Spectral analysis width

Analogous to the principal concept of multiplex CARS microspectroscopy (cf. Sect. 6.3.5), in multiplex SRS detection a pair of a broad-bandwidth pulse, eg., white-light femtosecond pulse, and a narrow-bandwidth picosecond pulse that determine the spectral width of the SRS spectrum and its inherent spectral resolution, respectively, is used to simultaneously excite multiple Raman resonances in the sample. Due to SRS, modulations appear in the spectrum of the transmitted broad-bandwidth pulse, which are read out using a photodiode array detector. Unlike SRS imaging, it is difficult to integrate phase-sensitive lock-in detection with a multiplex detector in order to directly retrieve the Raman spectrum from these modulations. Instead, two consecutive spectra, i.e., one with the narrow-bandwidth picosecond beam present and one with that beam blocked, are recorded. Their ratio allows the computation of the linear Raman spectrum that can readily be interpreted in a quantitative manner [49]. Unlike the spectral analysis of a multiplex CARS spectrum, no retrieval of hidden phase information is required to obtain the spontaneous Raman response in multiplex SRS microspectroscopy. 

In quantitative analysis usually calibration functions are needed which reflects the relation between the measured quantity (for instance, the radiant flux) and the concentration. The S/N ratio should be as high as possible in order to afford the maximum number of distinguishable intensity intervals. As a consequence, the spectral band width should... 

The technical specifications identified and described by most of the manufacturers of absorption photometers for medical use include wavelength accuracy, spectral half-width of spectral radiation flux at the detector, photometric accuracy, percentage of wavelength integrated, false radiation, and photometric short-time repeatability. As discussed previously [2], the Instrumental Performance Validation Procedures, issued by serious manufacturers of analytical instruments, indicate the methods and the reference materials required to test and to maintain optimum spectrometer performance in daily routine analysis. 

Excitation of the target molecule has been found80 for Na + S02 and N02. and has been studied later on in more detail for Na + NOz.81 The identity of the excited molecular species could be demonstrated by measuring the lifetime of the transitions under question. A pulsed beam of sputtered sodium, the pulse width being 10 //sec, was employed and the time between the excitation of the target gas and the observation with the photomultiplier was varied. The variation of the emission intensity with the delay time gives the lifetime of the excited state. The spectral analysis was made with interference filters of 70 A bandwidth some measurements have been made with sharp-cut filters. 

Taking the easy case of line broadening first, one way for the lines to be so wide is if the excited state lifetimes are very short, on the order of femtoseconds. Fourier analysis indicates that the spectral line width Ap of a transition of lifetime t (ignoring factors of it) is approximately 1/t, and so the fractional line width of the line Ap/pq 1/tpo- It is more convenient to use energy units of inverse wavelength (1/A., or cm" ). Let the energy of the center frequency be given as (in cm" ) with lifetime r. The fractional line width then is... 

Although conceptually straightforward, it is challenging to extract correlation times from spectra in this motional regime because spectral analysis requires more than line width measurements as is done with motionally narrowed spectra. It is usually best to use simulation techniques in the intermediate motional regime, whereby one computes a spectrum given a particular correlation time (or pair of correlation times if the motion is anisotropic). The result is then compared to the experimental spectrum. 

Fano factor The observed variance relative to the calculated Poisson distribution variance, as observed in the peak width in spectral analysis. 

HX-MS for proteins in lyophilized powders has developed over the past 5 years. Recent studies suggest that the method can provide detailed information on protein conformation, dynamics, and interactions with excipients in lyophilized solids and that HX with mass spectral peak width analysis can be used to screen protein formulations for the presence of nonnative subpopulations. Though the utility of the method for developing lyophilized protein formulations has not been fully tested, early results promote the wider development and application of the method. 

Our small-signal approximation only holds if the maximum interaction time T of the field (amplitude Eq) with the atom (matrix element Dab) is restricted to t T. Because the spectral analysis of a wave with the finite detection time T gives the spectral width Acd c IT (see also Sect. 3.2), we cannot assume monochromaticity, but have to take into account the frequency distribution of the interaction term. 

The amide I band was chosen for detailed analysis as its position is sensitive to protein secondary structure. The band arises predominately from v(C=0) stretching of the carbonyl group within the peptide (CONH) bond. Other minor contributing factors arise from v(CN) out-of-plane, 5(CCN) and 8(NH) in-plane vibrations (1). The broad nature of the amide I band is attributed to the presence of a number of secondary structures within the sample. Derivatives were used to deconvolve spectral band widths and positions. This resolution technique, together with deconvolution and curve fitting, is particularly useful for resolving components within a broad band envelope. 

If needed, spectral analysis of light from the output beam can be achieved using a simple monochromator with a multiwavelength detector (CCD or diode array). The spectral resolution is determined by the size of the monochromator, the width of the entrance slit, the density and order of the grating, and the distance between individual elements in the detector array. Fast temporal analysis may be achieved using a fast detector such as a streak camera with picosecond or subpicosecond temporal resolution. 

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