultaneously and it can be understood as the combination of two well known techniques Fourier transform spectroscopy (FTS) and Stellar Interferometry. The literature regarding both FTS and Stellar Interferometry is extensive, and the concepts presented here are the ones related to the work of this Thesis. 

Interferometry It is true to state that the renaissance of the RAIRS technique as a general use method in surface science laboratories came about through the use of Fourier-transform (FT) IR spectrometers. This advance was pioneered by Chesters et al. [41-43], who demonstrated that FT-RAIRS could obtain vibrational data on an adsorbed adlayer over a broad wavenumber regime of 4000—700 cm, with sensitivity to fractions of a ML of adsorbate (<0.01 ML of CO, <0.1 ML of hydrocarbon), and with high spectral resolution (typically l-4cm ). 

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