Phase problem in aperture synthesis systems

Synthesizing radioluminance distributions from phase-perturbed Fourier transforms, until now an ill-conditioned and therefore unsolvable problem without additional information, has become solvable inasumch as radio-luminance distributions are found to be finite functions of space coordinates with carrier regions existing where these functions are zero and inasmuch as the response of a narrow-band interferometer yields phase-perturbed Fourier transforms without loss of all information. Furthermore, with more than three antennas, phase information is available in the form of closure relations. The conditions under which this phase problem is solved for an aperture synthesis system are now established on the basis of actual observations and theoretical analysis, considering two fundamentally different cases: determining the distribution function f(x) from its phase-perturbed Fourier transform, and the transformation being linear.