Phase-angle spectrum

Phase correction may not always be possible. As stated above, the phase-angle spectrum is defined only where a signal exceeds the noise, which may not be the case for discrete emission spectra. In this instance, a double-sided interferogram must be collected and the magnitude spectrum computed. Discrete emission spectra are not commonly encountered in infrared spectrometry but occur in the ultraviolet-visible region for atomic emission spectrometry. 

Introducing the complex notation enables the impedance relationships to be presented as Argand diagrams in both Cartesian and polar co-ordinates (r,rp). The fomier leads to the Nyquist impedance spectrum, where the real impedance is plotted against the imaginary and the latter to the Bode spectrum, where both the modulus of impedance, r, and the phase angle are plotted as a fiinction of the frequency. In AC impedance tire cell is essentially replaced by a suitable model system in which the properties of the interface and the electrolyte are represented by appropriate electrical analogues and the impedance of the cell is then measured over a wide... 

Theory. If two or more fluorophores with different emission lifetimes contribute to the same broad, unresolved emission spectrum, their separate emission spectra often can be resolved by the technique of phase-resolved fluorometry. In this method the excitation light is modulated sinusoidally, usually in the radio-frequency range, and the emission is analyzed with a phase sensitive detector. The emission appears as a sinusoidally modulated signal, shifted in phase from the excitation modulation and partially demodulated by an amount dependent on the lifetime of the fluorophore excited state (5, Chapter 4). The detector phase can be adjusted to be exactly out-of-phase with the emission from any one fluorophore, so that the contribution to the total spectrum from that fluorophore is suppressed. For a sample with two fluorophores, suppressing the emission from one fluorophore leaves a spectrum caused only by the other, which then can be directly recorded. With more than two flurophores the problem is more complicated but a number of techniques for deconvoluting the complex emission curve have been developed making use of several modulation frequencies and measurement phase angles (79). 

Figure 4 Angle-resolved photoelectron spectra for Ni 100] ( 2x/2)R45°-CO. hv = 32 eV (a) angle of incidence, o = 60°, polar angle of emission, 0 = 0°. (b) a = 0 , 0 = 50°, Elk). Inset Gas phase photoelectron spectrum of CO at the same photon energy. After [10] and [11].

Eventually, as pores increase in size, additional equivalent circuit elements are required to account for the detection of these pores as discrete time constants in the low frequency end of the spectrum, Fig. 19C. As frequencies are scanned to lower values in recording the EIS spectrum, the frequency at which the decrease in phase shift (i.e., a decrease in absolute value of the phase angle) commences provides an indication of either the number density of fine pores or the dimensions of a smaller number of larger pores. The value of the pore resistance (/ pore) is a more direct indication of pore dimension. The interfacial capaci-... 

If the phase-sensitive detectors are adjusted to give a phase angle (Eq. 3.8) ( — 4>r ) = 0, the real part of the FT spectrum corresponds to pure absorption at the pulse frequency, but off-resonance lines display phase angles proportional to their off-resonance frequency as a consequence of limited rf power and nonzero pulse width (Eq. 2.55). However, acquisition of data as complex numbers from the two phase-sensitive detectors and subsequent processing with a complex Fourier transform permit us to obtain a spectrum that represents a pure absorption mode. 

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