In phase shift interferometry (PSI), several factors affect measurement accuracy, such as piezoelectric transducer (PZT) calibration (i.e. PZT slope error) and PZT nonlinearity, vibration, spurious reflection, source bandwidth, detector nonlinearity, and detector noise. The effects of these error sources on several algorithms to solve the phase of the wavefront are studied. When the simple arctangent formula is used, if the PZT slope is properly adjusted, the error due to the PZT quadratic nonlinearity can be tremendously reduced. An exact solution is derived to remove the error when the PZT quadratic nonlinearity is large. Although Carre's formula is insensitive to PZT slope, this formula is more sensitive to the detector nonlinearity than the simple arctangent formula. For most error sources, the error of the phase solved has a double-frequency characteristic. Thus, averaging two measured phases of two runs, which have a ninety degree phase shift related to each other, can effectively reduce the error. For a small vibration, the phase error has a very simple relation to the vibration amplitude, and a very complex relation to the vibration frequency. Although the error caused by vibration has this double-frequency characteristic, the averaging technique does not apply. The error caused by spurious reflection does not have such a characteristic. A new algorithm is proposed to eliminate the phase error caused by certain types of spurious reflection. When detector noise is concerned, the phase error is inversely proportional to the modulation of the intensity times the square root of the number of steps/buckets. For the shot noise, the phase error is inversely proportional to the fringe contrast times the square root of the total number of photons. In practice, the shot noise is very much smaller than the detector noise. In a practical environment, PZT calibration, vibration, and spurious reflection have much more prominent effects on the PSI than the source bandwidth, detector nonlinearity, and detector noise. When spurious reflection and vibration are under control, and the signal-to-noise ratio is about 20, the PSI has an accuracy of 2 degrees, i.e. 3.3nm at 633nm. Because vibration and detector noise are random error sources, the errors caused by them can be reduced by averaging many measurements. However, the error caused by the other discussed sources cannot be reduced by averaging many measurements.

Thesis (Ph.D.)--University of California, Berkeley, 1962. / "UC-34 Physics" -t.p. "TID-4500 (17th Ed.)" -t.p. Includes bibliographical references (p. 65-66).

Thesis (Ph.D.)--University of California, Berkeley, 1962. / "UC-34 Physics" -t.p. "TID-4500 (17th Ed.)" -t.p. Includes bibliographical references (p. 84-86).

The connection between phase shifts and the ANC has been explored in the frame of the effective range theory. The main result is that, in practice and under rather simple requirements, scattering states (phases shifts) can be correctly described and connected with bound states via the effective range function, and therefore, ANCs can be accurately determined thanks to the analytic properties of this function. This result has an important impact in stellar evolution due to the ANC and phases shifts are directly connected with capture cross sections which, for instance, determine partially the stage and evolution of stars.<p><p>As a first step, the effective range function is approximated via the effective range expansion which shows that a successful phase-shift description depends on how precise the effective range parameters are determined. Thus, a technique to compute accurately these parameters is developed here. Its construction is based on a set of recurrence relations at low energy, that allows a compact and general description of the truncated<p>effective range expansion. Several potential models are used to illustrate the effectiveness<p>of this technique and to discuss its numerical limitations. The results shows that a very good precision of the effective-range parameters can be achieved; nevertheless, to describe experimental phase shifts several effective-range parameters can be needed, which shows a limitation for practical applications.<p><p>As a second step, the effective range function is analyzed theoretically in an arbitrary energy range. This analysis shows that this function can be decomposed in such a way that contributions of bound states, resonances and background can be separated in a similar way as in the phenomenological R-matrix. In this new form experimental data can be better fitted because the free parameter space is reduced considerably,<p>and therefore, extrapolations are better handled. By construction, the method agrees with the scattering matrix properties which allows a simple calculation of resonances (locations and widths) and asymptotic normalization constants (ANCs). Several tests are successfully performed via potential models. Phase shifts for the 2 + partial wave of the 12C+α are analyzed with this method. They are correctly described including both<p>resonances at Ec.m. = 2.7 and 4.4 MeV. For the 6.92 MeV (2+) exited state of 16O, the ANC estimation 112(8) × 10 3 fm^−1/2 is obtained taking into account statistical errors. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished