Spectral interferometry

Evans, C. L., Potma, E. O., and Xie, X. S. 2004. Coherent anti-Stokes Raman scattering spectral interferometry Determination of the real and imaginary components of nonhnear snsceptihility )f for vibrational microscopy. Opt. Lett. 29 2923-25. 

In this chapter we explore several aspects of interferometric nonlinear microscopy. Our discussion is limited to methods that employ narrowband laser excitation i.e., interferences in the spectral domain are beyond the scope of this chapter. Phase-controlled spectral interferometry has been used extensively in broadband CARS microspectroscopy (Cui et al. 2006 Dudovich et al. 2002 Kee et al. 2006 Lim et al. 2005 Marks and Boppart 2004 Oron et al. 2003 Vacano et al. 2006), in addition to several applications in SHG (Tang et al. 2006) and two-photon excited fluorescence microscopy (Ando et al. 2002 Chuntonov et al. 2008 Dudovich et al. 2001 Tang et al. 2006). Here, we focus on interferences in the temporal and spatial domains for the purpose of generating new contrast mechanisms in the nonlinear imaging microscope. Special emphasis is given to the CARS technique, because it is sensitive to the phase response of the sample caused by the presence of spectroscopic resonances. 

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. 

Rhee H, Ha JH, Jeon SJ et al (2008) Femtosecond spectral interferometry of optical activity theory. J Chem Phys 129 094507... 

Lepetit L, Cheriaux G, Jofffe M (1995) Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy. J Opt Soc Am B 12 2467-2474... 

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]. 

Figure 3. The 2D-IR spectra of a broad-band system (dialanine) recorded by means of (a) time-domain interferometry and (b) spectral interferometry. The spectra are the same with the signal to noise available, although the spectral resolution is slightly better for the spectral interferometry in our arrangement.

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 ... 

The main point to be made here is that the phase shift data obtained from spectral interferometry has two contributions surface motion and optical effects. These two contributions to the phase versus time data can be separated by performing these experiments at two angles of incidence and two polarizations, at technique we term ultrafast d3mamic ellipsometry. The optical effects during shock breakout in nickel films were hidden because they produce phase shifts of the same sign as that caused by surface motion. Ultrafast dynamic ellipsometry allowed that contribution to be measured [71]. In our experiments on bare metals, the observed optical effects are due to changes in the material s complex conductivity under shock loading. We will see below that this is only one of several kinds of optical effects that can be observed in these and other materials. 

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. 

J.-M. Mariotti, S.T. Ridgway, Double Fourier spatio-spectral interferometry—combining high spectral and high spatial resolution in the near infrared. Astron. Astrophys. 195,350-363 (1988)... 

D.T. Leisawitz, M.R. Bolcar, R.G. Lyon, S.F. Maher, N. Memarsadeghi, S.A. Rinehart, E. 1. Sinukoff, Developing wide-field spado-spectral interferometry for far-infrared space applications, in Sod-... 

Chapter 3 focused in the spectro-spatial interferometer testbeds in which I have been involved dining my programme the FIRI laboratory testbed (based at Cardiff University) and WET, the Wide-fleld Imaging Interferometry Testbed (based at NASA s Goddard Space Flight Center). Both testbeds have demonstrated the theory of Double Fourier Spatio-Spectral Interferometry or the application of a Fourier... 

This theorem can be used to determine the correct relative phase factor. The entire spectral interferometry analysis described in this section is performed, changing the relative phase factor used until the projection of the real 2DPE spectrum in energy matches the spectrally resolved pump probe spectrum. In all of the work presented in this chapter, a non-frequency-dependent phase factor... 

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