Phase modulation frequency

Phase modulation Frequency modulation produced by shifting the phase of the carrier relative to an arbitrary reference point. This method of frequency modulation is often referred to as indirect FM. Ratio detector A detector used in an FM receiver to demodulate the FM signal. 

Figure 20.13. PA spectra of a sample consisting of a 5-pm layer of a silicone on a polycarbonate substrate measured with three superimposed phase modulation frequencies (a), 360 Hz (b), 60 Hz (c), 10 Hz. Many bands in the spectra of silicones have very high absorptivity, so that the strong silicone bands exhibit photoacoustic saturation even for such a thin layer. The bands of the polycarbonate (marked with arrows) can be seen to increase in intensity as the phase modulation frequency gets lower.

Fig. 1 shows the block diagram of the vibrometer, in which the most sensible to small phase variations interferometric scheme is employed. It consists of the microwave and the display units. The display unit consists of the power supply 1, controller 2 of the phase modulator 3, microprocessor unit 9 and low-frequency amplifier 10. The microwave unit contains the electromechanical phase modulator 3, a solid-state microwave oscillator 4, an attenuator 5, a bidirectional coupler 6, a horn antenna 7 and a microwave detector 11. The horn antenna is used for transmitting the microwave and receiving the reflected signal, which is mixed with the reference signal in the bidirectional coupler. In the reference channel the electromechanical phase modulator is used to provide automatic calibration of the instrument. To adjust the antenna beam to the object under test, the microwave unit is placed on the platform which can be shifted in vertical and horizontal planes. 

One advantage of the photon counting teclmique over the phase-shift method is that any non-exponential decay is readily seen and studied. It is possible to detect non-exponential decay in the phase-shift method too by making measurements as a fiinction of tlie modulation frequency, but it is more cumbersome. 

Flow which fluctuates with time, such as pulsating flow in arteries, is more difficult to experimentally quantify than steady-state motion because phase encoding of spatial coordinate(s) and/or velocity requires the acquisition of a series of transients. Then a different velocity is detected in each transient. Hence the phase-twist caused by the motion in the presence of magnetic field gradients varies from transient to transient. However if the motion is periodic, e.g., v(r,t)=VQsin (n t +( )q] with a spatially varying amplitude Vq=Vq(/-), a pulsation frequency co =co (r) and an arbitrary phase ( )q, the phase modulation of the acquired data set is described as follows ... 

Phase modulated PWM forwardmode full bridge Fixed frequency... 

The dependence of the in-phase and quadrature lock-in detected signals on the modulation frequency is considerably more complicated than for the case of monomolecular recombination. The steady state solution to this equation is straightforward, dN/dt = 0 Nss — fG/R, but there is not a general solution N(l) to the inhomogeneous differential equation. Furthermore, the generation rate will vary throughout the sample due to the Gaussian distribution of the pump intensity and absorption by the sample... 

For lock-in amplification the pump is modulated at a reference frequency w (see Fig. 7-1), which means that AT is not constant over time. Rather, its magnitude (and its phase) depends on the modulation frequency [8. In order to find the frequency-dependent A7 (cu), let us assume that the recombination dynamics are monomolecular with a single lifetime r. Then we can write for the number density of excitations N at time / ... 

Jablonski (48-49) developed a theory in 1935 in which he presented the now standard Jablonski diagram" of singlet and triplet state energy levels that is used to explain excitation and emission processes in luminescence. He also related the fluorescence lifetimes of the perpendicular and parallel polarization components of emission to the fluorophore emission lifetime and rate of rotation. In the same year, Szymanowski (50) measured apparent lifetimes for the perpendicular and parallel polarization components of fluorescein in viscous solutions with a phase fluorometer. It was shown later by Spencer and Weber (51) that phase shift methods do not give correct values for polarized lifetimes because the theory does not include the dependence on modulation frequency. 

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). 

A phase modulation can also be expressed as frequency modulation. The corresponding frequency deviation is the time derivative of the modulated phase angle (Pm t). According to the basic relationships Afrequency deviation Af(f) with respect to the carrier frequency fg, commonly known as the Doppler frequency shift... 

Equations (33) and (34) demonstrate that the motion quantities 5 (displacement) and v (velocity) are encoded in phase and frequency modulation of the detector output signal, purely referenced to the laser wavelength A. Tobeableto recover the time histories s(t) and v t) from the modulated detector signal, adequate phase and frequency demodulation techniques, or both, are utilized in the signal decoder blocks of a laser vibrometer. 

Both methods obtain the necessary sensitivity by modulating the electrode potential between two values which define two distinct states of the electrode surface thus the chemistry to be observed is directly modulated and may be detected with great sensitivity by an appropriate form of synchronous detection. In the case of EMIRS, the modulation frequency is made sufficiently high compared to the wavelength scanning rate to enable a phase sensitive detection system to be used whereas, for SNIFTIRS, the electrode potential is held for a sufficient period at each potential to accumulate data from several interferometric scans and, after an adequate number, the two sets of data are ratioed. 

Figure 6.2. (I) Conventional phosphorescence spectrum of 2,3-dichloroquinoxa-line in durene at 1.6°K. (II) am-PMDR spectrum, obtained by amplitude modulation of microwave radiation that pumps the tv-t, (1.055 GHz) zf transition with the detection at the modulation frequency. Only bands whose intensities change upon microwave radiation (1.055 GHz) and thus originate from tv or rz appear in the am-PMDR spectrum. Transitions from r and rv appear with opposite sign (phase-shifted by 180°). (Hb, lie ) Polarization of the am-PMDR spectral transitions, relative to the crystal axes. The band at 0,0-490 cm-1 originates from both the r and t spin states its intensity does not change upon the 1.055-GHz saturation (no band in II) however, its polarization does rhanp. (bands in Hb and IIc ). (Reproduced with permission from M. A. El-Sayed.tt7W)...

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