Amplitude and phase

The instrument uses a sinusoidal driver. The spectrum is very clean as we use a 14 bits signal generator. The probe signal is modulated in amplitude and phase by a defect signal. The demodulation is intended to extract the cartesian values X and Y of this modulation. 

If we suppose that the presence of a long axial emerging rectangular defect doesn t change the thickness e of the ring where the induction in the tube is not equal to zero but only its circumferential length, and also that it is it does not change the local induction in amplitude and phase, then the presence of the defect increases only the of the piece where the induction is not equal to zero, this increment is equal to 2he. 

Figure B3.4.18. A schematic use of coherent control in AB A -i- B, A -i- B dissociation use of a single high-frequency photon (co) or tluee low-intensity (a)/3) photons would lead to emerging wavefimctions in both arrangements. However, by properly combining the amplitudes and phases of the single- and tluee-photon paths, the wavefimction would emerge in a single channel.

A wide variety of useful phenomena that allow tire manipulation of tire wavelengtli, amplitude and phase of tire... 

Although 0-switching produces shortened pulses, typically 10-200 ns long, if we require pulses in the picosecond (10 s) or femtosecond (10 s) range the technique of mode locking may be used. This technique is applicable only to multimode operation of a laser and involves exciting many axial cavity modes but with the correct amplitude and phase relationship. The amplitudes and phases of the various modes are normally quite random. 

Each axial mode has its own characteristic pahem of nodal planes and the frequency separation Av between modes is given by Equation (9.4). If the radiation in the cavity can be modulated at a frequency of cjld then the modes of the cavity are locked both in amplitude and phase since t, the time for the radiation to make one round-trip of the cavity (a distance 2d), is given by... 

Take a blank Data Sheet B. Enter the plane number. Plaee a trial weight at any radius and any angle in that plane. Enter these values on the sheet. Now, operate the maehine at the balaneing speed, and measure the vibration amplitude and phase in eaeh plane. Repeat the proeedure for eaeh plane. (Plaee only one trial weight in only one plane at a time.) When finished, you should have as many Data Sheets B as the number of planes. 

Final Vibration Amplitude and Phase Before Balancing In-Plane... 

How do we find phase differences between diffracted spots from intensity changes following heavy-metal substitution We first use the intensity differences to deduce the positions of the heavy atoms in the crystal unit cell. Fourier summations of these intensity differences give maps of the vectors between the heavy atoms, the so-called Patterson maps (Figure 18.9). From these vector maps it is relatively easy to deduce the atomic arrangement of the heavy atoms, so long as there are not too many of them. From the positions of the heavy metals in the unit cell, one can calculate the amplitudes and phases of their contribution to the diffracted beams of the protein crystals containing heavy metals. 

Frequeney domain analysis is eoneerned with the ealeulation or measurement of the steady-state system output when responding to a eonstant amplitude, variable frequeney sinusoidal input. Steady-state errors, in terms of amplitude and phase relate direetly to the dynamie eharaeteristies, i.e. the transfer funetion, of the system. 

Resistivity. The 2-MHz LWD amplitude and phase-shift resistivity logs match the wireline deep and medium induction very well. Excellent results are obtained when the invasion is not severe (less than 40 in. in diameter) and in formations 20 f2 m or less. 

Mathematical techniques allow us to quantify total displacement caused by all vibrations, to convert the displacement measurements to velocity or acceleration, to separate this data into its components using FFT analysis, and to determine the amplitudes and phases of these functions. Such quantification is necessary if we are to isolate and correct abnormal vibrations in machinery. 

It was observed that with a linear circuit and in the absence of any source of energy (except probably the residual charges in condensers) the circuit becomes self-excited and builds up the voltage indefinitely until the insulation is punctured, which is in accordance with (6-138). In the second experiment these physicists inserted a nonlinear resistor in series with the circuit and obtained a stable oscillation with fixed amplitude and phase, as follows from the analysis of the differential equation (6-127). 

Intensity-modulated photocurrent spectroscopy has been used in combination with microwave reflectivity measurements to investigate hydrogen evolution at a p-type silicon45 and an n-type silicon.46 The measurement of amplitude and phase under harmonic generation of excess carriers, performed by Otaredian47 on silicon wafers in an attempt to separate bulk and surface recombination, should also be mentioned here. 

X-Ray diffraction from single crystals is the most direct and powerful experimental tool available to determine molecular structures and intermolecular interactions at atomic resolution. Monochromatic CuKa radiation of wavelength (X) 1.5418 A is commonly used to collect the X-ray intensities diffracted by the electrons in the crystal. The structure amplitudes, whose squares are the intensities of the reflections, coupled with their appropriate phases, are the basic ingredients to locate atomic positions. Because phases cannot be experimentally recorded, the phase problem has to be resolved by one of the well-known techniques the heavy-atom method, the direct method, anomalous dispersion, and isomorphous replacement.1 Once approximate phases of some strong reflections are obtained, the electron-density maps computed by Fourier summation, which requires both amplitudes and phases, lead to a partial solution of the crystal structure. Phases based on this initial structure can be used to include previously omitted reflections so that in a couple of trials, the entire structure is traced at a high resolution. Difference Fourier maps at this stage are helpful to locate ions and solvent molecules. Subsequent refinement of the crystal structure by well-known least-squares methods ensures reliable atomic coordinates and thermal parameters. 

If we apply Maxwell s equations to this boundary value problem we can derive a complete solution to the amplitude and phase of this field af every point in space. In general, however we can simplify the problem to describing the field at the entrance (or exit) aperture of a system and at the image plane (which is what we are really interested in the end). 

Since a heterodyne receiver is an amplitude and phase detector, it could nicely be used to correlate optical signals received at various remote sites. The local oscillator can be a single laser distributed by optical fiber to the various sites or local lasers that can be synchronized "a posteriori" by reference to a common source (e.g. a bright star). 

It is conceivable to detect amplitude and phase emitted by a celestial object at various observation sites and to correlate the results in order to create a huge interferometer (Fig. 3). Because laser can be very stable, the phase reference between lasers can be extracted at low data rate for example from the correlation of the interference signal of each laser with a high magnitude star. The main difference with communication case above is that the absolute phase of the thermal emission is meaningless only the phase correlation from site to site can be exploited. Emission of thermal source is governed by the Planck law. This law states that the probability of photon population of a mode is ... 

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