Frequency domain detection

In the time-domain detection of the vibrational coherence, the high-wavenumber limit of the spectral range is determined by the time width of the pump and probe pulses. Actually, the highest-wavenumber band identified in the time-domain fourth-order coherent Raman spectrum is the phonon band of Ti02 at 826 cm. Direct observation of a frequency-domain spectrum is free from the high-wavenum-ber limit. On the other hand, the narrow-bandwidth, picosecond light pulse will be less intense than the femtosecond pulse that is used in the time-domain method and may cause a problem in detecting weak fourth-order responses. 

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An overview of frequency-domain detection techniques is given in [88]. Frequency-domain techniques compare the phase shift and the modulation degree of the fluorescence with the modulated excitation. Modulation of the excitation is achieved either by actively modulating the light of a continuous laser or by using pulsed lasers of high repetition rate. With pulsed lasers, phase and modulation can be measured at the fundamental repetition frequency or at its harmonics. 

The idea to use frequency-domain detection for the measurement of fluorescent lifetimes dates back to 1921 [4], although the idea to measure small phase changes to determine short time intervals is much older [5]. The first instruments to measure non-spatially-resolved lifetimes in the 1920s were all based on frequency-domain detection. 

A method less common for lifetime measurements is the so-called pump-probe or double-pulse approach. Like time- and frequency-domain detection, the technique originates in non-spatially-resolved fluorescence spectroscopy [ 19]. In this technique, two very short excitation pulses follow each other. The first pulse excites fluorochromes inside the detection volume to full or partial saturation. The second pulse, or probe pulse, arrives at a variable (ns) time delay. If the time delay between the pulses is short compared to the fluorescence lifetime, most of the fluorochromes will still be in the excited state when the second pulse arrives so that the second pulse cannot excite additional fluorochromes and thus does not lead to additional fluorescence. If the time delay is long, most fluorochromes will have relaxed back to their ground state, so that the second pulse leads to... 

In spin relaxation theory (see, e.g., Zweers and Brom[1977]) this quantity is equal to the correlation time of two-level Zeeman system (r,). The states A and E have total spins of protons f and 2, respectively. The diagram of Zeeman splitting of the lowest tunneling AE octet n = 0 is shown in fig. 51. Since the spin wavefunction belongs to the same symmetry group as that of the hindered rotation, the spin and rotational states are fully correlated, and the transitions observed in the NMR spectra Am = + 1 and Am = 2 include, aside from the Zeeman frequencies, sidebands shifted by A. The special technique of dipole-dipole driven low-field NMR in the time and frequency domain [Weitenkamp et al. 1983 Clough et al. 1985] has allowed one to detect these sidebands directly. 

Comparative analysis directly compares two or more data sets in order to detect changes in the operating condition of mechanical or process systems. This type of analysis is limited to the direct comparison of the time-domain or frequency-domain signature generated by a machine. The method does not determine the actual dynamics of the system. Typically, the following data are used for this purpose (1) baseline data, (2) known machine condition, or (3) industrial reference data. 

The radiation pressure noise decreases rapidly with frequency, so we focus our attention on the worst case, the low frequency domain. Because of the seismic noise which is very large at low frequency, it will be very difficult to detect gw below a few hertz, so we put this as a limit. Equation (46) exhibits interesting features ... 

There are actually two independent time periods involved, t and t. The time period ti after the application of the first pulse is incremented systematically, and separate FIDs are obtained at each value of t. The second time period, represents the detection period and it is kept constant. The first set of Fourier transformations (of rows) yields frequency-domain spectra, as in the ID experiment. When these frequency-domain spectra are stacked together (data transposition), a new data matrix, or pseudo-FID, is obtained, S(absorption-mode signals are modulated in amplitude as a function of t. It is therefore necessary to carry out second Fourier transformation to convert this pseudo FID to frequency domain spectra. The second set of Fourier transformations (across columns) on S (/j, F. produces a two-dimensional spectrum S F, F ). This represents a general procedure for obtaining 2D spectra. 

Frequency domain performance has been analyzed with goodness-of-fit tests such as the Chi-square, Kolmogorov-Smirnov, and Wilcoxon Rank Sum tests. The studies by Young and Alward (14) and Hartigan et. al. (J 3) demonstrate the use of these tests for pesticide runoff and large-scale river basin modeling efforts, respectively, in conjunction with the paired-data tests. James and Burges ( 1 6 ) discuss the use of the above statistics and some additional tests in both the calibration and verification phases of model validation. They also discuss methods of data analysis for detection of errors this last topic needs additional research in order to consider uncertainties in the data which provide both the model input and the output to which model predictions are compared. 

Since TIRF produces an evanescent wave of typically 80 nm depth and several tens of microns width, detection of TIRF-induced fluorescence requires a camera-based (imaging) detector. Hence, implementing TIRF on scanning FLIM systems or multiphoton FLIM systems is generally not possible. To combine it with FLIM, a nanosecond-gated or high-frequency-modulated imaging detector is required in addition to a pulsed or modulated laser source. In this chapter, the implementation with of TIRF into a frequency-domain wide-field FLIM system is described. 

An endoscope, coupled with video rate wide field imager, operating in either the time or frequency domain [92] could be an invaluable tool for early detection of cancer or possibly other diseases whose AF signatures are yet to be studied. 

The development of new oximeters is also in progress, with the application of time- and frequency-domain techniques which are, in principle, capable of discriminating between the absorption and scattering contributions coming from human tissue, thus making possible the detection of tissue oxygenation37 39. 

M. Wolf, U. Wolf, J. H. Choi, R. Gupta, L. P. Safonova, and L. A. Paunescu. Functional frequency-domain near-infrared spectroscopy detects fast neuronal signal in the motor cortex. Neuroimage, 17 1868-1875, 2002. 

In frequency-domain FLIM, the optics and detection system (MCP image intensifier and slow scan CCD camera) are similar to that of time-domain FLIM, except for the light source, which consists of a CW laser and an acousto-optical modulator instead of a pulsed laser. The principle of lifetime measurement is the same as that described in Chapter 6 (Section 6.2.3.1). The phase shift and modulation depth are measured relative to a known fluorescence standard or to scattering of the excitation light. There are two possible modes of detection heterodyne and homodyne detection. 

The use of high-speed modulated excitation (f> kr + knr) combined with coherent detection methods has resulted in the popular techniques of frequency domain fluorometry, also known as phase-modulation fluorometry. These techniques can be used to determine the temporal characteristics of both fluorescence and phosphorescence and will also be addressed later in this chapter. 

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