Fringing errors

A delay error shifts the position of zero delay with respect to the overall intensity envelope, resulting in a substantial reduction of overall contrast. The contrast may vanish entirely if the zero delay position coincides with a minimum. Therefore, there is a relation between the allowable delay error max and the spectral bandwidth Aoj of the detected radiation if the amplitude error of the fringe modulation is to remain small, i. e., (5max = A /AA. 

The main consequences are twice. First, it results in contrast degradations as a function of the differential dispersion. This feature can be calibrated in order to correct this bias. The only limit concerns the degradation of the signal to noise ratio associated with the fringe modulation decay. The second drawback is an error on the phase closure acquisition. It results from the superposition of the phasor corresponding to the spectral channels. The wrapping and the nonlinearity of this process lead to a phase shift that is not compensated in the phase closure process. This effect depends on the three differential dispersions and on the spectral distribution. These effects have been demonstrated for the first time in the ISTROG experiment (Huss et al., 2001) at IRCOM as shown in Fig. 14. 

The measured or apparent hydrocarbon thickness is not only dependent on the capillary fringe but also on the actual hydrocarbon thickness in the formation (Figure 6.6b). In areas of relatively thin LNAPL accumulations, the error between the apparent well thickness and actual formation thickness can be more pronounced than in areas of thicker accumulations. The larger error reflects the relative difference between the thin layer of LNAPL in the formation and the height it is perched above the water table. The perched height is constant for thick and thin accumulations however, a thick accumulation can depress and even destroy the capillary fringe as illustrated in Figure 5.1. 

Fig. 1. Sedimentation equilibrium (72). The concentration of adrenodoxin was 0.45 mg per ml. The centrifugation was performed at 44,770 r.p.m. for 20 hrs. The error bars correspond to an estimated uncertainty of 10 p. in the determination of the fringe displacement...

In Fig. 11 we compare our decoherence calculation with the experiments by plotting the interference fringe visibility as a function of the laser power. We observe a good agreement between decoherence theory (solid line) and the experiment (circles). The experiment is reproducible within the indicated error bars for a given laser alignment, but small displacements of the laser focus will influence the shape and slope of the observed decoherence curve. The difference between the theoretical and the experimental curve is of the order of this variation. 

Figure 12 Boxes fringe visibility as a function of Bragg excitation frequency. Error bars uncertainty due to four measurements. We observe a clear double-peaked spectrum, which is finite-time broadened. Solid line double peaked Gaussian fit. The peaks are found at 139 10 Hz, near the expected Bogoliubov local density approximation average excitation energy (138 5 Hz).

A significant difference between the effectiveness of semiclassical and optimal treatments is apparent in Fig. 14. The optimal treatment provides an improvement in estimation procedure, and the difference is more than 10 standard deviations beyond the statistical error. High stability and visibility of interference fringes in the optical interferometer along with a high repetition rate of pulsed lasers made the improvement of the NFM phase prediction more evident than in a similar comparison that had been done with thermal neutrons [70] (see Fig. 15). 

Successful quantitative measurements of the thickness of the squalane primary film were possible after 18 and 42 hours of drainage. The film profiles determined from these measurements are shown in Figure 4. The film thickness was measured at various distances from a reference line drawn on the metal plate. The points plotted at about 1200-A. thickness correspond to the first-order interference fringe. These measurements demonstrate a sharp change in the slope of the film and also a tendency for the primary film to thicken over the 24-hour period. Undoubtedly there is some error in the measurement of film thickness where the thickness is changing abruptly and also near 100 A., where the Drude calculations of film thickness are invalid. 

However, such errors would not alter substantially the inference of an abrupt change in film slope just outside the first interference fringe. 

An apparatus specifically designed for plastics has been described by Wright (. ]. This makes u.se of a moire fringe extensometer. which is essentially digital in operation and hence does not introduce any errors due to drift in sensitivity with time. Comparatively less sophisticated apparatus will be adequate for materials of lower stiffness and for shorter times of test. 

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