On the calculation of theoretical Mach-Zehnder interferograms from the given velocity potential of a cylindrical supersonic free jet

Kurzfassung

From linear potential theory, the small density fluctuations of a supersonic free jet about the state in which it enters a medium with zero excess pressure are in the most general case give by an infinite double series of the Fourier-Bessel type. It is shown that the spatial density integration performed by a Mach-Zehnder interferometer can be done via analytical term-by-term integration of this series. Hence, the intensity of the light impinging on the screen of a hypothetical interferometer can in general be calculated analytically. For the case of D.C. Pack's classical solution for the axisymmetric free jet, theoretical fringe petterns are calculated and very good agreement with experiment is found.