Diffraction by a Screen Causing Large Random Phase Fluctuations

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Abstract
The propagation of a scalar wave is studied, after it has suffered changes of phase in its passage through an irregular refracting medium, such as the ionosphere. The rms phase fluctuations may be large; i.e. greater than one radian. The paper is in three parts. In the first, the receiver is at a great distance from the screen (Fraunhofer diffraction), and a formula is found for all even order moments of the amplitude, and for the correlation function of the even powers of the amplitude. The probability distribution of the amplitude is proved to be a Rice distribution. The multiple integrals expressing the moments of the amplitude reduce to sums of correlations of the original phase fluctuations amongst points over the screen, which are evaluated using combinatorial arguments.In the second part the variance of the square of the amplitude is calculated numerically for points near the screen (Fresnel diffraction). When the rms phase fluctuation is greater than one the variance is maximum near the point where the irregularities in the screen would bring the rays to a focus.In the third part radio star scintillation and scatter propagation are discussed in the light of the theory.

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