Fourier Transformation Theory for Averaged Functions, with Application to Very Long Baseline Radio Interferometry.
ARMY MILITARY PERSONNEL CENTER ALEXANDRIA VA
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This thesis investigates the effects on brightness function resolution when the visibility function is truncated and averaged. The causes of truncation and averaging which arise in cases where satellites are incorporated as interferometer elements are presented, and the basic Fourier transform relation between the visibility and brightness functions is reviewed. The standard Fourier transform method, which is based on a generalization of the Sampling or Nyquist theorem and does not account for the effects of truncation and averaging, is presented. The effects of truncation and averaging are illustrated for a double Gaussian model source using the standard Fourier inversion method. Theorems concerning the Fourier transformation of a truncated andor averaged visibility function are then developed, and an algorithm based on this study is developed. This algorithm attempts to enhance resolution by using a derived relationship between an average value of the visibility function and the true source brightness function. The algorithm is applied to several one-dimensional test cases to illustrate its potential. Author
- Active and Passive Radar Detection and Equipment
- Unmanned Spacecraft